1 2019 Age, Income, Kids, Marry EV and EC of One Check
This is the example vignette for function: snw_evuvw19_jmky from the PrjOptiSNW Package. 2019 integrated over VU and VW
1.1 Test SNW_EVUVW19_JMKY Defaults Dense
Set Parameters
Call the function with defaults.
clear all;
st_solu_type = 'bisec_vec';
% Solve the VFI Problem and get Value Function
% mp_params = snw_mp_param('default_tiny');
% mp_params = snw_mp_param('default_dense');
mp_params = snw_mp_param('default_docdense');
mp_params('beta') = 0.95;
mp_controls = snw_mp_control('default_test');
% set Unemployment Related Variables
xi=0.5; % Proportional reduction in income due to unemployment (xi=0 refers to 0 labor income; xi=1 refers to no drop in labor income)
b=0; % Unemployment insurance replacement rate (b=0 refers to no UI benefits; b=1 refers to 100 percent labor income replacement)
TR=100/58056; % Value of a welfare check (can receive multiple checks). TO DO: Update with alternative values
mp_params('xi') = xi;
mp_params('b') = b;
mp_params('TR') = TR;
% Check Numbers
% n_incgrid=201; % Number of income groups
% n_incgrid_aux=round(0.75*n_incgrid);
% inc_grid1=linspace(0,4,n_incgrid_aux)'; % 4 refers to 4*58056=232224 dollars in 2012USD
% inc_grid=[inc_grid1;linspace(4+((7-4)/(n_incgrid-n_incgrid_aux)),7,n_incgrid-n_incgrid_aux)']; % 7 refers to 7*58056=406392 dollars in 2012USD
n_incgrid=201; % Number of income groups
inc_grid=linspace(0,7,n_incgrid)';
mp_params('n_incgrid') = n_incgrid;
mp_params('inc_grid') = inc_grid;
% Solve for Unemployment Values
mp_controls('bl_print_vfi') = false;
mp_controls('bl_print_vfi_verbose') = false;
mp_controls('bl_print_ds') = false;
mp_controls('bl_print_ds_verbose') = false;
mp_controls('bl_print_precompute') = false;
mp_controls('bl_print_precompute_verbose') = false;
mp_controls('bl_print_a4chk') = false;
mp_controls('bl_print_a4chk_verbose') = false;
mp_controls('bl_print_evuvw20_jaeemk') = false;
mp_controls('bl_print_evuvw20_jaeemk_verbose') = false;
mp_controls('bl_print_evuvw19_jaeemk') = false;
mp_controls('bl_print_evuvw19_jaeemk_verbose') = false;
mp_controls('bl_print_evuvw19_jmky') = false;1.2 Solve VFI and Distributon
% Solve the Model to get V working and unemployed
[V_ss,ap_ss,cons_ss,mp_valpol_more_ss] = snw_vfi_main_bisec_vec(mp_params, mp_controls);
Completed SNW_VFI_MAIN_BISEC_VEC;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time=533.8122
inc_VFI = mp_valpol_more_ss('inc_VFI');
spouse_inc_VFI = mp_valpol_more_ss('spouse_inc_VFI');
total_inc_VFI = inc_VFI + spouse_inc_VFI;
% COVID year tax
mp_params('a2_covidyr') = mp_params('a2_covidyr_manna_heaven');
% 2020 V and C same as V_SS and cons_ss if tax the same
if (mp_params('a2_covidyr') == mp_params('a2'))
% mana from heaven
V_ss_2020 = V_ss;
cons_ss_2020 = cons_ss;
else
% change xi and b to for people without unemployment shock
% solving for employed but 2020 tax results
% a2_covidyr > a2, we increased tax in 2020 to pay for covid and other
% costs resolve for both employed and unemployed
xi = mp_params('xi');
b = mp_params('b');
mp_params('xi') = 1;
mp_params('b') = 0;
[V_ss_2020,~,cons_ss_2020,~] = snw_vfi_main_bisec_vec(mp_params, mp_controls, V_ss);
mp_params('xi') = xi;
mp_params('b') = b;
end
% Solve unemployment
[V_unemp_2020,~,cons_unemp_2020] = snw_vfi_main_bisec_vec(mp_params, mp_controls, V_ss);
Completed SNW_VFI_MAIN_BISEC_VEC 1 Period Unemp Shock;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time=328.3878
[Phi_true] = snw_ds_main(mp_params, mp_controls, ap_ss, cons_ss, mp_valpol_more_ss);
Completed SNW_DS_MAIN;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time=1486.9836
% Get Matrixes
cl_st_precompute_list = {'a', ...
