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ffs_abz_get_funcgrid.m
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ffs_abz_get_funcgrid.m
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%% Generate States, Choices and Shocks Grids and Get Functions (Borr + Save)
% *back to <https://fanwangecon.github.io Fan>'s
% <https://fanwangecon.github.io/CodeDynaAsset/ Dynamic Assets Repository>
% Table of Content.*
%%
function [armt_map, func_map] = ffs_abz_get_funcgrid(varargin)
%% FFS_ABZ_GET_FUNCGRID get funcs, params, states choices shocks grids
% centralized gateway for retrieving parameters, and solution grids and
% functions. Generate asset grid, and shock grid that accomandates two
% shocks jointly: one ar1 wage shock, one iid interest rate shock.
%
% @param param_map container parameter container
%
% @param support_map container support container
%
% @param bl_input_override boolean if true varargin contained param_map and
% support_map fully overrides local default. Local default is not invoked.
% This could be important for speed if this function is getting invoked
% within certain loops. Default is 0.
%
% @return armt_map container container with states, choices and shocks
% grids that are inputs for grid based solution algorithm
%
% @return func_map container container with function handles for
% consumption cash-on-hand etc.
%
% @example
%
% it_param_set = 2;
% bl_input_override = true;
% [param_map, support_map] = ffs_abz_set_default_param(it_param_set);
% [armt_map, func_map] = ffs_abz_get_funcgrid(param_map, support_map, bl_input_override);
%
% @include
%
% * <https://fanwangecon.github.io/CodeDynaAsset/m_abz/paramfunc/html/ffs_abz_set_functions.html ffs_abz_set_functions>
% * <https://fanwangecon.github.io/CodeDynaAsset/m_abz/paramfunc/html/ffs_abz_gen_borrsave_grid.html ffs_abz_gen_borrsave_grid>
% * <https://fanwangecon.github.io/CodeDynaAsset/tools/html/fft_gen_discrete_var.html fft_gen_discrete_var>
% * <https://github.com/FanWangEcon/CodeDynaAsset/blob/master/tools/ffto_gen_tauchen_jhl.m ffto_gen_tauchen_jhl>
% * <https://github.com/FanWangEcon/CodeDynaAsset/blob/master/tools/fft_gen_grid_loglin.m fft_gen_grid_loglin>
%
% @seealso
%
% * initialize parameters: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/paramfunc/html/ffs_abz_set_default_param.html ffs_abz_set_default_param>
% * initialize functions: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/paramfunc/html/ffs_abz_set_functions.html ffs_abz_set_functions>
% * set asset grid: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/paramfunc/html/ffs_abz_gen_borrsave_grid.html ffs_abz_gen_borrsave_grid>
% * set shock borrow rate: <https://fanwangecon.github.io/CodeDynaAsset/tools/html/fft_gen_discrete_var.html fft_gen_discrete_var>
% * set shock wage: <https://github.com/FanWangEcon/CodeDynaAsset/blob/master/tools/ffto_gen_tauchen_jhl.m ffto_gen_tauchen_jhl>
% * gateway function processing grid, paramters, functions: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/paramfunc/html/ffs_abz_get_funcgrid.html ffs_abz_get_funcgrid>
%
%% Default
if (~isempty(varargin))
% override when called from outside
[param_map, support_map] = varargin{:};
else
close all
% default internal run
it_param_set = 4;
[param_map, support_map] = ffs_abz_set_default_param(it_param_set);
support_map('bl_graph_funcgrids') = true;
support_map('bl_display_funcgrids') = true;
default_maps = {param_map, support_map};
% numvarargs is the number of varagin inputted
[default_maps{1:length(varargin)}] = varargin{:};
param_map = [param_map; default_maps{1}];
support_map = [support_map; default_maps{2}];
end
%% Parse Parameters 1
% param_map asset grid
params_group = values(param_map, {'fl_b_bd', 'bl_default', 'fl_a_min', 'fl_a_max', 'bl_loglin', 'fl_loglin_threshold', 'it_a_n'});
[fl_b_bd, bl_default, fl_a_min, fl_a_max, bl_loglin, fl_loglin_threshold, it_a_n] = params_group{:};
% param_map preference
params_group = values(param_map, {'fl_crra', 'fl_c_min'});
[fl_crra, fl_c_min] = params_group{:};
% param_map borrowing and price
params_group = values(param_map, {'bl_b_is_principle', 'fl_r_save', 'fl_w'});
[bl_b_is_principle, fl_r_save, fl_w] = params_group{:};
%% Parse Parameters 2
% param_map shock income
params_group = values(param_map, {'it_z_wage_n', 'fl_z_wage_mu', 'fl_z_wage_rho', 'fl_z_wage_sig'});
[it_z_wage_n, fl_z_wage_mu, fl_z_wage_rho, fl_z_wage_sig] = params_group{:};
% param_map shock borrowing interest
params_group = values(param_map, {'st_z_r_borr_drv_ele_type', 'st_z_r_borr_drv_prb_type', 'fl_z_r_borr_poiss_mean', ...
