Spillover Effects of Foreclosures on Neighborhood Property Values

Abstract

Previous studies have shown that foreclosure often results in vandalism, disinvestment and other negative spillover effects in the neighborhood. This paper extends these views into a formal theoretical model through pricing based on comparables. We project that the spillover effect of a foreclosure on neighborhood property values depends on two factors: the discount of foreclosure sale and the weight placed on the foreclosed property as a comparable in the valuation. The former is related to housing cycle and the latter varies by time of foreclosure and its distance from the subject property. Empirical results based on a 2006 sample show that this effect is significant within a radius of 0.9 km (roughly 10 blocks) and within 5 years from its liquidation. The most severe impact is an 8.7% discount on neighborhood property values, which gradually drops to anywhere between −1.2 to −1.7% for foreclosures liquidated within the past 5 years. These spillover effects vary slightly when the sample selection bias is taken into account. Based on an alternative sample of purchase transactions in 2003, the estimated spillover effects in booming years are reduced by half, confirming on the important role played by housing cycles.

Appendix

“Derivation” of the Hypothesis

The adjusted sale price based on each comparable sale price (i) is determined as follows,

$$ \widehat{P}_{{i,subject}} = P_{i} + {\sum\limits_{j = 1}^m {a_{j} {\left( {\Delta ^{{Characteristics{\text{ }}j}}_{{subject,i}} } \right)} + } }f{\left( {\Delta ^{{location}}_{{subject,i}} } \right)} + g{\left( {\Delta ^{{time\_sale}}_{{subject,i}} } \right)} $$

(A.1)

Thus, the final value estimate of the subject property can be computed as

$$\widehat{P}_{{subject}} = {\sum\limits_{i = 1}^n {W_{i} \widehat{P}_{{i,subject}} } }$$

(A.2)

The optimization problem for choosing weights and the number of comparable properties can be expressed as

$$\begin{aligned} & {\mathop {\min }\limits_{{\left( {n,W_{1} ,W_{2} ,...,W_{n} } \right)}} }{\left\{ {Var{\left( {{\sum\limits_{i = 1}^n {W_{i} \widehat{P}_{{i,subject}} } } - P_{{subject}} } \right)}} \right\}} \\ & {\text{ Subject\, to: }}\,\,\,{\text{ }}n \leqslant N{\text{ and }}{\sum\limits_{i = 1}^n {w_{i} = 1} } \\ \end{aligned} $$

(A.3)

When $\operatorname{cov} {\left( {\widehat{P}_{{i,subject}} - P_{{subject}} ,\widehat{P}_{{k,subject}} - P_{{subject}} } \right)} = 0$ for i ≠ k, then Eq. A.3 can be further simplified as,

$${\mathop {\min }\limits_{{\left( {W_{1} ,W_{2} ,...,W_{n} ,{\sum\limits_{i = 1}^n {W_{i} } } = 1,n \leqslant N} \right)}} }{\left\{ {{\sum\limits_{i = 1}^n {W^{2}_{i} } }\left. {\sigma ^{2}_{i} } \right)} \right\}}$$

(A.4)

where

$$ \sigma ^{2}_{i} = Var{\left( {\widehat{P}_{{i,subject}} - P_{{subject}} } \right)} $$

Generally speaking, the variance in Eq. A.4, $\sigma ^{2}_{i}$, should increase with time and distance. We can thus hypothesize:

$$ \frac{{\partial \sigma _{i} }} {{\partial \Delta ^{{time\_sale}}_{{subject,i}} }} > 0{\text{, }}\frac{{\partial \sigma _{i} }} {{\partial \Delta ^{{location}}_{{subject,i}} }} > 0 $$

(A.5)

Eq. A.4 and A.5 suggest that,

$$ \frac{{\partial W_{i} }} {{\partial \Delta ^{{time\_sale}}_{{subject,i}} }} < 0{\text{, }}\frac{{\partial W_{i} }} {{\partial \Delta ^{{location}}_{{subject,i}} }} < 0 $$

(A.6)

Thus, we can expect that

$$ \frac{{\partial W_{k} {\left( {d,t} \right)}}} {{\partial d}} < 0{\text{ and }}\frac{{\partial W_{k} {\left( {d,t} \right)}}} {{\partial t}} < 0 $$

(A.7)

From Eq. 6, we thus have

$$ \frac{{\partial \Delta }} {{\partial d}} = \overline{\theta } * P_{k} * \frac{{\partial W_{k} {\left( {d,t} \right)}}} {{\partial d}} < 0 $$

(A.8)

and,

$$ \frac{{\partial \Delta }} {{\partial t}} = \overline{\theta } * P_{k} * \frac{{\partial W_{k} {\left( {d,t} \right)}}} {{\partial t}} < 0 $$

(A.9)