Estimating the House Foreclosure Discount Corrected for Spatial Price Interdependence and Endogeneity of Marketing Time

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1 2009 V37 1: pp REAL ESTATE ECONOMICS Estimating the House Foreclosure Discount Corrected for Spatial Price Interdependence and Endogeneity of Marketing Time Terrence M. Clauretie and Nasser Daneshvary Most previous empirical research estimates a greater than 20% discount associated with the sale of foreclosed properties. Under the assumption that the real estate market is somewhat efficient, such a large discount would be counterintuitive. We argue, and empirically show, that the estimated foreclosure coefficients in most of the previous research are upward biased because they do not control for variables such as the physical condition of the property and the relationship between marketing time and price. Accounting for these factors and correcting for two types of spatial price interdependence, our results show that estimates of foreclosure discount reported by previous studies are about one-third higher than the true discount caused by foreclosure per se. To date there have been several research efforts designed to estimate the effect of foreclosure status on the price of single-family residences. Generally, the empirical results have revealed about a 20% discount associated with foreclosure status. However, it is often not clear whether researchers claim the discount is due to a stigma effect of foreclosure or a proxy effect for other property characteristics. A stigma effect refers to a discount for no other reason than the status of the property as foreclosed. No characteristics of the property differentiate foreclosed from nonforeclosed properties. Potential buyers see the foreclosure as a stigma, purchase the property with a large discount and resell it immediately, capturing a large windfall. The real estate market, however, while not perfectly efficient, is not likely to be so inefficient as to allow for such excess returns. Even if foreclosed properties are offered by motivated sellers, competition among buyers would mitigate opportunities for excess returns. The proxy effect refers to a discount because a foreclosed property may have other characteristics that affect price negatively, such as deteriorated physical condition and/or neighborhood characteristics. In this article, we develop a College of Business, Department of Finance, University of Nevada, Las Vegas, NV or Mike.clauretie@unlv.edu. College of Business, Department of Economics, University of Nevada, Las Vegas, NV or Nasser.daneshvary@unlv.edu. C 2009 American Real Estate and Urban Economics Association

2 44 Clauretie and Daneshvary model that accounts for spatial autocorrelation and endogeneity. Applying the model to a large data set, we separately estimate the stigma and proxy effects. Our results show that estimates of foreclosure discount reported by previous studies are about one-third higher than the true discount caused by foreclosure per se. In the next section, we review the relevant literature. In the following section, we clarify the difference between a pure stigma and a proxy effect. We also point out major weaknesses in prior research. Then, we present the data and empirical results. The last section is the conclusion. Review of the Literature Our review of the relevant literature identified six prior empirical research studies on foreclosure discount. Table 1 provides a summary of the previous works in chronological order. Shilling, Benjamin and Sirmans (1990) estimated the discount (from a normal market value) on residential condominium units that were foreclosed and sold by the lender in Baton Rouge, Louisiana, in Such properties were labeled distressed. Their estimate of the discount was 24%. Although they recognized that distressed properties may have not been properly maintained, they did point out that many of the condominiums were foreclosed on shortly after constructed and, for others, the lenders thoroughly rehabilitated the properties if they were deemed to be in disrepair. The authors attribute the discount to the sellers (lenders ) motivation to sell the properties quickly to avoid carrying costs. This implies that foreclosure status reduces marketing time and, thus, creates a discount. They also point out that buyers may require the discount to cover carrying costs during the lease-up of the properties. Their empirical model, however, did not control for time that the properties stayed on the market (TOM), the properties physical condition, occupancy status, whether or not the transaction was for cash or neighborhood characteristics. Forgey, Rutherford and VanBuskirk (1994) argue that, in order to reduce holding cost, sellers of foreclosed properties accept a lower price to reduce TOM. They estimate the discount on foreclosed single-family properties listed on a Multiple Listing Service (MLS) in Arlington, Texas, from 1991 to Of their sample of 2,482 properties, 280 were foreclosure sales. They found a foreclosure discount of 23%. As well, their empirical models did not account for TOM, the condition of the property or occupancy status. They did find, however, that cash sales resulted in a discount of 16%. To control for neighborhood characteristics, they included ZIP codes as a continuous (not a series of dummy) variable, producing inaccurate results.

3 Foreclosure Discount, Spatial Interdependence and Endogeneity 45 Table 1 Previous research on foreclosures. Variables No. of Foreclosure Author(s) Journal Property Type of Interest Data Year Obs. Discount Location Shilling et al. (1990) Journal of Real Estate Research Forgey et al. (1994) Journal of Real Estate Research Hardin and Wolverton (1996) Journal of Real Estate Research Springer (1996) The Journal of Real Estate Finance and Economics Carroll et al. (1997) Journal of Real Estate Research Pennington-Cross Journal of Real Estate (2006) Research Condos Value of seller financing, distance to LSU Single family FHA, VA financing, location Apartments Gross rent, vacancy, location Single family Seller motivation (relocation, list price) Single family HUD and bankowned properties Single family Metropolitan appreciation rate /? 24 Baton Rouge, LA ,482/ Arlington, TX /9 22 Phoenix, AZ ,317/ Arlington, TX ,974/ Las Vegas, NV , Nation Notes: Models included the standard (hedonic) physical characteristics and the variables of interest. The first number represents the total sample size. The second number is the number of observations of foreclosed units. All observations were foreclosed units based on loan information. No individual house characteristics were included. Aggregate area house prices were used.

