Mortgage Default Risks and High-Frequency Predictability of the U.S. Housing Market: A Reconsideration

Abstract

Recent evidence, based on a linear framework, tends to suggest that while mortgage default risks can predict weekly and monthly housing returns of the United States, the same does not hold at the daily frequency. We, however, indicate that the relationship between daily housing returns with mortgage default risks is in fact nonlinear, and hence a linear predictive model is misspecified. Given this, we use a k-th order nonparametric causality-in-quantiles test, which in turn allows us to test for predictability over the entire conditional distribution of not only housing returns, but also volatility, by controlling for misspecification due to nonlinearity. Based on this model, we show that mortgage default risks do indeed predict housing returns and volatility, barring at the extreme upper end of the respective conditional distributions.

Keywords:

• Mortgage default risks
• Housing returns and volatility
• higher-order nonparametric causality in quantiles test

JEL Codes:

• C22
• R30

Notes

1 When we applied the linear Granger causality test, we found that the null that MDRI does not Granger cause housing returns could not be rejected even at the 10% level of significance, given a χ² (6) statistic of 3.7396 with p-value 0.7119. Note the lag-length was chosen to be 6 based on the Schwarz Information Criterion and matches that of Chauvet et al. (2016). Interestingly, when we used an exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model, MDRI was found to significantly increase both returns and volatility at the 1% level of significance. Complete details of the linear Granger causality and EGARCH results are available upon request from the authors.

2 The Brock et al. (1996) test of nonlinearity when applied to the residuals from the housing returns equation used to test the linear Granger causality, rejected the null of i.i.d. residuals at the highest possible level of significance and across all dimensions. This result, highlighting nonlinearity between housing returns and the MDRI, has been reported in Table A1 in the Appendix of the paper.

3 The data can be accessed at: https://chandlerlutz.shinyapps.io/mdri-app/.

4 The log-returns ensure that the house price data is mean-reverting, while the MDRI is stationary in levels, which in turn meets the data requirements of the test employed.

5 As part of further analysis, we reconducted our test based on housing returns derived from a new set of daily housing price series constructed by Bollerslev et al., (2016). The daily housing price series covered 10 U.S. metropolitan statistical areas (MSAs). Following Wang (2014), we use the daily composite housing index $(P_{c,t}={\sum }_{i=1}^{10}{w}_i{P}_{i,t})$ as a proxy for the aggregate U.S. housing price, which in turn is computed as a weighted average. The 10 MSAs and the specific values of the weights ($w_i)$ used were: Boston (0.212), Chicago (0.074), Denver (0.089), Las Vegas (0.037), Los Angeles (0.050), Miami (0.015), New York (0.055), San Diego (0.118), San Francisco (0.272), and Washington D.C. (0.078), representing the total aggregate value of the housing stock in the 10 MSAs in the year 2000 (Wang, 2014). In Table A2 in the Appendix, we report the result of the k-th order causality-in-quantiles test from the MDRI on the housing return and volatility of the aggregate United States as well as the 10 MSAs, covering the period of January 3, 2006 until October 10, 2012. As can be seen, for the aggregate housing return, causality ranges between quantiles of 0.10 to 0.30 and then from 0.45 to 0.85 of the conditional distribution, while volatility is predictable by MDRI over the quantile range of 0.30 to 0.90. As far as the MSAs are concerned, barring the case of Boston and San Diego, MDRI predicts returns and/or volatility of the remaining eight cities. In general, MDRI is found to be a predictor of national and regional housing market movements, based on our higher-order nonparametric causality-in-quantiles test.