A Simultaneous Spatial Model of Hedonic Housing Price and Neighborhood Composition in U.S. Metropolitan Areas. Yan Bao

Transcription

1 A Simultaneous Spatial Model of Hedonic Housing Price and Neighborhood Composition in U.S. Metropolitan Areas Yan Bao 1. Introduction This paper addresses an endogeneity issue that has not been extensively studied in the housing literature. As a common practice, many researcher use racial composition as a neighborhood characteristic in the hedonic housing price equation with very few papers questioning its exogeneity. While the effect of neighborhood composition on housing price is clear in the hedonic housing price analysis, the relationship between the two variables may be simultaneous in nature. As Bianchi et al. (1982) pointed out, ghetto areas and neighborhoods with a large black population are typically associated with poor living conditions in terms of both housing and neighborhood qualities. In addition, Pattillo (2005) found that even middle-class blacks live in poorer neighborhoods than the majority of whites with a similar income level. The disproportionate selection of blacks into these residential locations may be attributed to blacks higher price elasticities of housing demand. Based on the assumption that blacks are overall more sensitive to housing prices than whites, I use a self-selection model to show that blacks tend to concentrate in neighborhoods where housing prices are lower. Thus, the effect of housing price on neighborhood composition confirms the simultaneous relationship which renders racial composition endogenous in the single equation hedonic housing price model. In order to eliminate the potential bias in the estimates caused by endogeneity, I develop a simultaneous equations model which includes both the hedonic housing price equation and other equations to explain neighborhood composition. From the estimation results of this model in five metropolitan areas, we can see that endogeneity should indeed raise our concern. For each 1

2 metropolitan area, housing price has a significant effect in almost all the neighborhood composition equations. Compared with the simultaneous equations model, the traditional hedonic price analysis leads to biases in the estimated effect of neighborhood composition. The problem is most severe in metropolitan areas with a high level of racial and ethnic diversity where some estimates do not even maintain their signs. The estimation results from all the metropolitan areas indicate whites distaste of integration with blacks through the negative effect of percentage of blacks on the housing price in each neighborhood. These results are consistent with the findings of previous literature. On the other hand, the effects of other minority groups on housing price appear to be ambiguous. Similar to percentage of blacks in all the metropolitan areas, percentage of Hispanics also has a negative effect on housing price in San Antonio. However, the effect becomes insignificant or even positive in the San Francisco Bay Area. One potential explanation for that is a higher level of tolerance towards Hispanic residents in the Bay Area which shifts the housing demand in Hispanic neighborhoods much less than the housing demand in black neighborhoods. Meanwhile, the uneven distribution of Hispanics tends to increase the housing price in the Hispanic ghetto due to the low elasticity of housing supply in the Bay Area. Percentage of Asians does not have a uniform effect on housing price throughout the Bay Area, which may be attributed to the diverse cultural backgrounds of the Asian population. Apart from discrimination in the housing market, there are other reasons for blacks, Hispanics and Asians to segregate from whites and other groups and live among their own race or ethnicity. The ports of entry theory which was developed to explain the clustering of blacks in the North no longer applies these days because the black migration movement has ended in the 1970s. However, this theory still applies to Hispanics and Asians who are driven towards their cohorts by their native languages. In addition, it explains the formation of Asian enclaves in metropolitan areas which contain a high percentage of Asian immigrants, especially those who entered the United States within ten years of the census. Even after we control for these causes of racial segregation in the model, there is still a large part of neighborhood composition that can only be explained by the spatial autoregressive regressors in the simultaneous equations system. The corresponding spatial coefficients capture the effect of racial compositions in adjacent neighborhoods on the racial composition of each 2

3 neighborhood. We can potentially interpret them as the racial preferences of each minority group. According to my estimation, each racial and ethnic group strongly desires to live among their own race or ethnicity and generally prefers to stay away from the other groups. These preferences contribute to a persistently high level of racial and ethnic segregation which is typical of U.S. metropolitan areas. Furthermore, the study shows that it is necessary to include the percentage of each major racial and ethnic group in the hedonic price equation when we study a metropolitan area with a high level of racial and ethnic diversity. Omitting any one of those can lead to biased estimates because they are correlated with one other according to the estimation results of the neighborhood composition equations. Thus, it is problematic to use only percentage of blacks to proxy neighborhood composition like some papers do in analyzing the housing markets of any racially diverse city like Boston or San Francisco. The simultaneous equations model I develop in this paper is a good solution to all the aforementioned problems we may come across in the traditional hedonic price analysis. The paper proceeds as follows. Section 2 reviews the traditional hedonic housing models and some extensions with a spatial structure. Section 3 points out an endogeneity issue with these models and shows its existence through a self-selection model. Section 4 lays out the simultaneous spatial model used in the empirical study. Section 5 provides identification for the explanatory variables included in the regressions. Section 6 describes the data set and offers some geographical information about each metropolitan areas in the study. Section 7 illustrates the estimation results. Section 8 provides some potential interpretation for the results. Section 9 concludes. 2. Review of Hedonic Housing Price Models Housing is typically the most important single expenditure in a household s budget on average, U.S. households spend 25 percent of their income on housing. One of the most common approach to model housing price is the hedonic analysis developed by Rosen (1974). In the theoretical framework provided by Rosen (1974), the hedonic price function is the market clearing function produced by the interaction of bid functions of households and offer 3