4 46 Clauretie and Daneshvary Hardin and Wolverton (1996) estimated the discount on foreclosed apartment complexes sold in the Phoenix, Arizona, area in 1993 and Foreclosed properties represented 9 of a total of 90 sales. They included variables representing the income potential of the properties (rent, vacancies, etc.). They found that foreclosed properties sold for 22% less than comparable nonforeclosed properties. They attribute the discount to seller motivation, namely the desire by institutional lenders to meet regulatory requirements related to the risk associated with their assets. Again, the empirical work did not control for TOM, property condition or cash sales. In a study on the effect of seller motivation on transaction price and TOM, Springer (1996) used data on 2,317 single-family homes sold between May 1991 and June 1993 in Arlington, Texas. He included foreclosure status as well as other motivation variables, such as relocation of the seller, property vacancy and eagerness in estimating price and TOM equations separately. He found that, after controlling for other types of seller motivations, foreclosed homes were sold more quickly with about a 4 to 6% discount. The study did not, however, account for the endogeneity of TOM in the price equation, and it did not include property condition or cash sales. Carroll, Clauretie and Neill (1997), using a sample of 1,974 single-family properties in Las Vegas, Nevada, found that, without properly controlling for neighborhood effects, a foreclosure discount of 12 to 14% emerges from the data. After controlling for neighborhood (ZIP codes entered as dummy variables), the discount was less: 8 to 10%. In addition, after controlling for nonforeclosed properties located in proximity to foreclosed properties, the discount on the latter nearly disappears, suggesting that the foreclosure status proxies for neighborhood, not property, characteristics. Their study also did not include variables representing TOM, occupancy status, cash sale or property condition. 1 Pennington-Cross (2006) evaluated the price of 12,280 foreclosed single-family properties sold nationwide for which the mortgages were originated from 1995 through He concludes that over the life of the loan foreclosed properties, whether sold by owner or lender, appreciated 22% less than the price of nonforeclosed properties in the same metropolitan area. He did not test whether foreclosure itself causes a decrease in selling price. His data set does not allow control for individual property or neighborhood characteristics. Thus, 1 Recently, Sirmans, Macpherson and Zietz (2005) reviewed approximately 125 studies that employed a hedonic model in estimating selling price. They identified five studies which included foreclosure as an independent variable, perhaps the same five studies that are reviewed so far. All five found a negative relationship with selling price. The remaining variables included in each study were not identified, however.

5 Foreclosure Discount, Spatial Interdependence and Endogeneity 47 the finding does not mean that foreclosed properties sell at a 22% discount to comparable nonforeclosed properties. It only means that the foreclosed properties may have physical, neighborhood or location characteristics that caused them to appreciate at a lower rate than properties in the same city. The characteristics that would have caused the lower appreciation rate may lead to the status of foreclosure. None of the articles reviewed thus far controlled for variables, such as property condition, transaction type (cash vs. financing sale) and vacancy status, that potentially impact transaction price and, thus, the size of the estimated foreclosure effect on price. In addition, although theoretically important and empirically recognized by the most recent studies of the housing market, no foreclosure study has tested models that recognize the endogenous relationship between price and TOM. 2 Finally, none of the previous studies of foreclosure have corrected for the spatial autocorrelation problems that might exist using a cross-section of house prices. 3 In short, all of the reviewed articles related to foreclosure utilize a single-equation ordinary least squares (OLS) test without consideration of the endogeneity of TOM and correction for spatial autocorrelation. Foreclosure Stigma and Proxy Effects Sellers of foreclosed or to-be-foreclosed properties may have a lower reservation price and accept a lower selling price due to several possibilities that include desire for shorter marketing time, lower direct and indirect carrying cost of the property, undesirable property condition and owner s need for liquidity. 4 In addition, such properties may sell for less due to a stigma attached to them, a foreclosure per se discount. Thus, a foreclosure-status variable may be considered as a proxy for many other variables as well as for a stigma effect. Omission of any or some of these potential variables 2 For examples of TOM and price endogeneity studies see Sirmans, Turnbull and Benjamin (1991), Yang and Yavas (1995), Yavas and Yang (1995), Knight (2002), Harding, Knight and Sirmans (2003) and Clauretie and Thistle (2007). 3 Carroll, Clauretie and Neill (1997) used a dummy variable to control for nonforeclosed properties within one block of each foreclosed properties. This approach, however, would not capture the complete spatial autocorrelation among all neighboring houses. 4 In addition, properties that are listed with a real estate agent will always involve a transaction cost, as opposed to bank or HUD-owned properties that may be marketed without listing with an agent. In the latter case, the buyer and seller can negotiate a lower price and allocate the commission between themselves. Thus, a lower property price may reflect the lower transaction cost, not the foreclosed status.

