Matlab FF_VFI_AZ_BISEC_LOOP Looped Exact FOC Solution for Optimal Savings Dynamic Programming Problem in Infinite Horizon
Fan Wang
2020-06-30
1 FF_VFI_AZ_BISEC_LOOP Savings Loop Exact (FOC) Examples
Go to the MLX, M, PDF, or HTML version of this file. Go back to fan’s MEconTools Toolbox (bookdown), Matlab Code Examples Repository (bookdown), or Math for Econ with Matlab Repository (bookdown).
Examples](https://fanwangecon.github.io/M4Econ/), or** Dynamic Asset This is the example vignette for function:ff_vfi_az_bisec_loopfrom the MEconTools Package. This function solves the dynamic programming problem for a (a,z) model. Households can save a, and face AR(1) shock z. The problem is solved over the infinite horizon.
This is the looped code, it is slow for larger state-space problems.
The code uses continuous choices, solved with bisection. The state-space is on a grid, but choice grids are in terms of percentage of resources to save and solved exactly.
Links to Other Code:
Core Savings/Borrowing Dynamic Programming Solution Functions that are functions in the MEconTools Package. :
Common Choice and States Grid Loop: ff_vfi_az_loop
Common Choice and States Grid Vectorized: ff_vfi_az_vec
States Grid + Continuous Exact Savings as Share of Cash-on-Hand, rely on FOC, Loop:ff_vfi_az_bisec_loop
States Grid + Continuous Exact Savings as Share of Cash-on-Hand, rely on FOC Vectorized: ff_vfi_az_bisec_vec
States Grid + Continuous Exact Savings as Share of Cash-on-Hand, VALUE comparison, Loop:ff_vfi_az_mzoom_loop
States Grid + Continuous Exact Savings as Share of Cash-on-Hand, VALUE comparison, Vectorized: ff_vfi_az_mzoom_vec
1.1 Test FF_VFI_AZ_BISEC_LOOP Defaults
Call the function with defaults. By default, shows the asset policy function summary. Model parameters can be changed by the mp_params.
%mp_params
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('fl_crra') = 1.5;
mp_params('fl_beta') = 0.94;
% call function
ff_vfi_az_bisec_loop(mp_params);
Elapsed time is 33.158577 seconds.
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_ffcmd ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ ______ ______ ________ ___ ______
ap 1 1 2 700 100 7 9863.4 14.091 14.388 1.0211 0 50.117
xxx TABLE:ap xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
______ ______ ______ ________ _______ _______ ______
r1 0 0 0 0.053491 0.25574 0.60604 1.1157
r2 0 0 0 0.053998 0.25571 0.6066 1.1163
r3 0 0 0 0.056449 0.25576 0.60907 1.1187
r4 0 0 0 0.061799 0.26016 0.6109 1.1239
r5 0 0 0 0.066463 0.26897 0.61141 1.1327
r96 43.388 43.52 43.701 43.925 44.222 44.68 45.228
r97 44.566 44.695 44.878 45.103 45.398 45.856 46.403
r98 45.761 45.892 46.072 46.298 46.592 47.05 47.597
r99 46.973 47.107 47.286 47.514 47.806 48.263 48.815
r100 48.206 48.338 48.519 48.746 49.037 49.497 50.1171.2 Test FF_VFI_AZ_BISEC_LOOP Speed Tests
Call the function with defaults. By default, shows the asset policy function summary. Model parameters can be changed by the mp_params.
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_timer') = true;
mp_support('ls_ffcmd') = {};
% A grid 50, shock grid 5:
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 50;
mp_params('it_z_n') = 5;
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 14.819629 seconds.
% A grid 750, shock grid 15:
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 750;
mp_params('it_z_n') = 15;
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 783.169420 seconds.
%A grid 600, shock grid 45:
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 600;
mp_params('it_z_n') = 45;
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 1955.142516 seconds.1.3 Test FF_VFI_AZ_BISEC_LOOP Control Outputs
Run the function first without any outputs;
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 50;
mp_params('it_z_n') = 5;
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_timer') = true;
mp_support('bl_print_params') = false;
mp_support('bl_print_iterinfo') = false;
mp_support('ls_ffcmd') = {};
ff_vfi_az_vec(mp_params, mp_support);
Elapsed time is 0.122166 seconds.Run the function and show policy function for savings choice. For ls_ffcmd, ls_ffsna, ls_ffgrh, can include these: ‘v’, ‘ap’, ‘c’, ‘y’, ‘coh’, ‘savefraccoh’. These are value, aprime savings choice, consumption, income, cash on hand, and savings fraction as cash-on-hand.
