# RDP 2019-01: Online Appendices: A Model of the Australian Housing Market Appendix E: Equations

## E.1 Estimated Equations

E1: Detached housing approvals (constant prices)

Signal equation: dlog(bahousevol)-@mean(dlog(bahousevol)) = c(1)*(log(bahousevol(−1)/rinc(−1))) + c(3)*(dlog(bahousevol(−1))-@mean(dlog(bahousevol(−1)))) + c(4)*(dlog(rdp(−1))-@mean(dlog(rdp(−1)))) + c(6)*gst + c(7)*gst(−1) + c(8)*gst(−2) + c(9)*(d(rvmr(−1))) + c(10)*(d(rvmr(−2))) + c(11)*(d(rvmr(−3))) + sv1 + e1

State Equation: sv1 = sv1(−1) + e2

Sspace: SS_HOUSE
Method: Maximum likelihood (BFGS / Marquardt steps)
Date: 12/21/18 Time: 14:14
Sample: 1987Q1 2018Q2
Included observations: 126
User prior mean: MPRIOR_HOUSE
User prior variance: VPRIOR_HOUSE
Convergence achieved after 26 iterations
Coefficient covariance computed using outer product of gradients

Coefficient Std. Error z-Statistic Prob.
C(1) −0.100361 0.048104 −2.086352 0.0369
C(3) 0.193319 0.091692 2.108346 0.0350
C(4) 0.696450 0.327964 2.123553 0.0337
C(6) −0.292142 0.302617 −0.965387 0.3344
C(7) −0.332333 0.290471 −1.144118 0.2526
C(8) 0.125014 0.276530 0.452083 0.6512
C(9) −0.040479 0.008707 −4.648956 0.0000
C(10) −0.016503 0.012830 −1.286257 0.1984
C(11) −0.004935 0.012121 −0.407153 0.6839
C(111) −0.040104 0.002944 −13.62391 0.0000
C(112) −0.003758 0.002652 −1.416771 0.1565
Final State Root MSE z-Statistic Prob.
SV1 0.106484 0.012567 8.473480 0.0000
Log likelihood 219.1583 Akaike info criterion −3.304100
Parameters 11 Schwarz criterion −3.056488
Diffuse priors 0 Hannan-Quinn criter. −3.203503

E2: Higher-density housing approvals (chain volume)

Signal equation: dlog(baothervol)-@mean(dlog(baothervol)) = c(1)*(log(baothervol(−1)/rinc(−1))) + c(3)*(dlog(baothervol(−1))-@mean(dlog(baothervol(−1)))) + c(4)*(dlog(baothervol(−2))-@mean(dlog(baothervol(−2)))) + c(5)*gst(−1) + c(6)*gst + c(7)*(dlog(rdp(−1))-@mean(dlog(rdp(−1)))) + c(8)*(dlog(rdp(−2))-@mean(dlog(rdp(−2)))) + c(11)*d(rvmr(−4)) + c(12)*d(rvmr(−5)) + c(13)*d(rvmr(−6)) + sv1 + e1

State Equation: sv1 = sv1(−1) + e2

Sspace: SS_OTHER
Method: Maximum likelihood (BFGS / Marquardt steps)
Date: 12/21/18 Time: 14:15
Sample: 1987Q1 2018Q2
Included observations: 126
User prior mean: MPRIOR_OTHER
User prior variance: VPRIOR_OTHER
Convergence achieved after 21 iterations
Coefficient covariance computed using outer product of gradients

Coefficient Std. Error z-Statistic Prob.
C(1) −0.218119 0.142448 −1.531222 0.1257
C(3) −0.359422 0.118268 −3.039046 0.0024
C(4) −0.235235 0.099542 −2.363170 0.0181
C(5) −0.352351 2.084274 −0.169052 0.8658
C(6) −0.134336 2.282680 −0.058850 0.9531
C(7) 2.865936 1.198789 2.390693 0.0168
C(8) 0.135682 1.277500 0.106209 0.9154
C(11) −0.047596 0.040156 −1.185266 0.2359
C(12) −0.019440 0.039047 −0.497867 0.6186
C(13) −0.040988 0.036529 −1.122076 0.2618
C(111) −0.127044 0.010181 −12.47890 0.0000
C(112) 0.012171 0.013181 0.923346 0.3558
Final State Root MSE z-Statistic Prob.
SV1 0.176248 0.040275 4.376168 0.0000
Log likelihood 74.64281 Akaike info criterion −0.994330
Parameters 12 Schwarz criterion −0.724208
Diffuse priors 0 Hannan-Quinn criter. −0.884588