6 48 Clauretie and Daneshvary may produce a significantly biased estimate of a pure foreclosure (stigma) effect. 5 No previous research on this issue attempts to disentangle the effect of stigma from the effects of the variables mentioned earlier. As an example, Forgey, Rutherford and VanBuskirk (1994) state that foreclosure status houses do sell at a discount of approximately 23% of the average sales prices of houses in the sample (p. 318). This statement implies that it is the status of foreclosure that causes the discount. Yet, earlier in the article they claim that foreclosed properties may be distressed. Similarly, Hardin and Wolverton (1996) state that foreclosure-status apartments sell at a 22% discount when compared to nonforeclosure apartment sales (p. 101). The study also mentions that one reason for the discount would be seller motivation in terms of avoiding carrying costs. In other words, the research tends to describe the discount in terms of stigma, but then indicates it could also represent a proxy for other variables. At least two articles, Carroll, Clauretie and Neill (1997) and Pennington-Cross (2006), question whether foreclosure discounts are due to the pure stigma effect. They point to large arbitrage profits that could be made in such cases. Theoretically, a buyer could purchase a foreclosed property at a 23% discount, resell the property shortly thereafter (no longer having a foreclosed status) and capture a windfall. The real estate market, while not perfectly efficient, is not likely to be so inefficient as to allow for such excess returns. Even if foreclosed properties are offered by motivated sellers, competition among 5 For example, assume that the true population price equation is P n = X n β + β f oreclosure (Foreclosure) + β BC (BC) + u n, where X n is a vector of all other explanatory variables and BC is an indicator for property s bad condition. Instead, we estimate P n = X n ˆβ + ˆβ f oreclosure (Foreclosure) + v n. Then, the estimated coefficient of foreclosure is ˆβ f oreclosure = β f oreclosure + β BC [Cov(Foreclosue, BC)/Var(Foreclosure)]. The second term on the right-hand side is the potential bias from omitting a property s bad condition. Bad condition adversely affects price; β BC < 0. The covariance of Foreclosure and BC is expected to be positive. Thus, if the true stigma effect of foreclosure on price is negative, β forclosure < 0, then the BC-omission bias, the proxy effect of foreclosure, will overstate the true stigma effect of the foreclosure coefficient by β BC [Cov(Foreclosue, BC)/Var(Foreclosure)] < 0. The reverse is true for the omission of the TOM variable, if the covariance of BC and TOM and the relationship between selling price and TOM are negative.

7 Foreclosure Discount, Spatial Interdependence and Endogeneity 49 buyers, especially those that specialize in foreclosed properties, would mitigate opportunities for excess returns. Nonetheless, there may still be some stigma effect associated with foreclosed properties. In order to estimate the stigma and nonstigma effects of a foreclosed property one must control for other negative property characteristics that are likely to be associated with foreclosed properties. We identify the following characteristics that are omitted from previous research. Property condition is the most likely and obvious. Foreclosed properties are more likely to be subject to neglect by the owner (whether the owner is the occupant, a bank or HUD). Occupants who anticipate foreclosure are much less likely to make needed repairs and upkeep for some time before the foreclosure process commences. In addition to stigma associated with foreclosure, the price TOM relationship literature identifies another form of stigma associated with prolonged marketing time. The search theory predicts that longer marketing time is associated with higher selling prices. Previous empirical studies, however, have shown a negative relationship between price and TOM. For a comprehensive survey see Clauretie and Thistle (2007). Taylor (1999) develops a theoretical model in which potential buyers use TOM as a signal, suspecting that the house is either overpriced or has a possible flaw that was discovered by previous prospective buyers. This gives rise to a potential buyer-herding situation and a reduced asking price over time. Jud, Seaks and Winkler (1996) make a somewhat similar argument and attribute the negative relationship to the stigma effect of prolonged TOM. 6 A very plausible explanation of the negative relationship is offered by Huang and Palmquist (2001). In investigating highway-noise effect on price and TOM, they found that market duration has a significant negative impact on the sale price. They concluded that, as the TOM increases, sellers adjust their reservation price, resulting in an observed negative price TOM relationship. Theoretically, foreclosure status reduces the seller s reservation price and, thus, TOM. Also it has been shown empirically that foreclosure status reduces TOM (Springer 1996). Therefore, the effects of foreclosure on price are both direct and indirect, via TOM. Omission of TOM may produce biased estimates of foreclosure. 6 The study by Sirmans, Macpherson and Zietz (2005) identified 18 hedonic models that included TOM as an independent variable in the price equation. In only one study the coefficient was positive. In the remaining 17 studies the coefficient of TOM was either negative (8) or not significant (9), mostly depending on whether TOM was entered as endogenous variable or not.

