Generate States/Choices/Shocks Grids, get Functions (Interpolated + Percentage + Risky + Safe Asset + Save + Borrow + R Shock)

back to Fan's Dynamic Assets Repository Table of Content.

Contents

function [armt_map, func_map] = ffs_ipwkbzr_get_funcgrid(varargin)

FFS_IPWKBZR_GET_FUNCGRID get funcs, params, states choices shocks grids

centralized gateway for retrieving parameters, and solution grids and functions. Similar to ffs_akz_get_funcgrid function. This code deals with problems with savings and borrowing.

This file is a continuation of ffs_ipwkz_get_funcgrid. A significant change here is the inclusion of borrowing shocks, which changes significantly the implementation of the two-stage solution structure. Specifically, for the coh matrix here, there is another dimension which is the borrowing interest rate shock states, which expands the number of cash-on-hand points given the same productivity shock z. So compared to ffs_ipwkz_get_funcgrid, the same number of columns for the mt_coh_wkb_full matirx, but more rows.

Note that for borrowing, we can not start at the min(coh(k,w-k,z)) reacheable given the w and k choice grids. That would be: min(coh(k,w-k,z)) < min(w). At min(coh), there is a single point, and also for all values between min(coh) and min(w), all percentage w_perc choices are below min(w), requiring extrapolation. It is in some sense safer to extrapolate by starting solution at min(coh) = min(w). Now, for the lowest levels of coh(k, w-k, z), which are < min(w), we now require extrapolation. But this extrapolation is straight forward, when coh < min(w), households have to default, the utility from default is the same regardless of the level of coh at the time of default. So nearest extrapolation is fully correct.

Note that the first stage w grid is based on cash-on-hand level reached by the coh(k,w-k,z) possible choice and shock combinations. This coh(k,w-k,z) > max(w), which also means that at max(coh) grid, the w_perc choices at higher points require extrapolation. Extrapolation is based on nearest extrapolation.

Note that even when w = 0, as long as interest rate is low, only the lowest level of borrowing is invalid.

All discussion of of the word wage refers to productivity shock.

@param param_map container parameter container

@param support_map container support container

@param bl_input_override boolean if true varargin contained param_map and support_map fully overrides local default. Local default is not invoked. This could be important for speed if this function is getting invoked within certain loops. Default is 0.

@return armt_map container container with states, choices and shocks grids that are inputs for grid based solution algorithm. Contains these:

armt_map base arrays:

  1. ar_interp_c_grid: 1 by I^c
  2. ar_interp_coh_grid: 1 by I^{coh}
  3. ar_w_level: 1 by I^{W=k+b}
  4. ar_w_perc: 1 by P^{W=k+b}
  5. ar_ak_perc: 1 by P^{k and b}

armt_map 1st stage level coh on hand related arrays:

  1. mt_interp_coh_grid_mesh_z_wage: I^{coh} by M^w
  2. mt_z_wage_mesh_interp_coh_grid: I^{coh} by M^w
  3. mt_interp_coh_grid_mesh_w_perc: I^{coh} by P^{LAM=k+b}
  4. mt_w_perc_mesh_interp_coh_grid: I^{coh} by P^{LAM=k+b}

armt_map 2nd stage reachable coh(k(w), a(w,k), z', r)

  1. mt_coh_wkb: (I^k x I^w x M^r) by (M^z)
  2. mt_z_wage_mesh_coh_wkb: (I^k x I^w x M^r) by (M^z)

armt_map 2nd stage additional arrays

  1. mt_k: (I^w) by (P^{k and b})
  2. ar_a_meshk: 1 by (I^w x P^{k and b})
  3. ar_k_mesha: 1 by (I^w x P^{k and b})
  4. ar_aplusk_mesh: 1 by (I^w x P^{k and b})
  5. it_ameshk_n: scalar

armt_map Shock Grids Arrays and Mesh

  1. ar_z_r_borr: 1 by (M^r)
  2. ar_z_r_borr_prob: 1 by (M^r)
  3. ar_z_wage: 1 by (M^z)
  4. ar_z_wage_prob: 1 by (M^z)
  5. ar_z_r_borr_mesh_wage_w1r2: 1 by (M^z x M^r)
  6. ar_z_wage_mesh_r_borr_w1r2: 1 by (M^z x M^r)
  7. ar_z_r_borr_mesh_wage_r1w2: 1 by (M^r x M^z)
  8. ar_z_wage_mesh_r_borr_r1w2: 1 by (M^r x M^z)

@return func_map container container with function handles for consumption cash-on-hand etc.

@example

  it_param_set = 2;
  bl_input_override = true;
  [param_map, support_map] = ffs_ipwkbzr_set_default_param(it_param_set);
  [armt_map, func_map] = ffs_ipwkbzr_get_funcgrid(param_map, support_map, bl_input_override);

@include

Default

if (~isempty(varargin))

    % override when called from outside
    [param_map, support_map] = varargin{:};

else

    close all;
    % default internal run
    [param_map, support_map] = ffs_ipwkbzr_set_default_param();

    support_map('bl_graph_funcgrids') = true;
    support_map('bl_graph_funcgrids_detail') = true;
    bl_display_funcgrids = true;
    support_map('bl_display_funcgrids') = bl_display_funcgrids;

    st_param_which = 'medium';

    if (ismember(st_param_which, ['default']))

        param_map('it_ak_perc_n') = 250;

    elseif (ismember(st_param_which, ['medium']))

        % to be able to visually see choice grid points
        param_map('fl_b_bd') = -20; % borrow bound, = 0 if save only
        param_map('fl_default_aprime') = 0;
        param_map('bl_default') = false; % if borrowing is default allowed

        param_map('fl_w_min') = param_map('fl_b_bd');
        param_map('it_w_perc_n') = 25;
        param_map('it_ak_perc_n') = 45;

        param_map('fl_w_interp_grid_gap') = 2;
        param_map('fl_coh_interp_grid_gap') = 2;

%         param_map('fl_z_r_borr_min') = 0.025;
%         param_map('fl_z_r_borr_max') = 0.95;
%         param_map('fl_z_r_borr_n') = 3;

        param_map('fl_z_r_borr_min') = 0.025;
        param_map('fl_z_r_borr_max') = 0.095;
        param_map('fl_z_r_borr_n') = 3;

    elseif (strcmp(st_param_which, 'small'))

        param_map('fl_z_r_borr_n') = 2;
        param_map('it_z_wage_n') = 3;

        param_map('fl_b_bd') = -20; % borrow bound, = 0 if save only
        param_map('fl_default_aprime') = 0;
        param_map('bl_default') = 0; % if borrowing is default allowed

        param_map('fl_w_min') = param_map('fl_b_bd');
        param_map('it_w_perc_n') = 5;
        param_map('it_ak_perc_n') = 6;

        param_map('fl_w_interp_grid_gap') = 3;
        param_map('fl_coh_interp_grid_gap') = 3;

        param_map('fl_z_r_borr_min') = 0.025;
        param_map('fl_z_r_borr_max') = 0.95;
        param_map('fl_z_r_borr_n') = 3;

    end

    param_map('it_z_n') = param_map('it_z_wage_n') * param_map('fl_z_r_borr_n');

    default_maps = {param_map, support_map};

    % numvarargs is the number of varagin inputted
    [default_maps{1:length(varargin)}] = varargin{:};
    param_map = [param_map; default_maps{1}];
    support_map = [support_map; default_maps{2}];

    % Display Parameters
    if (bl_display_funcgrids)
        fft_container_map_display(param_map);
        fft_container_map_display(support_map);
    end

end
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Display Parameters Specific to IPWKBZR
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Begin: Show all key and value pairs from container
CONTAINER NAME: PARAM_MAP
----------------------------------------
  Map with properties:

        Count: 20
      KeyType: char
    ValueType: any

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
pos = 1 ; key = bl_default ; val = true
pos = 2 ; key = fl_b_bd ; val = -20
pos = 3 ; key = fl_c_min ; val = 0.02
pos = 4 ; key = fl_default_wprime ; val = 0
pos = 5 ; key = fl_k_max ; val = 70
pos = 6 ; key = fl_w_max ; val = 50
pos = 7 ; key = fl_w_min ; val = -20
pos = 8 ; key = fl_z_r_borr_max ; val = 0.095
pos = 9 ; key = fl_z_r_borr_min ; val = 0.025
pos = 10 ; key = fl_z_r_borr_n ; val = 5
pos = 11 ; key = fl_z_r_borr_poiss_mean ; val = 20
pos = 12 ; key = fl_z_wage_mu ; val = 0
pos = 13 ; key = fl_z_wage_rho ; val = 0.8
pos = 14 ; key = fl_z_wage_sig ; val = 0.2
pos = 15 ; key = it_z_n ; val = 55
pos = 16 ; key = it_z_wage_n ; val = 11
pos = 17 ; key = st_model ; val = ipwkbzr
pos = 18 ; key = st_v_coh_z_interp_method ; val = method_cell
pos = 19 ; key = st_z_r_borr_drv_ele_type ; val = unif
pos = 20 ; key = st_z_r_borr_drv_prb_type ; val = poiss
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Scalars in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                              i     idx    value
                              __    ___    _____

    bl_default                 1     1         1
    fl_b_bd                    2     2       -20
    fl_c_min                   3     3      0.02
    fl_default_wprime          4     4         0
    fl_k_max                   5     5        70
    fl_w_max                   6     6        50
    fl_w_min                   7     7       -20
    fl_z_r_borr_max            8     8     0.095
    fl_z_r_borr_min            9     9     0.025
    fl_z_r_borr_n             10    10         5
    fl_z_r_borr_poiss_mean    11    11        20
    fl_z_wage_mu              12    12         0
    fl_z_wage_rho             13    13       0.8
    fl_z_wage_sig             14    14       0.2
    it_z_n                    15    15        55
    it_z_wage_n               16    16        11

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Strings in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                                i    idx
                                _    ___

    st_model                    1    17 
    st_v_coh_z_interp_method    2    18 
    st_z_r_borr_drv_ele_type    3    19 
    st_z_r_borr_drv_prb_type    4    20 

----------------------------------------
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Begin: Show all key and value pairs from container
CONTAINER NAME: SUPPORT_MAP
----------------------------------------
  Map with properties:

        Count: 5
      KeyType: char
    ValueType: any

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
pos = 1 ; key = st_img_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/img/
pos = 2 ; key = st_mat_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/mat/
pos = 3 ; key = st_mat_test_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//test/ff_ipwkbzr_ds_vecsv/mat/
pos = 4 ; key = st_matimg_path_root ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr/
pos = 5 ; key = st_profile_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/profile/
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Strings in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                           i    idx
                           _    ___

    st_img_path            1     1 
    st_mat_path            2     2 
    st_mat_test_path       3     3 
    st_matimg_path_root    4     4 
    st_profile_path        5     5 

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Display All Parameters with IPWKBZR overriding IPWKBZR
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Begin: Show all key and value pairs from container
CONTAINER NAME: PARAM_MAP
----------------------------------------
  Map with properties:

        Count: 41
      KeyType: char
    ValueType: any

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
pos = 1 ; key = bl_default ; val = true
pos = 2 ; key = fl_Amean ; val = 1
pos = 3 ; key = fl_alpha ; val = 0.36
pos = 4 ; key = fl_b_bd ; val = -20
pos = 5 ; key = fl_beta ; val = 0.94
pos = 6 ; key = fl_c_min ; val = 0.02
pos = 7 ; key = fl_coh_interp_grid_gap ; val = 0.1
pos = 8 ; key = fl_crra ; val = 1.5
pos = 9 ; key = fl_default_wprime ; val = 0
pos = 10 ; key = fl_delta ; val = 0.08
pos = 11 ; key = fl_k_max ; val = 70
pos = 12 ; key = fl_k_min ; val = 0
pos = 13 ; key = fl_nan_replace ; val = -9999
pos = 14 ; key = fl_r_save ; val = 0.025
pos = 15 ; key = fl_tol_dist ; val = 1e-05
pos = 16 ; key = fl_tol_pol ; val = 1e-05
pos = 17 ; key = fl_tol_val ; val = 1e-05
pos = 18 ; key = fl_w ; val = 0.44365
pos = 19 ; key = fl_w_interp_grid_gap ; val = 0.1
pos = 20 ; key = fl_w_max ; val = 50
pos = 21 ; key = fl_w_min ; val = -20
pos = 22 ; key = fl_z_r_borr_max ; val = 0.095
pos = 23 ; key = fl_z_r_borr_min ; val = 0.025
pos = 24 ; key = fl_z_r_borr_n ; val = 5
pos = 25 ; key = fl_z_r_borr_poiss_mean ; val = 20
pos = 26 ; key = fl_z_wage_mu ; val = 0
pos = 27 ; key = fl_z_wage_rho ; val = 0.8
pos = 28 ; key = fl_z_wage_sig ; val = 0.2
pos = 29 ; key = it_ak_perc_n ; val = 50
pos = 30 ; key = it_c_interp_grid_gap ; val = 0.0001
pos = 31 ; key = it_maxiter_dist ; val = 1000
pos = 32 ; key = it_maxiter_val ; val = 250
pos = 33 ; key = it_tol_pol_nochange ; val = 25
pos = 34 ; key = it_w_perc_n ; val = 50
pos = 35 ; key = it_z_n ; val = 55
pos = 36 ; key = it_z_wage_n ; val = 11
pos = 37 ; key = st_analytical_stationary_type ; val = eigenvector
pos = 38 ; key = st_model ; val = ipwkbzr
pos = 39 ; key = st_v_coh_z_interp_method ; val = method_cell
pos = 40 ; key = st_z_r_borr_drv_ele_type ; val = unif
pos = 41 ; key = st_z_r_borr_drv_prb_type ; val = poiss
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Scalars in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                              i     idx     value 
                              __    ___    _______

    bl_default                 1     1           1
    fl_Amean                   2     2           1
    fl_alpha                   3     3        0.36
    fl_b_bd                    4     4         -20
    fl_beta                    5     5        0.94
    fl_c_min                   6     6        0.02
    fl_coh_interp_grid_gap     7     7         0.1
    fl_crra                    8     8         1.5
    fl_default_wprime          9     9           0
    fl_delta                  10    10        0.08
    fl_k_max                  11    11          70
    fl_k_min                  12    12           0
    fl_nan_replace            13    13       -9999
    fl_r_save                 14    14       0.025
    fl_tol_dist               15    15       1e-05
    fl_tol_pol                16    16       1e-05
    fl_tol_val                17    17       1e-05
    fl_w                      18    18     0.44365
    fl_w_interp_grid_gap      19    19         0.1
    fl_w_max                  20    20          50
    fl_w_min                  21    21         -20
    fl_z_r_borr_max           22    22       0.095
    fl_z_r_borr_min           23    23       0.025
    fl_z_r_borr_n             24    24           5
    fl_z_r_borr_poiss_mean    25    25          20
    fl_z_wage_mu              26    26           0
    fl_z_wage_rho             27    27         0.8
    fl_z_wage_sig             28    28         0.2
    it_ak_perc_n              29    29          50
    it_c_interp_grid_gap      30    30      0.0001
    it_maxiter_dist           31    31        1000
    it_maxiter_val            32    32         250
    it_tol_pol_nochange       33    33          25
    it_w_perc_n               34    34          50
    it_z_n                    35    35          55
    it_z_wage_n               36    36          11

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Strings in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                                     i    idx
                                     _    ___

    st_analytical_stationary_type    1    37 
    st_model                         2    38 
    st_v_coh_z_interp_method         3    39 
    st_z_r_borr_drv_ele_type         4    40 
    st_z_r_borr_drv_prb_type         5    41 

----------------------------------------
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Begin: Show all key and value pairs from container
CONTAINER NAME: SUPPORT_MAP
----------------------------------------
  Map with properties:

        Count: 43
      KeyType: char
    ValueType: any

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
pos = 1 ; key = bl_display ; val = false
pos = 2 ; key = bl_display_defparam ; val = true
pos = 3 ; key = bl_display_dist ; val = false
pos = 4 ; key = bl_display_evf ; val = false
pos = 5 ; key = bl_display_final ; val = true
pos = 6 ; key = bl_display_final_dist ; val = false
pos = 7 ; key = bl_display_final_dist_detail ; val = false
pos = 8 ; key = bl_display_funcgrids ; val = false
pos = 9 ; key = bl_graph ; val = true
pos = 10 ; key = bl_graph_coh_t_coh ; val = true
pos = 11 ; key = bl_graph_evf ; val = false
pos = 12 ; key = bl_graph_funcgrids ; val = false
pos = 13 ; key = bl_graph_funcgrids_detail ; val = false
pos = 14 ; key = bl_graph_onebyones ; val = true
pos = 15 ; key = bl_graph_pol_lvl ; val = true
pos = 16 ; key = bl_graph_pol_pct ; val = true
pos = 17 ; key = bl_graph_val ; val = true
pos = 18 ; key = bl_img_save ; val = false
pos = 19 ; key = bl_mat ; val = false
pos = 20 ; key = bl_post ; val = true
pos = 21 ; key = bl_profile ; val = false
pos = 22 ; key = bl_profile_dist ; val = false
pos = 23 ; key = bl_time ; val = false
pos = 24 ; key = it_display_every ; val = 5
pos = 25 ; key = it_display_final_colmax ; val = 12
pos = 26 ; key = it_display_final_rowmax ; val = 100
pos = 27 ; key = it_display_summmat_colmax ; val = 7
pos = 28 ; key = it_display_summmat_rowmax ; val = 7
pos = 29 ; key = st_img_name_main ; val = _default
pos = 30 ; key = st_img_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/img/
pos = 31 ; key = st_img_prefix ; val = 
pos = 32 ; key = st_img_suffix ; val = _p4.png
pos = 33 ; key = st_mat_name_main ; val = _default
pos = 34 ; key = st_mat_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/mat/
pos = 35 ; key = st_mat_prefix ; val = 
pos = 36 ; key = st_mat_suffix ; val = _p4
pos = 37 ; key = st_mat_test_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//test/ff_ipwkbzr_ds_vecsv/mat/
pos = 38 ; key = st_matimg_path_root ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr/
pos = 39 ; key = st_profile_name_main ; val = _default
pos = 40 ; key = st_profile_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/profile/
pos = 41 ; key = st_profile_prefix ; val = 
pos = 42 ; key = st_profile_suffix ; val = _p4
pos = 43 ; key = st_title_prefix ; val = 
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Scalars in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                                    i     idx    value
                                    __    ___    _____

    bl_display                       1     1        0 
    bl_display_defparam              2     2        1 
    bl_display_dist                  3     3        0 
    bl_display_evf                   4     4        0 
    bl_display_final                 5     5        1 
    bl_display_final_dist            6     6        0 
    bl_display_final_dist_detail     7     7        0 
    bl_display_funcgrids             8     8        0 
    bl_graph                         9     9        1 
    bl_graph_coh_t_coh              10    10        1 
    bl_graph_evf                    11    11        0 
    bl_graph_funcgrids              12    12        0 
    bl_graph_funcgrids_detail       13    13        0 
    bl_graph_onebyones              14    14        1 
    bl_graph_pol_lvl                15    15        1 
    bl_graph_pol_pct                16    16        1 
    bl_graph_val                    17    17        1 
    bl_img_save                     18    18        0 
    bl_mat                          19    19        0 
    bl_post                         20    20        1 
    bl_profile                      21    21        0 
    bl_profile_dist                 22    22        0 
    bl_time                         23    23        0 
    it_display_every                24    24        5 
    it_display_final_colmax         25    25       12 
    it_display_final_rowmax         26    26      100 
    it_display_summmat_colmax       27    27        7 
    it_display_summmat_rowmax       28    28        7 

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Strings in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                            i     idx
                            __    ___

    st_img_name_main         1    29 
    st_img_path              2    30 
    st_img_prefix            3    31 
    st_img_suffix            4    32 
    st_mat_name_main         5    33 
    st_mat_path              6    34 
    st_mat_prefix            7    35 
    st_mat_suffix            8    36 
    st_mat_test_path         9    37 
    st_matimg_path_root     10    38 
    st_profile_name_main    11    39 
    st_profile_path         12    40 
    st_profile_prefix       13    41 
    st_profile_suffix       14    42 
    st_title_prefix         15    43 

----------------------------------------
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Begin: Show all key and value pairs from container
CONTAINER NAME: PARAM_MAP
----------------------------------------
  Map with properties:

        Count: 42
      KeyType: char
    ValueType: any

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
pos = 1 ; key = bl_default ; val = false
pos = 2 ; key = fl_Amean ; val = 1
pos = 3 ; key = fl_alpha ; val = 0.36
pos = 4 ; key = fl_b_bd ; val = -20
pos = 5 ; key = fl_beta ; val = 0.94
pos = 6 ; key = fl_c_min ; val = 0.02
pos = 7 ; key = fl_coh_interp_grid_gap ; val = 2
pos = 8 ; key = fl_crra ; val = 1.5
pos = 9 ; key = fl_default_aprime ; val = 0
pos = 10 ; key = fl_default_wprime ; val = 0
pos = 11 ; key = fl_delta ; val = 0.08
pos = 12 ; key = fl_k_max ; val = 70
pos = 13 ; key = fl_k_min ; val = 0
pos = 14 ; key = fl_nan_replace ; val = -9999
pos = 15 ; key = fl_r_save ; val = 0.025
pos = 16 ; key = fl_tol_dist ; val = 1e-05
pos = 17 ; key = fl_tol_pol ; val = 1e-05
pos = 18 ; key = fl_tol_val ; val = 1e-05
pos = 19 ; key = fl_w ; val = 0.44365
pos = 20 ; key = fl_w_interp_grid_gap ; val = 2
pos = 21 ; key = fl_w_max ; val = 50
pos = 22 ; key = fl_w_min ; val = -20
pos = 23 ; key = fl_z_r_borr_max ; val = 0.095
pos = 24 ; key = fl_z_r_borr_min ; val = 0.025
pos = 25 ; key = fl_z_r_borr_n ; val = 3
pos = 26 ; key = fl_z_r_borr_poiss_mean ; val = 20
pos = 27 ; key = fl_z_wage_mu ; val = 0
pos = 28 ; key = fl_z_wage_rho ; val = 0.8
pos = 29 ; key = fl_z_wage_sig ; val = 0.2
pos = 30 ; key = it_ak_perc_n ; val = 45
pos = 31 ; key = it_c_interp_grid_gap ; val = 0.0001
pos = 32 ; key = it_maxiter_dist ; val = 1000
pos = 33 ; key = it_maxiter_val ; val = 250
pos = 34 ; key = it_tol_pol_nochange ; val = 25
pos = 35 ; key = it_w_perc_n ; val = 25
pos = 36 ; key = it_z_n ; val = 33
pos = 37 ; key = it_z_wage_n ; val = 11
pos = 38 ; key = st_analytical_stationary_type ; val = eigenvector
pos = 39 ; key = st_model ; val = ipwkbzr
pos = 40 ; key = st_v_coh_z_interp_method ; val = method_cell
pos = 41 ; key = st_z_r_borr_drv_ele_type ; val = unif
pos = 42 ; key = st_z_r_borr_drv_prb_type ; val = poiss
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Scalars in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                              i     idx     value 
                              __    ___    _______

    bl_default                 1     1           0
    fl_Amean                   2     2           1
    fl_alpha                   3     3        0.36
    fl_b_bd                    4     4         -20
    fl_beta                    5     5        0.94
    fl_c_min                   6     6        0.02
    fl_coh_interp_grid_gap     7     7           2
    fl_crra                    8     8         1.5
    fl_default_aprime          9     9           0
    fl_default_wprime         10    10           0
    fl_delta                  11    11        0.08
    fl_k_max                  12    12          70
    fl_k_min                  13    13           0
    fl_nan_replace            14    14       -9999
    fl_r_save                 15    15       0.025
    fl_tol_dist               16    16       1e-05
    fl_tol_pol                17    17       1e-05
    fl_tol_val                18    18       1e-05
    fl_w                      19    19     0.44365
    fl_w_interp_grid_gap      20    20           2
    fl_w_max                  21    21          50
    fl_w_min                  22    22         -20
    fl_z_r_borr_max           23    23       0.095
    fl_z_r_borr_min           24    24       0.025
    fl_z_r_borr_n             25    25           3
    fl_z_r_borr_poiss_mean    26    26          20
    fl_z_wage_mu              27    27           0
    fl_z_wage_rho             28    28         0.8
    fl_z_wage_sig             29    29         0.2
    it_ak_perc_n              30    30          45
    it_c_interp_grid_gap      31    31      0.0001
    it_maxiter_dist           32    32        1000
    it_maxiter_val            33    33         250
    it_tol_pol_nochange       34    34          25
    it_w_perc_n               35    35          25
    it_z_n                    36    36          33
    it_z_wage_n               37    37          11

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Strings in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                                     i    idx
                                     _    ___

    st_analytical_stationary_type    1    38 
    st_model                         2    39 
    st_v_coh_z_interp_method         3    40 
    st_z_r_borr_drv_ele_type         4    41 
    st_z_r_borr_drv_prb_type         5    42 

----------------------------------------
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Begin: Show all key and value pairs from container
CONTAINER NAME: SUPPORT_MAP
----------------------------------------
  Map with properties:

        Count: 43
      KeyType: char
    ValueType: any

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
pos = 1 ; key = bl_display ; val = false
pos = 2 ; key = bl_display_defparam ; val = true
pos = 3 ; key = bl_display_dist ; val = false
pos = 4 ; key = bl_display_evf ; val = false
pos = 5 ; key = bl_display_final ; val = true
pos = 6 ; key = bl_display_final_dist ; val = false
pos = 7 ; key = bl_display_final_dist_detail ; val = false
pos = 8 ; key = bl_display_funcgrids ; val = true
pos = 9 ; key = bl_graph ; val = true
pos = 10 ; key = bl_graph_coh_t_coh ; val = true
pos = 11 ; key = bl_graph_evf ; val = false
pos = 12 ; key = bl_graph_funcgrids ; val = true
pos = 13 ; key = bl_graph_funcgrids_detail ; val = true
pos = 14 ; key = bl_graph_onebyones ; val = true
pos = 15 ; key = bl_graph_pol_lvl ; val = true
pos = 16 ; key = bl_graph_pol_pct ; val = true
pos = 17 ; key = bl_graph_val ; val = true
pos = 18 ; key = bl_img_save ; val = false
pos = 19 ; key = bl_mat ; val = false
pos = 20 ; key = bl_post ; val = true
pos = 21 ; key = bl_profile ; val = false
pos = 22 ; key = bl_profile_dist ; val = false
pos = 23 ; key = bl_time ; val = false
pos = 24 ; key = it_display_every ; val = 5
pos = 25 ; key = it_display_final_colmax ; val = 12
pos = 26 ; key = it_display_final_rowmax ; val = 100
pos = 27 ; key = it_display_summmat_colmax ; val = 7
pos = 28 ; key = it_display_summmat_rowmax ; val = 7
pos = 29 ; key = st_img_name_main ; val = _default
pos = 30 ; key = st_img_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/img/
pos = 31 ; key = st_img_prefix ; val = 
pos = 32 ; key = st_img_suffix ; val = _p4.png
pos = 33 ; key = st_mat_name_main ; val = _default
pos = 34 ; key = st_mat_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/mat/
pos = 35 ; key = st_mat_prefix ; val = 
pos = 36 ; key = st_mat_suffix ; val = _p4
pos = 37 ; key = st_mat_test_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//test/ff_ipwkbzr_ds_vecsv/mat/
pos = 38 ; key = st_matimg_path_root ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr/
pos = 39 ; key = st_profile_name_main ; val = _default
pos = 40 ; key = st_profile_path ; val = C:/Users/fan/CodeDynaAsset//m_ipwkbzr//solve/profile/
pos = 41 ; key = st_profile_prefix ; val = 
pos = 42 ; key = st_profile_suffix ; val = _p4
pos = 43 ; key = st_title_prefix ; val = 
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Scalars in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                                    i     idx    value
                                    __    ___    _____

    bl_display                       1     1        0 
    bl_display_defparam              2     2        1 
    bl_display_dist                  3     3        0 
    bl_display_evf                   4     4        0 
    bl_display_final                 5     5        1 
    bl_display_final_dist            6     6        0 
    bl_display_final_dist_detail     7     7        0 
    bl_display_funcgrids             8     8        1 
    bl_graph                         9     9        1 
    bl_graph_coh_t_coh              10    10        1 
    bl_graph_evf                    11    11        0 
    bl_graph_funcgrids              12    12        1 
    bl_graph_funcgrids_detail       13    13        1 
    bl_graph_onebyones              14    14        1 
    bl_graph_pol_lvl                15    15        1 
    bl_graph_pol_pct                16    16        1 
    bl_graph_val                    17    17        1 
    bl_img_save                     18    18        0 
    bl_mat                          19    19        0 
    bl_post                         20    20        1 
    bl_profile                      21    21        0 
    bl_profile_dist                 22    22        0 
    bl_time                         23    23        0 
    it_display_every                24    24        5 
    it_display_final_colmax         25    25       12 
    it_display_final_rowmax         26    26      100 
    it_display_summmat_colmax       27    27        7 
    it_display_summmat_rowmax       28    28        7 

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Strings in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                            i     idx
                            __    ___

    st_img_name_main         1    29 
    st_img_path              2    30 
    st_img_prefix            3    31 
    st_img_suffix            4    32 
    st_mat_name_main         5    33 
    st_mat_path              6    34 
    st_mat_prefix            7    35 
    st_mat_suffix            8    36 
    st_mat_test_path         9    37 
    st_matimg_path_root     10    38 
    st_profile_name_main    11    39 
    st_profile_path         12    40 
    st_profile_prefix       13    41 
    st_profile_suffix       14    42 
    st_title_prefix         15    43 

Parse Parameters 1a

params_group = values(param_map, {'bl_default', 'fl_b_bd', 'fl_w_min', 'fl_w_max'});
[bl_default, fl_b_bd, fl_w_min, fl_w_max] = params_group{:};

params_group = values(param_map, {'fl_crra', 'fl_c_min'});
[fl_crra, fl_c_min] = params_group{:};

params_group = values(param_map, {'fl_Amean', 'fl_alpha', 'fl_delta'});
[fl_Amean, fl_alpha, fl_delta] = params_group{:};

params_group = values(param_map, {'fl_r_save', 'fl_w'});
[fl_r_save, fl_w] = params_group{:};

Parse Parameters 1b

params_group = values(param_map, {...
    'it_w_perc_n', 'it_ak_perc_n',...
    'it_c_interp_grid_gap', 'fl_w_interp_grid_gap', 'fl_coh_interp_grid_gap'});
[it_w_perc_n, it_ak_perc_n,...
    it_c_interp_grid_gap, fl_w_interp_grid_gap, fl_coh_interp_grid_gap] = params_group{:};

params_group = values(param_map, {'st_v_coh_z_interp_method'});
[st_v_coh_z_interp_method] = params_group{:};

Parse Parameters 2

% param_map shock income
params_group = values(param_map, {'it_z_wage_n', 'fl_z_wage_mu', 'fl_z_wage_rho', 'fl_z_wage_sig'});
[it_z_wage_n, fl_z_wage_mu, fl_z_wage_rho, fl_z_wage_sig] = params_group{:};

% param_map shock borrowing interest
params_group = values(param_map, {'st_z_r_borr_drv_ele_type', 'st_z_r_borr_drv_prb_type', 'fl_z_r_borr_poiss_mean', ...
    'fl_z_r_borr_max', 'fl_z_r_borr_min', 'fl_z_r_borr_n'});
[st_z_r_borr_drv_ele_type, st_z_r_borr_drv_prb_type, fl_z_r_borr_poiss_mean, ...
    fl_z_r_borr_max, fl_z_r_borr_min, fl_z_r_borr_n] = params_group{:};

% param_map shock income
params_group = values(param_map, {'it_z_n'});
[it_z_n] = params_group{:};

Parse Parameters 3

params_group = values(support_map, {'bl_graph_funcgrids', 'bl_graph_funcgrids_detail', 'bl_display_funcgrids'});
[bl_graph_funcgrids, bl_graph_funcgrids_detail, bl_display_funcgrids] = params_group{:};
params_group = values(support_map, {'it_display_summmat_rowmax', 'it_display_summmat_colmax'});
[it_display_summmat_rowmax, it_display_summmat_colmax] = params_group{:};

F1: Get Shock: Income Shock (ar1)

[~, mt_z_wage_trans, ar_z_wage_prob, ar_z_wage] = ffto_gen_tauchen_jhl(fl_z_wage_mu,fl_z_wage_rho,fl_z_wage_sig,it_z_wage_n);

F2: Get Shock: Interest Rate Shock (iid)

% get borrowing grid and probabilities
param_dsv_map = containers.Map('KeyType','char', 'ValueType','any');
param_dsv_map('st_drv_ele_type') = st_z_r_borr_drv_ele_type;
param_dsv_map('st_drv_prb_type') = st_z_r_borr_drv_prb_type;
param_dsv_map('fl_poiss_mean') = fl_z_r_borr_poiss_mean;
param_dsv_map('fl_max') = fl_z_r_borr_max;
param_dsv_map('fl_min') = fl_z_r_borr_min;
param_dsv_map('fl_n') = fl_z_r_borr_n;
[ar_z_r_borr, ar_z_r_borr_prob] = fft_gen_discrete_var(param_dsv_map, true);

G: Generate Asset and Choice Grid for 2nd stage Problem

This generate triangular choice structure. Household choose total aggregate savings, and within that how much to put into risky capital and how much to put into safe assets, in percentages. See ffs_ipwkbzr_set_default_param for details.

if (~bl_default)
    fl_r_borr_max = max(ar_z_r_borr);
    fl_w_min_use = max(fl_w_min, -(fl_w)/fl_r_borr_max);
    fl_b_bd = fl_w_min_use;
else
    fl_w_min_use = fl_w_min;
end

% percentage grid for 1st stage choice problem, level grid for 2nd stage
% solving optimal k given w and z.
ar_w_perc = linspace(0, 1, it_w_perc_n);
it_w_interp_n = ((fl_w_max-fl_w_min_use)/(fl_w_interp_grid_gap));
ar_w_level_full = fft_array_add_zero(linspace(fl_w_min_use, fl_w_max, it_w_interp_n), true);
ar_w_level = ar_w_level_full;
it_w_interp_n = length(ar_w_level_full);

% max k given w, need to consider the possibility of borrowing.
ar_k_max = ar_w_level_full - fl_b_bd;

% k percentage choice grid
ar_ak_perc = linspace(0, 1, it_ak_perc_n);

% 2nd stage percentage choice matrixes
% (ar_k_max') is it_w_interp_n by 1, and (ar_ak_perc) is 1 by it_ak_perc_n
% mt_k is a it_w_interp_n by it_ak_perc_n matrix of choice points of k'
% conditional on w, each column is a different w, each row for each col a
% different k' value.
mt_k = (ar_k_max'*ar_ak_perc)';
mt_a = (ar_w_level_full - mt_k);

% can not have choice that are beyond feasible bound given the percentage
% structure here.
mt_bl_constrained = (mt_a < fl_b_bd);
if (sum(mt_bl_constrained) > 0 )
    error('at %s second stage choice points, percentage choice exceed bounds, can not happen',...
        num2str(sum(mt_bl_constrained)));
end

ar_a_meshk_full = mt_a(:);
ar_k_mesha_full = mt_k(:);

ar_a_meshk = ar_a_meshk_full;
ar_k_mesha = ar_k_mesha_full;


% iid transition matrix
mt_z_r_borr_prob_trans = repmat(ar_z_r_borr_prob, [length(ar_z_r_borr_prob), 1]);

F3: Get Shock: Mesh Shocks Together

R is outter, W is Inner

% Kronecker product to get full transition matrix for the two shocks
mt_z_trans = kron(mt_z_r_borr_prob_trans, mt_z_wage_trans);

% mesh the shock vectors
[mt_z_wage_mesh_r_borr_w1r2, mt_z_r_borr_mesh_wage_w1r2] = ndgrid(ar_z_wage, ar_z_r_borr);
ar_z_wage_mesh_r_borr_w1r2 = mt_z_wage_mesh_r_borr_w1r2(:)';
ar_z_r_borr_mesh_wage_w1r2 = mt_z_r_borr_mesh_wage_w1r2(:)';

% mesh the shock vectors
[mt_z_r_borr_mesh_wage_r1w2, mt_z_wage_mesh_r_borr_r1w2] = ndgrid(ar_z_r_borr, ar_z_wage);
ar_z_wage_mesh_r_borr_r1w2 = mt_z_wage_mesh_r_borr_r1w2(:)';
ar_z_r_borr_mesh_wage_r1w2 = mt_z_r_borr_mesh_wage_r1w2(:)';

if (bl_display_funcgrids)

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('Borrow R Shock: ar_z_r_borr_mesh_wage_w1r2');
    disp('Prod/Wage Shock: ar_z_wage_mesh_r_borr_w1r2');
    disp('show which shock is inner and which is outter');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    tb_two_shocks = array2table([ar_z_r_borr_mesh_wage_w1r2;...
                                 ar_z_wage_mesh_r_borr_w1r2]');
    cl_col_names = ["Borrow R Shock (Meshed)", "Wage R Shock (Meshed)"];
    cl_row_names = strcat('zi=', string((1:it_z_n)));
    tb_two_shocks.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);
    tb_two_shocks.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);

    it_row_display = it_z_wage_n*2;

    disp(size(tb_two_shocks));
    disp(head(tb_two_shocks, it_row_display));
    disp(tail(tb_two_shocks, it_row_display));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('Borrow R Shock: ar_z_wage_mesh_r_borr_r1w2');
    disp('Prod/Wage Shock: ar_z_r_borr_mesh_wage_r1w2');
    disp('show which shock is inner and which is outter');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');

    tb_two_shocks = array2table([ar_z_wage_mesh_r_borr_r1w2;...
                                 ar_z_r_borr_mesh_wage_r1w2]');
    cl_col_names = ["Borrow R Shock (Meshed)", "Wage R Shock (Meshed)"];
    cl_row_names = strcat('zi=', string((1:length(ar_z_r_borr_mesh_wage_r1w2))));
    tb_two_shocks.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);
    tb_two_shocks.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);

    it_row_display = fl_z_r_borr_n*2;

    disp(size(tb_two_shocks));
    disp(head(tb_two_shocks, it_row_display));
    disp(tail(tb_two_shocks, it_row_display));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('Borrow Rate Transition Matrix: mt_z_r_borr_prob_trans');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    it_col_n_keep = 15;
    it_row_n_keep = 15;
    [it_row_n, it_col_n] = size(mt_z_r_borr_prob_trans);
    [ar_it_cols, ar_it_rows] = fft_row_col_subset(it_col_n, it_col_n_keep, it_row_n, it_row_n_keep);
    cl_st_full_rowscols = cellstr([num2str(ar_z_r_borr', 'r%3.2f')]);
    tb_z_r_borr_prob_trans = array2table(round(mt_z_r_borr_prob_trans(ar_it_rows, ar_it_cols), 6));
    cl_col_names = strcat('zi=', num2str(ar_it_cols'), ':', cl_st_full_rowscols(ar_it_cols));
    cl_row_names = strcat('zi=', num2str(ar_it_rows'), ':', cl_st_full_rowscols(ar_it_rows));
    tb_z_r_borr_prob_trans.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);
    tb_z_r_borr_prob_trans.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);

    disp(size(tb_z_r_borr_prob_trans));
    disp(tb_z_r_borr_prob_trans);

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('Wage Prod Shock Transition Matrix: mt_z_r_borr_prob_trans');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    it_col_n_keep = 15;
    it_row_n_keep = 15;
    [it_row_n, it_col_n] = size(mt_z_wage_trans);
    [ar_it_cols, ar_it_rows] = fft_row_col_subset(it_col_n, it_col_n_keep, it_row_n, it_row_n_keep);
    cl_st_full_rowscols = cellstr([num2str(ar_z_wage', 'w%3.2f')]);
    tb_z_wage_trans = array2table(round(mt_z_wage_trans(ar_it_rows, ar_it_cols),6));
    cl_col_names = strcat('zi=', num2str(ar_it_cols'), ':', cl_st_full_rowscols(ar_it_cols));
    cl_row_names = strcat('zi=', num2str(ar_it_rows'), ':', cl_st_full_rowscols(ar_it_rows));
    tb_z_wage_trans.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);
    tb_z_wage_trans.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);

    disp(size(tb_z_wage_trans));
    disp(tb_z_wage_trans);

