RDP 201508: Housing Wealth Effects: Crosssectional Evidence from New Vehicle Registrations 5. Elasticity of New Vehicle Registrations to House Prices
August 2015 – ISSN 14485109 (Online)
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5.1 Contemporaneous Effect
Table 3 reports our first set of regression results.^{[11]} The dependent variable in each regression is the log change in per capita new passenger vehicle registrations between 2006 and 2011.
Regression (2) in Table 3 reports estimates of Equation (2) without the inclusion of any control variables. The coefficient of interest is , the elasticity of new passenger vehicle registrations with respect to gross housing wealth in each postcode. The estimated coefficient indicates that a 1 percentage point increase in gross housing wealth is associated with about a 0.5 per cent increase in per capita new passenger vehicle registrations. This is about twice the size of the raw correlation between growth in new vehicle registrations and house prices. The effect is larger because only households owning their home outright or with a mortgage experience an increase in housing equity when house prices rise, and the effect of housing equity on consumption is assumed to operate only through home owners. Mechanically, gross housing wealth is equal to the change in house prices scaled by the home ownership share, and so varies less than oneforone with house prices. Reassuringly, there is no evidence of endogeneity in our data between home ownership rates and house price growth: the correlation between the home ownership rate in 2006 and house price growth for the period 2006 to 2011 is very close to zero.
OLS (1) 
OLS (2) 
OLS (3) 
OLS (4) 
Median (5) 
Median (6) 


12.17* (6.34) 
13.67** (6.96) 
9.80* (5.24) 
8.99 (5.85) 

Δlhp_{2006–11}  0.24** (0.06)  
0.48*** (0.08) 
0.56*** (0.17) 
0.53*** (0.18) 
0.42** (0.17) 
0.37** (0.17) 

Δlmedinc_{2006–11}  0.05 (0.10) 
0.03 (0.10) 
0.08 (0.07) 
0.00 (0.07) 

−0.02 (0.38) 
−0.05 (0.40) 
−0.20 (0.34) 
−0.41 (0.35) 

Δrepay_{2006–11}  −1.12 (31.30) 
11.25 (33.78) 
0.22 (26.19) 
31.92 (26.82) 

Δur_{2006–11}  −0.22 (1.24) 
−0.06 (1.18) 
−1.60 (1.05) 
−1.34 (1.06) 

lmedinc_{2006}  −2.41 (8.29) 
−3.85 (8.73) 
−3.31 (6.46) 
−3.58 (6.70) 

−1.73** (0.79) 
−1.89** (0.87) 
−1.34** (0.68) 
−1.26* (0.75) 

repay_{2006}  −5.65 (12.92) 
−4.53 (13.65) 
−9.79 (11.81) 
−0.30 (11.89) 

ur_{2006}  −2.28*** (0.74) 
−2.26*** (0.75) 
−1.99*** (0.58) 
−1.84*** (0.59) 

Bachelor_{2006}  −1.06*** (0.22) 
−0.53** (0.24) 
−0.46** (0.19) 
−0.38* (0.20) 

TAFE_{2006}  −1.94** (0.97) 
−1.76* (1.02) 
−1.32* (0.73) 
−1.15 (0.76) 

Distance  0.20* (0.12) 
0.26** (0.12) 
0.23** (0.11) 
0.22* (0.11) 

Water front  2.43 (1.75) 
1.96 (1.92) 
0.52 (1.73) 
−0.37 (1.84) 

Observations  563  563  526  526  526  526 
R^{2}  0.03  0.07  0.23  0.24  
Pseudo R^{2}  0.17  0.18  
Region fixed effects  Yes  Yes  
State fixed effects  Yes  Yes  
Notes: See Table A2 for a description of each regression variable; ***, **, and * indicate statistical significance at the 1, 5, and 10 per cent levels, respectively; robust standard errors in parentheses 
Regressions (3) and (4) report estimates for Equation (2) including the full set of census data controls, and with state and regional fixed effects, respectively. The estimated elasticity is about 0.5 for both specifications, and precisely estimated. Regressions (5) and (6) report median regression estimates. In contrast to the OLS estimator which minimises the sum of squared errors, the median regression estimator minimises the sum of absolute errors, and so is less sensitive to extreme observations. The similarity between the OLS and median regression elasticity estimates indicates that the estimated relationship between new vehicle registrations and house prices is not driven by extreme observations.
Regressions (1) and (2) in Table 4 report estimates for Equation (3), using variation in the share of outright home owners and mortgagors across postcodes to tease apart differential effects of housing wealth for outright home owners and mortgagors. The estimated elasticities β^{outright} and are between 0.4 and 0.6 in each regression specification, indicating a similar relationship between changes in house prices and new vehicle registrations for outright home owners and mortgagors. This evidence is only suggestive though, because the data do not allow us to precisely tease apart any differences in the effect of house prices on consumption for those owning their home outright or with a mortgage.
(1)  (2)  (3)  (4)  

