2nd Stage Optimization for Risky + Safe Asset + 2 Stage Solution
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Contents
- FF_WKZ_EVF solves the k' vs b' problem given aggregate savings
- Default
- Parse Parameters
- Integrate E(V(coh(k',b'), z')|z, w)
- Reshape E(V(coh,z'|z,w)) to allow for maxing
- Maximize max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)) optimal value and index
- Reindex K' and B' Choices for each State at the Optimal w'=k'+b' choice
- Generate Optimal K' and B' on w(coh) percentage grid from w level grid
- Graph
- Graph 1, V and EV
- Graph 2, max(EV)
- Graph 3, max(EV), color regions, borrow save
- Graph 4, Optimal K' and B' Levels
function [mt_ev_condi_z_max, mt_ev_condi_z_max_idx, mt_ev_condi_z_max_kp, mt_ev_condi_z_max_bp] = ff_wkz_evf(varargin)
FF_WKZ_EVF solves the k' vs b' problem given aggregate savings
Rather than solving the two asset problem in one shot. We can separate the problem into two stages. This is the second stage of the problem. Here we find the optimal k' choice given w=k'+b'. max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)) is the maximization problem. Conditional on shock and w. Note that this problem is not conditional on cash-on-hand today, but conditional on w. We do not need to know the cash-on-hand in the current period to find the optimal k' choice conditional on w.
This means we can solve for the optimal relative allocation of risky and safe asset conditional on total savings. Note that we still need the value function mt_val, which is required to find EV.
@param mt_val matrix state_n ((I-1)*J/2+I) by shock_n. This is the value matrix each row is a feasible reachable state given the choice vectors/matrix and each column is a shock state.
@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
@return mt_ev_condi_z_max matrix choice_w_n by shock_n max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)) conditional on z and w, at the optimal k' choice (w=k'+b') what is the expected utility? This is the value result from the 2nd stage problem. Note the result integrates over z'.
@return mt_ev_condi_z_max_idx matrix choice_w_n by shock_n this is the argmax from max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)). Given the vector of k' choices, which index maximized conditional on z and w integrating over z'/
@return mt_ev_condi_z_max_kp matrix choice_w_n by shock_n the k' choice at max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w))
@return mt_ev_condi_z_max_bp matrix choice_w_n by shock_n the b'=w-k' choice at max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w))
@example
@include
Default
params_len = length(varargin); bl_input_override = 0; if (params_len == 5) bl_input_override = varargin{5}; end if (bl_input_override) % override when called from outside [mt_val, param_map, support_map, armt_map, ~] = varargin{:}; else clear all; close all; % Not default parameters, but parameters that generate defaults it_param_set = 4; bl_input_override = true; [param_map, support_map] = ffs_akz_set_default_param(it_param_set); support_map('bl_graph_evf') = true; support_map('bl_display_evf') = true; [armt_map, func_map] = ffs_akz_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); end
Parse Parameters
params_group = values(armt_map, {'mt_z_trans', 'ar_z',...
'ar_w', 'mt_k_wth_na', 'ar_k_mw_wth_na', 'ar_a_mw_wth_na'});
[mt_z_trans, ar_z, ar_w, mt_k_wth_na, ar_k_mw_wth_na, ar_a_mw_wth_na] = params_group{:};
params_group = values(param_map, {'it_z_n', 'fl_nan_replace', 'fl_b_bd'});
[it_z_n, fl_nan_replace, fl_b_bd] = params_group{:};
params_group = values(support_map, {'bl_graph_onebyones','bl_display_evf', 'bl_graph_evf'});
[bl_graph_onebyones, bl_display_evf, bl_graph_evf] = params_group{:};
params_group = values(support_map, {'bl_img_save', 'st_img_path', 'st_img_prefix', 'st_img_name_main', 'st_img_suffix'});
[bl_img_save, st_img_path, st_img_prefix, st_img_name_main, st_img_suffix] = params_group{:};
% append function name
st_func_name = 'ff_wkz_evf';
st_img_name_main = [st_func_name st_img_name_main];
Integrate E(V(coh(k',b'), z')|z, w)
Each column for a different state z, each value E(V(coh,z')|z) integrated already Here, each column is a current z, more to right higher EV dim(mt_ev_condi_z): Q by M Note that: mt_ev_condi_z = mt_val*mt_z_trans' is a mistake, that would be what we do in the ffs_akz_set_functions code where we loop over current z, and for each current z, grab out a particular row from the mt_z_trans that corresponds to a current shock's transition into all future states.
here, each column of mt_val corresponds to a state z, think of that as future state z. The input mt_val is V(coh, z), we need to integrate to get E(V(coh,z')|z).
mt_ev_condi_z = mt_val*mt_z_trans'; if (bl_display_evf) disp('mt_ev_condi_z: Q by M'); disp(size(mt_ev_condi_z)); summary(array2table(mt_ev_condi_z)); end