E3: Alterations and additions approvals (chain volume)

Signal equation: dlog((baaavol))-@mean(dlog((baaavol))) = c(1)*(log((baaavol(−1))/rinc(−1))) + c(2)*(dlog((baaavol(−1)))-@mean(dlog((baaavol(−1))))) + c(4)*(dlog(rdp(−1))-@mean(dlog(rdp(−1)))) + c(5)*(dlog(rdp(−2))-@mean(dlog(rdp(−2)))) + c(6)*gst + c(7)*gst(−1) + c(8)*d(rvmr(−1))+ c(9)*d(rvmr(−2)) + c(10)*d(rvmr(−3)) + sv1 + e1

State Equation: sv1 = sv1(−1) + e2

Sspace: SS_AA
Method: Maximum likelihood (BFGS / Marquardt steps)
Date: 12/21/18 Time: 14:15
Sample: 1987Q1 2018Q2
Included observations: 126
User prior mean: MPRIOR_AA
User prior variance: VPRIOR_AA
Convergence achieved after 23 iterations
Coefficient covariance computed using outer product of gradients

Coefficient Std. Error z-Statistic Prob.
C(1) −0.182937 0.096898 −1.887927 0.0590
C(2) −0.235186 0.092095 −2.553729 0.0107
C(4) 0.540372 0.355093 1.521776 0.1281
C(5) 0.237203 0.409203 0.579671 0.5621
C(6) −0.094603 0.406522 −0.232712 0.8160
C(7) −0.297929 0.357951 −0.832317 0.4052
C(8) −0.010476 0.012883 −0.813157 0.4161
C(9) −0.012689 0.015948 −0.795629 0.4262
C(10) −0.013542 0.015700 −0.862554 0.3884
C(111) −0.045972 0.003840 −11.97026 0.0000
C(112) 0.008298 0.004553 1.822503 0.0684
Final State Root MSE z-Statistic Prob.
SV1 0.175294 0.020432 8.579404 0.0000
Log likelihood 196.5964 Akaike info criterion −2.945975
Parameters 11 Schwarz criterion −2.698363
Diffuse priors 0 Hannan-Quinn criter. −2.845378

E4: Detached housing commencements (number)

Dependent Variable: DLOG(CHOUSENO) Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1988Q1 2018Q2
Included observations: 122

Variable Coefficient Std. Error t-Statistic Prob.
C −0.029263 0.003474 −8.423945 0.0000
LOG(BAHOUSENO(−1))-LOG(CHOUSENO(−1)) 0.942813 0.067582 13.95060 0.0000
DLOG(BAHOUSENO) 0.500654 0.048050 10.41949 0.0000
GST 0.037435 0.031027 1.206553 0.2300
GST(−1) −0.151889 0.032909 −4.615442 0.0000
R-squared 0.875946 Mean dependent var 0.001504
Adjusted R-squared 0.871705 S.D. dependent var 0.079474
S.E. of regression 0.028466 Akaike info criterion −4.240084
Sum squared resid 0.094807 Schwarz criterion −4.125165
Log likelihood 263.6451 Hannan-Quinn criter. −4.193407
F-statistic 206.5345 Durbin-Watson stat 1.968129
Prob(F-statistic) 0.000000

E5: Higher-density housing commencements (number)

Dependent Variable: DLOG(COTHERNO)
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1988Q1 2018Q2
Included observations: 122

Variable Coefficient Std. Error t-Statistic Prob.
C −0.068396 0.009727 −7.031357 0.0000
LOG(BAOTHERNO(−1))-LOG(COTHERNO(−1)) 0.872102 0.078301 11.13781 0.0000
DLOG(BAOTHERNO) 0.555883 0.055985 9.929168 0.0000
GST(−1) −0.115966 0.076289 −1.520094 0.1312
R-squared 0.617786 Mean dependent var 0.011185
Adjusted R-squared 0.608069 S.D. dependent var 0.118717
S.E. of regression 0.074322 Akaike info criterion −2.328587
Sum squared resid 0.651800 Schwarz criterion −2.236652
Log likelihood 146.0438 Hannan-Quinn criter. −2.291246
F-statistic 63.57588 Durbin-Watson stat 1.987865
Prob(F-statistic) 0.000000