4 functions of suppliers. In particular, housing is a heterogeneous commodity described by a package of characteristics H = (h 1,, h n ). A price P(H) = f(h 1,, h n ) is defined for each distinct package. Hedonic prices are defined as the marginal (implicit) prices of attributes p k P(H)/ h k (for k = 1,, n). Based on Rosen s framework, a wide range of hedonic housing price models have been developed and estimated. Some of the earliest works include those by Kain and Quigley (1970) and Freeman (1979). The housing attributes included in these models can generally be categorized into two major groups: The first group includes the characteristics of the residential structure. For homeowners, it includes housing quality, lot size, number of rooms, number of bathrooms, age of structure, etc. For renters, it also includes type of structure, rental term, presence of central heating, duration of tenant occupancy, etc. The second group, sometimes referred to as locational effects, comprises externalities associated with the geographic location of the dwelling. These include racial effects, measures of neighborhood prestige such as income and education level of residents, measures of accessibility such as distance to work [Kain (1962); Mills (1967); Harris et al. (1968)], school quality [Hanushek and Kain (1972); Jud and Watts (1981)], and other locational effects such as air quality [Nelson (1978); Harrison and Rubinfeld (1978)], landlord-tenant interaction [Sternlieb (1966)], proximity to shoreline [Brown and Pollakowski (1977)], etc. The aforementioned locational effects describe the impact of shared neighborhood characteristics on housing price. They are often referred to as neighborhood effects. A second level of locational effects incorporates the absolute spatial spillover effects. Specifically, they describe the impact of the prices of adjacent dwelling units on the price of a given one. These effects are referred to as adjacency effects by Can (1992). Adjacency effects cross over neighborhood boundaries. They lead to spatial dependence in the housing price determination process. Can (1990) first offered an autoregressive specification of the hedonic price function: P = f(wp, S, N, ρ, β, γ) + ε, where S and N are vectors of structural characteristics and neighborhood characteristics. The adjacency effects are captured by WP which consists of spatially weighted prices of adjacent housing units. This model corresponds more closely with the actual workings of the real estate institution in urban 4

5 housing markets because real estate agents usually appraise a house given the price history of houses in the immediate vicinity in addition to other substantive characteristics. The spatial hedonic price model proves to be useful in several empirical papers. Some recent applications investigate the effect of air quality [Kim et al. (2003); Anselin and Le Gallo (2006)] and airport noise [Cohen and Coughlin (2008)] on housing price. 3. A Self-Selection Model An endogeneity issue may arise in the traditional hedonic housing price model with the inclusion of racial composition as an explanatory variable because it may be affected by the housing price in each neighborhood. As reviewed by Clark (1991), many demographers believe that housing affordability is one of the main reasons for blacks to concentrate in certain areas of the city. The low housing price in the ghettos can be attributed to low qualities of the housing units and the neighborhood to a large extent. According to the study by Bianchi et al. (1982), blacks are more likely to live in crowded, structurally inadequate and older units. In addition, black ghettos are typically associated with widespread poverty, rodent infestations, rampant infectious diseases, and high crime rates. According to Pattillo s (2005) review, even middle-class blacks still live in poorer neighborhoods than the majority of whites on all measures. Furthermore, there is a large agglomeration of human service facilities in the ghettos such as group homes, halfway houses and drug/alcohol treatment clinics. Many of them are expected to generate negative property value effects. In their study of the Oakland housing market, Gabriel and Wolch (1984) observe that the ghetto area houses about half of the city s population but over three quarters of Oakland s facilities and service offerings. One historical reason for the disproportionate selection of blacks into such residential locations is collective action racism. Spear (1969) argues that ghettos are a result of collective actions taken by whites to enforce separation from blacks. While racial discrimination may have become less important than in the past, there is another reason for the racial segregation in the housing markets: blacks are more sensitive to housing prices and therefore purchase cheaper housing units than whites overall. 5

6 In de Leeuw s (1971) paper, he reviewed past cross-section studies of the housing demand in the United States and also estimated his own income and price elasticities from the 1960 Census data. The elasticities were estimated for various household groups differentiated by household size and race. According to his estimation, nonwhite renter households have higher price elasticities than all renter households regardless of race for any household size. The weighted average price elasticity for all renter households is -.71 while it is for nonwhite renter households. This means that nonwhite households are generally more sensitive to price changes in rental housing than white households. Since most of the nonwhite households in the United States are black and Hispanic, the estimation results suggest that blacks and Hispanics are more price elastic than white in the rental housing markets. Moreover, Carliner (1973) finds that price elasticities differ significantly between black and white homebuyers after controlling for income. These results are confirmed in a more recent study by Goodman (1990). According to his estimation, both black renters and black homeowners have higher price elasticities than their white counterparts. Based on the assumption that blacks are more sensitive to housing prices than whites, I will use a self-selection model to show that black homebuyers tend to choose residential locations where housing prices are lower. This model is an extension to the model developed by Mussa and Rosen (1978) in which the seller offers a menu of products with and lets the customers self-select from this menu. In Mussa and Rosen s model, the utility of a representative buyer is given by U = θq p. The product quality q is restricted to one dimension with larger values of q indicating higher quality varieties, and p is the associated price. The parameter θ represents the buyer s type. It measures the intensity of the buyer s taste for high quality (given the price). Thus, the preferences of potential buyers are described by the distribution of θ. A similar situation exists in housing markets. When deciding on their residential locations, homebuyers choose from a menu of housing units with varying prices and qualities. In order to study the relationship between the housing price and the neighborhood composition in a metropolitan area, I develop the following model which is slightly different than Mussa and Rosen s model. In my self-selection model, I assume that each homebuyer derives her utility from two attributes of her housing unit quality and price. The utility function (1) is non-linear and 6