'fl_z_r_borr_max', 'fl_z_r_borr_min', 'fl_z_r_borr_n'});
[st_z_r_borr_drv_ele_type, st_z_r_borr_drv_prb_type, fl_z_r_borr_poiss_mean, ...
fl_z_r_borr_max, fl_z_r_borr_min, fl_z_r_borr_n] = params_group{:};
%% Parse Parameters 3
% support_map controls
params_group = values(support_map, {'bl_graph_funcgrids', 'bl_display_funcgrids'});
[bl_graph_funcgrids, bl_display_funcgrids] = params_group{:};
params_group = values(support_map, {'it_display_summmat_rowmax', 'it_display_summmat_colmax'});
[it_display_summmat_rowmax, it_display_summmat_colmax] = params_group{:};
%% Get Shock: Income Shock (ar1)
[~, mt_z_wage_trans, ~, ar_z_wage] = ffto_gen_tauchen_jhl(fl_z_wage_mu,fl_z_wage_rho,fl_z_wage_sig,it_z_wage_n);
%% Get Shock: Interest Rate Shock (iid)
% get borrowing grid and probabilities
param_dsv_map = containers.Map('KeyType','char', 'ValueType','any');
param_dsv_map('st_drv_ele_type') = st_z_r_borr_drv_ele_type;
param_dsv_map('st_drv_prb_type') = st_z_r_borr_drv_prb_type;
param_dsv_map('fl_poiss_mean') = fl_z_r_borr_poiss_mean;
param_dsv_map('fl_max') = fl_z_r_borr_max;
param_dsv_map('fl_min') = fl_z_r_borr_min;
param_dsv_map('fl_n') = fl_z_r_borr_n;
[ar_z_r_borr, ar_z_r_borr_prob] = fft_gen_discrete_var(param_dsv_map, true);
% iid transition matrix
mt_z_r_borr_prob_trans = repmat(ar_z_r_borr_prob, [length(ar_z_r_borr_prob), 1]);
%% Get Shock: Mesh Shocks Together
% Kronecker product to get full transition matrix for the two shocks
mt_z_trans = kron(mt_z_r_borr_prob_trans, mt_z_wage_trans);
% mesh the shock vectors
[mt_z_wage_mesh_r_borr, mt_z_r_borr_mesh_wage] = ndgrid(ar_z_wage, ar_z_r_borr);
ar_z_r_borr_mesh_wage = mt_z_r_borr_mesh_wage(:)';
ar_z_wage_mesh_r_borr = mt_z_wage_mesh_r_borr(:)';
if (bl_display_funcgrids)
disp('----------------------------------------');
disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
disp('Borrow R Shock: ar_z_r_borr_mesh_wage');
disp('Prod/Wage Shock: mt_z_wage_mesh_r_borr');
disp('show which shock is inner and which is outter');
disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
tb_two_shocks = array2table([ar_z_r_borr_mesh_wage;...
