Solve For+Inf+Borr+Save+RShock Dynamic Programming Problem (Loop)

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Contents

function result_map = ff_abzr_fibs_vf(varargin)

FF_ABZ_FIBS_VF borr + save one asset formal informal + loop

This program solves the infinite horizon dynamic single asset and single shock problem with loops. This file contains codes that processes borrowing and handles formal and informal choices. With R Shock.

@param param_map container parameter container

@param support_map container support container

@param armt_map container container with states, choices and shocks grids that are inputs for grid based solution algorithm

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

@return result_map container contains policy function matrix, value function matrix, iteration results, and policy function, value function and iteration results tables.

keys included in result_map:

@example

@include

@seealso

Default

it_param_set = 4;
[param_map, support_map] = ffs_abzr_fibs_set_default_param(it_param_set);

% Note: param_map and support_map can be adjusted here or outside to override defaults
% To generate results as if formal informal do not matter
param_map('it_a_n') = 35;
param_map('fl_z_r_infbr_n') = 3;
param_map('it_z_wage_n') = 3;
param_map('it_z_n') = param_map('it_z_wage_n') * param_map('fl_z_r_infbr_n');
param_map('it_maxiter_val') = 20;
% param_map('fl_r_fsv') = 0.025;
% param_map('fl_r_fbr') = 0.035;
% param_map('bl_b_is_principle') = false;
% param_map('st_forbrblk_type') = 'seg3';
% param_map('fl_forbrblk_brmost') = -19;
% param_map('fl_forbrblk_brleast') = -1;
% param_map('fl_forbrblk_gap') = -1.5;
% param_map('bl_b_is_principle') = false;

[armt_map, func_map] = ffs_abzr_fibs_get_funcgrid(param_map, support_map); % 1 for override
default_params = {param_map support_map armt_map func_map};

Parse Parameters 1

% if varargin only has param_map and support_map,
params_len = length(varargin);
[default_params{1:params_len}] = varargin{:};
param_map = [param_map; default_params{1}];
support_map = [support_map; default_params{2}];
if params_len >= 1 && params_len <= 2
    % If override param_map, re-generate armt and func if they are not
    % provided
    bl_input_override = true;
    [armt_map, func_map] = ffs_abzr_fibs_get_funcgrid(param_map, support_map, bl_input_override);
else
    % Override all
    armt_map = [armt_map; default_params{3}];
    func_map = [func_map; default_params{4}];
end

% append function name
st_func_name = 'ff_abzr_fibs_vf';
support_map('st_profile_name_main') = [st_func_name support_map('st_profile_name_main')];
support_map('st_mat_name_main') = [st_func_name support_map('st_mat_name_main')];
support_map('st_img_name_main') = [st_func_name support_map('st_img_name_main')];

Parse Parameters 2

% armt_map
params_group = values(armt_map, {'ar_a', 'mt_z_trans', 'ar_z_r_infbr_mesh_wage', 'ar_z_wage_mesh_r_infbr'});
[ar_a, mt_z_trans, ar_z_r_infbr_mesh_wage, ar_z_wage_mesh_r_infbr] = params_group{:};

% Formal choice Menu/Grid and Interest Rate Menu/Grid
params_group = values(armt_map, {'ar_forbrblk_r', 'ar_forbrblk'});
[ar_forbrblk_r, ar_forbrblk] = params_group{:};

% func_map
params_group = values(func_map, {'f_util_log', 'f_util_crra', 'f_coh', 'f_cons_coh_fbis', 'f_cons_coh_save'});
[f_util_log, f_util_crra, f_coh, f_cons_coh_fbis, f_cons_coh_save] = params_group{:};

% param_map
params_group = values(param_map, {'it_a_n', 'it_z_n', 'fl_crra', 'fl_beta', 'fl_c_min',...
    'fl_nan_replace', 'bl_default', 'bl_bridge', 'bl_rollover', 'fl_default_aprime'});
[it_a_n, it_z_n, fl_crra, fl_beta, fl_c_min, ...
    fl_nan_replace, bl_default, bl_bridge, bl_rollover, fl_default_aprime] = params_group{:};
params_group = values(param_map, {'it_maxiter_val', 'fl_tol_val', 'fl_tol_pol', 'it_tol_pol_nochange'});
[it_maxiter_val, fl_tol_val, fl_tol_pol, it_tol_pol_nochange] = params_group{:};

% param_map, Formal informal
params_group = values(param_map, {'fl_r_fsv', 'bl_b_is_principle'});
[fl_r_fsv, bl_b_is_principle] = params_group{:};

% support_map
params_group = values(support_map, {'bl_profile', 'st_profile_path', ...
    'st_profile_prefix', 'st_profile_name_main', 'st_profile_suffix',...
    'bl_display_minccost', 'bl_display_infbridge', ...
    'bl_time', 'bl_display_defparam', 'bl_display', 'it_display_every', 'bl_post'});
[bl_profile, st_profile_path, ...
    st_profile_prefix, st_profile_name_main, st_profile_suffix, ...
    bl_display_minccost, bl_display_infbridge, ...
    bl_time, bl_display_defparam, bl_display, it_display_every, bl_post] = params_group{:};

Initialize Output Matrixes

mt_val_cur = zeros(it_a_n,it_z_n);
mt_val = mt_val_cur - 1;
mt_pol_a = zeros(it_a_n,it_z_n);
mt_pol_a_cur = mt_pol_a - 1;
mt_pol_cons = zeros(it_a_n,it_z_n);

% collect optimal borrowing formal and informal choices
mt_pol_b_bridge = zeros(it_a_n,it_z_n);
mt_pol_inf_borr_nobridge = zeros(it_a_n,it_z_n);
mt_pol_for_borr = zeros(it_a_n,it_z_n);
mt_pol_for_save = zeros(it_a_n,it_z_n);

Initialize Convergence Conditions

bl_vfi_continue = true;
it_iter = 0;
ar_val_diff_norm = zeros([it_maxiter_val, 1]);
ar_pol_diff_norm = zeros([it_maxiter_val, 1]);
mt_pol_perc_change = zeros([it_maxiter_val, it_z_n]);

Iterate Value Function

Loop solution with 4 nested loops

  1. loop 1: over exogenous states
  2. loop 2: over endogenous states
  3. loop 3: over choices
  4. loop 4: add future utility, integration--loop over future shocks
% Start Profile
if (bl_profile)
    close all;
    profile off;
    profile on;
end

% Start Timer
if (bl_time)
    tic;
end

% Utility at-Default/at-limiting-case-when-nodefault
if (fl_crra == 1)
    fl_u_cmin = f_util_log(fl_c_min);
else
    fl_u_cmin = f_util_crra(fl_c_min);
end


% Value Function Iteration
while bl_vfi_continue
    it_iter = it_iter + 1;

Iterate over a and z states

handling borrowing and default possibility

    % loop 1: over exogenous states
    for it_z_i = 1:it_z_n

        fl_z_r_borr = ar_z_r_infbr_mesh_wage(it_z_i);
        fl_z_wage = ar_z_wage_mesh_r_infbr(it_z_i);

        % loop 2: over endogenous states
        for it_a_j = 1:it_a_n
            % Get asset state
            fl_a = ar_a(it_a_j);

            % Initialize storage
            ar_val_cur = zeros(size(ar_a));
            ar_c_cur = zeros(size(ar_a));
            ar_b_bridge = zeros(size(ar_a));
            ar_inf_borr_nobridge = zeros(size(ar_a));
            ar_for_borr = zeros(size(ar_a));
            ar_for_save = zeros(size(ar_a));

            % calculate cash on hand
            fl_coh = f_coh(fl_z_wage, fl_a);

            % loop 3: over choices
            for it_ap_k = 1:it_a_n
                % get next period asset choice
                fl_ap = ar_a(it_ap_k);

Compute Consumption given Borrowing and Savings

find the today's consumption maximizing formal and informal choices given a' and coh. The formal and informal choices need to generate exactly a', but depending on which formal and informal joint choice is used, the consumption cost today a' is different. Note here, a is principle + interests. Three areas:

                if (fl_ap < 0)

                    % Calculate Bridge Loan Borrowing
                    if (bl_bridge && fl_coh < 0)

                        bl_input_override = true;
                        [fl_aprime_nobridge, fl_b_bridge, fl_c_bridge] = ffs_fibs_inf_bridge(...
                            bl_b_is_principle, fl_z_r_borr, fl_ap, fl_coh, ...
                            bl_display_infbridge, bl_input_override);

                    else

                        fl_aprime_nobridge = fl_ap;
                        fl_b_bridge = 0;
                        fl_c_bridge = 0;

                    end

                    % Find Optimal Formal Informal Borrow Save Combo
                    % calculate consumption gain from formal + informal
                    % borrowing and savings choices.
                    bl_input_override = true;
                    [fl_max_c_nobridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = ...
                        ffs_fibs_min_c_cost(...
                        bl_b_is_principle, fl_z_r_borr, fl_r_fsv, ...
                        ar_forbrblk_r, ar_forbrblk, ...
                        fl_aprime_nobridge, bl_display_minccost, bl_input_override);

                    % Compute Consumption given Formal and Informal joint
                    % consumption with formal borrow menu + bridge loans.
                    fl_c = f_cons_coh_fbis(fl_coh, fl_max_c_nobridge + fl_c_bridge);

                else

                    % consumption with savings
                    fl_c = f_cons_coh_save(fl_coh, fl_ap);

                    % assign values for formal and informal choices
                    % possible that fl_coh < 0, but if then fl_ap > 0 is
                    % not valid choice
                    [fl_b_bridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = deal(0, 0, 0, fl_ap);

                end

Compute Utility With Default

if rollover is not allowed and bridge is not allowed, then as long as coh <= 0, also treat as not allowed states. assign u(c)

                if (fl_c <= fl_c_min || ...
                    ( ~bl_rollover && ~bl_bridge && fl_coh < fl_c_min))

                    if (bl_default)
                        % defaults
                        % current utility: only today u(cmin)
                        ar_val_cur(it_ap_k) = fl_u_cmin;
                        % transition out next period, debt wiped out
                        for it_az_q = 1:it_z_n
                            ar_val_cur(it_ap_k) = ar_val_cur(it_ap_k) + ...
                                fl_beta*mt_z_trans(it_z_i, it_az_q)*mt_val_cur((ar_a == fl_default_aprime), it_az_q);
                        end

                        % Replace Consumption if default cmin
                        fl_c = fl_c_min;
                    else
                        % if default is not allowed: v = fl_nan_replace
                        ar_val_cur(it_ap_k) = fl_nan_replace;

                        % Replace Consumption if no default nan
                        fl_c = 0;
                    end