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('Full Transition Matrix: mt_z_trans');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    it_col_n_keep = it_z_wage_n*3;
    it_row_n_keep = it_z_wage_n*3;
    [it_row_n, it_col_n] = size(mt_z_trans);
    [ar_it_cols, ar_it_rows] = fft_row_col_subset(it_col_n, it_col_n_keep, it_row_n, it_row_n_keep);
    cl_st_full_rowscols = cellstr([num2str(ar_z_r_borr_mesh_wage_w1r2', 'r%3.2f;'), ...
                                   num2str(ar_z_wage_mesh_r_borr_w1r2', 'w%3.2f')]);
    tb_mt_z_trans = array2table(round(mt_z_trans(ar_it_rows, ar_it_cols),6));
    cl_col_names = strcat('i', num2str(ar_it_cols'), ':', cl_st_full_rowscols(ar_it_cols));
    cl_row_names = strcat('i', num2str(ar_it_rows'), ':', cl_st_full_rowscols(ar_it_rows));
    tb_mt_z_trans.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);
    tb_mt_z_trans.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);

    disp(size(tb_mt_z_trans));
    disp(tb_mt_z_trans);

end
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Borrow R Shock: ar_z_r_borr_mesh_wage_w1r2
Prod/Wage Shock: ar_z_wage_mesh_r_borr_w1r2
show which shock is inner and which is outter
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    33     2

             BorrowRShock_Meshed_    WageRShock_Meshed_
             ____________________    __________________

    zi_1            0.025                 0.34664      
    zi_2            0.025                 0.42338      
    zi_3            0.025                 0.51712      
    zi_4            0.025                 0.63162      
    zi_5            0.025                 0.77146      
    zi_6            0.025                 0.94226      
    zi_7            0.025                  1.1509      
    zi_8            0.025                  1.4057      
    zi_9            0.025                  1.7169      
    zi_10           0.025                   2.097      
    zi_11           0.025                  2.5613      
    zi_12            0.06                 0.34664      
    zi_13            0.06                 0.42338      
    zi_14            0.06                 0.51712      
    zi_15            0.06                 0.63162      
    zi_16            0.06                 0.77146      
    zi_17            0.06                 0.94226      
    zi_18            0.06                  1.1509      
    zi_19            0.06                  1.4057      
    zi_20            0.06                  1.7169      
    zi_21            0.06                   2.097      
    zi_22            0.06                  2.5613      

             BorrowRShock_Meshed_    WageRShock_Meshed_
             ____________________    __________________

    zi_12            0.06                 0.34664      
    zi_13            0.06                 0.42338      
    zi_14            0.06                 0.51712      
    zi_15            0.06                 0.63162      
    zi_16            0.06                 0.77146      
    zi_17            0.06                 0.94226      
    zi_18            0.06                  1.1509      
    zi_19            0.06                  1.4057      
    zi_20            0.06                  1.7169      
    zi_21            0.06                   2.097      
    zi_22            0.06                  2.5613      
    zi_23           0.095                 0.34664      
    zi_24           0.095                 0.42338      
    zi_25           0.095                 0.51712      
    zi_26           0.095                 0.63162      
    zi_27           0.095                 0.77146      
    zi_28           0.095                 0.94226      
    zi_29           0.095                  1.1509      
    zi_30           0.095                  1.4057      
    zi_31           0.095                  1.7169      
    zi_32           0.095                   2.097      
    zi_33           0.095                  2.5613      

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Borrow R Shock: ar_z_wage_mesh_r_borr_r1w2
Prod/Wage Shock: ar_z_r_borr_mesh_wage_r1w2
show which shock is inner and which is outter
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    33     2

            BorrowRShock_Meshed_    WageRShock_Meshed_
            ____________________    __________________

    zi_1          0.34664                 0.025       
    zi_2          0.34664                  0.06       
    zi_3          0.34664                 0.095       
    zi_4          0.42338                 0.025       
    zi_5          0.42338                  0.06       
    zi_6          0.42338                 0.095       

             BorrowRShock_Meshed_    WageRShock_Meshed_
             ____________________    __________________

    zi_28            2.097                 0.025       
    zi_29            2.097                  0.06       
    zi_30            2.097                 0.095       
    zi_31           2.5613                 0.025       
    zi_32           2.5613                  0.06       
    zi_33           2.5613                 0.095       

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Borrow Rate Transition Matrix: mt_z_r_borr_prob_trans
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
     3     3

                  zi_1_r0_03    zi_2_r0_06    zi_3_r0_10
                  __________    __________    __________

    zi_1_r0_03     0.004525      0.090498      0.90498  
    zi_2_r0_06     0.004525      0.090498      0.90498  
    zi_3_r0_10     0.004525      0.090498      0.90498  

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Wage Prod Shock Transition Matrix: mt_z_r_borr_prob_trans
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    11    11

                   zi_1_w0_35    zi_2_w0_42    zi_3_w0_52    zi_4_w0_63    zi_5_w0_77    zi_6_w0_94    zi_7_w1_15    zi_8_w1_41    zi_9_w1_72    zi_10_w2_10    zi_11_w2_56
                   __________    __________    __________    __________    __________    __________    __________    __________    __________    ___________    ___________

    zi_1_w0_35       0.30854       0.38293       0.24173      0.060598      0.005977      0.000229         3e-06             0             0             0              0  
    zi_2_w0_42        0.0968       0.28529       0.37595        0.1974      0.041098      0.003359      0.000106         1e-06             0             0              0  
    zi_3_w0_52      0.017864        0.1178       0.32451       0.35577       0.15534      0.026851      0.001818       4.8e-05             0             0              0  
    zi_4_w0_63      0.001866      0.026851       0.15534       0.35577       0.32451        0.1178      0.016897      0.000947         2e-05             0              0  
    zi_5_w0_77      0.000108      0.003359      0.041098        0.1974       0.37595       0.28529      0.086076      0.010241      0.000475         8e-06              0  
    zi_6_w0_94         3e-06      0.000229      0.005977      0.060598       0.24173       0.38293       0.24173      0.060598      0.005977      0.000229          3e-06  
    zi_7_w1_15             0         8e-06      0.000475      0.010241      0.086076       0.28529       0.37595        0.1974      0.041098      0.003359       0.000108  
    zi_8_w1_41             0             0         2e-05      0.000947      0.016897        0.1178       0.32451       0.35577       0.15534      0.026851       0.001866  
    zi_9_w1_72             0             0             0       4.8e-05      0.001818      0.026851       0.15534       0.35577       0.32451        0.1178       0.017864  
    zi_10_w2_10            0             0             0         1e-06      0.000106      0.003359      0.041098        0.1974       0.37595       0.28529         0.0968  
    zi_11_w2_56            0             0             0             0         3e-06      0.000229      0.005977      0.060598       0.24173       0.38293        0.30854  

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Full Transition Matrix: mt_z_trans
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    33    33

                       i1_r0_03_w0_35    i2_r0_03_w0_42    i3_r0_03_w0_52    i4_r0_03_w0_63    i5_r0_03_w0_77    i6_r0_03_w0_94    i7_r0_03_w1_15    i8_r0_03_w1_41    i9_r0_03_w1_72    i10_r0_03_w2_10    i11_r0_03_w2_56    i12_r0_06_w0_35    i13_r0_06_w0_42    i14_r0_06_w0_52    i15_r0_06_w0_63    i16_r0_06_w0_77    i17_r0_06_w0_94    i18_r0_06_w1_15    i19_r0_06_w1_41    i20_r0_06_w1_72    i21_r0_06_w2_10    i22_r0_06_w2_56    i23_r0_10_w0_35    i24_r0_10_w0_42    i25_r0_10_w0_52    i26_r0_10_w0_63    i27_r0_10_w0_77    i28_r0_10_w0_94    i29_r0_10_w1_15    i30_r0_10_w1_41    i31_r0_10_w1_72    i32_r0_10_w2_10    i33_r0_10_w2_56
                       ______________    ______________    ______________    ______________    ______________    ______________    ______________    ______________    ______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________

    i1_r0_03_w0_35        0.001396          0.001733          0.001094          0.000274           2.7e-05             1e-06                 0                 0                 0                 0                  0           0.027922           0.034654           0.021876           0.005484           0.000541            2.1e-05                  0                  0                  0                  0                  0            0.27922            0.34654            0.21876           0.054839           0.005409           0.000207              3e-06                  0                  0                  0                  0    
    i2_r0_03_w0_42        0.000438          0.001291          0.001701          0.000893          0.000186           1.5e-05                 0                 0                 0                 0                  0            0.00876           0.025818           0.034022           0.017864           0.003719           0.000304              1e-05                  0                  0                  0                  0           0.087602            0.25818            0.34022            0.17864           0.037193            0.00304            9.6e-05              1e-06                  0                  0                  0    
    i3_r0_03_w0_52         8.1e-05          0.000533          0.001468           0.00161          0.000703          0.000121             8e-06                 0                 0                 0                  0           0.001617           0.010661           0.029367           0.032196           0.014058            0.00243           0.000164              4e-06                  0                  0                  0           0.016167            0.10661            0.29367            0.32196            0.14058           0.024299           0.001645            4.3e-05                  0                  0                  0    
    i4_r0_03_w0_63           8e-06          0.000121          0.000703           0.00161          0.001468          0.000533           7.6e-05             4e-06                 0                 0                  0           0.000169            0.00243           0.014058           0.032196           0.029367           0.010661           0.001529            8.6e-05              2e-06                  0                  0           0.001689           0.024299            0.14058            0.32196            0.29367            0.10661           0.015291           0.000857            1.9e-05                  0                  0    
    i5_r0_03_w0_77               0           1.5e-05          0.000186          0.000893          0.001701          0.001291          0.000389           4.6e-05             2e-06                 0                  0              1e-05           0.000304           0.003719           0.017864           0.034022           0.025818            0.00779           0.000927            4.3e-05              1e-06                  0            9.8e-05            0.00304           0.037193            0.17864            0.34022            0.25818           0.077897           0.009268            0.00043              8e-06                  0    
    i6_r0_03_w0_94               0             1e-06           2.7e-05          0.000274          0.001094          0.001733          0.001094          0.000274           2.7e-05             1e-06                  0                  0            2.1e-05           0.000541           0.005484           0.021876           0.034654           0.021876           0.005484           0.000541            2.1e-05                  0              3e-06           0.000207           0.005409           0.054839            0.21876            0.34654            0.21876           0.054839           0.005409           0.000207              3e-06    
    i7_r0_03_w1_15               0                 0             2e-06           4.6e-05          0.000389          0.001291          0.001701          0.000893          0.000186           1.5e-05                  0                  0              1e-06            4.3e-05           0.000927            0.00779           0.025818           0.034022           0.017864           0.003719           0.000304              1e-05                  0              8e-06            0.00043           0.009268           0.077897            0.25818            0.34022            0.17864           0.037193            0.00304            9.8e-05    
    i8_r0_03_w1_41               0                 0                 0             4e-06           7.6e-05          0.000533          0.001468           0.00161          0.000703          0.000121              8e-06                  0                  0              2e-06            8.6e-05           0.001529           0.010661           0.029367           0.032196           0.014058            0.00243           0.000169                  0                  0            1.9e-05           0.000857           0.015291            0.10661            0.29367            0.32196            0.14058           0.024299           0.001689    
    i9_r0_03_w1_72               0                 0                 0                 0             8e-06          0.000121          0.000703           0.00161          0.001468          0.000533            8.1e-05                  0                  0                  0              4e-06           0.000164            0.00243           0.014058           0.032196           0.029367           0.010661           0.001617                  0                  0                  0            4.3e-05           0.001645           0.024299            0.14058            0.32196            0.29367            0.10661           0.016167    
    i10_r0_03_w2_10              0                 0                 0                 0                 0           1.5e-05          0.000186          0.000893          0.001701          0.001291           0.000438                  0                  0                  0                  0              1e-05           0.000304           0.003719           0.017864           0.034022           0.025818            0.00876                  0                  0                  0              1e-06            9.6e-05            0.00304           0.037193            0.17864            0.34022            0.25818           0.087602    
    i11_r0_03_w2_56              0                 0                 0                 0                 0             1e-06           2.7e-05          0.000274          0.001094          0.001733           0.001396                  0                  0                  0                  0                  0            2.1e-05           0.000541           0.005484           0.021876           0.034654           0.027922                  0                  0                  0                  0              3e-06           0.000207           0.005409           0.054839            0.21876            0.34654            0.27922    
    i12_r0_06_w0_35       0.001396          0.001733          0.001094          0.000274           2.7e-05             1e-06                 0                 0                 0                 0                  0           0.027922           0.034654           0.021876           0.005484           0.000541            2.1e-05                  0                  0                  0                  0                  0            0.27922            0.34654            0.21876           0.054839           0.005409           0.000207              3e-06                  0                  0                  0                  0    
    i13_r0_06_w0_42       0.000438          0.001291          0.001701          0.000893          0.000186           1.5e-05                 0                 0                 0                 0                  0            0.00876           0.025818           0.034022           0.017864           0.003719           0.000304              1e-05                  0                  0                  0                  0           0.087602            0.25818            0.34022            0.17864           0.037193            0.00304            9.6e-05              1e-06                  0                  0                  0    
    i14_r0_06_w0_52        8.1e-05          0.000533          0.001468           0.00161          0.000703          0.000121             8e-06                 0                 0                 0                  0           0.001617           0.010661           0.029367           0.032196           0.014058            0.00243           0.000164              4e-06                  0                  0                  0           0.016167            0.10661            0.29367            0.32196            0.14058           0.024299           0.001645            4.3e-05                  0                  0                  0    
    i15_r0_06_w0_63          8e-06          0.000121          0.000703           0.00161          0.001468          0.000533           7.6e-05             4e-06                 0                 0                  0           0.000169            0.00243           0.014058           0.032196           0.029367           0.010661           0.001529            8.6e-05              2e-06                  0                  0           0.001689           0.024299            0.14058            0.32196            0.29367            0.10661           0.015291           0.000857            1.9e-05                  0                  0    
    i16_r0_06_w0_77              0           1.5e-05          0.000186          0.000893          0.001701          0.001291          0.000389           4.6e-05             2e-06                 0                  0              1e-05           0.000304           0.003719           0.017864           0.034022           0.025818            0.00779           0.000927            4.3e-05              1e-06                  0            9.8e-05            0.00304           0.037193            0.17864            0.34022            0.25818           0.077897           0.009268            0.00043              8e-06                  0    
    i17_r0_06_w0_94              0             1e-06           2.7e-05          0.000274          0.001094          0.001733          0.001094          0.000274           2.7e-05             1e-06                  0                  0            2.1e-05           0.000541           0.005484           0.021876           0.034654           0.021876           0.005484           0.000541            2.1e-05                  0              3e-06           0.000207           0.005409           0.054839            0.21876            0.34654            0.21876           0.054839           0.005409           0.000207              3e-06    
    i18_r0_06_w1_15              0                 0             2e-06           4.6e-05          0.000389          0.001291          0.001701          0.000893          0.000186           1.5e-05                  0                  0              1e-06            4.3e-05           0.000927            0.00779           0.025818           0.034022           0.017864           0.003719           0.000304              1e-05                  0              8e-06            0.00043           0.009268           0.077897            0.25818            0.34022            0.17864           0.037193            0.00304            9.8e-05    
    i19_r0_06_w1_41              0                 0                 0             4e-06           7.6e-05          0.000533          0.001468           0.00161          0.000703          0.000121              8e-06                  0                  0              2e-06            8.6e-05           0.001529           0.010661           0.029367           0.032196           0.014058            0.00243           0.000169                  0                  0            1.9e-05           0.000857           0.015291            0.10661            0.29367            0.32196            0.14058           0.024299           0.001689    
    i20_r0_06_w1_72              0                 0                 0                 0             8e-06          0.000121          0.000703           0.00161          0.001468          0.000533            8.1e-05                  0                  0                  0              4e-06           0.000164            0.00243           0.014058           0.032196           0.029367           0.010661           0.001617                  0                  0                  0            4.3e-05           0.001645           0.024299            0.14058            0.32196            0.29367            0.10661           0.016167    
    i21_r0_06_w2_10              0                 0                 0                 0                 0           1.5e-05          0.000186          0.000893          0.001701          0.001291           0.000438                  0                  0                  0                  0              1e-05           0.000304           0.003719           0.017864           0.034022           0.025818            0.00876                  0                  0                  0              1e-06            9.6e-05            0.00304           0.037193            0.17864            0.34022            0.25818           0.087602    
    i22_r0_06_w2_56              0                 0                 0                 0                 0             1e-06           2.7e-05          0.000274          0.001094          0.001733           0.001396                  0                  0                  0                  0                  0            2.1e-05           0.000541           0.005484           0.021876           0.034654           0.027922                  0                  0                  0                  0              3e-06           0.000207           0.005409           0.054839            0.21876            0.34654            0.27922    
    i23_r0_10_w0_35       0.001396          0.001733          0.001094          0.000274           2.7e-05             1e-06                 0                 0                 0                 0                  0           0.027922           0.034654           0.021876           0.005484           0.000541            2.1e-05                  0                  0                  0                  0                  0            0.27922            0.34654            0.21876           0.054839           0.005409           0.000207              3e-06                  0                  0                  0                  0    
    i24_r0_10_w0_42       0.000438          0.001291          0.001701          0.000893          0.000186           1.5e-05                 0                 0                 0                 0                  0            0.00876           0.025818           0.034022           0.017864           0.003719           0.000304              1e-05                  0                  0                  0                  0           0.087602            0.25818            0.34022            0.17864           0.037193            0.00304            9.6e-05              1e-06                  0                  0                  0    
    i25_r0_10_w0_52        8.1e-05          0.000533          0.001468           0.00161          0.000703          0.000121             8e-06                 0                 0                 0                  0           0.001617           0.010661           0.029367           0.032196           0.014058            0.00243           0.000164              4e-06                  0                  0                  0           0.016167            0.10661            0.29367            0.32196            0.14058           0.024299           0.001645            4.3e-05                  0                  0                  0    
    i26_r0_10_w0_63          8e-06          0.000121          0.000703           0.00161          0.001468          0.000533           7.6e-05             4e-06                 0                 0                  0           0.000169            0.00243           0.014058           0.032196           0.029367           0.010661           0.001529            8.6e-05              2e-06                  0                  0           0.001689           0.024299            0.14058            0.32196            0.29367            0.10661           0.015291           0.000857            1.9e-05                  0                  0    
    i27_r0_10_w0_77              0           1.5e-05          0.000186          0.000893          0.001701          0.001291          0.000389           4.6e-05             2e-06                 0                  0              1e-05           0.000304           0.003719           0.017864           0.034022           0.025818            0.00779           0.000927            4.3e-05              1e-06                  0            9.8e-05            0.00304           0.037193            0.17864            0.34022            0.25818           0.077897           0.009268            0.00043              8e-06                  0    
    i28_r0_10_w0_94              0             1e-06           2.7e-05          0.000274          0.001094          0.001733          0.001094          0.000274           2.7e-05             1e-06                  0                  0            2.1e-05           0.000541           0.005484           0.021876           0.034654           0.021876           0.005484           0.000541            2.1e-05                  0              3e-06           0.000207           0.005409           0.054839            0.21876            0.34654            0.21876           0.054839           0.005409           0.000207              3e-06    
    i29_r0_10_w1_15              0                 0             2e-06           4.6e-05          0.000389          0.001291          0.001701          0.000893          0.000186           1.5e-05                  0                  0              1e-06            4.3e-05           0.000927            0.00779           0.025818           0.034022           0.017864           0.003719           0.000304              1e-05                  0              8e-06            0.00043           0.009268           0.077897            0.25818            0.34022            0.17864           0.037193            0.00304            9.8e-05    
    i30_r0_10_w1_41              0                 0                 0             4e-06           7.6e-05          0.000533          0.001468           0.00161          0.000703          0.000121              8e-06                  0                  0              2e-06            8.6e-05           0.001529           0.010661           0.029367           0.032196           0.014058            0.00243           0.000169                  0                  0            1.9e-05           0.000857           0.015291            0.10661            0.29367            0.32196            0.14058           0.024299           0.001689    
    i31_r0_10_w1_72              0                 0                 0                 0             8e-06          0.000121          0.000703           0.00161          0.001468          0.000533            8.1e-05                  0                  0                  0              4e-06           0.000164            0.00243           0.014058           0.032196           0.029367           0.010661           0.001617                  0                  0                  0            4.3e-05           0.001645           0.024299            0.14058            0.32196            0.29367            0.10661           0.016167    
    i32_r0_10_w2_10              0                 0                 0                 0                 0           1.5e-05          0.000186          0.000893          0.001701          0.001291           0.000438                  0                  0                  0                  0              1e-05           0.000304           0.003719           0.017864           0.034022           0.025818            0.00876                  0                  0                  0              1e-06            9.6e-05            0.00304           0.037193            0.17864            0.34022            0.25818           0.087602    
    i33_r0_10_w2_56              0                 0                 0                 0                 0             1e-06           2.7e-05          0.000274          0.001094          0.001733           0.001396                  0                  0                  0                  0                  0            2.1e-05           0.000541           0.005484           0.021876           0.034654           0.027922                  0                  0                  0                  0              3e-06           0.000207           0.005409           0.054839            0.21876            0.34654            0.27922    

Get Equations

[f_util_log, f_util_crra, f_util_standin, f_util_standin_coh, f_prod, f_inc, f_coh, f_cons] = ...
    ffs_ipwkbzr_set_functions(fl_crra, fl_c_min, fl_b_bd, fl_Amean, fl_alpha, fl_delta, fl_r_save, fl_w);

Generate Cash-on-Hand/State Matrix

The endogenous state variable is cash-on-hand, it has it_z_n*it_a_n number of points, covering all reachable points when ar_a is the choice vector and ar_z is the shock vector. requires inputs from get Asset and choice grids, get shock grids, and get equations above.

