List Prices in the US Housing Market

Abstract

A seller sets the list price based upon their ex-ante perception of the trade-off between marketing duration versus transaction price, which depends on the liquidity of the property and the depth of the market. As such, list prices reflect property, market, and seller characteristics. In addition, Genesove and Mayer (2001) and Bokhari and Geltner (2011) use prospect theory to motivate how expected nominal losses and gains from sale can also influence list prices. We consider these multiple factors affecting list prices through a rich dataset from the National Association of Realtors, which contains variables on seller motivations, structure liquidity, and other difficult to observe variables such as seller age, race, and income.

Appendices

Appendix 1: Sample Selection Bias

The NAR survey is sent to both buyers and sellers of homes. A small percentage of the buyers have purchased a new home but have not sold their previous residence. The unsold properties occur in each survey year. We thus examine for potential selection bias using the traditional Heckman two-step procedure and compute the IMR. The first step estimates a probit model of whether the house has sold or not, which Table 7 details. From this specification, we obtain the IMR, which is included in the second stage specifications of list prices.

IMR allow us to potentially control for those responders who have their home listed but may be less motivated to sell and thus have unique price-liquidity preferences. The results in Table 8 in Appendix 2 are consistent with this difference in price-liquidity preferences. The IMR computed from the specification in Table 7 is highly significant and positive in the TOM model in Table 8. This finding indicates a longer expected TOM for those sellers who have a lower propensity to sell.

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Table 7 Probability of sale

Appendix 2: Simultaneity

Search theory shows that prices and marketing durations are determined simultaneously. LPR should also be endogenous with the other two. We control for endogeneity using a system of simultaneous equations and 2SLS. Table 8 reports the instruments with the instrumented variable denoted in the heading. For brevity, the exogenous variables are omitted from Table 8 but available in a separate appendix.

Finding quality instruments is always a challenge in housing studies examining prices and TOM because the two outcomes are determined by the same set of attributes. In our case, the NAR dataset provides high-quality instruments that do not exhibit a correlation with the dependent variable in the second stage but economic theory, prior studies, or our analysis indicates have a potential relation with the instrumented variable.

We provide test statistics of each instrumented variable in the table detailing the second-stage structural equation. Because the model estimates a heteroscedasticity-robust variance-covariance matrix, we report Woolridge’s (1995) score test and regression-based test of exogeneity. A second test detects weak instruments. We report both Shea’s partial R² and the F statistic. The partial R² measures the correlation between the IV and the instruments after partialling out the effect of the exogenous variables. We note that the F statistic is generally statistically significant even with weak instruments. Thus, we take the recommendation of Stock et al. (2002) that the F statistic be greater than 10. To check the correlation between the instruments and structural error term, a third test statistic we examine and report is the Woolridge robust score of overidentifying restrictions. Again, the Woolridge (1995) score considers the robust variance-covariance matrix. With the understanding of the caution in interpreting the overidentification test argued by Parente and Santos Silva (2012), an insignificant test statistic implies the IV does not exhibit a statistically significant correlation with the error term in the structural equation.

Note, we use the linear probability model for the number of LPR to avoid the forbidden regression and incidental parameters problems. The forbidden regression makes the error of replacing a nonlinear function of an endogenous explanatory variable with the same nonlinear function of fitted values from a first-stage estimation (Woolridge (2010) and Angrist and Pischke (2008)). The incidental parameters problem arises with binary response variables like LPR. When fitting linear models, fixed effects correctly measure the mean value of the dependent variable for a particular attribute, location in our models. However, as the number of areas increases in our model, the slope coefficients on the fixed effect variables become biased (Neyman and Scott (1948)). We have 455 locational fixed effects so we use the linear probability model to avoid the incidental parameters problem.

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Table 8 First stage instruments