Selection Bias and Endogeneity

Another methodological issue is related to the sample selection bias. In order to make inferences about the entire stock of housing, it is necessary to assume that the houses sold are a representative sample, or sample selection bias would occur in analyzing housing sale samples.

Immergluck and Smith (2006a) found that foreclosures of single family homes significantly impacted property values within an eighth of mile, with a conservative estimate of each foreclosure resulting in a decline of 0.9% on single family property sales in 1999. However, Lin, Rosenblatt, and Yao (2009) analyzed the same Chicago market, but focused on 2003 and 2006. Their contribution to the literature was a more flexible estimation of the neighboring foreclosure effect. Lin, Rosenblatt, and Yao (2009) found that foreclosures had a significant negative marginal impact of -8.7% on neighborhood property values within 100 meters and five years from the foreclosure. Foreclosures further away in space had a much smaller, but still quite large effect: about a -4% negative marginal impact on neighboring sales within 400 meters. Lin, Rosenblatt,

and Yao (2009) found that the marginal foreclosure impact was larger in bad market (2006) when they estimated a model using sales data from 2003 and compared the results to the 2006 samples.

However, it is difficult to identify the difference in results from the two previous studies. They both analyzed the same market area but in different time periods, different data sources, and used only slightly different methodologies. As Schuetz, Been, and Ellen (2008) point out, both only use cross-sectional data, which may introduce neighborhood bias as housing sales near foreclosures are more likely to be in poor neighborhoods. Thus, Lin, Rosenblatt, and Yao (2009) used a simple two-step procedure to test, and they corrected sample bias with instrument. The authors used variables describing the characteristics of the loan and financial situation of borrowers.

An attempt to control for sample bias was made through use of a probit analysis using a sale as the binary dependent variable.7 _{Therefore, sample rules resulted in a}

specification error in the regression. Heckman (1979) offered a solution to this problem through a two stage estimator. First, a probit analysis of the full sample was performed to estimate the probability that an observation will have a value for the dependent variable. This is then used as a regressor in the subsequent hedonic regression to eliminate the specification error. This rule would identify what types of houses are more likely to have changed and would use variables that would not properly enter the hedonic index, that is, the sample selection rule says nothing about the value of the houses, just their probability of having a sale during the time period. Moreover, these results indicate that

7

Such a procedure is described by Heckman (1979). The logic of this approach is that the regression error

even though the housing which is sold is a biased sample of the total stock, represents strong pressure on neither the demand side or on the supply side (Rothenberg, Galster, Butler, and Pitkin, 1991).

Lin, Rosenblatt, and Yao (2009) found that the price-depressing effect was most severe within 2 years of a foreclosure and created an -8.7% discount in housing bust year (2006), which gradually diminished to as low as -1.7% at about 0.9 km (2700 feet) away. When correcting sample selection bias, the change in magnitude of spillovers was quite small and was approximately within a -1% reduction compared to the spatial-temporal effects of foreclosures, which has not been corrected for sample selection bias.

Another potential estimation problem is endogeneity. Discussion on endogeneity (reverse causation) is either very limited or weakly controlled in previous studies. The causal relationship between home prices and foreclosures is two-directional: high foreclosure activity can both cause and be caused by home price declines. Falling property values may lead to an increase in foreclosures by decreasing the equity that homeowners have in their properties. Mortgagors are much more likely to default on their loans if they owe more than the house is worth. Declines in home prices will increase the frequency with which homeowners find themselves with no equity and thus may be motivated to walk away from the property and the mortgage. Home foreclosures contribute to weakening prices by introducing additional supply to the inventory of unsold homes. As a result, they may be willing to sell for lower prices than resident homeowners. Under the ruthless option theory, it is clear that the default indicator will be negatively correlated with the house price error.

Lower neighborhood prices will also increase the chances of future foreclosures, so the process is to some degree endogenous, with foreclosures potentially causing lower neighborhood prices and then lower neighborhood prices causing more foreclosures. The critical question is whether foreclosures are the cause of the decline in values of nearby properties or merely a symptom of general decline in house prices (Harding, Rosenblatt, and Yao, 2009).

Endogeneity has remained an open problem in the literature. Endogeneity is a problem of spurious correlation between a regressor and the error term. The error term consists in part of omitted variables. Spatial statistics helps control for the influence of omitted variables, thus alleviating the need to instrument for endogenous variables (Brasington, 2001).

The following two recent studies control for endogeneity with instrument variable. First, Clauretie and Daneshvary (2009) addressed many of the shortcomings of earlier papers while estimating the foreclosure discount. Using data from the Las Vegas MLS, they built a sample of 1,302 foreclosed property sales and 8,498 non-distressed sales from November 2004 through November 2007. The authors extended their specification to include the spatially weighted prices of neighboring properties. In this specification, the resulting specification was a nonlinear model involving two endogenous variables (marketing on time and spatially lagged dependent variable) with spatially correlated disturbances. The authors estimated this model using generalized spatial two-stage least-squares (GS2SLS), developed by Kelejian and Prucha (1998, 1999). They estimated that the foreclosure discount, based on a single MSA, was

approximately -7.5% after controlling for property conditions, spatial effects, and marketing time. These results indicated that estimates of true discount caused by foreclosure were reduced by about one-third of foreclosure discount reported by previous studies (-22% ~ -28%).

Second, Ding and Quercia (2010) found that a higher level of subprime activity caused a decline in neighborhood property values and increased the price volatility. Because of the declined property value, the default risk of Community Advantage Program (CAP) loans in the same neighborhoods increased significantly. Overall, this study provided new evidence concerning the negative impacts of the concentration of subprime lending in certain neighborhoods. They used a two-stage least-squares (2SLS) analysis. In the first stage of the analysis, the neighborhood housing price change was regressed on MSA house price changes, neighborhood subprime activities, local economic conditions, and other explanatory variables in the model. It is assumed that area house price changes, subprime activities, and other neighborhood controls are uncorrelated with unobserved determinants of the CAP loan default behavior and that these instruments only influence the troublesome neighborhood house price change, controlling for the other covariates. In the second stage of the analysis, the CAP loan default was regressed on the predicted value of neighborhood house price changes, as well as other controls of individual borrower credit risk. The instruments, such as neighborhood subprime activities, were not included as regressors in the second stage, assuming they did not influence the default behavior directly.

endogenous to house prices but proper instruments for foreclosures are hard to find. Specifically, foreclosures are likely to be more common in neighborhoods where property values are lower, raising the concern of endogeneity (Leonard and Murdoch, 2009). However, it is difficult to tell whether value changes are a cause of foreclosures, and foreclosures are a cause of value change. The non-recursive inferring of causality thus requires very careful structuring of data sets as well as solving some technical issues associated with the regression models. Thus, further study needs to address methodological challenges to overcome the causality problem between housing price and foreclosures.

2.6.3 Marginal Impacts and Nonlinear Effects of Neighboring Foreclosures in