'inc', 'inc_unemp', 'spouse_inc', 'spouse_inc_unemp', 'ref_earn_wageind_grid', ...
'ap_idx_lower_ss', 'ap_idx_higher_ss', 'ap_idx_lower_weight_ss', ...
'inc_tot_ygroup_grid'};
mp_controls('bl_print_precompute_verbose') = false;1.3 Pre-Compute Matrixes and YMKY Mass
% Pre-compute
[mp_precompute_res] = snw_hh_precompute(mp_params, mp_controls, cl_st_precompute_list, ap_ss, Phi_true);
Wage quintile cutoffs=0.4645 0.71528 1.0335 1.5632
Completed SNW_HH_PRECOMPUTE;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time cost=405.413
inc_tot_ygroup_grid = mp_precompute_res('inc_tot_ygroup_grid');
% YMKY Mass
[Phi_true_jmky] = snw_evuvw19_jmky_mass(mp_params, mp_controls, Phi_true, inc_tot_ygroup_grid);
SNW_EVUVW19_JMKY_MASS Start
Completed SNW_EVUVW19_JMKY_MASS;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time=12.0748
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_outcomes ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ __________ ____ _________ ______ __________ __________ ________ ___ _________
Phi_true 1 1 6 4.37e+07 83 5.265e+05 45.793 1.0479e-06 1.5274e-05 14.576 0 0.0062366
Phi_true_jmky 2 2 4 1.6482e+05 82 2010 45.787 0.0002778 0.0011622 4.1836 0 0.0508021.4 Solve for 2019 Evuvw With 0 and 2 Checks
Zero checks:
% Solve ev 19 JAEEMK
welf_checks = 0;
[ev19_jaeemk_check0, ec19_jaeemk_check0, ev20_jaeemk_check0, ec20_jaeemk_check0] = ...
snw_evuvw19_jaeemk(...
welf_checks, st_solu_type, mp_params, mp_controls, ...
V_ss_2020, cons_ss_2020, V_unemp_2020, cons_unemp_2020, mp_precompute_res);
Completed SNW_A4CHK_WRK_BISEC_VEC;SNW_MP_PARAM=st_biden_or_trump_undefined;welf_checks=0;TR=0.0017225;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time cost=70.147
Completed SNW_A4CHK_UNEMP_BISEC_VEC;welf_checks=0;TR=0.0017225;xi=0.5;b=0;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time cost=69.9973
Completed SNW_EVUVW20_JAEEMK;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;timeEUEC=8.0308
Completed SNW_EVUVW19_JAEEMK;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time=4262.1969
% Solve ev 19 JMKY
[ev19_jmky_check0, ec19_jmky_check0] = snw_evuvw19_jmky(...
mp_params, mp_controls, ...
ev19_jaeemk_check0, ec19_jaeemk_check0, ...