8 50 Clauretie and Daneshvary The occupancy status of a property (owner occupied, vacant or rented) can have an effect on price. Knight (2002), for example, has shown that vacant properties sell at a discount from 8 to 12% below that of occupied properties. Anglin, Rutherford and Springer (2003) found only a 2% discount on vacant properties. If foreclosed properties are more likely to be vacant, then not controlling for vacancy status may produce a biased estimate of the foreclosure effect. That is, the foreclosure discount may partially reflect houses occupancy status. Many buyers specialize in purchasing foreclosed properties as investments. They may do so through a cash transaction. Properties sold in a cash transaction have reduced prices. Forgey, Rutherford and VanBuskirk (1994) found that property prices were reduced by 16% when purchased for cash. This is due to less uncertainty that the sale will be finalized and with a lower closing cost. Sales that involve financing are often subject to the condition that the financing be approved and incur additional closing costs (appraisal fees, discount points, credit-check fees, etc.). Removing uncertainty and additional closing costs results in a lower selling price. Correcting for two forms of spatial autocorrelation, we empirically analyze the relationship between selling price and foreclosure status. In addition, we investigate the effect of controlling for endogenous TOM, condition of the property, occupancy status and cash transactions on the size of the price foreclosure relationship. The Model Following the existing literature, we use the hedonic pricing model, which recognizes the house selling price as a function of the house and neighborhood characteristics, as well as a proxy for foreclosure. Of course, as the search and/or stigma theories suggest, and the most recent empirical literature shows, listing price affects the length of time that a property stays on the market. Seller s choice of listing and reservation prices also affects TOM, suggesting that TOM is an endogenous variable in the price equation. The general formulation of house hedonic pricing model can be expressed as P n = X n β + αtom n + u n, (1) where P n is the n 1 vector of selling price, X n is n k matrix of exogenous variables, TOM n is the n 1 vector of TOM, u n is the n 1 vector of regression disturbances, β is the k 1 vector of regression parameters and α is the scalar. The OLS estimation of Equation (1) assumes that TOM is exogenous and u n is i.i.d.

9 Foreclosure Discount, Spatial Interdependence and Endogeneity 51 There are several methodological concerns with the OLS estimation of the house selling price using a cross-section of houses. First, as discussed earlier, the TOM variable is endogenous. The second concerns two forms of spatial interdependence among cross-sectional housing units of observations. One form of dependence arises when the selling price of a house is affected by a weighted average of selling prices of neighboring units. This form of interdependence is referred to as spatial autoregressive models; see Kelejian and Prucha (1998). To account for this form of interdependence, a spatially lagged dependent variable, the weighted average of house prices sold in the neighborhood, is included among the explanatory variables. Of course, this variable is endogenous and is correlated with the disturbance term. Thus, OLS estimates of the parameters will be inconsistent. An additional form of interdependence arises from a spatially correlated disturbance term among the observations. Unless the price equation model is perfectly specified, the estimated parameters are inefficient and potentially biased. 7 An appropriate way to estimate house prices is to use an autoregressive spatial model with autoregressive error terms. Kelejian and Prucha (1998) developed a procedure to estimate endogenous spatially lagged models with a spatially correlated disturbance term. We modify their model to include the endogenous TOM as well as the endogenous spatially lagged dependent variables. Such model can be expressed as P n = X n β + λw n P n + αtom n + u n u n = ρw n ū n + ε n, (2) where W n is a n n spatial weighting matrix of known constants, P n is spatially lagged price of neighbors, ū n is generally referred to as spatial lag of u n, λ and ρ are autoregressive parameters to be estimated along with βs and α and ε n is the n 1 vector of i.i.d. disturbances. Elements of W n, w ij, represent the spatial relationship between house i and house j. The element w ij is nonzero only if prices of house i and house j are spatially correlated. Appling a Cochrane-Orcutt type transformation to Equation (2) yields (I n ρw n )P n = (I n ρw n )X n β + λ(i n ρw n )W n P n + α(i n ρw n )TOM n + ε n. (3) 7 The source of potential bias is the endogenous spatially lagged price variable. That is, if error terms associated with houses i and j are correlated, the price of house j,whichis the lagged explanatory variable for the price of house i, will be correlated with the error term in the price of the house i equation. Thus, the estimated coefficient of the lagged price variable will be biased.

10 52 Clauretie and Daneshvary Equation (3) is nonlinear and involves endogenous spatially lagged price and TOM variables, preventing the use of OLS or traditional two-stage least squares (2SLS) instrumental variable (IV) estimations. To our knowledge no past empirical housing study exists that has implemented an endogenous spatially lagged model with a spatially correlated disturbance term. Kelejian and Prucha s (1998, 1999) theoretical articles suggest the following generalized spatial two-stage least squares (GS2SLS) procedures, consisting of three steps. In the first step, the parameters in Equation (2) are estimated using an instrument matrix Z n. Matrix Z n includes (1) all exogenous explanatory variables (except the neighborhood variables) in the price equation, (2) their spatially weighted values and (3) the square of the spatially weighted values, as well as some exclusionary variables that affect TOM, but not price. 8 This step produces consistent estimators of the parameters, but it does not utilize information with respect to the spatially correlated error term; thus, the estimates are inefficient. The estimated residuals and a generalized method of moments can be used in the second step to consistently estimate the autoregressive parameter and the variance of the i.i.d. error term, ρ and σ 2 ε, (Kelejian and Prucha 1999). Given these estimates, the final step is to account for the spatial autocorrelation error term by making a Cochran-Orcutt type transformation of the data and estimating Equation (3). The transformed model is estimated via a traditional 2SLS using the elements of matrix Z n as instruments. To perform the above estimation procedure, first we need to obtain the average weight of matrix W n. There are several options for constructing such a matrix. The most common approach proceeds with calculating the Euclidean distance from observation i and its mth nearest neighbor, generating a cardinal maximum distance allowed, d max i. Then distances between every pair of observations j and i, d ij, are calculated and compared with d max i. The weight w ij is set equal to 1 if d ij d max i, and set to zero otherwise. To avoid a house predicting its own price, the diagonal elements of W n are set equal to zero. Each row of W n is then normalized by w ij / n j=1 w ij, so that each j i row of W n sums to 1. This process is referred to as row-standardized. For examples of this approach see Pace and Barry (1997) and Pace and Gilley (1997). The more recent literature, however, recognizes that a fixed cardinal distance approach (e.g., d max i ) produces an uneven number (differing densities) of 8 The neighborhood variables are correlated with both the spatially lagged and own house prices. As such, they do not satisfy the requirement of not directly affecting the dependent variable and are not included as instruments for the spatially lagged price.