E6: Detached housing completions (number)

Dependent Variable: DLOG(COMPHOUSENO)
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1988Q1 2018Q2
Included observations: 122

Variable Coefficient Std. Error t-Statistic Prob.
C −0.003440 0.003754 −0.916198 0.3614
LOG(COMPHOUSENO(−1))-LOG(CHOUSENO(−1)) −0.413561 0.037358 −11.07036 0.0000
GST 0.084368 0.042668 1.977293 0.0504
GST(−1) −0.092786 0.049826 −1.862187 0.0651
DLOG(CHOUSENO) 0.125903 0.057978 2.171558 0.0319
R-squared 0.592003 Mean dependent var 0.002075
Adjusted R-squared 0.578055 S.D. dependent var 0.062532
S.E. of regression 0.040619 Akaike info criterion −3.529051
Sum squared resid 0.193037 Schwarz criterion −3.414132
Log likelihood 220.2721 Hannan-Quinn criter. −3.482375
F-statistic 42.44173 Durbin-Watson stat 2.580016
Prob(F-statistic) 0.000000

E7: Higher-density housing completions (number)

Dependent Variable: DLOG(COMPOTHERNO)
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1988Q1 2018Q2
Included observations: 122

Variable Coefficient Std. Error t-Statistic Prob.
C −0.017681 0.009958 −1.775475 0.0785
LOG(COMPOTHERNO(−1))-LOG(COTHERNO(−1)) −0.360375 0.053542 −6.730742 0.0000
GST 0.254086 0.098086 2.590426 0.0108
GST(−1) −0.002845 0.101371 −0.028067 0.9777
DLOG(COTHERNO) 0.130662 0.076709 1.703351 0.0912
DLOG(COTHERNO(−1)) −0.246437 0.085383 −2.886243 0.0047
DLOG(COMPOTHERNO(−1)) −0.175762 0.078136 −2.249434 0.0264
R-squared 0.365085 Mean dependent var 0.011867
Adjusted R-squared 0.331959 S.D. dependent var 0.118004
S.E. of regression 0.096449 Akaike info criterion −1.783936
Sum squared resid 1.069781 Schwarz criterion −1.623050
Log likelihood 115.8201 Hannan-Quinn criter. −1.718589
F-statistic 11.02108 Durbin-Watson stat 2.133582
Prob(F-statistic) 0.000000

E8: Detached housing commencements (chain volume)

Dependent Variable: DLOG(CHOUSEVOL)
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1988Q1 2018Q2
Included observations: 122

Variable Coefficient Std. Error t-Statistic Prob.
C −0.002494 0.002707 −0.921417 0.3587
LOG(BAHOUSEVOL(−1))-LOG(CHOUSEVOL(−1)) 0.849068 0.065621 12.93905 0.0000
DLOG(BAHOUSEVOL) 0.480369 0.044405 10.81785 0.0000
GST(−1) −0.177607 0.034742 −5.112143 0.0000
R-squared 0.870611 Mean dependent var 0.003876
Adjusted R-squared 0.867322 S.D. dependent var 0.079932
S.E. of regression 0.029115 Akaike info criterion −4.202883
Sum squared resid 0.100027 Schwarz criterion −4.110948
Log likelihood 260.3759 Hannan-Quinn criter. −4.165542
F-statistic 264.6599 Durbin-Watson stat 1.887565
Prob(F-statistic) 0.000000

E9: Higher-density housing commencements (chain volume)

Dependent Variable: DLOG(COTHERVOL)
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1988Q1 2018Q2
Included observations: 122

