This website collects the relevant materials to the implementation of "Putting Home into Macroeconomics" by Greenwood et al. (1993) . Find the code and further details on GitHub , in the paper and pencil solutions or in the slides .
The numbering of the models is replicated from the original paper:
- Model 1: Model with home production minimized
- Model 2: Model with increased willingness to substitute between home and market
- Model 3: Model with increased incentive to substitute between home and market
- Model 4: Model with a more general home production function and highly correlated technology shocks
Additional models (not included in Greenwood et al., 1993):
- Model 2a: Adjusts Model 2 according to the suggestions of Greenwood et al. (1993) to increase the standard deviation of the home technology shock
- Model 4a: Adjusts Model 4 to achieve a more appropriate correlation between home and business investments
Specification of the model
Variables and Parameters
MOD - File
Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Found 18 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs ...
done
Preprocessing completed.
"Model with home production minimized (levels)"
"The numbering of the equations is referenced to the P&P solutions."
"Manuel Bieri and Michael Wagner (2023)"
"Replace (93) with (146) for steady state calculation"
Residuals of the static equations:
Equation number 1 : 0 : (41) Resource Constraint
Equation number 2 : 0 : (42) Household FOC w.r.t. hh
Equation number 3 : 0 : (43) Household FOC w.r.t. hm
Equation number 4 : 0 : (44) Household FOC w.r.t. kh
Equation number 5 : 0 : (45) Household FOC w.r.t. km
Equation number 6 : 0 : (46) Firm FOC w.r.t. km
Equation number 7 : 0 : (47) Firm FOC w.r.t. hm
Equation number 8 : 0 : (48) Market Output
Equation number 9 : 0 : (140) Total Consumption
Equation number 10 : 0 : (50) Leisure
Equation number 11 : 0 : (51) Home production
Equation number 12 : 0 : (52) Market Investments
Equation number 13 : 0 : (53) Home Investments
Equation number 14 : 0 : (54) Total Investments
Equation number 15 : 0 : (55) Total Capital
Equation number 16 : 0 : (56) Government Transfer
Equation number 17 : 0 : (57) Market Technology
Equation number 18 : 0 : (58) Home Technology
STEADY-STATE RESULTS:
C 0.487749
cm 0.439277
ch 0.556378
l 0.42
hm 0.33
hh 0.25
k 5.29596
km 2.35423
kh 2.94173
x 0.149208
xm 0.0663282
xh 0.0828803
r 0.0735909
T 0.186357
w 1.25829
y 0.588486
zm 1
zh 1
EIGENVALUES:
Modulus Real Imaginary
1.981e-15 -1.981e-15 0
0.95 0.95 0
0.95 0.95 0
0.9587 0.9587 0
1.118 1.118 0
6.897e+16 -6.897e+16 0
6.497e+17 -6.497e+17 0
Inf Inf 0
There are 4 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition is verified.
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.
Information about Model1_level (dynamic model)
The following variables appear with a lag and are therefore states:
km(-1)
kh(-1)
zm(-1)
zh(-1)
The following variables appear with a lead and are therefore forward-looking variables:
C(1)
cm(1)
ch(1)
r(1)
The following variables do not appear with a lead or lag and are therefore purely static variables:
l
hm
hh
k
x
xm
xh
T
w
y
MODEL SUMMARY
Number of variables: 18
Number of stochastic shocks: 2
Number of state variables: 4
Number of jumpers: 4
Number of static variables: 10
MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS
Variables eh em
eh 0.000098 0.000066
em 0.000066 0.000098
POLICY AND TRANSITION FUNCTIONS
C cm ch k km kh x xm xh l hm hh zm zh r w y T
Constant 0.487749 0.439277 0.556378 5.295963 2.354233 2.941730 0.149208 0.066328 0.082880 0.420000 0.330000 0.250000 1.000000 1.000000 0.073591 1.258289 0.588486 0.186357
km(-1) 0.020786 0.038970 -0.008548 1.025501 0.491373 0.534128 0.053795 -0.482830 0.536625 -0.009552 0.015238 -0.005686 0 0 -0.019659 0.140245 0.092765 0.019031
kh(-1) 0.052011 0.034096 0.079632 0.897253 0.429922 0.467331 -0.075053 0.431932 -0.506985 0.020404 -0.032550 0.012145 0 0 -0.005122 0.036538 -0.040957 -0.015665
zm(-1) 0.075352 0.165254 -0.069187 0.382630 0.508804 -0.126174 0.384419 0.511182 -0.126764 -0.077318 0.123341 -0.046023 0.950000 0 0.068737 0.705001 0.549672 0.210239
zh(-1) 0.138636 0 0.357042 0 0 0 0 0 0 0 0 0 0 0.950000 0 0 0 0
eh 0.145933 0 0.375833 0 0 0 0 0 0 0 0 0 0 1.000000 0 0 0 0
em 0.079318 0.173951 -0.072829 0.402769 0.535583 -0.132815 0.404651 0.538087 -0.133436 -0.081387 0.129832 -0.048445 1.000000 0 0.072355 0.742106 0.578602 0.221304
MOMENTS OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE SKEWNESS KURTOSIS
C 0.487751 0.002840 0.000008 0.159134 0.020044
cm 0.438100 0.002491 0.000006 0.200378 0.166740
ch 0.558257 0.004283 0.000018 0.085241 -0.166226
k 5.271560 0.022399 0.000502 0.348770 0.094117
km 2.342001 0.012739 0.000162 0.338340 0.098717
kh 2.929559 0.011357 0.000129 0.349776 0.114116
x 0.148830 0.005871 0.000034 0.014812 0.275360
xm 0.066146 0.005095 0.000026 0.100577 0.197232
xh 0.082684 0.003654 0.000013 -0.036397 0.347001
l 0.419995 0.001199 0.000001 0.020068 0.293021
hm 0.330008 0.001912 0.000004 -0.020068 0.293021
hh 0.249997 0.000713 0.000001 0.020068 0.293021
zm 0.998428 0.013412 0.000180 0.042164 0.245521
zh 1.007024 0.013487 0.000182 0.057305 -0.017576
r 0.073784 0.000966 0.000001 -0.100496 0.276275
w 1.254934 0.010513 0.000111 0.137039 0.206046
y 0.586930 0.008246 0.000068 0.076301 0.241715
T 0.185966 0.003087 0.000010 0.046102 0.252741
CORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE C cm ch k km kh x xm xh l hm hh zm zh r w y T
C 1.0000 0.8767 0.8952 0.4727 0.7003 0.1468 0.8290 0.6203 0.4670 -0.8105 0.8105 -0.8105 0.8374 0.9284 0.7206 0.8719 0.8550 0.8421
cm 0.8767 1.0000 0.5706 0.5666 0.8179 0.2001 0.9343 0.6869 0.5433 -0.9115 0.9115 -0.9115 0.9441 0.6713 0.8017 0.9901 0.9673 0.9504
ch 0.8952 0.5706 1.0000 0.2821 0.4379 0.0652 0.5499 0.4227 0.2941 -0.5395 0.5395 -0.5395 0.5551 0.9633 0.4876 0.5715 0.5639 0.5574
k 0.4727 0.5666 0.2821 1.0000 0.9375 0.9207 0.2405 -0.0301 0.4283 -0.1832 0.1832 -0.1832 0.2634 0.1664 -0.0372 0.4472 0.3424 0.2836
km 0.7003 0.8179 0.4379 0.9375 1.0000 0.7273 0.5625 0.2691 0.5285 -0.5129 0.5129 -0.5129 0.5826 0.3997 0.3126 0.7303 0.6475 0.5993
kh 0.1468 0.2001 0.0652 0.9207 0.7273 1.0000 -0.1566 -0.3611 0.2519 0.2139 -0.2139 0.2139 -0.1340 -0.1202 -0.4240 0.0627 -0.0510 -0.1130
x 0.8290 0.9343 0.5499 0.2405 0.5625 -0.1566 1.0000 0.7869 0.5095 -0.9982 0.9982 -0.9982 0.9977 0.7212 0.9557 0.9751 0.9942 0.9985
xm 0.6203 0.6869 0.4227 -0.0301 0.2691 -0.3611 0.7869 1.0000 -0.1301 -0.7935 0.7935 -0.7935 0.8163 0.5704 0.8743 0.7373 0.7677 0.7935
xh 0.4670 0.5433 0.2941 0.4283 0.5285 0.2519 0.5095 -0.1301 1.0000 -0.4975 0.4975 -0.4975 0.4647 0.3634 0.3164 0.5387 0.5269 0.4979
l -0.8105 -0.9115 -0.5395 -0.1832 -0.5129 0.2139 -0.9982 -0.7935 -0.4975 1.0000 -1.0000 1.0000 -0.9939 -0.7203 -0.9692 -0.9602 -0.9861 -0.9938
hm 0.8105 0.9115 0.5395 0.1832 0.5129 -0.2139 0.9982 0.7935 0.4975 -1.0000 1.0000 -1.0000 0.9939 0.7203 0.9692 0.9602 0.9861 0.9938
hh -0.8105 -0.9115 -0.5395 -0.1832 -0.5129 0.2139 -0.9982 -0.7935 -0.4975 1.0000 -1.0000 1.0000 -0.9939 -0.7203 -0.9692 -0.9602 -0.9861 -0.9938
zm 0.8374 0.9441 0.5551 0.2634 0.5826 -0.1340 0.9977 0.8163 0.4647 -0.9939 0.9939 -0.9939 1.0000 0.7195 0.9535 0.9803 0.9955 0.9993
zh 0.9284 0.6713 0.9633 0.1664 0.3997 -0.1202 0.7212 0.5704 0.3634 -0.7203 0.7203 -0.7203 0.7195 1.0000 0.6915 0.7017 0.7163 0.7199
r 0.7206 0.8017 0.4876 -0.0372 0.3126 -0.4240 0.9557 0.8743 0.3164 -0.9692 0.9692 -0.9692 0.9535 0.6915 1.0000 0.8752 0.9226 0.9452
w 0.8719 0.9901 0.5715 0.4472 0.7303 0.0627 0.9751 0.7373 0.5387 -0.9602 0.9602 -0.9602 0.9803 0.7017 0.8752 1.0000 0.9933 0.9845
y 0.8550 0.9673 0.5639 0.3424 0.6475 -0.0510 0.9942 0.7677 0.5269 -0.9861 0.9861 -0.9861 0.9955 0.7163 0.9226 0.9933 1.0000 0.9980
T 0.8421 0.9504 0.5574 0.2836 0.5993 -0.1130 0.9985 0.7935 0.4979 -0.9938 0.9938 -0.9938 0.9993 0.7199 0.9452 0.9845 0.9980 1.0000
AUTOCORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE 1 2 3 4 5
C 0.7470 0.5260 0.3534 0.2046 0.0694
cm 0.7757 0.5643 0.4034 0.2612 0.1229
ch 0.7198 0.4834 0.3030 0.1450 0.0203
k 0.9633 0.8730 0.7462 0.5962 0.4341
km 0.9169 0.7968 0.6617 0.5136 0.3576
kh 0.9455 0.8434 0.7130 0.5639 0.4039
x 0.7635 0.5098 0.3265 0.1772 0.0413
xm 0.2290 0.0880 0.0770 0.0517 -0.0324
xh 0.4512 0.2634 0.1808 0.1038 -0.0016
l 0.7665 0.5100 0.3245 0.1741 0.0379
hm 0.7665 0.5100 0.3245 0.1741 0.0379
hh 0.7665 0.5100 0.3245 0.1741 0.0379
zm 0.7267 0.4835 0.3137 0.1736 0.0412
zh 0.7328 0.4834 0.2946 0.1364 0.0072
r 0.6987 0.4596 0.2978 0.1640 0.0341
w 0.7649 0.5325 0.3615 0.2167 0.0801
y 0.7617 0.5162 0.3381 0.1910 0.0551
T 0.7483 0.5011 0.3247 0.1796 0.0452
VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent) (HP filter, lambda = 1600)
eh em Tot. lin. contr.
C 86.84 9.88 96.72
cm 43.65 49.64 93.29
ch 97.59 5.74 103.33
k 38.90 51.40 90.30
km 40.01 51.37 91.38
kh 39.46 50.46 89.92
x 45.15 48.28 93.43
xm 44.31 49.91 94.22
xh 44.69 49.31 94.00
l 45.24 48.12 93.36
hm 45.24 48.12 93.36
hh 45.24 48.12 93.36
zm 44.99 48.53 93.52
zh 100.11 0.00 100.11
r 45.07 48.06 93.13
w 44.40 49.07 93.47
y 44.86 48.63 93.50
T 45.00 48.49 93.49
Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples
Total computing time : 0h00m23s
Specification of the model
Variables and Parameters
MOD - File
Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Found 18 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs ...
done
Preprocessing completed.
"Model with increased willingness to substitute between home and market (levels)"
"The numbering of the equations is referenced to the P&P solutions."
"Manuel Bieri and Michael Wagner (2023)"
Residuals of the static equations:
Equation number 1 : 0 : (41) Resource Constraint
Equation number 2 : 0 : (42) Household FOC w.r.t. hh
Equation number 3 : 0 : (43) Household FOC w.r.t. hm
Equation number 4 : 0 : (44) Household FOC w.r.t. kh
Equation number 5 : 0 : (45) Household FOC w.r.t. km
Equation number 6 : 0 : (46) Firm FOC w.r.t. km
Equation number 7 : 0 : (47) Firm FOC w.r.t. hm
Equation number 8 : 0 : (48) Market Output
Equation number 9 : 0 : (49) Total Consumption
Equation number 10 : 0 : (50) Leisure
Equation number 11 : 0 : (51) Home production
Equation number 12 : 0 : (52) Market Investments
Equation number 13 : 0 : (53) Home Investments
Equation number 14 : 0 : (54) Total Investments
Equation number 15 : 0 : (55) Total Capital
Equation number 16 : 0 : (56) Government Transfer
Equation number 17 : 0 : (57) Market Technology
Equation number 18 : 0 : (58) Home Technology
STEADY-STATE RESULTS:
C 0.48553
cm 0.439277
ch 0.556378
l 0.42
hm 0.33
hh 0.25
k 5.29596
km 2.35423
kh 2.94173
x 0.149208
xm 0.0663282
xh 0.0828803
r 0.0735909
T 0.186357
w 1.25829
y 0.588486
zm 1
zh 1
EIGENVALUES:
Modulus Real Imaginary
1.344e-14 -1.344e-14 0
0.95 0.95 0
0.95 0.95 0
0.959 0.959 0
1.121 1.121 0
4.891e+16 4.891e+16 0
2.508e+17 -2.508e+17 0
Inf -Inf 0
There are 4 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition is verified.
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.
