Set Model Parameters (Risky + Safe Asset)

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Contents

function [param_map, support_map] = ffs_akz_set_default_param(varargin)

FFS_AKZ_SET_DEFAULT_PARAM setting model default parameters

two groups of default parameters stored in container maps. Explicitly solving for both a and k grids exponentially increase problem size, and we can not have state and choice grids that are as tight as for the az problem. Note that the defaults set it_w_n to have a far more limited number of points. For each w, we allow for combinations of a and k choices. Before, each aggregate savings choice only had one a associated with it.

The biggest change from ffs_az_set_default_param is that now we have two asset choices. Previous we had the a grid for the cash-on-hand and z (az) model.

Now a is w. There was only one asset before, so a was total savings. Now w is total savings w = a' + k'. Define choice grid in terms of the total savings, rather than a and k grids separately. If we define a and k with min and max separately, we will have a choice combo max(a) + max(k), this corresponds to one very high level of aggregate savings, but we are implicitly only allowing for dividing a and k evenly when we choose this. Implicitly, the higher the aggregate savings, the more limited the a and k combinations becomes when we define a and k grids separately. Geometrically, With aprime as the x-axis and kprime as the y-axis of choices, we need to define choices in terms of diagnoals (triangles) rather than vertical and horizontal lines (rectangles). See this graphically at the end of this page: ffs_akz_get_funcgrid which shows the triangular choice grids.

With our triangular shape, with w_n total saving grid points, we will have : w_n*(w_n-1)/2 + w_n total grid of a and k jointly. Specifically, with the benchmark grid of w_n = 45 points, we have (45-1)*45/2 + 45 = 1035 total a and k joint grid points.

@param it_subset integer default parameter control subsetting. it_subset = 1 is basic invoke quick test. it_subset = 2 is main invoke. it_subset = 3 is profiling invoke. it_subset = 4 is matlab publish.

@param bl_display_defparam boolean local printing

@return param_map container parameters needed for solving the model

@return support_map container programming control parameters like to graph to print etc

@example

it_param_set = 1; [param_map, support_map] =
ffs_akz_set_default_param(it_param_set);

Default

it_subset = 0;
if (isempty(varargin))
    bl_display_defparam = true;
else
    bl_display_defparam = false;
end
default_params = {it_subset bl_display_defparam};
[default_params{1:length(varargin)}] = varargin{:};
[it_subset, bl_display_defparam] = default_params{:};

Setting param_map container

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

% model name
param_map('st_model') = 'akz_wkz_iwkz';

% Preferences
param_map('fl_crra') = 1.5;
param_map('fl_beta') = 0.94;

% Production Function Productivity Shock Parameters
param_map('it_z_n') = 15;
param_map('fl_z_mu') = 0;
param_map('fl_z_rho') = 0.8;
param_map('fl_z_sig') = 0.2;

% CD Production Function Parameters
param_map('fl_Amean') = 1;
param_map('fl_alpha') = 0.36;
param_map('fl_delta') = 0.08;

% Prices shock is on k, not on labor, fl_w is fixed wage income
param_map('fl_w') = 1.28*0.3466; % min(z*w) from benchmark az model
param_map('fl_r_save') = 0.025;
param_map('fl_r_borr') = 0.025;

% Minimum Consumption, utility lower bound. The cmin parameter and
% fl_nan_replace parameter have no effects on value function, just for
% resetting invalid choice grid values. fl_nan_replace reset invalid k
% choice given w. fl_c_min resets invalid consumption levels due to w
% choices that are invalid. But this is the case when fl_w > 0.
param_map('fl_c_min') = 0.001;
param_map('fl_nan_replace') = -9999;

% Borrowing Related Parameters for AKBZ models the
% <https://github.com/FanWangEcon/CodeDynaAsset/tree/master/m_akz m_akz>
% models do not deal with default,
% <https://github.com/FanWangEcon/CodeDynaAsset/tree/master/m_akbz m_akbz>
% files do.
param_map('fl_b_bd') = 0; % borrow bound, = 0 if save only
param_map('fl_default_aprime') = 0; % if default, next period aprime
param_map('bl_default') = 0; % if borrowing is default allowed

% Assest Grids Toal savings aggregate grid (see discussion on top). 35
% points picked for
% param_map('fl_w_min') = param_map('fl_b_bd'); % but b_bd overrides this
param_map('fl_w_max') = 50;
param_map('it_w_n') = 50;

% Risky Capital Asset Vector see graph below for how it looks graphically
% in principle keep it_k_n the same as it_w_n to have equi-distance points
% in triangle choice grid.
param_map('fl_k_min') = 0;
% param_map('fl_k_max') = (param_map('fl_w_max') - param_map('fl_b_bd'));
param_map('it_ak_n') = param_map('it_w_n'); % grid for a and k the same