Variable Coefficient Std. Error t-Statistic Prob.
C 0.023119 0.010038 2.303231 0.0231
LOG(COTHERVOL(−1))-LOG(BAOTHERVOL(−1)) −0.850425 0.152079 −5.592015 0.0000
DLOG(BAOTHERVOL) 0.521388 0.065561 7.952758 0.0000
DLOG(BAOTHERVOL(−1)) 0.045953 0.123995 0.370607 0.7116
DLOG(BAOTHERVOL(−2)) −0.001397 0.090965 −0.015363 0.9878
DLOG(COTHERVOL(−1)) −0.115555 0.126230 −0.915439 0.3619
DLOG(COTHERVOL(−2)) −0.079271 0.085163 −0.930817 0.3539
GST(−1) 0.013992 0.108521 0.128935 0.8976
R-squared 0.584403 Mean dependent var 0.018657
Adjusted R-squared 0.558884 S.D. dependent var 0.157234
S.E. of regression 0.104429 Akaike info criterion −1.617292
Sum squared resid 1.243219 Schwarz criterion −1.433422
Log likelihood 106.6548 Hannan-Quinn criter. −1.542610
F-statistic 22.90064 Durbin-Watson stat 1.990594
Prob(F-statistic) 0.000000

E10: Alterations and additions commencements (chain volume)

Dependent Variable: DLOG(CAAVOL)
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1988Q1 2018Q2
Included observations: 122

Variable Coefficient Std. Error t-Statistic Prob.
C 0.034945 0.005187 6.736545 0.0000
LOG(CAAVOL(−1))-LOG(BAAAVOL(−1)) −0.691079 0.078361 −8.819172 0.0000
DLOG(BAAAVOL) 0.555305 0.068310 8.129244 0.0000
DLOG(BAAAVOL(−1)) −0.020150 0.067270 −0.299545 0.7651
GST(−1) −0.261513 0.047196 −5.540980 0.0000
R-squared 0.699772 Mean dependent var 0.002968
Adjusted R-squared 0.689508 S.D. dependent var 0.074833
S.E. of regression 0.041699 Akaike info criterion −3.476581
Sum squared resid 0.203436 Schwarz criterion −3.361662
Log likelihood 217.0714 Hannan-Quinn criter. −3.429904
F-statistic 68.17600 Durbin-Watson stat 2.147701
Prob(F-statistic) 0.000000

E11: Detached housing commencements (public, chain volume)

Dependent Variable: DLOG(CHOUSEVOL_PUBLIC)
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1988Q1 2018Q2
Included observations: 122

Variable Coefficient Std. Error t-Statistic Prob.
C 1.445465 0.411947 3.508864 0.0006
LOG(CHOUSEVOL_PUBLIC(−1)) −0.300257 0.084934 −3.535183 0.0006
DLOG(CHOUSEVOL_PUBLIC(−1)) −0.273546 0.104267 −2.623514 0.0099
DLOG(CHOUSEVOL_PUBLIC(−2)) −0.003812 0.104279 −0.036556 0.9709
DLOG(CHOUSEVOL_PUBLIC(−3)) 0.050814 0.091240 0.556925 0.5786
R-squared 0.264975 Mean dependent var −0.005281
Adjusted R-squared 0.239846 S.D. dependent var 0.277291
S.E. of regression 0.241762 Akaike info criterion 0.038390
Sum squared resid 6.838492 Schwarz criterion 0.153309
Log likelihood 2.658185 Hannan-Quinn criter. 0.085067
F-statistic 10.54455 Durbin-Watson stat 1.995702
Prob(F-statistic) 0.000000

E12: Higher-density housing commencements (public, chain volume)

Dependent Variable: DLOG(COTHERVOL_PUBLIC)
Method: Least Squares
Date: 12/21/18 Time: 14:15

Variable Coefficient Std. Error t-Statistic Prob.
C 1.137847 0.523628 2.173009 0.0318
LOG(COTHERVOL_PUBLIC(−1)) −0.243867 0.108272 −2.252360 0.0262
DLOG(COTHERVOL_PUBLIC(−1)) −0.486876 0.116198 −4.190062 0.0001
DLOG(COTHERVOL_PUBLIC(−2)) −0.313617 0.113914 −2.753106 0.0069
DLOG(COTHERVOL_PUBLIC(−3)) −0.381888 0.092696 −4.119792 0.0001
R-squared 0.418509 Mean dependent var −0.026037
Adjusted R-squared 0.398283 S.D. dependent var 0.881506
S.E. of regression 0.683788 Akaike info criterion 2.118435
Sum squared resid 53.77002 Schwarz criterion 2.234580
Log likelihood −122.1061 Hannan-Quinn criter. 2.165602
F-statistic 20.69185 Durbin-Watson stat 1.630574
Prob(F-statistic) 0.000000