7 separable as follows, which takes on a more general form than the utility in Mussa and Rosen s model. U(q, p) = u(q) v(p γ). (1) Here, u(q) is the utility derived from the housing quality q. Meanwhile, v(p γ) is the disutility associated with the housing price p, which depends on the homeowner s type γ 1. Unlike θ in the baseline model, the parameter γ measures the intensity of homebuyer s distaste for high price (given the quality). We can also interpret γ as the homebuyer s sensitivity to housing price. The more sensitive a homeowner is to the housing price, the stronger the price effect will be on her disutility. Therefore, it is natural to assume that 2 v(p γ) 0. (2) p γ This is simply the single crossing condition required in the self-selection model developed by Cooper (1984). I assume that the housing market is in equilibrium, so the quality and the price of each housing unit has already been determined. From a homebuyer s choice of residential location, we can gain some knowledge about his type or price sensitivity. Based on the assumption that blacks are more sensitive to the housing price than whites, I will show that blacks are more likely than whites to live in neighborhoods with lower housing prices. This provides an alternative explanation for the high level of racial segregation in U.S. metropolitan areas. Price sensitivity varies greatly among different homebuyers of any race. I assume that the distribution of γ among black homebuyers first-order stochastically dominates the distribution of γ among white homebuyers, i.e., F B (γ) < F W (γ), γ (0, + ). Here F B and F W are the cdf s of γ among black and white homebuyers respectively. As is shown in the Figure 1, the percentage of blacks whose price sensitivity is lower than any level is always smaller than the percentage of whites whose price sensitivity is lower than the same level except at the origin. This condition is in line with the assumptions that blacks are more sensitive to the housing price than whites. 1 γ is essentially 1/θ in Mussa and Rosen s utility function. Dividing the utility function by θ does not affect each buyer s choice, but it allows us to interpret the consumer type as price sensitivity. 7

8 Suppose that there are two adjacent neighborhoods H and L. The housing quality and price in neighborhood H are q H and p H while the housing quality and price in neighborhood L are q L and p L. Assume that q H > q L and p H > p L so that neighborhood L is considered the ghetto area. I will show that a larger percentage of blacks live in L than in H while a larger percentage of whites live in H than in L. 1 F W F B 0 γ γ Figure 1. Distribution of price sensitivity by race IC constraint: For any homeowner i who lives in neighborhood H, her utility must satisfy the following u i (q H, p H ) u i (q L, p L ). (3) Similarly, for any homeowner j who lives in neighborhood L, her utility must satisfy the following IC constraint: u j (q L, p L ) u j (q H, p H ). (4) Given the assumption that the utility function is separable, we can rewrite the first incentive constraint as: or equivalently, u(q H ) v(p H γ i ) u(q L ) v(p L γ i ), v(p H γ i ) v(p L γ i ) u(q H ) u(q L ). Recall that we made the assumption 2 v(p γ)/ p γ > 0. Thus, the following inequality must hold because p H > p L. v γ (ph γ) v γ (pl γ) 0. (5) 8

9 Let γ be the solution to the equation v(p H γ i ) v(p L γ i ) = u(q H ) u(q L ). Then any homeowner who lives in neighborhood H must have a price sensitivity γ that lies in the interval (0, γ ) because the left-hand side of the equation is monotonic in γ. Therefore, the percentage of blacks who live in neighborhood H is P B H = F B (γ ), and the percentage of whites who live in neighborhood H is P W H = F W (γ ). Since F B first-order stochastically dominates F W, we must have P B H < P W H. Meanwhile, the percentages of blacks and whites who live in neighborhood L are P B L = 1 P B H and P W L = 1 P W H. Obviously, we must have P B L < P W L. Let B and W be the total number of blacks and whites who live in neighborhoods H and L. Then the percentage of black residents in neighborhood H is PER B H = B P B H B P B H + W P W H, (6) and the percentage of black residents in neighborhood L is PER B L = B P B L B P B L + W P W L. (7) Based on conditions P B H < P W H and P B L < P W L, we can derive the following inequalities: and PER B H = PER B L = B P B H B P B H + W P W H < B P B L B P B L + W P W L > H B P B B P H H B + W P = B L B P B B P L L B + W P = B B B + W, (8) B B + W. (9) Obviously, these inequalities indicate that PER B H < PER B L, which means that blacks tend to concentrate in neighborhoods with low housing prices. Therefore, I draw the conclusion that the percentage of black residents in each neighborhood is negatively affected by the housing price in that neighborhood. This conclusion confirms the simultaneous nature of the housing price and the racial composition. Instead of hunting for proper instruments in the hedonic housing price equation, I will run simultaneous regressions of the racial composition on the housing price in each neighborhood to fix the endogeneity issue. 9