% Interpolation fl_coh_interp_grid_gap controls the number of coh points at
% which to solve the model it_c_interp_grid_gap determines the gap between
% consumption terpolation points. For consumption interpolation 10^-4 is
% extremely accurate, there should be no perceptible differences in value
% and policy functions when the it_c_interp_grid_gap <= 0.001 compared to
% actual evaluation
param_map('fl_coh_interp_grid_gap') = 0.1;
% param_map('it_coh_interp_n') = 500;
param_map('it_c_interp_grid_gap') = 10^-4;

% Solution Accuracy
param_map('it_maxiter_val') = 250;
param_map('it_maxiter_dist') = 1000;
param_map('st_analytical_stationary_type') = 'eigenvector';
param_map('fl_tol_val') = 10^-5;
param_map('fl_tol_pol') = 10^-5;
param_map('fl_tol_dist') = 10^-5;
param_map('it_tol_pol_nochange') = 25; % number of iterations where policy does not change

Setting support_map container

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

% root directory
[st_root_path] = preamble(false);
st_matimg_path_root = [st_root_path '/m_akz/'];
support_map('st_matimg_path_root') = st_matimg_path_root;

% timer
support_map('bl_time') = true;

% Print Controls
support_map('bl_display_defparam') = false;
support_map('bl_display') = true;
support_map('bl_display_dist') = false;
support_map('it_display_every') = 5; % how often to print results

% Profile Controls
support_map('bl_profile') = false;
support_map('bl_profile_dist') = false; % distribution profile
support_map('st_profile_path') = [st_matimg_path_root '/solve/profile/'];
support_map('st_profile_prefix') = [''];
support_map('st_profile_name_main') = ['_default'];
support_map('st_profile_suffix') = ['_p' num2str(it_subset)];

support_map('bl_post') = false;
% Final Print
support_map('bl_display_final') = false; % print finalized results
support_map('bl_display_final_dist') = false; % print finalized results
support_map('bl_display_final_dist_detail') = false;
support_map('it_display_final_rowmax') = 100; % max row to print (states/iters)
support_map('it_display_final_colmax') = 12; % max col to print (shocks)
it_display_summmat_rowmax = 7;
it_display_summmat_colmax = 7;
support_map('it_display_summmat_rowmax') = it_display_summmat_rowmax;
support_map('it_display_summmat_colmax') = it_display_summmat_colmax;

% Mat File Controls
support_map('bl_mat') = false;
support_map('st_mat_path') = [st_matimg_path_root '/solve/mat/'];
support_map('st_mat_prefix') = [''];
support_map('st_mat_name_main') = ['_default'];
support_map('st_mat_suffix') = ['_p' num2str(it_subset)];

% Graphing Controls
support_map('bl_graph') = false;
support_map('bl_graph_onebyones') = true;
support_map('bl_graph_val') = true;
support_map('bl_graph_pol_lvl') = true;
support_map('bl_graph_pol_pct') = true;
support_map('bl_graph_coh_t_coh') = true;

% Image Saving Controls (given graphing)
support_map('st_title_prefix') = '';
support_map('bl_img_save') = false;
support_map('st_img_path') = [st_matimg_path_root '/solve/img/'];
support_map('st_img_prefix') = [''];
support_map('st_img_name_main') = ['_default'];
support_map('st_img_suffix') = ['_p' num2str(it_subset) '.png'];

% Sub-function graphing controls
support_map('bl_graph_funcgrids') = false;
support_map('bl_display_funcgrids') = false;
support_map('bl_graph_evf') = false;
support_map('bl_display_evf') = false;

Subset Options

  1. it_subset = 1 is basic invoke quick test
  2. it_subset = 2 is main invoke
  3. it_subset = 3 is profiling invoke
  4. it_subset = 4 is matlab publish.
if (ismember(it_subset, [1,2,3,4]))
    if (ismember(it_subset, [1]))
        % TEST quick
        param_map('it_w_n') = 20;
        param_map('it_k_n') = param_map('it_w_n');
        param_map('it_z_n') = 3;
        param_map('it_maxiter_val') = 50;
        param_map('fl_coh_interp_grid_gap') = 0.25;
        param_map('it_c_interp_grid_gap') = 0.001;
        param_map('it_tol_pol_nochange') = 1000;
        support_map('bl_display') = true;
        support_map('it_display_every') = 1;
    end
    if (ismember(it_subset, [2, 4]))
        % close figures
        close all;
        % Main Run
        support_map('bl_time') = true;
        support_map('bl_display_defparam') = true;
        support_map('bl_display') = true;
        support_map('it_display_every') = 5;

        support_map('bl_post') = true;
        support_map('bl_display_final') = true;
        support_map('bl_mat') = false;
        support_map('bl_graph') = true;
        support_map('bl_graph_onebyones') = false;
        support_map('bl_img_save') = true;
        if (ismember(it_subset, [4]))
            support_map('bl_time') = false;
            support_map('bl_display') = false;
            support_map('bl_graph_onebyones') = true;
            support_map('bl_img_save') = false;
        end
    end
    if (ismember(it_subset, [3]))
        % Profile run
        support_map('bl_profile') = true;
        support_map('bl_display') = false; % don't print
        support_map('bl_time') = true;
    end
end