Information about Model2_level (dynamic model)
The following variables appear with a lag and are therefore states:
km(-1)
kh(-1)
zm(-1)
zh(-1)
The following variables appear with a lead and are therefore forward-looking variables:
C(1)
cm(1)
ch(1)
r(1)
The following variables do not appear with a lead or lag and are therefore purely static variables:
l
hm
hh
k
x
xm
xh
T
w
y
MODEL SUMMARY
Number of variables: 18
Number of stochastic shocks: 2
Number of state variables: 4
Number of jumpers: 4
Number of static variables: 10
MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS
Variables eh em
eh 0.000098 0.000066
em 0.000066 0.000098
POLICY AND TRANSITION FUNCTIONS
C cm ch k km kh x xm xh l hm hh zm zh r w y T
Constant 0.485530 0.439277 0.556378 5.295963 2.354233 2.941730 0.149208 0.066328 0.082880 0.420000 0.330000 0.250000 1.000000 1.000000 0.073591 1.258289 0.588486 0.186357
km(-1) 0.028395 0.067447 -0.033979 1.012012 0.524650 0.487362 0.040243 -0.449397 0.489640 -0.004497 0.027099 -0.022602 0 0 -0.017792 0.126931 0.107690 0.024739
kh(-1) 0.048393 0.018342 0.095981 0.901976 0.467605 0.434371 -0.070308 0.469791 -0.540099 0.018279 -0.041299 0.023020 0 0 -0.006498 0.046360 -0.051966 -0.019876
zm(-1) 0.140417 0.344114 -0.184888 0.244977 1.770066 -1.525089 0.246122 1.778340 -1.532217 -0.032593 0.155578 -0.122986 0.950000 0 0.073810 0.668813 0.590236 0.225753
zh(-1) 0.061570 -0.218340 0.507105 0.157430 -1.455181 1.612611 0.158166 -1.461982 1.620148 -0.051998 -0.047822 0.099820 0 0.950000 -0.007525 0.053683 -0.060174 -0.023015
eh 0.064810 -0.229832 0.533795 0.165716 -1.531769 1.697485 0.166490 -1.538929 1.705419 -0.054735 -0.050339 0.105074 0 1.000000 -0.007921 0.056508 -0.063341 -0.024227
em 0.147808 0.362225 -0.194619 0.257871 1.863228 -1.605357 0.259076 1.871937 -1.612860 -0.034308 0.163766 -0.129458 1.000000 0 0.077695 0.704013 0.621301 0.237635
MOMENTS OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE SKEWNESS KURTOSIS
C 0.485014 0.002761 0.000008 0.196578 0.131563
cm 0.435228 0.004110 0.000017 -0.006434 -0.160484
ch 0.561495 0.006846 0.000047 0.100825 -0.155606
k 5.269458 0.022079 0.000487 0.374386 0.104158
km 2.326409 0.021153 0.000447 0.015995 -0.097950
kh 2.943049 0.019249 0.000371 0.221307 -0.146786
x 0.148763 0.005872 0.000034 -0.027063 0.217330
xm 0.065690 0.012842 0.000165 0.044325 0.089116
xh 0.083074 0.013162 0.000173 -0.006561 -0.031397
l 0.419816 0.001187 0.000001 0.053851 0.271392
hm 0.328583 0.002546 0.000006 -0.107497 -0.169648
hh 0.251601 0.001846 0.000003 0.126714 -0.201924
zm 0.998428 0.013412 0.000180 0.042164 0.245521
zh 1.007024 0.013487 0.000182 0.057305 -0.017576
r 0.073903 0.000959 0.000001 -0.064637 0.255681
w 1.254082 0.010681 0.000114 0.121543 0.169162
y 0.583991 0.009153 0.000084 0.013378 0.018153
T 0.185098 0.003324 0.000011 -0.002398 0.077178
CORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE C cm ch k km kh x xm xh l hm hh zm zh r w y T
C 1.0000 0.5027 0.5628 0.5150 0.3815 0.1715 0.8734 0.2786 0.1178 -0.8748 0.5695 -0.2230 0.9029 0.8604 0.7870 0.9226 0.7860 0.8050
cm 0.5027 1.0000 -0.4317 0.4069 0.9337 -0.5593 0.6715 0.3563 -0.0481 -0.5293 0.9285 -0.9401 0.7052 0.0580 0.5405 0.7681 0.8798 0.8494
ch 0.5628 -0.4317 1.0000 0.1483 -0.4948 0.7138 0.2693 -0.0500 0.1689 -0.4067 -0.2935 0.6663 0.2678 0.8423 0.3044 0.2282 -0.0211 0.0279
k 0.5150 0.4069 0.1483 1.0000 0.6042 0.4830 0.2411 -0.0840 0.1895 -0.1715 0.1998 -0.1653 0.2512 0.2059 -0.0619 0.4366 0.3374 0.2848
km 0.3815 0.9337 -0.4948 0.6042 1.0000 -0.4058 0.4303 0.3483 -0.1478 -0.2669 0.7390 -0.8476 0.4905 -0.1310 0.2698 0.6023 0.6953 0.6473
kh 0.1715 -0.5593 0.7138 0.4830 -0.4058 1.0000 -0.1963 -0.4790 0.3798 0.0966 -0.5829 0.7418 -0.2509 0.3801 -0.3675 -0.1610 -0.3770 -0.3846
x 0.8734 0.6715 0.2693 0.2411 0.4303 -0.1963 1.0000 0.1734 0.2770 -0.9841 0.8401 -0.5259 0.9731 0.7439 0.8947 0.9644 0.9430 0.9583
xm 0.2786 0.3563 -0.0500 -0.0840 0.3483 -0.4790 0.1734 1.0000 -0.8983 -0.1098 0.2256 -0.2406 0.3896 0.0325 0.5053 0.2919 0.2712 0.3133
xh 0.1178 -0.0481 0.1689 0.1895 -0.1478 0.3798 0.2770 -0.8983 1.0000 -0.3319 0.1547 0.0001 0.0540 0.3002 -0.0939 0.1455 0.1561 0.1219
l -0.8748 -0.5293 -0.4067 -0.1715 -0.2669 0.0966 -0.9841 -0.1098 -0.3319 1.0000 -0.7417 0.3800 -0.9439 -0.8348 -0.8950 -0.9182 -0.8690 -0.8938
hm 0.5695 0.9285 -0.2935 0.1998 0.7390 -0.5829 0.8401 0.2256 0.1547 -0.7417 1.0000 -0.9023 0.8223 0.2627 0.7133 0.8424 0.9558 0.9419
hh -0.2230 -0.9401 0.6663 -0.1653 -0.8476 0.7418 -0.5259 -0.2406 0.0001 0.3800 -0.9023 1.0000 -0.5272 0.1745 -0.4084 -0.5715 -0.7595 -0.7244
zm 0.9029 0.7052 0.2678 0.2512 0.4905 -0.2509 0.9731 0.3896 0.0540 -0.9439 0.8223 -0.5272 1.0000 0.7195 0.9421 0.9767 0.9409 0.9637
zh 0.8604 0.0580 0.8423 0.2059 -0.1310 0.3801 0.7439 0.0325 0.3002 -0.8348 0.2627 0.1745 0.7195 1.0000 0.7076 0.6836 0.5033 0.5464
r 0.7870 0.5405 0.3044 -0.0619 0.2698 -0.3675 0.8947 0.5053 -0.0939 -0.8950 0.7133 -0.4084 0.9421 0.7076 1.0000 0.8481 0.8167 0.8641
w 0.9226 0.7681 0.2282 0.4366 0.6023 -0.1610 0.9644 0.2919 0.1455 -0.9182 0.8424 -0.5715 0.9767 0.6836 0.8481 1.0000 0.9636 0.9692
y 0.7860 0.8798 -0.0211 0.3374 0.6953 -0.3770 0.9430 0.2712 0.1561 -0.8690 0.9558 -0.7595 0.9409 0.5033 0.8167 0.9636 1.0000 0.9962
T 0.8050 0.8494 0.0279 0.2848 0.6473 -0.3846 0.9583 0.3133 0.1219 -0.8938 0.9419 -0.7244 0.9637 0.5464 0.8641 0.9692 0.9962 1.0000
AUTOCORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE 1 2 3 4 5
C 0.7567 0.5397 0.3702 0.2255 0.0859
cm 0.8068 0.5728 0.4005 0.2474 0.1149
ch 0.7990 0.5357 0.3229 0.1509 0.0134
k 0.9623 0.8708 0.7432 0.5926 0.4303
km 0.8104 0.6306 0.4891 0.3429 0.2131
kh 0.7616 0.5437 0.3846 0.2213 0.0877
x 0.7444 0.4923 0.3157 0.1652 0.0356
xm -0.0274 -0.1091 0.0152 -0.0410 -0.0623
xh -0.0389 -0.1228 0.0084 -0.0621 -0.0720
l 0.7211 0.4715 0.2989 0.1482 0.0225
hm 0.8079 0.5424 0.3511 0.1908 0.0559
hh 0.8357 0.5671 0.3634 0.1946 0.0580
zm 0.7267 0.4835 0.3137 0.1736 0.0412
zh 0.7328 0.4834 0.2946 0.1364 0.0072
r 0.6864 0.4522 0.2958 0.1641 0.0349
w 0.7663 0.5328 0.3620 0.2169 0.0813
y 0.7841 0.5342 0.3551 0.2041 0.0699
T 0.7697 0.5183 0.3403 0.1915 0.0578
VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent) (HP filter, lambda = 1600)
eh em Tot. lin. contr.
C 74.41 21.07 95.47
cm 1.71 97.56 99.27
ch 79.86 27.88 107.73
k 38.01 52.51 90.52
km 13.35 85.64 98.99
kh 29.57 73.16 102.73
x 48.80 43.99 92.78
xm 9.16 94.63 103.79
xh 19.46 83.69 103.15
l 64.38 28.73 93.11
hm 5.23 91.94 97.17
hh 7.36 96.38 103.73
zm 44.99 48.53 93.52
zh 100.11 0.00 100.11
r 46.79 47.10 93.89
w 41.19 51.98 93.17
y 19.69 74.41 94.10
T 23.66 70.16 93.82
Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples
Total computing time : 0h00m05s
Specification of the model
Variables and Parameters
MOD - File
Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Found 18 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs ...
done
Preprocessing completed.
"Model with increased incentive to substitute between home and market (levels)"
"The numbering of the equations is referenced to the P&P solutions."
"Manuel Bieri and Michael Wagner (2023)"
Residuals of the static equations:
Equation number 1 : 0 : (41) Resource Constraint
Equation number 2 : 0 : (42) Household FOC w.r.t. hh
Equation number 3 : 0 : (43) Household FOC w.r.t. hm
Equation number 4 : 0 : (44) Household FOC w.r.t. kh
Equation number 5 : 0 : (45) Household FOC w.r.t. km
Equation number 6 : 0 : (46) Firm FOC w.r.t. km
Equation number 7 : 0 : (47) Firm FOC w.r.t. hm
Equation number 8 : 0 : (48) Market Output
Equation number 9 : 0 : (49) Total Consumption
Equation number 10 : 0 : (50) Leisure
Equation number 11 : 0 : (51) Home production
Equation number 12 : 0 : (52) Market Investments
Equation number 13 : 0 : (53) Home Investments
Equation number 14 : 0 : (54) Total Investments
Equation number 15 : 0 : (55) Total Capital
Equation number 16 : 0 : (56) Government Transfer
Equation number 17 : 0 : (57) Market Technology
Equation number 18 : 0 : (58) Home Technology
STEADY-STATE RESULTS:
C 0.486412
cm 0.439277
ch 0.556378
l 0.42
hm 0.33
hh 0.25
k 5.29596
km 2.35423
kh 2.94173
x 0.149208
xm 0.0663282
xh 0.0828803
r 0.0735909
T 0.186357
w 1.25829
y 0.588486
zm 1
zh 1
EIGENVALUES:
Modulus Real Imaginary
2.311e-14 2.311e-14 0
0.95 0.95 0
0.95 0.95 0
0.9588 0.9588 0
1.119 1.119 0
1.313e+18 -1.313e+18 0
Inf Inf 0
Inf Inf 0
There are 4 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition is verified.
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.