mt_ev_condi_z: Q by M
1275 15
Variables:
mt_ev_condi_z1: 1275×1 double
Values:
Min -0.81272
Median 3.5842
Max 3.9521
mt_ev_condi_z2: 1275×1 double
Values:
Min -0.81272
Median 3.5886
Max 3.9533
mt_ev_condi_z3: 1275×1 double
Values:
Min -0.81272
Median 3.5923
Max 3.9548
mt_ev_condi_z4: 1275×1 double
Values:
Min -0.81272
Median 3.5971
Max 3.9567
mt_ev_condi_z5: 1275×1 double
Values:
Min -0.81272
Median 3.6021
Max 3.9589
mt_ev_condi_z6: 1275×1 double
Values:
Min -0.81272
Median 3.6063
Max 3.9615
mt_ev_condi_z7: 1275×1 double
Values:
Min -0.81272
Median 3.6112
Max 3.9647
mt_ev_condi_z8: 1275×1 double
Values:
Min -0.81272
Median 3.6166
Max 3.9684
mt_ev_condi_z9: 1275×1 double
Values:
Min -0.81272
Median 3.6269
Max 3.9729
mt_ev_condi_z10: 1275×1 double
Values:
Min -0.81272
Median 3.6386
Max 3.9782
mt_ev_condi_z11: 1275×1 double
Values:
Min -0.81272
Median 3.6488
Max 3.9844
mt_ev_condi_z12: 1275×1 double
Values:
Min -0.81272
Median 3.6622
Max 3.9919
mt_ev_condi_z13: 1275×1 double
Values:
Min -0.81272
Median 3.6752
Max 4.0006
mt_ev_condi_z14: 1275×1 double
Values:
Min -0.81272
Median 3.6865
Max 4.0106
mt_ev_condi_z15: 1275×1 double
Values:
Min -0.81272
Median 3.6915
Max 4.0212
Reshape E(V(coh,z'|z,w)) to allow for maxing
dim(mt_ev_condi_z): IxJ by M
[it_mt_bp_rown, it_mt_bp_coln] = size(mt_k_wth_na); mt_ev_condi_z_full = zeros(it_mt_bp_rown*it_mt_bp_coln, it_z_n); mt_ev_condi_z_full(~isnan(ar_k_mw_wth_na),:) = mt_ev_condi_z; mt_ev_condi_z_full(isnan(ar_k_mw_wth_na),:) = fl_nan_replace; mt_ev_condi_z_full = reshape(mt_ev_condi_z_full, [it_mt_bp_rown, it_mt_bp_coln*it_z_n]);
Maximize max_{k'}(E(V(coh(k',b'=w-k'),z'|z,w)) optimal value and index
Maximization, find optimal k'/b' combination given z and w=k'+b'
[ar_ev_condi_z_max, ar_ev_condi_z_max_idx] = max(mt_ev_condi_z_full); mt_ev_condi_z_max = reshape(ar_ev_condi_z_max, [it_mt_bp_coln, it_z_n]); mt_ev_condi_z_max_idx = reshape(ar_ev_condi_z_max_idx, [it_mt_bp_coln, it_z_n]); if (bl_display_evf) disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_full: J by IxM'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_full)); % disp(head(array2table(mt_ev_condi_z_full), 20)); % disp(tail(array2table(mt_ev_condi_z_full), 20)); disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_max: I by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_max)); disp(head(array2table(mt_ev_condi_z_max), 20)); disp(tail(array2table(mt_ev_condi_z_max), 20)); disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_max_idx: I by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_max_idx)); disp(head(array2table(mt_ev_condi_z_max_idx), 20)); disp(tail(array2table(mt_ev_condi_z_max_idx), 20)); end
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mt_ev_condi_z_full: J by IxM
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50 750
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mt_ev_condi_z_max: I by M
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mt_ev_condi_z_max1 mt_ev_condi_z_max2 mt_ev_condi_z_max3 mt_ev_condi_z_max4 mt_ev_condi_z_max5 mt_ev_condi_z_max6 mt_ev_condi_z_max7 mt_ev_condi_z_max8 mt_ev_condi_z_max9 mt_ev_condi_z_max10 mt_ev_condi_z_max11 mt_ev_condi_z_max12 mt_ev_condi_z_max13 mt_ev_condi_z_max14 mt_ev_condi_z_max15
__________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ ___________________ ___________________ ___________________ ___________________ ___________________ ___________________
-0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272 -0.81272
0.59991 0.62626 0.6565 0.68987 0.72611 0.76523 0.80732 0.85245 0.90072 0.95216 1.0068 1.0646 1.1251 1.1871 1.247
1.0598 1.0812 1.106 1.1334 1.1634 1.196 1.2313 1.2694 1.3104 1.3545 1.4016 1.4519 1.5049 1.5595 1.6126
1.3692 1.385 1.4041 1.4277 1.4536 1.4819 1.5127 1.5461 1.5823 1.6213 1.6632 1.7081 1.7558 1.8051 1.8533
1.6051 1.6177 1.6328 1.6517 1.6732 1.6985 1.726 1.756 1.7886 1.8239 1.862 1.9029 1.9466 1.9919 2.0363
1.7958 1.8062 1.8188 1.8346 1.8525 1.8737 1.8986 1.926 1.9559 1.9883 2.0234 2.0612 2.1017 2.1438 2.1851
1.9559 1.9648 1.9756 1.9891 2.0045 2.0227 2.0443 2.0692 2.0969 2.127 2.1597 2.195 2.2328 2.2724 2.3112
2.0939 2.1016 2.1111 2.1228 2.1364 2.1524 2.1714 2.1934 2.219 2.2472 2.2779 2.3111 2.3468 2.3841 2.4209
2.2151 2.222 2.2304 2.2408 2.2529 2.2672 2.2841 2.3038 2.3268 2.3534 2.3824 2.4138 2.4477 2.4831 2.5181
2.3232 2.3294 2.3369 2.3463 2.3572 2.3701 2.3854 2.4032 2.4241 2.4486 2.4761 2.506 2.5382 2.572 2.6055
2.4208 2.4264 2.4332 2.4418 2.4516 2.4634 2.4773 2.4936 2.5127 2.5352 2.5611 2.5897 2.6205 2.6529 2.6849
2.5096 2.5148 2.521 2.5289 2.5379 2.5487 2.5615 2.5766 2.5942 2.6149 2.639 2.6664 2.6959 2.727 2.7578
2.5912 2.596 2.6017 2.609 2.6174 2.6273 2.6392 2.6531 2.6694 2.6887 2.7111 2.7371 2.7655 2.7955 2.8251
2.6667 2.6711 2.6764 2.6832 2.691 2.7002 2.7112 2.7242 2.7394 2.7574 2.7784 2.8028 2.8302 2.8591 2.8878