10 4. Empirical Model Similar to the hedonic price equation, we can construct another regression equation to explain the racial composition in each neighhborhood: PER b = f(w PER b, P, N, ρ, β, γ) + ε, where PER b is the percentage of blacks in the neighborhood. The spatial lag W PER b captures the tendency of blacks to concentrate in black neighborhoods. The housing price P has a negative effect on the percentage of blacks in each neighborhood due to their high sensitivities to housing prices as shown in Section 3. To complete the regression equation, N are vectors of structural characteristics and neighborhood characteristics that can be used as exogenous variables to explain neighborhood composition. In the empirical study, I use the following simultaneous equations model with a spatial autoregressive structure. P H = α 1 WP H + α 2 PER b + X 1 γ 1 + ε 1, (10) PER b = β 1 W PER b + β 2 P H + X 2 γ 2 + ε 2. (11) The first equation is a generalized hedonic housing price function while the second equation fixes the endogeneity issue mentioned in Section 3. Here, P H is the vector of housing prices, and PER b is the vector of percentage black in each neighborhood. Each equation has one spatial lag in which W represents the weighting matrix. X 1 and X 2 are the exogenous variables. We may allow the disturbances ε 1 and ε 2 to have spatial structures, but that does not affect the consistency of 2SLS and GMM estimators. The spatial lag in equation (10) allows housing prices to be spatially correlated across different neighborhoods. Meanwhile, I assume that the housing price in each neighborhood directly depends on the percentage of blacks in the neighborhood and other exogenous variables contained in X 1 following the housing literature. The spatial lag in equation (11) captures blacks tendency to cluster purely caused by their preferences of living among their own race. Following the results in Section 3, I assume that the percentage of blacks in each neighborhood directly depends on the housing price in the neighborhood and other exogenous variables contained in X 2. This model helps us identify the effect of racial composition on housing price without any bias caused by the endogeneity that is present in the traditional hedonic price model with a single equation (10). The simultaneous equations system (10)-(11) works in a metropolitan area 10

11 whose population consists mainly of whites and blacks. The underlying assumption is that other racial and ethnic minorities account for a negligible portion of the population and are scattered randomly across the metropolitan area, which is why their effects in the housing market are treated as white noise and included in the error term. If we want to study a metropolitan area in which Hispanics or Asians are the only minority group comprising a significant portion of population instead of blacks, then we can simply replace PER b with PER h or PER a, i.e., the percentage of Hispanics or Asians. The effects of blacks will then be treated as white noise. In particular, when I consider the San Antonio (TX) MSA in the next section, I will explore the simultaneous relationship between housing price and percentage of Hispanics across different neighborhoods. The empirical model is as follows. P H = α 1 WP H + α 2 PER h + X 1 γ 1 + ε 1, (12) PER h = β 1 W PER h + β 2 P H + X 2 γ 2 + ε 2. (13) Suppose that the simultaneous equations system (10)-(11) is the true underlying model in our study. Then the traditional hedonic price model with a single equation (10) is misspecified and may lead to biased estimators. In the literature, some researchers do not include the spatial lag WP H in the hedonic price equation and estimate the parameters by OLS. However, when the spatial lag is present in the equation, we have to use instruments to resolve its endogeneity. A common approach is to estimate the single equation model (10) by 2SLS with instruments WX, WX 2, etc., where X includes all the exogenous variables. In the current setting, X includes PER b and X 1 if we ignore the simultaneous process in equation (11). For simplicity, I only use WX as instruments for the spatial lag. Let θ = (α 1 β 1 γ 1 ). Thus, the 2SLS estimator for the parameters is θ = (Z Q(Q Q) 1 Q Z) 1 Z Q(Q Q) 1 Q P H, where Z = (WP H PER b X 1 ) and Q = (WPER b WX 1 PER b X 1 ). Using equation (10), we can rewrite the estimator as θ = θ + (Z Q(Q Q) 1 Q Z) 1 Z Q(Q Q) 1 Q ε 1. The estimator is unbiased only if the second term equals zero. However, the endogeneity of PER b will lead to bias in the estimator. In order to see this, let us first rewrite the simultaneous equations model as [B I A W]Y = Xγ + ε. Here, Y = P H, X = X 1 0, ε = ε 1 PER b 0 X 2 ε, A = α 1 0, B = 1 β α 2 β 2 1, and γ = γ γ 2 11

