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: ffy_rouwenhorst from the MEconTools Package. See also ffy_tauchen function from the MEconTools Package. This function discretize a mean zero AR1 process, uses Rouwenhorst (1995). See AR 1 Example for some details on how the AR1 process works. And See Kopecky and Suen (2010).
Call the function with defaults.
ffy_rouwenhorst();
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CONTAINER NAME: mp_container_map ND Array (Matrix etc)
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i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ___ ____ _______ ________ ______ ______
ar_disc_ar1 1 1 2 5 5 1 0 0 0.39528 Inf -0.5 0.5
mt_disc_ar1_trans 2 11 2 25 5 5 5 0.2 0.18246 0.91229 0.0016 0.5136
xxx TABLE:ar_disc_ar1 xxxxxxxxxxxxxxxxxx
c1
_____
r1 -0.5
r2 -0.25
r3 0
r4 0.25
r5 0.5
xxx TABLE:mt_disc_ar1_trans xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5
______ ______ ______ ______ ______
r1 0.4096 0.4096 0.1536 0.0256 0.0016
r2 0.1024 0.4864 0.3264 0.0784 0.0064
r3 0.0256 0.2176 0.5136 0.2176 0.0256
r4 0.0064 0.0784 0.3264 0.4864 0.1024
r5 0.0016 0.0256 0.1536 0.4096 0.4096
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CONTAINER NAME: mp_container_map Scalars
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i idx value
_ ___ _____
fl_ar1_beg 1 2 -0.5
fl_ar1_end 2 3 0.5
fl_ar1_persistence 3 4 0.6
fl_ar1_step 4 5 0.25
fl_p0 5 6 0.8
fl_q0 6 7 0.8
fl_shk_std 7 8 0.2
fl_sig_ar1 8 9 0.25
it_std_bound 9 10 0 With a grid of 10 points, the Rwouenhorst bounds on standard deviations are equall to Tauchen bounds of 3. With the not extremely persistent shock process here, the Tauchen and Rouwenhorst Results are very similar.
[fl_ar1_persistence, fl_shk_std, it_disc_points, bl_verbose] = ...
deal(0.60, 0.10, 10, true);
ffy_rouwenhorst(fl_ar1_persistence, fl_shk_std, it_disc_points, bl_verbose);
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CONTAINER NAME: mp_container_map ND Array (Matrix etc)
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i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ __________ __________ _______ __________ ________ _______
ar_disc_ar1 1 1 2 10 10 1 5.5511e-17 5.5511e-18 0.2523 4.5451e+16 -0.375 0.375
mt_disc_ar1_trans 2 11 2 100 10 10 10 0.1 0.11724 1.1724 5.12e-07 0.33477
xxx TABLE:ar_disc_ar1 xxxxxxxxxxxxxxxxxx
c1
_________
r1 -0.375
r2 -0.29167
r3 -0.20833
r4 -0.125
r5 -0.041667
r6 0.041667
r7 0.125
r8 0.20833
r9 0.29167
r10 0.375
xxx TABLE:mt_disc_ar1_trans xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7 c8 c9 c10
__________ __________ __________ _________ ________ ________ _________ __________ __________ __________
r1 0.13422 0.30199 0.30199 0.17616 0.06606 0.016515 0.0027525 0.00029491 1.8432e-05 5.12e-07
r2 0.033554 0.20133 0.32716 0.26424 0.12662 0.038535 0.0075694 0.00093389 6.6048e-05 2.048e-06
r3 0.0083886 0.081789 0.26267 0.32755 0.21401 0.082747 0.019741 0.0028677 0.00023347 8.192e-06
r4 0.0020972 0.028312 0.14038 0.30946 0.30369 0.15877 0.047989 0.0084603 0.00081101 3.2768e-05
r5 0.00052429 0.009044 0.061145 0.20246 0.33477 0.25969 0.10585 0.023642 0.0027525 0.00013107
r6 0.00013107 0.0027525 0.023642 0.10585 0.25969 0.33477 0.20246 0.061145 0.009044 0.00052429
r7 3.2768e-05 0.00081101 0.0084603 0.047989 0.15877 0.30369 0.30946 0.14038 0.028312 0.0020972
r8 8.192e-06 0.00023347 0.0028677 0.019741 0.082747 0.21401 0.32755 0.26267 0.081789 0.0083886
r9 2.048e-06 6.6048e-05 0.00093389 0.0075694 0.038535 0.12662 0.26424 0.32716 0.20133 0.033554
r10 5.12e-07 1.8432e-05 0.00029491 0.0027525 0.016515 0.06606 0.17616 0.30199 0.30199 0.13422
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CONTAINER NAME: mp_container_map Scalars
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i idx value
_ ___ ________
fl_ar1_beg 1 2 -0.375
fl_ar1_end 2 3 0.375
fl_ar1_persistence 3 4 0.6
fl_ar1_step 4 5 0.083333
fl_p0 5 6 0.8
fl_q0 6 7 0.8
fl_shk_std 7 8 0.1
fl_sig_ar1 8 9 0.125
it_std_bound 9 10 0[fl_ar1_persistence, fl_shk_std, it_disc_points, bl_verbose] = ...