E13: Alterations and additions commencements (public, chain volume)

Dependent Variable: DLOG(CAAVOL_PUBLIC)
Method: Least Squares
Date: 12/21/18 Time: 14:15

Variable Coefficient Std. Error t-Statistic Prob.
C 0.329528 0.203860 1.616447 0.1087
LOG(CAAVOL_PUBLIC(−1)) −0.089483 0.055559 −1.610592 0.1100
DLOG(CAAVOL_PUBLIC(−1)) −0.409814 0.100261 −4.087488 0.0001
DLOG(CAAVOL_PUBLIC(−2)) −0.354218 0.098821 −3.584432 0.0005
DLOG(CAAVOL_PUBLIC(−3)) −0.067145 0.094554 −0.710124 0.4791
R-squared 0.245474 Mean dependent var 0.001079
Adjusted R-squared 0.219230 S.D. dependent var 0.442842
S.E. of regression 0.391301 Akaike info criterion 1.002094
Sum squared resid 17.60839 Schwarz criterion 1.118240
Log likelihood −55.12565 Hannan-Quinn criter. 1.049261
F-statistic 9.353387 Durbin-Watson stat 2.010975
Prob(F-statistic) 0.000001

E14: Detached housing work done (chain volume)

Dependent Variable: DLOG(WDHOUSEVOL)
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1988Q1 2018Q2
Included observations: 122

Variable Coefficient Std. Error t-Statistic Prob.
C 0.001749 0.002150 0.813601 0.4176
LOG(WDHOUSEVOL(−1))-LOG(CHOUSEVOL_PRIVATE(−1)) −0.470003 0.047843 −9.823940 0.0000
DLOG(WDHOUSEVOL(−1)) −0.009624 0.045602 −0.211036 0.8332
DLOG(WDHOUSEVOL(−2)) −0.080804 0.035412 −2.281850 0.0243
DLOG(CHOUSEVOL_PRIVATE) 0.423758 0.034183 12.39687 0.0000
GST 0.145296 0.024069 6.036560 0.0000
GST(−1) −0.139260 0.033024 −4.216923 0.0000
R-squared 0.872137 Mean dependent var 0.005211
Adjusted R-squared 0.865466 S.D. dependent var 0.063272
S.E. of regression 0.023207 Akaike info criterion −4.633037
Sum squared resid 0.061936 Schwarz criterion −4.472150
Log likelihood 289.6152 Hannan-Quinn criter. −4.567690
F-statistic 130.7335 Durbin-Watson stat 2.045568
Prob(F-statistic) 0.000000

E15: Higher-density housing work done (chain volume)

Dependent Variable: DLOG(WDOTHERVOL)
Method: Least Squares
Date: 12/21/18 Time: 14:15

Variable Coefficient Std. Error t-Statistic Prob.
C 0.006704 0.004129 1.623705 0.1072
LOG(WDOTHERVOL(−1))-LOG(COTHERVOL_PRIVATE(−1)) −0.194171 0.053496 −3.629636 0.0004
DLOG(COTHERVOL_PRIVATE) 0.130603 0.027947 4.673220 0.0000
DLOG(COTHERVOL_PRIVATE(−1)) 0.037821 0.046647 0.810807 0.4192
DLOG(COTHERVOL_PRIVATE(−2)) 0.073610 0.039601 1.858790 0.0657
DLOG(COTHERVOL_PRIVATE(−3)) 0.078526 0.032522 2.414587 0.0174
GST 0.164214 0.045213 3.632027 0.0004
GST(−1) −0.236190 0.045392 −5.203370 0.0000
R-squared 0.621852 Mean dependent var 0.017915
Adjusted R-squared 0.598218 S.D. dependent var 0.067410
S.E. of regression 0.042729 Akaike info criterion −3.403547
Sum squared resid 0.204484 Schwarz criterion −3.217714
Log likelihood 212.2128 Hannan-Quinn criter. −3.328079
F-statistic 26.31148 Durbin-Watson stat 2.008478
Prob(F-statistic) 0.000000

E16: Alterations and additions work done (chain volume)