12 Thus, Y = [B I A W] 1 (Xγ + ε). Let [B I A W] 1 = Λ 11 Λ 12. Then we Λ 21 Λ 22 can rewrite PER b = Λ 21 X 1 γ 1 + Λ 22 X 2 γ 2 + Λ 21 ε 1 + Λ 22 ε 2. Clearly, PER b is correlated with ε 1, which causes the previous 2SLS estimator to be biased. Therefore, we cannot simply estimate the single equation model without accounting for the endogeneity of percentage of blacks. Instead, we should conduct a systematic estimation of the simultaneous equations model. As illustrated above, the simultaneous equations system can be rewritten as a high order spatial autoregressive model: Y = α 1 W 1 Y + α 2 W 2 Y + β 1 W 3 Y + α 2 W 4 Y + Xγ + ε, where W 1 = W 0 0 0, W 2 = 0 I 0 0, W 3 = W and W 4 = 0 0 I 0. The new regression equation contains four spatial lags with different weighting matrices. The key to the estimation procedure is constructing proper instruments for the spatial lags. We can obtain consistent estimates of the coefficients in this model by 2SLS [Kelejian and Prucha (2004)] and GMM [Lee and Liu (2010)] methods. As is mentioned above, the two-equation model applies to metropolitan areas whose population consists primarily of whites and one other racial or ethnic group. When we analyze a more diverse metropolitan area with a large presence of more than on minority group, it is not appropriate to treat the effect of any of these groups as white noise in the housing market. Section 3 illustrates that the percentage of each racial and ethnic group may be simultaneously determined with the percentage of other groups in the same neighborhood, which calls for a simultaneous system with multiple equations. In Section 7, the San Jose (CA) MSA is one of the more diverse metropolitan areas that I study. Both Hispanics and Asians account for a significant portion of its population, which is why I set up the following three-equation system. P H = α 1 WP H + α 2 PER h + α 3 PER a + X 1 δ 1 + ε 1, (14) PER h = β 1 P H + β 2 W PER h + β 3 PER a + X 2 δ 2 + ε 2, (15) PER a = γ 1 P H + γ 2 PER h + γ 3 W PER a + X 3 δ 3 + ε 3. (16) Now the housing price depends on both percentage of Hispanics and percentage of Asians in equation (14). The spatial autoregressive coefficients in equations (15) and (16), β 2 and γ 3, capture Hispanics and Asians tendency to live among their own ethnicity or race while β 3 and γ 2 capture each group s tendency to integrate with or segregate from the other group. 12

13 To take things one step further, we can consider a metropolitan area with significant portions of blacks, Hispanics and Asians spread unevenly across space. From the empirical model (14)-(16) it is a simple extension to a four-equation system. This system will be discussed in the Section 7 when I study the highly diverse San Francisco MSA. 5. Parameter Identification A. Housing Price Equation The endogeneity of racial composition in the hedonic housing price model is the central theme of this study. Its effect on the housing price is one of the neighborhood effects that are studied most extensively in the literature. There has been some debate over this effect. Findings of many earlier papers such as the following indicate that otherwise identical housing units are more expensive in the black ghetto than in the white submarket. These price differentials are referred to as ghetto markups in urban housing markets. Researchers use various measures of racial composition as an explanatory variable in the hedonic price model. Kain and Quigley (1970) studied the housing value and rent of 1,500 dwellings in St. Louis. They included percentage white in the census tract as a regressor and obtained a negative coefficient. Ridker and Henning (1967) used census tract level data on owner-occupied housing in St. Louis. They included percentage nonwhite residents in the regression and obtained a positive coefficient. There are at least three theories that explain the housing price differentials between black and white areas. Firstly, racial price differentials result if white landlords and realtors charge blacks more than whites for the same dwelling unit. This is the case of pure racial price discrimination. Another theory contends that blacks must pay a premium for housing because of collusive behaviors among whites in the housing market [Kain and Quigley (1975)]. Thus, high demands in limited areas lead to higher prices in the ghetto. Finally, racial price differentials may also come from differences in the preferences of blacks and whites for racial composition of their neighborhoods (Bailey 1966). The most common assumption is that whites prefer segregation and blacks prefer integration. The reluctance of whites to live in black submarkets leads to lower demands, which tends to cause the housing price to decrease in the ghetto. 13

14 The earlier results are challenged by Schafer (1979). He argues that housing price depend on both the race of the occupant and the racial composition of the neighborhood. By including both in his study of the Boston housing market, he finds that households headed by a black resident pay more for their housing units while percentage black in the neighborhood has a negative effect on housing price. The effect of neighborhood racial composition is consistent with the theory of whites distaste for racial integration. Studies of more recent periods have also cast doubt on the existence of racial price differentials in U.S. housing markets. An analysis of the Boston and Pittsburgh housing markets by Schnare and Struyk (1978) finds that ghetto markups present in 1960 disappeared by 1970, and suggests that price differentials are largely a function of changes in the conditions of supply and demand in the black and white submarkets. As shown in Section 7, my estimation results are consistent with the more recent findings and reject the existence of ghetto markups. In all the metropolitan areas, the percentage of blacks in each neighborhood has a negative effect on the housing price in that neighborhood, which supports the theory of whites taste for segregation. Section 5 reveals the simultaneous nature of the housing price and the racial composition in each neighborhood, which causes racial composition to be an endogenous variable in the housing price equation. The other endogenous regressor in the equation is the spatial lag which captures the adjacency effect as Can (1992) refers to. In her empirical study, she obtains significantly positive spatial coefficients. Besides the endogenous regressors, the housing literature has also covered the exogenous variables in this study. The number of rooms and the number of bedrooms in the unit typically have positive effects on the housing price as shown by many researchers in the literature such as Kain and Quigley (1970). They use the price of each individual housing unit as the dependent variable. If I use the same dependent variable, then for the purpose of my study each unit needs to be matched to the neighborhood where it is located, which census data do not allow. Therefore, I construct an alternative housing price index for each neighborhood as the average housing price divided by the average number of rooms among units in the neighborhood 2. This changes the effects of the number of rooms and the number of bedrooms in the housing price equation. 2 I also tried using the average housing price in each neighborhood as the dependent variable, which does not change the key results of the empirical study. 14