  1. mt_coh_wkb_full: this is the (I^k x I^w) by (M^r x M^z) matrix, where rows = it_w_interp_n*it_ak_perc_n, and cols = fl_z_r_borr_n*it_z_wage_n.
  2. mt_coh_wkb_full: this is the (I^k x I^w x M^r) by (M^z) matrix, where rows = it_w_interp_n*it_ak_perc_n*fl_z_r_borr_n, and cols = it_z_wage_n.
mt_coh_wkb_full = f_coh(ar_z_r_borr_mesh_wage_r1w2, ar_z_wage_mesh_r_borr_r1w2, ...
                        ar_a_meshk_full, ar_k_mesha_full);

it_coh_wkb_reshape_rows = it_w_interp_n*it_ak_perc_n*fl_z_r_borr_n;
it_coh_wkb_reshape_cols = it_z_wage_n;
mt_coh_wkb_full = reshape(mt_coh_wkb_full, [it_coh_wkb_reshape_rows, it_coh_wkb_reshape_cols]);

% Generate Aggregate Variables
ar_aplusk_mesh = ar_a_meshk_full + ar_k_mesha_full;

if (bl_display_funcgrids || bl_graph_funcgrids)

    % Genereate Table
    tab_ak_choices = array2table([ar_aplusk_mesh, ar_k_mesha_full, ar_a_meshk_full]);
    cl_col_names = {'ar_aplusk_mesh', 'ar_k_mesha_full', 'ar_a_meshk_full'};
    tab_ak_choices.Properties.VariableNames = cl_col_names;

    % Label Table Variables
    tab_ak_choices.Properties.VariableDescriptions{'ar_aplusk_mesh'} = ...
        '*ar_aplusk_mesha*: ar_aplusk_mesha = ar_a_meshk_full + ar_k_mesha_full;';
    tab_ak_choices.Properties.VariableDescriptions{'ar_a_meshk_full'} = ...
        '*ar_a_meshk_full*:';
    tab_ak_choices.Properties.VariableDescriptions{'ar_k_mesha_full'} = ...
        '*ar_k_mesha_full*:';

    cl_var_desc = tab_ak_choices.Properties.VariableDescriptions;
    for it_var_name = 1:length(cl_var_desc)
        disp(cl_var_desc{it_var_name});
    end

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('tab_ak_choices');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    it_rows_toshow = length(ar_w_level)*2;
    disp(size(tab_ak_choices));
    disp(head(array2table(tab_ak_choices), it_rows_toshow));
    disp(tail(array2table(tab_ak_choices), it_rows_toshow));

    % Generate Shock Full Mat to See coh_wkb_full zr and zw
    mt_z_r_borr_mwge_makfull = zeros([length(ar_a_meshk_full), it_z_n]) + ar_z_r_borr_mesh_wage_r1w2;
    mt_z_wage_mesh_r_makfull = zeros([length(ar_a_meshk_full), it_z_n]) + ar_z_wage_mesh_r_borr_r1w2;
    % use the same reshape command as above
    mt_z_r_borr_mwge_makfull = reshape(mt_z_r_borr_mwge_makfull, [it_coh_wkb_reshape_rows, it_coh_wkb_reshape_cols]);
    mt_z_wage_mesh_r_makfull = reshape(mt_z_wage_mesh_r_makfull, [it_coh_wkb_reshape_rows, it_coh_wkb_reshape_cols]);

    % Generate W and K Choices Full Mat to see which w and k
    mt_aplusk_mesh = zeros([length(ar_a_meshk_full), it_z_n]) + ar_aplusk_mesh;
    mt_a_meshk_full = zeros([length(ar_a_meshk_full), it_z_n]) + ar_a_meshk_full;
    mt_k_mesha_full = zeros([length(ar_a_meshk_full), it_z_n]) + ar_k_mesha_full;
    % use the same reshape command as above
    mt_aplusk_mesh = reshape(mt_aplusk_mesh, [it_coh_wkb_reshape_rows, it_coh_wkb_reshape_cols]);
    mt_a_meshk_full = reshape(mt_a_meshk_full, [it_coh_wkb_reshape_rows, it_coh_wkb_reshape_cols]);
    mt_k_mesha_full = reshape(mt_k_mesha_full, [it_coh_wkb_reshape_rows, it_coh_wkb_reshape_cols]);

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('mt_coh_wkb_full');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_coh_wkb_full));
    disp(head(array2table(mt_coh_wkb_full), it_rows_toshow));
    disp(tail(array2table(mt_coh_wkb_full), it_rows_toshow));

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('Shock Borrow R: mt_z_r_borr_mwge_makfull');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_z_r_borr_mwge_makfull));
    disp(head(array2table(mt_z_r_borr_mwge_makfull), it_rows_toshow));
    disp(tail(array2table(mt_z_r_borr_mwge_makfull), it_rows_toshow));
    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('Shock Productivity: mt_z_wage_mesh_r_makfull');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_z_wage_mesh_r_makfull));
    disp(head(array2table(mt_z_wage_mesh_r_makfull), it_rows_toshow));
    disp(tail(array2table(mt_z_wage_mesh_r_makfull), it_rows_toshow));
    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('W = Aprime + Kprime; mt_aplusk_mesh');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_aplusk_mesh));
    disp(head(array2table(mt_aplusk_mesh), it_rows_toshow));
    disp(tail(array2table(mt_aplusk_mesh), it_rows_toshow));
    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('Kprime: mt_k_mesha_full');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_k_mesha_full));
    disp(head(array2table(mt_k_mesha_full), it_rows_toshow));
    disp(tail(array2table(mt_k_mesha_full), it_rows_toshow));
    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('Aprime: mt_a_meshk_full');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_a_meshk_full));
    disp(head(array2table(mt_a_meshk_full), it_rows_toshow));
    disp(tail(array2table(mt_a_meshk_full), it_rows_toshow));

end
*ar_aplusk_mesha*: ar_aplusk_mesha = ar_a_meshk_full + ar_k_mesha_full;
*ar_k_mesha_full*:
*ar_a_meshk_full*:
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
tab_ak_choices
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
        1215           3

    tab_ak_choices1    tab_ak_choices2    tab_ak_choices3
    ar_aplusk_mesh     ar_k_mesha_full    ar_a_meshk_full
    _______________    _______________    _______________

         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
         -4.67                  0               -4.67    
       -2.4832                  0             -2.4832    
       -2.4832             0.0497             -2.5329    
       -2.4832             0.0994             -2.5826    
       -2.4832             0.1491             -2.6323    
       -2.4832             0.1988              -2.682    
       -2.4832             0.2485             -2.7317    
       -2.4832             0.2982             -2.7814    
       -2.4832             0.3479             -2.8311    
       -2.4832             0.3976             -2.8808    

    tab_ak_choices1    tab_ak_choices2    tab_ak_choices3
    ar_aplusk_mesh     ar_k_mesha_full    ar_a_meshk_full
    _______________    _______________    _______________

        47.813             42.941              4.8724    
        47.813             44.134              3.6796    
        47.813             45.326              2.4868    
        47.813             46.519               1.294    
        47.813             47.712             0.10122    
        47.813             48.905             -1.0916    
        47.813             50.098             -2.2844    
        47.813              51.29             -3.4772    
        47.813             52.483               -4.67    
            50                  0                  50    
            50             1.2425              48.758    
            50              2.485              47.515    
            50             3.7275              46.273    
            50               4.97               45.03    
            50             6.2125              43.788    
            50              7.455              42.545    
            50             8.6975              41.303    
            50               9.94               40.06    
            50             11.182              38.818    
            50             12.425              37.575    
            50             13.667              36.333    
            50              14.91               35.09    
            50             16.152              33.848    
            50             17.395              32.605    
            50             18.637              31.363    
            50              19.88               30.12    
            50             21.122              28.878    
            50             22.365              27.635    
            50             23.607              26.393    
            50              24.85               25.15    
            50             26.092              23.908    
            50             27.335              22.665    
            50             28.577              21.423    
            50              29.82               20.18    
            50             31.062              18.938    
            50             32.305              17.695    
            50             33.547              16.453    
            50              34.79               15.21    
            50             36.032              13.968    
            50             37.275              12.725    
            50             38.517              11.483    
            50              39.76               10.24    
            50             41.002              8.9975    
            50             42.245               7.755    
            50             43.487              6.5125    
            50              44.73                5.27    
            50             45.972              4.0275    
            50             47.215               2.785    
            50             48.457              1.5425    
            50               49.7             0.30002    
            50             50.942            -0.94248    
            50             52.185              -2.185    
            50             53.427             -3.4275    
            50              54.67               -4.67    

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
mt_coh_wkb_full
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
        3645          11

    mt_coh_wkb_full1    mt_coh_wkb_full2    mt_coh_wkb_full3    mt_coh_wkb_full4    mt_coh_wkb_full5    mt_coh_wkb_full6    mt_coh_wkb_full7    mt_coh_wkb_full8    mt_coh_wkb_full9    mt_coh_wkb_full10    mt_coh_wkb_full11
    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    _________________    _________________

        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431             -4.3431              -4.3431             -4.3431              -4.3431     
        -2.1016             -2.1016             -2.1016             -2.1016             -2.1016             -2.1016             -2.1016             -2.1016              -2.1016             -2.1016              -2.1016     
        -1.9892             -1.9631             -1.9313             -1.8925              -1.845              -1.787             -1.7162             -1.6298              -1.5241             -1.3951              -1.2376     
        -1.9611             -1.9276             -1.8868             -1.8369              -1.776             -1.7016             -1.6108             -1.4998              -1.3642             -1.1986             -0.99641     
        -1.9426             -1.9039             -1.8566             -1.7989             -1.7284             -1.6423             -1.5372             -1.4088              -1.2519             -1.0603             -0.82629     
        -1.9287             -1.8858             -1.8334             -1.7694             -1.6912             -1.5957             -1.4791             -1.3367              -1.1627            -0.95019             -0.69064     
        -1.9177             -1.8712             -1.8144             -1.7451             -1.6604             -1.5569             -1.4305             -1.2762              -1.0876            -0.85735             -0.57609     
        -1.9087              -1.859             -1.7984             -1.7243             -1.6339             -1.5234             -1.3884             -1.2236              -1.0223            -0.77639             -0.47605     
        -1.9011             -1.8486             -1.7845             -1.7062             -1.6106             -1.4938             -1.3512             -1.1769             -0.96413             -0.7042             -0.38673     
        -1.8947             -1.8396             -1.7723             -1.6902             -1.5899             -1.4673             -1.3176             -1.1348             -0.91154            -0.63881              -0.3057     

    mt_coh_wkb_full1    mt_coh_wkb_full2    mt_coh_wkb_full3    mt_coh_wkb_full4    mt_coh_wkb_full5    mt_coh_wkb_full6    mt_coh_wkb_full7    mt_coh_wkb_full8    mt_coh_wkb_full9    mt_coh_wkb_full10    mt_coh_wkb_full11
    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    _________________    _________________

         46.285              46.582              46.945              47.388               47.93              48.591              49.399              50.385               51.59              53.061               54.859      
         46.173              46.473               46.84              47.287              47.834              48.502              49.317              50.314               51.53              53.016               54.832      
         46.061              46.364              46.734              47.186              47.738              48.412              49.236              50.241               51.47               52.97               54.803      
         45.949              46.255              46.628              47.084              47.641              48.322              49.153              50.168              51.408              52.923               54.773      
         45.836              46.145              46.522              46.982              47.544              48.231               49.07              50.094              51.346              52.874               54.741      
         45.647              45.958              46.339              46.803               47.37              48.063              48.909              49.943              51.206              52.748               54.631      
          45.45              45.765              46.148              46.617              47.189              47.888              48.741              49.784              51.058              52.613               54.513      
         45.254              45.571              45.957               46.43              47.007              47.712              48.573              49.624              50.909              52.477               54.393      
         45.057              45.376              45.766              46.243              46.825              47.535              48.403              49.464              50.759              52.341               54.272      
         51.694              51.694              51.694              51.694              51.694              51.694              51.694              51.694              51.694              51.694               51.694      
         51.938              52.021              52.122              52.246              52.397              52.582              52.808              53.083               53.42              53.831               54.333      
         51.914               52.02               52.15              52.309              52.503               52.74               53.03              53.383              53.815              54.343               54.987      
         51.859              51.982              52.133              52.317              52.541              52.815               53.15               53.56              54.059               54.67               55.415      
         51.789              51.926              52.093              52.297              52.546               52.85              53.222              53.675               54.23              54.907               55.734      
          51.71              51.859              52.039               52.26               52.53               52.86              53.263              53.754              54.355              55.089               55.985      
         51.625              51.783              51.977              52.213              52.501              52.853              53.283              53.808              54.449              55.233                56.19      
         51.536              51.703              51.907              52.156              52.461              52.833              53.288              53.843              54.521              55.349               56.361      
         51.442              51.618              51.832              52.094              52.413              52.804              53.281              53.863              54.575              55.444               56.505      
         51.346              51.529              51.753              52.026              52.359              52.767              53.264              53.872              54.614              55.521               56.628      
         51.248              51.438               51.67              51.954                52.3              52.723               53.24              53.871              54.642              55.584               56.734      
         51.147              51.344              51.584              51.878              52.236              52.674              53.209              53.862               54.66              55.634               56.825      
         51.045              51.248              51.496              51.799              52.169              52.621              53.172              53.846               54.67              55.675               56.903      
         50.941               51.15              51.405              51.717              52.098              52.563              53.131              53.825              54.672              55.707               56.971      
         50.836              51.051              51.313              51.633              52.024              52.502              53.085              53.798              54.668              55.731               57.029      
          50.73               50.95              51.219              51.547              51.948              52.438              53.036              53.766              54.658              55.748               57.079      
         50.623              50.848              51.123              51.459               51.87              52.371              52.983               53.73              54.643              55.759               57.121      
         50.515              50.745              51.026               51.37              51.789              52.301              52.927              53.691              54.624              55.764               57.156      
         50.406              50.641              50.928              51.279              51.707              52.229              52.868              53.648              54.601              55.764               57.185      
         50.297              50.536              50.829              51.186              51.623              52.156              52.807              53.602              54.573               55.76               57.209      
         50.186               50.43              50.728              51.092              51.537               52.08              52.743              53.553              54.543              55.751               57.227      
         50.075              50.324              50.627              50.998               51.45              52.003              52.678              53.502              54.509              55.739               57.241      
         49.964              50.216              50.525              50.902              51.362              51.924               52.61              53.448              54.472              55.723               57.251      
         49.852              50.108              50.422              50.805              51.272              51.843              52.541              53.393              54.433              55.704               57.256      
         49.739                  50              50.318              50.707              51.182              51.761               52.47              53.335              54.391              55.682               57.258      
         49.626              49.891              50.214              50.608               51.09              51.678              52.397              53.275              54.347              55.657               57.256      
         49.513              49.781              50.109              50.509              50.997              51.594              52.323              53.213              54.301              55.629               57.251      
         49.399              49.671              50.003              50.408              50.904              51.509              52.247               53.15              54.252              55.599               57.243      
         49.285               49.56              49.896              50.307              50.809              51.422              52.171              53.085              54.202              55.566               57.232      
          49.17              49.449               49.79              50.206              50.714              51.335              52.093              53.019               54.15              55.531               57.219      
         49.055              49.337              49.682              50.103              50.618              51.246              52.014              52.951              54.096              55.494               57.202      
          48.94              49.225              49.574              50.001              50.521              51.157              51.933              52.882              54.041              55.456               57.184      
         48.824              49.113              49.466              49.897              50.424              51.067              51.852              52.812              53.984              55.415               57.163      
         48.708                  49              49.357              49.793              50.326              50.976               51.77               52.74              53.925              55.372                57.14      
         48.592              48.887              49.248              49.689              50.227              50.884              51.687              52.668              53.865              55.328               57.115      
         48.475              48.774              49.138              49.584              50.127              50.792              51.603              52.594              53.804              55.282               57.088      
         48.359               48.66              49.028              49.478              50.028              50.699              51.518              52.519              53.742              55.235               57.059      
         48.242              48.546              48.918              49.372              49.927              50.605              51.432              52.443              53.678              55.186               57.028      
         48.125              48.432              48.807              49.266              49.826               50.51              51.346              52.367              53.613              55.136               56.996      
         48.007              48.317              48.696              49.159              49.725              50.415              51.259              52.289              53.547              55.084               56.962      
          47.89              48.203              48.585              49.052              49.623               50.32              51.171              52.211              53.481              55.032               56.926      
         47.706              48.022              48.408              48.879              49.455              50.158              51.017              52.065              53.347              54.912               56.823      
         47.501              47.819              48.209              48.684              49.265              49.974               50.84              51.898              53.191              54.769               56.697      
         47.296              47.617              48.009              48.489              49.075               49.79              50.664              51.731              53.034              54.626                56.57      
          47.09              47.414               47.81              48.294              48.884              49.605              50.486              51.562              52.876              54.482               56.442      

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Shock Borrow R: mt_z_r_borr_mwge_makfull
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
        3645          11

    mt_z_r_borr_mwge_makfull1    mt_z_r_borr_mwge_makfull2    mt_z_r_borr_mwge_makfull3    mt_z_r_borr_mwge_makfull4    mt_z_r_borr_mwge_makfull5    mt_z_r_borr_mwge_makfull6    mt_z_r_borr_mwge_makfull7    mt_z_r_borr_mwge_makfull8    mt_z_r_borr_mwge_makfull9    mt_z_r_borr_mwge_makfull10    mt_z_r_borr_mwge_makfull11
    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    __________________________    __________________________

              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           
              0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                        0.025                         0.025           

    mt_z_r_borr_mwge_makfull1    mt_z_r_borr_mwge_makfull2    mt_z_r_borr_mwge_makfull3    mt_z_r_borr_mwge_makfull4    mt_z_r_borr_mwge_makfull5    mt_z_r_borr_mwge_makfull6    mt_z_r_borr_mwge_makfull7    mt_z_r_borr_mwge_makfull8    mt_z_r_borr_mwge_makfull9    mt_z_r_borr_mwge_makfull10    mt_z_r_borr_mwge_makfull11
    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    __________________________    __________________________

              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           
              0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                        0.095                         0.095           

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Shock Productivity: mt_z_wage_mesh_r_makfull
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
        3645          11

    mt_z_wage_mesh_r_makfull1    mt_z_wage_mesh_r_makfull2    mt_z_wage_mesh_r_makfull3    mt_z_wage_mesh_r_makfull4    mt_z_wage_mesh_r_makfull5    mt_z_wage_mesh_r_makfull6    mt_z_wage_mesh_r_makfull7    mt_z_wage_mesh_r_makfull8    mt_z_wage_mesh_r_makfull9    mt_z_wage_mesh_r_makfull10    mt_z_wage_mesh_r_makfull11
    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    __________________________    __________________________

             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          

    mt_z_wage_mesh_r_makfull1    mt_z_wage_mesh_r_makfull2    mt_z_wage_mesh_r_makfull3    mt_z_wage_mesh_r_makfull4    mt_z_wage_mesh_r_makfull5    mt_z_wage_mesh_r_makfull6    mt_z_wage_mesh_r_makfull7    mt_z_wage_mesh_r_makfull8    mt_z_wage_mesh_r_makfull9    mt_z_wage_mesh_r_makfull10    mt_z_wage_mesh_r_makfull11
    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    _________________________    __________________________    __________________________

             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          
             0.34664                      0.42338                      0.51712                      0.63162                      0.77146                      0.94226                      1.1509                       1.4057                       1.7169                        2.097                         2.5613          

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
W = Aprime + Kprime; mt_aplusk_mesh
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
        3645          11

    mt_aplusk_mesh1    mt_aplusk_mesh2    mt_aplusk_mesh3    mt_aplusk_mesh4    mt_aplusk_mesh5    mt_aplusk_mesh6    mt_aplusk_mesh7    mt_aplusk_mesh8    mt_aplusk_mesh9    mt_aplusk_mesh10    mt_aplusk_mesh11
    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    ________________    ________________