2.7369 2.7409 2.7459 2.7522 2.7595 2.7681 2.7785 2.7906 2.8048 2.8217 2.8414 2.8644 2.8906 2.9186 2.9464
2.8024 2.8062 2.8109 2.8168 2.8236 2.8317 2.8414 2.8528 2.8662 2.8821 2.9007 2.9223 2.9474 2.9745 3.0014
2.8639 2.8675 2.8719 2.8775 2.8839 2.8915 2.9007 2.9114 2.9241 2.9391 2.9566 2.9771 3.0008 3.0271 3.0532
2.9219 2.9253 2.9294 2.9347 2.9407 2.948 2.9566 2.9668 2.9788 2.993 3.0096 3.0291 3.0516 3.0769 3.1023
2.9767 2.9799 2.9838 2.9888 2.9945 3.0014 3.0096 3.0192 3.0306 3.0441 3.0599 3.0785 3.0999 3.1241 3.1489
3.0286 3.0316 3.0354 3.0401 3.0456 3.0521 3.0599 3.069 3.0799 3.0927 3.1078 3.1255 3.146 3.1691 3.1932
mt_ev_condi_z_max1 mt_ev_condi_z_max2 mt_ev_condi_z_max3 mt_ev_condi_z_max4 mt_ev_condi_z_max5 mt_ev_condi_z_max6 mt_ev_condi_z_max7 mt_ev_condi_z_max8 mt_ev_condi_z_max9 mt_ev_condi_z_max10 mt_ev_condi_z_max11 mt_ev_condi_z_max12 mt_ev_condi_z_max13 mt_ev_condi_z_max14 mt_ev_condi_z_max15
__________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ __________________ ___________________ ___________________ ___________________ ___________________ ___________________ ___________________
3.4711 3.4731 3.4755 3.4785 3.4821 3.4863 3.4914 3.4973 3.5044 3.5129 3.5228 3.5346 3.5483 3.5639 3.5804
3.5031 3.505 3.5074 3.5103 3.5137 3.5178 3.5227 3.5285 3.5354 3.5436 3.5532 3.5647 3.578 3.5931 3.6092
3.5341 3.536 3.5382 3.5411 3.5444 3.5484 3.5531 3.5588 3.5654 3.5734 3.5828 3.5938 3.6068 3.6215 3.6371
3.5642 3.566 3.5682 3.5709 3.5742 3.578 3.5826 3.5881 3.5946 3.6023 3.6114 3.6222 3.6348 3.6491 3.6643
3.5934 3.5951 3.5973 3.5999 3.6031 3.6068 3.6113 3.6166 3.6229 3.6304 3.6393 3.6498 3.662 3.6759 3.6907
3.6217 3.6234 3.6255 3.6281 3.6312 3.6348 3.6392 3.6443 3.6505 3.6578 3.6664 3.6766 3.6885 3.7021 3.7165
3.6493 3.651 3.653 3.6555 3.6585 3.662 3.6663 3.6713 3.6773 3.6844 3.6928 3.7027 3.7143 3.7276 3.7416
3.6762 3.6778 3.6797 3.6822 3.6851 3.6885 3.6927 3.6976 3.7034 3.7103 3.7185 3.7282 3.7395 3.7524 3.7661
3.7023 3.7039 3.7058 3.7082 3.711 3.7144 3.7184 3.7232 3.7288 3.7356 3.7436 3.753 3.7641 3.7767 3.7901
3.7278 3.7293 3.7312 3.7335 3.7363 3.7395 3.7435 3.7481 3.7537 3.7602 3.768 3.7773 3.788 3.8003 3.8134
3.7526 3.7541 3.7559 3.7582 3.7609 3.7641 3.7679 3.7725 3.7779 3.7843 3.7919 3.8009 3.8115 3.8235 3.8362
3.7769 3.7783 3.7801 3.7823 3.7849 3.788 3.7918 3.7962 3.8015 3.8078 3.8152 3.824 3.8343 3.8461 3.8586
3.8005 3.8019 3.8037 3.8059 3.8084 3.8114 3.8151 3.8194 3.8246 3.8307 3.838 3.8466 3.8567 3.8682 3.8804
3.8236 3.825 3.8267 3.8289 3.8313 3.8343 3.8379 3.8421 3.8472 3.8532 3.8603 3.8687 3.8786 3.8898 3.9018
3.8462 3.8476 3.8492 3.8513 3.8538 3.8567 3.8602 3.8643 3.8693 3.8751 3.8821 3.8903 3.9 3.911 3.9227
3.8683 3.8696 3.8713 3.8733 3.8757 3.8785 3.882 3.886 3.8909 3.8966 3.9034 3.9115 3.9209 3.9317 3.9432
3.8899 3.8912 3.8928 3.8948 3.8972 3.8999 3.9033 3.9073 3.912 3.9176 3.9243 3.9322 3.9414 3.952 3.9633
3.9111 3.9124 3.9139 3.9159 3.9182 3.9209 3.9242 3.9281 3.9327 3.9382 3.9447 3.9525 3.9616 3.9719 3.9829
3.9318 3.9331 3.9346 3.9365 3.9387 3.9414 3.9446 3.9484 3.953 3.9584 3.9648 3.9724 3.9813 3.9914 4.0022
3.9521 3.9533 3.9548 3.9567 3.9589 3.9615 3.9647 3.9684 3.9729 3.9782 3.9844 3.9919 4.0006 4.0106 4.0212
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mt_ev_condi_z_max_idx: I by M
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mt_ev_condi_z_max_idx1 mt_ev_condi_z_max_idx2 mt_ev_condi_z_max_idx3 mt_ev_condi_z_max_idx4 mt_ev_condi_z_max_idx5 mt_ev_condi_z_max_idx6 mt_ev_condi_z_max_idx7 mt_ev_condi_z_max_idx8 mt_ev_condi_z_max_idx9 mt_ev_condi_z_max_idx10 mt_ev_condi_z_max_idx11 mt_ev_condi_z_max_idx12 mt_ev_condi_z_max_idx13 mt_ev_condi_z_max_idx14 mt_ev_condi_z_max_idx15
______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 4 4 4 4 4 4 4 4 4 4 4 4 4
3 3 4 4 5 5 5 5 5 5 5 5 5 5 5
3 3 4 4 5 5 6 6 6 6 6 6 6 6 6
3 3 4 4 5 5 6 7 7 7 7 7 7 7 7
3 3 4 4 5 5 6 7 8 8 8 8 8 8 8
3 3 4 4 5 5 6 7 8 9 9 9 9 9 9
3 3 4 4 5 5 6 7 9 10 10 10 10 10 10
3 3 4 4 5 5 6 7 9 10 11 11 11 11 11
3 3 4 4 5 5 6 7 9 10 12 12 12 12 12
3 3 4 4 5 5 6 7 9 10 12 13 13 13 13
3 3 4 4 5 5 6 7 9 10 12 14 14 14 14
3 3 4 4 5 5 6 7 9 10 12 14 15 15 15
3 3 4 4 5 5 6 7 9 10 12 14 16 16 16
3 3 4 4 5 5 6 7 9 10 12 14 16 17 17
3 3 4 4 5 5 6 7 9 10 12 14 16 18 18
3 3 4 4 5 5 6 7 9 10 12 14 16 19 19
3 3 4 4 5 5 6 7 9 10 12 14 16 19 20
mt_ev_condi_z_max_idx1 mt_ev_condi_z_max_idx2 mt_ev_condi_z_max_idx3 mt_ev_condi_z_max_idx4 mt_ev_condi_z_max_idx5 mt_ev_condi_z_max_idx6 mt_ev_condi_z_max_idx7 mt_ev_condi_z_max_idx8 mt_ev_condi_z_max_idx9 mt_ev_condi_z_max_idx10 mt_ev_condi_z_max_idx11 mt_ev_condi_z_max_idx12 mt_ev_condi_z_max_idx13 mt_ev_condi_z_max_idx14 mt_ev_condi_z_max_idx15
______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
3 3 4 4 5 5 6 7 9 10 12 14 16 19 22
Reindex K' and B' Choices for each State at the Optimal w'=k'+b' choice