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_print_params') = false;
mp_support('bl_print_iterinfo') = false;
% ls_ffcmd: summary print which outcomes
mp_support('ls_ffcmd') = {};
% ls_ffsna: detail print which outcomes
mp_support('ls_ffsna') = {'savefraccoh'};
% ls_ffgrh: graphical print which outcomes
mp_support('ls_ffgrh') = {'savefraccoh'};
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 20.812511 seconds.
xxx ff_vfi_az_vec, outcome=savefraccoh xxxxxxxxxxxxxxxxxxxxxxxxxxx
group a mean_z_0_4858 mean_z_0_67798 mean_z_0_9462 mean_z_1_3205 mean_z_1_8429
_____ ________ _____________ ______________ _____________ _____________ _____________
1 0 0 0 0.067239 0.20859 0.35953
2 0.002975 0 0 0.069375 0.20829 0.36032
3 0.016829 0 0 0.070901 0.2139 0.36215
4 0.046375 0 0.0061439 0.087319 0.2266 0.36264
5 0.095198 0.0087684 0.034403 0.1168 0.2468 0.37473
6 0.1663 0.054361 0.077248 0.1522 0.26639 0.39151
7 0.26234 0.099892 0.13132 0.19388 0.29929 0.41281
8 0.38568 0.15958 0.19309 0.24112 0.33017 0.43088
9 0.53852 0.23417 0.25553 0.29215 0.37436 0.45969
10 0.72291 0.3071 0.31656 0.34812 0.41153 0.48386
11 0.94076 0.37595 0.37503 0.40842 0.44925 0.50992
12 1.1939 0.43881 0.42941 0.45755 0.48697 0.54367
13 1.484 0.49509 0.48129 0.50381 0.53262 0.56979
14 1.8128 0.54489 0.53018 0.54642 0.56778 0.59634
15 2.1817 0.58871 0.57382 0.58548 0.60055 0.6282
16 2.5924 0.62716 0.61258 0.62076 0.63101 0.65249
17 3.0463 0.66079 0.64682 0.65243 0.65884 0.6752
18 3.5449 0.69027 0.67709 0.68069 0.68423 0.69638
19 4.0894 0.71621 0.70376 0.70596 0.70724 0.71591
20 4.6813 0.73703 0.72732 0.72848 0.72799 0.73385
21 5.3218 0.75326 0.74813 0.7485 0.74673 0.75021
22 6.0121 0.76913 0.76657 0.76632 0.76364 0.76535
23 6.7536 0.78536 0.78286 0.78231 0.77889 0.7842
24 7.5474 0.79983 0.79745 0.79653 0.79269 0.79678
25 8.3948 0.81271 0.81039 0.80929 0.80514 0.80831
26 9.2967 0.82418 0.82198 0.82076 0.81637 0.81875
27 10.254 0.8345 0.83242 0.83114 0.82656 0.82833
28 11.269 0.84377 0.84176 0.84042 0.83584 0.83706
29 12.342 0.85214 0.85024 0.84884 0.8442 0.84499
30 13.473 0.85964 0.85781 0.85647 0.85183 0.85232
31 14.665 0.86648 0.86471 0.86337 0.85879 0.85897
32 15.918 0.87264 0.87099 0.86965 0.86507 0.86507
33 17.233 0.87826 0.87667 0.87533 0.87161 0.87063
34 18.611 0.88338 0.88186 0.88052 0.87771 0.87582
35 20.053 0.88802 0.88656 0.88528 0.88326 0.88052
36 21.56 0.8923 0.89089 0.88967 0.88833 0.88485
37 23.133 0.89614 0.89486 0.89364 0.8926 0.88888
38 24.773 0.89974 0.89852 0.8973 0.89626 0.8926
39 26.481 0.90304 0.90182 0.90072 0.89968 0.89608
40 28.258 0.90603 0.90493 0.90383 0.90279 0.89925
41 30.104 0.90884 0.90774 0.9067 0.90572 0.90218
42 32.021 0.9114 0.91036 0.90932 0.90841 0.90493
43 34.01 0.91378 0.9128 0.91183 0.91091 0.90749
44 36.07 0.91598 0.91506 0.91408 0.91317 0.90987
45 38.204 0.91805 0.91714 0.91622 0.91537 0.91207
46 40.412 0.91994 0.91909 0.91817 0.91732 0.91415
47 42.695 0.92171 0.92086 0.92001 0.91921 0.9161
48 45.053 0.92336 0.92257 0.92171 0.92092 0.91799
49 47.488 0.92489 0.92409 0.92336 0.92257 0.92025
50 50 0.92629 0.92562 0.92489 0.92428 0.92403 
Run the function and show summaries for savings and fraction of coh saved:
mp_params('it_a_n') = 100;
mp_params('it_z_n') = 9;
mp_support('ls_ffcmd') = {'ap', 'savefraccoh'};
mp_support('ls_ffsna') = {};
mp_support('ls_ffgrh') = {};
mp_support('bl_vfi_store_all') = true; % store c(a,z), y(a,z)
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 57.010652 seconds.
