Risky + Safe Asset (Save + Borr + R Shock) Interpolated-Percentage (Optimized-Vectorized)

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FF_IPWKBZR_VF_VECSV solve infinite horizon exo shock + endo asset problem
Default
Parse Parameters 1
Parse Parameters 2, Asset Arrays
Parse Parameters 2, interp_coh related matrixes
Parse Parameters 3, reachable cash-on-hand
Parse Parameters 4, other asset arrays
Parse Parameters 5, Others
Initialize Output Matrixes
Initialize Convergence Conditions
Pre-calculate u(c)
Iterate Value Function
Interpolate V(coh, Z) 1: Splinterp2
Interpolate V(coh, Z) 2: griddedInterpolant(V)
Interpolate V(coh, Z) 3: Store in Cell
Interpolate V(coh, Z) 4: Single Call Full Matrix
Interpolate V(coh, Z) 5: Matrix Store
Solve Second Stage Problem k*(w,z)
Solve First Stage Problem w*(z) given k*(w,z)
A. Interpolate FULL to get k*(w_perc, z), b*(k,w) based on k*(w_level, z)
B. Calculate UPDATE u(c): u(c(coh_level, w_perc)) given k*_interp, b*_interp
C. Interpolate FULL EV(k*(coh_level, w_perc, z), w - b*|z) based on EV(k*(w_level, z))
D. Compute FULL U(coh_level, w_perc, z) over all w_perc
E. Optimize Over Choices: max_{w_perc} U(coh_level, w_perc, z)
F. Store Results
Check Tolerance and Continuation
Process Optimal Choices
Display Various Containers
Display 1 support_map
Display 2 armt_map
Display 3 param_map
Display 4 func_map
Display 5 result_map

function result_map = ff_ipwkbzr_vf_vecsv(varargin)

FF_IPWKBZR_VF_VECSV solve infinite horizon exo shock + endo asset problem

This program solves the infinite horizon dynamic savings and risky capital asset problem with some ar1 shock. This is the two step solution with interpolation and with percentage asset grids version of ff_iwkz_vf_vecsv. See that file for more descriptions.

@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:

mt_val matrix states_n by shock_n matrix of converged value function grid
mt_pol_a matrix states_n by shock_n matrix of converged policy function grid
ar_val_diff_norm array if bl_post = true it_iter_last by 1 val function difference between iteration
ar_pol_diff_norm array if bl_post = true it_iter_last by 1 policy function difference between iterations
mt_pol_perc_change matrix if bl_post = true it_iter_last by shock_n the proportion of grid points at which policy function changed between current and last iteration for each element of shock

@example

@include

Default

it_param_set = 1: quick test
it_param_set = 2: benchmark run
it_param_set = 3: benchmark profile
it_param_set = 4: press publish button

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

% parameters can be set inside ffs_ipwkbzr_set_default_param or updated here
% param_map('it_w_perc_n') = 50;
% param_map('it_ak_perc_n') = param_map('it_w_perc_n');
% param_map('fl_coh_interp_grid_gap') = 0.025;
% param_map('it_c_interp_grid_gap') = 0.001;
% param_map('fl_w_interp_grid_gap') = 0.25;
% param_map('it_w_perc_n') = 100;
% param_map('it_ak_perc_n') = param_map('it_w_perc_n');
% param_map('fl_z_r_borr_n') = 5;
% param_map('it_z_wage_n') = 15;
% param_map('it_z_n') = param_map('it_z_wage_n') * param_map('fl_z_r_borr_n');
% param_map('fl_coh_interp_grid_gap') = 0.1;
% param_map('it_c_interp_grid_gap') = 10^-4;
% param_map('fl_w_interp_grid_gap') = 0.1;

st_param_which = 'default';

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

    % default

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

    param_map('it_w_perc_n') = 20;
    param_map('it_ak_perc_n') = param_map('it_w_perc_n');
    param_map('it_z_wage_n') = 4;
    param_map('fl_z_r_borr_n') = 4;
    param_map('it_z_n') = param_map('it_z_wage_n') * param_map('fl_z_r_borr_n');

elseif ismember(st_param_which, ['ff_ipwkbz_vf_vecsv'])

    % ff_ipwkbzr_evf default
    param_map('fl_z_r_borr_min') = 0.095;
    param_map('fl_z_r_borr_max') = 0.095;
    param_map('fl_z_r_borr_n') = 1;

    param_map('fl_r_save') = 0.025;

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

end

% get armt and func map
[armt_map, func_map] = ffs_ipwkbzr_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_ipwkbzr_get_funcgrid(param_map, support_map);
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_ipwkbzr_vf_vecsv';
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, Asset Arrays

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

ar_interp_c_grid: 1 by I^c, 1st stage consumption interpolation
ar_interp_coh_grid: 1 by I^{coh}, 1st stage value function V(coh,z)
ar_w_perc: 1 by P^{W=k+b}, 1st stage w \in {w_perc(coh)} choice set
ar_w_level: 1 by I^{W=k+b}, 2nd stage k*(w,z) w grid
ar_ak_perc: 1 by P^{k and b}, 2nd stage k \in {ask_perc(w,z)} set

params_group = values(armt_map, {...
    'ar_interp_c_grid', 'ar_interp_coh_grid', ...
    'ar_w_perc', 'ar_w_level', 'ar_ak_perc'});
[ar_interp_c_grid, ar_interp_coh_grid, ...
    ar_w_perc, ar_w_level, ar_ak_perc] = params_group{:};

