Appendix for “How the Housing and Financial Wealth Effects
have changed over Time”
February 2011
Abstract
This appendix includes results referred to in Brady and Stimel (2011) but not included in
the text for brevity.1 Included are results from unit root tests on the variables in Brady
and Stimel (2011); a figure showing the residuals on which cointegration tests were
performed; impulse response functions (IRFs) generated from VAR estimation with
typical standard error bands (corresponding to Figures 2 through 5 in Brady and Stimel
(2011); and both linear projection IRFs and VAR IRFs of the variables in response to a
shock to consumption.
Ryan R. Brady
Department of Economics
United States Naval Academy
589 McNair Road, Stop 10D
Annapolis, MD 21402-5030
410-293-6883
rbrady@usna.edu
Derek Stimel
Menlo College
461Brawner Hall
1000 El Camino Real
Atherton, CA 94027-4301
650-543-3752
dstimel@menlo.edu
1
Brady, Ryan, and Derek Stimel (2011) “How the Housing and Financial Wealth Effects have changed
over time,” United States Naval Academy Working Paper, #2011-31.
Table A1: Unit Root Test Statistics, 1952:1 to 2009:4
Test: Ho: Variable is I(1)
Variable
Consumption
Liabilities
Tangible Assets
Financial Assets
Disposable Income
Augmented Dickey-Fuller Test
Phillips-Perron Test
No
No
Intercept or Intercept Intercept Intercept or Intercept Intercept
Trend
Only
and Trend
Trend
Only
and Trend
3.43
-1.28
-2.64
9.82
-1.50
-2.44
[0.99]
[0.64]
[0.26]
[1.00]
[0.53]
[0.36]
1.69
-1.52
-3.58
5.69
-1.93
-3.03
[0.98]
[0.52]
[0.03]
[1.00]
[0.32]
[0.13]
1.69
-1.24
-5.18
2.66
-1.41
-2.51
[0.98]
[0.66]
[0.00]
[1.00]
[0.58]
[0.32]
2.55
-0.71
-2.12
2.82
-0.74
-2.10
[0.99]
[0.84]
[0.53]
[1.00]
[0.83]
[0.54]
7.13
-1.88
-2.24
7.77
-2.09
-2.14
[1.00]
[0.34]
[0.47]
[1.00]
[0.25]
[0.52]
Test: Ho: Variable is I(2)
-1.89
-4.03
-4.15
-13.20
-14.98
-15.02
[0.06]
[0.00]
[0.01]
[0.00]
[0.00]
[0.00]
-1.99
-2.67
-2.80
-6.39
-9.00
-9.25
Liabilities
[0.05]
[0.08]
[0.20]
[0.00]
[0.00]
[0.00]
-3.74
-4.14
-4.19
-8.67
-9.31
-9.40
Tangible Assets
[0.00]
[0.00]
[0.01]
[0.00]
[0.00]
[0.00]
-11.77
-12.19
-12.16
-11.77
-12.30
-12.28
Financial Assets
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
-4.39
-16.84
-17.00
-15.40
-16.86
-17.01
Disposable Income
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
Notes: The null hypotheses of both unit root tests are that the series contains a unit root. Tstatistics and adjusted t-statistics with associated p-values (in brackets). Augmented Dickey-Fuller
test with Schwarz criterion selection of up to 8 Lags. Phillips-Perron test with automatic bandwith
selection using Newey-West bandwidth.
Consumption
Figure A.1 The Residual Series
8
Consumption on Constant, Disposable Income, Net Worth
6
Consumption on Constant, Disposable Income, Total Assets
Consumption on Constant, Disposable Income, Financial Assets, Tangible Assets
Consumption on Constant, Disposable Income, Financial Assets, Tangible Assets, Liabilities
4
2
0
-2
-4
-6
Notes: Residuals generated from single-equation ordinary least squares regressions; the variables in each regression are listed in
the legend above. The sample for each regression spans 1952 through 2009. See text for variable definitions.
Figure A2: VAR-generated Impulse Responses from a one percent shock to Tangible Assets
1952:1 to 1972:3
Percent (%)
Consumption
0.5
0.0
-0.5
-1.0
-1.5
-2.0
Liabilities
Tangible Assets
1
0
-1
-2
5
10
15
-3
20
Financial Assets
1.0
0.5
0.0
-0.5
-1.0
5
10
15
20
5
10
15
20
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
5
10
15
Income
20
0.5
0.0
-0.5
-1.0
-1.5
-2.0
5
10
15
20
15
20
15
20
15
20
1973:4 to 1985:1
Percent (%)
Consumption
1.6
1.2
0.8
0.4
0.0
-0.4
5
10
15
Liabilities
20
4
3
2
1
0
-1
-2
Tangible Assets
3
2
1
0
5
10
15
20
-1
5
10
15
Financial Assets
1.2
0.8
0.4
0.0
-0.4
-0.8
20
5
10
15
Income
1.5
1.0
0.5
0.0
-0.5
-1.0
20
5
10
1985:2 to 1998:2
Consumption
Liabilities
Percent (%)
0.5
0.0
-0.5
-1.0
-1.5
5
10
15
20
2
1
0
-1
-2
-3
5
10
15
Tangible Assets
20
3
2
1
0
-1
-2
-3
5
10
15
Financial Assets
20
4
2
0
-2
-4
-6
5
10
15
Income
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
20
5
10
1998:3 to 2009:4
Percent (%)
Consumption
.8
.6
.4
.2
.0
-.2
Tangible Assets
Liabilities
Financial Assets
2.8
4
2.0
10
15
2
2
1.2
5
Income
3
1
0.4
0
0
-0.4
20
-2
-1
5
10
15
20
5
10
15
20
5
10
15
20
.6
.4
.2
.0
-.2
-.4
5
10
Notes: Impulse responses generated from a five-variable VAR with short run restrictions imposed (variable
order is as shown across the columns). The solid line represents the IRF, the dashed lines represent the
asymptotic plus and minus two-standard error bands. The horizon is measured in quarters. See text for
variable definitions and sample divisions. Each sub-sample estimated with two lags.