Information about Model3_level (dynamic model)
The following variables appear with a lag and are therefore states:
km(-1)
kh(-1)
zm(-1)
zh(-1)
The following variables appear with a lead and are therefore forward-looking variables:
C(1)
cm(1)
ch(1)
r(1)
The following variables do not appear with a lead or lag and are therefore purely static variables:
l
hm
hh
k
x
xm
xh
T
w
y
MODEL SUMMARY
Number of variables: 18
Number of stochastic shocks: 2
Number of state variables: 4
Number of jumpers: 4
Number of static variables: 10
MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS
Variables eh em
eh 0.000098 0.000000
em 0.000000 0.000098
POLICY AND TRANSITION FUNCTIONS
C cm ch k km kh x xm xh l hm hh zm zh r w y T
Constant 0.486412 0.439277 0.556378 5.295963 2.354233 2.941730 0.149208 0.066328 0.082880 0.420000 0.330000 0.250000 1.000000 1.000000 0.073591 1.258289 0.588486 0.186357
km(-1) 0.023896 0.050852 -0.019295 1.020037 0.501918 0.518120 0.048305 -0.472236 0.520541 -0.007483 0.020318 -0.012835 0 0 -0.018859 0.134543 0.099157 0.021476
kh(-1) 0.050332 0.027226 0.086608 0.899497 0.442605 0.456892 -0.072799 0.444673 -0.517472 0.019432 -0.036218 0.016786 0 0 -0.005699 0.040656 -0.045573 -0.017431
zm(-1) 0.099213 0.234153 -0.116790 0.333251 0.922366 -0.589115 0.334808 0.926677 -0.591869 -0.060983 0.138670 -0.077687 0.950000 0 0.071149 0.687793 0.568961 0.217616
zh(-1) 0.109722 -0.085243 0.419144 0.057236 -0.476979 0.534215 0.057504 -0.479209 0.536712 -0.019265 -0.022045 0.041310 0 0.950000 -0.003469 0.024747 -0.027739 -0.010610
eh 0.115497 -0.089729 0.441205 0.060249 -0.502083 0.562332 0.060530 -0.504430 0.564960 -0.020279 -0.023205 0.043484 0 1.000000 -0.003651 0.026049 -0.029199 -0.011168
em 0.104434 0.246477 -0.122937 0.350790 0.970911 -0.620121 0.352430 0.975449 -0.623020 -0.064193 0.145969 -0.081776 1.000000 0 0.074894 0.723992 0.598906 0.229070
MOMENTS OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE SKEWNESS KURTOSIS
C 0.483116 0.002241 0.000005 0.223111 0.252501
cm 0.432682 0.003551 0.000013 -0.061527 -0.109662
ch 0.558371 0.006808 0.000046 0.110269 -0.145682
k 5.202103 0.021465 0.000461 0.246990 -0.307295
km 2.297613 0.017327 0.000300 0.037105 -0.044579
kh 2.904489 0.014538 0.000211 0.233101 -0.388492
x 0.146656 0.005399 0.000029 -0.115059 -0.205699
xm 0.064759 0.009610 0.000092 -0.007359 0.065986
xh 0.081897 0.008896 0.000079 0.014709 -0.125087
l 0.420095 0.001042 0.000001 0.132899 -0.175851
hm 0.328812 0.002321 0.000005 -0.152477 -0.218183
hh 0.251093 0.001416 0.000002 0.142776 -0.135349
zm 0.991608 0.012529 0.000157 -0.071352 -0.172101
zh 1.007024 0.013487 0.000182 0.057305 -0.017576
r 0.074218 0.000896 0.000001 -0.111796 -0.151059
w 1.243258 0.010007 0.000100 -0.021977 -0.181894
y 0.579338 0.008675 0.000075 -0.091798 -0.206679
T 0.183790 0.003165 0.000010 -0.100804 -0.211038
CORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE C cm ch k km kh x xm xh l hm hh zm zh r w y T
C 1.0000 0.2924 0.6072 0.4746 0.2802 0.3667 0.5563 0.1355 0.1913 -0.5933 0.3035 -0.0607 0.5548 0.7957 0.4364 0.5953 0.4659 0.4694
cm 0.2924 1.0000 -0.5822 0.4609 0.9233 -0.4200 0.8740 0.4898 0.0013 -0.8106 0.9457 -0.9533 0.8939 -0.3054 0.7480 0.9306 0.9532 0.9387
ch 0.6072 -0.5822 1.0000 0.0205 -0.5290 0.6607 -0.2532 -0.2918 0.1615 0.1690 -0.5277 0.7405 -0.2711 0.9302 -0.2505 -0.2671 -0.3959 -0.3809
k 0.4746 0.4609 0.0205 1.0000 0.7389 0.5958 0.2582 -0.1166 0.2826 -0.1933 0.2219 -0.2214 0.2555 0.0438 -0.0766 0.4514 0.3494 0.2918
km 0.2802 0.9233 -0.5290 0.7389 1.0000 -0.1009 0.6807 0.3312 0.0552 -0.5942 0.7602 -0.8085 0.7038 -0.3465 0.4623 0.8135 0.8015 0.7645
kh 0.3667 -0.4200 0.6607 0.5958 -0.1009 1.0000 -0.4300 -0.5669 0.3515 0.4229 -0.5785 0.6368 -0.4616 0.4776 -0.6640 -0.3031 -0.4395 -0.4804
x 0.5563 0.8740 -0.2532 0.2582 0.6807 -0.4300 1.0000 0.4082 0.1659 -0.9930 0.9553 -0.8348 0.9831 0.1068 0.9034 0.9718 0.9800 0.9852
xm 0.1355 0.4898 -0.2918 -0.1166 0.3312 -0.5669 0.4082 1.0000 -0.8325 -0.3729 0.4478 -0.4595 0.5622 -0.1880 0.6876 0.4464 0.4545 0.4969
xh 0.1913 0.0013 0.1615 0.2826 0.0552 0.3515 0.1659 -0.8325 1.0000 -0.1998 0.0959 -0.0102 -0.0107 0.2679 -0.1946 0.1075 0.1038 0.0611
l -0.5933 -0.8106 0.1690 -0.1933 -0.5942 0.4229 -0.9930 -0.3729 -0.1998 1.0000 -0.9233 0.7772 -0.9674 -0.1981 -0.9083 -0.9439 -0.9497 -0.9596
hm 0.3035 0.9457 -0.5277 0.2219 0.7602 -0.5785 0.9553 0.4478 0.0959 -0.9233 1.0000 -0.9592 0.9461 -0.1905 0.8695 0.9352 0.9816 0.9815
hh -0.0607 -0.9533 0.7405 -0.2214 -0.8085 0.6368 -0.8348 -0.4595 -0.0102 0.7772 -0.9592 1.0000 -0.8385 0.4580 -0.7563 -0.8380 -0.9097 -0.9022
zm 0.5548 0.8939 -0.2711 0.2555 0.7038 -0.4616 0.9831 0.5622 -0.0107 -0.9674 0.9461 -0.8385 1.0000 0.0705 0.9391 0.9756 0.9777 0.9884
zh 0.7957 -0.3054 0.9302 0.0438 -0.3465 0.4776 0.1068 -0.1880 0.2679 -0.1981 -0.1905 0.4580 0.0705 1.0000 0.0801 0.0600 -0.0585 -0.0389
r 0.4364 0.7480 -0.2505 -0.0766 0.4623 -0.6640 0.9034 0.6876 -0.1946 -0.9083 0.8695 -0.7563 0.9391 0.0801 1.0000 0.8407 0.8683 0.9026
w 0.5953 0.9306 -0.2671 0.4514 0.8135 -0.3031 0.9718 0.4464 0.1075 -0.9439 0.9352 -0.8380 0.9756 0.0600 0.8407 1.0000 0.9856 0.9807
y 0.4659 0.9532 -0.3959 0.3494 0.8015 -0.4395 0.9800 0.4545 0.1038 -0.9497 0.9816 -0.9097 0.9777 -0.0585 0.8683 0.9856 1.0000 0.9973
T 0.4694 0.9387 -0.3809 0.2918 0.7645 -0.4804 0.9852 0.4969 0.0611 -0.9596 0.9815 -0.9022 0.9884 -0.0389 0.9026 0.9807 0.9973 1.0000
AUTOCORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE 1 2 3 4 5
C 0.7664 0.5508 0.3821 0.2362 0.0958
cm 0.7725 0.5457 0.3812 0.2244 0.0981
ch 0.7820 0.5194 0.3107 0.1384 0.0017
k 0.9649 0.8777 0.7558 0.6129 0.4595
km 0.8403 0.6761 0.5332 0.3840 0.2515
kh 0.8082 0.6181 0.4657 0.3056 0.1703
x 0.7795 0.5196 0.3376 0.1826 0.0495
xm 0.0091 -0.0796 0.0272 -0.0490 -0.0425
xh 0.0003 -0.0923 0.0172 -0.0641 -0.0501
l 0.7753 0.5133 0.3314 0.1781 0.0452
hm 0.7996 0.5324 0.3386 0.1732 0.0385
hh 0.8018 0.5355 0.3361 0.1645 0.0304
zm 0.7139 0.4733 0.3185 0.1727 0.0499
zh 0.7328 0.4834 0.2946 0.1364 0.0072
r 0.6505 0.4213 0.2900 0.1522 0.0389
w 0.7708 0.5386 0.3748 0.2249 0.0945
y 0.7823 0.5310 0.3525 0.1953 0.0635
T 0.7631 0.5114 0.3375 0.1825 0.0532
VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent) (HP filter, lambda = 1600)
eh em Tot. lin. contr.
C 59.51 36.52 96.03
cm 13.68 91.05 104.72
ch 92.75 12.87 105.62
k 0.16 100.22 100.38
km 15.29 88.41 103.70
kh 27.26 77.62 104.88
x 1.32 97.90 99.22
xm 25.85 80.13 105.98
xh 38.24 66.08 104.32
l 3.16 94.61 97.77
hm 8.51 95.14 103.65
hh 28.68 78.18 106.85
zm 0.00 100.11 100.11
zh 100.11 0.00 100.11
r 0.44 100.02 100.46
w 0.18 99.93 100.11
y 2.36 99.38 101.74
T 1.61 99.88 101.49
Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples
Total computing time : 0h00m06s
Specification of the model
Variables and Parameters
MOD - File
Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Found 18 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs ...
done
Preprocessing completed.
"Model with a more general home production function and highly correlated technology shocks (levels)"
"The numbering of the equations is referenced to the P&P solutions."
"Manuel Bieri and Michael Wagner (2023)"
"Replace (83) with (160) for steady state calculation"
"Replace (90) with (161) for steady state calculation"
"Replace (92) with (162) for steady state calculation"
"Replace (94) with (163) for steady state calculation"
Residuals of the static equations:
Equation number 1 : 0 : (41) Resource Constraint
Equation number 2 : 0 : (150) Household FOC w.r.t. hh
Equation number 3 : 0 : (43) Household FOC w.r.t. hm
Equation number 4 : 0 : (151) Household FOC w.r.t. kh
Equation number 5 : 0 : (45) Household FOC w.r.t. km
Equation number 6 : 0 : (46) Firm FOC w.r.t. km
Equation number 7 : 0 : (47) Firm FOC w.r.t. hm
Equation number 8 : 0 : (48) Market Output
Equation number 9 : 0 : (49) Total Consumption
Equation number 10 : 0 : (50) Leisure
Equation number 11 : 0 : (152) Home production
Equation number 12 : 0 : (52) Market Investments
Equation number 13 : 0 : (53) Home Investments
Equation number 14 : 0 : (54) Total Investments
Equation number 15 : 0 : (55) Total Capital
Equation number 16 : 0 : (56) Government Transfer
Equation number 17 : 0 : (57) Market Technology
Equation number 18 : 0 : (58) Home Technology
STEADY-STATE RESULTS:
C 0.438194
cm 0.485786
ch 0.373203
l 0.42
hm 0.33
hh 0.25
k 3.64518
km 2.35423
kh 1.29094
x 0.102699
xm 0.0663282
xh 0.036371
r 0.0735909
T 0.186357
w 1.25829
y 0.588486
zm 1
zh 1
EIGENVALUES:
Modulus Real Imaginary
6.571e-16 6.571e-16 0
0.95 0.95 0
0.95 0.95 0
0.9576 0.9576 0
1.138 1.138 0
3.252e+16 3.252e+16 0
5.615e+17 5.615e+17 0
Inf Inf 0
There are 4 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition is verified.
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.
Information about Model4_Level (dynamic model)
The following variables appear with a lag and are therefore states:
km(-1)
kh(-1)
zm(-1)
zh(-1)
The following variables appear with a lead and are therefore forward-looking variables:
C(1)
cm(1)
ch(1)
r(1)
The following variables do not appear with a lead or lag and are therefore purely static variables:
l
hm
hh
k
x
xm
xh
T
w
y
MODEL SUMMARY
Number of variables: 18
Number of stochastic shocks: 2
Number of state variables: 4
Number of jumpers: 4
Number of static variables: 10
MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS
Variables eh em
eh 0.000098 0.000097
em 0.000097 0.000098
POLICY AND TRANSITION FUNCTIONS
C cm ch k km kh x xm xh l hm hh zm zh r w y T
Constant 0.438194 0.485786 0.373203 3.645176 2.354233 1.290943 0.102699 0.066328 0.036371 0.420000 0.330000 0.250000 1.000000 1.000000 0.073591 1.258289 0.588486 0.186357
km(-1) 0.039997 0.091331 -0.027324 0.975077 0.825027 0.150049 0.003134 -0.147616 0.150751 0.005573 0.016589 -0.022162 0 0 -0.019446 0.138728 0.094465 0.019681
kh(-1) 0.061807 0.022038 0.113366 0.861675 0.729077 0.132599 -0.110797 0.732484 -0.843282 0.019414 -0.070540 0.051125 0 0 -0.011099 0.079184 -0.088760 -0.033949
zm(-1) 0.139569 0.367858 -0.159571 0.223068 1.125348 -0.902279 0.224111 1.130607 -0.906497 -0.027528 0.156955 -0.129427 0.950000 0 0.074027 0.667267 0.591969 0.226416
zh(-1) 0.059729 -0.221792 0.427133 0.144967 -1.309327 1.454294 0.145645 -1.315447 1.461092 -0.048428 -0.060517 0.108945 0 0.950000 -0.009522 0.067933 -0.076148 -0.029125
eh 0.062872 -0.233466 0.449613 0.152597 -1.378239 1.530836 0.153310 -1.384681 1.537991 -0.050977 -0.063702 0.114679 0 1.000000 -0.010024 0.071508 -0.080155 -0.030658
em 0.146915 0.387219 -0.167970 0.234809 1.184576 -0.949768 0.235906 1.190113 -0.954207 -0.028977 0.165216 -0.136239 1.000000 0 0.077923 0.702386 0.623125 0.238333
MOMENTS OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE SKEWNESS KURTOSIS
C 0.441222 0.003066 0.000009 0.072640 -0.164274
cm 0.489080 0.002260 0.000005 0.096019 -0.162549
ch 0.375864 0.004593 0.000021 0.076483 -0.064774
k 3.683101 0.015838 0.000251 -0.007451 -0.164697
km 2.381422 0.013107 0.000172 -0.066384 -0.169135
kh 1.301679 0.008339 0.000070 0.036008 -0.250802
x 0.104040 0.004739 0.000022 0.036960 0.095368
xm 0.067299 0.004753 0.000023 -0.015762 0.065135
xh 0.036741 0.005672 0.000032 0.110315 0.024732
l 0.419832 0.001018 0.000001 -0.038545 0.130850
hm 0.330201 0.001091 0.000001 0.023852 0.077120
hh 0.249967 0.000482 0.000000 0.081748 -0.014877
zm 1.005770 0.013591 0.000185 0.057051 0.056263
zh 1.007024 0.013487 0.000182 0.057305 -0.017576
r 0.073327 0.000993 0.000001 0.020836 0.300708
w 1.267432 0.010473 0.000110 0.069702 -0.117182
y 0.593120 0.006644 0.000044 0.060033 -0.049223
T 0.187686 0.002590 0.000007 0.053226 0.024016
CORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE C cm ch k km kh x xm xh l hm hh zm zh r w y T
C 1.0000 0.8967 0.9586 0.5463 0.0487 0.9610 0.9325 0.5033 0.3573 -0.9208 0.8070 0.1182 0.9693 0.9676 0.8682 0.9955 0.9702 0.9632
cm 0.8967 1.0000 0.7335 0.7491 0.3926 0.8056 0.7739 0.4288 0.2872 -0.7263 0.7805 -0.2328 0.8187 0.7803 0.6455 0.9002 0.8922 0.8549
ch 0.9586 0.7335 1.0000 0.3571 -0.1776 0.9573 0.9340 0.4969 0.3639 -0.9466 0.7370 0.3311 0.9616 0.9837 0.9178 0.9495 0.9157 0.9289
k 0.5463 0.7491 0.3571 1.0000 0.8505 0.5625 0.2404 0.4327 -0.1617 -0.1904 0.1942 -0.0374 0.3326 0.3301 0.0620 0.5012 0.4263 0.3588
km 0.0487 0.3926 -0.1776 0.8505 1.0000 0.0434 -0.2658 0.2557 -0.4363 0.3254 -0.2058 -0.2214 -0.1755 -0.1998 -0.4322 0.0057 -0.0560 -0.1327
kh 0.9610 0.8056 0.9573 0.5625 0.0434 1.0000 0.8744 0.4199 0.3787 -0.8731 0.6923 0.2769 0.9075 0.9410 0.7970 0.9428 0.8977 0.8900
x 0.9325 0.7739 0.9340 0.2404 -0.2658 0.8744 1.0000 0.2858 0.5960 -0.9963 0.9261 0.0078 0.9893 0.9820 0.9737 0.9568 0.9765 0.9896
xm 0.5033 0.4288 0.4969 0.4327 0.2557 0.4199 0.2858 1.0000 -0.5992 -0.2991 0.0639 0.4871 0.4147 0.3937 0.3373 0.4490 0.3497 0.3521
xh 0.3573 0.2872 0.3639 -0.1617 -0.4363 0.3787 0.5960 -0.5992 1.0000 -0.5817 0.7202 -0.4017 0.4790 0.4905 0.5308 0.4231 0.5228 0.5317
l -0.9208 -0.7263 -0.9466 -0.1904 0.3254 -0.8731 -0.9963 -0.2991 -0.5817 1.0000 -0.8979 -0.0796 -0.9853 -0.9848 -0.9852 -0.9425 -0.9577 -0.9766
hm 0.8070 0.7805 0.7370 0.1942 -0.2058 0.6923 0.9261 0.0639 0.7202 -0.8979 1.0000 -0.3674 0.8873 0.8455 0.8720 0.8590 0.9261 0.9281
hh 0.1182 -0.2328 0.3311 -0.0374 -0.2214 0.2769 0.0078 0.4871 -0.4017 -0.0796 -0.3674 1.0000 0.0725 0.1659 0.1070 0.0460 -0.0736 -0.0382
zm 0.9693 0.8187 0.9616 0.3326 -0.1755 0.9075 0.9893 0.4147 0.4790 -0.9853 0.8873 0.0725 1.0000 0.9916 0.9615 0.9826 0.9841 0.9933
zh 0.9676 0.7803 0.9837 0.3301 -0.1998 0.9410 0.9820 0.3937 0.4905 -0.9848 0.8455 0.1659 0.9916 1.0000 0.9533 0.9743 0.9658 0.9768
r 0.8682 0.6455 0.9178 0.0620 -0.4322 0.7970 0.9737 0.3373 0.5308 -0.9852 0.8720 0.1070 0.9615 0.9533 1.0000 0.8936 0.9141 0.9442
w 0.9955 0.9002 0.9495 0.5012 0.0057 0.9428 0.9568 0.4490 0.4231 -0.9425 0.8590 0.0460 0.9826 0.9743 0.8936 1.0000 0.9887 0.9833
y 0.9702 0.8922 0.9157 0.4263 -0.0560 0.8977 0.9765 0.3497 0.5228 -0.9577 0.9261 -0.0736 0.9841 0.9658 0.9141 0.9887 1.0000 0.9966
T 0.9632 0.8549 0.9289 0.3588 -0.1327 0.8900 0.9896 0.3521 0.5317 -0.9766 0.9281 -0.0382 0.9933 0.9768 0.9442 0.9833 0.9966 1.0000
AUTOCORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE 1 2 3 4 5
C 0.7815 0.5442 0.3535 0.1916 0.0510
cm 0.7688 0.6020 0.4624 0.3234 0.1850
ch 0.8053 0.5386 0.3244 0.1499 0.0057
k 0.9537 0.8494 0.7073 0.5421 0.3663
km 0.9323 0.8162 0.6730 0.5107 0.3432
kh 0.7634 0.5344 0.3518 0.1867 0.0520
x 0.6539 0.4198 0.2571 0.1168 0.0030
xm 0.3725 0.2046 0.1442 0.0400 0.0071
xh -0.0127 -0.0998 -0.0349 -0.0656 -0.0192
l 0.6847 0.4421 0.2677 0.1200 0.0004
hm 0.4615 0.2730 0.1820 0.0861 0.0088
hh 0.5399 0.3484 0.2502 0.1410 0.0469
zm 0.7333 0.4846 0.2971 0.1424 0.0116
zh 0.7328 0.4834 0.2946 0.1364 0.0072
r 0.7489 0.4965 0.3037 0.1462 0.0122
w 0.7425 0.5102 0.3308 0.1774 0.0447
y 0.6677 0.4468 0.2907 0.1531 0.0353
T 0.6781 0.4462 0.2810 0.1396 0.0196
VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent) (HP filter, lambda = 1600)
eh em Tot. lin. contr.