deal(0.90, 0.02, 7, true);
[ar_z, mt_z_trans] = ffy_tauchen(fl_ar1_persistence, fl_shk_std, it_disc_points, bl_verbose);
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CONTAINER NAME: mp_container_map ND Array (Matrix etc)
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i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ __________ __________ ________ __________ ________ _______
ar_disc_ar1 1 1 2 7 7 1 2.7756e-17 3.9651e-18 0.099119 2.4998e+16 -0.13765 0.13765
mt_disc_ar1_trans 2 6 2 49 7 7 7 0.14286 0.24922 1.7445 0 0.74865
xxx TABLE:ar_disc_ar1 xxxxxxxxxxxxxxxxxx
c1
__________
r1 -0.13765
r2 -0.091766
r3 -0.045883
r4 1.3878e-17
r5 0.045883
r6 0.091766
r7 0.13765
xxx TABLE:mt_disc_ar1_trans xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
__________ __________ __________ __________ __________ __________ __________
r1 0.67682 0.32022 0.0029525 2.2423e-07 1.058e-13 0 0
r2 0.054147 0.7002 0.24422 0.0014299 6.5815e-08 1.8541e-14 0
r3 0.00012097 0.084213 0.73627 0.17874 0.00065947 1.8356e-08 3.1086e-15
r4 4.8643e-09 0.00028953 0.12539 0.74865 0.12539 0.00028953 4.8643e-09
r5 3.0921e-15 1.8356e-08 0.00065947 0.17874 0.73627 0.084213 0.00012097
r6 2.9554e-23 1.8558e-14 6.5815e-08 0.0014299 0.24422 0.7002 0.054147
r7 4.1477e-33 2.8319e-22 1.0576e-13 2.2423e-07 0.0029525 0.32022 0.67682
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CONTAINER NAME: mp_container_map Scalars
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i idx value
_ ___ ________
fl_ar1_persistence 1 2 0.9
fl_ar1_step 2 3 0.045883
fl_shk_std 3 4 0.02
it_std_bound 4 5 3
ar_z_stationary = mt_z_trans^1000;
ar_z_stationary = ar_z_stationary(1,:);
fl_labor_agg = ar_z_stationary*exp(ar_z);
ar_z = exp(ar_z')/fl_labor_agg;[fl_ar1_persistence, fl_shk_std, it_disc_points, bl_verbose] = ...
deal(0.01, 0.01, 7, true);
ffy_rouwenhorst(fl_ar1_persistence, fl_shk_std, it_disc_points, bl_verbose);
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CONTAINER NAME: mp_container_map ND Array (Matrix etc)
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i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ___ _______ ________ ________ _________ ________
ar_disc_ar1 1 1 2 7 7 1 0 0 0.017639 Inf -0.024496 0.024496
mt_disc_ar1_trans 2 11 2 49 7 7 7 0.14286 0.10985 0.76893 0.014711 0.31252
xxx TABLE:ar_disc_ar1 xxxxxxxxxxxxxxxxxx
c1
__________
r1 -0.024496
r2 -0.016331
r3 -0.0081654
r4 0
r5 0.0081654
r6 0.016331
r7 0.024496
xxx TABLE:mt_disc_ar1_trans xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
________ ________ _______ _______ _______ ________ ________
r1 0.016586 0.097547 0.23904 0.31241 0.22966 0.090047 0.014711
r2 0.016258 0.096266 0.23749 0.31247 0.23124 0.091266 0.015008
r3 0.015936 0.094997 0.23594 0.31251 0.23281 0.092497 0.015311
r4 0.01562 0.093741 0.23438 0.31252 0.23438 0.093741 0.01562
r5 0.015311 0.092497 0.23281 0.31251 0.23594 0.094997 0.015936
r6 0.015008 0.091266 0.23124 0.31247 0.23749 0.096266 0.016258
r7 0.014711 0.090047 0.22966 0.31241 0.23904 0.097547 0.016586
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CONTAINER NAME: mp_container_map Scalars
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i idx value
_ ___ _________
fl_ar1_beg 1 2 -0.024496
fl_ar1_end 2 3 0.024496
fl_ar1_persistence 3 4 0.01
fl_ar1_step 4 5 0.0081654
fl_p0 5 6 0.505
fl_q0 6 7 0.505
fl_shk_std 7 8 0.01
fl_sig_ar1 8 9 0.010001
it_std_bound 9 10 0[fl_ar1_persistence, fl_shk_std, it_disc_points, bl_verbose] = ...