Subset Options for Distribution solutions

  1. it_subset = 5 is basic invoke quick test
  2. it_subset = 6 is invoke full test
  3. it_subset = 7 is profiling invoke
  4. it_subset = 8 is matlab publish
  5. it_subset = 9 is invoke operational (only final stats) and coh graph
if (ismember(it_subset, [5,6,7,8,9]))
    if (ismember(it_subset, [5]))
        % TEST quick (need to enough to have distribution)
        param_map('it_w_n') = 20;
        param_map('it_k_n') = param_map('it_w_n');
        param_map('it_z_n') = 3;
        param_map('it_maxiter_val') = 50;
        param_map('fl_coh_interp_grid_gap') = 0.25;
        param_map('it_c_interp_grid_gap') = 0.001;
        param_map('it_tol_pol_nochange') = 1000;
        support_map('bl_display') = true;
        support_map('it_display_every') = 1;
        support_map('bl_display_dist') = true;
    end
    if (ismember(it_subset, [6, 8, 9]))
        % close all
        close all;
        % Main Run
        support_map('bl_time') = true;
        support_map('bl_display_defparam') = true;
        support_map('bl_display') = false;
        support_map('bl_display_dist') = true;
        support_map('it_display_every') = 20;

        support_map('bl_post') = true;
        support_map('bl_display_final_dist') = true;
        support_map('bl_mat') = false;
        support_map('bl_graph') = true;
        support_map('bl_graph_onebyones') = false;
        support_map('bl_img_save') = true;

        % do not generate all graphs when solving for distribution
        support_map('bl_graph_val') = false;
        support_map('bl_graph_pol_lvl') = false;
        support_map('bl_graph_pol_pct') = false;
        support_map('bl_graph_coh_t_coh') = true;

        if (ismember(it_subset, [8, 9]))
            support_map('bl_time') = false;
            support_map('bl_display') = false;
            support_map('bl_display_dist') = false;
            support_map('bl_display_final_dist_detail') = true;
            support_map('bl_graph_onebyones') = true;
            support_map('bl_img_save') = false;
            if (ismember(it_subset, [9]))
                % quietly turn off all graphs, only tables
                support_map('bl_display_final_dist_detail') = false;
                support_map('bl_display_defparam') = false;
                support_map('bl_graph_coh_t_coh') = false;
            end
        end

    end
    if (ismember(it_subset, [7]))
        % Profile run
        support_map('bl_profile_dist') = true;
        support_map('bl_display') = false; % don't print
        support_map('bl_display_dist') = false; % don't print
        support_map('bl_time') = true;
    end
end

Display

if (bl_display_defparam)
    fft_container_map_display(param_map, it_display_summmat_rowmax, it_display_summmat_colmax);
    fft_container_map_display(support_map, it_display_summmat_rowmax, it_display_summmat_colmax);
end
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Begin: Show all key and value pairs from container
CONTAINER NAME: PARAM_MAP
----------------------------------------
  Map with properties:

        Count: 31
      KeyType: char
    ValueType: any

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pos = 1 ; key = bl_default ; val = 0
pos = 2 ; key = fl_Amean ; val = 1
pos = 3 ; key = fl_alpha ; val = 0.36
pos = 4 ; key = fl_b_bd ; val = 0
pos = 5 ; key = fl_beta ; val = 0.94
pos = 6 ; key = fl_c_min ; val = 0.001
pos = 7 ; key = fl_coh_interp_grid_gap ; val = 0.1
pos = 8 ; key = fl_crra ; val = 1.5
pos = 9 ; key = fl_default_aprime ; val = 0
pos = 10 ; key = fl_delta ; val = 0.08
pos = 11 ; key = fl_k_min ; val = 0
pos = 12 ; key = fl_nan_replace ; val = -9999
pos = 13 ; key = fl_r_borr ; val = 0.025
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_max ; val = 50
pos = 20 ; key = fl_z_mu ; val = 0
pos = 21 ; key = fl_z_rho ; val = 0.8
pos = 22 ; key = fl_z_sig ; val = 0.2
pos = 23 ; key = it_ak_n ; val = 50
pos = 24 ; key = it_c_interp_grid_gap ; val = 0.0001
pos = 25 ; key = it_maxiter_dist ; val = 1000
pos = 26 ; key = it_maxiter_val ; val = 250
pos = 27 ; key = it_tol_pol_nochange ; val = 25
pos = 28 ; key = it_w_n ; val = 50
pos = 29 ; key = it_z_n ; val = 15
pos = 30 ; key = st_analytical_stationary_type ; val = eigenvector
pos = 31 ; key = st_model ; val = akz_wkz_iwkz
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Scalars in Container and Sizes and Basic Statistics
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                              i     idx     value 
                              __    ___    _______