          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
          -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67              -4.67               -4.67     
        -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832             -2.4832     
        -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832             -2.4832     
        -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832             -2.4832     
        -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832             -2.4832     
        -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832             -2.4832     
        -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832             -2.4832     
        -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832             -2.4832     
        -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832             -2.4832     
        -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832            -2.4832             -2.4832     

    mt_aplusk_mesh1    mt_aplusk_mesh2    mt_aplusk_mesh3    mt_aplusk_mesh4    mt_aplusk_mesh5    mt_aplusk_mesh6    mt_aplusk_mesh7    mt_aplusk_mesh8    mt_aplusk_mesh9    mt_aplusk_mesh10    mt_aplusk_mesh11
    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    _______________    ________________    ________________

        47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813              47.813              47.813     
        47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813              47.813              47.813     
        47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813              47.813              47.813     
        47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813              47.813              47.813     
        47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813              47.813              47.813     
        47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813              47.813              47.813     
        47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813              47.813              47.813     
        47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813              47.813              47.813     
        47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813             47.813              47.813              47.813     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     
            50                 50                 50                 50                 50                 50                 50                 50                 50                  50                  50     

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Kprime: mt_k_mesha_full
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
        3645          11

    mt_k_mesha_full1    mt_k_mesha_full2    mt_k_mesha_full3    mt_k_mesha_full4    mt_k_mesha_full5    mt_k_mesha_full6    mt_k_mesha_full7    mt_k_mesha_full8    mt_k_mesha_full9    mt_k_mesha_full10    mt_k_mesha_full11
    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    _________________    _________________

              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
         0.0497              0.0497              0.0497              0.0497              0.0497              0.0497              0.0497              0.0497              0.0497              0.0497               0.0497      
         0.0994              0.0994              0.0994              0.0994              0.0994              0.0994              0.0994              0.0994              0.0994              0.0994               0.0994      
         0.1491              0.1491              0.1491              0.1491              0.1491              0.1491              0.1491              0.1491              0.1491              0.1491               0.1491      
         0.1988              0.1988              0.1988              0.1988              0.1988              0.1988              0.1988              0.1988              0.1988              0.1988               0.1988      
         0.2485              0.2485              0.2485              0.2485              0.2485              0.2485              0.2485              0.2485              0.2485              0.2485               0.2485      
         0.2982              0.2982              0.2982              0.2982              0.2982              0.2982              0.2982              0.2982              0.2982              0.2982               0.2982      
         0.3479              0.3479              0.3479              0.3479              0.3479              0.3479              0.3479              0.3479              0.3479              0.3479               0.3479      
         0.3976              0.3976              0.3976              0.3976              0.3976              0.3976              0.3976              0.3976              0.3976              0.3976               0.3976      

    mt_k_mesha_full1    mt_k_mesha_full2    mt_k_mesha_full3    mt_k_mesha_full4    mt_k_mesha_full5    mt_k_mesha_full6    mt_k_mesha_full7    mt_k_mesha_full8    mt_k_mesha_full9    mt_k_mesha_full10    mt_k_mesha_full11
    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    _________________    _________________

         42.941              42.941              42.941              42.941              42.941              42.941              42.941              42.941              42.941              42.941               42.941      
         44.134              44.134              44.134              44.134              44.134              44.134              44.134              44.134              44.134              44.134               44.134      
         45.326              45.326              45.326              45.326              45.326              45.326              45.326              45.326              45.326              45.326               45.326      
         46.519              46.519              46.519              46.519              46.519              46.519              46.519              46.519              46.519              46.519               46.519      
         47.712              47.712              47.712              47.712              47.712              47.712              47.712              47.712              47.712              47.712               47.712      
         48.905              48.905              48.905              48.905              48.905              48.905              48.905              48.905              48.905              48.905               48.905      
         50.098              50.098              50.098              50.098              50.098              50.098              50.098              50.098              50.098              50.098               50.098      
          51.29               51.29               51.29               51.29               51.29               51.29               51.29               51.29               51.29               51.29                51.29      
         52.483              52.483              52.483              52.483              52.483              52.483              52.483              52.483              52.483              52.483               52.483      
              0                   0                   0                   0                   0                   0                   0                   0                   0                   0                    0      
         1.2425              1.2425              1.2425              1.2425              1.2425              1.2425              1.2425              1.2425              1.2425              1.2425               1.2425      
          2.485               2.485               2.485               2.485               2.485               2.485               2.485               2.485               2.485               2.485                2.485      
         3.7275              3.7275              3.7275              3.7275              3.7275              3.7275              3.7275              3.7275              3.7275              3.7275               3.7275      
           4.97                4.97                4.97                4.97                4.97                4.97                4.97                4.97                4.97                4.97                 4.97      
         6.2125              6.2125              6.2125              6.2125              6.2125              6.2125              6.2125              6.2125              6.2125              6.2125               6.2125      
          7.455               7.455               7.455               7.455               7.455               7.455               7.455               7.455               7.455               7.455                7.455      
         8.6975              8.6975              8.6975              8.6975              8.6975              8.6975              8.6975              8.6975              8.6975              8.6975               8.6975      
           9.94                9.94                9.94                9.94                9.94                9.94                9.94                9.94                9.94                9.94                 9.94      
         11.182              11.182              11.182              11.182              11.182              11.182              11.182              11.182              11.182              11.182               11.182      
         12.425              12.425              12.425              12.425              12.425              12.425              12.425              12.425              12.425              12.425               12.425      
         13.667              13.667              13.667              13.667              13.667              13.667              13.667              13.667              13.667              13.667               13.667      
          14.91               14.91               14.91               14.91               14.91               14.91               14.91               14.91               14.91               14.91                14.91      
         16.152              16.152              16.152              16.152              16.152              16.152              16.152              16.152              16.152              16.152               16.152      
         17.395              17.395              17.395              17.395              17.395              17.395              17.395              17.395              17.395              17.395               17.395      
         18.637              18.637              18.637              18.637              18.637              18.637              18.637              18.637              18.637              18.637               18.637      
          19.88               19.88               19.88               19.88               19.88               19.88               19.88               19.88               19.88               19.88                19.88      
         21.122              21.122              21.122              21.122              21.122              21.122              21.122              21.122              21.122              21.122               21.122      
         22.365              22.365              22.365              22.365              22.365              22.365              22.365              22.365              22.365              22.365               22.365      
         23.607              23.607              23.607              23.607              23.607              23.607              23.607              23.607              23.607              23.607               23.607      
          24.85               24.85               24.85               24.85               24.85               24.85               24.85               24.85               24.85               24.85                24.85      
         26.092              26.092              26.092              26.092              26.092              26.092              26.092              26.092              26.092              26.092               26.092      
         27.335              27.335              27.335              27.335              27.335              27.335              27.335              27.335              27.335              27.335               27.335      
         28.577              28.577              28.577              28.577              28.577              28.577              28.577              28.577              28.577              28.577               28.577      
          29.82               29.82               29.82               29.82               29.82               29.82               29.82               29.82               29.82               29.82                29.82      
         31.062              31.062              31.062              31.062              31.062              31.062              31.062              31.062              31.062              31.062               31.062      
         32.305              32.305              32.305              32.305              32.305              32.305              32.305              32.305              32.305              32.305               32.305      
         33.547              33.547              33.547              33.547              33.547              33.547              33.547              33.547              33.547              33.547               33.547      
          34.79               34.79               34.79               34.79               34.79               34.79               34.79               34.79               34.79               34.79                34.79      
         36.032              36.032              36.032              36.032              36.032              36.032              36.032              36.032              36.032              36.032               36.032      
         37.275              37.275              37.275              37.275              37.275              37.275              37.275              37.275              37.275              37.275               37.275      
         38.517              38.517              38.517              38.517              38.517              38.517              38.517              38.517              38.517              38.517               38.517      
          39.76               39.76               39.76               39.76               39.76               39.76               39.76               39.76               39.76               39.76                39.76      
         41.002              41.002              41.002              41.002              41.002              41.002              41.002              41.002              41.002              41.002               41.002      
         42.245              42.245              42.245              42.245              42.245              42.245              42.245              42.245              42.245              42.245               42.245      
         43.487              43.487              43.487              43.487              43.487              43.487              43.487              43.487              43.487              43.487               43.487      
          44.73               44.73               44.73               44.73               44.73               44.73               44.73               44.73               44.73               44.73                44.73      
         45.972              45.972              45.972              45.972              45.972              45.972              45.972              45.972              45.972              45.972               45.972      
         47.215              47.215              47.215              47.215              47.215              47.215              47.215              47.215              47.215              47.215               47.215      
         48.457              48.457              48.457              48.457              48.457              48.457              48.457              48.457              48.457              48.457               48.457      
           49.7                49.7                49.7                49.7                49.7                49.7                49.7                49.7                49.7                49.7                 49.7      
         50.942              50.942              50.942              50.942              50.942              50.942              50.942              50.942              50.942              50.942               50.942      
         52.185              52.185              52.185              52.185              52.185              52.185              52.185              52.185              52.185              52.185               52.185      
         53.427              53.427              53.427              53.427              53.427              53.427              53.427              53.427              53.427              53.427               53.427      
          54.67               54.67               54.67               54.67               54.67               54.67               54.67               54.67               54.67               54.67                54.67      

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Aprime: mt_a_meshk_full
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
        3645          11

    mt_a_meshk_full1    mt_a_meshk_full2    mt_a_meshk_full3    mt_a_meshk_full4    mt_a_meshk_full5    mt_a_meshk_full6    mt_a_meshk_full7    mt_a_meshk_full8    mt_a_meshk_full9    mt_a_meshk_full10    mt_a_meshk_full11
    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    _________________    _________________

          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
          -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67                -4.67     
        -2.4832             -2.4832             -2.4832             -2.4832             -2.4832             -2.4832             -2.4832             -2.4832             -2.4832              -2.4832              -2.4832     
        -2.5329             -2.5329             -2.5329             -2.5329             -2.5329             -2.5329             -2.5329             -2.5329             -2.5329              -2.5329              -2.5329     
        -2.5826             -2.5826             -2.5826             -2.5826             -2.5826             -2.5826             -2.5826             -2.5826             -2.5826              -2.5826              -2.5826     
        -2.6323             -2.6323             -2.6323             -2.6323             -2.6323             -2.6323             -2.6323             -2.6323             -2.6323              -2.6323              -2.6323     
         -2.682              -2.682              -2.682              -2.682              -2.682              -2.682              -2.682              -2.682              -2.682               -2.682               -2.682     
        -2.7317             -2.7317             -2.7317             -2.7317             -2.7317             -2.7317             -2.7317             -2.7317             -2.7317              -2.7317              -2.7317     
        -2.7814             -2.7814             -2.7814             -2.7814             -2.7814             -2.7814             -2.7814             -2.7814             -2.7814              -2.7814              -2.7814     
        -2.8311             -2.8311             -2.8311             -2.8311             -2.8311             -2.8311             -2.8311             -2.8311             -2.8311              -2.8311              -2.8311     
        -2.8808             -2.8808             -2.8808             -2.8808             -2.8808             -2.8808             -2.8808             -2.8808             -2.8808              -2.8808              -2.8808     

    mt_a_meshk_full1    mt_a_meshk_full2    mt_a_meshk_full3    mt_a_meshk_full4    mt_a_meshk_full5    mt_a_meshk_full6    mt_a_meshk_full7    mt_a_meshk_full8    mt_a_meshk_full9    mt_a_meshk_full10    mt_a_meshk_full11
    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    ________________    _________________    _________________

          4.8724              4.8724              4.8724              4.8724              4.8724              4.8724              4.8724              4.8724              4.8724              4.8724               4.8724     
          3.6796              3.6796              3.6796              3.6796              3.6796              3.6796              3.6796              3.6796              3.6796              3.6796               3.6796     
          2.4868              2.4868              2.4868              2.4868              2.4868              2.4868              2.4868              2.4868              2.4868              2.4868               2.4868     
           1.294               1.294               1.294               1.294               1.294               1.294               1.294               1.294               1.294               1.294                1.294     
         0.10122             0.10122             0.10122             0.10122             0.10122             0.10122             0.10122             0.10122             0.10122             0.10122              0.10122     
         -1.0916             -1.0916             -1.0916             -1.0916             -1.0916             -1.0916             -1.0916             -1.0916             -1.0916             -1.0916              -1.0916     
         -2.2844             -2.2844             -2.2844             -2.2844             -2.2844             -2.2844             -2.2844             -2.2844             -2.2844             -2.2844              -2.2844     
         -3.4772             -3.4772             -3.4772             -3.4772             -3.4772             -3.4772             -3.4772             -3.4772             -3.4772             -3.4772              -3.4772     
           -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67     
              50                  50                  50                  50                  50                  50                  50                  50                  50                  50                   50     
          48.758              48.758              48.758              48.758              48.758              48.758              48.758              48.758              48.758              48.758               48.758     
          47.515              47.515              47.515              47.515              47.515              47.515              47.515              47.515              47.515              47.515               47.515     
          46.273              46.273              46.273              46.273              46.273              46.273              46.273              46.273              46.273              46.273               46.273     
           45.03               45.03               45.03               45.03               45.03               45.03               45.03               45.03               45.03               45.03                45.03     
          43.788              43.788              43.788              43.788              43.788              43.788              43.788              43.788              43.788              43.788               43.788     
          42.545              42.545              42.545              42.545              42.545              42.545              42.545              42.545              42.545              42.545               42.545     
          41.303              41.303              41.303              41.303              41.303              41.303              41.303              41.303              41.303              41.303               41.303     
           40.06               40.06               40.06               40.06               40.06               40.06               40.06               40.06               40.06               40.06                40.06     
          38.818              38.818              38.818              38.818              38.818              38.818              38.818              38.818              38.818              38.818               38.818     
          37.575              37.575              37.575              37.575              37.575              37.575              37.575              37.575              37.575              37.575               37.575     
          36.333              36.333              36.333              36.333              36.333              36.333              36.333              36.333              36.333              36.333               36.333     
           35.09               35.09               35.09               35.09               35.09               35.09               35.09               35.09               35.09               35.09                35.09     
          33.848              33.848              33.848              33.848              33.848              33.848              33.848              33.848              33.848              33.848               33.848     
          32.605              32.605              32.605              32.605              32.605              32.605              32.605              32.605              32.605              32.605               32.605     
          31.363              31.363              31.363              31.363              31.363              31.363              31.363              31.363              31.363              31.363               31.363     
           30.12               30.12               30.12               30.12               30.12               30.12               30.12               30.12               30.12               30.12                30.12     
          28.878              28.878              28.878              28.878              28.878              28.878              28.878              28.878              28.878              28.878               28.878     
          27.635              27.635              27.635              27.635              27.635              27.635              27.635              27.635              27.635              27.635               27.635     
          26.393              26.393              26.393              26.393              26.393              26.393              26.393              26.393              26.393              26.393               26.393     
           25.15               25.15               25.15               25.15               25.15               25.15               25.15               25.15               25.15               25.15                25.15     
          23.908              23.908              23.908              23.908              23.908              23.908              23.908              23.908              23.908              23.908               23.908     
          22.665              22.665              22.665              22.665              22.665              22.665              22.665              22.665              22.665              22.665               22.665     
          21.423              21.423              21.423              21.423              21.423              21.423              21.423              21.423              21.423              21.423               21.423     
           20.18               20.18               20.18               20.18               20.18               20.18               20.18               20.18               20.18               20.18                20.18     
          18.938              18.938              18.938              18.938              18.938              18.938              18.938              18.938              18.938              18.938               18.938     
          17.695              17.695              17.695              17.695              17.695              17.695              17.695              17.695              17.695              17.695               17.695     
          16.453              16.453              16.453              16.453              16.453              16.453              16.453              16.453              16.453              16.453               16.453     
           15.21               15.21               15.21               15.21               15.21               15.21               15.21               15.21               15.21               15.21                15.21     
          13.968              13.968              13.968              13.968              13.968              13.968              13.968              13.968              13.968              13.968               13.968     
          12.725              12.725              12.725              12.725              12.725              12.725              12.725              12.725              12.725              12.725               12.725     
          11.483              11.483              11.483              11.483              11.483              11.483              11.483              11.483              11.483              11.483               11.483     
           10.24               10.24               10.24               10.24               10.24               10.24               10.24               10.24               10.24               10.24                10.24     
          8.9975              8.9975              8.9975              8.9975              8.9975              8.9975              8.9975              8.9975              8.9975              8.9975               8.9975     
           7.755               7.755               7.755               7.755               7.755               7.755               7.755               7.755               7.755               7.755                7.755     
          6.5125              6.5125              6.5125              6.5125              6.5125              6.5125              6.5125              6.5125              6.5125              6.5125               6.5125     
            5.27                5.27                5.27                5.27                5.27                5.27                5.27                5.27                5.27                5.27                 5.27     
          4.0275              4.0275              4.0275              4.0275              4.0275              4.0275              4.0275              4.0275              4.0275              4.0275               4.0275     
           2.785               2.785               2.785               2.785               2.785               2.785               2.785               2.785               2.785               2.785                2.785     
          1.5425              1.5425              1.5425              1.5425              1.5425              1.5425              1.5425              1.5425              1.5425              1.5425               1.5425     
         0.30002             0.30002             0.30002             0.30002             0.30002             0.30002             0.30002             0.30002             0.30002             0.30002              0.30002     
        -0.94248            -0.94248            -0.94248            -0.94248            -0.94248            -0.94248            -0.94248            -0.94248            -0.94248            -0.94248             -0.94248     
          -2.185              -2.185              -2.185              -2.185              -2.185              -2.185              -2.185              -2.185              -2.185              -2.185               -2.185     
         -3.4275             -3.4275             -3.4275             -3.4275             -3.4275             -3.4275             -3.4275             -3.4275             -3.4275             -3.4275              -3.4275     
           -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67               -4.67                -4.67     

Check if COH is within Borrowing Bounds

some coh levels are below borrowing bound, can not borrow enough to pay debt

mt_bl_coh_wkb_invalid = (mt_coh_wkb_full < fl_b_bd);

% (k,a) invalid if coh(k,a,z) < bd for any z
ar_bl_wkb_invalid = max(mt_bl_coh_wkb_invalid,[], 2);
mt_bl_wkb_invalid = reshape(ar_bl_wkb_invalid, [it_ak_perc_n, it_w_interp_n*fl_z_r_borr_n]);

% find the first w_level choice where some k(w) percent choices are valid?
ar_bl_w_level_invalid =  min(mt_bl_wkb_invalid, [], 1);

% w choices can not be lower than fl_w_level_min_valid. If w choices are
% lower, given the current borrowing interest rate as well as the minimum
% income level in the future, and the maximum borrowing level available
% next period, and given the shock distribution, there exists some state in
% the future when the household when making this choice will be unable to
% borrow sufficiently to maintain positive consumption.
ar_w_level_full_dup = repmat(ar_w_level_full, [1,fl_z_r_borr_n]);
fl_w_level_min_valid = min(ar_w_level_full_dup(~ar_bl_w_level_invalid));

Update Valid 2nd stage choice matrix

ar_w_level = linspace(fl_w_level_min_valid, fl_w_max, it_w_interp_n); ar_k_max = ar_w_level - fl_b_bd; mt_k = (ar_k_max'*ar_ak_perc)'; mt_a = (ar_w_level - mt_k); ar_a_meshk = mt_a(:); ar_k_mesha = mt_k(:);

Generate 2nd Stage Cash-on-Hand Points for Interpolation

% it_ak_perc_n = length(ar_ak_perc);
% it_w_interp_n = length(ar_w_level);
it_wak_n = it_w_interp_n*it_ak_perc_n;

% mt_coh_wkb = mt_coh_wkb_full(~ar_bl_wkb_invalid, :);
mt_coh_wkb = mt_coh_wkb_full;


mt_coh_wkb_mesh_z_r_borr = repmat(mt_coh_wkb_full, [1, fl_z_r_borr_n]);
mt_z_r_borr_mesh_coh_wkb = repmat(ar_z_r_borr, [size(mt_coh_wkb,1),1]);

mt_z_wage_mesh_coh_wkb = repmat(ar_z_wage, [size(mt_coh_wkb,1),1]);
mt_z_mesh_coh_wkb = repmat((1:it_z_n), [size(mt_coh_wkb,1), 1]);
mt_z_mesh_coh_wkb_seg = repmat((1:it_z_n), [it_wak_n, 1]);

if (ismember(st_v_coh_z_interp_method, ["method_cell"]))

    cl_mt_coh_wkb_mesh_z_r_borr = cell([fl_z_r_borr_n, 1]);
    for it_z_r_borr_ctr = 1:1:fl_z_r_borr_n
        it_mt_val_row_start = it_wak_n*(it_z_r_borr_ctr-1) + 1;
        it_mt_val_row_end = it_mt_val_row_start + it_wak_n - 1;
        cl_mt_coh_wkb_mesh_z_r_borr{it_z_r_borr_ctr} = ...
            mt_coh_wkb_mesh_z_r_borr(it_mt_val_row_start:it_mt_val_row_end, :);
    end

elseif (ismember(st_v_coh_z_interp_method, ["method_idx_a", "method_idx_b"]))