15 Dwelling age is another characteristic commonly included as an exogenous variable in the hedonic housing price equation. In their study of the New Haven housing market, Grether and Mieszkowski (1974) find that the effect of age on housing price is nonlinear, with younger dwellings depreciating more rapidly than older ones. By including both dwelling age and age squared in the regression, I can approximate the nonlinear effect. Various demographic factors are sometimes used as neighborhood characteristics such as percentage of married couples, percentage of households with children [Clapp et al. (2008)], and percentage of older residents [Can (1992)]. These groups are generally expected to value housing properties more than others. Some of the other neighborhood characteristics are related to prestige such as income and education level of residents [Freeman (1979)], and accessibility such as distance to work [Kain (1962); Mills (1967); Harris et al. (1968)]. They are all included as exogenous variables in my study. Finally, housing prices are significantly higher in the central city than in its suburbs, as pointed out by Goodman (1978). Thus, I also include distance to the central business district (CBD) as an exogenous variable. B. Neighborhood Composition Equations In order to remedy the endogeneity issue with the housing price equation, the neighborhood composition equations are added into the simultaneous system in which the percentage of blacks or other minority residents in the neighborhood becomes the dependent variable. As illustrated in Section 3, housing price has negative effect on the percentage of black residents in each neighborhood. Naturally, it is included as an endogenous regressor, and the corresponding coefficient measures the sensitivity of each minority group to housing prices. Similar to the housing price equation, I also impose a spatial structure on the neighborhood composition equations based on the assumption that racial composition is spatially correlated across neighborhoods. This assumption is rooted in the high level of racial segregation in U.S. metropolitan areas. Various studies have shown the rise and decline of the American ghetto in different historical periods and the persistence of racial segregation to this day [Cutler et al. (1999); Massey and Denton (1987)]. 15

16 A prevalent theory for racial segregation is decentralized racism which says that segregation is enforced by individual whites decisions to live with other whites. Clark (1991) collected data from telephone surveys conducted in five U.S. cities as part of litigation related to desegregation cases. The survey results suggest that most white respondents prefer neighborhoods that are at least 80% white. By comparison, most black households prefer neighborhoods that are 50/50. These results generally support the consensus in the literature which says that whites prefer segregation and blacks prefer integration. To be more precise, whites in general are unwilling to discriminate against a small percentage of blacks in the neighborhood, but they are reluctant to fully integrate with blacks in the housing markets. These results, however, do not explain the high level of racial segregation in many metropolitan areas. One of the most popular models that attempt to explain the residential patterns of different racial groups is the tipping model developed by Schelling (1972). Based on the various racial preferences among blacks and whites, the model makes the assumption that each white individual or household has a tolerance level for the percentage of blacks in their neighborhood. The individual or household will move to a new location once the percentage reaches the threshold of their tolerance. This threshold is calling the tipping point. Schelling concludes that the dynamics are inherently unstable, and the only stable equilibria are the situations of all white and all black. Clark (1991) extends the tipping model by allowing for tipping points among black individuals and households as well as among whites. His model suggests that any outcome with racially mixed neighborhoods is unstable. Hence, at any point in time, blacks are more likely to move into a predominantly black neighborhood, and whites are more likely to move into a predominantly white neighborhood. If each neighborhood is small enough compared with the metropolitan area, we can expect neighborhood compositions to be highly correlated across space. While most housing research in the literature focuses on blacks, few papers study other racial and ethnic groups such as Hispanics and Asians. According to the aforementioned telephone survey conducted in Los Angeles, Hispanics display similar preferences for integration with blacks as whites do. Hence, the tipping model also predicts a high level of segregation between Hispanics and blacks. Meanwhile, whites are generally reluctant to live in neighborhoods with a large Hispanic population although they have higher tolerance for 16

