This is the example vignette for function: snw_vfi_main from the PrjOptiSNW Package. This function solves for policy function fully iteratively using matlab minimizer. Small Solution Analysis.This produces the same result as snw_vfi_main_bisec_vec, except slower. The purpose of this function is to confirm that the results from snw_vfi_main_bisec_vec is correct.
Call the function with defaults parameters.
mp_param = snw_mp_param('default_small');
[V_VFI,ap_VFI,cons_VFI,mp_valpol_more] = snw_vfi_main(mp_param);
SNW_VFI_MAIN: Finished Age Group:18 of 18
SNW_VFI_MAIN: Finished Age Group:17 of 18
SNW_VFI_MAIN: Finished Age Group:16 of 18
SNW_VFI_MAIN: Finished Age Group:15 of 18
SNW_VFI_MAIN: Finished Age Group:14 of 18
SNW_VFI_MAIN: Finished Age Group:13 of 18
SNW_VFI_MAIN: Finished Age Group:12 of 18
SNW_VFI_MAIN: Finished Age Group:11 of 18
SNW_VFI_MAIN: Finished Age Group:10 of 18
SNW_VFI_MAIN: Finished Age Group:9 of 18
SNW_VFI_MAIN: Finished Age Group:8 of 18
SNW_VFI_MAIN: Finished Age Group:7 of 18
SNW_VFI_MAIN: Finished Age Group:6 of 18
SNW_VFI_MAIN: Finished Age Group:5 of 18
SNW_VFI_MAIN: Finished Age Group:4 of 18
SNW_VFI_MAIN: Finished Age Group:3 of 18
SNW_VFI_MAIN: Finished Age Group:2 of 18
SNW_VFI_MAIN: Finished Age Group:1 of 18
Elapsed time is 515.239525 seconds.
Completed SNW_VFI_MAIN;SNW_MP_PARAM=default_small;SNW_MP_CONTROL=default_baseDefine the matrix dimensions names and dimension vector values. Policy and Value Functions share the same ND dimensional structure.
% Grids:
age_grid = [19, 22:5:97, 100];
agrid = mp_param('agrid')';
eta_H_grid = mp_param('eta_H_grid')';
eta_S_grid = mp_param('eta_S_grid')';
ar_st_eta_HS_grid = string(cellstr([num2str(eta_H_grid', 'hz=%3.2f;'), num2str(eta_S_grid', 'wz=%3.2f')]));
edu_grid = [0,1];
marry_grid = [0,1];
kids_grid = (1:1:mp_param('n_kidsgrid'))';
% NaN(n_jgrid,n_agrid,n_etagrid,n_educgrid,n_marriedgrid,n_kidsgrid);
cl_mp_datasetdesc = {};
cl_mp_datasetdesc{1} = containers.Map({'name', 'labval'}, {'age', age_grid});
cl_mp_datasetdesc{2} = containers.Map({'name', 'labval'}, {'savings', agrid});
cl_mp_datasetdesc{3} = containers.Map({'name', 'labval'}, {'eta', 1:length(eta_H_grid)});
cl_mp_datasetdesc{4} = containers.Map({'name', 'labval'}, {'edu', edu_grid});
cl_mp_datasetdesc{5} = containers.Map({'name', 'labval'}, {'marry', marry_grid});
cl_mp_datasetdesc{6} = containers.Map({'name', 'labval'}, {'kids', kids_grid});First, analyze Savings Levels and Shocks, Aggregate Over All Others, and do various other calculations.
% Generate some Data
mp_support_graph = containers.Map('KeyType', 'char', 'ValueType', 'any');
mp_support_graph('cl_st_xtitle') = {'Savings States, a'};
mp_support_graph('st_legend_loc') = 'best';
mp_support_graph('bl_graph_logy') = true; % do not logMEAN(VAL(A,Z)), MEAN(AP(A,Z)), MEAN(C(A,Z))
Tabulate value and policies along savings and shocks:
% Set
% NaN(n_jgrid,n_agrid,n_etagrid,n_educgrid,n_marriedgrid,n_kidsgrid);
ar_permute = [1,4,5,6,3,2];
% Value Function
tb_az_v = ff_summ_nd_array("MEAN(VAL(A,Z))", V_VFI, true, ["mean"], 4, 1, cl_mp_datasetdesc, ar_permute);
xxx MEAN(VAL(A,Z)) xxxxxxxxxxxxxxxxxxxxxxxxxxx
group savings mean_eta_1 mean_eta_2 mean_eta_3 mean_eta_4 mean_eta_5
_____ _________ __________ __________ __________ __________ __________
1 0 -17.721 -9.4697 -4.6571 -1.7924 -0.23581
2 0.0097656 -17.284 -9.3219 -4.5706 -1.7215 -0.16909
3 0.078125 -15.196 -8.4993 -4.1004 -1.3514 0.17326
4 0.26367 -11.907 -7.0394 -3.3075 -0.78441 0.67194
5 0.625 -8.4194 -5.2786 -2.3615 -0.19487 1.1461
6 1.2207 -5.393 -3.5129 -1.3918 0.35026 1.5392
7 2.1094 -3.0352 -1.9483 -0.50577 0.84352 1.8533