    % This is borrowing with default or not condition
    fl_min_mt_coh = fl_b_bd;

    cl_mt_coh_wkb_mesh_z_r_borr = cell([fl_z_r_borr_n, 1]);
    for it_z_r_borr_ctr = 1:1:fl_z_r_borr_n
        it_mt_val_row_start = it_wak_n*(it_z_r_borr_ctr-1) + 1;
        it_mt_val_row_end = it_mt_val_row_start + it_wak_n - 1;

        mt_coh_wkb_mesh_z_r_borr_seg = ...
            1 + ((mt_coh_wkb_mesh_z_r_borr(it_mt_val_row_start:it_mt_val_row_end, :) - fl_min_mt_coh)/fl_coh_interp_grid_gap);

        cl_mt_coh_wkb_mesh_z_r_borr{it_z_r_borr_ctr} = mt_coh_wkb_mesh_z_r_borr_seg;

    end

end

Generate 1st Stage States: Interpolation Cash-on-hand Interpolation Grid

For the iwkz problems, we solve the problem along a grid of cash-on-hand values, the interpolate to find v(k',b',z) at (k',b') choices. Crucially, we have to coh matrxies

fl_min_mt_coh = fl_b_bd;

fl_max_mt_coh = max(max(mt_coh_wkb));

% This is savings only condition
% fl_min_mt_coh = min(min(mt_coh_wkb));

% This could be condition if no defaults are allowed
% fl_min_mt_coh = fl_w_level_min_valid;


it_coh_interp_n = (fl_max_mt_coh-fl_min_mt_coh)/(fl_coh_interp_grid_gap);
ar_interp_coh_grid = fft_array_add_zero(linspace(fl_min_mt_coh, fl_max_mt_coh, it_coh_interp_n), true);
mt_interp_coh_grid_mesh_w_perc = repmat(ar_interp_coh_grid, [it_w_perc_n, 1]);
it_coh_interp_n = length(ar_interp_coh_grid);

[mt_interp_coh_grid_mesh_z_wage, mt_z_wage_mesh_interp_coh_grid] = ndgrid(ar_interp_coh_grid, ar_z_wage);

mt_interp_coh_grid_mesh_z = repmat(ar_interp_coh_grid', [1, it_z_n]);
% This is meshed index, 1:it_z_n index for, common value each column
mt_z_mesh_interp_coh_grid = repmat((1:it_z_n), [it_coh_interp_n, 1]);

Generate 1st Stage Choices: Interpolation Cash-on-hand Interpolation Grid

previously, our ar_w was the first stage choice grid, the grid was the same for all coh levels. Now, for each coh level, there is a different ar_w. ar_interp_coh_grid is (1 by ar_interp_coh_grid) and ar_w_perc is ( 1 by it_w_perc_n). Conditional on z, each choice matrix is (it_w_perc_n by ar_interp_coh_grid). Here we are pre-computing the choice matrix. This could be a large matrix if the choice grid is large. This is the matrix of aggregate savings choices

if (fl_min_mt_coh < 0)
    % borrowing bound is below zero
    mt_w_perc_mesh_interp_coh_grid = ((ar_interp_coh_grid-fl_min_mt_coh)'*ar_w_perc)' + fl_min_mt_coh;
else
    % savings only
    mt_w_perc_mesh_interp_coh_grid = ((ar_interp_coh_grid)'*ar_w_perc)';
end

Generate Interpolation Consumption Grid

We also interpolate over consumption to speed the program up. We only solve for u(c) at this grid for the iwkz problmes, and then interpolate other c values.

fl_c_max = max(max(mt_coh_wkb_full)) - fl_b_bd;
it_interp_c_grid_n = (fl_c_max-fl_c_min)/(it_c_interp_grid_gap);
ar_interp_c_grid = linspace(fl_c_min, fl_c_max, it_interp_c_grid_n);

Initialize armt_map to store, state, choice, shock matrixes

armt_map = containers.Map('KeyType','char', 'ValueType','any');
armtdesc_map = containers.Map('KeyType','char', 'ValueType','any');

Store armt_map (1): base arrays

Dimensions of Various Grids: I for level grid, M for shock grid, P for percent grid. Dimensions are:

  1. ar_interp_c_grid: 1 by I^c
  2. ar_interp_coh_grid: 1 by I^{coh}
  3. ar_w_level: 1 by I^{W=k+b}
  4. ar_w_perc: 1 by P^{W=k+b}
  5. ar_ak_perc: 1 by P^{k and b}

more descriptions:

  1. ar_interp_c_grid: 1 by I^c, 1st stage consumption interpolation
  2. ar_interp_coh_grid: 1 by I^{coh}, 1st stage value function V(coh,z)
  3. ar_w_level: 1 by I^{W=k+b}, 2nd stage k*(w,z) w grid. 2nd stage, level of w over which we solve the optimal percentage k' choices. Need to generate interpolant based on this so that we know optimal k* given ar_w_perc(coh) in the 1st stage
  4. ar_w_perc: 1 by P^{W=k+b}, 1st stage w \in {w_perc(coh)} choice set. 1st stage, percentage w choice given coh, at each coh level the number of choice points is the same for this problem with percentage grid points.
  5. ar_ak_perc: 1 by P^{k and b}, 2nd stage k \in {ask_perc(w,z)} set
armt_map('ar_interp_c_grid') = ar_interp_c_grid;
armt_map('ar_interp_coh_grid') = ar_interp_coh_grid;
armt_map('ar_w_level') = ar_w_level;
armt_map('ar_w_perc') = ar_w_perc;
armt_map('ar_ak_perc') = ar_ak_perc;

Store armt_map (2): 1st stage level coh on hand related arrays

Dimensions of Various Grids: I for level grid, M for shock grid, P for percent grid. Dimensions are:

  1. mt_interp_coh_grid_mesh_z_wage: I^{coh} by M^w
  2. mt_z_wage_mesh_interp_coh_grid: I^{coh} by M^w
  3. mt_interp_coh_grid_mesh_w_perc: I^{coh} by P^{LAM=k+b}
  4. mt_w_perc_mesh_interp_coh_grid: I^{coh} by P^{LAM=k+b}

more descriptions:

  1. mt_w_perc_mesh_interp_coh_grid 1st stage, generate w(coh, percent), meaning the level of w given coh and the percentage grid of ar_w_perc. Mesh this with the coh grid, Rows here correspond to percentage of w choices, columns correspond to cash-on-hand. The columns of cash-on-hand is determined by ar_interp_coh_grid, because we solve the 1st stage problem at that coh grid.
armt_map('mt_interp_coh_grid_mesh_z_wage') = mt_interp_coh_grid_mesh_z_wage;
armt_map('mt_z_wage_mesh_interp_coh_grid') = mt_z_wage_mesh_interp_coh_grid;

armt_map('mt_interp_coh_grid_mesh_w_perc') = mt_interp_coh_grid_mesh_w_perc;
armt_map('mt_w_perc_mesh_interp_coh_grid') = mt_w_perc_mesh_interp_coh_grid;

armt_map('mt_interp_coh_grid_mesh_z') = mt_interp_coh_grid_mesh_z;
armt_map('mt_z_mesh_interp_coh_grid') = mt_z_mesh_interp_coh_grid;

Store armt_map (3): 2nd stage reachable coh(k(w), a(w,k), z', r)

Dimensions of Various Grids: I for level grid, M for shock grid, P for percent grid. These are grids for 1st stage solution

  1. mt_coh_wkb: (I^k x I^w x M^r) by (M^z)
  2. mt_z_wage_mesh_coh_wkb: (I^k x I^w x M^r) by (M^z)
armt_map('mt_coh_wkb') = mt_coh_wkb_full;
armt_map('mt_coh_wkb_mesh_z_r_borr') = mt_coh_wkb_mesh_z_r_borr;

armt_map('mt_z_mesh_coh_wkb') = mt_z_mesh_coh_wkb;
armt_map('mt_z_wage_mesh_coh_wkb') = mt_z_wage_mesh_coh_wkb;

armt_map('cl_mt_coh_wkb_mesh_z_r_borr') = cl_mt_coh_wkb_mesh_z_r_borr;
armt_map('mt_z_mesh_coh_wkb_seg') = mt_z_mesh_coh_wkb_seg;

% armt_map('mt_z_r_borr_mesh_coh_wkb') = mt_z_r_borr_mesh_coh_wkb;

Store armt_map (4): 2nd stage additional arrays

Dimensions of Various Grids: I for level grid, M for shock grid, P for percent grid. These are grids for 1st stage solution

  1. mt_k: (I^w) by (P^{k and b})
  2. ar_a_meshk: 1 by (I^w x P^{k and b})
  3. ar_k_mesha: 1 by (I^w x P^{k and b})
  4. ar_aplusk_mesh: 1 by (I^w x P^{k and b})
  5. it_ameshk_n: scalar
armt_map('mt_k') = mt_k;
armt_map('ar_a_meshk') = ar_a_meshk;
armt_map('ar_k_mesha') = ar_k_mesha;
armt_map('ar_aplusk_mesh') = ar_aplusk_mesh;
armt_map('it_ameshk_n') = length(ar_a_meshk);

Store armt_map (5): Shock Grids Arrays and Mesh

Dimensions of Various Grids: I for level grid, M for shock grid, P for percent grid. These are grids for 1st stage solution

  1. ar_z_r_borr: 1 by (M^r)
  2. ar_z_r_borr_prob: 1 by (M^r)
  3. ar_z_wage: 1 by (M^z)
  4. ar_z_wage_prob: 1 by (M^z)
  5. ar_z_r_borr_mesh_wage_w1r2: 1 by (M^z x M^r)
  6. ar_z_wage_mesh_r_borr_w1r2: 1 by (M^z x M^r)
  7. ar_z_r_borr_mesh_wage_r1w2: 1 by (M^r x M^z)
  8. ar_z_wage_mesh_r_borr_r1w2: 1 by (M^r x M^z)
armt_map('ar_z_r_borr') = ar_z_r_borr;
armt_map('ar_z_r_borr_prob') = ar_z_r_borr_prob;

armt_map('ar_z_wage') = ar_z_wage;
armt_map('ar_z_wage_prob') = ar_z_wage_prob;

armt_map('ar_z_r_borr_mesh_wage_w1r2') = ar_z_r_borr_mesh_wage_w1r2;
armt_map('ar_z_wage_mesh_r_borr_w1r2') = ar_z_wage_mesh_r_borr_w1r2;
armt_map('ar_z_r_borr_mesh_wage_r1w2') = ar_z_r_borr_mesh_wage_r1w2;
armt_map('ar_z_wage_mesh_r_borr_r1w2') = ar_z_wage_mesh_r_borr_r1w2;

armt_map('mt_z_trans') = mt_z_trans;

Store Function Map

func_map = containers.Map('KeyType','char', 'ValueType','any');
func_map('f_util_log') = f_util_log;
func_map('f_util_crra') = f_util_crra;
func_map('f_util_standin') = f_util_standin;
func_map('f_util_standin_coh') = f_util_standin_coh;
func_map('f_prod') = f_prod;
func_map('f_inc') = f_inc;
func_map('f_coh') = f_coh;
func_map('f_cons') = f_cons;

Graph

if (bl_graph_funcgrids)

Generate Limited Legends

8 graph points, 2 levels of borrow rates, and 4 levels of rbr rates

    ar_it_z_r_borr = ([1 round((fl_z_r_borr_n)/2) (fl_z_r_borr_n)]);
    ar_it_z_wage = ([1 round((it_z_wage_n)/2) (it_z_wage_n)]);

    % combine by index
    mt_it_z_graph = ar_it_z_wage' + it_z_wage_n*(ar_it_z_r_borr-1);
    ar_it_z_graph = mt_it_z_graph(:)';
    ar_it_z_graph_zwage = ([1 round((it_z_wage_n)/4) 2*round((it_z_wage_n)/4) 3*round((it_z_wage_n)/4) (it_z_wage_n)]);

    % legends index final
    cl_st_legendCell = cellstr([num2str(ar_z_r_borr_mesh_wage_w1r2', 'zr=%3.2f;'), ...
                                num2str(ar_z_wage_mesh_r_borr_w1r2', 'zw=%3.2f')]);

    % legends index final full mat wage only
    cl_st_legendCell_zwage = cellstr([num2str(ar_z_wage', 'zw=%3.2f')]);

Graph 1: a and k choice grid graphs

compare the figure here to the same figure in ffs_akz_get_funcgrid. there the grid points are on an even grid, half of the grid points have NA. for the grid here, the grid points get denser as we get closer to low w = k'+b' levels. This is what is different visually about percentage points based choice grid for the 2nd stage problem.

    figure('PaperPosition', [0 0 7 4]);
    hold on;

    chart = plot(mt_a, mt_k, 'blue');
    clr = jet(numel(chart));
    for m = 1:numel(chart)
        set(chart(m),'Color',clr(m,:))
    end
%     if (length(ar_w_level_full) <= 100)
        scatter(ar_a_meshk, ar_k_mesha, 3, 'filled', ...
            'MarkerEdgeColor', 'b', 'MarkerFaceColor', 'b');
%     end
    if (length(ar_w_level_full) <= 100)
        gf_invalid_scatter = scatter(mt_a_meshk_full(ar_bl_wkb_invalid),...
                                     mt_k_mesha_full(ar_bl_wkb_invalid),...
                20, 'O', 'MarkerEdgeColor', 'black', 'MarkerFaceColor', 'black');
    end

    xline(0);
    yline(0);

    title('Risky K Percentage Grids Given w=k+a (2nd Stage)')
    ylabel('Capital Choice (mt\_k)')
    xlabel({'Borrowing (<0) or Saving (>0) (mt\_a)'...
        'Each Diagonal Line a Different w=k+a level'...
        'Percentage for Risky K along Each Diagonal'})

    legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/4)  numel(chart)]);
    legendCell = cellstr(num2str(ar_w_level', 'k+a=%3.2f'));

    if (length(ar_w_level_full) <= 100)
        chart(length(chart)+1) = gf_invalid_scatter;
        legendCell{length(legendCell) + 1} = 'Invalid: COH(a,b,z)<bar(b) some z';
        legend(chart([legend2plot length(legendCell)]), legendCell([legend2plot length(legendCell)]), 'Location', 'northeast');
    else
        legend(chart([legend2plot]), legendCell([legend2plot]), 'Location', 'northeast');
    end

    grid on;

Graph 2: coh by shock

compare the figure here to the same figure in ffs_akz_get_funcgrid. there the grid points are on an even grid. Visually, one could see that the blue/red line segments here are always the same length, but in the ffs_akz_get_funcgrid figure, they are increasingly longer as we move towards the right. They are even because the number of percentage points available is constant regardless of w = k' + b' levels. But previously, the number of grid points available is increasing as w increases since choice grid is based on levels.

    figure('PaperPosition', [0 0 7 4]);
    chart = plot(0:1:(size(mt_coh_wkb_full,1)-1), mt_coh_wkb_full);
    clr = jet(numel(chart));
    for m = 1:numel(chart)
        set(chart(m),'Color',clr(m,:))
    end

    % zero lines
    xline(0);
    yline(0);

    % invalid points separating lines
    yline_borrbound = yline(fl_b_bd);
    yline_borrbound.HandleVisibility = 'on';
    yline_borrbound.LineStyle = '--';
    yline_borrbound.Color = 'blue';
    yline_borrbound.LineWidth = 2.5;

    title('Cash-on-Hand given w(k+b),k,z');
    ylabel('Cash-on-Hand (mt\_coh\_wkb\_full)');
    xlabel({'Index of Cash-on-Hand Discrete Point (0:1:(size(mt\_coh\_wkb\_full,1)-1))'...
            'Super-Segment: borrow r; Sub-Segment: w=k+b; within seg increasing k'...
            'For each w and z, coh maximizing k is different'});

    cl_st_legendCell_here = cl_st_legendCell_zwage;

    cl_st_legendCell_here{length(cl_st_legendCell_here) + 1} = 'borrow-constraint';
    chart(length(chart)+1) = yline_borrbound;
    legend(chart([ar_it_z_graph_zwage length(cl_st_legendCell_here)]), ...
                  cl_st_legendCell_here([ar_it_z_graph_zwage length(cl_st_legendCell_here)]), 'Location', 'southeast');

    grid on;

Graph 3: 1st State Aggregate Savings Choices by COH interpolation grids

    figure('PaperPosition', [0 0 7 4]);
    hold on;

    chart = plot(ar_interp_coh_grid, mt_w_perc_mesh_interp_coh_grid');

    clr = jet(numel(chart));
    for m = 1:numel(chart)
        set(chart(m),'Color',clr(m,:))
    end
    if (length(ar_interp_coh_grid) <= 100)
        [~, mt_interp_coh_grid_mesh_w_perc] = ndgrid(ar_w_perc, ar_interp_coh_grid);
        scatter(mt_interp_coh_grid_mesh_w_perc(:), mt_w_perc_mesh_interp_coh_grid(:), 3, 'filled', ...
            'MarkerEdgeColor', 'b', 'MarkerFaceColor', 'b');
    end

    % invalid points separating lines
    yline_borrbound = yline(fl_w_level_min_valid);
    yline_borrbound.HandleVisibility = 'on';
    yline_borrbound.LineStyle = '--';
    yline_borrbound.Color = 'red';
    yline_borrbound.LineWidth = 2.5;

    xline0 = xline(0);
    xline0.HandleVisibility = 'off';
    yline0 = yline(0);
    yline0.HandleVisibility = 'off';

    title({'Aggregate Savings Percentage Grids (1st Stage)' ...
           'y=mt\_w\_by\_interp\_coh\_interp\_grid, and, y=ar\_interp\_coh\_grid'});
    ylabel('1st Stage Aggregate Savings Choices');
    xlabel({'Cash-on-Hand Levels (Interpolation Points)'...
            'w(coh)>min-agg-save, coh(k(w),w-k)>=bar(b)'});

    legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/4)  numel(chart)]);
    legendCell = cellstr(num2str(ar_w_perc', 'ar w perc=%3.2f'));
    legendCell{length(legendCell) + 1} = 'min-agg-save';
    chart(length(chart)+1) = yline_borrbound;
    legend(chart([legend2plot length(legendCell)]), legendCell([legend2plot length(legendCell)]), 'Location', 'northwest');

    grid on;
end

Graph Details, Generally do Not Run

if (bl_graph_funcgrids_detail)

Graph 1: 2nd stage coh reached by k' b' choices by index

    figure('PaperPosition', [0 0 7 4]);
    ar_coh_kpzgrid_unique = unique(sort(mt_coh_wkb_full(:)));
    scatter(1:length(ar_coh_kpzgrid_unique), ar_coh_kpzgrid_unique);
    xline(0);
    yline(0);
    title('Cash-on-Hand given w(k+b),k,z');
    ylabel('Cash-on-Hand (y=ar\_coh\_kpzgrid\_unique)');
    xlabel({'Index of Cash-on-Hand Discrete Point' 'x = 1:length(ar\_coh\_kpzgrid\_unique)'});
    grid on;

Graph 2: 2nd stage coh reached by k' b' choices by coh

    figure('PaperPosition', [0 0 7 4]);
    ar_coh_kpzgrid_unique = unique(sort(mt_coh_wkb_full(:)));
    scatter(ar_coh_kpzgrid_unique, ar_coh_kpzgrid_unique, '.');
    xline(0);
    yline(0);
    title('Cash-on-Hand given w(k+b),k,z; See Clearly Sparsity Density of Grid across Z');
    ylabel('Cash-on-Hand (y = ar\_coh\_kpzgrid\_unique)');
    xlabel({'Cash-on-Hand' 'x = ar\_coh\_kpzgrid\_unique'});
    grid on;
end

Display

if (bl_display_funcgrids)

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('ar_z_wage');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(ar_z_wage));
    disp(ar_z_wage);

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('ar_w_level_full');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(ar_w_level_full));
    disp(ar_w_level_full);

    disp('----------------------------------------');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp('mt_z_trans');
    disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
    disp(size(mt_z_trans));
    disp(head(array2table(mt_z_trans), 10));
    disp(tail(array2table(mt_z_trans), 10));

end
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
ar_z_wage
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
     1    11

