How the Housing Crisis Changed the Pricing Function for Residential Buyers

Abstract

This study uses econometric techniques to search for discrete structural changes in residential pricing equations. The study looks specifically at house pricing during the recent financial crisis to search for significant breaks in coefficients that indicate a functional change in the data. While the effects of the crisis are often captured by using a single dummy variable, this paper considers the possibility that the crisis not only reduced prices but may have affected the impact of the explanatory variables in the model. The absence of such a break, on the other hand, would suggest that variables affecting the pricing function are stable over a variety of market conditions. The results of this study suggest that a structural break does exist, and that a dummy variable is insufficient to capture the impact of this break. The methodologies employed in this study can also be used to look for less obvious structural breaks that may exist in a housing data set. The results should be of interest to buyers and sellers of residential properties, agents specializing in residential properties, and researchers looking to better capture the impact of various events on housing prices.

Keywords:

• Hedonic modeling
• structural breaks

Acknowledgments

The authors would like to thank the Charleston Trident Association of Realtors for providing multiple listing service (MLS) data. Any errors are our own.

Notes

1 The instruments used are generally taken from a time-on-market hazard model, which is beyond the scope of this paper. In this application, the instruments for LnTOM are ATYP, DOP, NOMKT, and POOL, which are defined in Table 1 and replicate the selection of instruments from past research, especially Allen, Benefield, & Cain (2016), from which the data set is also taken.

2 Table 4 provides a complete list of variables included in the X matrix.

3 This characterization is a simplification of Bai & Perron’s full approach, which is designed for time-series data which may be subject to serial correlation. In the case of housing sales, where there are many observations per time period and no individual houses with multiple observations tracked over time, many of the sophisticated solutions developed by Bai & Perron are neither easily applied nor necessary, allowing the simplifications described here.

4 The double-maximum tests and the sup F_T(l + 1|l) test rely on the sup F_T statistic, which does not follow a standard F distribution. Bai & Perron (1998) provide critical values for the asymptotic distribution when the number of explanatory variables in the model with no breaks is from 1 to 10, and this research uses the critical values for 10. Although this number falls far short of the number of variables actually used, for this distribution the critical values actually decrease with the number of explanatory variables, so the tests are actually somewhat more stringent than the stated level of the test implies. Given the large sample size of the data, this additional stringency seems appropriate.

5 Unlike traditional likelihood ratio tests, the sup MZ statistic does not follow a standard χ² distribution. Andrews (1993) provides critical values for the asymptotic distribution when the number of explanatory variables in the model with no breaks is from 1 to 20, and this research uses the critical values for 20. As with the Bai & Perron test, this number falls far short of the number of variables actually used, and for this distribution the critical values do not decrease with the number of explanatory variables. This implies the tests are actually not as stringent than the stated level of the test implies. For this reason, and because breaks in coefficients are of more interest to the research question of this paper than breaks in the variance, the present discussion places somewhat more emphasis on the Bai & Perron results than on the sup MZ test.

6 This is also one reason we do not use more granular time units such as months or weeks. Structural break identification depends crucially on having enough observations between breaks to estimate the model, and interpreting the breaks as discrete shifts rather than time-varying parameters requires restrictions on break frequency.

7 A possible concern in a relatively small sample is the influence of outliers on the overall results. To address this, the 1% of observations with the highest residuals in the no-break model were dropped, and the results run with the smaller sample. The conclusions of the model selection procedures remained broadly the same, with all procedures choosing one or two breaks between the first and third quarters of 2008. The signs, significance, and order of magnitude of the estimated coefficients were similarly unaffected.

8 The model selection and estimation is implemented in Stata 14. The basic code used is available from the authors by request.

9 The two-break model adds a break after the first quarter of 2008. The second break coincides with the break in the one-break model, at the end of the third quarter of 2008. This means that both models have the same before and after interpretations, but the two-break model adds a two-quarter intermediate time frame. We suspect that this may be capturing a more gradual transition in market participant behavior than a single discrete break implies. Given this likely interpretation and the fact that the sup F_T(l + 1|l) test is statistically insignificant for a second break, we feel comfortable proceeding with our interpretation of the single-break results.