ar_z_wage_mesh_r_borr]');
cl_col_names = ["Borrow R Shock (Meshed)", "Wage R Shock (Meshed)"];
cl_row_names = strcat('zi=', string((1:length(ar_z_r_borr_mesh_wage))));
tb_two_shocks.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);
tb_two_shocks.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);
it_row_display = it_z_wage_n*2;
disp(size(tb_two_shocks));
disp(head(tb_two_shocks, it_row_display));
disp(tail(tb_two_shocks, it_row_display));
disp('----------------------------------------');
disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
disp('Borrow Rate Transition Matrix: mt_z_r_borr_prob_trans');
disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
it_col_n_keep = 15;
it_row_n_keep = 15;
[it_row_n, it_col_n] = size(mt_z_r_borr_prob_trans);
[ar_it_cols, ar_it_rows] = fft_row_col_subset(it_col_n, it_col_n_keep, it_row_n, it_row_n_keep);
cl_st_full_rowscols = cellstr([num2str(ar_z_r_borr', 'r%3.2f')]);
tb_z_r_borr_prob_trans = array2table(round(mt_z_r_borr_prob_trans(ar_it_rows, ar_it_cols), 6));
cl_col_names = strcat('zi=', num2str(ar_it_cols'), ':', cl_st_full_rowscols(ar_it_cols));
cl_row_names = strcat('zi=', num2str(ar_it_rows'), ':', cl_st_full_rowscols(ar_it_cols));
tb_z_r_borr_prob_trans.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);
tb_z_r_borr_prob_trans.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);
disp(size(tb_z_r_borr_prob_trans));
disp(tb_z_r_borr_prob_trans);
disp('----------------------------------------');
disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
disp('Wage Prod Shock Transition Matrix: mt_z_r_borr_prob_trans');
disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
it_col_n_keep = 15;
it_row_n_keep = 15;
[it_row_n, it_col_n] = size(mt_z_wage_trans);
[ar_it_cols, ar_it_rows] = fft_row_col_subset(it_col_n, it_col_n_keep, it_row_n, it_row_n_keep);
cl_st_full_rowscols = cellstr([num2str(ar_z_wage', 'w%3.2f')]);
tb_z_wage_trans = array2table(round(mt_z_wage_trans(ar_it_rows, ar_it_cols),6));
cl_col_names = strcat('zi=', num2str(ar_it_cols'), ':', cl_st_full_rowscols(ar_it_cols));
cl_row_names = strcat('zi=', num2str(ar_it_rows'), ':', cl_st_full_rowscols(ar_it_cols));
tb_z_wage_trans.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);
tb_z_wage_trans.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);
disp(size(tb_z_wage_trans));
disp(tb_z_wage_trans);
disp('----------------------------------------');
disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
disp('Full Transition Matrix: mt_z_trans');
disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx');
it_col_n_keep = it_z_wage_n*3;
it_row_n_keep = it_z_wage_n*3;
[it_row_n, it_col_n] = size(mt_z_trans);
[ar_it_cols, ar_it_rows] = fft_row_col_subset(it_col_n, it_col_n_keep, it_row_n, it_row_n_keep);
cl_st_full_rowscols = cellstr([num2str(ar_z_r_borr_mesh_wage', 'r%3.2f;'), ...
num2str(ar_z_wage_mesh_r_borr', 'w%3.2f')]);
tb_mt_z_trans = array2table(round(mt_z_trans(ar_it_rows, ar_it_cols),6));
cl_col_names = strcat('i', num2str(ar_it_cols'), ':', cl_st_full_rowscols(ar_it_cols));
cl_row_names = strcat('i', num2str(ar_it_rows'), ':', cl_st_full_rowscols(ar_it_cols));
tb_mt_z_trans.Properties.VariableNames = matlab.lang.makeValidName(cl_col_names);
tb_mt_z_trans.Properties.RowNames = matlab.lang.makeValidName(cl_row_names);
disp(size(tb_mt_z_trans));
disp(tb_mt_z_trans);
end
%% Get Equations
[f_util_log, f_util_crra, f_util_standin, f_awithr_to_anor, f_coh, f_cons_coh, f_cons_checkcmin] = ...