  Columns 1 through 7

    0.3466    0.4234    0.5171    0.6316    0.7715    0.9423    1.1509

  Columns 8 through 11

    1.4057    1.7169    2.0970    2.5613

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
ar_w_level_full
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
     1    27

  Columns 1 through 7

   -4.6700   -2.4832   -0.2964         0    1.8904    4.0772    6.2640

  Columns 8 through 14

    8.4508   10.6376   12.8244   15.0112   17.1980   19.3848   21.5716

  Columns 15 through 21

   23.7584   25.9452   28.1320   30.3188   32.5056   34.6924   36.8792

  Columns 22 through 27

   39.0660   41.2528   43.4396   45.6264   47.8132   50.0000

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
mt_z_trans
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
    33    33

    mt_z_trans1    mt_z_trans2    mt_z_trans3    mt_z_trans4    mt_z_trans5    mt_z_trans6    mt_z_trans7    mt_z_trans8    mt_z_trans9    mt_z_trans10    mt_z_trans11    mt_z_trans12    mt_z_trans13    mt_z_trans14    mt_z_trans15    mt_z_trans16    mt_z_trans17    mt_z_trans18    mt_z_trans19    mt_z_trans20    mt_z_trans21    mt_z_trans22    mt_z_trans23    mt_z_trans24    mt_z_trans25    mt_z_trans26    mt_z_trans27    mt_z_trans28    mt_z_trans29    mt_z_trans30    mt_z_trans31    mt_z_trans32    mt_z_trans33
    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________

     0.0013961      0.0017327      0.0010938      0.0002742     2.7045e-05     1.0372e-06     1.5288e-08     8.5744e-11     1.8158e-13      1.4418e-16               0        0.027922        0.034654        0.021876       0.0054839      0.00054091      2.0745e-05      3.0576e-07      1.7149e-09      3.6315e-12      2.8836e-15               0         0.27922         0.34654         0.21876        0.054839       0.0054091      0.00020745      3.0576e-06      1.7149e-08      3.6315e-11      2.8836e-14               0 
    0.00043801      0.0012909      0.0017011      0.0008932     0.00018597       1.52e-05      4.819e-07     5.8589e-09     2.7059e-11      4.7123e-14      3.0644e-17       0.0087602        0.025818        0.034022        0.017864       0.0037193        0.000304      9.6379e-06      1.1718e-07      5.4117e-10      9.4246e-13      6.1288e-16        0.087602         0.25818         0.34022         0.17864        0.037193         0.00304      9.6379e-05      1.1718e-06      5.4117e-09      9.4246e-12      6.1288e-15 
    8.0834e-05     0.00053304      0.0014684      0.0016098     0.00070291      0.0001215      8.225e-06     2.1546e-07       2.16e-09      8.2123e-12      1.1765e-14       0.0016167        0.010661        0.029367        0.032196        0.014058       0.0024299       0.0001645      4.3092e-06      4.3201e-08      1.6425e-10      2.3531e-13        0.016167         0.10661         0.29367         0.32196         0.14058        0.024299        0.001645      4.3092e-05      4.3201e-07      1.6425e-09      2.3531e-12 
    8.4426e-06      0.0001215     0.00070291      0.0016098      0.0014684     0.00053304     7.6456e-05     4.2848e-06     9.2704e-08      7.6605e-10      2.3997e-12      0.00016885       0.0024299        0.014058        0.032196        0.029367        0.010661       0.0015291      8.5696e-05      1.8541e-06      1.5321e-08      4.7995e-11       0.0016885        0.024299         0.14058         0.32196         0.29367         0.10661        0.015291      0.00085696      1.8541e-05      1.5321e-07      4.7995e-10 
    4.8778e-07       1.52e-05     0.00018597      0.0008932      0.0017011      0.0012909     0.00038949     4.6338e-05     2.1488e-06       3.838e-08        2.62e-10      9.7556e-06        0.000304       0.0037193        0.017864        0.034022        0.025818       0.0077897      0.00092676      4.2976e-05       7.676e-07      5.2399e-09      9.7556e-05         0.00304        0.037193         0.17864         0.34022         0.25818        0.077897       0.0092676      0.00042976       7.676e-06      5.2399e-08 
    1.5374e-08     1.0372e-06     2.7045e-05      0.0002742      0.0010938      0.0017327      0.0010938      0.0002742     2.7045e-05      1.0372e-06      1.5374e-08      3.0748e-07      2.0745e-05      0.00054091       0.0054839        0.021876        0.034654        0.021876       0.0054839      0.00054091      2.0745e-05      3.0748e-07      3.0748e-06      0.00020745       0.0054091        0.054839         0.21876         0.34654         0.21876        0.054839       0.0054091      0.00020745      3.0748e-06 
      2.62e-10      3.838e-08     2.1488e-06     4.6338e-05     0.00038949      0.0012909      0.0017011      0.0008932     0.00018597        1.52e-05      4.8778e-07      5.2399e-09       7.676e-07      4.2976e-05      0.00092676       0.0077897        0.025818        0.034022        0.017864       0.0037193        0.000304      9.7556e-06      5.2399e-08       7.676e-06      0.00042976       0.0092676        0.077897         0.25818         0.34022         0.17864        0.037193         0.00304      9.7556e-05 
    2.3997e-12     7.6605e-10     9.2704e-08     4.2848e-06     7.6456e-05     0.00053304      0.0014684      0.0016098     0.00070291       0.0001215      8.4426e-06      4.7995e-11      1.5321e-08      1.8541e-06      8.5696e-05       0.0015291        0.010661        0.029367        0.032196        0.014058       0.0024299      0.00016885      4.7995e-10      1.5321e-07      1.8541e-05      0.00085696        0.015291         0.10661         0.29367         0.32196         0.14058        0.024299       0.0016885 
    1.1765e-14     8.2123e-12       2.16e-09     2.1546e-07      8.225e-06      0.0001215     0.00070291      0.0016098      0.0014684      0.00053304      8.0834e-05      2.3531e-13      1.6425e-10      4.3201e-08      4.3092e-06       0.0001645       0.0024299        0.014058        0.032196        0.029367        0.010661       0.0016167      2.3531e-12      1.6425e-09      4.3201e-07      4.3092e-05        0.001645        0.024299         0.14058         0.32196         0.29367         0.10661        0.016167 
    3.0784e-17     4.7123e-14     2.7059e-11     5.8589e-09      4.819e-07       1.52e-05     0.00018597      0.0008932      0.0017011       0.0012909      0.00043801      6.1568e-16      9.4246e-13      5.4117e-10      1.1718e-07      9.6379e-06        0.000304       0.0037193        0.017864        0.034022        0.025818       0.0087602      6.1568e-15      9.4246e-12      5.4117e-09      1.1718e-06      9.6379e-05         0.00304        0.037193         0.17864         0.34022         0.25818        0.087602 

    mt_z_trans1    mt_z_trans2    mt_z_trans3    mt_z_trans4    mt_z_trans5    mt_z_trans6    mt_z_trans7    mt_z_trans8    mt_z_trans9    mt_z_trans10    mt_z_trans11    mt_z_trans12    mt_z_trans13    mt_z_trans14    mt_z_trans15    mt_z_trans16    mt_z_trans17    mt_z_trans18    mt_z_trans19    mt_z_trans20    mt_z_trans21    mt_z_trans22    mt_z_trans23    mt_z_trans24    mt_z_trans25    mt_z_trans26    mt_z_trans27    mt_z_trans28    mt_z_trans29    mt_z_trans30    mt_z_trans31    mt_z_trans32    mt_z_trans33
    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ___________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________    ____________

    0.00043801      0.0012909      0.0017011      0.0008932     0.00018597       1.52e-05      4.819e-07     5.8589e-09     2.7059e-11      4.7123e-14      3.0644e-17       0.0087602        0.025818        0.034022        0.017864       0.0037193        0.000304      9.6379e-06      1.1718e-07      5.4117e-10      9.4246e-13      6.1288e-16        0.087602         0.25818         0.34022         0.17864        0.037193         0.00304      9.6379e-05      1.1718e-06      5.4117e-09      9.4246e-12      6.1288e-15 
    8.0834e-05     0.00053304      0.0014684      0.0016098     0.00070291      0.0001215      8.225e-06     2.1546e-07       2.16e-09      8.2123e-12      1.1765e-14       0.0016167        0.010661        0.029367        0.032196        0.014058       0.0024299       0.0001645      4.3092e-06      4.3201e-08      1.6425e-10      2.3531e-13        0.016167         0.10661         0.29367         0.32196         0.14058        0.024299        0.001645      4.3092e-05      4.3201e-07      1.6425e-09      2.3531e-12 
    8.4426e-06      0.0001215     0.00070291      0.0016098      0.0014684     0.00053304     7.6456e-05     4.2848e-06     9.2704e-08      7.6605e-10      2.3997e-12      0.00016885       0.0024299        0.014058        0.032196        0.029367        0.010661       0.0015291      8.5696e-05      1.8541e-06      1.5321e-08      4.7995e-11       0.0016885        0.024299         0.14058         0.32196         0.29367         0.10661        0.015291      0.00085696      1.8541e-05      1.5321e-07      4.7995e-10 
    4.8778e-07       1.52e-05     0.00018597      0.0008932      0.0017011      0.0012909     0.00038949     4.6338e-05     2.1488e-06       3.838e-08        2.62e-10      9.7556e-06        0.000304       0.0037193        0.017864        0.034022        0.025818       0.0077897      0.00092676      4.2976e-05       7.676e-07      5.2399e-09      9.7556e-05         0.00304        0.037193         0.17864         0.34022         0.25818        0.077897       0.0092676      0.00042976       7.676e-06      5.2399e-08 
    1.5374e-08     1.0372e-06     2.7045e-05      0.0002742      0.0010938      0.0017327      0.0010938      0.0002742     2.7045e-05      1.0372e-06      1.5374e-08      3.0748e-07      2.0745e-05      0.00054091       0.0054839        0.021876        0.034654        0.021876       0.0054839      0.00054091      2.0745e-05      3.0748e-07      3.0748e-06      0.00020745       0.0054091        0.054839         0.21876         0.34654         0.21876        0.054839       0.0054091      0.00020745      3.0748e-06 
      2.62e-10      3.838e-08     2.1488e-06     4.6338e-05     0.00038949      0.0012909      0.0017011      0.0008932     0.00018597        1.52e-05      4.8778e-07      5.2399e-09       7.676e-07      4.2976e-05      0.00092676       0.0077897        0.025818        0.034022        0.017864       0.0037193        0.000304      9.7556e-06      5.2399e-08       7.676e-06      0.00042976       0.0092676        0.077897         0.25818         0.34022         0.17864        0.037193         0.00304      9.7556e-05 
    2.3997e-12     7.6605e-10     9.2704e-08     4.2848e-06     7.6456e-05     0.00053304      0.0014684      0.0016098     0.00070291       0.0001215      8.4426e-06      4.7995e-11      1.5321e-08      1.8541e-06      8.5696e-05       0.0015291        0.010661        0.029367        0.032196        0.014058       0.0024299      0.00016885      4.7995e-10      1.5321e-07      1.8541e-05      0.00085696        0.015291         0.10661         0.29367         0.32196         0.14058        0.024299       0.0016885 
    1.1765e-14     8.2123e-12       2.16e-09     2.1546e-07      8.225e-06      0.0001215     0.00070291      0.0016098      0.0014684      0.00053304      8.0834e-05      2.3531e-13      1.6425e-10      4.3201e-08      4.3092e-06       0.0001645       0.0024299        0.014058        0.032196        0.029367        0.010661       0.0016167      2.3531e-12      1.6425e-09      4.3201e-07      4.3092e-05        0.001645        0.024299         0.14058         0.32196         0.29367         0.10661        0.016167 
    3.0784e-17     4.7123e-14     2.7059e-11     5.8589e-09      4.819e-07       1.52e-05     0.00018597      0.0008932      0.0017011       0.0012909      0.00043801      6.1568e-16      9.4246e-13      5.4117e-10      1.1718e-07      9.6379e-06        0.000304       0.0037193        0.017864        0.034022        0.025818       0.0087602      6.1568e-15      9.4246e-12      5.4117e-09      1.1718e-06      9.6379e-05         0.00304        0.037193         0.17864         0.34022         0.25818        0.087602 
    4.2894e-20     1.4434e-16     1.8158e-13     8.5744e-11     1.5288e-08     1.0372e-06     2.7045e-05      0.0002742      0.0010938       0.0017327       0.0013961      8.5788e-19      2.8868e-15      3.6315e-12      1.7149e-09      3.0576e-07      2.0745e-05      0.00054091       0.0054839        0.021876        0.034654        0.027922      8.5788e-18      2.8868e-14      3.6315e-11      1.7149e-08      3.0576e-06      0.00020745       0.0054091        0.054839         0.21876         0.34654         0.27922 

Display

if (bl_display_funcgrids)
    fft_container_map_display(armt_map, it_display_summmat_rowmax, it_display_summmat_colmax);
    fft_container_map_display(func_map, it_display_summmat_rowmax, it_display_summmat_colmax);
end
----------------------------------------
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Begin: Show all key and value pairs from container
CONTAINER NAME: ARMT_MAP
----------------------------------------
  Map with properties:

        Count: 31
      KeyType: char
    ValueType: any

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
pos = 1 ; key = ar_a_meshk ;rown= 1215 ,coln= 1
ar_a_meshk :mu= 8.5778 ,sd= 12.4414 ,min= -4.67 ,max= 50
                     zi_1_c1
                     _______

    zi_1_R1            -4.67
    zi_2_R2            -4.67
    zi_3_R3            -4.67
    zi_608_R608       8.4508
    zi_1213_r1213     -2.185
    zi_1214_r1214    -3.4275
    zi_1215_r1215      -4.67

pos = 2 ; key = ar_ak_perc ;rown= 1 ,coln= 45
ar_ak_perc :mu= 0.5 ,sd= 0.2985 ,min= 0 ,max= 1
               zi_1_C1    zi_2_C2     zi_3_C3     zi_23_c23    zi_43_c43    zi_44_c44    zi_45_c45
               _______    ________    ________    _________    _________    _________    _________

    zi_1_r1       0       0.022727    0.045455       0.5        0.95455      0.97727         1    

pos = 3 ; key = ar_aplusk_mesh ;rown= 1215 ,coln= 1
ar_aplusk_mesh :mu= 21.8256 ,sd= 16.6607 ,min= -4.67 ,max= 50
                     zi_1_c1
                     _______

    zi_1_R1           -4.67 
    zi_2_R2           -4.67 
    zi_3_R3           -4.67 
    zi_608_R608      21.572 
    zi_1213_r1213        50 
    zi_1214_r1214        50 
    zi_1215_r1215        50 

pos = 4 ; key = ar_interp_c_grid ;rown= 1 ,coln= 619078
ar_interp_c_grid :mu= 30.9739 ,sd= 17.8713 ,min= 0.02 ,max= 61.9279
               zi_1_C1    zi_2_C2    zi_3_C3    zi_309539_c309539    zi_619076_c619076    zi_619077_c619077    zi_619078_c619078
               _______    _______    _______    _________________    _________________    _________________    _________________

    zi_1_r1     0.02      0.0201     0.0202          30.974               61.928               61.928               61.928      

pos = 5 ; key = ar_interp_coh_grid ;rown= 1 ,coln= 30
ar_interp_coh_grid :mu= 25.4175 ,sd= 19.1171 ,min= -4.67 ,max= 57.2579
               zi_1_C1    zi_2_C2    zi_3_C3     zi_15_c15    zi_28_c28    zi_29_c29    zi_30_c30
               _______    _______    ________    _________    _________    _________    _________

    zi_1_r1     -4.67     -2.4583    -0.24656     24.082       52.834       55.046       57.258  

pos = 6 ; key = ar_k_mesha ;rown= 1215 ,coln= 1
ar_k_mesha :mu= 13.2478 ,sd= 12.4414 ,min= 0 ,max= 54.67
                     zi_1_c1
                     _______

    zi_1_R1               0 
    zi_2_R2               0 
    zi_3_R3               0 
    zi_608_R608      13.121 
    zi_1213_r1213    52.185 
    zi_1214_r1214    53.427 
    zi_1215_r1215     54.67 

pos = 7 ; key = ar_w_level ;rown= 1 ,coln= 27
ar_w_level :mu= 21.8256 ,sd= 16.9711 ,min= -4.67 ,max= 50
               zi_1_C1    zi_2_C2    zi_3_C3     zi_14_c14    zi_25_c25    zi_26_c26    zi_27_c27
               _______    _______    ________    _________    _________    _________    _________

    zi_1_r1     -4.67     -2.4832    -0.29638     21.572       45.626       47.813         50    

pos = 8 ; key = ar_w_perc ;rown= 1 ,coln= 25
ar_w_perc :mu= 0.5 ,sd= 0.30666 ,min= 0 ,max= 1
               zi_1_C1    zi_2_C2     zi_3_C3     zi_13_c13    zi_23_c23    zi_24_c24    zi_25_c25
               _______    ________    ________    _________    _________    _________    _________

    zi_1_r1       0       0.041667    0.083333       0.5        0.91667      0.95833         1    

pos = 9 ; key = ar_z_r_borr ;rown= 1 ,coln= 3
ar_z_r_borr :mu= 0.06 ,sd= 0.035 ,min= 0.025 ,max= 0.095
               zi_1_c1    zi_2_c2    zi_3_c3
               _______    _______    _______

    zi_1_r1     0.025      0.06       0.095 

pos = 10 ; key = ar_z_r_borr_mesh_wage_r1w2 ;rown= 1 ,coln= 33
ar_z_r_borr_mesh_wage_r1w2 :mu= 0.06 ,sd= 0.02902 ,min= 0.025 ,max= 0.095
               zi_1_C1    zi_2_C2    zi_3_C3    zi_17_c17    zi_31_c31    zi_32_c32    zi_33_c33
               _______    _______    _______    _________    _________    _________    _________

    zi_1_r1     0.025      0.06       0.095       0.06         0.025        0.06         0.095  

pos = 11 ; key = ar_z_r_borr_mesh_wage_w1r2 ;rown= 1 ,coln= 33
ar_z_r_borr_mesh_wage_w1r2 :mu= 0.06 ,sd= 0.02902 ,min= 0.025 ,max= 0.095
               zi_1_C1    zi_2_C2    zi_3_C3    zi_17_c17    zi_31_c31    zi_32_c32    zi_33_c33
               _______    _______    _______    _________    _________    _________    _________

    zi_1_r1     0.025      0.025      0.025       0.06         0.095        0.095        0.095  

pos = 12 ; key = ar_z_r_borr_prob ;rown= 1 ,coln= 3
ar_z_r_borr_prob :mu= 0.33333 ,sd= 0.49692 ,min= 0.0045249 ,max= 0.90498
                zi_1_c1     zi_2_c2     zi_3_c3
               _________    ________    _______

    zi_1_r1    0.0045249    0.090498    0.90498

pos = 13 ; key = ar_z_wage ;rown= 1 ,coln= 11
ar_z_wage :mu= 1.1422 ,sd= 0.72828 ,min= 0.34664 ,max= 2.5613
               zi_1_C1    zi_2_C2    zi_3_C3    zi_6_C6    zi_9_C9    zi_10_c10    zi_11_c11
               _______    _______    _______    _______    _______    _________    _________

    zi_1_r1    0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  

pos = 14 ; key = ar_z_wage_mesh_r_borr_r1w2 ;rown= 1 ,coln= 33
ar_z_wage_mesh_r_borr_r1w2 :mu= 1.1422 ,sd= 0.70515 ,min= 0.34664 ,max= 2.5613
               zi_1_C1    zi_2_C2    zi_3_C3    zi_17_c17    zi_31_c31    zi_32_c32    zi_33_c33
               _______    _______    _______    _________    _________    _________    _________

    zi_1_r1    0.34664    0.34664    0.34664     0.94226      2.5613       2.5613       2.5613  

pos = 15 ; key = ar_z_wage_mesh_r_borr_w1r2 ;rown= 1 ,coln= 33
ar_z_wage_mesh_r_borr_w1r2 :mu= 1.1422 ,sd= 0.70515 ,min= 0.34664 ,max= 2.5613
               zi_1_C1    zi_2_C2    zi_3_C3    zi_17_c17    zi_31_c31    zi_32_c32    zi_33_c33
               _______    _______    _______    _________    _________    _________    _________

    zi_1_r1    0.34664    0.42338    0.51712     0.94226      1.7169        2.097       2.5613  

pos = 16 ; key = ar_z_wage_prob ;rown= 1 ,coln= 11
ar_z_wage_prob :mu= 0.090909 ,sd= 0.084822 ,min= 0.0039324 ,max= 0.23011
                zi_1_C1     zi_2_C2     zi_3_C3     zi_6_C6    zi_9_C9     zi_10_c10    zi_11_c11
               _________    ________    ________    _______    ________    _________    _________