Figure A3: VAR-generated Impulse Responses from a one percent shock to Financial Assets
1952:1 to 1973:3
Percent (%)
Consumption
.4
.3
.2
.1
.0
-.1
-.2
5
10
15
Liabilities
20
.6
.4
.2
.0
-.2
-.4
5
10
15
Tangible Assets
20
.4
.3
.2
.1
.0
-.1
Financial Assets
Income
1.2
.4
0.8
.2
0.4
5
10
15
20
0.0
.0
-0.4
-.2
5
10
15
20
5
10
15
20
15
20
15
20
15
20
1973:4 to 1985:1
Percent (%)
Consumption
.4
.2
.0
-.2
-.4
-.6
5
10
15
Liabilities
20
0.8
0.4
0.0
-0.4
-0.8
-1.2
5
10
15
Tangible Assets
20
Financial Assets
0.4
1.5
0.0
1.0
-0.4
0.5
-0.8
0.0
-1.2
-0.5
5
10
15
20
5
10
15
Income
20
.4
.2
.0
-.2
-.4
-.6
5
10
1985:2 to 1998:2
Percent (%)
Consumption
.8
.6
.4
.2
.0
-.2
-.4
5
10
15
Liabilities
20
1.2
0.8
0.4
0.0
-0.4
-0.8
Tangible Assets
Financial Assets
2.0
1.0
0.0
5
10
15
20
-1.0
5
10
15
20
3
2
1
0
-1
-2
5
10
15
Income
20
1.2
0.8
0.4
0.0
-0.4
-0.8
5
10
1998:3 to 2009:4
Percent (%)
Consumption
Liabilities
.04
-.04
-.12
-.20
5
10
15
20
.4
.2
.0
-.2
-.4
-.6
-.8
5
Notes: See notes to Figure A2.
10
15
Tangible Assets
20
0.8
0.4
0.0
-0.4
-0.8
-1.2
5
10
15
Financial Assets
20
1.5
1.0
0.5
0.0
-0.5
-1.0
Income
.08
.00
-.08
5
10
15
20
-.16
5
10
Figure A4: VAR-generated Impulse Responses from a one percent shock to Liabilities
1952:1 to 1973:3
Percent (%)
Consumption
1.2
0.8
0.4
0.0
-0.4
-0.8
5
10
15
Liabilities
20
3.0
2.5
2.0
1.5
1.0
0.5
5
10
15
Tangible Assets
20
0.8
0.4
0.0
-0.4
-0.8
-1.2
5
10
15
Financial Assets
20
2.0
1.5
1.0
0.5
0.0
-0.5
5
10
15
Income
20
1.2
0.8
0.4
0.0
-0.4
-0.8
5
10
15
20
15
20
15
20
15
20
1973:4 to 1985:1
Percent (%)
Consumption
2
1
0
-1
-2
-3
-4
Liabilities
Tangible Assets
2
-2
-6
5
10
15
20
-10
5
10
15
20
4
2
0
-2
-4
-6
-8
5
10
15
Financial Assets
20
2
1
0
-1
-2
-3
Income
2
0
-2
5
10
15
20
-4
5
10
1985:2 to 1998:2
Percent (%)
Consumption
1.2
0.8
0.4
0.0
-0.4
-0.8
5
10
15
Liabilities
20
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
5
10
15
Tangible Assets
20
4
3
2
1
0
-1
-2
Financial Assets
Income
4
2
0
5
10
15
20
-2
5
10
15
20
1.6
1.2
0.8
0.4
0.0
-0.4
-0.8
5
10
1998:3 to 2009:4
Percent (%)
Consumption
.6
.4
.2
.0
-.2
-.4
-.6
5
10
15
Liabilities
20
2
1
0
-1
-2
-3
5
Notes: See notes to Figure A2.