The K' and B' Optimal Choices Associated with EV opti dim(mt_ev_condi_z_max_kp): I by M
ar_add_grid = linspace(0, it_mt_bp_rown*(it_mt_bp_coln-1), it_mt_bp_coln); mt_ev_condi_z_max_idx = mt_ev_condi_z_max_idx + ar_add_grid'; if (bl_display_evf) disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_max_idx: I by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_max_idx)); disp(head(array2table(mt_ev_condi_z_max_idx), 20)); disp(tail(array2table(mt_ev_condi_z_max_idx), 20)); end mt_ev_condi_z_max_kp = reshape(ar_k_mw_wth_na(mt_ev_condi_z_max_idx(:)), [it_mt_bp_coln, it_z_n]); mt_ev_condi_z_max_bp = reshape(ar_a_mw_wth_na(mt_ev_condi_z_max_idx(:)), [it_mt_bp_coln, it_z_n]); if (bl_display_evf) disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_max_kp: I by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_max_kp)); disp(head(array2table(mt_ev_condi_z_max_kp), 20)); disp(tail(array2table(mt_ev_condi_z_max_kp), 20)); disp('----------------------------------------'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp('mt_ev_condi_z_max_bp: I by M'); disp('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'); disp(size(mt_ev_condi_z_max_bp)); disp(head(array2table(mt_ev_condi_z_max_bp), 20)); disp(tail(array2table(mt_ev_condi_z_max_bp), 20)); end
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mt_ev_condi_z_max_idx1 mt_ev_condi_z_max_idx2 mt_ev_condi_z_max_idx3 mt_ev_condi_z_max_idx4 mt_ev_condi_z_max_idx5 mt_ev_condi_z_max_idx6 mt_ev_condi_z_max_idx7 mt_ev_condi_z_max_idx8 mt_ev_condi_z_max_idx9 mt_ev_condi_z_max_idx10 mt_ev_condi_z_max_idx11 mt_ev_condi_z_max_idx12 mt_ev_condi_z_max_idx13 mt_ev_condi_z_max_idx14 mt_ev_condi_z_max_idx15
______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
52 52 52 52 52 52 52 52 52 52 52 52 52 52 52
103 103 103 103 103 103 103 103 103 103 103 103 103 103 103
153 153 154 154 154 154 154 154 154 154 154 154 154 154 154
203 203 204 204 205 205 205 205 205 205 205 205 205 205 205
253 253 254 254 255 255 256 256 256 256 256 256 256 256 256
303 303 304 304 305 305 306 307 307 307 307 307 307 307 307
353 353 354 354 355 355 356 357 358 358 358 358 358 358 358
403 403 404 404 405 405 406 407 408 409 409 409 409 409 409
453 453 454 454 455 455 456 457 459 460 460 460 460 460 460
503 503 504 504 505 505 506 507 509 510 511 511 511 511 511
553 553 554 554 555 555 556 557 559 560 562 562 562 562 562
603 603 604 604 605 605 606 607 609 610 612 613 613 613 613
653 653 654 654 655 655 656 657 659 660 662 664 664 664 664
703 703 704 704 705 705 706 707 709 710 712 714 715 715 715
753 753 754 754 755 755 756 757 759 760 762 764 766 766 766
803 803 804 804 805 805 806 807 809 810 812 814 816 817 817
853 853 854 854 855 855 856 857 859 860 862 864 866 868 868
903 903 904 904 905 905 906 907 909 910 912 914 916 919 919
953 953 954 954 955 955 956 957 959 960 962 964 966 969 970
mt_ev_condi_z_max_idx1 mt_ev_condi_z_max_idx2 mt_ev_condi_z_max_idx3 mt_ev_condi_z_max_idx4 mt_ev_condi_z_max_idx5 mt_ev_condi_z_max_idx6 mt_ev_condi_z_max_idx7 mt_ev_condi_z_max_idx8 mt_ev_condi_z_max_idx9 mt_ev_condi_z_max_idx10 mt_ev_condi_z_max_idx11 mt_ev_condi_z_max_idx12 mt_ev_condi_z_max_idx13 mt_ev_condi_z_max_idx14 mt_ev_condi_z_max_idx15
______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________
1503 1503 1504 1504 1505 1505 1506 1507 1509 1510 1512 1514 1516 1519 1522
1553 1553 1554 1554 1555 1555 1556 1557 1559 1560 1562 1564 1566 1569 1572
1603 1603 1604 1604 1605 1605 1606 1607 1609 1610 1612 1614 1616 1619 1622
1653 1653 1654 1654 1655 1655 1656 1657 1659 1660 1662 1664 1666 1669 1672
1703 1703 1704 1704 1705 1705 1706 1707 1709 1710 1712 1714 1716 1719 1722
1753 1753 1754 1754 1755 1755 1756 1757 1759 1760 1762 1764 1766 1769 1772
1803 1803 1804 1804 1805 1805 1806 1807 1809 1810 1812 1814 1816 1819 1822
1853 1853 1854 1854 1855 1855 1856 1857 1859 1860 1862 1864 1866 1869 1872
1903 1903 1904 1904 1905 1905 1906 1907 1909 1910 1912 1914 1916 1919 1922
1953 1953 1954 1954 1955 1955 1956 1957 1959 1960 1962 1964 1966 1969 1972
2003 2003 2004 2004 2005 2005 2006 2007 2009 2010 2012 2014 2016 2019 2022
2053 2053 2054 2054 2055 2055 2056 2057 2059 2060 2062 2064 2066 2069 2072
2103 2103 2104 2104 2105 2105 2106 2107 2109 2110 2112 2114 2116 2119 2122
2153 2153 2154 2154 2155 2155 2156 2157 2159 2160 2162 2164 2166 2169 2172
2203 2203 2204 2204 2205 2205 2206 2207 2209 2210 2212 2214 2216 2219 2222
2253 2253 2254 2254 2255 2255 2256 2257 2259 2260 2262 2264 2266 2269 2272
2303 2303 2304 2304 2305 2305 2306 2307 2309 2310 2312 2314 2316 2319 2322
2353 2353 2354 2354 2355 2355 2356 2357 2359 2360 2362 2364 2366 2369 2372
2403 2403 2404 2404 2405 2405 2406 2407 2409 2410 2412 2414 2416 2419 2422
2453 2453 2454 2454 2455 2455 2456 2457 2459 2460 2462 2464 2466 2469 2472
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mt_ev_condi_z_max_kp: I by M