Dependent Variable: DLOG(WDAAVOL)
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1988Q1 2018Q2
Included observations: 122

Variable Coefficient Std. Error t-Statistic Prob.
C 0.016480 0.002778 5.932315 0.0000
LOG(WDAAVOL(−1))-LOG(CAAVOL_PRIVATE(−1)) −0.546629 0.056386 −9.694322 0.0000
DLOG(CAAVOL_PRIVATE) 0.370454 0.042306 8.756560 0.0000
GST 0.101486 0.027391 3.705069 0.0003
GST(−1) −0.244923 0.035605 −6.878841 0.0000
R-squared 0.797175 Mean dependent var 0.003186
Adjusted R-squared 0.790241 S.D. dependent var 0.058981
S.E. of regression 0.027013 Akaike info criterion −4.344888
Sum squared resid 0.085374 Schwarz criterion −4.229969
Log likelihood 270.0381 Hannan-Quinn criter. −4.298211
F-statistic 114.9628 Durbin-Watson stat 2.220353
Prob(F-statistic) 0.000000

E17: Rental vacancy rate (%)

Dependent Variable: VACANCY/100
Method: Least Squares (Gauss-Newton / Marquardt steps)
Date: 12/21/18 Time: 14:15
Sample: 1983Q1 2018Q2
Included observations: 142
Convergence achieved after 6 iterations
White heteroskedasticity-consistent standard errors & covariance using outer product of gradients
VACANCY/100 = EXCESS_COMP + C(1)*(VACANCY(−1) – C(2))/100 + VACANCY(−1)/100 + C(3)*D(UR(−1)/100)

Coefficient Std. Error t-Statistic Prob.
C(1) −0.151162 0.024864 −6.079593 0.0000
C(2) 2.412196 0.121069 19.92407 0.0000
C(3) 0.206798 0.082588 2.503981 0.0134
R-squared 0.919038 Mean dependent var 0.027989
Adjusted R-squared 0.917873 S.D. dependent var 0.007645
S.E. of regression 0.002191 Akaike info criterion −9.388018
Sum squared resid 0.000667 Schwarz criterion −9.325571
Log likelihood 669.5493 Hannan-Quinn criter. −9.362642
Durbin-Watson stat 1.720493

E18: CPI rents (real, deflated using trimmed mean CPI)

Dependent Variable: DLOG(RENT_CPI)-INF_3Y
Method: Least Squares (Gauss-Newton / Marquardt steps)
Date: 12/21/18 Time: 14:15
Sample: 1983Q1 2018Q2
Included observations: 142
Convergence achieved after 4 iterations
White heteroskedasticity-consistent standard errors & covariance using outer product of gradients
DLOG(RENT_CPI)-INF_3Y = C(1)/400 + C(2)*(VACANCY(−5) – VACANCY_NATURAL)/100 + C(3)*D(VACANCY(−1)/100) + C(4) *D(VACANCY(−2)/100) + C(5)*D(VACANCY(−3)/100) + C(6) *D(VACANCY(−4)/100) + C(7)*(DLOG(RENT_CPI(−1))-INF_3Y(−1)-C(1)/400) + C(8)*(DLOG(RENT_CPI(−2))-INF_3Y(−2)-C(1)/400) + C(9) *((DLOG(RINC)+DLOG(RINC(−1)))/2-LR_INC) + C(10)*(DLOG(RINC(−2))-LR_INC)

Coefficient Std. Error t-Statistic Prob.
C(1) 0.901008 0.352870 2.553370 0.0118
C(2) −0.102501 0.040655 −2.521242 0.0129
C(3) −0.119479 0.097738 −1.222447 0.2237
C(4) −0.262032 0.121775 −2.151767 0.0332
C(5) −0.300454 0.097070 −3.095218 0.0024
C(6) −0.175276 0.097626 −1.795394 0.0749
C(7) 0.529930 0.118757 4.462286 0.0000
C(8) 0.193711 0.107003 1.810343 0.0725
C(9) 0.036692 0.019010 1.930111 0.0557
C(10) 0.048468 0.012212 3.968832 0.0001
R-squared 0.800702 Mean dependent var 0.000355
Adjusted R-squared 0.787114 S.D. dependent var 0.005090
S.E. of regression 0.002349 Akaike info criterion −9.202105
Sum squared resid 0.000728 Schwarz criterion −8.993948
Log likelihood 663.3494 Hannan-Quinn criter. −9.117518
Durbin-Watson stat 2.035132