8 3.3496 -1.2918 -0.66899 0.26902 1.2874 2.1081
9 5 -0.030416 0.32906 0.92609 1.6707 2.3215
10 7.1191 0.87699 1.0879 1.4656 1.9934 2.5052
11 9.7656 1.5329 1.6594 1.8992 2.267 2.6661
12 12.998 2.0119 2.0896 2.2435 2.4983 2.8056
13 16.875 2.366 2.4149 2.5152 2.6918 2.9253
14 21.455 2.6312 2.6629 2.7294 2.8524 3.0281
15 26.797 2.8329 2.8539 2.8987 2.9852 3.1169
16 32.959 2.9883 3.0025 3.0334 3.0948 3.1935
17 40 3.1097 3.1195 3.1411 3.1853 3.2595
18 47.979 3.2056 3.2125 3.2279 3.2601 3.3161
19 56.953 3.2822 3.2872 3.2984 3.322 3.3647
20 66.982 3.3441 3.3478 3.356 3.3736 3.4063
21 78.125 3.3947 3.3974 3.4035 3.4168 3.442
22 90.439 3.4363 3.4383 3.4429 3.4531 3.4727
23 103.98 3.4708 3.4724 3.4759 3.4837 3.4991
24 118.82 3.4997 3.5009 3.5036 3.5097 3.5218
25 135 3.5241 3.525 3.5271 3.5319 3.5415
% Aprime Choice
tb_az_ap = ff_summ_nd_array("MEAN(AP(A,Z))", ap_VFI, true, ["mean"], 4, 1, cl_mp_datasetdesc, ar_permute);
xxx MEAN(AP(A,Z)) xxxxxxxxxxxxxxxxxxxxxxxxxxx
group savings mean_eta_1 mean_eta_2 mean_eta_3 mean_eta_4 mean_eta_5
_____ _________ __________ __________ __________ __________ __________
1 0 3.2168e-05 0.0034996 0.049878 0.24382 0.89299
2 0.0097656 0.00055444 0.0053208 0.053281 0.24787 0.89865
3 0.078125 0.021863 0.029684 0.083029 0.28062 0.93971
4 0.26367 0.13322 0.14773 0.20012 0.3888 1.0591
5 0.625 0.39134 0.41043 0.45332 0.64573 1.3087
6 1.2207 0.84131 0.86393 0.91226 1.0928 1.745
7 2.1094 1.5303 1.5542 1.6156 1.7559 2.3963
8 3.3496 2.4876 2.5118 2.573 2.6876 3.3398
9 5 3.7642 3.7887 3.8498 3.9922 4.592
10 7.1191 5.4275 5.4525 5.5145 5.6929 6.1933
11 9.7656 7.4794 7.5043 7.5679 7.7532 8.1877
12 12.998 9.9124 9.9329 9.9956 10.186 10.627
13 16.875 12.928 12.95 13.005 13.196 13.715
14 21.455 16.529 16.548 16.604 16.783 17.374
15 26.797 20.601 20.618 20.668 20.837 21.462
16 32.959 25.307 25.325 25.37 25.525 26.151
17 40 30.667 30.69 30.742 30.886 31.487
18 47.979 36.761 36.782 36.841 36.999 37.562
19 56.953 43.773 43.795 43.847 44.012 44.56
20 66.982 51.605 51.628 51.688 51.85 52.403
21 78.125 59.955 59.978 60.038 60.211 60.768
22 90.439 69.267 69.29 69.352 69.528 70.097
23 103.98 79.753 79.774 79.834 80.008 80.586
24 118.82 91.116 91.14 91.201 91.367 91.942
25 135 103.47 103.49 103.55 103.72 104.29
% Consumption Choices
tb_az_c = ff_summ_nd_array("MEAN(C(A,Z))", cons_VFI, true, ["mean"], 4, 1, cl_mp_datasetdesc, ar_permute);
xxx MEAN(C(A,Z)) xxxxxxxxxxxxxxxxxxxxxxxxxxx
group savings mean_eta_1 mean_eta_2 mean_eta_3 mean_eta_4 mean_eta_5
_____ _________ __________ __________ __________ __________ __________
1 0 0.30273 0.43104 0.68779 1.2165 2.3367
2 0.0097656 0.31374 0.44069 0.69581 1.2239 2.3424
3 0.078125 0.37308 0.49662 0.74605 1.2709 2.3811
4 0.26367 0.48039 0.59638 0.846 1.3793 2.478
5 0.625 0.64735 0.75736 1.0152 1.5439 2.6496
6 1.2207 0.89648 1.0013 1.2519 1.7913 2.9071
7 2.1094 1.2479 1.3498 1.5854 2.1634 3.2903
8 3.3496 1.7393 1.8394 2.0734 2.6754 3.7896
9 5 2.3872 2.4859 2.7182 3.2909 4.4564
10 7.1191 3.1917 3.289 3.5191 4.0542 5.3181
11 9.7656 4.2188 4.3155 4.543 5.07 6.3986
12 12.998 5.5439 5.6447 5.8722 6.3933 7.7142
13 16.875 7.0334 7.133 7.3676 7.8866 9.1285
14 21.455 8.754 8.8551 9.0887 9.6188 10.789
15 26.797 10.886 10.989 11.228 11.768 12.903
16 32.959 13.336 13.438 13.682 14.235 15.368
17 40 16.151 16.249 16.485 17.049 18.207
18 47.979 19.321 19.42 19.649 20.2 21.394
19 56.953 22.728 22.827 23.062 23.605 24.816
20 66.982 26.539 26.636 26.864 27.41 28.615
21 78.125 31.124 31.221 31.45 31.985 33.186
22 90.439 36.108 36.205 36.431 36.963 38.152
23 103.98 41.345 41.444 41.673 42.206 43.386
24 118.82 47.202 47.298 47.525 48.066 49.248
25 135 53.632 53.731 53.962 54.496 55.685