Parse Parameters 2, interp_coh related matrixes

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

mt_interp_coh_grid_mesh_z_wage: I^{coh} by M^w
mt_z_wage_mesh_interp_coh_grid: I^{coh} by M^w
mt_interp_coh_grid_mesh_w_perc: I^{coh} by P^{LAM=k+b}
mt_w_perc_mesh_interp_coh_grid: I^{coh} by P^{LAM=k+b}

params_group = values(armt_map, {...
    'mt_interp_coh_grid_mesh_z_wage', ...
    'mt_interp_coh_grid_mesh_w_perc', ...
    'mt_z_wage_mesh_interp_coh_grid', ...
    'mt_w_perc_mesh_interp_coh_grid', ...
    'mt_interp_coh_grid_mesh_z', 'mt_z_mesh_interp_coh_grid', ...
    'cl_mt_coh_wkb_mesh_z_r_borr', 'mt_z_mesh_coh_wkb_seg'});
[mt_interp_coh_grid_mesh_z_wage, ...
    mt_interp_coh_grid_mesh_w_perc, ...
    mt_z_wage_mesh_interp_coh_grid, ...
    mt_w_perc_mesh_interp_coh_grid, ...
    mt_interp_coh_grid_mesh_z, mt_z_mesh_interp_coh_grid, ...
    cl_mt_coh_wkb_mesh_z_r_borr, mt_z_mesh_coh_wkb_seg] = params_group{:};

Parse Parameters 3, reachable cash-on-hand

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

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

params_group = values(armt_map, {...
    'mt_coh_wkb', 'mt_coh_wkb_mesh_z_r_borr', 'mt_z_mesh_coh_wkb', 'mt_z_wage_mesh_coh_wkb'});
[mt_coh_wkb, mt_coh_wkb_mesh_z_r_borr, mt_z_mesh_coh_wkb, mt_z_wage_mesh_coh_wkb] = params_group{:};

Parse Parameters 4, other asset arrays

params_group = values(armt_map, {'ar_a_meshk', 'ar_k_mesha'});
[ar_a_meshk, ar_k_mesha] = params_group{:};

Parse Parameters 5, Others

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

% param_map
params_group = values(param_map, {'fl_crra', 'fl_beta', ...
    'fl_nan_replace', 'fl_c_min', 'bl_default', 'fl_default_wprime'});
[fl_crra, fl_beta, fl_nan_replace, fl_c_min, bl_default, fl_default_wprime] = 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{:};
params_group = values(param_map, {'it_z_n', 'fl_z_r_borr_n', 'it_z_wage_n'});
[it_z_n, fl_z_r_borr_n, it_z_wage_n] = params_group{:};
params_group = values(param_map, {'st_v_coh_z_interp_method'});
[st_v_coh_z_interp_method] = 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_time', 'bl_display_defparam', 'bl_graph_evf', 'bl_display', 'it_display_every', 'bl_post'});
[bl_profile, st_profile_path, ...
    st_profile_prefix, st_profile_name_main, st_profile_suffix, ...
    bl_time, bl_display_defparam, bl_graph_evf, bl_display, it_display_every, bl_post] = 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{:};

Initialize Output Matrixes

mt_val_cur = zeros(length(ar_interp_coh_grid),it_z_n);
mt_val = mt_val_cur - 1;
mt_pol_a = zeros(length(ar_interp_coh_grid),it_z_n);
mt_pol_a_cur = mt_pol_a - 1;
mt_pol_k = zeros(length(ar_interp_coh_grid),it_z_n);
mt_pol_k_cur = mt_pol_k - 1;
mt_pol_idx = zeros(length(ar_interp_coh_grid),it_z_n);

% We did not need these in ff_oz_vf or ff_oz_vf_vec
% see
% <https://fanwangecon.github.io/M4Econ/support/speed/partupdate/fs_u_c_partrepeat_main.html
% fs_u_c_partrepeat_main> for why store using cells.
cl_u_c_store = cell([it_z_n, 1]);
cl_c_valid_idx = cell([it_z_n, 1]);
cl_w_kstar_interp_z = cell([it_z_n, 1]);
for it_z_i = 1:it_z_n
    cl_w_kstar_interp_z{it_z_i} = zeros([length(ar_w_perc), length(ar_interp_coh_grid)]) - 1;
end

clmt_val_wkb_interpolated = cell([fl_z_r_borr_n, 1]);

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]);

Pre-calculate u(c)

Interpolation, see fs_u_c_partrepeat_main for why interpolate over u(c)

% Evaluate
if (fl_crra == 1)
    ar_interp_u_of_c_grid = f_util_log(ar_interp_c_grid);
    fl_u_cmin = f_util_log(fl_c_min);
else
    ar_interp_u_of_c_grid = f_util_crra(ar_interp_c_grid);
    fl_u_cmin = f_util_crra(fl_c_min);
end
ar_interp_u_of_c_grid(ar_interp_c_grid <= fl_c_min) = fl_u_cmin;

% Get Interpolant
f_grid_interpolant_spln = griddedInterpolant(ar_interp_c_grid, ar_interp_u_of_c_grid, 'spline', 'nearest');

Iterate Value Function

Loop solution with 4 nested loops

loop 1: over exogenous states
loop 2: over endogenous states
loop 3: over choices
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

% Value Function Iteration
while bl_vfi_continue

    it_iter = it_iter + 1;