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50 15
mt_ev_condi_z_max_kp1 mt_ev_condi_z_max_kp2 mt_ev_condi_z_max_kp3 mt_ev_condi_z_max_kp4 mt_ev_condi_z_max_kp5 mt_ev_condi_z_max_kp6 mt_ev_condi_z_max_kp7 mt_ev_condi_z_max_kp8 mt_ev_condi_z_max_kp9 mt_ev_condi_z_max_kp10 mt_ev_condi_z_max_kp11 mt_ev_condi_z_max_kp12 mt_ev_condi_z_max_kp13 mt_ev_condi_z_max_kp14 mt_ev_condi_z_max_kp15
_____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1.0204 1.0204 1.0204 1.0204 1.0204 1.0204 1.0204 1.0204 1.0204 1.0204 1.0204 1.0204 1.0204 1.0204 1.0204
2.0408 2.0408 2.0408 2.0408 2.0408 2.0408 2.0408 2.0408 2.0408 2.0408 2.0408 2.0408 2.0408 2.0408 2.0408
2.0408 2.0408 3.0612 3.0612 3.0612 3.0612 3.0612 3.0612 3.0612 3.0612 3.0612 3.0612 3.0612 3.0612 3.0612
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 4.0816 4.0816 4.0816 4.0816 4.0816 4.0816 4.0816 4.0816 4.0816
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 5.102 5.102 5.102 5.102 5.102 5.102 5.102 5.102
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 6.1224 6.1224 6.1224 6.1224 6.1224 6.1224 6.1224
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 7.1429 7.1429 7.1429 7.1429 7.1429 7.1429 7.1429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 7.1429 8.1633 8.1633 8.1633 8.1633 8.1633 8.1633
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 9.1837 9.1837 9.1837 9.1837 9.1837
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 10.204 10.204 10.204 10.204 10.204
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 11.224 11.224 11.224 11.224
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 12.245 12.245 12.245 12.245
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 13.265 13.265 13.265
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 14.286 14.286 14.286
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 15.306 15.306
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 16.327 16.327
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 17.347 17.347
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 18.367
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 19.388
mt_ev_condi_z_max_kp1 mt_ev_condi_z_max_kp2 mt_ev_condi_z_max_kp3 mt_ev_condi_z_max_kp4 mt_ev_condi_z_max_kp5 mt_ev_condi_z_max_kp6 mt_ev_condi_z_max_kp7 mt_ev_condi_z_max_kp8 mt_ev_condi_z_max_kp9 mt_ev_condi_z_max_kp10 mt_ev_condi_z_max_kp11 mt_ev_condi_z_max_kp12 mt_ev_condi_z_max_kp13 mt_ev_condi_z_max_kp14 mt_ev_condi_z_max_kp15
_____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
2.0408 2.0408 3.0612 3.0612 4.0816 4.0816 5.102 6.1224 8.1633 9.1837 11.224 13.265 15.306 18.367 21.429
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mt_ev_condi_z_max_bp: I by M
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50 15
mt_ev_condi_z_max_bp1 mt_ev_condi_z_max_bp2 mt_ev_condi_z_max_bp3 mt_ev_condi_z_max_bp4 mt_ev_condi_z_max_bp5 mt_ev_condi_z_max_bp6 mt_ev_condi_z_max_bp7 mt_ev_condi_z_max_bp8 mt_ev_condi_z_max_bp9 mt_ev_condi_z_max_bp10 mt_ev_condi_z_max_bp11 mt_ev_condi_z_max_bp12 mt_ev_condi_z_max_bp13 mt_ev_condi_z_max_bp14 mt_ev_condi_z_max_bp15
_____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1.0204 1.0204 0 0 0 0 0 0 0 0 0 0 0 0 0
2.0408 2.0408 1.0204 1.0204 0 0 0 0 0 0 0 0 0 0 0
3.0612 3.0612 2.0408 2.0408 1.0204 1.0204 0 0 0 0 0 0 0 0 0
4.0816 4.0816 3.0612 3.0612 2.0408 2.0408 1.0204 0 0 0 0 0 0 0 0
5.102 5.102 4.0816 4.0816 3.0612 3.0612 2.0408 1.0204 0 0 0 0 0 0 0
6.1224 6.1224 5.102 5.102 4.0816 4.0816 3.0612 2.0408 1.0204 0 0 0 0 0 0
7.1429 7.1429 6.1224 6.1224 5.102 5.102 4.0816 3.0612 1.0204 0 0 0 0 0 0
8.1633 8.1633 7.1429 7.1429 6.1224 6.1224 5.102 4.0816 2.0408 1.0204 0 0 0 0 0
9.1837 9.1837 8.1633 8.1633 7.1429 7.1429 6.1224 5.102 3.0612 2.0408 0 0 0 0 0
10.204 10.204 9.1837 9.1837 8.1633 8.1633 7.1429 6.1224 4.0816 3.0612 1.0204 0 0 0 0
11.224 11.224 10.204 10.204 9.1837 9.1837 8.1633 7.1429 5.102 4.0816 2.0408 0 0 0 0
12.245 12.245 11.224 11.224 10.204 10.204 9.1837 8.1633 6.1224 5.102 3.0612 1.0204 0 0 0
13.265 13.265 12.245 12.245 11.224 11.224 10.204 9.1837 7.1429 6.1224 4.0816 2.0408 0 0 0
14.286 14.286 13.265 13.265 12.245 12.245 11.224 10.204 8.1633 7.1429 5.102 3.0612 1.0204 0 0
15.306 15.306 14.286 14.286 13.265 13.265 12.245 11.224 9.1837 8.1633 6.1224 4.0816 2.0408 0 0
16.327 16.327 15.306 15.306 14.286 14.286 13.265 12.245 10.204 9.1837 7.1429 5.102 3.0612 0 0
17.347 17.347 16.327 16.327 15.306 15.306 14.286 13.265 11.224 10.204 8.1633 6.1224 4.0816 1.0204 0
mt_ev_condi_z_max_bp1 mt_ev_condi_z_max_bp2 mt_ev_condi_z_max_bp3 mt_ev_condi_z_max_bp4 mt_ev_condi_z_max_bp5 mt_ev_condi_z_max_bp6 mt_ev_condi_z_max_bp7 mt_ev_condi_z_max_bp8 mt_ev_condi_z_max_bp9 mt_ev_condi_z_max_bp10 mt_ev_condi_z_max_bp11 mt_ev_condi_z_max_bp12 mt_ev_condi_z_max_bp13 mt_ev_condi_z_max_bp14 mt_ev_condi_z_max_bp15