C 98.41 0.67 99.08
cm 82.27 12.63 94.91
ch 100.58 1.21 101.78
k 94.83 2.19 97.02
km 92.18 4.98 97.16
kh 98.58 4.14 102.72
x 96.77 1.47 98.24
xm 93.25 9.69 102.94
xh 97.21 5.18 102.40
l 98.48 0.49 98.97
hm 80.46 14.49 94.96
hh 48.53 51.89 100.42
zm 96.61 1.69 98.31
zh 100.11 0.00 100.11
r 96.27 1.88 98.14
w 96.58 1.68 98.26
y 92.81 4.22 97.03
T 93.65 3.64 97.30
Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples
Total computing time : 0h00m06s
| S.D. of Market Output | Total Investment Relative to Market Outptut* | Market Consumption Relative to Market Outptut* | Market Hours Relative to Market Outptut* | Market Wage Relative to Market Outptut* | Market Hours Relative to Market Wage* | Market Hours and Market Wage** | Investment in Business and Household Capital** | |
|---|---|---|---|---|---|---|---|---|
| Data*** | 1.96 | 2.61 | 0.54 | 0.78 | 0.73 | 1.06 | -0.12 | 0.3 |
| Model 1 | 1.4 | 2.81 | 0.4 | 0.41 | 0.6 | 0.69 | 0.96 | -0.13 |
| Model 2 | 1.56 | 2.53 | 0.6 | 0.5 | 0.55 | 0.91 | 0.84 | -0.9 |
| Model 2a | 2.36 | 2.73 | 1.36 | 0.94 | 0.35 | 2.66 | -0.01 | -1 |
| Model 3 | 1.47 | 2.45 | 0.55 | 0.48 | 0.54 | 0.88 | 0.94 | -0.83 |
| Model 4 | 1.13 | 4.09 | 0.41 | 0.29 | 0.74 | 0.4 | 0.86 | -0.6 |
| Model 4a | 1.3 | 3.1 | 0.38 | 0.37 | 0.64 | 0.57 | 0.96 | 0.26 |
Specification of the model
Variables and Parameters
MOD - File
Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Found 18 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs ...
done
Preprocessing completed.
"Model with home production minimized (logs)"
"The numbering of the equations is referenced to the P&P solutions."
"Manuel Bieri and Michael Wagner (2023)"
"Replace (93) with (146) for steady state calculation"
Residuals of the static equations:
Equation number 1 : 0 : (113) Resource Constraint
Equation number 2 : 0 : (114) Household FOC w.r.t. hh
Equation number 3 : 0 : (115) Household FOC w.r.t. hm
Equation number 4 : 0 : (116) Household FOC w.r.t. kh
Equation number 5 : 0 : (117) Household FOC w.r.t. km
Equation number 6 : 0 : (118) Firm FOC w.r.t. km
Equation number 7 : 0 : (119) Firm FOC w.r.t. hm
Equation number 8 : 0 : (120) Market Output
Equation number 9 : 0 : (145) Total Consumption
Equation number 10 : 0 : (122) Leisure
Equation number 11 : 0 : (123) Home production
Equation number 12 : 0 : (124) Market Investments
Equation number 13 : 0 : (125) Home Investments
Equation number 14 : 0 : (126) Total Investments
Equation number 15 : 0 : (127) Total Capital
Equation number 16 : 0 : (128) Government Transfer
Equation number 17 : 0 : (129) Market Technology
Equation number 18 : 0 : (130) Home Technology
STEADY-STATE RESULTS:
C -0.717953
cm -0.822625
ch -0.586307
l -0.867501
hm -1.10866
hh -1.38629
k 1.66694
km 0.856215
kh 1.079
x -1.90241
xm -2.71314
xh -2.49036
r -2.60923
T -1.68009
w 0.229753
y -0.530203
zm 0
zh 0
EIGENVALUES:
Modulus Real Imaginary
7.594e-16 7.594e-16 0
0.95 0.95 0
0.95 0.95 0
0.9587 0.9587 0
1.118 1.118 0
6.003e+16 -6.003e+16 0
Inf Inf 0
Inf Inf 0
There are 4 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition is verified.
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.
Information about Model1_log (dynamic model)
The following variables appear with a lag and are therefore states:
km(-1)
kh(-1)
zm(-1)
zh(-1)
The following variables appear with a lead and are therefore forward-looking variables:
C(1)
cm(1)
ch(1)
r(1)
The following variables do not appear with a lead or lag and are therefore purely static variables:
l
hm
hh
k
x
xm
xh
T
w
y
MODEL SUMMARY
Number of variables: 18
Number of stochastic shocks: 2
Number of state variables: 4
Number of jumpers: 4
Number of static variables: 10
MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS
Variables eh em
eh 0.000098 0.000066
em 0.000066 0.000098
POLICY AND TRANSITION FUNCTIONS
C cm ch k km kh x xm xh l hm hh zm zh r w y T
Constant -0.717953 -0.822625 -0.586307 1.666945 0.856215 1.078998 -1.902411 -2.713141 -2.490358 -0.867501 -1.108663 -1.386294 0 0 -2.609234 0.229753 -0.530203 -1.680092
km(-1) 0.100327 0.208854 -0.036168 0.455870 0.491373 0.427457 0.848779 -17.137435 15.242941 -0.053543 0.108708 -0.053543 0 0 -0.628896 0.262396 0.371104 0.240413
kh(-1) 0.313689 0.228336 0.421038 0.498394 0.537209 0.467331 -1.479718 19.156677 -17.994788 0.142913 -0.290157 0.142913 0 0 -0.204735 0.085422 -0.204735 -0.247281
zm(-1) 0.154489 0.376194 -0.124353 0.072249 0.216123 -0.042891 2.576385 7.706867 -1.529480 -0.184091 0.373760 -0.184091 0.950000 0 0.934045 0.560285 0.934045 1.128150
zh(-1) 0.284236 0 0.641725 0 0 0 0 0 0 0 0 0 0 0.950000 0 0 0 0
eh 0.299196 0 0.675500 0 0 0 0 0 0 0 0 0 0 1.000000 0 0 0 0
em 0.162620 0.395994 -0.130898 0.076052 0.227498 -0.045149 2.711985 8.112491 -1.609979 -0.193780 0.393432 -0.193780 1.000000 0 0.983205 0.589774 0.983205 1.187527
MOMENTS OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE SKEWNESS KURTOSIS
C -0.717950 0.005823 0.000034 0.159134 0.020044
cm -0.825304 0.005671 0.000032 0.200378 0.166740
ch -0.582929 0.007699 0.000059 0.085241 -0.166226
k 1.662337 0.004229 0.000018 0.348770 0.094117
km 0.851019 0.005411 0.000029 0.338340 0.098717
kh 1.074860 0.003861 0.000015 0.349776 0.114116
x -1.904947 0.039346 0.001548 0.014812 0.275360
xm -2.715888 0.076812 0.005900 0.100577 0.197232
xh -2.492726 0.044089 0.001944 -0.036397 0.347001
l -0.867512 0.002854 0.000008 0.020068 0.293021
hm -1.108638 0.005794 0.000034 -0.020068 0.293021
hh -1.386306 0.002854 0.000008 0.020068 0.293021
zm -0.001572 0.013412 0.000180 0.042164 0.245521
zh 0.007024 0.013487 0.000182 0.057305 -0.017576
r -2.606610 0.013125 0.000172 -0.100496 0.276275
w 0.227086 0.008355 0.000070 0.137039 0.206046
y -0.532845 0.014013 0.000196 0.076301 0.241715
T -1.682189 0.016563 0.000274 0.046102 0.252741
CORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE C cm ch k km kh x xm xh l hm hh zm zh r w y T
C 1.0000 0.8767 0.8952 0.4727 0.7003 0.1468 0.8290 0.6203 0.4670 -0.8105 0.8105 -0.8105 0.8374 0.9284 0.7206 0.8719 0.8550 0.8421
cm 0.8767 1.0000 0.5706 0.5666 0.8179 0.2001 0.9343 0.6869 0.5433 -0.9115 0.9115 -0.9115 0.9441 0.6713 0.8017 0.9901 0.9673 0.9504
ch 0.8952 0.5706 1.0000 0.2821 0.4379 0.0652 0.5499 0.4227 0.2941 -0.5395 0.5395 -0.5395 0.5551 0.9633 0.4876 0.5715 0.5639 0.5574
k 0.4727 0.5666 0.2821 1.0000 0.9375 0.9207 0.2405 -0.0301 0.4283 -0.1832 0.1832 -0.1832 0.2634 0.1664 -0.0372 0.4472 0.3424 0.2836
km 0.7003 0.8179 0.4379 0.9375 1.0000 0.7273 0.5625 0.2691 0.5285 -0.5129 0.5129 -0.5129 0.5826 0.3997 0.3126 0.7303 0.6475 0.5993
kh 0.1468 0.2001 0.0652 0.9207 0.7273 1.0000 -0.1566 -0.3611 0.2519 0.2139 -0.2139 0.2139 -0.1340 -0.1202 -0.4240 0.0627 -0.0510 -0.1130
x 0.8290 0.9343 0.5499 0.2405 0.5625 -0.1566 1.0000 0.7869 0.5095 -0.9982 0.9982 -0.9982 0.9977 0.7212 0.9557 0.9751 0.9942 0.9985
xm 0.6203 0.6869 0.4227 -0.0301 0.2691 -0.3611 0.7869 1.0000 -0.1301 -0.7935 0.7935 -0.7935 0.8163 0.5704 0.8743 0.7373 0.7677 0.7935
xh 0.4670 0.5433 0.2941 0.4283 0.5285 0.2519 0.5095 -0.1301 1.0000 -0.4975 0.4975 -0.4975 0.4647 0.3634 0.3164 0.5387 0.5269 0.4979
l -0.8105 -0.9115 -0.5395 -0.1832 -0.5129 0.2139 -0.9982 -0.7935 -0.4975 1.0000 -1.0000 1.0000 -0.9939 -0.7203 -0.9692 -0.9602 -0.9861 -0.9938
hm 0.8105 0.9115 0.5395 0.1832 0.5129 -0.2139 0.9982 0.7935 0.4975 -1.0000 1.0000 -1.0000 0.9939 0.7203 0.9692 0.9602 0.9861 0.9938
hh -0.8105 -0.9115 -0.5395 -0.1832 -0.5129 0.2139 -0.9982 -0.7935 -0.4975 1.0000 -1.0000 1.0000 -0.9939 -0.7203 -0.9692 -0.9602 -0.9861 -0.9938
zm 0.8374 0.9441 0.5551 0.2634 0.5826 -0.1340 0.9977 0.8163 0.4647 -0.9939 0.9939 -0.9939 1.0000 0.7195 0.9535 0.9803 0.9955 0.9993
zh 0.9284 0.6713 0.9633 0.1664 0.3997 -0.1202 0.7212 0.5704 0.3634 -0.7203 0.7203 -0.7203 0.7195 1.0000 0.6915 0.7017 0.7163 0.7199
r 0.7206 0.8017 0.4876 -0.0372 0.3126 -0.4240 0.9557 0.8743 0.3164 -0.9692 0.9692 -0.9692 0.9535 0.6915 1.0000 0.8752 0.9226 0.9452
w 0.8719 0.9901 0.5715 0.4472 0.7303 0.0627 0.9751 0.7373 0.5387 -0.9602 0.9602 -0.9602 0.9803 0.7017 0.8752 1.0000 0.9933 0.9845
y 0.8550 0.9673 0.5639 0.3424 0.6475 -0.0510 0.9942 0.7677 0.5269 -0.9861 0.9861 -0.9861 0.9955 0.7163 0.9226 0.9933 1.0000 0.9980
T 0.8421 0.9504 0.5574 0.2836 0.5993 -0.1130 0.9985 0.7935 0.4979 -0.9938 0.9938 -0.9938 0.9993 0.7199 0.9452 0.9845 0.9980 1.0000
AUTOCORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE 1 2 3 4 5
C 0.7470 0.5260 0.3534 0.2046 0.0694
cm 0.7757 0.5643 0.4034 0.2612 0.1229
ch 0.7198 0.4834 0.3030 0.1450 0.0203
k 0.9633 0.8730 0.7462 0.5962 0.4341
km 0.9169 0.7968 0.6617 0.5136 0.3576
kh 0.9455 0.8434 0.7130 0.5639 0.4039
x 0.7635 0.5098 0.3265 0.1772 0.0413
xm 0.2290 0.0880 0.0770 0.0517 -0.0324
xh 0.4512 0.2634 0.1808 0.1038 -0.0016
l 0.7665 0.5100 0.3245 0.1741 0.0379
hm 0.7665 0.5100 0.3245 0.1741 0.0379
hh 0.7665 0.5100 0.3245 0.1741 0.0379
zm 0.7267 0.4835 0.3137 0.1736 0.0412
zh 0.7328 0.4834 0.2946 0.1364 0.0072
r 0.6987 0.4596 0.2978 0.1640 0.0341
w 0.7649 0.5325 0.3615 0.2167 0.0801
y 0.7617 0.5162 0.3381 0.1910 0.0551
T 0.7483 0.5011 0.3247 0.1796 0.0452
VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent) (HP filter, lambda = 1600)
eh em Tot. lin. contr.
C 86.84 9.88 96.72
cm 43.65 49.64 93.29
ch 97.59 5.74 103.33
k 38.90 51.40 90.30
km 40.01 51.37 91.38
kh 39.46 50.46 89.92
x 45.15 48.28 93.43
xm 44.31 49.91 94.22
xh 44.69 49.31 94.00
l 45.24 48.12 93.36
hm 45.24 48.12 93.36
hh 45.24 48.12 93.36
zm 44.99 48.53 93.52
zh 100.11 0.00 100.11
r 45.07 48.06 93.13
w 44.40 49.07 93.47
y 44.86 48.63 93.50
T 45.00 48.49 93.49
Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples
Total computing time : 0h00m05s
Specification of the model
Variables and Parameters
MOD - File
Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Found 18 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs ...
done
Preprocessing completed.