17 Hispanics than for blacks. If we use a spatial structure in the neighborhood composition equation, we need to allow for the possibility that the percentage of each racial and ethnic group is simultaneously determined with the percentage of other groups in the same neighborhood. The simultaneous spatial model described in Section 4 contains spatial lags that capture these correlations. The spatial coefficients indicate the tendency of each minority group to integrate with other groups or segregate from them. They can potentially be interpreted as the racial preferences of each minority group. The demography literature provides us with some candidates for exogenous variables that can be used in the neighborhood composition equations. In particular, the ports of entry theory asserts that recent migrants cluster with their own group to recreate the social milieu and to find the consumer goods of their homeland. This theory has an important role in the historical trends of black migration from the South to the North [Drake and Cayton (1993; Spear (1969)]. While the black migration movement may have ended in the 1970s, this theory still applies to Hispanic and Asian immigrants who continue to gather in their respective ethnic enclaves because of language and cultural barriers. Thus, I use some neighborhood characteristics related to immigrants as explanatory variables in the regression. These include the percentage of residents who were foreign born and those who do not speak English at home in the census tract. In their case studies of several U.S. cities, Cutler et al. (1999) do not only find that the level of racial segregation has persisted over time, but they also discover that the location of the ghettos has remained largely stable, with few neighborhoods experiencing drastic changes in their racial composition. Furthermore, the ghettos are often located downriver in the southern portion of the metropolitan area. For example, in the DC metropolitan area, highways were built in the 1950s to allow tourists and commuters to drive downtown. As Williams (2001) explains, these white flight highways trapped and discharged rainwater, oozing with oil, into the now thoroughly contaminated river, leaving urban blacks in the polluted ghettos. These findings lead me to include the neighborhood composition in the last census and neighborhood latitude as exogenous variables to explain the current neighborhood composition. Finally, residential white flight from large central cities causes the central cities to be much more diverse than the suburbs. Thus, I also include distance to the central business district (CBD) as an exogenous variable in the neighborhood composition equations. 17

18 6. Data Description The data used in this paper is Census 2000 sample data, which include detailed population and housing data collected from a 1-in-6 sample and weighted to represent the total population. It was the last year that the census bureau used the long form questionnaire. Some of the information used in this study is not available in Census Since racial composition and many explanatory variables are measured on the neighborhood level, it is important to choose a reasonable definition of a neighborhood first. Many papers in the housing literature use census tracts which are geographic regions defined for census purposes with an average population of about 4,000. In this paper, I use block groups as the proxy for neighborhoods. Block groups are statistical subdivisions of a census tract with an average population of about 1,500. A block group is the smallest geographic unit for which the Census Bureau tabulates sample data. The smaller size makes it a more reasonable definition of neighborhood. It also means that there are more block groups than tracts in each metropolitan area, which gives us more data and thus a higher degree of freedom in the estimation procedure. However, the data at the block group level are not as comprehensive as at the tract level. Hence, I will not use a seemingly exhaustive list of explanatory variables as some papers do in their hedonic housing price analysis. Households can be divided into homeowners and renters. The housing price for the two types of households can be represented by home value and rent respectively. Throughout this study, I will only consider the price of owner-occupied housing. Accordingly, the housing quality variables also refer to owner-occupied housing units. In the traditional hedonic housing price model, researchers usually use the price of each individual housing unit as the dependent variable. In order to use the same variable in this study, we need to match each housing unit to the block group where it is located. This kind of data is not available. Therefore, an alternative price index is constructed as the market value of each housing unit divided by the number of rooms in it. This price index represents the average value of each room in the unit, which reflects some aspects of the traditional price index. It is very easy to compute, and for the purpose of this study, it may be the best alternative. As I explained in 18

19 Section 5, the key results do not change if I use the average housing price in each neighborhood as the dependent variable instead. As the first attempt to examine the endogeneity in the traditional hedonic housing price equation, I will start with the two-equation system (1)-(2) which applies to metropolitan areas whose population consists mainly of whites and blacks. Due to historic reasons, we may suspect that the residential patterns of blacks are quite different between the North and the South. In order to compare the effect of racial composition on housing price in the two regions, I have picked the Columbus (OH) MSA and the Atlanta (GA) MSA as representatives of Midwestern and Southern metropolitan areas. Table 1 provides some information on the racial composition of these two metropolitan areas. Table 1. Racial composition of Columbus (OH) MSA and Atlanta (GA) MSA Racial/Ethnic Composition Columbus (OH) MSA Atlanta (GA) MSA %White 82.0% 63.5% %Black 12.6% 28.5% %Hispanic 1.8% 6.3% %Asian 2.3% 3.1% %Block groups with less than 10% Hispanics 98.5% 84.8% %Block groups with less than 10% Asians 95.6% 93.1% There are significant portions of whites and blacks in both metropolitan areas whereas the effect of Hispanics and Asians may be considered negligible due to the small sizes of these two groups. In the Columbus MSA, 98.5% of the block groups contain less than 10% Hispanics and 95.6% contain less than 10% Asians. Hence, there is very little variation in the distribution of Hispanics and Asians across different neighborhoods. It is probably reasonable to treat their effects as white noise. We can use the same reasoning for the Atlanta MSA. These assumptions can our lives much easier. However, it is quite straightforward to extend the model if we do not believe Hispanics and Asians are evenly distributed. The extended model will be discussed when I study the San Francisco Bay Area which is much more racially and ethnically diverse. The following figures illustrate the distribution of housing prices and blacks across block groups in these two metropolitan areas. 19

20 Figure 2. Spatial distribution of housing price and neighborhood composition in Columbus (OH) MSA Figure 2 shows that blacks mostly reside in the central city area of the Columbus MSA. The suburban neighborhoods generally contain less than 7.8% blacks. Within Columbus city proper, there is a clear east-west divide between blacks and whites. Meanwhile, housing prices tend to be lower on the east side with high concentration of blacks. Figure 3. Spatial distribution of housing price and neighborhood composition in Atlanta (GA) MSA 20

