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IPWKZ_EVF CRS investment Percentage based grid vs Grid
One type of risky investment is the stocks kind, with constant returns to scale and full depreciation. We have the ipwkz=interpolated-percentage-grid-based-2-stage-solution. What is the point of this algorithm, vs, iwkz which seems pretty good?. When we solve the risky physical investment choice, the 2nd stage of the two problems are not very different it seems, but when the level of optimal risky investment changes smoothly as aggregate savings increase (which is the case when we have risky stocks) it makes a very big difference whether we use ipwkz or iwkz.
Below I call the two 2nd stage solution files when we have stocks and you can see clearly the percentage solution is very accurate at low levels of aggregate savings choices. The levels choices don't look visually different, but when we do percentage, which allows for zooming in to optimal choices with low w levels, you see the difference.
Compare to fsi_ipwkz_vf_vecsv_physicalk which is the companion file.
@include
close all % Production Function fl_Amean = 1.0265; fl_alpha = 1; fl_delta = 1; fl_r = 0.03; fl_w = 0; % Shock Parameter, iid shocks fl_z_rho = 0.005; fl_z_sig = 0.05; % Choice Min and Max fl_b_bd = 0; fl_w_max = 50; % Grids, level grid is upper triangle, percentage grid is full N by N % it_ak_n = 250; % it_ak_perc_n = round(sqrt(it_ak_n*(it_ak_n-1)/2+it_ak_n)); it_ak_perc_n = 177; % Display bl_graph_evf = true; bl_display_evf = false;
Solve 2nd Stage Percentage Grid k(w,z) choices, ipkwz
If it is important to get low level choices percentage levels properly, one need to use the percentage grid solution. Below. I show the percentage grid based solution when risky investment has CRS and full depreciation, the "stock" example. This investment. We only solve the second stage problem.
close all; % Not default parameters, but parameters that generate defaults it_param_set = 4; bl_input_override = true; [param_map, support_map] = ffs_ipwkz_set_default_param(it_param_set); support_map('bl_graph_evf') = bl_graph_evf; support_map('bl_display_evf') = bl_display_evf; % 177 because 177^2 = 31375 approximately, which is the grid for the level % grid below, for fair comparison param_map('fl_b_bd') = fl_b_bd; param_map('fl_w_max') = fl_w_max; param_map('fl_w_min') = param_map('fl_b_bd'); param_map('it_ak_perc_n') = it_ak_perc_n; param_map('fl_w_interp_grid_gap') = (param_map('fl_w_max')-param_map('fl_b_bd'))/param_map('it_ak_perc_n'); % note shock is log normal param_map('fl_Amean') = fl_Amean; param_map('fl_alpha') = fl_alpha; param_map('fl_delta') = fl_delta; param_map('fl_r') = fl_r; param_map('fl_w') = fl_w; % Shock Parameter, iid shocks param_map('fl_z_rho') = fl_z_rho; param_map('fl_z_sig') = fl_z_sig; [armt_map, func_map] = ffs_ipwkz_get_funcgrid(param_map, support_map, bl_input_override); % 1 for override % Generating Defaults params_group = values(armt_map, {'ar_a_meshk', 'ar_k_mesha', 'ar_z'}); [ar_a_meshk, ar_k_mesha, ar_z] = params_group{:}; params_group = values(func_map, {'f_util_standin'}); [f_util_standin] = params_group{:}; mt_val = f_util_standin(ar_z, ar_a_meshk, ar_k_mesha); % Call Program ff_ipwkz_evf(mt_val, param_map, support_map, armt_map, bl_input_override);
Warning: Ignoring extra legend entries.
Solve 2nd Stage Fixed Level Grid k(w,z) choices, akz/wkz/iwkz
This is the grid in the akz/wkz/iwkz problems, we have a fixed grid, not a percentage based grid.
% Not default parameters, but parameters that generate defaults it_param_set = 4; bl_input_override = true; [param_map, support_map] = ffs_ipwkz_set_default_param(it_param_set); support_map('bl_graph_evf') = bl_graph_evf; support_map('bl_display_evf') = bl_display_evf; param_map('fl_b_bd') = fl_b_bd; param_map('fl_w_max') = fl_w_max; param_map('fl_w_min') = param_map('fl_b_bd'); param_map('it_ak_n') = it_ak_n; param_map('it_w_n') = param_map('it_ak_n'); % this requires 250*(250-1)/2+250 = 31375 solution points % note shock is log normal param_map('fl_Amean') = fl_Amean; param_map('fl_alpha') = fl_alpha; param_map('fl_delta') = fl_delta; param_map('fl_r') = fl_r; param_map('fl_w') = fl_w; % Shock Parameter, iid shocks param_map('fl_z_rho') = fl_z_rho; param_map('fl_z_sig') = fl_z_sig; [armt_map, func_map] = ffs_ipwkz_get_funcgrid(param_map, support_map, bl_input_override); % 1 for override % Generating Defaults params_group = values(armt_map, {'ar_a_meshk', 'ar_k_mesha', 'ar_z'}); [ar_a_meshk, ar_k_mesha, ar_z] = params_group{:}; params_group = values(func_map, {'f_util_standin'}); [f_util_standin] = params_group{:}; mt_val = f_util_standin(ar_z, ar_a_meshk, ar_k_mesha); % Call Program ff_wkz_evf(mt_val, param_map, support_map, armt_map, bl_input_override);
Warning: Ignoring extra legend entries.