"Model with increased willingness to substitute between home and market (logs)"
"The numbering of the equations is referenced to the P&P solutions."
"Manuel Bieri and Michael Wagner (2023)"
Residuals of the static equations:
Equation number 1 : 0 : (113) Resource Constraint
Equation number 2 : 0 : (114) Household FOC w.r.t. hh
Equation number 3 : 0 : (115) Household FOC w.r.t. hm
Equation number 4 : 0 : (116) Household FOC w.r.t. kh
Equation number 5 : 0 : (117) Household FOC w.r.t. km
Equation number 6 : 0 : (118) Firm FOC w.r.t. km
Equation number 7 : 0 : (119) Firm FOC w.r.t. hm
Equation number 8 : 0 : (120) Market Output
Equation number 9 : 0 : (121) Total Consumption
Equation number 10 : 0 : (122) Leisure
Equation number 11 : 0 : (123) Home production
Equation number 12 : 0 : (124) Market Investments
Equation number 13 : 0 : (125) Home Investments
Equation number 14 : 0 : (126) Total Investments
Equation number 15 : 0 : (127) Total Capital
Equation number 16 : 0 : (128) Government Transfer
Equation number 17 : 0 : (129) Market Technology
Equation number 18 : 0 : (130) Home Technology
STEADY-STATE RESULTS:
C -0.722515
cm -0.822625
ch -0.586307
l -0.867501
hm -1.10866
hh -1.38629
k 1.66694
km 0.856215
kh 1.079
x -1.90241
xm -2.71314
xh -2.49036
r -2.60923
T -1.68009
w 0.229753
y -0.530203
zm 0
zh 0
EIGENVALUES:
Modulus Real Imaginary
4.792e-15 4.792e-15 0
0.95 0.95 0
0.95 0.95 0
0.959 0.959 0
1.121 1.121 0
1.619e+16 1.619e+16 0
1.757e+16 1.757e+16 0
5.479e+18 5.479e+18 0
There are 4 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition is verified.
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.
Information about Model2_log (dynamic model)
The following variables appear with a lag and are therefore states:
km(-1)
kh(-1)
zm(-1)
zh(-1)
The following variables appear with a lead and are therefore forward-looking variables:
C(1)
cm(1)
ch(1)
r(1)
The following variables do not appear with a lead or lag and are therefore purely static variables:
l
hm
hh
k
x
xm
xh
T
w
y
MODEL SUMMARY
Number of variables: 18
Number of stochastic shocks: 2
Number of state variables: 4
Number of jumpers: 4
Number of static variables: 10
MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS
Variables eh em
eh 0.000098 0.000066
em 0.000066 0.000098
POLICY AND TRANSITION FUNCTIONS
C cm ch k km kh x xm xh l hm hh zm zh r w y T
Constant -0.722515 -0.822625 -0.586307 1.666945 0.856215 1.078998 -1.902411 -2.713141 -2.490358 -0.867501 -1.108663 -1.386294 0 0 -2.609234 0.229753 -0.530203 -1.680092
km(-1) 0.137683 0.361471 -0.143777 0.449873 0.524650 0.390030 0.634953 -15.950781 13.908325 -0.025205 0.193327 -0.212846 0 0 -0.569189 0.237485 0.430811 0.312527
kh(-1) 0.293202 0.122833 0.507478 0.501017 0.584295 0.434371 -1.386172 20.835750 -19.170121 0.128027 -0.368155 0.270878 0 0 -0.259770 0.108385 -0.259770 -0.313753
zm(-1) 0.289204 0.783363 -0.332307 0.046257 0.751865 -0.518433 1.649520 26.811232 -18.487110 -0.077601 0.471449 -0.491942 0.950000 0 1.002974 0.531525 1.002974 1.211404
zh(-1) 0.126810 -0.497044 0.911440 0.029726 -0.618112 0.548184 1.060033 -22.041653 19.548047 -0.123805 -0.144916 0.399282 0 0.950000 -0.102253 0.042663 -0.102253 -0.123502
eh 0.133484 -0.523204 0.959410 0.031291 -0.650645 0.577036 1.115824 -23.201740 20.576892 -0.130321 -0.152543 0.420297 0 1.000000 -0.107635 0.044909 -0.107635 -0.130002
em 0.304426 0.824593 -0.349797 0.048692 0.791437 -0.545719 1.736337 28.222350 -19.460116 -0.081686 0.496262 -0.517834 1.000000 0 1.055763 0.559500 1.055763 1.275162
MOMENTS OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE SKEWNESS KURTOSIS
C -0.723576 0.005687 0.000032 0.196578 0.131563
cm -0.831843 0.009355 0.000088 -0.006434 -0.160484
ch -0.577109 0.012305 0.000151 0.100825 -0.155606
k 1.661940 0.004169 0.000017 0.374386 0.104158
km 0.844396 0.008985 0.000081 0.015995 -0.097950
kh 1.079446 0.006543 0.000043 0.221307 -0.146786
x -1.905394 0.039357 0.001549 -0.027063 0.217330
xm -2.722764 0.193611 0.037485 0.044325 0.089116
xh -2.488026 0.158811 0.025221 -0.006561 -0.031397
l -0.867938 0.002826 0.000008 0.053851 0.271392
hm -1.112957 0.007716 0.000060 -0.107497 -0.169648
hh -1.379892 0.007385 0.000055 0.126714 -0.201924
zm -0.001572 0.013412 0.000180 0.042164 0.245521
zh 0.007024 0.013487 0.000182 0.057305 -0.017576
r -2.604989 0.013031 0.000170 -0.064637 0.255681
w 0.226410 0.008488 0.000072 0.121543 0.169162
y -0.537840 0.015554 0.000242 0.013378 0.018153
T -1.686847 0.017834 0.000318 -0.002398 0.077178
CORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE C cm ch k km kh x xm xh l hm hh zm zh r w y T
C 1.0000 0.5027 0.5628 0.5150 0.3815 0.1715 0.8734 0.2786 0.1178 -0.8748 0.5695 -0.2230 0.9029 0.8604 0.7870 0.9226 0.7860 0.8050
cm 0.5027 1.0000 -0.4317 0.4069 0.9337 -0.5593 0.6715 0.3563 -0.0481 -0.5293 0.9285 -0.9401 0.7052 0.0580 0.5405 0.7681 0.8798 0.8494
ch 0.5628 -0.4317 1.0000 0.1483 -0.4948 0.7138 0.2693 -0.0500 0.1689 -0.4067 -0.2935 0.6663 0.2678 0.8423 0.3044 0.2282 -0.0211 0.0279
k 0.5150 0.4069 0.1483 1.0000 0.6042 0.4830 0.2411 -0.0840 0.1895 -0.1715 0.1998 -0.1653 0.2512 0.2059 -0.0619 0.4366 0.3374 0.2848
km 0.3815 0.9337 -0.4948 0.6042 1.0000 -0.4058 0.4303 0.3483 -0.1478 -0.2669 0.7390 -0.8476 0.4905 -0.1310 0.2698 0.6023 0.6953 0.6473
kh 0.1715 -0.5593 0.7138 0.4830 -0.4058 1.0000 -0.1963 -0.4790 0.3798 0.0966 -0.5829 0.7418 -0.2509 0.3801 -0.3675 -0.1610 -0.3770 -0.3846
x 0.8734 0.6715 0.2693 0.2411 0.4303 -0.1963 1.0000 0.1734 0.2770 -0.9841 0.8401 -0.5259 0.9731 0.7439 0.8947 0.9644 0.9430 0.9583
xm 0.2786 0.3563 -0.0500 -0.0840 0.3483 -0.4790 0.1734 1.0000 -0.8983 -0.1098 0.2256 -0.2406 0.3896 0.0325 0.5053 0.2919 0.2712 0.3133
xh 0.1178 -0.0481 0.1689 0.1895 -0.1478 0.3798 0.2770 -0.8983 1.0000 -0.3319 0.1547 0.0001 0.0540 0.3002 -0.0939 0.1455 0.1561 0.1219
l -0.8748 -0.5293 -0.4067 -0.1715 -0.2669 0.0966 -0.9841 -0.1098 -0.3319 1.0000 -0.7417 0.3800 -0.9439 -0.8348 -0.8950 -0.9182 -0.8690 -0.8938
hm 0.5695 0.9285 -0.2935 0.1998 0.7390 -0.5829 0.8401 0.2256 0.1547 -0.7417 1.0000 -0.9023 0.8223 0.2627 0.7133 0.8424 0.9558 0.9419
hh -0.2230 -0.9401 0.6663 -0.1653 -0.8476 0.7418 -0.5259 -0.2406 0.0001 0.3800 -0.9023 1.0000 -0.5272 0.1745 -0.4084 -0.5715 -0.7595 -0.7244
zm 0.9029 0.7052 0.2678 0.2512 0.4905 -0.2509 0.9731 0.3896 0.0540 -0.9439 0.8223 -0.5272 1.0000 0.7195 0.9421 0.9767 0.9409 0.9637
zh 0.8604 0.0580 0.8423 0.2059 -0.1310 0.3801 0.7439 0.0325 0.3002 -0.8348 0.2627 0.1745 0.7195 1.0000 0.7076 0.6836 0.5033 0.5464
r 0.7870 0.5405 0.3044 -0.0619 0.2698 -0.3675 0.8947 0.5053 -0.0939 -0.8950 0.7133 -0.4084 0.9421 0.7076 1.0000 0.8481 0.8167 0.8641
w 0.9226 0.7681 0.2282 0.4366 0.6023 -0.1610 0.9644 0.2919 0.1455 -0.9182 0.8424 -0.5715 0.9767 0.6836 0.8481 1.0000 0.9636 0.9692
y 0.7860 0.8798 -0.0211 0.3374 0.6953 -0.3770 0.9430 0.2712 0.1561 -0.8690 0.9558 -0.7595 0.9409 0.5033 0.8167 0.9636 1.0000 0.9962
T 0.8050 0.8494 0.0279 0.2848 0.6473 -0.3846 0.9583 0.3133 0.1219 -0.8938 0.9419 -0.7244 0.9637 0.5464 0.8641 0.9692 0.9962 1.0000
AUTOCORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE 1 2 3 4 5
C 0.7567 0.5397 0.3702 0.2255 0.0859
cm 0.8068 0.5728 0.4005 0.2474 0.1149
ch 0.7990 0.5357 0.3229 0.1509 0.0134
k 0.9623 0.8708 0.7432 0.5926 0.4303
km 0.8104 0.6306 0.4891 0.3429 0.2131
kh 0.7616 0.5437 0.3846 0.2213 0.0877
x 0.7444 0.4923 0.3157 0.1652 0.0356
xm -0.0274 -0.1091 0.0152 -0.0410 -0.0623
xh -0.0389 -0.1228 0.0084 -0.0621 -0.0720
l 0.7211 0.4715 0.2989 0.1482 0.0225
hm 0.8079 0.5424 0.3511 0.1908 0.0559
hh 0.8357 0.5671 0.3634 0.1946 0.0580
zm 0.7267 0.4835 0.3137 0.1736 0.0412
zh 0.7328 0.4834 0.2946 0.1364 0.0072
r 0.6864 0.4522 0.2958 0.1641 0.0349
w 0.7663 0.5328 0.3620 0.2169 0.0813
y 0.7841 0.5342 0.3551 0.2041 0.0699
T 0.7697 0.5183 0.3403 0.1915 0.0578
VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent) (HP filter, lambda = 1600)
eh em Tot. lin. contr.
C 74.41 21.07 95.47
cm 1.71 97.56 99.27
ch 79.86 27.88 107.73
k 38.01 52.51 90.52
km 13.35 85.64 98.99
kh 29.57 73.16 102.73
x 48.80 43.99 92.78
xm 9.16 94.63 103.79
xh 19.46 83.69 103.15
l 64.38 28.73 93.11
hm 5.23 91.94 97.17
hh 7.36 96.38 103.73
zm 44.99 48.53 93.52
zh 100.11 0.00 100.11
r 46.79 47.10 93.89
w 41.19 51.98 93.17
y 19.69 74.41 94.10
T 23.66 70.16 93.82
Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples
Total computing time : 0h00m05s
Specification of the model
Variables and Parameters
MOD - File
Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Found 18 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs ...
done
Preprocessing completed.
"Model with increased willingness to substitute between home and market (logs)"
"The numbering of the equations is referenced to the P&P solutions."
"Manuel Bieri and Michael Wagner (2023)"
Residuals of the static equations:
Equation number 1 : 0 : (113) Resource Constraint
Equation number 2 : 0 : (114) Household FOC w.r.t. hh
Equation number 3 : 0 : (115) Household FOC w.r.t. hm
Equation number 4 : 0 : (116) Household FOC w.r.t. kh
Equation number 5 : 0 : (117) Household FOC w.r.t. km
Equation number 6 : 0 : (118) Firm FOC w.r.t. km
Equation number 7 : 0 : (119) Firm FOC w.r.t. hm
Equation number 8 : 0 : (120) Market Output
Equation number 9 : 0 : (121) Total Consumption
Equation number 10 : 0 : (122) Leisure
Equation number 11 : 0 : (123) Home production
Equation number 12 : 0 : (124) Market Investments
Equation number 13 : 0 : (125) Home Investments
Equation number 14 : 0 : (126) Total Investments
Equation number 15 : 0 : (127) Total Capital
Equation number 16 : 0 : (128) Government Transfer
Equation number 17 : 0 : (129) Market Technology
Equation number 18 : 0 : (130) Home Technology
STEADY-STATE RESULTS:
C -0.722515
cm -0.822625
ch -0.586307
l -0.867501
hm -1.10866
hh -1.38629
k 1.66694
km 0.856215
kh 1.079
x -1.90241
xm -2.71314
xh -2.49036
r -2.60923
T -1.68009
w 0.229753
y -0.530203
zm 0
zh 0
EIGENVALUES:
Modulus Real Imaginary
4.792e-15 4.792e-15 0
0.95 0.95 0
0.95 0.95 0
0.959 0.959 0
1.121 1.121 0
1.619e+16 1.619e+16 0
1.757e+16 1.757e+16 0
5.479e+18 5.479e+18 0
There are 4 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition is verified.
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.