8.22 (5.96) 
10.19 (6.53) 

−22.98** (11.18) 
−28.17** (11.62) 

13.61 (9.94) 
16.07 (10.44) 

12.52* (7.44) 
14.69* (7.92) 

0.69*** (0.20) 
0.65*** (0.20) 

−0.53 (0.56) 
−0.60 (0.57) 

0.45 (0.54) 
0.49 (0.56) 

0.63* (0.36) 
0.57 (0.37) 

Δlmedinc_{2006–11}  0.05 (0.10) 
0.03 (0.10) 
0.04 (0.10) 
0.03 (0.10) 
−0.04 (0.40) 
−0.07 (0.41) 
−0.07 (0.37) 
−0.08 (0.38) 

Δrepay_{2006–11}  0.50 (33.62) 
12.25 (35.32) 
−7.77 (31.27) 
1.27 (34.37) 
Δur_{2006–11}  −0.22 (1.26) 
−0.08 (1.19) 
−0.79 (1.33) 
−0.83 (1.26) 
lmedinc_{2006}  −3.33 (9.87) 
−5.53 (9.90) 
−1.94 (8.38) 
−3.52 (8.82) 
−1.80* (0.94) 
−2.03** (1.01) 
−4.48*** (1.63) 
−5.14*** (1.74) 

repay_{2006}  −11.15 (32.20) 
−14.48 (33.93) 
−6.60 (13.68) 
−5.33 (14.53) 
ur_{2006}  −2.25*** (0.76) 
−2.22*** (0.77) 
−2.88*** (0.74) 
−2.80*** (0.76) 
Bachelor_{2006}  −0.60*** (0.23) 
−0.52** (0.24) 
−0.46** (0.23) 
−0.38 (0.25) 
TAFE_{2006}  −1.97** (1.00) 
−1.82* (1.04) 
−1.74* (0.97) 
−1.32 (1.03) 
Distance  0.20* (0.12) 
0.25** (0.12) 
0.09 (0.12) 
0.15 (0.13) 
Water front  2.54 (1.73) 
2.06 (1.95) 
3.64* (1.90) 
3.11 (2.03) 
Observations  526  526  526  526 
R^{2}  0.24  0.24  0.25  0.25 
Region fixed effects  Yes  Yes  
State fixed effects  Yes  Yes  
Notes: See Table A2 for a description of each regression variable; ***, **, and * indicate statistical significance at the 1, 5, and 10 per cent levels, respectively; robust standard errors in parentheses 
As a placebo test, regressions (3) and (4) in Table 4 include an interaction between the share of renters and the log change in house prices for each postcode. A positive coefficient on this variable would likely indicate that a third factor is responsible for at least some of the estimated relationship between changes in house prices and new vehicle registrations. The coefficient on the placebo rentersequity variable Δlhp_{2006–11} is negative, indicating that the estimated positive relationship between house prices and new vehicle registrations is unlikely to be caused by a third factor. Because some renters are prospective home buyers, the negative coefficient could indicate that prospective buyers reduce consumption when house prices rise. But the relationship between new vehicle registrations and house prices for renters is imprecisely estimated, and we cannot reject there being no relationship at conventional levels of significance. To avoid the estimated relationship between housing wealth and new vehicle registrations for owners being affected by an imprecisely estimated effect for renters, we omit the rentersequity variable in other regressions, imposing our prior that there is no relationship between house prices and new vehicle registrations for renters. This has the effect of reducing the estimated elasticity of new vehicle registrations to gross housing wealth for home owners by about 0.1, as can be seen by comparison of regressions (3) and (4) in Table 4 with regressions (3) and (4) in Table 3.
5.2 Longevity of the Effect
The cumulative effect of a change in housing wealth on consumption depends on whether the effect on spending is sustained over time. Thus far we have focused on estimating a contemporaneous effect; in our preferred specification, we estimate an elasticity of new passenger vehicle registrations with respect to gross housing wealth of 0.4–0.5. If this reflects households using increases in housing wealth to fund a onetime increase in current spending, then current consumption growth will tend to be negatively related to past changes in housing wealth as consumption returns to its prior level. Conversely, if spending funded by an increase in housing wealth is smoothed over time, we should expect to see no relationship between past changes in housing wealth and current consumption growth. Finally, a positive relationship between past changes in housing wealth and current consumption is consistent with sluggishness in the adjustment of consumption to changes in housing wealth.
To investigate these possibilities, we augment Equation (2) with changes in gross housing equity over the periods 1996 to 2001 and 2001 to 2006. The correlation in house price growth between these time periods is low, providing statistical power to determine the timing of changes in housing wealth on new vehicle registrations. Estimation results are reported in Table 5. Because house price data for fewer postcodes is available for earlier time periods, Table 5 also reports estimates for the baseline regression specification using a common data sample. Reassuringly, the baseline results are little different. Growth in new vehicle registrations over the period 2006 to 2011 is negatively related to house price growth over the period 2001 to 2006, but the estimated effect is about onethird the magnitude of the contemporaneous effect. The sum of the coefficients is positive, indicating that the contemporaneous relationship between housing wealth and new vehicle registrations is largely sustained over time. Changes in housing wealth over the period 1996 to 2001 are estimated to have had a negligible relationship with growth in new vehicle registrations over the period 2006 to 2011. Overall, these results indicate that an increase in house prices is associated with an elevated level of new registrations for a sustained period of time, but that the shortrun relationship is likely to be larger than the longrun relationship.
(1)  (2)  (3)  (4)  