_____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ _____________________ ______________________ ______________________ ______________________ ______________________ ______________________ ______________________
28.571 28.571 27.551 27.551 26.531 26.531 25.51 24.49 22.449 21.429 19.388 17.347 15.306 12.245 9.1837
29.592 29.592 28.571 28.571 27.551 27.551 26.531 25.51 23.469 22.449 20.408 18.367 16.327 13.265 10.204
30.612 30.612 29.592 29.592 28.571 28.571 27.551 26.531 24.49 23.469 21.429 19.388 17.347 14.286 11.224
31.633 31.633 30.612 30.612 29.592 29.592 28.571 27.551 25.51 24.49 22.449 20.408 18.367 15.306 12.245
32.653 32.653 31.633 31.633 30.612 30.612 29.592 28.571 26.531 25.51 23.469 21.429 19.388 16.327 13.265
33.673 33.673 32.653 32.653 31.633 31.633 30.612 29.592 27.551 26.531 24.49 22.449 20.408 17.347 14.286
34.694 34.694 33.673 33.673 32.653 32.653 31.633 30.612 28.571 27.551 25.51 23.469 21.429 18.367 15.306
35.714 35.714 34.694 34.694 33.673 33.673 32.653 31.633 29.592 28.571 26.531 24.49 22.449 19.388 16.327
36.735 36.735 35.714 35.714 34.694 34.694 33.673 32.653 30.612 29.592 27.551 25.51 23.469 20.408 17.347
37.755 37.755 36.735 36.735 35.714 35.714 34.694 33.673 31.633 30.612 28.571 26.531 24.49 21.429 18.367
38.776 38.776 37.755 37.755 36.735 36.735 35.714 34.694 32.653 31.633 29.592 27.551 25.51 22.449 19.388
39.796 39.796 38.776 38.776 37.755 37.755 36.735 35.714 33.673 32.653 30.612 28.571 26.531 23.469 20.408
40.816 40.816 39.796 39.796 38.776 38.776 37.755 36.735 34.694 33.673 31.633 29.592 27.551 24.49 21.429
41.837 41.837 40.816 40.816 39.796 39.796 38.776 37.755 35.714 34.694 32.653 30.612 28.571 25.51 22.449
42.857 42.857 41.837 41.837 40.816 40.816 39.796 38.776 36.735 35.714 33.673 31.633 29.592 26.531 23.469
43.878 43.878 42.857 42.857 41.837 41.837 40.816 39.796 37.755 36.735 34.694 32.653 30.612 27.551 24.49
44.898 44.898 43.878 43.878 42.857 42.857 41.837 40.816 38.776 37.755 35.714 33.673 31.633 28.571 25.51
45.918 45.918 44.898 44.898 43.878 43.878 42.857 41.837 39.796 38.776 36.735 34.694 32.653 29.592 26.531
46.939 46.939 45.918 45.918 44.898 44.898 43.878 42.857 40.816 39.796 37.755 35.714 33.673 30.612 27.551
47.959 47.959 46.939 46.939 45.918 45.918 44.898 43.878 41.837 40.816 38.776 36.735 34.694 31.633 28.571
Generate Optimal K' and B' on w(coh) percentage grid from w level grid
Graph
if (bl_graph_evf)
Graph 1, V and EV
if (~bl_graph_onebyones) figure('PaperPosition', [0 0 14 4]); hold on; end for subplot_j=1:1:2 if (~bl_graph_onebyones) hAxis(subplot_j) = subplot(1,2,subplot_j); else figure('PaperPosition', [0 0 7 4]); end if (subplot_j==1) chart = plot(mt_val); end if (subplot_j==2) chart = plot(mt_ev_condi_z); end clr = jet(numel(chart)); for m = 1:numel(chart) set(chart(m),'Color',clr(m,:)) end legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/3) numel(chart)]); legendCell = cellstr(num2str(ar_z', 'shock=%3.2f')); legend(chart(legend2plot), legendCell(legend2plot), 'Location','southeast'); if (subplot_j==1) title('V(coh,zp); w(k+b),k,z'); end if (subplot_j==2) title('E_z(V(coh,zp|z))'); end ylabel('Next Period Value'); xlabel({'Index of Cash-on-Hand Discrete Point'... 'Each Segment is a w=k+b; within segment increasing k'... 'EV and V identical if shock is fully persistent'}); grid on; grid minor; end % Share y axis if (~bl_graph_onebyones) linkaxes(hAxis,'y'); end % save file if (bl_img_save) mkdir(support_map('st_img_path')); st_file_name = [st_img_prefix st_img_name_main '_vev' st_img_suffix]; saveas(gcf, strcat(st_img_path, st_file_name)); end
Graph 2, max(EV)
if (~bl_graph_onebyones) figure('PaperPosition', [0 0 7 4]); end for sub_j=1:1:1 if (sub_j==1) mt_outcome = mt_ev_condi_z_max; st_y_label = 'max_{k''}(E(V(coh(k'',b''=w-k''),z''|z,w))'; end if (~bl_graph_onebyones) subplot(1,1,sub_j) else figure('PaperPosition', [0 0 7 4]); end hold on; ar_it_z_graph = ([1 round((it_z_n)/4) round(2*((it_z_n)/4)) round(3*((it_z_n)/4)) (it_z_n)]); clr = jet(length(ar_it_z_graph)); i_ctr = 0; for i = ar_it_z_graph i_ctr = i_ctr + 1; ar_x = ar_w; ar_y = mt_outcome(:, i); scatter(ar_x, ar_y, 5, ... 'MarkerEdgeColor', clr(i_ctr,:), ... 'MarkerFaceColor', clr(i_ctr,:)); end grid on; grid minor; title(['2nd Stage Exp Value at Optimal K given W=K''+B''']) ylabel(st_y_label) xlabel({'Aggregate Savings'}) legendCell = cellstr(num2str(ar_z', 'shock=%3.2f')); legendCell{length(legendCell) + 1} = 'max-agg-save'; legend(legendCell([ar_it_z_graph length(legendCell)]), 'Location','southeast'); xline0 = xline(0); xline0.HandleVisibility = 'off'; yline0 = yline(0); yline0.HandleVisibility = 'off'; end % save file if (bl_img_save) mkdir(support_map('st_img_path')); st_file_name = [st_img_prefix st_img_name_main '_maxev' st_img_suffix]; saveas(gcf, strcat(st_img_path, st_file_name)); end
Warning: Ignoring extra legend entries.