----------------------------------------
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CONTAINER NAME: mp_ffcmd ND Array (Matrix etc)
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i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ _______ _______ ________ ___ _______
ap 1 1 2 900 100 9 12926 14.362 14.544 1.0127 0 51.171
savefraccoh 2 2 2 900 100 9 621.24 0.69027 0.26896 0.38965 0 0.92739
xxx TABLE:ap xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7 c8 c9
______ ______ ______ __________ ________ _______ _______ ______ ______
r1 0 0 0 0 0.087442 0.27778 0.58243 1.0038 1.5724
r2 0 0 0 0 0.087962 0.27828 0.58297 1.0044 1.5731
r3 0 0 0 0 0.090477 0.28074 0.58547 1.0069 1.5755
r4 0 0 0 0.00055771 0.09279 0.28605 0.5907 1.0122 1.5808
r5 0 0 0 0.0059496 0.09602 0.29477 0.59952 1.0209 1.5895
r96 43.845 43.923 44.022 44.198 44.428 44.722 45.103 45.546 46.186
r97 45.031 45.101 45.208 45.384 45.613 45.91 46.293 46.735 47.382
r98 46.237 46.297 46.411 46.59 46.818 47.115 47.501 47.948 48.605
r99 47.46 47.512 47.635 47.812 48.041 48.34 48.726 49.191 49.869
r100 48.703 48.746 48.878 49.055 49.283 49.586 49.978 50.495 51.171
xxx TABLE:savefraccoh xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7 c8 c9
_______ _______ _______ __________ ________ _______ _______ _______ _______
r1 0 0 0 0 0.066018 0.16569 0.27445 0.37369 0.46243
r2 0 0 0 0 0.066384 0.16593 0.27463 0.37381 0.46256
r3 0 0 0 0 0.068154 0.16715 0.27549 0.37442 0.46292
r4 0 0 0 0.00052879 0.069619 0.16978 0.27726 0.37564 0.46378
r5 0 0 0 0.0055946 0.071572 0.17405 0.28025 0.37766 0.46512
r96 0.92458 0.92354 0.92226 0.92171 0.92116 0.92055 0.91994 0.91842 0.91811
r97 0.92531 0.92416 0.92306 0.92251 0.92196 0.92141 0.92086 0.91933 0.91915
r98 0.92605 0.9247 0.92379 0.9233 0.92275 0.9222 0.92171 0.92031 0.92031
r99 0.92672 0.92525 0.92452 0.92403 0.92348 0.923 0.92251 0.92147 0.92184
r100 0.92739 0.9258 0.92525 0.92477 0.92422 0.92379 0.92342 0.92336 0.923671.4 Test FF_VFI_AZ_BISEC_LOOP Change Interest Rate and Discount
Show only save fraction of cash on hand:
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_print_params') = false;
mp_support('bl_print_iterinfo') = false;
mp_support('ls_ffcmd') = {'savefraccoh'};
mp_support('ls_ffsna') = {};
mp_support('ls_ffgrh') = {};
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 100;
mp_params('it_z_n') = 7;
mp_params('fl_a_max') = 50;
mp_params('st_grid_type') = 'grid_powerspace';Solve the model with several different interest rates and discount factor:
% Lower Savings Incentives
mp_params('fl_beta') = 0.80;
mp_params('fl_r') = 0.01;
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 10.824225 seconds.
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_ffcmd ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ _______ _______ ________ ___ _______
savefraccoh 1 1 2 700 100 7 357.85 0.51122 0.27528 0.53848 0 0.79965
xxx TABLE:savefraccoh xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
_______ _______ _______ _______ _______ __________ ________
r1 0 0 0 0 0 0.00022362 0.041544
r2 0 0 0 0 0 0.00022362 0.041544
r3 0 0 0 0 0 0.0011391 0.041544
r4 0 0 0 0 0 0.0016884 0.041483
r5 0 0 0 0 0 0.0034584 0.04136
r96 0.79586 0.79275 0.78945 0.78591 0.78225 0.77853 0.77059
r97 0.79684 0.79379 0.79055 0.78713 0.78359 0.77993 0.77212
r98 0.79782 0.79482 0.79171 0.78835 0.78488 0.78127 0.77365
r99 0.79873 0.79586 0.79275 0.78951 0.7861 0.78262 0.77548
r100 0.79965 0.79684 0.79385 0.79061 0.78732 0.7839 0.7781
% Higher Savings Incentives
mp_params('fl_beta') = 0.95;
mp_params('fl_r') = 0.04;
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 53.369195 seconds.