11 Foreclosure Discount, Spatial Interdependence and Endogeneity 53 interdependent housing units among the observations. This outcome is not consistent with the real estate appraisers practice, which uses a fixed number of nearest neighbors to appraise house prices. Pace et al. (1998) and Pace et al. (2000) use a fixed number of nearest neighbors with individual weight declining to zero for the farthest neighbor, an ordinal approach that assures an even density of spatially lagged values. This approach is consistent with appraisers practice of the grid adjustment method of estimating house prices. Pace and Gilley (1998) report results using the weighted average of 7 and 10 lagged prices. They found very similar results. Ratcliffe (1972) concludes that a weight average of less than 5 is unsafe and that of more than 10 is unnecessary. Thus, within the range of 5 to 10, the choice of the number of nearest neighbors is somewhat arbitrary. In the empirical section, we use eight nearest neighbors to obtain the weight matrix, W n. 9 Empirical Analysis Variables and Data We model the natural logarithm of selling price as a function of physical and neighborhood characteristics, TOM, property condition, occupancy status, cash/mortgage sale and, of course, foreclosure status. Our empirical model includes a vector of physical characteristics typically found in hedonic models (see Table 2) and a vector of neighborhood characteristics that is composed of percent of population ages 25 35, percent of population with a college degree, percent of households with a child at home, median income and location indicators for two upscale large-planned communities in the Las Vegas, Nevada, area: Sun City Anthem and Sun City Summerlin. 10 To properly account for foreclosure effect, we include an indicator for whether the property was in foreclosure status and four indicators related to property condition (excellent, good, fair and poor), assessed by the listing agent/broker at the time of listing. Other indicator variables include: whether the transaction was a cash sale, whether the property was vacant and whether it was occupied by owner or a tenant at the time of sale. 9 Note that, unlike most previous foreclosure research, our autoregressive spatialautoregressive error terms model picks up any negative effect that a foreclosed home may have on the price of nonforeclosed neighboring homes. 10 The neighborhood variables, for more than 60 ZIP code areas, come from the data that are collected and analyzed by the Center for Business and Economic Research at University of Nevoda, Las Vegas.

12 54 Clauretie and Daneshvary Table 2 Definition, descriptive statistics and expected effect of variables on price. Nonforeclosed Sample Foreclosed Sample Description Abbreviated Name Mean S.D. Mean S.D. Expected Sign Selling Price Price 343, , , ,135 Dept Var. Days on Market Time-on-Market ? (TOM) Property Physical and Neighborhood Characteristics Property age Age Negative Building square footage Square Footage-B Positive Lot square footage Square Footage-L Positive Number of bedrooms Beds Negative Number of bathrooms Baths Positive Number of garages Garage Positive Property has a fireplace Fireplace Positive Property has a pool Pool Positive Property has a spa Spa Positive Two-story building Two Story Negative Percent Age %Age Negative Percent with a College Degree % College Positive Percent with a Child at Home % Child Negative Median Income (in 0.000) Income Positive Sun City Summerlin Summerlin Positive Sun City Anthem Anthem Positive

13 Foreclosure Discount, Spatial Interdependence and Endogeneity 55 Property Condition Condition excellent Excellent (reference group) Condition fair Fair Negative Condition good Good Negative Condition poor Poor Negative Sold Cash Cash Negative Commission Is Variable Variable Comm Positive Occupancy Status Occupied by a tenant Tenant Negative Vacant Vacant Negative Monthly Time Trend (quadratic) Trend Positive Instrumental Variable for TOM Monthly unemployment rate UR Monthly change in population (10) 3 Change Pop Proxy for agent s experience (agent ID) Experience Source: Greater Las Vegas Association of Realtors (GLVAR).