Graph 3, max(EV), color regions, borrow save
% Borrow Vs Save [ar_z_mw, ar_w_mz] = meshgrid(ar_z, ar_w); mt_it_borr_idx = (mt_ev_condi_z_max_bp < 0); mt_it_riskyhalf_idx = ((mt_ev_condi_z_max_kp./mt_ev_condi_z_max_bp) > 0.5); mt_it_kzero_idx = (mt_ev_condi_z_max_kp == 0); mt_it_isnan_idx = (isnan(mt_ev_condi_z_max_kp)); figure('PaperPosition', [0 0 7 4]); % States: ar_w, ar_z % Choices: mt_ev_condi_z_max_kp, mt_ev_condi_z_max_bp hold on; it_sca_size = 10; chart_br = scatter(ar_w_mz(mt_it_borr_idx),... ar_z_mw(mt_it_borr_idx),... it_sca_size, 'blue', 'filled'); % legend([chart_br], {'Borrow'}, 'Location','northeast'); chart_khalf = scatter(ar_w_mz(~mt_it_borr_idx & mt_it_riskyhalf_idx),... ar_z_mw(~mt_it_borr_idx & mt_it_riskyhalf_idx),... it_sca_size, 'black', 'filled'); % legend([chart_khalf], {'Save >0.5 K'}, 'Location','northeast'); chart_sv = scatter(ar_w_mz(~mt_it_borr_idx & ~mt_it_riskyhalf_idx),... ar_z_mw(~mt_it_borr_idx & ~mt_it_riskyhalf_idx),... it_sca_size, 'red', 'filled'); % legend([chart_sv], {'Save <0.5 K'}, 'Location','northeast'); chart_invalid = scatter(ar_w_mz(mt_it_kzero_idx | mt_it_isnan_idx),... ar_z_mw(mt_it_kzero_idx | mt_it_isnan_idx),... it_sca_size, 'yellow', 'filled'); legend([chart_br, chart_khalf, chart_sv, chart_invalid], ... {'Borrow','Save >0.5 K','Save <0.5 K', 'k=0 or k=nan'}, 'Location','northeast'); title('Borrow and Save Regions') ylabel('Shocks') xlabel({'Total Savings w=k+b'}) grid on; % save file if (bl_img_save) mkdir(support_map('st_img_path')); st_file_name = [st_img_prefix st_img_name_main '_maxbrsv' st_img_suffix]; saveas(gcf, strcat(st_img_path, st_file_name)); end
Graph 4, Optimal K' and B' Levels
[~, ar_w_mz] = meshgrid(ar_z, ar_w);
for sub_j=1:1:4
if (bl_graph_onebyones)
figure('PaperPosition', [0 0 7 4]);
end
if (sub_j==1)
if (~bl_graph_onebyones)
figure('PaperPosition', [0 0 14 4]);
subplot(1,2,sub_j);
end
mt_y = mt_ev_condi_z_max_bp;
end
if (sub_j==2)
if (~bl_graph_onebyones)
subplot(1,2,sub_j);
end
mt_y = mt_ev_condi_z_max_kp;
end
if (sub_j==3)
if (~bl_graph_onebyones)
figure('PaperPosition', [0 0 14 4]);
subplot(1,2,sub_j-2);
end
mt_y = zeros(size(mt_ev_condi_z_max_bp));
mt_it_borr_idx = (mt_ev_condi_z_max_bp < 0);
mt_y(mt_it_borr_idx) = -mt_ev_condi_z_max_bp(mt_it_borr_idx)/fl_b_bd;
mt_y(~mt_it_borr_idx) = mt_ev_condi_z_max_bp(~mt_it_borr_idx)./ar_w_mz(~mt_it_borr_idx);
end
if (sub_j==4)
if (~bl_graph_onebyones)
subplot(1,2,sub_j-2);
end
mt_y = mt_ev_condi_z_max_kp./(ar_w'-fl_b_bd);
end
hold on;
chart = plot(ar_w, mt_y);
clr = jet(numel(chart));
if (length(ar_w) <= 50)
scatter(ar_w_mz(:), mt_y(:), 5, 'filled');
end
for m = 1:numel(chart)
set(chart(m),'Color',clr(m,:))
end
legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/3) numel(chart)]);
legendCell = cellstr(num2str(ar_z', 'shock=%3.2f'));
xline0 = xline(0);
xline0.HandleVisibility = 'off';
yline0 = yline(0);
yline0.HandleVisibility = 'off';
grid on;
if (sub_j<=2)
hline = refline([1 0]);
hline.Color = 'k';
hline.LineStyle = ':';
hline.HandleVisibility = 'off';
end
if (sub_j==1)
title('B Choices of W');
ylabel('B Choices');
xlabel({'Total Savings w=k+b'});
legend(chart(legend2plot), legendCell(legend2plot), 'Location','northwest');
end
if (sub_j==2)
title('K Choices of W');
ylabel('K Choices');
xlabel({'Total Savings w=k+b'});
legend(chart(legend2plot), legendCell(legend2plot), 'Location','northwest');
end
if (sub_j==3)
title('B Fraction of Borrow Max and Save');
ylabel('B/bar(B) if br or B/W if sv');
xlabel({'Total Savings w=k+b'});
% set(gca, 'YScale', 'log');
ylim([-1.1 1.1]);
legend(chart(legend2plot), legendCell(legend2plot), 'Location','northwest');
end
if (sub_j==4)
title('K Fraction Choices of Total K Possible');
ylabel('K/(W-bar(b)) ');
xlabel({'Total Savings w=k+b'});
% set(gca, 'YScale', 'log');
ylim([0 1.1]);
legend(chart(legend2plot), legendCell(legend2plot), 'Location','northeast');
end
end
% save file
if (bl_img_save)
mkdir(support_map('st_img_path'));
st_file_name = [st_img_prefix st_img_name_main '_wkbopti' st_img_suffix];
saveas(gcf, strcat(st_img_path, st_file_name));
end
end
end
ans =
Columns 1 through 7
-0.8127 -0.8127 -0.8127 -0.8127 -0.8127 -0.8127 -0.8127
0.5999 0.6263 0.6565 0.6899 0.7261 0.7652 0.8073
1.0598 1.0812 1.1060 1.1334 1.1634 1.1960 1.2313
1.3692 1.3850 1.4041 1.4277 1.4536 1.4819 1.5127
1.6051 1.6177 1.6328 1.6517 1.6732 1.6985 1.7260
1.7958 1.8062 1.8188 1.8346 1.8525 1.8737 1.8986
1.9559 1.9648 1.9756 1.9891 2.0045 2.0227 2.0443
2.0939 2.1016 2.1111 2.1228 2.1364 2.1524 2.1714
2.2151 2.2220 2.2304 2.2408 2.2529 2.2672 2.2841
2.3232 2.3294 2.3369 2.3463 2.3572 2.3701 2.3854
2.4208 2.4264 2.4332 2.4418 2.4516 2.4634 2.4773
2.5096 2.5148 2.5210 2.5289 2.5379 2.5487 2.5615