11.53 (8.09) 
11.59 (8.24) 
11.21 (9.10) 
12.49 (9.34) 

0.62*** (0.19) 
0.66*** (0.20) 
0.55*** (0.20) 
0.59*** (0.20) 

−0.14 (0.16) 
−0.20 (0.17) 

0.06 (0.07) 
0.04 (0.07) 

Δlmedinc_{2006–11}  0.07 (0.12) 
0.09 (0.12) 
0.06 (0.12) 
0.07 (0.12) 
−0.24 (0.55) 
−0.26 (0.55) 
−0.16 (0.56) 
−0.20 (0.56) 

Δrepay_{2006–11}  6.59 (36.82) 
13.35 (37.34) 
18.24 (40.32) 
26.73 (39.82) 
Δur_{2006–11}  −0.23 (1.78) 
0.07 (1.76) 
0.07 (1.72) 
0.32 (1.70) 
lmedinc_{2006}  −3.80 (10.00) 
−1.80 (10.15) 
−5.70 (10.76) 
−3.79 (10.79) 
−1.61 (1.05) 
−1.63 (1.06) 
−1.50 (1.17) 
−1.63 (1.19) 

repay_{2006}  −4.25 (15.27) 
−3.03 (16.22) 
−3.74 (15.92) 
−0.82 (16.88) 
ur_{2006}  −2.46*** (0.89) 
−2.23** (0.91) 
−2.24** (0.88) 
−1.95** (0.92) 
Bachelor_{2006}  −0.55* (0.30) 
−0.58* (0.30) 
−0.49 (0.33) 
−0.50 (0.32) 
TAFE_{2006}  −2.05* (1.07) 
−1.98* (1.07) 
−1.67 (1.15) 
−1.56 (1.16) 
Distance  0.24 (0.15) 
0.28* (0.15) 
0.28* (0.17) 
0.35** (0.17) 
Water front  0.93 (2.38) 
0.82 (2.35) 
0.39 (2.66) 
0.21 (2.65) 
Observations  375  375  375  375 
R^{2}  0.27  0.27  0.28  0.28 
Region fixed effects  Yes  Yes  
State fixed effects  Yes  Yes  
Notes: See Table A2 for a description of each regression variable; ***, **, and * indicate statistical significance at the 1, 5, and 10 per cent levels, respectively; robust standard errors in parentheses 
Footnote
The robust standard errors reported account for sampling variability, assuming the dataset is small relative to the population. But the census data we use accounts for a large share of the total population. Interpreted as descriptive statistics, the uncertainty around our regression parameters is smaller than indicated by the robust standard errors reported. Interpreted as estimated average causal effects, additional uncertainty remains if each postcode has a potentially different sensitivity of consumption to changes in housing wealth: we do not observe counterfactual house price growth for each postcode. Abadie et al (2014) find that standard errors for causal inference with large datasets are generally smaller than the conventional robust standard errors we report. [11]