14 56 Clauretie and Daneshvary The length of time needed to generate an acceptable offer, and thus selling price, depends on the broker-effort level. Actual broker effort is unobservable, but depends on the commission rates offered (Sirmans, Turnbull and Benjamin 1991). We account for commission incentive by including an indicator equal to one if the listing commission is variable versus a flat rate. 11 To capture changes in the market conditions over the sample period, a monthly time-trend variable and its squared values are also included. Finally, the price equation includes two endogenous variables: the spatially lagged price and the number of days that the property was on the market before a sales contract was signed (TOM). These variables must be instrumented to use the GS2SLS estimations. Based on the previous studies and the model outline in Equation (3), we use the following variables as instruments. The spatially lagged price is instrumented by spatially weighted lagged independent variables in the price equation, except the neighborhood variables; see Kelejian and Prucha (2004). The TOM is instrumented by broker experience and market housing demand. An agent s experience, skill, training and expertise are important in identifying potential buyers and making faster sales; see Yang and Yavas (1995) and Jud, Seaks and Winkler (1996). Thus, we include a proxy for the agent s years of experiences in the local market. 12 Local demand conditions are represented by the monthly unemployment rate and change in population; see Sirmans, Turnbull and Benjamin (1991). Together these variables satisfy the identification condition of the price equation. The sample of properties for this study comes from the homes sold out of MLS sponsored by the GLVAR. We eliminated properties that were extremely atypical and were with miscoded observations, and we restricted the data to properties sold in the ZIP codes representing the Las Vegas metropolitan area. 13 Then we picked a sample that consists of all single-family homes with foreclosure status and about 12% of nonforeclosure-status single-family homes that were sold in Clark County, Nevada, from November 2004 through the end of 11 The total commission rate that is a part of the listing contract is not provided by the sources of our sample, the Greater Las Vegas Association of Realtors R (GLVAR). 12 The GLVAR was not able to provide information on the year a broker joined the organization. Broker members, however, are given an identification number when they join the GLVAR. The ID number is assigned chronologically as members join. Given the limitations of this variable we are of the opinion that some information is better than none. Thus, using the assigned identification numbers, we can proxy the extent of the agent s experience in the Las Vegas real estate market. And, of course, some brokers could have easily had some experience previous to joining the GLVAR. 13 We eliminated all condominiums and single-family properties with a sales price less than $100,000 or greater than $2,000,000, price per square foot less than $100 or greater than $500, lot square feet below 1,200 or above 45,000 and building square feet below 800 or above 4,000.

15 Foreclosure Discount, Spatial Interdependence and Endogeneity 57 November The final sample consists of 1,302 foreclosed and 8,498 regular single-family homes. 15 Variable names, definitions and descriptive statistics by foreclosure status and expected sign of each independent variable on price are provided in Table 2. Table 2 indicates several differences between the foreclosed and nonforeclosed samples. The average foreclosed property was sold for $26,415 less, had about 160 and 325 square feet more of living space and land space, respectively, and was about a year older. On average, the foreclosed properties were on the market for eight more days. A significantly larger percentage of foreclosed homes than nonforeclosed was cash sales (4.9% vs. 13.4%) and was sold with a variable commission rate (13.5% vs. 30.5%). Not surprisingly, the distribution of the two samples with respect to property conditions is significantly different. About 1.5% of nonforeclosed homes and about 10% of foreclosed homes were assessed as being in a poor condition. On the other hand, about 45% of nonforeclosed homes and about 10% of foreclosed homes were assessed as being in excellent condition. In fact, partial correlation coefficients between foreclosure status, on one hand, and fair, good and excellent condition indicators, on the other hand, are 0.108, and 0.230, respectively, and are statistically significant at the 0.01% level. Thus, these simple analyses confirm the notion that foreclosure status should, in part, proxy for other property characteristics. Before we perform the empirical testing of our models, it is important to check whether there are areas/neighborhoods in the Las Vegas Valley with a concentration of foreclosure properties. Using each property s latitude and longitude, we map foreclosed and nonforeclosed samples separately. Figures 1 and 2 show the maps of the observations in samples of nonforeclosed and foreclosed properties, respectively. The figures clearly show similar distributions of the properties between the two subsamples. 14 Nevada allows for a deed-of-trust as a security device. The power-of-sell is approximately four months and there is no statutory right of redemption. Nevada allows a deficiency judgment after a court hearing on the fair market value of the property. Foreclosed properties are sold at auction, sold by direct sale from a lender (REO) to a buyer or listed with the MLS. 15 Estimation of the model outlined in Equation (3) requires the creation of the weighted matrix, its square and mathematical operations. The computational cost increases exponentially with the sample size. Thus, we restricted the analyzed data set to include 12% of all nonforeclosed homes. The nonforeclosed subsample is a stratified sample with respect to ZIP code and time of sale, thus, maintaining the location and time proportionalities with the total market activities.

16 58 Clauretie and Daneshvary Figure 1 Geographial distribution of a sample of 8,498 nonforeclosed single-family houses sold in Clark County, Nevada, November 2004 November Latitude Longitude Empirical Results To provide a baseline for comparison and to allow us to investigate omitted variables, endogeneity and spatial autocorrelation issues, the log of house price was first estimated with OLS using physical and neighborhood characteristics, as is done by the existing empirical literature of foreclosure. Then, we expand our model specifications to account for endogeneity of the TOM and property conditions using 2SLS estimators. Finally, we correct our model specification for two forms of spatial autocorrelations by estimating spatially lagged autoregressive models with autoregressive disturbance terms using GS2SLS outlined earlier We thank Kelly Pace for proving the Spatial Statistics Toolbox 2 in MatLab, which can handle obtaining the weighting spatial matrix for large data sets. We also thank Harry H. Kelejian and Ingmar R. Prucha for providing their program for estimation of the GS2SLS models.