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_ffcmd ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ _______ _______ ________ ___ _______
savefraccoh 1 1 2 700 100 7 481.37 0.68768 0.27118 0.39435 0 0.92702
xxx TABLE:savefraccoh xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
_______ _______ _______ ________ _______ _______ _______
r1 0 0 0 0.065774 0.18076 0.30655 0.41654
r2 0 0 0 0.066201 0.18101 0.30674 0.4166
r3 0 0 0 0.06791 0.18223 0.30747 0.41709
r4 0 0 0 0.069619 0.18467 0.30759 0.41812
r5 0 0 0 0.071694 0.18876 0.30838 0.41983
r96 0.92428 0.92245 0.92178 0.92116 0.92049 0.91872 0.91824
r97 0.92501 0.92324 0.92257 0.92196 0.92129 0.91958 0.91921
r98 0.92574 0.92397 0.92336 0.92275 0.92208 0.92049 0.92025
r99 0.92647 0.9247 0.92409 0.92348 0.92287 0.92147 0.92159
r100 0.92702 0.92544 0.92483 0.92422 0.92373 0.92336 0.923481.5 Test FF_VFI_AZ_BISEC_LOOP Changing Risk Aversion
Here, again, show fraction of coh saved in summary tabular form, but also show it graphically.
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_print_params') = false;
mp_support('bl_print_iterinfo') = false;
mp_support('ls_ffcmd') = {'savefraccoh'};
mp_support('ls_ffsna') = {};
mp_support('ls_ffgrh') = {'savefraccoh'};
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 100;
mp_params('it_z_n') = 7;
mp_params('fl_a_max') = 50;
mp_params('st_grid_type') = 'grid_powerspace';Solve the model with different risk aversion levels, higher preferences for risk:
% Lower Risk Aversion
mp_params('fl_crra') = 0.5;
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 47.635241 seconds.
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_ffcmd ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ ______ _______ ________ ___ _______
savefraccoh 1 1 2 700 100 7 452.13 0.6459 0.28031 0.43398 0 0.90359
xxx TABLE:savefraccoh xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
_______ _______ _______ _________ ________ _______ _______
r1 0 0 0 0.0047401 0.089089 0.19822 0.30783
r2 0 0 0 0.0051674 0.089394 0.1984 0.30796
r3 0 0 0 0.0060218 0.090676 0.19926 0.30851
r4 0 0 0 0.0082801 0.092812 0.20115 0.30973
r5 0 0 0 0.012247 0.092995 0.2042 0.31174
r96 0.90047 0.89925 0.89828 0.8973 0.89632 0.89376 0.89297
r97 0.90127 0.90017 0.89919 0.89828 0.8973 0.8948 0.89394
r98 0.90206 0.90102 0.90011 0.89919 0.89828 0.89577 0.89498
r99 0.90279 0.90188 0.90102 0.90011 0.89919 0.89681 0.8959
r100 0.90359 0.90273 0.90188 0.90096 0.90011 0.89803 0.89687
When risk aversion increases, at every state-space point, the household wants to save more.
% Higher Risk Aversion
mp_params('fl_crra') = 5;
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 46.937845 seconds.
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_ffcmd ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ _______ _______ ________ ___ _______
savefraccoh 1 1 2 700 100 7 502.71 0.71816 0.25437 0.3542 0 0.93587
xxx TABLE:savefraccoh xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
_______ _______ ________ _______ _______ _______ _______
r1 0 0 0.047037 0.15537 0.27573 0.3909 0.48782
r2 0 0 0.047525 0.15531 0.27591 0.39102 0.48795
r3 0 0 0.049844 0.1569 0.27695 0.3917 0.48837
r4 0 0 0.054788 0.16025 0.27915 0.3931 0.48929
r5 0 0 0.062905 0.16569 0.28275 0.39542 0.49075
r96 0.93307 0.93258 0.93203 0.93154 0.9302 0.92995 0.92971
r97 0.93374 0.93325 0.93276 0.93227 0.93111 0.93105 0.93117
r98 0.93441 0.93398 0.93349 0.93307 0.93209 0.93227 0.9327
r99 0.93508 0.93465 0.93423 0.93392 0.93331 0.93368 0.93435
r100 0.93575 0.93539 0.93508 0.9349 0.93496 0.93526 0.93587
1.6 Test FF_VFI_AZ_BISEC_LOOP with Higher Uncertainty
Increase the standard deviation of the Shock.