ffs_abz_set_functions(fl_crra, fl_c_min, fl_r_save, fl_w);
%% Get Asset and Choice Grid
% note this requires ar_z
if (bl_loglin)
% C:\Users\fan\M4Econ\asset\grid\ff_grid_loglin.m
ar_a = fft_gen_grid_loglin(it_a_n, fl_a_max, fl_a_min, fl_loglin_threshold);
else
fl_r_borr_max = max(ar_z_r_borr);
[ar_a, fl_borr_yminbd, fl_borr_ymaxbd] = ffs_abz_gen_borrsave_grid(...
fl_b_bd, bl_default, ar_z_wage, fl_w, ...
bl_b_is_principle, fl_r_borr_max, fl_a_min, fl_a_max, it_a_n);
end
%% Store
armt_map = containers.Map('KeyType','char', 'ValueType','any');
armt_map('ar_a') = ar_a;
armt_map('mt_z_trans') = mt_z_trans;
armt_map('ar_z_r_borr_mesh_wage') = ar_z_r_borr_mesh_wage;
armt_map('ar_z_wage_mesh_r_borr') = ar_z_wage_mesh_r_borr;
armt_map('ar_z_r_borr') = ar_z_r_borr;
armt_map('ar_z_r_borr_prob') = ar_z_r_borr_prob; % Exo. Prob
func_map = containers.Map('KeyType','char', 'ValueType','any');
func_map('f_util_log') = f_util_log;
func_map('f_util_crra') = f_util_crra;
func_map('f_util_standin') = f_util_standin;
func_map('f_coh') = f_coh;
func_map('f_cons_coh') = f_cons_coh;
func_map('f_cons_checkcmin') = f_cons_checkcmin;
func_map('f_awithr_to_anor') = f_awithr_to_anor;
%% Graph: A, Shocks, COH, and Defaults
% # y-axis : coh(a,z)
% # x-axis : a
% # color: z
% # overlay: coh points points where there is default.
if (bl_graph_funcgrids)
% mesh a and and z
[mt_a_mesh_z, mt_z_mesh_a] = ndgrid(ar_a, ar_z_wage);
% cash-on-hand given a and z
mt_coh = f_coh(mt_z_mesh_a, mt_a_mesh_z);
% loop over level vs log graphs
for sub_j=1:1:1
figure('PaperPosition', [0 0 7 4]);
if (sub_j == 1)
x_mat = mt_a_mesh_z;
y_mat = mt_coh;
st_title = 'coh(a,z)';
st_ylabel = 'Cash-on-hand(a, z)';
st_xlabel = 'Asset States (Choices)';
fl_b_bd_graph = fl_b_bd;
fl_borr_yminbd_graph = fl_borr_yminbd;
fl_borr_ymaxbd_graph = fl_borr_ymaxbd;
else
x_mat = log(mt_a_mesh_z - min(min(mt_a_mesh_z)) + 1);
y_mat = log(mt_coh - min(min(mt_coh)) + 1);
st_title = 'coh(a,z) log scale';
st_ylabel = 'log(Cash-on-hand(a, z) - min(coh) + 1)';
st_xlabel = 'log(a - min(a) + 1)';
fl_b_bd_graph = log(fl_b_bd - min(min(mt_a_mesh_z)) + 1);
fl_borr_yminbd_graph = log(fl_borr_yminbd - min(min(mt_a_mesh_z)) + 1);
fl_borr_ymaxbd_graph = log(fl_borr_ymaxbd - min(min(mt_a_mesh_z)) + 1);
end
% plot main x and y
chart = plot(x_mat, y_mat, 'blue');
% add color based on z
clr = jet(numel(chart));
for m = 1:numel(chart)
set(chart(m), 'Color', clr(m,:))
end
% if (length(ar_w_level_full) <= 100)
% scatter(ar_a_meshk, ar_k_mesha, 3, 'filled', ...
% 'MarkerEdgeColor', 'b', 'MarkerFaceColor', 'b');
% end
% if (length(ar_w_level_full) <= 100)
% gf_invalid_scatter = scatter(ar_a_meshk_full(ar_bl_wkb_invalid),...
% ar_k_mesha_full(ar_bl_wkb_invalid),...