                    % no action, defaulting
                    fl_b_bridge = 0;
                    fl_inf_borr_nobridge = 0;
                    fl_for_borr = 0;
                    fl_for_save = 0;

                else
                    % Solve Optimization Problem: max_{a'} u(c(a,a',z)) + beta*EV(a',z')
                    % borrowed enough to pay debt (and borrowing limit not exceeded)
                    % saved only the coh available.
                    % current utility
                    if (fl_crra == 1)
                        ar_val_cur(it_ap_k) = f_util_log(fl_c);
                    else
                        ar_val_cur(it_ap_k) = f_util_crra(fl_c);
                    end
                    % loop 4: add future utility, integration--loop over future shocks
                    for it_az_q = 1:it_z_n
                        ar_val_cur(it_ap_k) = ar_val_cur(it_ap_k) + ...
                            fl_beta*mt_z_trans(it_z_i, it_az_q)*mt_val_cur(it_ap_k, it_az_q);
                    end
                end

Store Values

                % Could get the formal and informal values from
                % ffs_fibs_min_c_cost_bridge.m
%                 bl_input_override = true;
%                 [fl_c, fl_b_bridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = ...
%                     ffs_fibs_min_c_cost_bridge(fl_ap, fl_coh, ...
%                     param_map, support_map, armt_map, func_map, bl_input_override);

                % Store consumption
                ar_c_cur(it_ap_k) = fl_c;

                % Save/Update Borrowing Information
                ar_b_bridge(it_ap_k) = fl_b_bridge;
                ar_inf_borr_nobridge(it_ap_k) = fl_inf_borr_nobridge;
                ar_for_borr(it_ap_k) = fl_for_borr;
                ar_for_save(it_ap_k) = fl_for_save;
            end

Optimize over Next Period Asset Choices

optimal choice value

            [fl_opti_val_z, fl_opti_idx_z] = max(ar_val_cur);
            fl_opti_aprime_z = ar_a(fl_opti_idx_z);
            fl_opti_c_z = ar_c_cur(fl_opti_idx_z);

            % corresponding optimal borrowing and savings choices
            fl_opti_b_bridge = ar_b_bridge(fl_opti_idx_z);
            fl_opti_inf_borr_nobridge = ar_inf_borr_nobridge(fl_opti_idx_z);
            fl_opti_for_borr = ar_for_borr(fl_opti_idx_z);
            fl_opti_for_save = ar_for_save(fl_opti_idx_z);

Find Optimal Choices for Defaults or Not

Handle Default is optimal or not

            if (fl_opti_c_z <= fl_c_min)
                if (bl_default)
                    % if defaulting is optimal choice, at these states, not required
                    % to default, non-default possible, but default could be optimal
                    fl_opti_aprime_z = fl_default_aprime;
                else
                    % if default is not allowed, then next period same state as now
                    % this is absorbing state, this is the limiting case, single
                    % state space point, lowest a and lowest shock has this.
                    fl_opti_aprime_z = min(ar_a);
                end
            end

Store Optimal Choices and Value Given(a,z)

            % store overal savings, value and consumption
            mt_val(it_a_j,it_z_i) = fl_opti_val_z;
            mt_pol_a(it_a_j,it_z_i) = fl_opti_aprime_z;
            mt_pol_cons(it_a_j,it_z_i) = fl_opti_c_z;

            % store savings and borrowing formal and inf optimal choices
            mt_pol_b_bridge(it_a_j,it_z_i) = fl_opti_b_bridge;
            mt_pol_inf_borr_nobridge(it_a_j,it_z_i) = fl_opti_inf_borr_nobridge;
            mt_pol_for_borr(it_a_j,it_z_i) = fl_opti_for_borr;
            mt_pol_for_save(it_a_j,it_z_i) = fl_opti_for_save;
        end
    end

Check Tolerance and Continuation

    % Difference across iterations
    ar_val_diff_norm(it_iter) = norm(mt_val - mt_val_cur);
    ar_pol_diff_norm(it_iter) = norm(mt_pol_a - mt_pol_a_cur);
    mt_pol_perc_change(it_iter, :) = sum((mt_pol_a ~= mt_pol_a_cur))/(it_a_n);

    % Update
    mt_val_cur = mt_val;
    mt_pol_a_cur = mt_pol_a;

    % Print Iteration Results
    if (bl_display && (rem(it_iter, it_display_every)==0))
        fprintf('VAL it_iter:%d, fl_diff:%d, fl_diff_pol:%d\n', ...
            it_iter, ar_val_diff_norm(it_iter), ar_pol_diff_norm(it_iter));
        tb_valpol_iter = array2table([mean(mt_val_cur,1); mean(mt_pol_a_cur,1); ...
            mt_val_cur(it_a_n,:); mt_pol_a_cur(it_a_n,:)]);
        tb_valpol_iter.Properties.VariableNames = strcat('z', string((1:size(mt_val_cur,2))));
        tb_valpol_iter.Properties.RowNames = {'mval', 'map', 'Hval', 'Hap'};
        disp('mval = mean(mt_val_cur,1), average value over a')
        disp('map  = mean(mt_pol_a_cur,1), average choice over a')
        disp('Hval = mt_val_cur(it_a_n,:), highest a state val')
        disp('Hap = mt_pol_a_cur(it_a_n,:), highest a state choice')
        disp(tb_valpol_iter);
    end

    % Continuation Conditions:
    % 1. if value function convergence criteria reached
    % 2. if policy function variation over iterations is less than
    % threshold
    if (it_iter == (it_maxiter_val + 1))
        bl_vfi_continue = false;
    elseif ((it_iter == it_maxiter_val) || ...
            (ar_val_diff_norm(it_iter) < fl_tol_val) || ...
            (sum(ar_pol_diff_norm(max(1, it_iter-it_tol_pol_nochange):it_iter)) < fl_tol_pol))
        % Fix to max, run again to save results if needed
        it_iter_last = it_iter;
        it_iter = it_maxiter_val;
    end
end

% End Timer
if (bl_time)
    toc;
end

% End Profile
if (bl_profile)
    profile off
    profile viewer
    st_file_name = [st_profile_prefix st_profile_name_main st_profile_suffix];
    profsave(profile('info'), strcat(st_profile_path, st_file_name));
end

Process Optimal Choices

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

result_map('cl_mt_pol_a') = {mt_pol_a, zeros(1)};
result_map('cl_mt_coh') = {f_coh(ar_z_r_infbr_mesh_wage, ar_a'), zeros(1)};

result_map('cl_mt_pol_c') = {mt_pol_cons, zeros(1)};
result_map('cl_mt_pol_b_bridge') = {mt_pol_b_bridge, zeros(1)};
result_map('cl_mt_pol_inf_borr_nobridge') = {mt_pol_inf_borr_nobridge, zeros(1)};
result_map('cl_mt_pol_for_borr') = {mt_pol_for_borr, zeros(1)};
result_map('cl_mt_pol_for_save') = {mt_pol_for_save, zeros(1)};

result_map('ar_st_pol_names') = ["cl_mt_pol_a", "cl_mt_pol_coh", "cl_mt_pol_c", ...
    "cl_mt_pol_b_bridge", "cl_mt_pol_inf_borr_nobridge", "cl_mt_pol_for_borr", "cl_mt_pol_for_save"];

% Get Discrete Choice Outcomes
result_map = ffs_fibs_identify_discrete(result_map, bl_input_override);

Post Solution Graph and Table Generation

Note in comparison with abzr, results here, even when using identical parameters would differ because in abzr solved where choices are principle. Here choices are principle + interests in order to facilitate using the informal choice functions.

Note that this means two things are different, on the one hand, the value of asset for to coh is different based on the grid of assets. If the asset grid is negative, now per grid point, there is more coh because that grid point of asset no longer has interest rates. On the other hand, if one has positive asset grid point on arrival, that is worth less to coh. Additionally, when making choices for the next period, now choices aprime includes interests. What these mean is that the a grid no longer has the same meaning. We should expect at higher savings levels, for the same grid points, if optimal grid choices are the same as before, consumption should be lower when b includes interest rates and principle. This is however, not true when arriving in a period with negative a levels, for the same negative a level and same a prime negative choice, could have higher consumption here becasue have to pay less interests on debt. This tends to happen for smaller levels of borrowing choices.

Graphically, when using interest + principle, big difference in consumption as a fraction of (coh - aprime) figure. In those figures, when counting in principles only, the gap in coh and aprime is consumption, but now, as more is borrowed only a small fraction of coh and aprime gap is consumption, becuase aprime/(1+r) is put into consumption.

if (bl_post)
    bl_input_override = true;
    result_map('ar_val_diff_norm') = ar_val_diff_norm(1:it_iter_last);
    result_map('ar_pol_diff_norm') = ar_pol_diff_norm(1:it_iter_last);
    result_map('mt_pol_perc_change') = mt_pol_perc_change(1:it_iter_last, :);

    % Standard AZ graphs
    result_map = ff_az_vf_post(param_map, support_map, armt_map, func_map, result_map, bl_input_override);

    % Graphs for results_map with FIBS contents
    result_map = ff_az_fibs_vf_post(param_map, support_map, armt_map, func_map, result_map, bl_input_override);
end
valgap = norm(mt_val - mt_val_cur): value function difference across iterations
polgap = norm(mt_pol_a - mt_pol_a_cur): policy function difference across iterations
z1 = z1 perc change: sum((mt_pol_a ~= mt_pol_a_cur))/(it_a_n): percentage of state space points conditional on shock where the policy function is changing across iterations
               valgap    polgap    zi1_zr_0_025_zw_0_33902    zi2_zr_0_025_zw_0_92155    zi3_zr_0_025_zw_2_505    zi4_zr_0_06_zw_0_33902    zi5_zr_0_06_zw_0_92155    zi6_zr_0_06_zw_2_505    zi7_zr_0_095_zw_0_33902    zi8_zr_0_095_zw_0_92155    zi9_zr_0_095_zw_2_505
               ______    ______    _______________________    _______________________    _____________________    ______________________    ______________________    ____________________    _______________________    _______________________    _____________________