Information about Model2a_log (dynamic model)
The following variables appear with a lag and are therefore states:
km(-1)
kh(-1)
zm(-1)
zh(-1)
The following variables appear with a lead and are therefore forward-looking variables:
C(1)
cm(1)
ch(1)
r(1)
The following variables do not appear with a lead or lag and are therefore purely static variables:
l
hm
hh
k
x
xm
xh
T
w
y
MODEL SUMMARY
Number of variables: 18
Number of stochastic shocks: 2
Number of state variables: 4
Number of jumpers: 4
Number of static variables: 10
MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS
Variables eh em
eh 0.002025 0.000298
em 0.000298 0.000098
POLICY AND TRANSITION FUNCTIONS
C cm ch k km kh x xm xh l hm hh zm zh r w y T
Constant -0.722515 -0.822625 -0.586307 1.666945 0.856215 1.078998 -1.902411 -2.713141 -2.490358 -0.867501 -1.108663 -1.386294 0 0 -2.609234 0.229753 -0.530203 -1.680092
km(-1) 0.137683 0.361471 -0.143777 0.449873 0.524650 0.390030 0.634953 -15.950781 13.908325 -0.025205 0.193327 -0.212846 0 0 -0.569189 0.237485 0.430811 0.312527
kh(-1) 0.293202 0.122833 0.507478 0.501017 0.584295 0.434371 -1.386172 20.835750 -19.170121 0.128027 -0.368155 0.270878 0 0 -0.259770 0.108385 -0.259770 -0.313753
zm(-1) 0.289204 0.783363 -0.332307 0.046257 0.751865 -0.518433 1.649520 26.811232 -18.487110 -0.077601 0.471449 -0.491942 0.950000 0 1.002974 0.531525 1.002974 1.211404
zh(-1) 0.126810 -0.497044 0.911440 0.029726 -0.618112 0.548184 1.060033 -22.041653 19.548047 -0.123805 -0.144916 0.399282 0 0.950000 -0.102253 0.042663 -0.102253 -0.123502
eh 0.133484 -0.523204 0.959410 0.031291 -0.650645 0.577036 1.115824 -23.201740 20.576892 -0.130321 -0.152543 0.420297 0 1.000000 -0.107635 0.044909 -0.107635 -0.130002
em 0.304426 0.824593 -0.349797 0.048692 0.791437 -0.545719 1.736337 28.222350 -19.460116 -0.081686 0.496262 -0.517834 1.000000 0 1.055763 0.559500 1.055763 1.275162
MOMENTS OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE SKEWNESS KURTOSIS
C -0.719093 0.014702 0.000216 0.118816 0.051653
cm -0.849901 0.031951 0.001021 -0.076000 -0.108066
ch -0.544276 0.071336 0.005089 0.082092 -0.078528
k 1.660790 0.004384 0.000019 0.388034 0.065827
km 0.825988 0.033351 0.001112 -0.049482 -0.053571
kh 1.092108 0.030575 0.000935 0.078781 -0.116648
x -1.906697 0.064295 0.004134 0.033143 0.066653
xm -2.745785 0.855290 0.731521 -0.131882 0.036981
xh -2.471950 0.781335 0.610484 0.129286 0.037330
l -0.869105 0.006482 0.000042 -0.018356 0.091965
hm -1.124904 0.022154 0.000491 -0.085660 -0.141560
hh -1.362160 0.034086 0.001162 0.088410 -0.124505
zm -0.001572 0.013412 0.000180 0.042164 0.245521
zh 0.031862 0.061175 0.003742 0.057305 -0.017576
r -2.600524 0.016160 0.000261 0.031523 0.264658
w 0.224547 0.008338 0.000070 0.047686 0.004791
y -0.551650 0.023564 0.000555 -0.071272 -0.055123
T -1.699729 0.022473 0.000505 -0.087414 -0.058608
CORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE C cm ch k km kh x xm xh l hm hh zm zh r w y T
C 1.0000 -0.8892 0.9662 0.6526 -0.8736 0.9310 0.5118 -0.1428 0.2010 -0.7224 -0.8070 0.9232 0.7965 0.9592 0.8407 0.6013 -0.5459 -0.4468
cm -0.8892 1.0000 -0.9771 -0.4382 0.9779 -0.9668 -0.3592 0.2189 -0.2450 0.6384 0.9117 -0.9861 -0.4803 -0.9418 -0.6286 -0.2642 0.7636 0.7068
ch 0.9662 -0.9771 1.0000 0.5505 -0.9574 0.9779 0.4405 -0.1898 0.2315 -0.6958 -0.8891 0.9851 0.6412 0.9768 0.7453 0.4286 -0.6842 -0.6061
k 0.6526 -0.4382 0.5505 1.0000 -0.3802 0.5900 0.2740 -0.0576 0.0910 -0.3703 -0.4566 0.5100 0.4833 0.5366 0.3490 0.4953 -0.2540 -0.2142
km -0.8736 0.9779 -0.9574 -0.3802 1.0000 -0.9711 -0.5266 0.3979 -0.4266 0.7697 0.8069 -0.9382 -0.5373 -0.9656 -0.6036 -0.3761 0.6255 0.5657
kh 0.9310 -0.9668 0.9779 0.5900 -0.9711 1.0000 0.5304 -0.3622 0.3959 -0.7675 -0.8222 0.9506 0.5938 0.9814 0.6170 0.4562 -0.6116 -0.5491
x 0.5118 -0.3592 0.4405 0.2740 -0.5266 0.5304 1.0000 -0.8114 0.8590 -0.9476 0.0181 0.2872 0.7266 0.6214 0.3577 0.8795 0.3283 0.3977
xm -0.1428 0.2189 -0.1898 -0.0576 0.3979 -0.3622 -0.8114 1.0000 -0.9962 0.7491 -0.1842 -0.0813 -0.1987 -0.3692 0.1868 -0.4706 -0.3397 -0.3283
xh 0.2010 -0.2450 0.2315 0.0910 -0.4266 0.3959 0.8590 -0.9962 1.0000 -0.7966 0.1641 0.1137 0.2817 0.4155 -0.1106 0.5426 0.3463 0.3465
l -0.7224 0.6384 -0.6958 -0.3703 0.7697 -0.7675 -0.9476 0.7491 -0.7966 1.0000 0.2953 -0.5728 -0.7578 -0.8333 -0.5041 -0.8112 -0.0094 -0.0852
hm -0.8070 0.9117 -0.8891 -0.4566 0.8069 -0.8222 0.0181 -0.1842 0.1641 0.2953 1.0000 -0.9523 -0.3256 -0.7721 -0.6308 -0.0136 0.9353 0.8865
hh 0.9232 -0.9861 0.9851 0.5100 -0.9382 0.9506 0.2872 -0.0813 0.1137 -0.5728 -0.9523 1.0000 0.5214 0.9286 0.7023 0.2709 -0.7994 -0.7333
zm 0.7965 -0.4803 0.6412 0.4833 -0.5373 0.5938 0.7266 -0.1987 0.2817 -0.7578 -0.3256 0.5214 1.0000 0.7195 0.8616 0.9119 0.0166 0.1461
zh 0.9592 -0.9418 0.9768 0.5366 -0.9656 0.9814 0.6214 -0.3692 0.4155 -0.8333 -0.7721 0.9286 0.7195 1.0000 0.7233 0.5724 -0.5233 -0.4406
r 0.8407 -0.6286 0.7453 0.3490 -0.6036 0.6170 0.3577 0.1868 -0.1106 -0.5041 -0.6308 0.7023 0.8616 0.7233 1.0000 0.5772 -0.3888 -0.2582
w 0.6013 -0.2642 0.4286 0.4953 -0.3761 0.4562 0.8795 -0.4706 0.5426 -0.8112 -0.0136 0.2709 0.9119 0.5724 0.5772 1.0000 0.3410 0.4439
y -0.5459 0.7636 -0.6842 -0.2540 0.6255 -0.6116 0.3283 -0.3397 0.3463 -0.0094 0.9353 -0.7994 0.0166 -0.5233 -0.3888 0.3410 1.0000 0.9905
T -0.4468 0.7068 -0.6061 -0.2142 0.5657 -0.5491 0.3977 -0.3283 0.3465 -0.0852 0.8865 -0.7333 0.1461 -0.4406 -0.2582 0.4439 0.9905 1.0000
AUTOCORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE 1 2 3 4 5
C 0.8231 0.5616 0.3483 0.1760 0.0270
cm 0.8149 0.5466 0.3309 0.1522 0.0074
ch 0.8214 0.5526 0.3339 0.1563 0.0083
k 0.9115 0.7839 0.6421 0.4879 0.3316
km 0.7328 0.4853 0.2984 0.1374 0.0126
kh 0.7352 0.4876 0.2993 0.1358 0.0072
x 0.2278 0.0839 0.0673 0.0146 -0.0146
xm -0.0350 -0.1162 -0.0455 -0.0693 -0.0163
xh -0.0295 -0.1131 -0.0452 -0.0676 -0.0196
l 0.3439 0.1770 0.1192 0.0410 -0.0081
hm 0.8072 0.5381 0.3245 0.1465 -0.0009
hh 0.8453 0.5698 0.3429 0.1586 0.0054
zm 0.7267 0.4835 0.3137 0.1736 0.0412
zh 0.7328 0.4834 0.2946 0.1364 0.0072
r 0.7555 0.5070 0.3245 0.1666 0.0434
w 0.5495 0.3548 0.2517 0.1509 0.0496
y 0.6983 0.4513 0.2790 0.1258 -0.0028
T 0.6900 0.4436 0.2760 0.1263 -0.0031
VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent) (HP filter, lambda = 1600)
eh em Tot. lin. contr.
C 95.34 3.15 98.50
cm 95.48 8.36 103.84
ch 100.73 0.83 101.56
k 46.00 47.48 93.48
km 96.61 6.22 102.83
kh 99.16 3.35 102.51
x 79.39 16.48 95.87
xm 97.98 4.85 102.82
xh 98.52 3.46 101.98
l 91.40 5.46 96.86
hm 92.89 11.15 104.04
hh 98.59 4.52 103.12
zm 44.99 48.53 93.52
zh 100.11 0.00 100.11
r 66.64 30.63 97.27
w 39.71 53.87 93.58
y 71.69 32.42 104.11
T 59.60 44.19 103.79
Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples
Total computing time : 0h00m05s
Specification of the model
Variables and Parameters
MOD - File
Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Found 18 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs ...
done
Preprocessing completed.
"Model with increased incentive to substitute between home and market (logs)"
"The numbering of the equations is referenced to the P&P solutions."
"Manuel Bieri and Michael Wagner (2023)"
Residuals of the static equations:
Equation number 1 : 0 : (113) Resource Constraint
Equation number 2 : 0 : (114) Household FOC w.r.t. hh
Equation number 3 : 0 : (115) Household FOC w.r.t. hm
Equation number 4 : 0 : (116) Household FOC w.r.t. kh
Equation number 5 : 0 : (117) Household FOC w.r.t. km
Equation number 6 : 0 : (118) Firm FOC w.r.t. km
Equation number 7 : 0 : (119) Firm FOC w.r.t. hm
Equation number 8 : 0 : (120) Market Output
Equation number 9 : 0 : (121) Total Consumption
Equation number 10 : 0 : (122) Leisure
Equation number 11 : 0 : (123) Home production
Equation number 12 : 0 : (124) Market Investments
Equation number 13 : 0 : (125) Home Investments
Equation number 14 : 0 : (126) Total Investments
Equation number 15 : 0 : (127) Total Capital
Equation number 16 : 0 : (128) Government Transfer
Equation number 17 : 0 : (129) Market Technology
Equation number 18 : 0 : (130) Home Technology
STEADY-STATE RESULTS:
C -0.720698
cm -0.822625
ch -0.586307
l -0.867501
hm -1.10866
hh -1.38629
k 1.66694
km 0.856215
kh 1.079
x -1.90241
xm -2.71314
xh -2.49036
r -2.60923
T -1.68009
w 0.229753
y -0.530203
zm 0
zh 0
EIGENVALUES:
Modulus Real Imaginary
1.325e-14 -1.325e-14 0
0.95 0.95 0
0.95 0.95 0
0.9588 0.9588 0
1.119 1.119 0
9.549e+13 9.549e+13 0
Inf Inf 0
Inf Inf 0
There are 4 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition is verified.
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.