Phi_true, Phi_true_jmky, inc_tot_ygroup_grid);
Completed SNW_EVUVW19_JMKY;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time=18.7645
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_outcomes ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ __________ ____ _________ ___________ __________ __________ ________ ________ _________
Phi_true 1 1 6 4.37e+07 83 5.265e+05 45.793 1.0479e-06 1.5274e-05 14.576 0 0.0062366
Phi_true_jmky 2 2 4 1.6482e+05 82 2010 45.787 0.0002778 0.0011622 4.1836 0 0.050802
ec19_jaeemk 3 3 6 4.3173e+07 82 5.265e+05 1.9659e+08 4.5535 5.3256 1.1696 0.032905 64.526
ec19_jmky 4 4 4 1.6482e+05 82 2010 3.4206e+05 2.0753 2.1275 1.0251 0 15.419
ev19_jaeemk 5 5 6 4.3173e+07 82 5.265e+05 -6.521e+08 -15.104 21.412 -1.4176 -486.8 -0.01597
ev19_jmky 6 6 4 1.6482e+05 82 2010 -2.1785e+06 -13.217 18.17 -1.3747 -360.71 0Two checks:
% Solve ev 19 JAEEMK
welf_checks = 1;
[ev19_jaeemk_check2, ec19_jaeemk_check2, ev20_jaeemk_check2, ec20_jaeemk_check2] = ...
snw_evuvw19_jaeemk(...
welf_checks, st_solu_type, mp_params, mp_controls, ...
V_ss_2020, cons_ss_2020, V_unemp_2020, cons_unemp_2020, mp_precompute_res);
Completed SNW_A4CHK_WRK_BISEC_VEC;SNW_MP_PARAM=st_biden_or_trump_undefined;welf_checks=1;TR=0.0017225;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time cost=70.5745
Completed SNW_A4CHK_UNEMP_BISEC_VEC;welf_checks=1;TR=0.0017225;xi=0.5;b=0;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time cost=71.0724
Completed SNW_EVUVW20_JAEEMK;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;timeEUEC=7.8471
Completed SNW_EVUVW19_JAEEMK;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time=4279.3292
% Solve ev 19 JMKY
[ev19_jmky_check2, ec19_jmky_check2] = snw_evuvw19_jmky(...
mp_params, mp_controls, ...
ev19_jaeemk_check2, ec19_jaeemk_check2, ...
Phi_true, Phi_true_jmky, inc_tot_ygroup_grid);
Completed SNW_EVUVW19_JMKY;SNW_MP_PARAM=default_docdense;SNW_MP_CONTROL=default_test;time=19.3794
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_outcomes ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ __________ ____ _________ ___________ __________ __________ ________ ________ _________
Phi_true 1 1 6 4.37e+07 83 5.265e+05 45.793 1.0479e-06 1.5274e-05 14.576 0 0.0062366
Phi_true_jmky 2 2 4 1.6482e+05 82 2010 45.787 0.0002778 0.0011622 4.1836 0 0.050802
ec19_jaeemk 3 3 6 4.3173e+07 82 5.265e+05 1.966e+08 4.5538 5.3256 1.1695 0.034479 64.528
ec19_jmky 4 4 4 1.6482e+05 82 2010 3.421e+05 2.0756 2.1275 1.025 0 15.419
ev19_jaeemk 5 5 6 4.3173e+07 82 5.265e+05 -6.5176e+08 -15.096 21.377 -1.416 -482.41 -0.01597
ev19_jmky 6 6 4 1.6482e+05 82 2010 -2.1774e+06 -13.211 18.125 -1.372 -358.58 0Differences between Checks in Expected Value and Expected Consumption
mn_V_U_gain_check = ev19_jmky_check2 - ev19_jmky_check0;
mn_MPC_U_gain_share_check = (ec19_jmky_check2 - ec19_jmky_check0)./(welf_checks*mp_params('TR'));1.5 Dense Param Results Define Frames
Define the matrix dimensions names and dimension vector values. Policy and Value Functions share the same ND dimensional structure.