17 Foreclosure Discount, Spatial Interdependence and Endogeneity 59 Figure 2 Geographical distribution of 1,302 multiple listing service listed foreclosed single-family houses sold in Clark County, Nevada, November 2004 November Latitude Longitude Table 3 reports the heteroskedasticity-corrected results of OLS (columns 1 and 2), 2SLS (columns 3 and 4) and GS2SLS (columns 5 7) estimations. Concentrating on the physical and neighborhood characteristics, the estimated coefficients are consistent across all seven models and are consistent with findings of previous research. The physical characteristics have their expected sign and are, in general, statistically significant. 17 The signs of the neighborhoodindicator variables, Summerlin and Anthem, are as expected. The coefficients of these variables are statistically significant in OLS models, but they become insignificant in GS2SLS models that control for spatial autocorrelation. Other neighborhood variables, except median income, have the expected sign. Age and income variables are, however, statistically insignificant. Effects of 17 The negative marginal effect of number of bedrooms is also expected and consistent with the finding in the previous literature. Holding other physical characteristics, such as square feet of living area constant, consumers prefer a few large rooms rather than several small rooms.

18 60 Clauretie and Daneshvary Table 3 Heteroskedasticity-corrected ordinary least squares (OLS), two-stage least squares (2SLS) and generalized spatial two-stage least squares (GS2SLS) estimates of the natural logarithm of selling price. OLS Estimates 2SLS Estimates GS2SLS Estimates Variables (1) (2) (3) (4) (5) (6) (7) Spatial Lagged Price (3.46) (3.69) (3.51) Foreclosure (23.12) (23.10) (14.76) (10.95) (25.72) (19.93) (18.13) Time-on-Market (30 days) (1.04) (2.56) (2.62) (1.59) (1.12) (0.71) Poor (8.58) (19.12) (18.47) Fair (7.01) (13.26) (12.95) Good (0.62) (5.97) (6.18) Cash (5.00) Vacant (3.02) Tenant Age (19.39) (19.37) (12.29) (11.83) (19.77) (18.79) (18.94) Age Squared (10.41) (10.39) (5.79) (5.37) (11.62) (11.23) (11.46) Square Footage-B (10) (32.53) (32.55) (17.83) (16.91) (38.27) (39.14) (40.23) (3.01)

19 Foreclosure Discount, Spatial Interdependence and Endogeneity 61 Square Footage-B Squared (10) 6 (9.97) (10.02) (9.01) (8.64) (15.66) (15.53) (15.74) Square Footage-L Squared (10) 3 (14.48) (14.49) (13.80) (13.69) (35.75) (36.85) (36.80) Square Footage-L Squared (10) 6 (4.28) (4.28) (4.24) (4.26) (17.73) (18.24) (18.07) Beds (5.28) (5.33) (4.45) (4.25) (2.14) (1.42) (1.38) Baths (9.31) (9.32) (8.22) (8.31) (11.38) (11.83) (12.16) Fireplace (16.05) (16.05) (11.84) (11.46) (14.61) (15.16) (15.27) Garage (12.81) (12.80) (9.05) (8.63) (17.14) (17.69) (18.02) Pool (19.50) (19.43) (7.82) (7.50) (16.20) (16.99) (17.31) Spa (8.05) (8.06) (6.25) (5.99) (8.10) (8.07) (7.79) Two Story (11.73) (11.72) (9.04) (8.83) (14.18) (14.45) (14.89) Summerlin (3.25) (3.24) (1.56) (1.52) (0.08) (0.03) (0.17) Anthem (2.05) (2.08) (2.69) (2.76) (1.20) (1.13) (1.23) (Continued)

20 62 Clauretie and Daneshvary Table 3 Continued. OLS Estimates 2SLS Estimates GS2SLS Estimates Variables (1) (2) (3) (4) (5) (6) (7) %Age (0.07) (0.08) (0.47) (0.47) (0.73) (0.74) (0.76) % College (27.87) (27.88) (20.60) (19.94) (18.39) (18.80) (19.32) % Child (7.09) (7.09) (5.37) (5.01) (3.71) (3.56) (3.61) Income (1.59) (1.55) (0.89) (0.91) (0.54) (0.85) (1.12) Variable Comm (1.57) (1.60) (2.17) (1.62) (0.98) (0.07) (0.21) Trend (33.82) (33.79) (24.34) (23.54) (42.07) (43.22) (43.43) Trend Squared (33.54) (33.29) (11.95) (11.42) (33.23) (35.28) (36.74) _cons (636.61) (637.09) (502.07) (511.61) (613.06) (632.24) (642.35) Adjusted R Autocorrelation Coefficient, ˆρ (13.12) (13.41) (13.10) p value: chi-squared test of over identification (orthogonality) of instruments Note: t values are given in parenthesis. See Table 2 for variable definition and source of data., And significance at the 1%, 5% and 10% levels, respectively.