Information about Model3_log (dynamic model)
The following variables appear with a lag and are therefore states:
km(-1)
kh(-1)
zm(-1)
zh(-1)
The following variables appear with a lead and are therefore forward-looking variables:
C(1)
cm(1)
ch(1)
r(1)
The following variables do not appear with a lead or lag and are therefore purely static variables:
l
hm
hh
k
x
xm
xh
T
w
y
MODEL SUMMARY
Number of variables: 18
Number of stochastic shocks: 2
Number of state variables: 4
Number of jumpers: 4
Number of static variables: 10
MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS
Variables eh em
eh 0.000098 0.000000
em 0.000000 0.000098
POLICY AND TRANSITION FUNCTIONS
C cm ch k km kh x xm xh l hm hh zm zh r w y T
Constant -0.720698 -0.822625 -0.586307 1.666945 0.856215 1.078998 -1.902411 -2.713141 -2.490358 -0.867501 -1.108663 -1.386294 0 0 -2.609234 0.229753 -0.530203 -1.680092
km(-1) 0.115658 0.272531 -0.081645 0.453441 0.501918 0.414645 0.762165 -16.761425 14.786094 -0.041945 0.144950 -0.120866 0 0 -0.603324 0.251727 0.396676 0.271299
kh(-1) 0.304396 0.182329 0.457922 0.499640 0.553056 0.456892 -1.435278 19.721770 -18.367022 0.136106 -0.322860 0.197516 0 0 -0.227810 0.095050 -0.227810 -0.275151
zm(-1) 0.203968 0.533041 -0.209911 0.062925 0.391790 -0.200261 2.243896 13.971094 -7.141246 -0.145197 0.420213 -0.310749 0.950000 0 0.966822 0.546609 0.966822 1.167739
zh(-1) 0.225574 -0.194052 0.753344 0.010807 -0.202605 0.181599 0.385391 -7.224813 6.475750 -0.045869 -0.066803 0.165240 0 0.950000 -0.047136 0.019667 -0.047136 -0.056932
eh 0.237446 -0.204265 0.792994 0.011376 -0.213268 0.191157 0.405675 -7.605066 6.816579 -0.048283 -0.070319 0.173936 0 1.000000 -0.049617 0.020702 -0.049617 -0.059928
em 0.214703 0.561096 -0.220959 0.066237 0.412411 -0.210802 2.361996 14.706415 -7.517101 -0.152839 0.442329 -0.327104 1.000000 0 1.017708 0.575378 1.017708 1.229199
MOMENTS OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE SKEWNESS KURTOSIS
C -0.727476 0.004608 0.000021 0.223111 0.252501
cm -0.837638 0.008083 0.000065 -0.061527 -0.109662
ch -0.582725 0.012236 0.000150 0.110269 -0.145682
k 1.649222 0.004053 0.000016 0.246990 -0.307295
km 0.832165 0.007360 0.000054 0.037105 -0.044579
kh 1.066338 0.004942 0.000024 0.233101 -0.388492
x -1.919520 0.036181 0.001309 -0.115059 -0.205699
xm -2.736802 0.144889 0.020993 -0.007359 0.065986
xh -2.502224 0.107339 0.011522 0.014709 -0.125087
l -0.867274 0.002482 0.000006 0.132899 -0.175851
hm -1.112262 0.007033 0.000049 -0.152477 -0.218183
hh -1.381924 0.005665 0.000032 0.142776 -0.135349
zm -0.008392 0.012529 0.000157 -0.071352 -0.172101
zh 0.007024 0.013487 0.000182 0.057305 -0.017576
r -2.600717 0.012175 0.000148 -0.111796 -0.151059
w 0.217807 0.007952 0.000063 -0.021977 -0.181894
y -0.545748 0.014741 0.000217 -0.091798 -0.206679
T -1.693867 0.016985 0.000288 -0.100804 -0.211038
CORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE C cm ch k km kh x xm xh l hm hh zm zh r w y T
C 1.0000 0.2924 0.6072 0.4746 0.2802 0.3667 0.5563 0.1355 0.1913 -0.5933 0.3035 -0.0607 0.5548 0.7957 0.4364 0.5953 0.4659 0.4694
cm 0.2924 1.0000 -0.5822 0.4609 0.9233 -0.4200 0.8740 0.4898 0.0013 -0.8106 0.9457 -0.9533 0.8939 -0.3054 0.7480 0.9306 0.9532 0.9387
ch 0.6072 -0.5822 1.0000 0.0205 -0.5290 0.6607 -0.2532 -0.2918 0.1615 0.1690 -0.5277 0.7405 -0.2711 0.9302 -0.2505 -0.2671 -0.3959 -0.3809
k 0.4746 0.4609 0.0205 1.0000 0.7389 0.5958 0.2582 -0.1166 0.2826 -0.1933 0.2219 -0.2214 0.2555 0.0438 -0.0766 0.4514 0.3494 0.2918
km 0.2802 0.9233 -0.5290 0.7389 1.0000 -0.1009 0.6807 0.3312 0.0552 -0.5942 0.7602 -0.8085 0.7038 -0.3465 0.4623 0.8135 0.8015 0.7645
kh 0.3667 -0.4200 0.6607 0.5958 -0.1009 1.0000 -0.4300 -0.5669 0.3515 0.4229 -0.5785 0.6368 -0.4616 0.4776 -0.6640 -0.3031 -0.4395 -0.4804
x 0.5563 0.8740 -0.2532 0.2582 0.6807 -0.4300 1.0000 0.4082 0.1659 -0.9930 0.9553 -0.8348 0.9831 0.1068 0.9034 0.9718 0.9800 0.9852
xm 0.1355 0.4898 -0.2918 -0.1166 0.3312 -0.5669 0.4082 1.0000 -0.8325 -0.3729 0.4478 -0.4595 0.5622 -0.1880 0.6876 0.4464 0.4545 0.4969
xh 0.1913 0.0013 0.1615 0.2826 0.0552 0.3515 0.1659 -0.8325 1.0000 -0.1998 0.0959 -0.0102 -0.0107 0.2679 -0.1946 0.1075 0.1038 0.0611
l -0.5933 -0.8106 0.1690 -0.1933 -0.5942 0.4229 -0.9930 -0.3729 -0.1998 1.0000 -0.9233 0.7772 -0.9674 -0.1981 -0.9083 -0.9439 -0.9497 -0.9596
hm 0.3035 0.9457 -0.5277 0.2219 0.7602 -0.5785 0.9553 0.4478 0.0959 -0.9233 1.0000 -0.9592 0.9461 -0.1905 0.8695 0.9352 0.9816 0.9815
hh -0.0607 -0.9533 0.7405 -0.2214 -0.8085 0.6368 -0.8348 -0.4595 -0.0102 0.7772 -0.9592 1.0000 -0.8385 0.4580 -0.7563 -0.8380 -0.9097 -0.9022
zm 0.5548 0.8939 -0.2711 0.2555 0.7038 -0.4616 0.9831 0.5622 -0.0107 -0.9674 0.9461 -0.8385 1.0000 0.0705 0.9391 0.9756 0.9777 0.9884
zh 0.7957 -0.3054 0.9302 0.0438 -0.3465 0.4776 0.1068 -0.1880 0.2679 -0.1981 -0.1905 0.4580 0.0705 1.0000 0.0801 0.0600 -0.0585 -0.0389
r 0.4364 0.7480 -0.2505 -0.0766 0.4623 -0.6640 0.9034 0.6876 -0.1946 -0.9083 0.8695 -0.7563 0.9391 0.0801 1.0000 0.8407 0.8683 0.9026
w 0.5953 0.9306 -0.2671 0.4514 0.8135 -0.3031 0.9718 0.4464 0.1075 -0.9439 0.9352 -0.8380 0.9756 0.0600 0.8407 1.0000 0.9856 0.9807
y 0.4659 0.9532 -0.3959 0.3494 0.8015 -0.4395 0.9800 0.4545 0.1038 -0.9497 0.9816 -0.9097 0.9777 -0.0585 0.8683 0.9856 1.0000 0.9973
T 0.4694 0.9387 -0.3809 0.2918 0.7645 -0.4804 0.9852 0.4969 0.0611 -0.9596 0.9815 -0.9022 0.9884 -0.0389 0.9026 0.9807 0.9973 1.0000
AUTOCORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE 1 2 3 4 5
C 0.7664 0.5508 0.3821 0.2362 0.0958
cm 0.7725 0.5457 0.3812 0.2244 0.0981
ch 0.7820 0.5194 0.3107 0.1384 0.0017
k 0.9649 0.8777 0.7558 0.6129 0.4595
km 0.8403 0.6761 0.5332 0.3840 0.2515
kh 0.8082 0.6181 0.4657 0.3056 0.1703
x 0.7795 0.5196 0.3376 0.1826 0.0495
xm 0.0091 -0.0796 0.0272 -0.0490 -0.0425
xh 0.0003 -0.0923 0.0172 -0.0641 -0.0501
l 0.7753 0.5133 0.3314 0.1781 0.0452
hm 0.7996 0.5324 0.3386 0.1732 0.0385
hh 0.8018 0.5355 0.3361 0.1645 0.0304
zm 0.7139 0.4733 0.3185 0.1727 0.0499
zh 0.7328 0.4834 0.2946 0.1364 0.0072
r 0.6505 0.4213 0.2900 0.1522 0.0389
w 0.7708 0.5386 0.3748 0.2249 0.0945
y 0.7823 0.5310 0.3525 0.1953 0.0635
T 0.7631 0.5114 0.3375 0.1825 0.0532
VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent) (HP filter, lambda = 1600)
eh em Tot. lin. contr.
C 59.51 36.52 96.03
cm 13.68 91.05 104.72
ch 92.75 12.87 105.62
k 0.16 100.22 100.38
km 15.29 88.41 103.70
kh 27.26 77.62 104.88
x 1.32 97.90 99.22
xm 25.85 80.13 105.98
xh 38.24 66.08 104.32
l 3.16 94.61 97.77
hm 8.51 95.14 103.65
hh 28.68 78.18 106.85
zm 0.00 100.11 100.11
zh 100.11 0.00 100.11
r 0.44 100.02 100.46
w 0.18 99.93 100.11
y 2.36 99.38 101.74
T 1.61 99.88 101.49
Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples
Total computing time : 0h00m05s
Specification of the model
Variables and Parameters
MOD - File
Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Found 18 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs ...
done
Preprocessing completed.
"Model with a more general home production function and highly correlated technology shocks (logs)"
"The numbering of the equations is referenced to the P&P solutions."
"Manuel Bieri and Michael Wagner (2023)"
"Replace (83) with (160) for steady state calculation"
"Replace (90) with (161) for steady state calculation"
"Replace (92) with (162) for steady state calculation"
"Replace (94) with (163) for steady state calculation"
Residuals of the static equations:
Equation number 1 : 0 : (113) Resource Constraint
Equation number 2 : 0 : (165) Household FOC w.r.t. hh
Equation number 3 : 0 : (115) Household FOC w.r.t. hm
Equation number 4 : 0 : (167) Household FOC w.r.t. kh
Equation number 5 : 0 : (117) Household FOC w.r.t. km
Equation number 6 : 0 : (118) Firm FOC w.r.t. km
Equation number 7 : 0 : (119) Firm FOC w.r.t. hm
Equation number 8 : 0 : (120) Market Output
Equation number 9 : 0 : (121) Total Consumption
Equation number 10 : 0 : (122) Leisure
Equation number 11 : 0 : (174) Home production
Equation number 12 : 0 : (124) Market Investments
Equation number 13 : 0 : (125) Home Investments
Equation number 14 : 0 : (126) Total Investments
Equation number 15 : 0 : (127) Total Capital
Equation number 16 : 0 : (128) Government Transfer
Equation number 17 : 0 : (129) Market Technology
Equation number 18 : 0 : (130) Home Technology
STEADY-STATE RESULTS:
C -0.825093
cm -0.721986
ch -0.985633
l -0.867501
hm -1.10866
hh -1.38629
k 1.2934
km 0.856215
kh 0.255373
x -2.27595
xm -2.71314
xh -3.31398
r -2.60923
T -1.68009
w 0.229753
y -0.530203
zm 0
zh 0
EIGENVALUES:
Modulus Real Imaginary
2.49e-16 2.49e-16 0
0.95 0.95 0
0.95 0.95 0
0.9576 0.9576 0
1.138 1.138 0
4.764e+15 -4.764e+15 0
1.182e+16 -1.182e+16 0
1.997e+19 1.997e+19 0
There are 4 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition is verified.
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.
Information about Model4_Log (dynamic model)
The following variables appear with a lag and are therefore states:
km(-1)
kh(-1)
zm(-1)
zh(-1)
The following variables appear with a lead and are therefore forward-looking variables:
C(1)
cm(1)
ch(1)
r(1)
The following variables do not appear with a lead or lag and are therefore purely static variables:
l
hm
hh
k
x
xm
xh
T
w
y
MODEL SUMMARY
Number of variables: 18
Number of stochastic shocks: 2
Number of state variables: 4
Number of jumpers: 4
Number of static variables: 10
MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS
Variables eh em
eh 0.000098 0.000097
em 0.000097 0.000098
POLICY AND TRANSITION FUNCTIONS
C cm ch k km kh x xm xh l hm hh zm zh r w y T
Constant -0.825093 -0.721986 -0.985633 1.293405 0.856215 0.255373 -2.275951 -2.713141 -3.313982 -0.867501 -1.108663 -1.386294 0 0 -2.609234 0.229753 -0.530203 -1.680092
km(-1) 0.214888 0.442610 -0.172364 0.629752 0.825027 0.273638 0.071852 -5.239453 9.757830 0.031237 0.118350 -0.208701 0 0 -0.622092 0.259558 0.377908 0.248630
kh(-1) 0.182087 0.058564 0.392143 0.305163 0.399789 0.132599 -1.392737 14.256325 -29.931198 0.059673 -0.275948 0.264000 0 0 -0.194709 0.081239 -0.194709 -0.235172
zm(-1) 0.318510 0.757242 -0.427572 0.061195 0.478010 -0.698930 2.182207 17.045662 -24.923581 -0.065543 0.475622 -0.517709 0.950000 0 1.005919 0.530297 1.005919 1.214961
zh(-1) 0.136306 -0.456563 1.144505 0.039770 -0.556159 1.126536 1.418168 -19.832406 40.171845 -0.115305 -0.183384 0.435780 0 0.950000 -0.129396 0.053988 -0.129396 -0.156286
eh 0.143480 -0.480593 1.204743 0.041863 -0.585430 1.185828 1.492809 -20.876216 42.286153 -0.121374 -0.193036 0.458716 0 1.000000 -0.136206 0.056830 -0.136206 -0.164511
em 0.335274 0.797097 -0.450076 0.064416 0.503169 -0.735716 2.297059 17.942802 -26.235349 -0.068992 0.500655 -0.544957 1.000000 0 1.058862 0.558207 1.058862 1.278906
MOMENTS OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE SKEWNESS KURTOSIS
C -0.818183 0.006996 0.000049 0.072640 -0.164274
cm -0.715206 0.004653 0.000022 0.096019 -0.162549
ch -0.978503 0.012307 0.000151 0.076483 -0.064774
k 1.303809 0.004345 0.000019 -0.007451 -0.164697
km 0.867764 0.005567 0.000031 -0.066384 -0.169135
kh 0.263689 0.006460 0.000042 0.036008 -0.250802
x -2.262894 0.046144 0.002129 0.036960 0.095368
xm -2.698506 0.071663 0.005136 -0.015762 0.065135
xh -3.303802 0.155960 0.024324 0.110315 0.024732
l -0.867900 0.002423 0.000006 -0.038545 0.130850
hm -1.108053 0.003306 0.000011 0.023852 0.077120
hh -1.386427 0.001927 0.000004 0.081748 -0.014877
zm 0.005770 0.013591 0.000185 0.057051 0.056263
zh 0.007024 0.013487 0.000182 0.057305 -0.017576
r -2.612818 0.013494 0.000182 0.020836 0.300708
w 0.237019 0.008323 0.000069 0.069702 -0.117182
y -0.522327 0.011290 0.000127 0.060033 -0.049223
T -1.672961 0.013900 0.000193 0.053226 0.024016
CORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE C cm ch k km kh x xm xh l hm hh zm zh r w y T
C 1.0000 0.8967 0.9586 0.5463 0.0487 0.9610 0.9325 0.5033 0.3573 -0.9208 0.8070 0.1182 0.9693 0.9676 0.8682 0.9955 0.9702 0.9632
cm 0.8967 1.0000 0.7335 0.7491 0.3926 0.8056 0.7739 0.4288 0.2872 -0.7263 0.7805 -0.2328 0.8187 0.7803 0.6455 0.9002 0.8922 0.8549
ch 0.9586 0.7335 1.0000 0.3571 -0.1776 0.9573 0.9340 0.4969 0.3639 -0.9466 0.7370 0.3311 0.9616 0.9837 0.9178 0.9495 0.9157 0.9289
k 0.5463 0.7491 0.3571 1.0000 0.8505 0.5625 0.2404 0.4327 -0.1617 -0.1904 0.1942 -0.0374 0.3326 0.3301 0.0620 0.5012 0.4263 0.3588
km 0.0487 0.3926 -0.1776 0.8505 1.0000 0.0434 -0.2658 0.2557 -0.4363 0.3254 -0.2058 -0.2214 -0.1755 -0.1998 -0.4322 0.0057 -0.0560 -0.1327
kh 0.9610 0.8056 0.9573 0.5625 0.0434 1.0000 0.8744 0.4199 0.3787 -0.8731 0.6923 0.2769 0.9075 0.9410 0.7970 0.9428 0.8977 0.8900
x 0.9325 0.7739 0.9340 0.2404 -0.2658 0.8744 1.0000 0.2858 0.5960 -0.9963 0.9261 0.0078 0.9893 0.9820 0.9737 0.9568 0.9765 0.9896
xm 0.5033 0.4288 0.4969 0.4327 0.2557 0.4199 0.2858 1.0000 -0.5992 -0.2991 0.0639 0.4871 0.4147 0.3937 0.3373 0.4490 0.3497 0.3521
xh 0.3573 0.2872 0.3639 -0.1617 -0.4363 0.3787 0.5960 -0.5992 1.0000 -0.5817 0.7202 -0.4017 0.4790 0.4905 0.5308 0.4231 0.5228 0.5317
l -0.9208 -0.7263 -0.9466 -0.1904 0.3254 -0.8731 -0.9963 -0.2991 -0.5817 1.0000 -0.8979 -0.0796 -0.9853 -0.9848 -0.9852 -0.9425 -0.9577 -0.9766
hm 0.8070 0.7805 0.7370 0.1942 -0.2058 0.6923 0.9261 0.0639 0.7202 -0.8979 1.0000 -0.3674 0.8873 0.8455 0.8720 0.8590 0.9261 0.9281
hh 0.1182 -0.2328 0.3311 -0.0374 -0.2214 0.2769 0.0078 0.4871 -0.4017 -0.0796 -0.3674 1.0000 0.0725 0.1659 0.1070 0.0460 -0.0736 -0.0382
zm 0.9693 0.8187 0.9616 0.3326 -0.1755 0.9075 0.9893 0.4147 0.4790 -0.9853 0.8873 0.0725 1.0000 0.9916 0.9615 0.9826 0.9841 0.9933
zh 0.9676 0.7803 0.9837 0.3301 -0.1998 0.9410 0.9820 0.3937 0.4905 -0.9848 0.8455 0.1659 0.9916 1.0000 0.9533 0.9743 0.9658 0.9768
r 0.8682 0.6455 0.9178 0.0620 -0.4322 0.7970 0.9737 0.3373 0.5308 -0.9852 0.8720 0.1070 0.9615 0.9533 1.0000 0.8936 0.9141 0.9442
w 0.9955 0.9002 0.9495 0.5012 0.0057 0.9428 0.9568 0.4490 0.4231 -0.9425 0.8590 0.0460 0.9826 0.9743 0.8936 1.0000 0.9887 0.9833
y 0.9702 0.8922 0.9157 0.4263 -0.0560 0.8977 0.9765 0.3497 0.5228 -0.9577 0.9261 -0.0736 0.9841 0.9658 0.9141 0.9887 1.0000 0.9966
T 0.9632 0.8549 0.9289 0.3588 -0.1327 0.8900 0.9896 0.3521 0.5317 -0.9766 0.9281 -0.0382 0.9933 0.9768 0.9442 0.9833 0.9966 1.0000
AUTOCORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE 1 2 3 4 5
C 0.7815 0.5442 0.3535 0.1916 0.0510
cm 0.7688 0.6020 0.4624 0.3234 0.1850
ch 0.8053 0.5386 0.3244 0.1499 0.0057
k 0.9537 0.8494 0.7073 0.5421 0.3663
km 0.9323 0.8162 0.6730 0.5107 0.3432
kh 0.7634 0.5344 0.3518 0.1867 0.0520
x 0.6539 0.4198 0.2571 0.1168 0.0030
xm 0.3725 0.2046 0.1442 0.0400 0.0071
xh -0.0127 -0.0998 -0.0349 -0.0656 -0.0192
l 0.6847 0.4421 0.2677 0.1200 0.0004
hm 0.4615 0.2730 0.1820 0.0861 0.0088
hh 0.5399 0.3484 0.2502 0.1410 0.0469
zm 0.7333 0.4846 0.2971 0.1424 0.0116
zh 0.7328 0.4834 0.2946 0.1364 0.0072
r 0.7489 0.4965 0.3037 0.1462 0.0122
w 0.7425 0.5102 0.3308 0.1774 0.0447
y 0.6677 0.4468 0.2907 0.1531 0.0353
T 0.6781 0.4462 0.2810 0.1396 0.0196
VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent) (HP filter, lambda = 1600)
eh em Tot. lin. contr.