    iter=1     34.947    333.76                  1                          1                         1                         1                         1                        1                        1                          1                         1       
    iter=2     28.244    366.57            0.97143                          1                   0.97143                   0.97143                         1                  0.97143                  0.97143                    0.94286                   0.97143       
    iter=3     23.071    120.05            0.94286                    0.94286                   0.91429                   0.91429                   0.94286                  0.91429                  0.91429                    0.88571                   0.91429       
    iter=4      19.47    60.515            0.82857                        0.8                   0.85714                   0.82857                   0.82857                  0.82857                      0.8                        0.8                   0.82857       
    iter=5     16.059    36.853            0.71429                    0.74286                   0.71429                   0.68571                   0.74286                  0.74286                  0.68571                    0.71429                   0.71429       
    iter=6     13.181    25.786            0.51429                    0.54286                   0.57143                   0.48571                   0.51429                  0.54286                  0.48571                    0.48571                   0.57143       
    iter=7     11.259     18.92                0.4                    0.34286                   0.51429                   0.34286                   0.34286                  0.51429                  0.37143                        0.4                   0.51429       
    iter=8     9.1095    17.168            0.34286                    0.34286                   0.34286                   0.31429                   0.34286                  0.31429                  0.28571                    0.31429                   0.31429       
    iter=9     7.5744     14.05            0.28571                    0.22857                   0.22857                   0.25714                   0.22857                  0.22857                      0.2                    0.22857                   0.22857       
    iter=10    6.6664    13.878            0.22857                        0.2                   0.17143                   0.22857                       0.2                  0.17143                  0.28571                    0.22857                   0.17143       
    iter=11    5.4902     20.72            0.17143                        0.2                   0.22857                   0.17143                   0.17143                      0.2                  0.14286                    0.14286                       0.2       
    iter=12    5.0571    9.0431           0.085714                   0.085714                   0.11429                   0.11429                  0.085714                  0.11429                 0.085714                   0.085714                   0.11429       
    iter=13    4.6102    9.4693            0.11429                   0.085714                   0.17143                   0.11429                  0.085714                  0.11429                  0.14286                   0.085714                   0.11429       
    iter=14    4.2667     8.449           0.085714                    0.11429                  0.085714                  0.085714                   0.11429                 0.085714                 0.085714                    0.11429                  0.085714       
    iter=15    3.8104    8.2637           0.085714                    0.11429                  0.085714                  0.085714                  0.085714                  0.11429                 0.085714                   0.085714                  0.085714       
    iter=16    3.3395    6.6607           0.057143                   0.085714                   0.14286                  0.057143                  0.028571                 0.085714                 0.057143                   0.028571                  0.085714       
    iter=17    2.9591    3.9195                  0                   0.057143                  0.028571                         0                  0.028571                 0.057143                        0                   0.028571                  0.028571       
    iter=18     2.661    5.1959           0.028571                   0.028571                  0.057143                  0.028571                  0.028571                 0.057143                 0.057143                   0.028571                  0.057143       
    iter=19    2.4269    5.3547           0.028571                   0.057143                  0.057143                  0.028571                  0.028571                 0.057143                 0.057143                   0.028571                  0.085714       
    iter=20    2.1847    3.9195           0.028571                   0.028571                  0.057143                  0.028571                  0.028571                 0.028571                 0.028571                   0.057143                  0.028571       

tb_val: V(a,z) value at each state space point
                     zi1_zr_0_025_zw_0_33902    zi2_zr_0_025_zw_0_92155    zi3_zr_0_025_zw_2_505    zi4_zr_0_06_zw_0_33902    zi5_zr_0_06_zw_0_92155    zi6_zr_0_06_zw_2_505    zi7_zr_0_095_zw_0_33902    zi8_zr_0_095_zw_0_92155    zi9_zr_0_095_zw_2_505
                     _______________________    _______________________    _____________________    ______________________    ______________________    ____________________    _______________________    _______________________    _____________________

    a1=-20                   -12.099                    -8.1147                  -0.38024                   -12.099                  -8.3086                  -0.55589                  -12.099                    -8.3086                  -0.80097       
    a2=-17.8788              -10.437                    -6.9026                    0.7499                   -10.722                  -7.0682                   0.60139                  -11.232                    -7.2947                   0.40971       
    a3=-15.7576              -9.5896                    -5.9184                    1.8008                   -9.8257                  -6.0587                    1.6768                  -10.185                     -6.237                    1.5278       
    a4=-13.6364              -8.6049                    -4.9175                    2.8003                   -8.7982                   -5.035                    2.6982                  -9.0615                     -5.172                    2.5879       
    a5=-11.5152               -7.547                      -3.86                    3.7931                   -7.7032                   -4.006                    3.7111                  -7.8961                    -4.1077                    3.6322       
    a6=-9.39394              -6.4536                    -2.8104                    4.7509                   -6.5771                  -2.9791                    4.6871                  -6.7168                    -3.0518                    4.6341       
    a7=-7.27273              -5.3368                    -1.7702                    5.9014                   -5.4315                  -1.9608                    5.6981                  -5.5298                    -2.0103                     5.607       
    a8=-5.15152              -4.0649                   -0.73605                    7.0534                    -4.134                  -0.9103                    6.9498                  -4.1972                   -0.98105                    6.8593       
    a9=-3.0303               -2.7027                     1.6591                    7.9807                   -2.7489                   1.5691                    7.9534                   -2.782                     1.4986                     7.944       
    a10=-0.909091            -1.2893                     3.3795                    8.8185                   -1.3151                   3.3555                    8.8185                   -1.324                     3.3473                    8.8185       
    a11=0                   -0.36459                      3.992                    9.0212                  -0.38421                    3.992                    9.0212                 -0.39088                      3.992                    9.0212       
    a12=1.21212              0.48383                     4.5403                    9.3049                   0.48383                   4.5403                    9.3049                  0.48383                     4.5403                    9.3049       
    a13=3.33333               1.5552                      5.253                    9.6903                    1.5552                    5.253                    9.6903                   1.5552                      5.253                    9.6903       
    a14=5.45455               2.5123                     5.9309                    10.054                    2.5123                   5.9309                    10.054                   2.5123                     5.9309                    10.054       
    a15=7.57576               3.4029                     6.5759                    10.399                    3.4029                   6.5759                    10.399                   3.4029                     6.5759                    10.399       
    a16=9.69697                4.234                     7.1897                    10.725                     4.234                   7.1897                    10.725                    4.234                     7.1897                    10.725       
    a17=11.8182               5.0055                     7.7737                    11.031                    5.0055                   7.7737                    11.031                   5.0055                     7.7737                    11.031       
    a18=13.9394                 5.74                       8.33                    11.319                      5.74                     8.33                    11.319                     5.74                       8.33                    11.319       
    a19=16.0606               6.5822                     8.8679                     11.59                    6.5822                   8.8679                     11.59                   6.5822                     8.8679                     11.59       
    a20=18.1818               7.4822                     9.3882                    11.842                    7.4822                   9.3882                    11.842                   7.4822                     9.3882                    11.842       
    a21=20.303                8.3143                     9.8847                    12.079                    8.3143                   9.8847                    12.079                   8.3143                     9.8847                    12.079       
    a22=22.4242                9.085                     10.358                    12.298                     9.085                   10.358                    12.298                    9.085                     10.358                    12.298       
    a23=24.5455               9.5586                     10.732                    12.508                    9.5586                   10.732                    12.508                   9.5586                     10.732                    12.508       
    a24=26.6667               9.9524                     11.039                    12.713                    9.9524                   11.039                    12.713                   9.9524                     11.039                    12.713       
    a25=28.7879               10.308                     11.328                    12.913                    10.308                   11.328                    12.913                   10.308                     11.328                    12.913       
    a26=30.9091               10.601                      11.57                      13.1                    10.601                    11.57                      13.1                   10.601                      11.57                      13.1       
    a27=33.0303               10.846                     11.773                    13.259                    10.846                   11.773                    13.259                   10.846                     11.773                    13.259       
    a28=35.1515               11.085                     11.962                    13.405                    11.085                   11.962                    13.405                   11.085                     11.962                    13.405       
    a29=37.2727               11.317                     12.147                    13.538                    11.317                   12.147                    13.538                   11.317                     12.147                    13.538       
    a30=39.3939                11.54                     12.328                    13.668                     11.54                   12.328                    13.668                    11.54                     12.328                    13.668       
    a31=41.5152               11.755                     12.503                    13.795                    11.755                   12.503                    13.795                   11.755                     12.503                    13.795       
    a32=43.6364               11.962                     12.674                    13.918                    11.962                   12.674                    13.918                   11.962                     12.674                    13.918       
    a33=45.7576               12.164                      12.84                    14.037                    12.164                    12.84                    14.037                   12.164                      12.84                    14.037       
    a34=47.8788                12.36                     13.002                    14.154                     12.36                   13.002                    14.154                    12.36                     13.002                    14.154       
    a35=50                    12.549                      13.16                    14.267                    12.549                    13.16                    14.267                   12.549                      13.16                    14.267       

tb_pol_a: optimal asset choice for each state space point
                     zi1_zr_0_025_zw_0_33902    zi2_zr_0_025_zw_0_92155    zi3_zr_0_025_zw_2_505    zi4_zr_0_06_zw_0_33902    zi5_zr_0_06_zw_0_92155    zi6_zr_0_06_zw_2_505    zi7_zr_0_095_zw_0_33902    zi8_zr_0_095_zw_0_92155    zi9_zr_0_095_zw_2_505
                     _______________________    _______________________    _____________________    ______________________    ______________________    ____________________    _______________________    _______________________    _____________________

    a1=-20                         0                        -20                       -20                         0                         0                      -20                        0                          0                       -20       
    a2=-17.8788                  -20                        -20                   -17.879                       -20                       -20                  -17.879                      -20                        -20                   -17.879       
    a3=-15.7576              -17.879                    -17.879                   -15.758                   -17.879                   -17.879                  -15.758                  -17.879                    -17.879                   -15.758       
    a4=-13.6364              -15.758                    -15.758                   -13.636                   -15.758                   -15.758                  -13.636                  -15.758                    -15.758                   -13.636       
    a5=-11.5152              -13.636                    -11.515                   -11.515                   -13.636                   -13.636                  -11.515                  -13.636                    -13.636                   -11.515       
    a6=-9.39394              -11.515                    -9.3939                   -9.3939                   -11.515                   -11.515                  -9.3939                  -11.515                    -11.515                   -9.3939       
    a7=-7.27273              -9.3939                    -7.2727                   -5.1515                   -9.3939                   -9.3939                  -5.1515                  -9.3939                    -9.3939                   -7.2727       
    a8=-5.15152              -7.2727                    -5.1515                   -3.0303                   -7.2727                   -5.1515                  -3.0303                  -7.2727                    -7.2727                   -3.0303       
    a9=-3.0303               -5.1515                    -3.0303                  -0.90909                   -5.1515                   -3.0303                 -0.90909                  -5.1515                    -3.0303                  -0.90909       
    a10=-0.909091            -3.0303                   -0.90909                         0                   -3.0303                  -0.90909                        0                  -3.0303                   -0.90909                         0       
    a11=0                   -0.90909                          0                         0                  -0.90909                         0                        0                 -0.90909                          0                         0       
    a12=1.21212                    0                          0                    1.2121                         0                         0                   1.2121                        0                          0                    1.2121       
    a13=3.33333               1.2121                     1.2121                    3.3333                    1.2121                    1.2121                   3.3333                   1.2121                     1.2121                    3.3333       
    a14=5.45455               3.3333                     3.3333                    5.4545                    3.3333                    3.3333                   5.4545                   3.3333                     3.3333                    5.4545       
    a15=7.57576               5.4545                     5.4545                    7.5758                    5.4545                    5.4545                   7.5758                   5.4545                     5.4545                    7.5758       
    a16=9.69697               7.5758                     7.5758                     9.697                    7.5758                    7.5758                    9.697                   7.5758                     7.5758                     9.697       
    a17=11.8182                9.697                      9.697                    11.818                     9.697                     9.697                   11.818                    9.697                      9.697                    11.818       
    a18=13.9394               11.818                     11.818                    13.939                    11.818                    11.818                   13.939                   11.818                     11.818                    13.939       
    a19=16.0606               13.939                     13.939                    16.061                    13.939                    13.939                   16.061                   13.939                     13.939                    16.061       
    a20=18.1818               16.061                     16.061                    18.182                    16.061                    16.061                   18.182                   16.061                     16.061                    18.182       
    a21=20.303                18.182                     18.182                    20.303                    18.182                    18.182                   20.303                   18.182                     18.182                    20.303       
    a22=22.4242               20.303                     20.303                    22.424                    20.303                    20.303                   22.424                   20.303                     20.303                    22.424       
    a23=24.5455               22.424                     22.424                    24.545                    22.424                    22.424                   24.545                   22.424                     22.424                    24.545       
    a24=26.6667               24.545                     24.545                    26.667                    24.545                    24.545                   26.667                   24.545                     24.545                    26.667       
    a25=28.7879               26.667                     26.667                    26.667                    26.667                    26.667                   26.667                   26.667                     26.667                    26.667       
    a26=30.9091               28.788                     28.788                    28.788                    28.788                    28.788                   28.788                   28.788                     28.788                    28.788       
    a27=33.0303               28.788                     30.909                    30.909                    28.788                    30.909                   30.909                   28.788                     30.909                    30.909       
    a28=35.1515               30.909                      33.03                     33.03                    30.909                     33.03                    33.03                   30.909                      33.03                     33.03       
    a29=37.2727                33.03                      33.03                    35.152                     33.03                     33.03                   35.152                    33.03                      33.03                    35.152       
    a30=39.3939               35.152                     35.152                    37.273                    35.152                    35.152                   37.273                   35.152                     35.152                    37.273       
    a31=41.5152               37.273                     37.273                    39.394                    37.273                    37.273                   39.394                   37.273                     37.273                    39.394       
    a32=43.6364               39.394                     39.394                    41.515                    39.394                    39.394                   41.515                   39.394                     39.394                    41.515       
    a33=45.7576               41.515                     41.515                    43.636                    41.515                    41.515                   43.636                   41.515                     41.515                    43.636       
    a34=47.8788               43.636                     43.636                    45.758                    43.636                    43.636                   45.758                   43.636                     43.636                    45.758       
    a35=50                    45.758                     45.758                    47.879                    45.758                    45.758                   47.879                   45.758                     45.758                    47.879       