% 20, 'O', 'MarkerEdgeColor', 'black', 'MarkerFaceColor', 'black');
% end
% add various borrowing bound lines
% add 0 lines
xline(0);
yline(0);
% add 45 degrees line
hline = refline([1 0]);
hline.Color = 'k';
hline.LineStyle = ':';
hline.HandleVisibility = 'off';
hline.LineWidth = 2.5;
title(st_title)
ylabel(st_ylabel)
grid on;
grid minor;
legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/4) numel(chart)]);
legendCell = cellstr(num2str(ar_z_wage', 'z=%3.2f'));
chart(length(chart)+1) = hline;
legendCell{length(legendCell) + 1} = 'if coh(a,z) >= a';
legend2plot = [legend2plot length(legendCell)];
% if borrow plot additional borrowing bound lines
if (fl_b_bd >= 0 )
ar_legend_ele = [legend2plot];
xlabel({st_xlabel})
else
% add fl_b_bd exo borrow line
if (fl_b_bd >= min(ar_a))
xline_borrbound = xline(fl_b_bd_graph);
xline_borrbound.HandleVisibility = 'on';
xline_borrbound.LineStyle = '-';
xline_borrbound.Color = 'black';
xline_borrbound.LineWidth = 2.5;
yline_borrbound = yline(fl_b_bd_graph);
yline_borrbound.HandleVisibility = 'off';
yline_borrbound.LineStyle = '-';
yline_borrbound.Color = 'black';
yline_borrbound.LineWidth = 1;
end
xline_yminbd = xline(fl_borr_yminbd_graph);
xline_yminbd.HandleVisibility = 'on';
xline_yminbd.LineStyle = '--';
xline_yminbd.Color = 'red';
xline_yminbd.LineWidth = 2.5;
yline_yminbd = yline(fl_borr_yminbd_graph);
yline_yminbd.HandleVisibility = 'off';
yline_yminbd.LineStyle = '--';
yline_yminbd.Color = 'red';
yline_yminbd.LineWidth = 1;
if (bl_default)
xline_ymaxbd = xline(fl_borr_ymaxbd_graph);
xline_ymaxbd.HandleVisibility = 'on';
xline_ymaxbd.LineStyle = '--';
xline_ymaxbd.Color = 'blue';
xline_ymaxbd.LineWidth = 2.5;
yline_ymaxbd = yline(fl_borr_ymaxbd_graph);
yline_ymaxbd.HandleVisibility = 'on';
yline_ymaxbd.LineStyle = ':';
yline_ymaxbd.Color = 'blue';
yline_ymaxbd.LineWidth = 2.5;
end
% add bound line legends
it_addlines_cn = 0;
if (fl_b_bd >= min(ar_a))
it_addlines_cn = it_addlines_cn + 1;
chart(length(chart)+1) = xline_borrbound;
legendCell{length(legendCell) + 1} = 'exo. borrow bound fbbd';
end
it_addlines_cn = it_addlines_cn + 1;
chart(length(chart)+1) = xline_yminbd;
legendCell{length(legendCell) + 1} = 'neg min inc: -zmin*w/r (no default)';
if (bl_default)
it_addlines_cn = it_addlines_cn + 1;
chart(length(chart)+1) = xline_ymaxbd;
legendCell{length(legendCell) + 1} = 'neg max inc: -zmax*w/r (default)';
it_addlines_cn = it_addlines_cn + 1;
chart(length(chart)+1) = yline_ymaxbd;
legendCell{length(legendCell) + 1} = 'must default if coh(a,z)<dot-line';
end
% draw legend
ar_legend_ele = [legend2plot length(legendCell)-it_addlines_cn:1:length(legendCell)];
xlabel({st_xlabel 'if coh(a,z) < a, then a''(a,z)<a'})
end
% draw legends
legend(chart(unique(ar_legend_ele)), legendCell(unique(ar_legend_ele)), 'Location', 'northwest');
end
end
%% Display
if (bl_display_funcgrids)
disp('ar_z_wage');
disp(size(ar_z_wage));
disp(ar_z_wage);
disp('ar_z_r_borr');
disp(size(ar_z_r_borr));
disp(ar_z_r_borr);
fft_container_map_display(armt_map, it_display_summmat_rowmax, it_display_summmat_colmax);
fft_container_map_display(func_map, it_display_summmat_rowmax, it_display_summmat_colmax);
end
end