    zi_1_r1    0.0039324    0.016056    0.051615    0.23011    0.051615    0.016056     0.0039324

pos = 17 ; key = cl_mt_coh_wkb_mesh_z_r_borr ;rown= 1215 ,coln= 33
cl_mt_coh_wkb_mesh_z_r_borr :mu= 23.9244 ,sd= 17.0645 ,min= -4.3431 ,max= 57.2579
                     zi_1_C1    zi_2_C2    zi_3_C3    zi_17_c17    zi_31_c31    zi_32_c32    zi_33_c33
                     _______    _______    _______    _________    _________    _________    _________

    zi_1_R1          -4.3431    -4.3431    -4.3431     -4.3431      -4.3431      -4.3431      -4.3431 
    zi_2_R2          -4.3431    -4.3431    -4.3431     -4.3431      -4.3431      -4.3431      -4.3431 
    zi_3_R3          -4.3431    -4.3431    -4.3431     -4.3431      -4.3431      -4.3431      -4.3431 
    zi_608_R608       22.053     22.246     22.483      23.557       25.514       26.474       27.647 
    zi_1213_r1213     47.654     47.972     48.362      50.127       53.344       54.922        56.85 
    zi_1214_r1214     47.535     47.857     48.249       50.03       53.274       54.866        56.81 
    zi_1215_r1215     47.417     47.741     48.137      49.932       53.203       54.808       56.769 

pos = 18 ; key = it_ameshk_n ; val = 1215
pos = 19 ; key = mt_coh_wkb ;rown= 3645 ,coln= 11
mt_coh_wkb :mu= 23.8912 ,sd= 17.0935 ,min= -4.67 ,max= 57.2579
                     zi_1_C1    zi_2_C2    zi_3_C3    zi_6_C6    zi_9_C9    zi_10_c10    zi_11_c11
                     _______    _______    _______    _______    _______    _________    _________

    zi_1_R1          -4.3431    -4.3431    -4.3431    -4.3431    -4.3431     -4.3431      -4.3431 
    zi_2_R2          -4.3431    -4.3431    -4.3431    -4.3431    -4.3431     -4.3431      -4.3431 
    zi_3_R3          -4.3431    -4.3431    -4.3431    -4.3431    -4.3431     -4.3431      -4.3431 
    zi_1823_r1823     22.053     22.246     22.483     23.557     25.514      26.474       27.647 
    zi_3643_r3643     47.501     47.819     48.209     49.974     53.191      54.769       56.697 
    zi_3644_r3644     47.296     47.617     48.009      49.79     53.034      54.626        56.57 
    zi_3645_r3645      47.09     47.414      47.81     49.605     52.876      54.482       56.442 

pos = 20 ; key = mt_coh_wkb_mesh_z_r_borr ;rown= 3645 ,coln= 33
mt_coh_wkb_mesh_z_r_borr :mu= 23.8912 ,sd= 17.0933 ,min= -4.67 ,max= 57.2579
                     zi_1_C1    zi_2_C2    zi_3_C3    zi_17_c17    zi_31_c31    zi_32_c32    zi_33_c33
                     _______    _______    _______    _________    _________    _________    _________

    zi_1_R1          -4.3431    -4.3431    -4.3431     -4.3431      -4.3431      -4.3431      -4.3431 
    zi_2_R2          -4.3431    -4.3431    -4.3431     -4.3431      -4.3431      -4.3431      -4.3431 
    zi_3_R3          -4.3431    -4.3431    -4.3431     -4.3431      -4.3431      -4.3431      -4.3431 
    zi_1823_r1823     22.053     22.246     22.483      23.557       25.514       26.474       27.647 
    zi_3643_r3643     47.501     47.819     48.209      49.974       53.191       54.769       56.697 
    zi_3644_r3644     47.296     47.617     48.009       49.79       53.034       54.626        56.57 
    zi_3645_r3645      47.09     47.414      47.81      49.605       52.876       54.482       56.442 

pos = 21 ; key = mt_interp_coh_grid_mesh_w_perc ;rown= 25 ,coln= 30
mt_interp_coh_grid_mesh_w_perc :mu= 25.4175 ,sd= 18.8083 ,min= -4.67 ,max= 57.2579
                 zi_1_C1    zi_2_C2    zi_3_C3     zi_15_c15    zi_28_c28    zi_29_c29    zi_30_c30
                 _______    _______    ________    _________    _________    _________    _________

    zi_1_R1       -4.67     -2.4583    -0.24656     24.082       52.834       55.046       57.258  
    zi_2_R2       -4.67     -2.4583    -0.24656     24.082       52.834       55.046       57.258  
    zi_3_R3       -4.67     -2.4583    -0.24656     24.082       52.834       55.046       57.258  
    zi_13_r13     -4.67     -2.4583    -0.24656     24.082       52.834       55.046       57.258  
    zi_23_r23     -4.67     -2.4583    -0.24656     24.082       52.834       55.046       57.258  
    zi_24_r24     -4.67     -2.4583    -0.24656     24.082       52.834       55.046       57.258  
    zi_25_r25     -4.67     -2.4583    -0.24656     24.082       52.834       55.046       57.258  

pos = 22 ; key = mt_interp_coh_grid_mesh_z ;rown= 30 ,coln= 33
mt_interp_coh_grid_mesh_z :mu= 25.4175 ,sd= 18.8052 ,min= -4.67 ,max= 57.2579
                 zi_1_C1     zi_2_C2     zi_3_C3     zi_17_c17    zi_31_c31    zi_32_c32    zi_33_c33
                 ________    ________    ________    _________    _________    _________    _________

    zi_1_R1         -4.67       -4.67       -4.67       -4.67        -4.67        -4.67        -4.67 
    zi_2_R2       -2.4583     -2.4583     -2.4583     -2.4583      -2.4583      -2.4583      -2.4583 
    zi_3_R3      -0.24656    -0.24656    -0.24656    -0.24656     -0.24656     -0.24656     -0.24656 
    zi_15_r15      24.082      24.082      24.082      24.082       24.082       24.082       24.082 
    zi_28_r28      52.834      52.834      52.834      52.834       52.834       52.834       52.834 
    zi_29_r29      55.046      55.046      55.046      55.046       55.046       55.046       55.046 
    zi_30_r30      57.258      57.258      57.258      57.258       57.258       57.258       57.258 

pos = 23 ; key = mt_interp_coh_grid_mesh_z_wage ;rown= 30 ,coln= 11
mt_interp_coh_grid_mesh_z_wage :mu= 25.4175 ,sd= 18.8243 ,min= -4.67 ,max= 57.2579
                 zi_1_C1     zi_2_C2     zi_3_C3     zi_6_C6     zi_9_C9     zi_10_c10    zi_11_c11
                 ________    ________    ________    ________    ________    _________    _________

    zi_1_R1         -4.67       -4.67       -4.67       -4.67       -4.67       -4.67        -4.67 
    zi_2_R2       -2.4583     -2.4583     -2.4583     -2.4583     -2.4583     -2.4583      -2.4583 
    zi_3_R3      -0.24656    -0.24656    -0.24656    -0.24656    -0.24656    -0.24656     -0.24656 
    zi_15_r15      24.082      24.082      24.082      24.082      24.082      24.082       24.082 
    zi_28_r28      52.834      52.834      52.834      52.834      52.834      52.834       52.834 
    zi_29_r29      55.046      55.046      55.046      55.046      55.046      55.046       55.046 
    zi_30_r30      57.258      57.258      57.258      57.258      57.258      57.258       57.258 

pos = 24 ; key = mt_k ;rown= 45 ,coln= 27
mt_k :mu= 13.2478 ,sd= 12.4414 ,min= 0 ,max= 54.67
                 zi_1_C1    zi_2_C2    zi_3_C3    zi_14_c14    zi_25_c25    zi_26_c26    zi_27_c27
                 _______    _______    _______    _________    _________    _________    _________

    zi_1_R1         0            0          0           0            0            0            0  
    zi_2_R2         0       0.0497     0.0994      0.5964       1.1431       1.1928       1.2425  
    zi_3_R3         0       0.0994     0.1988      1.1928       2.2862       2.3856        2.485  
    zi_23_r23       0       1.0934     2.1868      13.121       25.148       26.242       27.335  
    zi_43_r43       0       2.0874     4.1748      25.049        48.01       50.098       52.185  
    zi_44_r44       0       2.1371     4.2742      25.645       49.153        51.29       53.427  
    zi_45_r45       0       2.1868     4.3736      26.242       50.296       52.483        54.67  

pos = 25 ; key = mt_w_perc_mesh_interp_coh_grid ;rown= 25 ,coln= 30
mt_w_perc_mesh_interp_coh_grid :mu= 10.3738 ,sd= 14.22 ,min= -4.67 ,max= 57.2579
                 zi_1_C1    zi_2_C2    zi_3_C3     zi_15_c15    zi_28_c28    zi_29_c29    zi_30_c30
                 _______    _______    ________    _________    _________    _________    _________

    zi_1_R1       -4.67       -4.67       -4.67      -4.67         -4.67        -4.67        -4.67 
    zi_2_R2       -4.67     -4.5778     -4.4857     -3.472        -2.274      -2.1818      -2.0897 
    zi_3_R3       -4.67     -4.4857     -4.3014     -2.274       0.12206      0.30637      0.49068 
    zi_13_r13     -4.67     -3.5641     -2.4583     9.7061        24.082       25.188       26.294 
    zi_23_r23     -4.67     -2.6426    -0.61518     21.686        48.042        50.07       52.097 
    zi_24_r24     -4.67     -2.5504    -0.43087     22.884        50.438       52.558       54.678 
    zi_25_r25     -4.67     -2.4583    -0.24656     24.082        52.834       55.046       57.258 

pos = 26 ; key = mt_z_mesh_coh_wkb ;rown= 3645 ,coln= 33
mt_z_mesh_coh_wkb :mu= 17 ,sd= 9.5219 ,min= 1 ,max= 33
                     zi_1_C1    zi_2_C2    zi_3_C3    zi_17_c17    zi_31_c31    zi_32_c32    zi_33_c33
                     _______    _______    _______    _________    _________    _________    _________

    zi_1_R1             1          2          3          17           31           32           33    
    zi_2_R2             1          2          3          17           31           32           33    
    zi_3_R3             1          2          3          17           31           32           33    
    zi_1823_r1823       1          2          3          17           31           32           33    
    zi_3643_r3643       1          2          3          17           31           32           33    
    zi_3644_r3644       1          2          3          17           31           32           33    
    zi_3645_r3645       1          2          3          17           31           32           33    

pos = 27 ; key = mt_z_mesh_coh_wkb_seg ;rown= 1215 ,coln= 33
mt_z_mesh_coh_wkb_seg :mu= 17 ,sd= 9.522 ,min= 1 ,max= 33
                     zi_1_C1    zi_2_C2    zi_3_C3    zi_17_c17    zi_31_c31    zi_32_c32    zi_33_c33
                     _______    _______    _______    _________    _________    _________    _________

    zi_1_R1             1          2          3          17           31           32           33    
    zi_2_R2             1          2          3          17           31           32           33    
    zi_3_R3             1          2          3          17           31           32           33    
    zi_608_R608         1          2          3          17           31           32           33    
    zi_1213_r1213       1          2          3          17           31           32           33    
    zi_1214_r1214       1          2          3          17           31           32           33    
    zi_1215_r1215       1          2          3          17           31           32           33    

pos = 28 ; key = mt_z_mesh_interp_coh_grid ;rown= 30 ,coln= 33
mt_z_mesh_interp_coh_grid :mu= 17 ,sd= 9.5267 ,min= 1 ,max= 33
                 zi_1_C1    zi_2_C2    zi_3_C3    zi_17_c17    zi_31_c31    zi_32_c32    zi_33_c33
                 _______    _______    _______    _________    _________    _________    _________

    zi_1_R1         1          2          3          17           31           32           33    
    zi_2_R2         1          2          3          17           31           32           33    
    zi_3_R3         1          2          3          17           31           32           33    
    zi_15_r15       1          2          3          17           31           32           33    
    zi_28_r28       1          2          3          17           31           32           33    
    zi_29_r29       1          2          3          17           31           32           33    
    zi_30_r30       1          2          3          17           31           32           33    

pos = 29 ; key = mt_z_trans ;rown= 33 ,coln= 33
mt_z_trans :mu= 0.030303 ,sd= 0.077699 ,min= 0 ,max= 0.34654
                  zi_1_C1       zi_2_C2       zi_3_C3      zi_17_c17     zi_31_c31     zi_32_c32     zi_33_c33 
                 __________    __________    __________    __________    __________    __________    __________

    zi_1_R1       0.0013961     0.0017327     0.0010938    2.0745e-05    3.6315e-11    2.8836e-14             0
    zi_2_R2      0.00043801     0.0012909     0.0017011      0.000304    5.4117e-09    9.4246e-12    6.1288e-15
    zi_3_R3      8.0834e-05    0.00053304     0.0014684     0.0024299    4.3201e-07    1.6425e-09    2.3531e-12
    zi_17_r17    1.5374e-08    1.0372e-06    2.7045e-05      0.034654     0.0054091    0.00020745    3.0748e-06
    zi_31_r31    1.1765e-14    8.2123e-12      2.16e-09     0.0024299       0.29367       0.10661      0.016167
    zi_32_r32    3.0784e-17    4.7123e-14    2.7059e-11      0.000304       0.34022       0.25818      0.087602
    zi_33_r33    4.2894e-20    1.4434e-16    1.8158e-13    2.0745e-05       0.21876       0.34654       0.27922

pos = 30 ; key = mt_z_wage_mesh_coh_wkb ;rown= 3645 ,coln= 11
mt_z_wage_mesh_coh_wkb :mu= 1.1422 ,sd= 0.69439 ,min= 0.34664 ,max= 2.5613
                     zi_1_C1    zi_2_C2    zi_3_C3    zi_6_C6    zi_9_C9    zi_10_c10    zi_11_c11
                     _______    _______    _______    _______    _______    _________    _________

    zi_1_R1          0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_2_R2          0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_3_R3          0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_1823_r1823    0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_3643_r3643    0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_3644_r3644    0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_3645_r3645    0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  

pos = 31 ; key = mt_z_wage_mesh_interp_coh_grid ;rown= 30 ,coln= 11
mt_z_wage_mesh_interp_coh_grid :mu= 1.1422 ,sd= 0.69544 ,min= 0.34664 ,max= 2.5613
                 zi_1_C1    zi_2_C2    zi_3_C3    zi_6_C6    zi_9_C9    zi_10_c10    zi_11_c11
                 _______    _______    _______    _______    _______    _________    _________

    zi_1_R1      0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_2_R2      0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_3_R3      0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_15_r15    0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_28_r28    0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_29_r29    0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  
    zi_30_r30    0.34664    0.42338    0.51712    0.94226    1.7169       2.097       2.5613  

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Matrix in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                                      i     idx    rowN       colN         mean        std          min         max  
                                      __    ___    ____    __________    ________    ________    _________    _______

    ar_a_meshk                         1     1     1215             1      8.5778      12.441        -4.67         50
    ar_ak_perc                         2     2        1            45         0.5      0.2985            0          1
    ar_aplusk_mesh                     3     3     1215             1      21.826      16.661        -4.67         50
    ar_interp_c_grid                   4     4        1    6.1908e+05      30.974      17.871         0.02     61.928
    ar_interp_coh_grid                 5     5        1            30      25.418      19.117        -4.67     57.258
    ar_k_mesha                         6     6     1215             1      13.248      12.441            0      54.67
    ar_w_level                         7     7        1            27      21.826      16.971        -4.67         50
    ar_w_perc                          8     8        1            25         0.5     0.30666            0          1
    ar_z_r_borr                        9     9        1             3        0.06       0.035        0.025      0.095
    ar_z_r_borr_mesh_wage_r1w2        10    10        1            33        0.06     0.02902        0.025      0.095
    ar_z_r_borr_mesh_wage_w1r2        11    11        1            33        0.06     0.02902        0.025      0.095
    ar_z_r_borr_prob                  12    12        1             3     0.33333     0.49692    0.0045249    0.90498
    ar_z_wage                         13    13        1            11      1.1422     0.72828      0.34664     2.5613
    ar_z_wage_mesh_r_borr_r1w2        14    14        1            33      1.1422     0.70515      0.34664     2.5613
    ar_z_wage_mesh_r_borr_w1r2        15    15        1            33      1.1422     0.70515      0.34664     2.5613
    ar_z_wage_prob                    16    16        1            11    0.090909    0.084822    0.0039324    0.23011
    cl_mt_coh_wkb_mesh_z_r_borr       17    17     1215            33      23.924      17.064      -4.3431     57.258
    mt_coh_wkb                        18    19     3645            11      23.891      17.093        -4.67     57.258
    mt_coh_wkb_mesh_z_r_borr          19    20     3645            33      23.891      17.093        -4.67     57.258
    mt_interp_coh_grid_mesh_w_perc    20    21       25            30      25.418      18.808        -4.67     57.258
    mt_interp_coh_grid_mesh_z         21    22       30            33      25.418      18.805        -4.67     57.258
    mt_interp_coh_grid_mesh_z_wage    22    23       30            11      25.418      18.824        -4.67     57.258
    mt_k                              23    24       45            27      13.248      12.441            0      54.67
    mt_w_perc_mesh_interp_coh_grid    24    25       25            30      10.374       14.22        -4.67     57.258
    mt_z_mesh_coh_wkb                 25    26     3645            33          17      9.5219            1         33
    mt_z_mesh_coh_wkb_seg             26    27     1215            33          17       9.522            1         33
    mt_z_mesh_interp_coh_grid         27    28       30            33          17      9.5267            1         33
    mt_z_trans                        28    29       33            33    0.030303    0.077699            0    0.34654
    mt_z_wage_mesh_coh_wkb            29    30     3645            11      1.1422     0.69439      0.34664     2.5613
    mt_z_wage_mesh_interp_coh_grid    30    31       30            11      1.1422     0.69544      0.34664     2.5613

----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Scalars in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                   i    idx    value
                   _    ___    _____

    it_ameshk_n    1    18     1215 

----------------------------------------
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Begin: Show all key and value pairs from container
CONTAINER NAME: FUNC_MAP
----------------------------------------
  Map with properties:

        Count: 8
      KeyType: char
    ValueType: any

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
----------------------------------------
----------------------------------------
pos = 1 ; key = f_coh ; val = @(fl_r_borr,z,b,k)(f_prod(z,k)+k*(1-fl_delta)+fl_w+b.*(1+fl_r_save).*(b>0)+b.*(1+fl_r_borr).*(b<=0))
pos = 2 ; key = f_cons ; val = @(coh,bprime,kprime)(coh-kprime-bprime)
pos = 3 ; key = f_inc ; val = @(fl_r_borr,z,b,k)(f_prod(z,k)-(fl_delta)*k+fl_w+b.*(fl_r_save).*(b>0)+b.*(fl_r_borr).*(b<=0))
pos = 4 ; key = f_prod ; val = @(z,k)((fl_Amean.*(z)).*(k.^(fl_alpha)))
pos = 5 ; key = f_util_crra ; val = @(c)(((c).^(1-fl_crra)-1)./(1-fl_crra))
pos = 6 ; key = f_util_log ; val = @(c)log(c)
pos = 7 ; key = f_util_standin ; val = @(fl_r_borr,z,b,k)f_util_log((f_coh(fl_r_borr,z,b,k)-fl_b_bd).*((f_coh(fl_r_borr,z,b,k)-fl_b_bd)>fl_c_min)+fl_c_min.*((f_coh(fl_r_borr,z,b,k)-fl_b_bd)<=fl_c_min))
pos = 8 ; key = f_util_standin_coh ; val = @(coh,fl_r_borr)f_util_log((coh-fl_b_bd).*((coh>0)&(((coh-fl_b_bd)./(1))>fl_c_min))+((coh-fl_b_bd)./(1)).*((coh<=0)&(((coh-fl_b_bd)./(1))>fl_c_min))+(fl_c_min./(1+fl_r_borr)).*((((coh-fl_b_bd)./(1))<=fl_c_min)))
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Scalars in Container and Sizes and Basic Statistics
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                          i    idx    xFunction
                          _    ___    _________

    f_coh                 1     1         1    
    f_cons                2     2         2    
    f_inc                 3     3         3    
    f_prod                4     4         4    
    f_util_crra           5     5         5    
    f_util_log            6     6         6    
    f_util_standin        7     7         7    
    f_util_standin_coh    8     8         8    

end
ans = 

  Map with properties:

        Count: 31
      KeyType: char
    ValueType: any