E19: Housing prices (real, deflated using trimmed mean CPI)

Dependent Variable: DLOG(RDP*TCPI)-INF_3Y
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1983Q1 2018Q2
Included observations: 142
White heteroskedasticity-consistent standard errors & covariance

Variable Coefficient Std. Error t-Statistic Prob.
C 0.142670 0.054624 2.611829 0.0100
LOG(RRENT(−1)/RDP(−1))-LOG(UC(−1)) 0.022656 0.008718 2.598784 0.0104
DLOG(RDP(−1)*TCPI(−1))-INF_3Y(−1) 0.739314 0.067829 10.89963 0.0000
D(RVMR(−1)) −0.009176 0.002430 −3.776474 0.0002
D(RVMR(−2)) −0.005238 0.001890 −2.771782 0.0064
R-squared 0.692894 Mean dependent var 0.005482
Adjusted R-squared 0.683928 S.D. dependent var 0.020764
S.E. of regression 0.011673 Akaike info criterion −6.028431
Sum squared resid 0.018669 Schwarz criterion −5.924352
Log likelihood 433.0186 Hannan-Quinn criter. −5.986137
F-statistic 77.27517 Durbin-Watson stat 1.596512
Prob(F-statistic) 0.000000 Wald F-statistic 62.04658
Prob(Wald F-statistic) 0.000000

Dependent Variable: DLOG(WAP)
Method: Least Squares
Date: 12/21/18 Time: 14:15
Sample: 1983Q1 2018Q2
Included observations: 142
White heteroskedasticity-consistent standard errors & covariance

Variable Coefficient Std. Error t-Statistic Prob.
C 0.000287 0.000136 2.106600 0.0369
DLOG(WAP(−1)) 0.514310 0.078829 6.524362 0.0000
DLOG(WAP(−2)) 0.414611 0.078701 5.268156 0.0000
R-squared 0.809737 Mean dependent var 0.004009
Adjusted R-squared 0.806999 S.D. dependent var 0.000811
S.E. of regression 0.000356 Akaike info criterion −13.01993
Sum squared resid 1.77E-05 Schwarz criterion −12.95748
Log likelihood 927.4147 Hannan-Quinn criter. −12.99455
F-statistic 295.7839 Durbin-Watson stat 1.879626
Prob(F-statistic) 0.000000 Wald F-statistic 367.9006
Prob(Wald F-statistic) 0.000000

E21: Real household disposable income

Dependent Variable: DLOG(RINC_PER_CAPITA)
Method: Least Squares (Gauss-Newton / Marquardt steps)
Date: 12/21/18 Time: 14:15
White heteroskedasticity-consistent standard errors & covariance
DLOG(RINC_PER_CAPITA) = C(1) + C(2)*DLOG(RINC_PER_CAPITA(−1)) + C(3)*DLOG(RINC_PER_CAPITA(−2)) + C(4)*DLOG(RINC_PER_CAPIT A(−3)) + C(5)*DLOG(RINC_PER_CAPITA(−4)) + C(6)*GST(−1) – 0.0016 *((RVMR(−1)-RVMR(−41)))

Coefficient Std. Error t-Statistic Prob.
C(1) 0.003605 0.001225 2.943859 0.0039
C(2) −0.207404 0.115951 −1.788723 0.0760
C(3) 0.091408 0.096884 0.943483 0.3472
C(4) 0.158653 0.094180 1.684576 0.0945
C(5) 0.049565 0.079508 0.623391 0.5341
C(6) 0.058458 0.002246 26.03123 0.0000
R-squared 0.068745 Mean dependent var 0.002491
Adjusted R-squared 0.032081 S.D. dependent var 0.014902
S.E. of regression 0.014661 Akaike info criterion −5.563235
Sum squared resid 0.027297 Schwarz criterion −5.432843
Log likelihood 375.9551 Hannan-Quinn criter. −5.510249
F-statistic 1.875019 Durbin-Watson stat 1.451208
Prob(F-statistic) 0.103194 Wald F-statistic 573.6565
Prob(Wald F-statistic) 0.000000