mp_support = containers.Map('KeyType','char', 'ValueType','any');
mp_support('bl_print_params') = false;
mp_support('bl_print_iterinfo') = false;
mp_support('ls_ffcmd') = {'savefraccoh'};
mp_support('ls_ffsna') = {};
mp_support('ls_ffgrh') = {};
mp_params = containers.Map('KeyType','char', 'ValueType','any');
mp_params('it_a_n') = 150;
mp_params('it_z_n') = 15;
mp_params('fl_a_max') = 50;
mp_params('st_grid_type') = 'grid_powerspace';
% graph color spectrum
mp_params('cl_colors') = 'copper';Lower standard deviation of shock:
% Lower Risk Aversion
mp_params('fl_shk_std') = 0.10;
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 150.979328 seconds.
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_ffcmd ND Array (Matrix etc)
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i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ _______ _______ ________ ___ _______
savefraccoh 1 1 2 2250 150 15 1507.5 0.67001 0.28668 0.42788 0 0.92568
xxx TABLE:savefraccoh xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c11 c12 c13 c14 c15
_______ _______ _______ _______ _______ _______ _______ _______ _______ _______
r1 0 0 0 0 0 0.13847 0.18485 0.23026 0.27378 0.31729
r2 0 0 0 0 0 0.13853 0.18491 0.23032 0.27384 0.31736
r3 0 0 0 0 0 0.13895 0.18528 0.23063 0.27408 0.3176
r4 0 0 0 0 0 0.13987 0.18607 0.2313 0.27469 0.31809
r5 0 0 0 0 0 0.14011 0.18735 0.2324 0.27567 0.31888
r146 0.92373 0.92354 0.9233 0.92312 0.92287 0.92086 0.92068 0.92049 0.91952 0.91933
r147 0.92422 0.92403 0.92385 0.92361 0.92342 0.92141 0.92123 0.92098 0.92007 0.91988
r148 0.9247 0.92452 0.92434 0.92409 0.92391 0.9219 0.92171 0.92153 0.92062 0.92043
r149 0.92519 0.92501 0.92483 0.92458 0.9244 0.92245 0.92226 0.92208 0.92116 0.9211
r150 0.92568 0.9255 0.92531 0.92507 0.92489 0.92293 0.92275 0.92257 0.92245 0.92232Higher shock standard deviation: low shock high asset save more, high shock more asset save less, high shock low asset save more:
% Higher Risk Aversion
mp_params('fl_shk_std') = 0.40;
ff_vfi_az_bisec_loop(mp_params, mp_support);
Elapsed time is 136.803951 seconds.
----------------------------------------
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CONTAINER NAME: mp_ffcmd ND Array (Matrix etc)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ______ _______ _______ ________ ___ _______
savefraccoh 1 1 2 2250 150 15 1685.6 0.74914 0.22909 0.3058 0 0.93679
xxx TABLE:savefraccoh xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c11 c12 c13 c14 c15
_______ _______ _______ _______ _______ _______ _______ _______ _______ _______
r1 0 0 0 0 0 0.5264 0.61264 0.68271 0.73922 0.78433
r2 0 0 0 0 0 0.52646 0.61264 0.68271 0.73922 0.78433
r3 0 0 0 0 0 0.52658 0.6127 0.68271 0.73922 0.78433
r4 0 0 0 0 0 0.52682 0.61288 0.68283 0.73928 0.78439
r5 0 0 0 0 0 0.52731 0.61313 0.68295 0.73934 0.78439
r146 0.92983 0.92928 0.92873 0.92806 0.92739 0.92269 0.92354 0.9258 0.92904 0.93331
r147 0.9302 0.92971 0.9291 0.92849 0.92788 0.92361 0.92477 0.9269 0.93001 0.93423
r148 0.93056 0.93008 0.92953 0.92892 0.92831 0.92458 0.92593 0.928 0.93105 0.93508
r149 0.93093 0.93044 0.92995 0.92934 0.92873 0.9258 0.92702 0.9291 0.93203 0.936
r150 0.9313 0.93087 0.93032 0.92977 0.92916 0.92696 0.92818 0.93014 0.93294 0.93679