21 Foreclosure Discount, Spatial Interdependence and Endogeneity 63 education and children are significant in all specifications. Variable broker commission rate compared to flat rates does not affect the selling price. The coefficients of the time trend and its square are statistically significant and are positive and negative, respectively, reflecting the market experience for the period under consideration. Finally, adjusted R 2 for the OLS models are about Our primary interest is to obtain an unbiased estimate of foreclosure effect on price. As discussed earlier, omission of relevant variables, such as property condition, from the price equation may result in an overstated negative foreclosure effect. Starting with OLS baseline estimates in column 1 of Table 3, foreclosure status reduces selling price by about 10%. 18 This is almost identical to the findings by Carroll, Clauretie and Neill (1997) which used a data set for for the same city as ours and found that after controlling for neighborhood effect the foreclosure discount is between 8.45% and 9.72%. When TOM is added as an exogenous variable to the OLS model, the size of the foreclosure effect does not change and the coefficient of the TOM is insignificant (column 2). The results of the 2SLS models are reported in columns 3 and 4 of Table 3. Unlike the OLS results, the 2SLS estimates of TOM coefficients are negative and statistically significant at the 1% level, lending support for a marketing-time stigma effect when autocorrelation is not controlled. On average, an additional 30 days on the market reduces the selling price by about 6%. 19 Not accounting for property conditions (columns 3), the foreclosure status reduces price by about 11.3%. Controlling for property condition (column 4) reduces the foreclosure discount to 9.7%, a drop of 1.6 percentage points. These results imply that estimates of foreclosure discount reported by previous studies are about 16.5% (1.6 compared with 9.7) higher than the true discount caused by foreclosure per se. We attribute the difference to the proxy effect of foreclosure Given that the dependent variable, price, is measured in natural logarithm, the percentage effect of the foreclosure variable on price is calculated as Exp (β foreclosure) 1 = Exp ( 0.105) 1 = 9.968%. Throughout this article, we use this conversion when discussing the size of the foreclosure effect on price. 19 Given that the average days on the market is about 56 days (see Table 2), the estimated average reduction in price due to TOM is about 10 11%. 20 As these results imply and the distributions of values in Table 2 show, there is a close association between the foreclosure status and property condition. Such association may cause alarm that the estimated models may suffer from a high level of collinearity. Of course, the only two solutions when there is a high degree of multicollinearity among variables are either to omit some variables or to increase the sample size. We performed a diagnostic test using variance inflationary factor (VIF) criteria. The VIF values for foreclosure, good condition, fair condition and poor condition variables were 1.57, 2.48, 1.57 and 1.22, respectively. These results suggest the estimated models do

22 64 Clauretie and Daneshvary Referring back to our discussion of the endogeneity of TOM variable, three variables (broker experience, monthly unemployment rate and population change) were used as instruments for TOM. To check for the appropriateness of these instruments, we perform two tests in estimating 2SLS and GS2SLS models reported in columns 3 7. First, the chi-square test of Hall and Peixe (2003) rejected the null hypothesis of redundancy/irrelevance of each instrument at 5% or better. Second, the chi-square tests of overidentification/orthogonality (Hansen 1982), which are reported in Table 3, show that we cannot reject the hypothesis that the three variables are orthogonal to the error term and/or are valid instruments. The results of GS2SLS models that correct for both the endogeneity and autocorrelation are reported in columns 5 through 7 of Table 3. The estimated autoregressive parameters, ˆρ, are about 0.53 and statistically significant at the 5% level or better. These estimates are consistent with those found by Dubin (1988). The coefficient of the spatially lagged price indicates an elasticity of 0.2%. That is, a 1% increase in the average selling price of neighbors house increases the own-price by about 0.2%. The coefficient of the TOM variable is small and negative but insignificant, suggesting that when corrected for spatial autocorrelation the price TOM relationship becomes insignificant. In addition, the comparison of 2SLS and GS2SLS results suggest that the potential TOM stigma effect does not exist in isolation, but only in relationship to the TOM of the neighboring homes. 21 Consistent with this finding, note that the estimated coefficients of property physical characteristics, such as number of baths, are, in general, smaller in the autocorrelation-corrected models than in the OLS or 2SLS models. Column 5 of Table 3 shows that, correcting for endogeneity and autocorrelation and not accounting for property condition, the foreclosure discount is about 10%. When property-condition variables are added, column 6, the discount drops to about 7.9%, a drop of 2.1 percentage points. Further controlling for occupancy status and cash sales (column 7) reduces the foreclosure discount to 7.5%. These results (comparison of columns 5 and 7) suggest that estimates of foreclosure discount reported by previous studies are about one-third higher not suffer from a high degree of collinearity. Furthermore, comparison of results from the models that exclude property condition with the results of the models that include property condition, column 3 versus 4 and column 5 versus 6, shows stable t values and robustness of other variables size, sign and level of significance. 21 In technical terms, endogeneity is a problem associated with the potential omitted variables being correlated with the included variables. Spatial autoregressive models with autoregressive error terms control for the influence of such omitted variables, reducing the potential for the existence and the size of biased estimates and, thus, the need to correct for endogeneity.