## E.2 Identities and Calibrated Equations Used for Simulations

E22 $cas h t =cash_ex p t$
E23 $vm r t =vm r t−1 +Δ( cas h t )$
E24 $rvm r t =vm r t −( ( tcpi tcp i t−12 ) 1 3 −1 )*100$
E25 $i_10y_bon d t =exp( 1 40 ∑ i=1 40 ln( cash_ex p t+i ) )$
E26 $u c t =rvmr_ex p t +uc_running_cos t t +uc_transaction_cos t t +uc_depreciatio n t −uc_appreciatio n t$
E27 $rvmr_ex p t = ( 1+ vmr_ex p t 100 ) / ( 1+ inf_ex p t 100 ) *100−100$
E28 $vmr_ex p t =vmr+( i_10y_bon d t −cas h t )−average_sprea d t$
E29 $inf_ex p t =0.9*inf_ex p t−1 +0.1*( tcp i t tcp i t−4 −1 )*100$
E30 $uc_appreciatio n t =uc_appreciatio n t−1$
E31 $uc_depreciatio n t =uc_depreciatio n t−1$
E32 $un_transaction_cos t t =uc_transaction_cos t t−1$
E33 $un_running_cos t t =uc_running_cos t t−1$
E34 $Δln( tcp i t )=0.30*Δln( tcp i t−1 )+0.25*Δln( tcp i t−2 )+0.20*Δln( tcp i t−3 ) +0.15*Δln( tcp i t−4 )+0.1*0.025/4$
E35 $inf_3 y t = ( ln( tcp i t )−ln( tcp i t−12 ) ) / 12$
E36 $rren t t = rent_cp i t / tcp i t$
E37 $yiel d t = rren t t / rd p t *yield_adj*100$
E38 $comptotaln o t =comphousen o t +compothern o t$
E39 $stock_n o t =stock_n o t−1 +comptotaln o t *( 1−demolition_rat e t )$
E40 $stoc k t =stoc k t−1 *( 1−depreciation_rat e t )+natdi$
E41 $demolition_rat e t = 1 20 ∑ i=1 20 demolition_rat e t−1$
E42 $depreciation_rat e t = 1 4 ∑ i=1 4 depreciation_rat e t−1$
E43 $Δln( bahouseavo l t )= λ house *( log( bahouseavo l t−1 ( rin c t−1 wa p t−1 ) )− 1 8 ∑ i=1 8 log( bahouseavo l t−i ( rin c t−i wa p t−i ) ) ) +lr_inc_per_wap$
E44 $bahousen o t = bahousevo l t / bahouseavo l t *1000$
E45 $Δln( baotheravo l t )= λ other *( log( baotheravo l t−1 ( rin c t−1 wa p t−1 ) )− 1 8 ∑ i=1 8 log( baotheravo l t−i ( rin c t−i wa p t−i ) ) ) +lr_inc_per_wap$
E46 $baothern o t = baothervo l t / baotheravo l t *1000$
E47 $chousevol_privat e t =chousevo l t −chousevol_publi c t$
E48 $Δln( nahousevo l t )=Δln( wdhousevo l t )$
E49 $cothervol_privat e t =cothervo l t −cothervol_publi c t$
E50 $Δln( naothervo l t )=Δln( wdothervo l t )$
E51 $caavol_privat e t =caavo l t −caavol_publi c t$
E52 $Δln( naaavo l t )=Δln( wdaavo l t )$
E53 $batotalvo l t =baaavo l t +bahousevo l t +baothervo l t$
E54 $batotaln o t =bahousen o t +baothern o t$
E55 $nanewvo l t =nahousevo l t +naothervo l t$
E56 $natd i t =nanewvo l t +naaavo l t$
E57 $natdiva l t =natd i t *ipd_natd i t / 100$
E58 $inv_to_incom e t = natd i t / rin c t$
E59 $rin c t =rinc_per_capit a t *wa p t$
E60 $ah s t = wa p t stock_n o t *1000$
E61 $excess_com p t = ( Δ( stock_n o t )− Δ( wa p t ) ( 1 20 ∑ i=1 20 ah s t−i+1 ) ) / stock_n o t$
E62 $Δ( u r t )=−0.5*( Δln( rin c t )−lr_inc )*100$