10
15
Tangible Assets
20
1
0
-1
-2
-3
-4
5
10
15
Financial Assets
20
3
2
1
0
-1
-2
-3
Income
.6
.2
-.2
5
10
15
20
-.6
5
10
Figure A5: VAR-generated Impulse Responses from a one percent shock to Income
1952:1 to 1973:3
Consumption
Liabilities
Tangible Assets
Percent (%)
1.0
0.5
0.5
-0.5
0.0
-1.5
-0.5
-1.0
5
10
15
20
-2.5
5
10
15
20
1.5
1.0
0.5
0.0
-0.5
-1.0
5
10
15
Financial Assets
20
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
5
10
15
Income
20
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
5
10
15
20
15
20
15
20
15
20
1973:4 to 1985:1
Percent (%)
Consumption
0.8
0.4
0.0
-0.4
-0.8
-1.2
5
10
15
Liabilities
20
2
1
0
-1
-2
-3
Tangible Assets
Financial Assets
2
1
0
-1
5
10
15
20
-2
5
10
15
20
0.8
0.4
0.0
-0.4
-0.8
-1.2
5
10
15
Income
20
1.5
1.0
0.5
0.0
-0.5
-1.0
5
10
1985:2 to 1998:2
Percent (%)
Consumption
Liabilities
1.6
0.8
0.0
-0.8
5
10
15
20
4
3
2
1
0
-1
-2
Tangible Assets
Financial Assets
6
4
2
0
5
10
15
20
-2
5
10
15
20
8
6
4
2
0
-2
-4
Income
3
2
1
0
5
10
15
20
-1
5
10
1998:3 to 2009:4
Percent (%)
Consumption
Liabilities
0.8
0.4
0.0
-0.4
5
10
15
20
4
3
2
1
0
-1
Tangible Assets
Financial Assets
4
2
0
5
Notes: See notes to Figure A2.
10
15
20
-2
5
10
15
20
4
2
0
-2
-4
-6
Income
1.2
0.8
0.4
0.0
5
10
15
20
-0.4
5
10
Figure A6: VAR-generated Impulse Responses from a one percent shock to Consumption
1952:1 to 1973:3
Percent (%)
Consumption
2.0
1.5
1.0
0.5
0.0
-0.5
Liabilities
Tangible Assets
2
1
0
-1
5
10
15
20
-2
5
10
15
20
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
Financial Assets
Income
2
2.0
1
1.0
0
5
10
15
20
-1
0.0
-2
-1.0
5
10
15
20
5
10
15
20
15
20
15
20
15
20
1973:4 to 1985:1
Percent (%)
Consumption
4
3
2
1
0
-1
-2
Liabilities
Tangible Assets
8
4
0
5
10
15
20
-4
5
10
15
20
8
6
4
2
0
-2
5
10
15
Financial Assets
20
3
2
1
0
-1
-2
Income
3
1
-1
5
10
15
20
-3
5
10
1985:2 to 1998:2
Percent (%)
Consumption
3
2
1
0
-1
-2
5
10
15
Liabilities
20
Tangible Assets
2
2
0
-2
-2
-6
-4
5
10
15
20
-10
5
10
15
Financial Assets
20
8
4
0
-4
-8
-12
Income
2
0
-2
5
10
15
20
-4
5
10
1998:3 to 2009:4
Percent (%)
Consumption
1.2
0.8
0.4
0.0
-0.4
-0.8
5
10
15
Liabilities
20
3
2
1
0
-1
-2
-3
5
Notes: See notes to Figure A2.
10
15
Tangible Assets
20
6
4
2
0
-2
-4
-6
5
10
15
Financial Assets
20
4
2
0
-2
-4
-6
Income
1.0
0.5
0.0
-0.5
5
10
15
20
-1.0
5
10
Figure A7: Impulse Responses from a one percent shock to Consumption
Percent (%)
consumption
2.0
1.0
0.0
-1.0
liabilities
6
3
0
5 10 15 20
-3
Percent (%)
consumption
2.5
1.5
0.5
-0.5
Percent (%)
1.5
0.5
-0.5
-1.5
5 10 15 20
liabilities
5 10 15 20
4
2
0
-2
consumption
2
0
5 10 15 20
-2
0.8
0
0.0
-0.4
-2
5 10 15 20
-1.2
1.6
0.8
0.0
-0.8
5 10 15 20
5 10 15 20
-4
5 10 15 20
5 10 15 20
financial assets
5
3
1
-1
-3
6
2
-2
-6
0
5 10 15 20
-2
3
1
5 10 15 20
-1
financial assets
0
-8
5 10 15 20
income
financial assets
3
0.5
1
-1
-0.5
-3
-5
-1.5
5 10 15 20
8
5 10 15 20
income
4
2
financial assets
5
3
1
-1
-3
1998:3 to 2004
tangible assets
liabilities
3
1
-1
-3
5 10 15 20
1985:2 to 1998:2
tangible assets
1.2
0.4
-0.8
5 10 15 20
1973:4 to 1985:1
tangible assets
4
liabilities
consumption
Percent (%)
1952 to 1973:3
tangible assets
1.2
0.4
-0.4
-1.2
5 10 15 20
5 10 15 20
income
5 10 15 20
income
5 10 15 20
Notes: The impulse response functions (IRFs) are estimated using Jordà's (2005) linear projection
technique. The solid line represents the impulse response function; the dashed lines are Jordà’s (2009)
95 percent conditional confidence bands. The horizon for each IRF is measured in quarters. See text
for variable definitions.