% Grids:
age_grid = 18:99;
marry_grid = [0,1];
kids_grid = (1:1:mp_params('n_kidsgrid'))';
inc_grid = mp_params('inc_grid');
cl_mp_datasetdesc = {};
cl_mp_datasetdesc{1} = containers.Map({'name', 'labval'}, {'age', age_grid});
cl_mp_datasetdesc{2} = containers.Map({'name', 'labval'}, {'marry', marry_grid});
cl_mp_datasetdesc{3} = containers.Map({'name', 'labval'}, {'kids', kids_grid});
cl_mp_datasetdesc{4} = containers.Map({'name', 'labval'}, {'ylower', inc_grid});1.6 Analyze Marginal Value and MPC over Y(a,eta), Conditional On Kids, Marry, Age, Education
Income is generated by savings and shocks, what are the income levels generated by all the shock and savings points conditional on kids, marital status, age and educational levels. Plot on the Y axis MPC, and plot on the X axis income levels, use colors to first distinguish between different a levels, then use colors to distinguish between different eta levles.
Set Up date, Select Age 37, unmarried, no kids, lower education:
% NaN(n_jgrid,n_agrid,n_etagrid,n_educgrid,n_marriedgrid,n_kidsgrid);
% 38 year old, unmarried, no kids, lower educated
% Only Household Head Shock Matters so select up to 'n_eta_H_grid'
mn_V_W_gain_check_use = ev19_jmky_check2 - ev19_jmky_check0;
mn_C_W_gain_check_use = ec19_jmky_check2 - ec19_jmky_check0;Select Age, Education, Marital, Kids Count:s
% Selections
it_age = 21; % +18
it_marital = 1; % 1 = unmarried
it_kids = 1; % 1 = kids is zero
% Select: NaN(n_jgrid-1,n_marriedgrid,n_kidsgrid,n_incgrid);
mn_C_W_gain_check_jemk = mn_C_W_gain_check_use(it_age, it_marital, it_kids, :);
mn_V_W_gain_check_jemk = mn_V_W_gain_check_use(it_age, it_marital, it_kids, :);
% Reshape, so shock is the first dim, a is the second
ar_C_W_gain_check_jemk = mn_C_W_gain_check_jemk(:);
ar_V_W_gain_check_jemk = mn_V_W_gain_check_jemk(:);Marginal Value Gains, Color as Shock, Conditional on Age, Marital, Kids, and Education
How do shocks and a impact marginal value. First plot one asset level, variation comes only from increasingly higher shocks:
figure();
scatter(inc_grid, ar_V_W_gain_check_jemk, 100);
title({'MN\_V\_W\_GAIN\_CHECK(Y(A, eta)), Lowest A, J38M0E0K0', ...
'Each Circle is A Different Shock Level'});
xlabel('Y(a,eta) = Spouse + Household head Income Joint');
ylabel('MN\_V\_W\_GAIN\_CHECK(A, eta)');
grid on;
grid minor;
figure();
it_shock = 1;
scatter((inc_grid), log(ar_V_W_gain_check_jemk), 100);
title({'MN\_V\_W\_GAIN\_CHECK(Y(A, eta)), Lowest A, J38M0E0K0', ...
'Each Circle is A Different Shock Level'});
xlabel(' of Y(a,eta) = Spouse + Household head Income Joint');
ylabel(' of MN\_V\_W\_GAIN\_CHECK(A, eta)');
grid on;
grid minor;
Marginal Consumption Gains, Color as Shock, Conditional on Age, Marital, Kids, and Education
Plot all asset levels:
figure();
scatter(inc_grid, ar_C_W_gain_check_jemk, 100);
title({'(MN\_C\_W\_GAIN\_CHECK(Y,eta)), All A (Savings) Levels, J38M0E0K0', ...
'Color Represent different A Savings State, Circle-Group=Shock'});
xlabel('income(a,eps)');
ylabel('MN\_C\_W\_GAIN\_CHECK(EM,J)');
grid on;
grid minor;
figure();
scatter((inc_grid), log(ar_C_W_gain_check_jemk), 100);
title({'(MN\_C\_W\_GAIN\_CHECK(Y,eta)), All A (Savings) Levels, J38M0E0K0', ...
'Color Represent different A Savings State, Circle-Group=Shock'});
xlabel('log of income(a,eps)');
ylabel('log of (MN\_V\_W\_GAIN\_CHECK(EM,J))');
grid on;
grid minor;