mt_pol_b_bridge_print: bridge loans
                       zi1_zr_0_025_zw_0_33902    zi2_zr_0_025_zw_0_92155    zi3_zr_0_025_zw_2_505    zi4_zr_0_06_zw_0_33902    zi5_zr_0_06_zw_0_92155    zi6_zr_0_06_zw_2_505    zi7_zr_0_095_zw_0_33902    zi8_zr_0_095_zw_0_92155    zi9_zr_0_095_zw_2_505
                       _______________________    _______________________    _____________________    ______________________    ______________________    ____________________    _______________________    _______________________    _____________________

    coh1=-19.968                     0                    -19.291                   -17.213                         0                        0                  -17.801                         0                          0                   -18.389       
    coh2=-17.8468              -17.881                    -17.117                   -15.039                   -18.492                  -17.701                  -15.553                   -19.102                    -18.286                   -16.066       
    coh3=-15.7256              -15.707                    -14.942                   -12.865                   -16.243                  -15.453                  -13.304                   -16.779                    -15.963                   -13.744       
    coh4=-13.6044              -13.532                    -12.768                   -10.691                   -13.995                  -13.204                  -11.056                   -14.457                     -13.64                   -11.421       
    coh5=-11.4832              -11.358                    -10.594                   -8.5164                   -11.746                  -10.956                  -8.8072                   -12.134                    -11.317                    -9.098       
    coh6=-9.36194               -9.184                    -8.4197                   -6.3422                   -9.4976                  -8.7072                  -6.5588                   -9.8112                    -8.9947                   -6.7753       
    coh7=-7.24073              -7.0098                    -6.2455                    -4.168                   -7.2491                  -6.4587                  -4.3103                   -7.4885                     -6.672                   -4.4526       
    coh8=-5.11952              -4.8355                    -4.0712                   -1.9937                   -5.0006                  -4.2103                  -2.0618                   -5.1657                    -4.3493                   -2.1299       
    coh9=-2.9983               -2.6613                     -1.897                         0                   -2.7521                  -1.9618                        0                    -2.843                    -2.0265                         0       
    coh10=-0.877091           -0.48703                          0                         0                  -0.50366                        0                        0                  -0.52029                          0                         0       
    coh11=0.032                      0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh12=1.24412                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh13=3.36533                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh14=5.48655                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh15=7.60776                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh16=9.72897                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh17=11.8502                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh18=13.9714                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh19=16.0926                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh20=18.2138                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh21=20.335                     0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh22=22.4562                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh23=24.5775                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh24=26.6987                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh25=28.8199                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh26=30.9411                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh27=33.0623                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh28=35.1835                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh29=37.3047                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh30=39.4259                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh31=41.5472                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh32=43.6684                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh33=45.7896                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh34=47.9108                    0                          0                         0                         0                        0                        0                         0                          0                         0       
    coh35=50.032                     0                          0                         0                         0                        0                        0                         0                          0                         0       

mt_pol_inf_borr_nobridge_print: Informal loans that is not bridge loan
                       zi1_zr_0_025_zw_0_33902    zi2_zr_0_025_zw_0_92155    zi3_zr_0_025_zw_2_505    zi4_zr_0_06_zw_0_33902    zi5_zr_0_06_zw_0_92155    zi6_zr_0_06_zw_2_505    zi7_zr_0_095_zw_0_33902    zi8_zr_0_095_zw_0_92155    zi9_zr_0_095_zw_2_505
                       _______________________    _______________________    _____________________    ______________________    ______________________    ____________________    _______________________    _______________________    _____________________

    coh1=-19.968                     0                   -0.70907                   -2.7866                         0                         0                  -2.1988                        0                           0                 -0.54604       
    coh2=-17.8468               -2.119                    -2.8833                   -2.8396                   -1.5085                   -2.2988                  -2.3261                        0                    -0.64937                 -0.74756       
    coh3=-15.7256              -2.1721                    -2.9363                   -2.8927                   -1.6357                   -2.4261                  -2.4534                 -0.03441                    -0.85088                        0       
    coh4=-13.6044              -2.2251                    -2.9894                   -2.9457                    -1.763                   -2.5534                  -2.5806                 -0.23593                           0                        0       
    coh5=-11.4832              -2.2781                   -0.92119                   -2.9987                   -1.8903                   -2.6807                  -2.7079                 -0.43744                           0                        0       
    coh6=-9.36194              -2.3312                   -0.97422                   -3.0517                   -2.0176                   -2.8079                  -2.8352                 -0.63896                           0                        0       
    coh7=-7.24073              -2.3842                    -1.0273                  -0.98356                   -2.1448                   -2.9352                 -0.84124                 -0.84047                   -0.059443                 -0.15763       
    coh8=-5.11952              -2.4372                    -1.0803                   -1.0366                   -2.2721                  -0.94126                 -0.96851                        0                    -0.26096                        0       
    coh9=-2.9983               -2.4902                    -1.1333                  -0.90909                   -2.3994                   -1.0685                 -0.90909                        0                           0                        0       
    coh10=-0.877091            -2.5433                   -0.90909                         0                   -2.5266                  -0.90909                        0                        0                           0                        0       
    coh11=0.032               -0.90909                          0                         0                  -0.90909                         0                        0                        0                           0                        0       
    coh12=1.24412                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh13=3.36533                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh14=5.48655                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh15=7.60776                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh16=9.72897                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh17=11.8502                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh18=13.9714                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh19=16.0926                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh20=18.2138                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh21=20.335                     0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh22=22.4562                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh23=24.5775                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh24=26.6987                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh25=28.8199                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh26=30.9411                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh27=33.0623                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh28=35.1835                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh29=37.3047                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh30=39.4259                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh31=41.5472                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh32=43.6684                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh33=45.7896                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh34=47.9108                    0                          0                         0                         0                         0                        0                        0                           0                        0       
    coh35=50.032                     0                          0                         0                         0                         0                        0                        0                           0                        0       

mt_pol_for_borr_print: formal borrowing
                       zi1_zr_0_025_zw_0_33902    zi2_zr_0_025_zw_0_92155    zi3_zr_0_025_zw_2_505    zi4_zr_0_06_zw_0_33902    zi5_zr_0_06_zw_0_92155    zi6_zr_0_06_zw_2_505    zi7_zr_0_095_zw_0_33902    zi8_zr_0_095_zw_0_92155    zi9_zr_0_095_zw_2_505
                       _______________________    _______________________    _____________________    ______________________    ______________________    ____________________    _______________________    _______________________    _____________________

    coh1=-19.968                  0                          0                         0                        0                         0                        0                            0                          0                    -1.065       
    coh2=-17.8468                 0                          0                         0                        0                         0                        0                       -1.065                     -1.065                    -1.065       
    coh3=-15.7256                 0                          0                         0                        0                         0                        0                       -1.065                     -1.065                   -2.6625       
    coh4=-13.6044                 0                          0                         0                        0                         0                        0                       -1.065                    -2.6625                   -2.6625       
    coh5=-11.4832                 0                          0                         0                        0                         0                        0                       -1.065                    -2.6625                   -2.6625       
    coh6=-9.36194                 0                          0                         0                        0                         0                        0                       -1.065                    -2.6625                   -2.6625       
    coh7=-7.24073                 0                          0                         0                        0                         0                        0                       -1.065                    -2.6625                   -2.6625       
    coh8=-5.11952                 0                          0                         0                        0                         0                        0                      -2.6625                    -2.6625                    -1.065       
    coh9=-2.9983                  0                          0                         0                        0                         0                        0                      -2.6625                     -1.065                    -1.065       
    coh10=-0.877091               0                          0                         0                        0                         0                        0                      -2.6625                     -1.065                         0       
    coh11=0.032                   0                          0                         0                        0                         0                        0                       -1.065                          0                         0       
    coh12=1.24412                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh13=3.36533                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh14=5.48655                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh15=7.60776                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh16=9.72897                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh17=11.8502                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh18=13.9714                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh19=16.0926                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh20=18.2138                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh21=20.335                  0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh22=22.4562                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh23=24.5775                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh24=26.6987                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh25=28.8199                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh26=30.9411                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh27=33.0623                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh28=35.1835                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh29=37.3047                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh30=39.4259                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh31=41.5472                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh32=43.6684                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh33=45.7896                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh34=47.9108                 0                          0                         0                        0                         0                        0                            0                          0                         0       
    coh35=50.032                  0                          0                         0                        0                         0                        0                            0                          0                         0       

mt_pol_for_save_print: formal savings
                       zi1_zr_0_025_zw_0_33902    zi2_zr_0_025_zw_0_92155    zi3_zr_0_025_zw_2_505    zi4_zr_0_06_zw_0_33902    zi5_zr_0_06_zw_0_92155    zi6_zr_0_06_zw_2_505    zi7_zr_0_095_zw_0_33902    zi8_zr_0_095_zw_0_92155    zi9_zr_0_095_zw_2_505
                       _______________________    _______________________    _____________________    ______________________    ______________________    ____________________    _______________________    _______________________    _____________________