C 98.41 0.67 99.08
cm 82.27 12.63 94.91
ch 100.58 1.21 101.78
k 94.83 2.19 97.02
km 92.18 4.98 97.16
kh 98.58 4.14 102.72
x 96.77 1.47 98.24
xm 93.25 9.69 102.94
xh 97.21 5.18 102.40
l 98.48 0.49 98.97
hm 80.46 14.49 94.96
hh 48.53 51.89 100.42
zm 96.61 1.69 98.31
zh 100.11 0.00 100.11
r 96.27 1.88 98.14
w 96.58 1.68 98.26
y 92.81 4.22 97.03
T 93.65 3.64 97.30
Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples
Total computing time : 0h00m05s
Specification of the model
Variables and Parameters
MOD - File
Starting Dynare (version 5.3).
Calling Dynare with arguments: none
Starting preprocessing of the model file ...
Found 18 equation(s).
Evaluating expressions...done
Computing static model derivatives (order 1).
Computing dynamic model derivatives (order 1).
Processing outputs ...
done
Preprocessing completed.
"Model with a more general home production function and highly correlated technology shocks (logs)"
"The numbering of the equations is referenced to the P&P solutions."
"Manuel Bieri and Michael Wagner (2023)"
"Replace (83) with (160) for steady state calculation"
"Replace (90) with (161) for steady state calculation"
"Replace (92) with (162) for steady state calculation"
"Replace (94) with (163) for steady state calculation"
Residuals of the static equations:
Equation number 1 : 0 : (113) Resource Constraint
Equation number 2 : 0 : (165) Household FOC w.r.t. hh
Equation number 3 : 0 : (115) Household FOC w.r.t. hm
Equation number 4 : 0 : (167) Household FOC w.r.t. kh
Equation number 5 : 0 : (117) Household FOC w.r.t. km
Equation number 6 : 0 : (118) Firm FOC w.r.t. km
Equation number 7 : 0 : (119) Firm FOC w.r.t. hm
Equation number 8 : 0 : (120) Market Output
Equation number 9 : 0 : (121) Total Consumption
Equation number 10 : 0 : (122) Leisure
Equation number 11 : 0 : (174) Home production
Equation number 12 : 0 : (124) Market Investments
Equation number 13 : 0 : (125) Home Investments
Equation number 14 : 0 : (126) Total Investments
Equation number 15 : 0 : (127) Total Capital
Equation number 16 : 0 : (128) Government Transfer
Equation number 17 : 0 : (129) Market Technology
Equation number 18 : 0 : (130) Home Technology
STEADY-STATE RESULTS:
C -0.737024
cm -0.805701
ch -0.641431
l -0.867501
hm -1.10866
hh -1.38629
k 1.61539
km 0.856215
kh 0.984179
x -1.95397
xm -2.71314
xh -2.58518
r -2.60923
T -1.68009
w 0.229753
y -0.530203
zm 0
zh 0
EIGENVALUES:
Modulus Real Imaginary
1.52e-15 1.52e-15 0
0.95 0.95 0
0.95 0.95 0
0.9586 0.9586 0
1.124 1.124 0
1.563e+16 1.563e+16 0
1.941e+16 1.941e+16 0
Inf Inf 0
There are 4 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition is verified.
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.
Information about Model4a_Log (dynamic model)
The following variables appear with a lag and are therefore states:
km(-1)
kh(-1)
zm(-1)
zh(-1)
The following variables appear with a lead and are therefore forward-looking variables:
C(1)
cm(1)
ch(1)
r(1)
The following variables do not appear with a lead or lag and are therefore purely static variables:
l
hm
hh
k
x
xm
xh
T
w
y
MODEL SUMMARY
Number of variables: 18
Number of stochastic shocks: 2
Number of state variables: 4
Number of jumpers: 4
Number of static variables: 10
MATRIX OF COVARIANCE OF EXOGENOUS SHOCKS
Variables eh em
eh 0.000098 0.000097
em 0.000097 0.000098
POLICY AND TRANSITION FUNCTIONS
C cm ch k km kh x xm xh l hm hh zm zh r w y T
Constant -0.737024 -0.805701 -0.641431 1.615390 0.856215 0.984179 -1.953966 -2.713141 -2.585177 -0.867501 -1.108663 -1.386294 0 0 -2.609234 0.229753 -0.530203 -1.680092
km(-1) 0.148119 0.372552 -0.147655 0.471318 0.564448 0.389374 0.584499 -14.531601 13.884929 -0.017567 0.183093 -0.212169 0 0 -0.576410 0.240497 0.423590 0.303806
kh(-1) 0.279611 0.117859 0.492780 0.477161 0.571446 0.394201 -1.421708 20.377549 -20.602549 0.120184 -0.358388 0.271162 0 0 -0.252878 0.105509 -0.252878 -0.305429
zm(-1) 0.296670 0.783146 -0.344439 0.047324 0.719524 -0.544134 1.687559 25.657939 -19.403620 -0.073548 0.468557 -0.494935 0.950000 0 1.000934 0.532377 1.000934 1.208940
zh(-1) 0.124092 -0.496238 0.941605 0.031914 -0.628107 0.612656 1.138023 -22.398049 21.847061 -0.125534 -0.145547 0.403018 0 0.950000 -0.102698 0.042849 -0.102698 -0.124040
eh 0.130623 -0.522356 0.991163 0.033593 -0.661165 0.644901 1.197919 -23.576893 22.996907 -0.132141 -0.153207 0.424230 0 1.000000 -0.108103 0.045104 -0.108103 -0.130568
em 0.312285 0.824364 -0.362568 0.049815 0.757393 -0.572773 1.776378 27.008357 -20.424863 -0.077419 0.493218 -0.520984 1.000000 0 1.053615 0.560397 1.053615 1.272568
MOMENTS OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE SKEWNESS KURTOSIS
C -0.730202 0.006202 0.000038 0.067488 -0.197722
cm -0.799512 0.004909 0.000024 0.116819 -0.112857
ch -0.633774 0.008625 0.000074 0.058364 -0.167782
k 1.625290 0.003982 0.000016 -0.013917 -0.165784
km 0.867171 0.004953 0.000025 -0.022307 -0.138607
kh 0.993151 0.003439 0.000012 0.034573 -0.059143
x -1.941620 0.040430 0.001635 0.045775 0.101004
xm -2.699240 0.057528 0.003309 0.126624 -0.005587
xh -2.574199 0.044880 0.002014 0.002398 -0.115911
l -0.867995 0.002854 0.000008 -0.040244 0.138550
hm -1.108097 0.004787 0.000023 0.028126 0.219398
hh -1.386210 0.001890 0.000004 -0.034802 0.162273
zm 0.005770 0.013591 0.000185 0.057051 0.056263
zh 0.007024 0.013487 0.000182 0.057305 -0.017576
r -2.612434 0.013343 0.000178 0.026502 0.278517
w 0.236859 0.008368 0.000070 0.071054 -0.098754
y -0.522532 0.013027 0.000170 0.064325 0.014599
T -1.673086 0.015639 0.000245 0.056693 0.064484
CORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE C cm ch k km kh x xm xh l hm hh zm zh r w y T
C 1.0000 0.9362 0.9646 0.5228 0.5111 0.4901 0.9501 0.7935 0.7140 -0.9299 0.9230 -0.7266 0.9637 0.9620 0.8582 0.9944 0.9778 0.9667
cm 0.9362 1.0000 0.8103 0.6686 0.7201 0.5427 0.8412 0.7338 0.5969 -0.8012 0.8612 -0.8465 0.8640 0.8261 0.7093 0.9314 0.9147 0.8877
ch 0.9646 0.8103 1.0000 0.3699 0.3118 0.4099 0.9526 0.7722 0.7423 -0.9489 0.8924 -0.5761 0.9583 0.9839 0.8984 0.9588 0.9437 0.9455
k 0.5228 0.6686 0.3699 1.0000 0.9686 0.9491 0.2381 0.1798 0.2005 -0.1765 0.2195 -0.2858 0.2819 0.2796 0.0129 0.4493 0.3692 0.3099
km 0.5111 0.7201 0.3118 0.9686 1.0000 0.8410 0.2471 0.2461 0.1409 -0.1799 0.2682 -0.4402 0.2923 0.2578 0.0301 0.4548 0.3907 0.3308
kh 0.4901 0.5427 0.4099 0.9491 0.8410 1.0000 0.2052 0.0795 0.2579 -0.1562 0.1378 -0.0642 0.2431 0.2818 -0.0100 0.4016 0.3086 0.2553
x 0.9501 0.8412 0.9526 0.2381 0.2471 0.2052 1.0000 0.8220 0.7664 -0.9975 0.9858 -0.7649 0.9981 0.9913 0.9724 0.9742 0.9880 0.9954
xm 0.7935 0.7338 0.7722 0.1798 0.2461 0.0795 0.8220 1.0000 0.2642 -0.8146 0.8212 -0.6787 0.8429 0.8068 0.8351 0.8134 0.8242 0.8346
xh 0.7140 0.5969 0.7423 0.2005 0.1409 0.2579 0.7664 0.2642 1.0000 -0.7706 0.7433 -0.5300 0.7397 0.7688 0.7050 0.7324 0.7435 0.7444
l -0.9299 -0.8012 -0.9489 -0.1765 -0.1799 -0.1562 -0.9975 -0.8146 -0.7706 1.0000 -0.9793 0.7371 -0.9925 -0.9898 -0.9842 -0.9572 -0.9747 -0.9864
hm 0.9230 0.8612 0.8924 0.2195 0.2682 0.1378 0.9858 0.8212 0.7433 -0.9793 1.0000 -0.8585 0.9832 0.9558 0.9595 0.9585 0.9831 0.9891
hh -0.7266 -0.8465 -0.5761 -0.2858 -0.4402 -0.0642 -0.7649 -0.6787 -0.5300 0.7371 -0.8585 1.0000 -0.7689 -0.6844 -0.7109 -0.7760 -0.8138 -0.8040
zm 0.9637 0.8640 0.9583 0.2819 0.2923 0.2431 0.9981 0.8429 0.7397 -0.9925 0.9832 -0.7689 1.0000 0.9916 0.9628 0.9837 0.9931 0.9980
zh 0.9620 0.8261 0.9839 0.2796 0.2578 0.2818 0.9913 0.8068 0.7688 -0.9898 0.9558 -0.6844 0.9916 1.0000 0.9559 0.9745 0.9771 0.9835
r 0.8582 0.7093 0.8984 0.0129 0.0301 -0.0100 0.9724 0.8351 0.7050 -0.9842 0.9595 -0.7109 0.9628 0.9559 1.0000 0.8985 0.9296 0.9517
w 0.9944 0.9314 0.9588 0.4493 0.4548 0.4016 0.9742 0.8134 0.7324 -0.9572 0.9585 -0.7760 0.9837 0.9745 0.8985 1.0000 0.9945 0.9878
y 0.9778 0.9147 0.9437 0.3692 0.3907 0.3086 0.9880 0.8242 0.7435 -0.9747 0.9831 -0.8138 0.9931 0.9771 0.9296 0.9945 1.0000 0.9979
T 0.9667 0.8877 0.9455 0.3099 0.3308 0.2553 0.9954 0.8346 0.7444 -0.9864 0.9891 -0.8040 0.9980 0.9835 0.9517 0.9878 0.9979 1.0000
AUTOCORRELATION OF SIMULATED VARIABLES (HP filter, lambda = 1600)
VARIABLE 1 2 3 4 5
C 0.7650 0.5370 0.3549 0.1978 0.0605
cm 0.8091 0.6075 0.4390 0.2858 0.1405
ch 0.7462 0.5013 0.3101 0.1498 0.0186
k 0.9576 0.8560 0.7149 0.5496 0.3732
km 0.9448 0.8382 0.7002 0.5407 0.3701
kh 0.9305 0.8105 0.6632 0.4937 0.3196
x 0.7306 0.4798 0.2927 0.1360 0.0065
xm 0.4860 0.2935 0.1968 0.1023 -0.0093
xh 0.3788 0.2003 0.1653 0.0355 -0.0459
l 0.7279 0.4760 0.2883 0.1311 0.0025
hm 0.7356 0.4837 0.2983 0.1428 0.0120
hh 0.7874 0.5345 0.3501 0.1954 0.0595
zm 0.7333 0.4846 0.2971 0.1424 0.0116
zh 0.7328 0.4834 0.2946 0.1364 0.0072
r 0.7317 0.4828 0.2948 0.1412 0.0106
w 0.7524 0.5160 0.3326 0.1766 0.0420
y 0.7429 0.4992 0.3148 0.1594 0.0269
T 0.7367 0.4891 0.3031 0.1481 0.0167
VARIANCE DECOMPOSITION SIMULATING ONE SHOCK AT A TIME (in percent) (HP filter, lambda = 1600)
eh em Tot. lin. contr.
C 98.42 0.68 99.09
cm 82.52 12.61 95.14
ch 100.37 2.11 102.48
k 94.91 2.11 97.02
km 86.50 9.57 96.08
kh 88.92 10.13 99.05
x 96.66 1.53 98.19
xm 64.44 34.99 99.43
xh 58.49 40.83 99.32
l 97.73 0.88 98.60
hm 87.62 8.29 95.92
hh 39.80 53.03 92.83
zm 96.61 1.69 98.31
zh 100.11 0.00 100.11
r 96.72 1.64 98.36
w 96.23 1.89 98.11
y 93.54 3.71 97.25
T 94.27 3.21 97.48
Note: numbers do not add up to 100 due to non-zero correlation of simulated shocks in small samples
Total computing time : 0h00m05s