deal(0.99, 0.99, 7, true);
ffy_rouwenhorst(fl_ar1_persistence, fl_shk_std, it_disc_points, bl_verbose);
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CONTAINER NAME: mp_container_map ND Array (Matrix etc)
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i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ __________ __________ _______ _________ __________ _______
ar_disc_ar1 1 1 2 7 7 1 3.5527e-15 5.0753e-16 12.378 2.439e+16 -17.19 17.19
mt_disc_ar1_trans 2 11 2 49 7 7 7 0.14286 0.34148 2.3904 1.5625e-14 0.97059
xxx TABLE:ar_disc_ar1 xxxxxxxxxxxxxxxxxx
c1
_______
r1 -17.19
r2 -11.46
r3 -5.7301
r4 0
r5 5.7301
r6 11.46
r7 17.19
xxx TABLE:mt_disc_ar1_trans xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
__________ __________ __________ __________ __________ __________ __________
r1 0.97037 0.029257 0.00036756 2.4627e-06 9.2815e-09 1.8656e-11 1.5625e-14
r2 0.0048762 0.9705 0.024382 0.00024504 1.2314e-06 3.0938e-09 3.1094e-12
r3 2.4504e-05 0.009753 0.97057 0.019506 0.00014703 4.9254e-07 6.1877e-10
r4 1.2313e-07 7.3513e-05 0.01463 0.97059 0.01463 7.3513e-05 1.2313e-07
r5 6.1877e-10 4.9254e-07 0.00014703 0.019506 0.97057 0.009753 2.4504e-05
r6 3.1094e-12 3.0938e-09 1.2314e-06 0.00024504 0.024382 0.9705 0.0048762
r7 1.5625e-14 1.8656e-11 9.2815e-09 2.4627e-06 0.00036756 0.029257 0.97037
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CONTAINER NAME: mp_container_map Scalars
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i idx value
_ ___ ______
fl_ar1_beg 1 2 -17.19
fl_ar1_end 2 3 17.19
fl_ar1_persistence 3 4 0.99
fl_ar1_step 4 5 5.7301
fl_p0 5 6 0.995
fl_q0 6 7 0.995
fl_shk_std 7 8 0.99
fl_sig_ar1 8 9 7.0179
it_std_bound 9 10 0[fl_ar1_persistence, fl_shk_std, it_disc_points, bl_verbose] = ...
deal(0.01, 0.01, 7, true);
ffy_rouwenhorst(fl_ar1_persistence, fl_shk_std, it_disc_points, bl_verbose);
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CONTAINER NAME: mp_container_map ND Array (Matrix etc)
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i idx ndim numel rowN colN sum mean std coefvari min max
_ ___ ____ _____ ____ ____ ___ _______ ________ ________ _________ ________
ar_disc_ar1 1 1 2 7 7 1 0 0 0.017639 Inf -0.024496 0.024496
mt_disc_ar1_trans 2 11 2 49 7 7 7 0.14286 0.10985 0.76893 0.014711 0.31252
xxx TABLE:ar_disc_ar1 xxxxxxxxxxxxxxxxxx
c1
__________
r1 -0.024496
r2 -0.016331
r3 -0.0081654
r4 0
r5 0.0081654
r6 0.016331
r7 0.024496
xxx TABLE:mt_disc_ar1_trans xxxxxxxxxxxxxxxxxx
c1 c2 c3 c4 c5 c6 c7
________ ________ _______ _______ _______ ________ ________
r1 0.016586 0.097547 0.23904 0.31241 0.22966 0.090047 0.014711
r2 0.016258 0.096266 0.23749 0.31247 0.23124 0.091266 0.015008
r3 0.015936 0.094997 0.23594 0.31251 0.23281 0.092497 0.015311
r4 0.01562 0.093741 0.23438 0.31252 0.23438 0.093741 0.01562
r5 0.015311 0.092497 0.23281 0.31251 0.23594 0.094997 0.015936
r6 0.015008 0.091266 0.23124 0.31247 0.23749 0.096266 0.016258
r7 0.014711 0.090047 0.22966 0.31241 0.23904 0.097547 0.016586
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CONTAINER NAME: mp_container_map Scalars
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i idx value
_ ___ _________
fl_ar1_beg 1 2 -0.024496
fl_ar1_end 2 3 0.024496
fl_ar1_persistence 3 4 0.01
fl_ar1_step 4 5 0.0081654
fl_p0 5 6 0.505
fl_q0 6 7 0.505
fl_shk_std 7 8 0.01
fl_sig_ar1 8 9 0.010001
it_std_bound 9 10 0