2.5912 2.5960 2.6017 2.6090 2.6174 2.6273 2.6392
2.6667 2.6711 2.6764 2.6832 2.6910 2.7002 2.7112
2.7369 2.7409 2.7459 2.7522 2.7595 2.7681 2.7785
2.8024 2.8062 2.8109 2.8168 2.8236 2.8317 2.8414
2.8639 2.8675 2.8719 2.8775 2.8839 2.8915 2.9007
2.9219 2.9253 2.9294 2.9347 2.9407 2.9480 2.9566
2.9767 2.9799 2.9838 2.9888 2.9945 3.0014 3.0096
3.0286 3.0316 3.0354 3.0401 3.0456 3.0521 3.0599
3.0780 3.0809 3.0844 3.0889 3.0941 3.1003 3.1077
3.1250 3.1278 3.1312 3.1355 3.1404 3.1463 3.1534
3.1699 3.1726 3.1758 3.1799 3.1847 3.1903 3.1971
3.2129 3.2155 3.2186 3.2225 3.2271 3.2325 3.2390
3.2542 3.2566 3.2596 3.2633 3.2677 3.2729 3.2792
3.2937 3.2961 3.2990 3.3026 3.3068 3.3118 3.3178
3.3318 3.3341 3.3369 3.3403 3.3444 3.3492 3.3550
3.3685 3.3707 3.3734 3.3767 3.3806 3.3853 3.3909
3.4039 3.4060 3.4086 3.4118 3.4156 3.4201 3.4255
3.4381 3.4401 3.4426 3.4457 3.4494 3.4537 3.4590
3.4711 3.4731 3.4755 3.4785 3.4821 3.4863 3.4914
3.5031 3.5050 3.5074 3.5103 3.5137 3.5178 3.5227
3.5341 3.5360 3.5382 3.5411 3.5444 3.5484 3.5531
3.5642 3.5660 3.5682 3.5709 3.5742 3.5780 3.5826
3.5934 3.5951 3.5973 3.5999 3.6031 3.6068 3.6113
3.6217 3.6234 3.6255 3.6281 3.6312 3.6348 3.6392
3.6493 3.6510 3.6530 3.6555 3.6585 3.6620 3.6663
3.6762 3.6778 3.6797 3.6822 3.6851 3.6885 3.6927
3.7023 3.7039 3.7058 3.7082 3.7110 3.7144 3.7184
3.7278 3.7293 3.7312 3.7335 3.7363 3.7395 3.7435
3.7526 3.7541 3.7559 3.7582 3.7609 3.7641 3.7679
3.7769 3.7783 3.7801 3.7823 3.7849 3.7880 3.7918
3.8005 3.8019 3.8037 3.8059 3.8084 3.8114 3.8151
3.8236 3.8250 3.8267 3.8289 3.8313 3.8343 3.8379
3.8462 3.8476 3.8492 3.8513 3.8538 3.8567 3.8602
3.8683 3.8696 3.8713 3.8733 3.8757 3.8785 3.8820
3.8899 3.8912 3.8928 3.8948 3.8972 3.8999 3.9033
3.9111 3.9124 3.9139 3.9159 3.9182 3.9209 3.9242
3.9318 3.9331 3.9346 3.9365 3.9387 3.9414 3.9446
3.9521 3.9533 3.9548 3.9567 3.9589 3.9615 3.9647
Columns 8 through 14
-0.8127 -0.8127 -0.8127 -0.8127 -0.8127 -0.8127 -0.8127
0.8525 0.9007 0.9522 1.0068 1.0646 1.1251 1.1871
1.2694 1.3104 1.3545 1.4016 1.4519 1.5049 1.5595
1.5461 1.5823 1.6213 1.6632 1.7081 1.7558 1.8051
1.7560 1.7886 1.8239 1.8620 1.9029 1.9466 1.9919
1.9260 1.9559 1.9883 2.0234 2.0612 2.1017 2.1438
2.0692 2.0969 2.1270 2.1597 2.1950 2.2328 2.2724
2.1934 2.2190 2.2472 2.2779 2.3111 2.3468 2.3841
2.3038 2.3268 2.3534 2.3824 2.4138 2.4477 2.4831
2.4032 2.4241 2.4486 2.4761 2.5060 2.5382 2.5720
2.4936 2.5127 2.5352 2.5611 2.5897 2.6205 2.6529
2.5766 2.5942 2.6149 2.6390 2.6664 2.6959 2.7270
2.6531 2.6694 2.6887 2.7111 2.7371 2.7655 2.7955
2.7242 2.7394 2.7574 2.7784 2.8028 2.8302 2.8591
2.7906 2.8048 2.8217 2.8414 2.8644 2.8906 2.9186
2.8528 2.8662 2.8821 2.9007 2.9223 2.9474 2.9745
2.9114 2.9241 2.9391 2.9566 2.9771 3.0008 3.0271
2.9668 2.9788 2.9930 3.0096 3.0291 3.0516 3.0769
3.0192 3.0306 3.0441 3.0599 3.0785 3.0999 3.1241
3.0690 3.0799 3.0927 3.1078 3.1255 3.1460 3.1691
3.1165 3.1268 3.1391 3.1535 3.1704 3.1901 3.2122
3.1618 3.1717 3.1834 3.1972 3.2134 3.2322 3.2535
3.2052 3.2146 3.2259 3.2391 3.2547 3.2727 3.2931
3.2467 3.2558 3.2666 3.2793 3.2942 3.3116 3.3313
3.2866 3.2953 3.3057 3.3179 3.3323 3.3491 3.3680
3.3249 3.3334 3.3434 3.3551 3.3690 3.3851 3.4034
3.3619 3.3700 3.3796 3.3910 3.4044 3.4200 3.4376
3.3975 3.4053 3.4147 3.4256 3.4386 3.4536 3.4707
3.4319 3.4395 3.4485 3.4591 3.4716 3.4862 3.5028
3.4652 3.4725 3.4812 3.4915 3.5036 3.5177 3.5338
3.4973 3.5044 3.5129 3.5228 3.5346 3.5483 3.5639
3.5285 3.5354 3.5436 3.5532 3.5647 3.5780 3.5931
3.5588 3.5654 3.5734 3.5828 3.5938 3.6068 3.6215
3.5881 3.5946 3.6023 3.6114 3.6222 3.6348 3.6491
3.6166 3.6229 3.6304 3.6393 3.6498 3.6620 3.6759
3.6443 3.6505 3.6578 3.6664 3.6766 3.6885 3.7021
3.6713 3.6773 3.6844 3.6928 3.7027 3.7143 3.7276
3.6976 3.7034 3.7103 3.7185 3.7282 3.7395 3.7524
3.7232 3.7288 3.7356 3.7436 3.7530 3.7641 3.7767
3.7481 3.7537 3.7602 3.7680 3.7773 3.7880 3.8003
3.7725 3.7779 3.7843 3.7919 3.8009 3.8115 3.8235
3.7962 3.8015 3.8078 3.8152 3.8240 3.8343 3.8461
3.8194 3.8246 3.8307 3.8380 3.8466 3.8567 3.8682
3.8421 3.8472 3.8532 3.8603 3.8687 3.8786 3.8898
3.8643 3.8693 3.8751 3.8821 3.8903 3.9000 3.9110
3.8860 3.8909 3.8966 3.9034 3.9115 3.9209 3.9317
3.9073 3.9120 3.9176 3.9243 3.9322 3.9414 3.9520
3.9281 3.9327 3.9382 3.9447 3.9525 3.9616 3.9719
3.9484 3.9530 3.9584 3.9648 3.9724 3.9813 3.9914
3.9684 3.9729 3.9782 3.9844 3.9919 4.0006 4.0106
Column 15
-0.8127
1.2470
1.6126
1.8533
2.0363
2.1851
2.3112
2.4209
2.5181
2.6055
2.6849
2.7578
2.8251
2.8878
2.9464
3.0014
3.0532
3.1023
3.1489
3.1932
3.2355
3.2760
3.3148
3.3521
3.3881
3.4228
3.4564
3.4889
3.5203
3.5508
3.5804
3.6092
3.6371
3.6643
3.6907
3.7165
3.7416
3.7661
3.7901
3.8134
3.8362
3.8586
3.8804
3.9018
3.9227
3.9432
3.9633
3.9829
4.0022
4.0212