    coh1=-19.968                    0                          0                         0                         0                         0                        0                         0                          0                         0       
    coh2=-17.8468                   0                          0                         0                         0                         0                        0                    0.1671                          0                         0       
    coh3=-15.7256                   0                          0                         0                         0                         0                        0                         0                          0                   0.64843       
    coh4=-13.6044                   0                          0                         0                         0                         0                        0                         0                     0.5451                   0.44691       
    coh5=-11.4832                   0                          0                         0                         0                         0                        0                         0                    0.34359                    0.2454       
    coh6=-9.36194                   0                          0                         0                         0                         0                        0                         0                    0.14207                  0.043882       
    coh7=-7.24073                   0                          0                         0                         0                         0                        0                         0                          0                         0       
    coh8=-5.11952                   0                          0                         0                         0                         0                        0                   0.55551                          0                   0.16456       
    coh9=-2.9983                    0                          0                         0                         0                         0                        0                     0.354                   0.061238                   0.15591       
    coh10=-0.877091                 0                          0                         0                         0                         0                        0                   0.15248                    0.15591                         0       
    coh11=0.032                     0                          0                         0                         0                         0                        0                   0.15591                          0                         0       
    coh12=1.24412                   0                          0                    1.2121                         0                         0                   1.2121                         0                          0                    1.2121       
    coh13=3.36533              1.2121                     1.2121                    3.3333                    1.2121                    1.2121                   3.3333                    1.2121                     1.2121                    3.3333       
    coh14=5.48655              3.3333                     3.3333                    5.4545                    3.3333                    3.3333                   5.4545                    3.3333                     3.3333                    5.4545       
    coh15=7.60776              5.4545                     5.4545                    7.5758                    5.4545                    5.4545                   7.5758                    5.4545                     5.4545                    7.5758       
    coh16=9.72897              7.5758                     7.5758                     9.697                    7.5758                    7.5758                    9.697                    7.5758                     7.5758                     9.697       
    coh17=11.8502               9.697                      9.697                    11.818                     9.697                     9.697                   11.818                     9.697                      9.697                    11.818       
    coh18=13.9714              11.818                     11.818                    13.939                    11.818                    11.818                   13.939                    11.818                     11.818                    13.939       
    coh19=16.0926              13.939                     13.939                    16.061                    13.939                    13.939                   16.061                    13.939                     13.939                    16.061       
    coh20=18.2138              16.061                     16.061                    18.182                    16.061                    16.061                   18.182                    16.061                     16.061                    18.182       
    coh21=20.335               18.182                     18.182                    20.303                    18.182                    18.182                   20.303                    18.182                     18.182                    20.303       
    coh22=22.4562              20.303                     20.303                    22.424                    20.303                    20.303                   22.424                    20.303                     20.303                    22.424       
    coh23=24.5775              22.424                     22.424                    24.545                    22.424                    22.424                   24.545                    22.424                     22.424                    24.545       
    coh24=26.6987              24.545                     24.545                    26.667                    24.545                    24.545                   26.667                    24.545                     24.545                    26.667       
    coh25=28.8199              26.667                     26.667                    26.667                    26.667                    26.667                   26.667                    26.667                     26.667                    26.667       
    coh26=30.9411              28.788                     28.788                    28.788                    28.788                    28.788                   28.788                    28.788                     28.788                    28.788       
    coh27=33.0623              28.788                     30.909                    30.909                    28.788                    30.909                   30.909                    28.788                     30.909                    30.909       
    coh28=35.1835              30.909                      33.03                     33.03                    30.909                     33.03                    33.03                    30.909                      33.03                     33.03       
    coh29=37.3047               33.03                      33.03                    35.152                     33.03                     33.03                   35.152                     33.03                      33.03                    35.152       
    coh30=39.4259              35.152                     35.152                    37.273                    35.152                    35.152                   37.273                    35.152                     35.152                    37.273       
    coh31=41.5472              37.273                     37.273                    39.394                    37.273                    37.273                   39.394                    37.273                     37.273                    39.394       
    coh32=43.6684              39.394                     39.394                    41.515                    39.394                    39.394                   41.515                    39.394                     39.394                    41.515       
    coh33=45.7896              41.515                     41.515                    43.636                    41.515                    41.515                   43.636                    41.515                     41.515                    43.636       
    coh34=47.9108              43.636                     43.636                    45.758                    43.636                    43.636                   45.758                    43.636                     43.636                    45.758       
    coh35=50.032               45.758                     45.758                    47.879                    45.758                    45.758                   47.879                    45.758                     45.758                    47.879       

Display Various Containers

if (bl_display_defparam)

Display 1 support_map

    fft_container_map_display(support_map);
----------------------------------------
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Begin: Show all key and value pairs from container
CONTAINER NAME: SUPPORT_MAP
----------------------------------------
  Map with properties:

        Count: 43
      KeyType: char
    ValueType: any

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----------------------------------------
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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_final ; val = true
pos = 5 ; key = bl_display_final_dist ; val = false
pos = 6 ; key = bl_display_final_dist_detail ; val = false
pos = 7 ; key = bl_display_funcgrids ; val = false
pos = 8 ; key = bl_display_infbridge ; val = false
pos = 9 ; key = bl_display_minccost ; val = false
pos = 10 ; key = bl_graph ; val = true
pos = 11 ; key = bl_graph_coh_t_coh ; val = true
pos = 12 ; key = bl_graph_discrete ; val = true
pos = 13 ; key = bl_graph_forinf_discrete ; val = true
pos = 14 ; key = bl_graph_forinf_pol_lvl ; val = true
pos = 15 ; key = bl_graph_forinf_pol_pct ; val = true
pos = 16 ; key = bl_graph_funcgrids ; val = false
pos = 17 ; key = bl_graph_onebyones ; val = true
pos = 18 ; key = bl_graph_pol_lvl ; val = true
pos = 19 ; key = bl_graph_pol_pct ; val = true
pos = 20 ; key = bl_graph_val ; val = true
pos = 21 ; key = bl_img_save ; val = false
pos = 22 ; key = bl_mat ; val = false
pos = 23 ; key = bl_post ; val = true
pos = 24 ; key = bl_profile ; val = false
pos = 25 ; key = bl_profile_dist ; val = false
pos = 26 ; key = bl_time ; val = false
pos = 27 ; key = it_display_every ; val = 5
pos = 28 ; key = it_display_final_colmax ; val = 15
pos = 29 ; key = it_display_final_rowmax ; val = 100
pos = 30 ; key = st_img_name_main ; val = ff_abzr_fibs_vf_default
pos = 31 ; key = st_img_path ; val = C:/Users/fan/CodeDynaAsset//m_fibs//m_abzr_solve/img/
pos = 32 ; key = st_img_prefix ; val = 
pos = 33 ; key = st_img_suffix ; val = _p4.png
pos = 34 ; key = st_mat_name_main ; val = ff_abzr_fibs_vf_default
pos = 35 ; key = st_mat_path ; val = C:/Users/fan/CodeDynaAsset//m_fibs//m_abzr_solve/mat/
pos = 36 ; key = st_mat_prefix ; val = 
pos = 37 ; key = st_mat_suffix ; val = _p4
pos = 38 ; key = st_matimg_path_root ; val = C:/Users/fan/CodeDynaAsset//m_fibs/
pos = 39 ; key = st_profile_name_main ; val = ff_abzr_fibs_vf_default
pos = 40 ; key = st_profile_path ; val = C:/Users/fan/CodeDynaAsset//m_fibs//m_abzr_solve/profile/
pos = 41 ; key = st_profile_prefix ; val = 
pos = 42 ; key = st_profile_suffix ; val = _p4
pos = 43 ; 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        0 
    bl_display_defparam              2     2        1 
    bl_display_dist                  3     3        0 
    bl_display_final                 4     4        1 
    bl_display_final_dist            5     5        0 
    bl_display_final_dist_detail     6     6        0 
    bl_display_funcgrids             7     7        0 
    bl_display_infbridge             8     8        0 
    bl_display_minccost              9     9        0 
    bl_graph                        10    10        1 
    bl_graph_coh_t_coh              11    11        1 
    bl_graph_discrete               12    12        1 
    bl_graph_forinf_discrete        13    13        1 
    bl_graph_forinf_pol_lvl         14    14        1 
    bl_graph_forinf_pol_pct         15    15        1 
    bl_graph_funcgrids              16    16        0 
    bl_graph_onebyones              17    17        1 
    bl_graph_pol_lvl                18    18        1 
    bl_graph_pol_pct                19    19        1 
    bl_graph_val                    20    20        1 
    bl_img_save                     21    21        0 
    bl_mat                          22    22        0 
    bl_post                         23    23        1 
    bl_profile                      24    24        0 
    bl_profile_dist                 25    25        0 
    bl_time                         26    26        0 
    it_display_every                27    27        5 
    it_display_final_colmax         28    28       15 
    it_display_final_rowmax         29    29      100 

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

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

Display 2 armt_map

    fft_container_map_display(armt_map);
----------------------------------------
----------------------------------------
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Begin: Show all key and value pairs from container
CONTAINER NAME: ARMT_MAP
----------------------------------------
  Map with properties:

        Count: 6
      KeyType: char
    ValueType: any

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----------------------------------------
----------------------------------------
pos = 1 ; key = ar_a ;rown= 1 ,coln= 35
ar_a :mu= 14.5714 ,sd= 20.9645 ,min= -20 ,max= 50
               zi_1_C1    zi_2_C2    zi_3_C3    zi_18_c18    zi_33_c33    zi_34_c34    zi_35_c35
               _______    _______    _______    _________    _________    _________    _________

    zi_1_r1      -20      -17.879    -15.758     13.939       45.758       47.879         50    

pos = 2 ; key = ar_forbrblk ;rown= 1 ,coln= 9
ar_forbrblk :mu= -7.0556 ,sd= 6.3809 ,min= -19 ,max= 0
               zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
               _______    _______    _______    _______    _______    _______    _______

    zi_1_r1      -19       -14.5       -10       -5.5       -2.5        -1          0   

pos = 3 ; key = ar_forbrblk_r ;rown= 1 ,coln= 9
ar_forbrblk_r :mu= 0.065 ,sd= 0 ,min= 0.065 ,max= 0.065
               zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
               _______    _______    _______    _______    _______    _______    _______

    zi_1_r1     0.065      0.065      0.065      0.065      0.065      0.065      0.065 

pos = 4 ; key = ar_z_r_infbr_mesh_wage ;rown= 1 ,coln= 9
ar_z_r_infbr_mesh_wage :mu= 0.06 ,sd= 0.030311 ,min= 0.025 ,max= 0.095
               zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
               _______    _______    _______    _______    _______    _______    _______

    zi_1_r1     0.025      0.025      0.025      0.06       0.095      0.095      0.095 

pos = 5 ; key = ar_z_wage_mesh_r_infbr ;rown= 1 ,coln= 9
ar_z_wage_mesh_r_infbr :mu= 1.2552 ,sd= 0.97072 ,min= 0.33902 ,max= 2.505
               zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
               _______    _______    _______    _______    _______    _______    _______

    zi_1_r1    0.33902    0.92155     2.505     0.92155    0.33902    0.92155     2.505 

pos = 6 ; key = mt_z_trans ;rown= 9 ,coln= 9
mt_z_trans :mu= 0.11111 ,sd= 0.26844 ,min= 1.8172e-13 ,max= 0.89374
                zi_1_c1       zi_2_c2      zi_3_c3       zi_5_c5      zi_7_c7      zi_8_c8      zi_9_c9  
               __________    _________    __________    _________    __________    ________    __________

    zi_1_r1     0.0042226    0.0003023    1.8172e-13    0.0060459       0.84452    0.060459    3.6344e-11
    zi_2_r2    2.8098e-05    0.0044687    2.8098e-05     0.089374     0.0056196     0.89374     0.0056196
    zi_3_r3    1.8172e-13    0.0003023     0.0042226    0.0060459    3.6344e-11    0.060459       0.84452
    zi_4_r4     0.0042226    0.0003023    1.8172e-13    0.0060459       0.84452    0.060459    3.6344e-11
    zi_5_r5    2.8098e-05    0.0044687    2.8098e-05     0.089374     0.0056196     0.89374     0.0056196
    zi_6_r6    1.8172e-13    0.0003023     0.0042226    0.0060459    3.6344e-11    0.060459       0.84452
    zi_7_r7     0.0042226    0.0003023    1.8172e-13    0.0060459       0.84452    0.060459    3.6344e-11
    zi_8_r8    2.8098e-05    0.0044687    2.8098e-05     0.089374     0.0056196     0.89374     0.0056196
    zi_9_r9    1.8172e-13    0.0003023     0.0042226    0.0060459    3.6344e-11    0.060459       0.84452

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

    ar_a                      1     1      1       35      14.571      20.964           -20         50
    ar_forbrblk               2     2      1        9     -7.0556      6.3809           -19          0
    ar_forbrblk_r             3     3      1        9       0.065           0         0.065      0.065
    ar_z_r_infbr_mesh_wage    4     4      1        9        0.06    0.030311         0.025      0.095
    ar_z_wage_mesh_r_infbr    5     5      1        9      1.2552     0.97072       0.33902      2.505
    mt_z_trans                6     6      9        9     0.11111     0.26844    1.8172e-13    0.89374

Display 3 param_map

    fft_container_map_display(param_map);
----------------------------------------
----------------------------------------
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Begin: Show all key and value pairs from container
CONTAINER NAME: PARAM_MAP
----------------------------------------
  Map with properties:

        Count: 42
      KeyType: char
    ValueType: any

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----------------------------------------
----------------------------------------
pos = 1 ; key = bl_b_is_principle ; val = false
pos = 2 ; key = bl_bridge ; val = true
pos = 3 ; key = bl_default ; val = true
pos = 4 ; key = bl_loglin ; val = false
pos = 5 ; key = bl_rollover ; val = true
pos = 6 ; key = fl_a_max ; val = 50
pos = 7 ; key = fl_a_min ; val = 0
pos = 8 ; key = fl_b_bd ; val = -20
pos = 9 ; key = fl_beta ; val = 0.94
pos = 10 ; key = fl_c_min ; val = 0.02
pos = 11 ; key = fl_crra ; val = 1.5
pos = 12 ; key = fl_default_aprime ; val = 0
pos = 13 ; key = fl_forbrblk_brleast ; val = -1
pos = 14 ; key = fl_forbrblk_brmost ; val = -19
pos = 15 ; key = fl_forbrblk_gap ; val = -1.5
pos = 16 ; key = fl_loglin_threshold ; val = 1
pos = 17 ; key = fl_nan_replace ; val = -99999
pos = 18 ; key = fl_r_fbr ; val = 0.065
pos = 19 ; key = fl_r_fsv ; val = 0.025
pos = 20 ; key = fl_tol_dist ; val = 1e-05
pos = 21 ; key = fl_tol_pol ; val = 1e-05
pos = 22 ; key = fl_tol_val ; val = 1e-05
pos = 23 ; key = fl_w ; val = 1.28
pos = 24 ; key = fl_z_r_infbr_max ; val = 0.095
pos = 25 ; key = fl_z_r_infbr_min ; val = 0.025
pos = 26 ; key = fl_z_r_infbr_n ; val = 3
pos = 27 ; key = fl_z_r_infbr_poiss_mean ; val = 20
pos = 28 ; key = fl_z_wage_mu ; val = 0
pos = 29 ; key = fl_z_wage_rho ; val = 0.8
pos = 30 ; key = fl_z_wage_sig ; val = 0.2
pos = 31 ; key = it_a_n ; val = 35
pos = 32 ; key = it_maxiter_dist ; val = 1000
pos = 33 ; key = it_maxiter_val ; val = 20
pos = 34 ; key = it_tol_pol_nochange ; val = 25
pos = 35 ; key = it_trans_power_dist ; val = 1000
pos = 36 ; key = it_z_n ; val = 9
pos = 37 ; key = it_z_wage_n ; val = 3
pos = 38 ; key = st_analytical_stationary_type ; val = eigenvector
pos = 39 ; key = st_forbrblk_type ; val = seg3
pos = 40 ; key = st_model ; val = abzr_fibs
pos = 41 ; key = st_z_r_infbr_drv_ele_type ; val = unif
pos = 42 ; key = st_z_r_infbr_drv_prb_type ; val = poiss
----------------------------------------
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Scalars in Container and Sizes and Basic Statistics
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                               i     idx    value 
                               __    ___    ______

    bl_b_is_principle           1     1          0
    bl_bridge                   2     2          1
    bl_default                  3     3          1
    bl_loglin                   4     4          0
    bl_rollover                 5     5          1
    fl_a_max                    6     6         50
    fl_a_min                    7     7          0
    fl_b_bd                     8     8        -20
    fl_beta                     9     9       0.94
    fl_c_min                   10    10       0.02
    fl_crra                    11    11        1.5
    fl_default_aprime          12    12          0
    fl_forbrblk_brleast        13    13         -1
    fl_forbrblk_brmost         14    14        -19
    fl_forbrblk_gap            15    15       -1.5
    fl_loglin_threshold        16    16          1
    fl_nan_replace             17    17     -99999
    fl_r_fbr                   18    18      0.065
    fl_r_fsv                   19    19      0.025
    fl_tol_dist                20    20      1e-05
    fl_tol_pol                 21    21      1e-05
    fl_tol_val                 22    22      1e-05
    fl_w                       23    23       1.28
    fl_z_r_infbr_max           24    24      0.095
    fl_z_r_infbr_min           25    25      0.025
    fl_z_r_infbr_n             26    26          3
    fl_z_r_infbr_poiss_mean    27    27         20
    fl_z_wage_mu               28    28          0
    fl_z_wage_rho              29    29        0.8
    fl_z_wage_sig              30    30        0.2
    it_a_n                     31    31         35
    it_maxiter_dist            32    32       1000
    it_maxiter_val             33    33         20
    it_tol_pol_nochange        34    34         25
    it_trans_power_dist        35    35       1000
    it_z_n                     36    36          9
    it_z_wage_n                37    37          3

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

    st_analytical_stationary_type    1    38 
    st_forbrblk_type                 2    39 
    st_model                         3    40 
    st_z_r_infbr_drv_ele_type        4    41 
    st_z_r_infbr_drv_prb_type        5    42 

Display 4 func_map

    fft_container_map_display(func_map);
----------------------------------------
----------------------------------------
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Begin: Show all key and value pairs from container
CONTAINER NAME: FUNC_MAP
----------------------------------------
  Map with properties:

        Count: 8
      KeyType: char
    ValueType: any

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----------------------------------------
----------------------------------------
pos = 1 ; key = f_bprime ; val = @(fl_r_inf,ar_for_borr,ar_inf_borr,ar_for_save)(ar_for_borr./(1+fl_r_fbr)+ar_inf_borr./(1+fl_r_inf)+ar_for_save./(1+fl_r_fsv))
pos = 2 ; key = f_coh ; val = @(ar_z,ar_b)(ar_z*fl_w+ar_b)
pos = 3 ; key = f_cons_coh_fbis ; val = @(coh,ar_bprime_in_c)(coh+ar_bprime_in_c)
pos = 4 ; key = f_cons_coh_save ; val = @(coh,ar_for_save)(coh-ar_for_save./(1+fl_r_fsv))
pos = 5 ; key = f_inc ; val = @(ar_z,fl_r_inf,ar_for_borr,ar_inf_borr,ar_for_save)(ar_z*fl_w+((ar_for_borr./(1+fl_r_fbr))*fl_r_fbr+(ar_inf_borr./(1+fl_r_inf))*fl_r_inf+(ar_for_save./(1+fl_r_fsv))*fl_r_fsv))
pos = 6 ; key = f_util_crra ; val = @(c)(((c).^(1-fl_crra)-1)./(1-fl_crra))
pos = 7 ; key = f_util_log ; val = @(c)log(c)
pos = 8 ; key = f_util_standin ; val = @(z,b)f_util_log(f_coh_simple(z,b).*(f_coh_simple(z,b)>0)+fl_c_min.*(f_coh_simple(z,b)<=0))
----------------------------------------
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Scalars in Container and Sizes and Basic Statistics
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                       i    idx    xFunction
                       _    ___    _________

    f_bprime           1     1         1    
    f_coh              2     2         2    
    f_cons_coh_fbis    3     3         3    
    f_cons_coh_save    4     4         4    
    f_inc              5     5         5    
    f_util_crra        6     6         6    
    f_util_log         7     7         7    
    f_util_standin     8     8         8    

Display 5 result_map

    fft_container_map_display(result_map);
----------------------------------------
----------------------------------------
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Begin: Show all key and value pairs from container
CONTAINER NAME: RESULT_MAP
----------------------------------------
  Map with properties:

        Count: 21
      KeyType: char
    ValueType: any

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----------------------------------------
----------------------------------------
pos = 1 ; key = ar_pol_diff_norm ;rown= 20 ,coln= 1
ar_pol_diff_norm :mu= 54.4267 ,sd= 104.7628 ,min= 3.9195 ,max= 366.5666
                 zi_1_c1
                 _______

    zi_1_R1      333.76 
    zi_2_R2      366.57 
    zi_3_R3      120.05 
    zi_4_R4      60.515 
    zi_5_R5      36.853 
    zi_16_r16    6.6607 
    zi_17_r17    3.9195 
    zi_18_r18    5.1959 
    zi_19_r19    5.3547 
    zi_20_r20    3.9195 

pos = 2 ; key = ar_st_pol_names ; val = cl_mt_pol_a cl_mt_pol_coh cl_mt_pol_c cl_mt_pol_b_bridge cl_mt_pol_inf_borr_nobridge cl_mt_pol_for_borr cl_mt_pol_for_save
pos = 3 ; key = ar_val_diff_norm ;rown= 20 ,coln= 1
ar_val_diff_norm :mu= 10.3193 ,sd= 9.4342 ,min= 2.1847 ,max= 34.9467
                 zi_1_c1
                 _______

    zi_1_R1      34.947 
    zi_2_R2      28.244 
    zi_3_R3      23.071 
    zi_4_R4       19.47 
    zi_5_R5      16.059 
    zi_16_r16    3.3395 
    zi_17_r17    2.9591 
    zi_18_r18     2.661 
    zi_19_r19    2.4269 
    zi_20_r20    2.1847 

pos = 4 ; key = cl_mt_coh ;rown= 35 ,coln= 9
cl_mt_coh :mu= 14.6482 ,sd= 20.6957 ,min= -19.968 ,max= 50.1216
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1      -19.968    -19.968    -19.968    -19.923    -19.878    -19.878    -19.878
    zi_2_R2      -17.847    -17.847    -17.847    -17.802    -17.757    -17.757    -17.757
    zi_3_R3      -15.726    -15.726    -15.726    -15.681    -15.636    -15.636    -15.636
    zi_4_R4      -13.604    -13.604    -13.604     -13.56    -13.515    -13.515    -13.515
    zi_5_R5      -11.483    -11.483    -11.483    -11.438    -11.394    -11.394    -11.394
    zi_31_r31     41.547     41.547     41.547     41.592     41.637     41.637     41.637
    zi_32_r32     43.668     43.668     43.668     43.713     43.758     43.758     43.758
    zi_33_r33      45.79      45.79      45.79     45.834     45.879     45.879     45.879
    zi_34_r34     47.911     47.911     47.911     47.956         48         48         48
    zi_35_r35     50.032     50.032     50.032     50.077     50.122     50.122     50.122

pos = 5 ; key = cl_mt_pol_a ;rown= 35 ,coln= 9
cl_mt_pol_a :mu= 13.1554 ,sd= 19.4264 ,min= -20 ,max= 47.8788
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1            0        -20        -20          0          0          0        -20
    zi_2_R2          -20        -20    -17.879        -20        -20        -20    -17.879
    zi_3_R3      -17.879    -17.879    -15.758    -17.879    -17.879    -17.879    -15.758
    zi_4_R4      -15.758    -15.758    -13.636    -15.758    -15.758    -15.758    -13.636
    zi_5_R5      -13.636    -11.515    -11.515    -13.636    -13.636    -13.636    -11.515
    zi_31_r31     37.273     37.273     39.394     37.273     37.273     37.273     39.394
    zi_32_r32     39.394     39.394     41.515     39.394     39.394     39.394     41.515
    zi_33_r33     41.515     41.515     43.636     41.515     41.515     41.515     43.636
    zi_34_r34     43.636     43.636     45.758     43.636     43.636     43.636     45.758
    zi_35_r35     45.758     45.758     47.879     45.758     45.758     45.758     47.879

pos = 6 ; key = cl_mt_pol_b_bridge ;rown= 35 ,coln= 9
cl_mt_pol_b_bridge :mu= -2.3811 ,sd= 5.0158 ,min= -19.2909 ,max= 0
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1            0    -19.291    -17.213          0          0          0    -18.389
    zi_2_R2      -17.881    -17.117    -15.039    -17.701    -19.102    -18.286    -16.066
    zi_3_R3      -15.707    -14.942    -12.865    -15.453    -16.779    -15.963    -13.744
    zi_4_R4      -13.532    -12.768    -10.691    -13.204    -14.457     -13.64    -11.421
    zi_5_R5      -11.358    -10.594    -8.5164    -10.956    -12.134    -11.317     -9.098
    zi_31_r31          0          0          0          0          0          0          0
    zi_32_r32          0          0          0          0          0          0          0
    zi_33_r33          0          0          0          0          0          0          0
    zi_34_r34          0          0          0          0          0          0          0
    zi_35_r35          0          0          0          0          0          0          0

pos = 7 ; key = cl_mt_pol_c ;rown= 35 ,coln= 9
cl_mt_pol_c :mu= 3.5624 ,sd= 1.7106 ,min= 0.02 ,max= 6.538
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1        0.02     0.69178    2.7186       0.02        0.02      0.02     1.4987 
    zi_2_R2      2.0674       2.813    2.7704     2.1687     0.83697     1.593     1.6827 
    zi_3_R3      2.1191      2.8647    2.8221     2.2888      1.0314    1.7771     1.8674 
    zi_4_R4      2.1708      2.9165    2.8738     2.4089      1.2155    1.9682      2.064 
    zi_5_R5      2.2226     0.89872    2.9256     2.5289      1.3995    2.1648     2.2606 
    zi_31_r31    5.5855      6.3311    6.2885     6.3311      5.5855    6.3311     6.2885 
    zi_32_r32    5.6372      6.3828    6.3402     6.3828      5.6372    6.3828     6.3402 
    zi_33_r33    5.6889      6.4346    6.3919     6.4346      5.6889    6.4346     6.3919 
    zi_34_r34    5.7407      6.4863    6.4437     6.4863      5.7407    6.4863     6.4437 
    zi_35_r35    5.7924       6.538    6.4954      6.538      5.7924     6.538     6.4954 

pos = 8 ; key = cl_mt_pol_for_borr ;rown= 35 ,coln= 9
cl_mt_pol_for_borr :mu= -0.1606 ,sd= 0.56727 ,min= -2.6625 ,max= 0
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1         0          0          0          0            0           0     -1.065
    zi_2_R2         0          0          0          0       -1.065      -1.065     -1.065
    zi_3_R3         0          0          0          0       -1.065      -1.065    -2.6625
    zi_4_R4         0          0          0          0       -1.065     -2.6625    -2.6625
    zi_5_R5         0          0          0          0       -1.065     -2.6625    -2.6625
    zi_31_r31       0          0          0          0            0           0          0
    zi_32_r32       0          0          0          0            0           0          0
    zi_33_r33       0          0          0          0            0           0          0
    zi_34_r34       0          0          0          0            0           0          0
    zi_35_r35       0          0          0          0            0           0          0

pos = 9 ; key = cl_mt_pol_for_save ;rown= 35 ,coln= 9
cl_mt_pol_for_save :mu= 16.0744 ,sd= 15.8057 ,min= 0 ,max= 47.8788
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1           0          0          0          0          0           0          0
    zi_2_R2           0          0          0          0     0.1671           0          0
    zi_3_R3           0          0          0          0          0           0    0.64843
    zi_4_R4           0          0          0          0          0      0.5451    0.44691
    zi_5_R5           0          0          0          0          0     0.34359     0.2454
    zi_31_r31    37.273     37.273     39.394     37.273     37.273      37.273     39.394
    zi_32_r32    39.394     39.394     41.515     39.394     39.394      39.394     41.515
    zi_33_r33    41.515     41.515     43.636     41.515     41.515      41.515     43.636
    zi_34_r34    43.636     43.636     45.758     43.636     43.636      43.636     45.758
    zi_35_r35    45.758     45.758     47.879     45.758     45.758      45.758     47.879

pos = 10 ; key = cl_mt_pol_inf_borr_nobridge ;rown= 35 ,coln= 9
cl_mt_pol_inf_borr_nobridge :mu= -0.37735 ,sd= 0.83417 ,min= -3.0517 ,max= 0
                 zi_1_c1    zi_2_c2     zi_3_c3    zi_5_c5    zi_7_c7     zi_8_c8     zi_9_c9 
                 _______    ________    _______    _______    ________    ________    ________

    zi_1_R1            0    -0.70907    -2.7866          0           0           0    -0.54604
    zi_2_R2       -2.119     -2.8833    -2.8396    -2.2988           0    -0.64937    -0.74756
    zi_3_R3      -2.1721     -2.9363    -2.8927    -2.4261    -0.03441    -0.85088           0
    zi_4_R4      -2.2251     -2.9894    -2.9457    -2.5534    -0.23593           0           0
    zi_5_R5      -2.2781    -0.92119    -2.9987    -2.6807    -0.43744           0           0
    zi_31_r31          0           0          0          0           0           0           0
    zi_32_r32          0           0          0          0           0           0           0
    zi_33_r33          0           0          0          0           0           0           0
    zi_34_r34          0           0          0          0           0           0           0
    zi_35_r35          0           0          0          0           0           0           0

pos = 11 ; key = mt_it_b_bridge_idx ;rown= 35 ,coln= 9
mt_it_b_bridge_idx :mu= 0.24127 ,sd= 0.42853 ,min= 0 ,max= 1
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      true       true       false      false      false      true  
    zi_2_R2       true       true       true       true       true       true       true  
    zi_3_R3       true       true       true       true       true       true       true  
    zi_4_R4       true       true       true       true       true       true       true  
    zi_5_R5       true       true       true       true       true       true       true  
    zi_31_r31     false      false      false      false      false      false      false 
    zi_32_r32     false      false      false      false      false      false      false 
    zi_33_r33     false      false      false      false      false      false      false 
    zi_34_r34     false      false      false      false      false      false      false 
    zi_35_r35     false      false      false      false      false      false      false 

pos = 12 ; key = mt_it_for_only_nbdg ;rown= 35 ,coln= 9
mt_it_for_only_nbdg :mu= 0 ,sd= 0 ,min= 0 ,max= 0
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      false      false      false      false      false      false 
    zi_2_R2       false      false      false      false      false      false      false 
    zi_3_R3       false      false      false      false      false      false      false 
    zi_4_R4       false      false      false      false      false      false      false 
    zi_5_R5       false      false      false      false      false      false      false 
    zi_31_r31     false      false      false      false      false      false      false 
    zi_32_r32     false      false      false      false      false      false      false 
    zi_33_r33     false      false      false      false      false      false      false 
    zi_34_r34     false      false      false      false      false      false      false 
    zi_35_r35     false      false      false      false      false      false      false 

pos = 13 ; key = mt_it_fr_brrsv_nbdg ;rown= 35 ,coln= 9
mt_it_fr_brrsv_nbdg :mu= 0.050794 ,sd= 0.21993 ,min= 0 ,max= 1
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      false      false      false      false      false      false 
    zi_2_R2       false      false      false      false      true       false      false 
    zi_3_R3       false      false      false      false      false      false      true  
    zi_4_R4       false      false      false      false      false      true       true  
    zi_5_R5       false      false      false      false      false      true       true  
    zi_31_r31     false      false      false      false      false      false      false 
    zi_32_r32     false      false      false      false      false      false      false 
    zi_33_r33     false      false      false      false      false      false      false 
    zi_34_r34     false      false      false      false      false      false      false 
    zi_35_r35     false      false      false      false      false      false      false 

