RDP 2017-05: The Property Ladder after the Financial Crisis: The First Step is a Stretch but Those Who Make It Are Doing OK Appendix C: Extensions and Robustness Tests

C.1 Interacting the Main Demographic Variables with the Post-2007 Dummy

To assess whether there has been a change in the relationship between demographic factors and FHBs between the pre- and post-2007 period we re-estimate Model 1 and include interaction terms between the main demographic variables and the post-2007 dummy. Results from this estimation are shown in Model 1a (Table C1) and indicate no significant difference in the coefficients between periods.

Table C1: Determinants of Being an Indebted FHB Household
  Model 1 Baseline model Model 1a Interaction effects
Post-2007 dummy −0.31*** −0.34***
Age 0.11*** 0.10***
Age squared −0.00*** −0.00***
Age × Post-2007 dummy na 0.01
Age squared × Post-2007 dummy na −0.00
Household disposable income ($'000) 0.00*** 0.00***
Couple household 0.70*** 0.84***
Couple household × Post-2007 dummy na −0.27
Tertiary education 0.27*** 0.26***
Tertiary education × Post-2007 dummy na 0.02
Migrant household −0.12** −0.12**
Household size −0.13*** −0.13***
Full-time employee 0.57*** 0.57***
Unemployment expectations (> 50%) −0.45** −0.46**
Constant −3.61** −3.59**
Observations 20,699 20,699
Pseudo R-squared 0.18 0.21

Notes: The coefficients on the explanatory variables in a probit model indicate the sign and statistical significance of the relationship with the dependent variable only and do not provide information on the magnitude of these relationships; *, ** and *** indicate statistical significance at the 10, 5 and 1 per cent levels, respectively

Sources: Authors' calculations; HILDA Survey Release 14.0

C.2 Including Time Fixed Effects

Park and Phillips (2000) discuss the challenges of using non-stationary explanatory variables in discrete choice models. In particular, they argue that convergence is not guaranteed in binary choice models with integrated regressors.

To evaluate if our results are influenced by the non-stationarity of the state housing price indices, we include time fixed effects instead of the post-2007 dummy in Model 3a (see Table C2 for results). Using this approach, we get quantitatively similar results to Model 3, suggesting that non-stationarity is not an issue here.

C.3 Local Government Area (LGA) Housing Prices

We also test whether the state housing price index is not capturing some other state-time fixed effect by also estimating the model using APM data on LGA-level housing prices.

It should be noted that these more disaggregated data are only available for the capital cities of Sydney, Melbourne and Brisbane, and only cover the period 2001 to 2012, which results in a smaller sample size for estimation of Model 3b. Despite these limitations, we find that using the alternative housing prices measure in Model 3b provides very similar results to Model 3 (Table C2).

Table C2: Determinants of Being an Indebted FHB Household
Average marginal effects, percentage points
  Model 3 Baseline model Model 3a Time fixed effects Model 3b LGA-level housing prices
Post-2007 dummy 0.00 na −0.32
Age 1.00*** 1.00*** 1.00***
Age squared −0.02*** −0.00*** −0.00***
Household disposable income ($'000) 0.03*** 0.03*** 0.06***
Couple household 6.88*** 6.90*** 6.34***
Household size −1.38*** −1.36** −1.92***
Tertiary education 3.52*** 3.57*** 4.63***
Migrant household −0.68 −0.59 −0.48
Full-time employee 4.83*** 4.82*** 4.11***
Unemployment expectations (> 50%) −3.47*** −3.49*** −1.94*
State housing price index (log) −0.08*** −0.07*** na
LGA housing price index (log) na na −0.08***
First home buyer incentives ($'000) 0.12*** 0.04 0.17***
Variable mortgage rate 0.04 na −0.78**
Major urban area −2.34*** −2.38*** −1.11***
State fixed effects Yes Yes Yes
Time fixed effects No Yes No
Observations 20,699 20,699 7,871
Pseudo R-squared 0.21 0.20 0.23

Notes: Average marginal effects are calculated for each household based on the observed values of the explanatory variables for that household and are then averaged across all households; *, ** and *** indicate statistical significance at the 10, 5 and 1 per cent levels, respectively

Sources: APM; Authors' calculations; HILDA Survey Release 14.0; RBA

C.4 Alternative Models of Debt Levels for FHBs

It is not obvious which particular measure of household debt should be used as a dependent variable. Each choice implicitly embeds a particular functional relationship between debt, income and asset values. In this section, we vary the functional form of the dependent variable to test for the sensitivity of our results to this choice. Model 6 from Table 4 is re-estimated using log FHB mortgage debt and the FHB debt-to-assets ratio as alternative dependent variables. To test how sensitive the model is to extreme values of the FHB debt-to-income ratio we also estimate a median, rather than a mean, regression. Results from these alternative specifications are largely in line with Model 6 (once allowance is made for changes in the coefficient restrictions implicit in the different specifications).

Table C3: Regression Results for Robustness Checks of Equation (2)
  Model 7 ln(Debt) Model 8 Debt-to-assets ratio Model 9 Median regression
Post-2007 dummy −0.058 0.004 −0.499***
Age 0.048** −0.005 na
Age squared −0.001*** 0.000 na
Household disposable income ($'000) 0.001*** 0.000 −0.010***
Couple household 0.206*** 0.034** −0.009
Household size −0.042* −0.007 −0.144***
Tertiary education 0.171*** 0.005 0.255**
Migrant household −0.036 −0.030** −0.019
Full-time employee 0.204*** 0.114*** 0.481**
State housing price index (log) 0.843*** 0.066** 1.992***
First home buyer incentives ($'000) 0.002 0.002 0.011
Variable mortgage rate 0.023 0.005 0.016
Major urban area 0.305*** −0.004 0.585***
Lambda na na 0.519
Lambda squared na na −0.082
Constant −0.069 0.413** −6.838***
State fixed effects Yes Yes Yes
Observations 1,100 1,149 1,048
Adjusted R-squared 0.319 0.115 0.217(a)

Notes: Due to missing values of the different dependent variables, sample sizes vary across Models 7 to 9; *, ** and *** indicate statistical significance at the 10, 5 and 1 per cent levels, respectively
(a) A pseudo R-squared is computed

Sources: APM; Authors' calculations; HILDA Survey Release 14.0; RBA