21 The black ghettos in the Atlanta MSA are also mostly located in the central city area, but have extended a little into suburban areas. Atlanta city proper has a north-south divide between whites and blacks. The housing price is also significantly lower on the south side of town which is predominantly black. The simultaneous analysis can also be applied to other racial and ethnic groups. In the United States, the concentration of Hispanics and Asians happens for very different historic and contemporaneous reasons than the formation of black ghettos. Hence, an interesting issue is whether Hispanic and Asian concentration in U.S. cities affect housing prices in the same way the black ghetto does. The next metropolitan area in this study is the San Antonio (TX) MSA. It is selected for its large Hispanic population typical of Texan cities and also due to its simple racial composition. Table 2 provides the racial composition of the San Antonio MSA. According to Table 2, Hispanics make up about half of the population in the metropolitan area. On the other hand, an overwhelming major of block groups contain less than 10% blacks or Asians. Hence, their effects will be treated as white noise in the empirical model (12)-(13). Table 2. Racial composition of San Antonio (TX) MSA Racial/Ethnic Composition San Antonio (TX) MSA %White 71.5% %Black 6.1% %Hispanic 50.4% %Asian 1.4% %Block groups with less than 10% Blacks 82.7% %Block groups with less than 10% Asians 98.7% According to Figure 4, the San Antonio MSA maintains a clear ethnic divide between Hispanics and non-hispanic whites. Housing prices are generally lower on the southwest side where Hispanics are predominant, which makes the Hispanic residential situation similar to the situation of blacks in Columbus and Atlanta. 21

22 Figure 4. Spatial distribution of housing price and neighborhood composition in San Antonio (TX) MSA To complete the study, I will study the San Francisco Bay Area which has the highest percentage of Asians among major metropolitan areas in the continental U.S. However, we may not ignore the other racial and ethnic groups which also have considerable sizes in the metropolitan area. Table 3. Racial composition of San Francisco Bay Area Racial/Ethnic Composition San Jose (CA) MSA San Francisco-Oakland MSA %White 54.0% 56.6% %Black 2.6% 9.5% %Hispanic 24.7% 17.8% %Asian 24.8% 19.2% %Block groups with less than 10% Blacks 98.4% 73.6% %Block groups with less than 10% Hispanics 35.2% 46.6% %Block groups with less than 10% Asians 27.0% 42.4% The San Francisco Bay Area contains two major MSAs commonly used for statistical purposes: the San Francisco-Oakland MSA in the north and the San Jose MSA in the south. Table 3 shows that Hispanics and Asians each represent about a quarter of the population in the 22

23 San Jose MSA while blacks represent only 2.6%. On the other hand, the San Francisco-Oakland MSA contains about 10% blacks, 18% Hispanics and 20% Asians. None of the three groups seems small enough to be treated as white noise in the empirical model. Figures 5 and 6 depict the spatial distribution of housing price and neighborhood composition in these two metropolitan areas. Figure 5. Spatial distribution of housing price and neighborhood composition in San Jose (CA) MSA In the South Bay, the majority of Asians and a significant portion of Hispanics live in San Jose city proper. Many of them reside on the east side of the city while the west side is predominantly white. Housing prices are generally higher near the central city. Within San Jose city proper, housing prices are significantly higher on the west side with mostly white residents. 23

24 Figure 6. Spatial distribution of housing price and neighborhood composition in San Francisco-Oakland MSA The North Bay is where most of the black population in the Bay Area resides, particularly in the Oakland vicinity on the east side of the bay where housing prices are generally lower than the rest of the metropolitan area. Small pockets of Hispanics and Asians can also be found in Oakland, but larger portions of these two groups reside on the San Francisco Peninsula. The 24

25 suburban areas outside the cities of San Francisco and Oakland are predominantly white, with small percentages of blacks, Hispanics and Asians. The block groups near the city of San Francisco have the highest housing prices while those near the city of Oakland have some of the lowest housing prices. Table 4 provides some summary statistics of the housing and neighborhood characteristics for each of the metropolitan areas in the study. Table 4. Summary statistics Block Group Average Columbus Atlanta San San San Jose Antonio Francisco Housing Price $115,602 $140,760 $74,262 $468,496 $368,367 Housing Price Index $17,911 $21,379 $12,752 $79,157 $64,450 #Rooms #Bedrooms Age of Structure (year) %Senior Householder 18.3% 15.2% 22.6% 16.8% 19.8% %Married Couple 49.3% 51.6% 52.5% 58.4% 48.9% %Children Present 32.4% 35.4% 36.5% 37.0% 31.3% Household Income $45,579 $51,946 $36,971 $79,183 $65,380 %Higher Education 26.5% 29.0% 18.5% 40.6% 38.4% Commute Time (minute) Distance to CBD (mile) %Foreign Born 4.4% 9.2% 10.9% 31.5% 26.5% %Do not speak English at Home 7.1% 12.2% 42.6% 16.6% 34.9% 7. Estimation Results As I illustrated in Section 4, I will start with the two-equation empirical model (10)-(11) to analyze the relationship between the housing price and the neighborhood composition in the 25