pos = 14 ; key = mt_it_frin_brr_nbdg ;rown= 35 ,coln= 9
mt_it_frin_brr_nbdg :mu= 0.038095 ,sd= 0.19173 ,min= 0 ,max= 1
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      false      false      false      false      false      true  
    zi_2_R2       false      false      false      false      false      true       true  
    zi_3_R3       false      false      false      false      true       true       false 
    zi_4_R4       false      false      false      false      true       false      false 
    zi_5_R5       false      false      false      false      true       false      false 
    zi_31_r31     false      false      false      false      false      false      false 
    zi_32_r32     false      false      false      false      false      false      false 
    zi_33_r33     false      false      false      false      false      false      false 
    zi_34_r34     false      false      false      false      false      false      false 
    zi_35_r35     false      false      false      false      false      false      false 

pos = 15 ; key = mt_it_frmsavng_only ;rown= 35 ,coln= 9
mt_it_frmsavng_only :mu= 0.66667 ,sd= 0.47215 ,min= 0 ,max= 1
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      false      false      false      false      false      false 
    zi_2_R2       false      false      false      false      false      false      false 
    zi_3_R3       false      false      false      false      false      false      false 
    zi_4_R4       false      false      false      false      false      false      false 
    zi_5_R5       false      false      false      false      false      false      false 
    zi_31_r31     true       true       true       true       true       true       true  
    zi_32_r32     true       true       true       true       true       true       true  
    zi_33_r33     true       true       true       true       true       true       true  
    zi_34_r34     true       true       true       true       true       true       true  
    zi_35_r35     true       true       true       true       true       true       true  

pos = 16 ; key = mt_it_inf_only_nbdg ;rown= 35 ,coln= 9
mt_it_inf_only_nbdg :mu= 0.18095 ,sd= 0.38559 ,min= 0 ,max= 1
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1       false      true       true       false      false      false      false 
    zi_2_R2       true       true       true       true       false      false      false 
    zi_3_R3       true       true       true       true       false      false      false 
    zi_4_R4       true       true       true       true       false      false      false 
    zi_5_R5       true       true       true       true       false      false      false 
    zi_31_r31     false      false      false      false      false      false      false 
    zi_32_r32     false      false      false      false      false      false      false 
    zi_33_r33     false      false      false      false      false      false      false 
    zi_34_r34     false      false      false      false      false      false      false 
    zi_35_r35     false      false      false      false      false      false      false 

pos = 17 ; key = mt_pol_perc_change ;rown= 20 ,coln= 9
mt_pol_perc_change :mu= 0.34714 ,sd= 0.34206 ,min= 0 ,max= 1
                 zi_1_c1     zi_2_c2     zi_3_c3     zi_5_c5     zi_7_c7     zi_8_c8     zi_9_c9 
                 ________    ________    ________    ________    ________    ________    ________

    zi_1_R1             1           1           1           1           1           1           1
    zi_2_R2       0.97143           1     0.97143           1     0.97143     0.94286     0.97143
    zi_3_R3       0.94286     0.94286     0.91429     0.94286     0.91429     0.88571     0.91429
    zi_4_R4       0.82857         0.8     0.85714     0.82857         0.8         0.8     0.82857
    zi_5_R5       0.71429     0.74286     0.71429     0.74286     0.68571     0.71429     0.71429
    zi_16_r16    0.057143    0.085714     0.14286    0.028571    0.057143    0.028571    0.085714
    zi_17_r17           0    0.057143    0.028571    0.028571           0    0.028571    0.028571
    zi_18_r18    0.028571    0.028571    0.057143    0.028571    0.057143    0.028571    0.057143
    zi_19_r19    0.028571    0.057143    0.057143    0.028571    0.057143    0.028571    0.085714
    zi_20_r20    0.028571    0.028571    0.057143    0.028571    0.028571    0.057143    0.028571

pos = 18 ; key = mt_val ;rown= 35 ,coln= 9
mt_val :mu= 6.5837 ,sd= 6.8499 ,min= -12.0994 ,max= 14.2674
                 zi_1_c1    zi_2_c2    zi_3_c3     zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9 
                 _______    _______    ________    _______    _______    _______    ________

    zi_1_R1      -12.099    -8.1147    -0.38024    -8.3086    -12.099    -8.3086    -0.80097
    zi_2_R2      -10.437    -6.9026      0.7499    -7.0682    -11.232    -7.2947     0.40971
    zi_3_R3      -9.5896    -5.9184      1.8008    -6.0587    -10.185     -6.237      1.5278
    zi_4_R4      -8.6049    -4.9175      2.8003     -5.035    -9.0615     -5.172      2.5879
    zi_5_R5       -7.547      -3.86      3.7931     -4.006    -7.8961    -4.1077      3.6322
    zi_31_r31     11.755     12.503      13.795     12.503     11.755     12.503      13.795
    zi_32_r32     11.962     12.674      13.918     12.674     11.962     12.674      13.918
    zi_33_r33     12.164      12.84      14.037      12.84     12.164      12.84      14.037
    zi_34_r34      12.36     13.002      14.154     13.002      12.36     13.002      14.154
    zi_35_r35     12.549      13.16      14.267      13.16     12.549      13.16      14.267

pos = 19 ; key = tb_pol_a ;rown= 35 ,coln= 9
tb_pol_a :mu= 13.1554 ,sd= 19.4264 ,min= -20 ,max= 47.8788
                 zi_1_c1    zi_2_c2    zi_3_c3    zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9
                 _______    _______    _______    _______    _______    _______    _______

    zi_1_R1            0        -20        -20          0          0          0        -20
    zi_2_R2          -20        -20    -17.879        -20        -20        -20    -17.879
    zi_3_R3      -17.879    -17.879    -15.758    -17.879    -17.879    -17.879    -15.758
    zi_4_R4      -15.758    -15.758    -13.636    -15.758    -15.758    -15.758    -13.636
    zi_5_R5      -13.636    -11.515    -11.515    -13.636    -13.636    -13.636    -11.515
    zi_31_r31     37.273     37.273     39.394     37.273     37.273     37.273     39.394
    zi_32_r32     39.394     39.394     41.515     39.394     39.394     39.394     41.515
    zi_33_r33     41.515     41.515     43.636     41.515     41.515     41.515     43.636
    zi_34_r34     43.636     43.636     45.758     43.636     43.636     43.636     45.758
    zi_35_r35     45.758     45.758     47.879     45.758     45.758     45.758     47.879

pos = 20 ; key = tb_val ;rown= 35 ,coln= 9
tb_val :mu= 6.5837 ,sd= 6.8499 ,min= -12.0994 ,max= 14.2674
                 zi_1_c1    zi_2_c2    zi_3_c3     zi_5_c5    zi_7_c7    zi_8_c8    zi_9_c9 
                 _______    _______    ________    _______    _______    _______    ________

    zi_1_R1      -12.099    -8.1147    -0.38024    -8.3086    -12.099    -8.3086    -0.80097
    zi_2_R2      -10.437    -6.9026      0.7499    -7.0682    -11.232    -7.2947     0.40971
    zi_3_R3      -9.5896    -5.9184      1.8008    -6.0587    -10.185     -6.237      1.5278
    zi_4_R4      -8.6049    -4.9175      2.8003     -5.035    -9.0615     -5.172      2.5879
    zi_5_R5       -7.547      -3.86      3.7931     -4.006    -7.8961    -4.1077      3.6322
    zi_31_r31     11.755     12.503      13.795     12.503     11.755     12.503      13.795
    zi_32_r32     11.962     12.674      13.918     12.674     11.962     12.674      13.918
    zi_33_r33     12.164      12.84      14.037      12.84     12.164      12.84      14.037
    zi_34_r34      12.36     13.002      14.154     13.002      12.36     13.002      14.154
    zi_35_r35     12.549      13.16      14.267      13.16     12.549      13.16      14.267

pos = 21 ; key = tb_valpol_alliter ;rown= 20 ,coln= 11
tb_valpol_alliter :mu= 6.17 ,sd= 34.6715 ,min= 0 ,max= 366.5666
                 zi_1_C1    zi_2_C2    zi_3_C3     zi_6_C6     zi_9_C9     zi_10_c10    zi_11_c11
                 _______    _______    ________    ________    ________    _________    _________

    zi_1_R1      34.947     333.76            1           1           1           1            1 
    zi_2_R2      28.244     366.57      0.97143     0.97143     0.97143     0.94286      0.97143 
    zi_3_R3      23.071     120.05      0.94286     0.91429     0.91429     0.88571      0.91429 
    zi_4_R4       19.47     60.515      0.82857     0.82857         0.8         0.8      0.82857 
    zi_5_R5      16.059     36.853      0.71429     0.68571     0.68571     0.71429      0.71429 
    zi_16_r16    3.3395     6.6607     0.057143    0.057143    0.057143    0.028571     0.085714 
    zi_17_r17    2.9591     3.9195            0           0           0    0.028571     0.028571 
    zi_18_r18     2.661     5.1959     0.028571    0.028571    0.057143    0.028571     0.057143 
    zi_19_r19    2.4269     5.3547     0.028571    0.028571    0.057143    0.028571     0.085714 
    zi_20_r20    2.1847     3.9195     0.028571    0.028571    0.028571    0.057143     0.028571 

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

    ar_pol_diff_norm                1     1      20       1       54.427     104.76     3.9195    366.57
    ar_val_diff_norm                2     3      20       1       10.319     9.4342     2.1847    34.947
    cl_mt_coh                       3     4      35       9       14.648     20.696    -19.968    50.122
    cl_mt_pol_a                     4     5      35       9       13.155     19.426        -20    47.879
    cl_mt_pol_b_bridge              5     6      35       9      -2.3811     5.0158    -19.291         0
    cl_mt_pol_c                     6     7      35       9       3.5624     1.7106       0.02     6.538
    cl_mt_pol_for_borr              7     8      35       9      -0.1606    0.56727    -2.6625         0
    cl_mt_pol_for_save              8     9      35       9       16.074     15.806          0    47.879
    cl_mt_pol_inf_borr_nobridge     9    10      35       9     -0.37735    0.83417    -3.0517         0
    mt_it_b_bridge_idx             10    11      35       9      0.24127    0.42853          0         1
    mt_it_for_only_nbdg            11    12      35       9            0          0          0         0
    mt_it_fr_brrsv_nbdg            12    13      35       9     0.050794    0.21993          0         1
    mt_it_frin_brr_nbdg            13    14      35       9     0.038095    0.19173          0         1
    mt_it_frmsavng_only            14    15      35       9      0.66667    0.47215          0         1
    mt_it_inf_only_nbdg            15    16      35       9      0.18095    0.38559          0         1
    mt_pol_perc_change             16    17      20       9      0.34714    0.34206          0         1
    mt_val                         17    18      35       9       6.5837     6.8499    -12.099    14.267
    tb_pol_a                       18    19      35       9       13.155     19.426        -20    47.879
    tb_val                         19    20      35       9       6.5837     6.8499    -12.099    14.267
    tb_valpol_alliter              20    21      20      11         6.17     34.672          0    366.57

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

    ar_st_pol_names    1     2 

end
end