    bl_default                 1     1           0
    fl_Amean                   2     2           1
    fl_alpha                   3     3        0.36
    fl_b_bd                    4     4           0
    fl_beta                    5     5        0.94
    fl_c_min                   6     6       0.001
    fl_coh_interp_grid_gap     7     7         0.1
    fl_crra                    8     8         1.5
    fl_default_aprime          9     9           0
    fl_delta                  10    10        0.08
    fl_k_min                  11    11           0
    fl_nan_replace            12    12       -9999
    fl_r_borr                 13    13       0.025
    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_max                  19    19          50
    fl_z_mu                   20    20           0
    fl_z_rho                  21    21         0.8
    fl_z_sig                  22    22         0.2
    it_ak_n                   23    23          50
    it_c_interp_grid_gap      24    24      0.0001
    it_maxiter_dist           25    25        1000
    it_maxiter_val            26    26         250
    it_tol_pol_nochange       27    27          25
    it_w_n                    28    28          50
    it_z_n                    29    29          15

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

    st_analytical_stationary_type    1    30 
    st_model                         2    31 

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

        Count: 41
      KeyType: char
    ValueType: any

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pos = 1 ; key = bl_display ; val = true
pos = 2 ; key = bl_display_defparam ; val = false
pos = 3 ; key = bl_display_dist ; val = false
pos = 4 ; key = bl_display_evf ; val = false
pos = 5 ; key = bl_display_final ; val = false
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 = false
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_onebyones ; val = true
pos = 14 ; key = bl_graph_pol_lvl ; val = true
pos = 15 ; key = bl_graph_pol_pct ; val = true
pos = 16 ; key = bl_graph_val ; val = true
pos = 17 ; key = bl_img_save ; val = false
pos = 18 ; key = bl_mat ; val = false
pos = 19 ; key = bl_post ; val = false
pos = 20 ; key = bl_profile ; val = false
pos = 21 ; key = bl_profile_dist ; val = false
pos = 22 ; key = bl_time ; val = true
pos = 23 ; key = it_display_every ; val = 5
pos = 24 ; key = it_display_final_colmax ; val = 12
pos = 25 ; key = it_display_final_rowmax ; val = 100
pos = 26 ; key = it_display_summmat_colmax ; val = 7
pos = 27 ; key = it_display_summmat_rowmax ; val = 7
pos = 28 ; key = st_img_name_main ; val = _default
pos = 29 ; key = st_img_path ; val = C:/Users/fan/CodeDynaAsset//m_akz//solve/img/
pos = 30 ; key = st_img_prefix ; val = 
pos = 31 ; key = st_img_suffix ; val = _p0.png
pos = 32 ; key = st_mat_name_main ; val = _default
pos = 33 ; key = st_mat_path ; val = C:/Users/fan/CodeDynaAsset//m_akz//solve/mat/
pos = 34 ; key = st_mat_prefix ; val = 
pos = 35 ; key = st_mat_suffix ; val = _p0
pos = 36 ; key = st_matimg_path_root ; val = C:/Users/fan/CodeDynaAsset//m_akz/
pos = 37 ; key = st_profile_name_main ; val = _default
pos = 38 ; key = st_profile_path ; val = C:/Users/fan/CodeDynaAsset//m_akz//solve/profile/
pos = 39 ; key = st_profile_prefix ; val = 
pos = 40 ; key = st_profile_suffix ; val = _p0
pos = 41 ; key = st_title_prefix ; val = 
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Scalars in Container and Sizes and Basic Statistics
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                                    i     idx    value
                                    __    ___    _____

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

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

    st_img_name_main         1    28 
    st_img_path              2    29 
    st_img_prefix            3    30 
    st_img_suffix            4    31 
    st_mat_name_main         5    32 
    st_mat_path              6    33 
    st_mat_prefix            7    34 
    st_mat_suffix            8    35 
    st_matimg_path_root      9    36 
    st_profile_name_main    10    37 
    st_profile_path         11    38 
    st_profile_prefix       12    39 
    st_profile_suffix       13    40 
    st_title_prefix         14    41 

end
ans = 

  Map with properties:

        Count: 31
      KeyType: char
    ValueType: any