Hedonic Estimates of Neighborhood Ethnic Preferences

Abstract

This article uses a new hedonic technique to examine households’ ethnic preferences and help assessors estimate the impact of neighborhood ethnicity on housing prices. A hedonic function, which relates housing and neighborhood characteristics to house values, is the envelope of households’ bids for these characteristics. This article derives this envelope by combining theories about household sorting across neighborhoods with constant-elasticity demand functions for neighborhood characteristics and housing. Estimates for the Cleveland area in 2000 find that some households prefer neighborhoods without black or Hispanic residents, whereas others prefer largely black or Hispanic neighborhoods, and that house values reflect ethnic preferences.

Keywords

hedonics ethnicity prejudice

Households leave clues about their preferences in their bids for housing. This article uses a new technique to explore clues of this type concerning neighborhood ethnicity. Scholars have long been interested in the impact of neighborhood ethnicity on house values because this impact could reflect prejudice, discrimination, or disparities in current income and wealth caused by past oppression.¹ The technique employed here, taken from Yinger (2013), extracts the range of preferences for neighborhood ethnicity from a house-value regression. This technique also informs housing appraisal and property tax assessment. Ethnicity can have a substantial impact on property values, so accurate assessments require methods to estimate this impact.

This technique is applied to house sales in the Cleveland area in 2000. This area is an excellent setting for this study because it has large black and Hispanic populations, a history as one of the nation’s most segregated areas, and relatively rapid decline in segregation (particularly black–white segregation) from 1980 to 2000 (Iceland and Weinberg 2002). Most neighborhoods in the area are predominantly white, non-Hispanic, but some neighborhoods have a high concentration of black households. Few neighborhoods are more than two-thirds Hispanic, and only five neighborhoods have shares of both blacks and Hispanics above one-quarter. The average neighborhood is 19.9 percent black and 3.8 percent Hispanic.

The estimations indicate that neighborhood ethnicity has a large impact on property values and that ethnic preferences vary widely. Some households have a strong preference for neighborhoods without any black or Hispanic residents whereas others prefer either a largely black or a largely Hispanic neighborhood. Housing discrimination does not appear to influence housing prices in the Cleveland area. Finally, a preference for nonminority neighbors tends to increase with income and with factors associated with better schools.

Why Might Ethnicity Affect Housing Prices?

The literature, reviewed in Zabel (2008), identifies four principal reasons why neighborhood ethnicity influences housing prices. First, many people are prejudiced against members of one ethnic group or another. In the United States, surveys indicate that prejudice has declined over time, but many people in every major ethnic group still express prejudice against people in other ethnic groups. See, for example, Charles (2006) and Krysan et al. (2009). Using video portraits of various neighborhoods and random assignment of the race of the actors posing as residents, Krysan et al. (2009) found that whites and blacks care about the race of their neighbors, not just about neighborhood quality. “More specifically, for whites living in metropolitan Chicago and Detroit, neighborhoods portrayed as having only black residents were viewed less favorably than identical neighborhoods with either only white residents or a mix of white and black residents” (p. 548). Black respondents also cared about neighborhood racial composition, but

[w]hen neighborhoods had identical observable social class characteristics, it was the all-white neighborhood that was evaluated as least desirable by African-Americans. The evaluations for the racially mixed and the all-black neighborhoods were generally indistinguishable…, and both were rated more highly than the white neighborhood. (p. 550)

Prejudice leads many households to prefer, and therefore to bid more for housing, in neighborhoods where members of their own ethnic group are concentrated than elsewhere. People also might bid more for housing where their own ethnic group is concentrated because they expect better access to ethnic restaurants, certain places of worship, or other organizations. The survey evidence also demonstrates, however, that ethnic attitudes vary across households and that some households prefer integration. Moreover, Ihlanfeldt and Scafidi (2004) show that prejudice and integration are simultaneously determined, with weaker prejudice for people who have experienced integration, all else equal. Thus, simply including ethnic composition in a hedonic regression is not satisfactory, because it does not allow variation in attitudes.

One common practice (see Zabel 2008) is to divide an urban area into regions based on ethnic composition and then to estimate a separate relationship between ethnic composition and housing prices in each region, assuming common within-region preferences. The trouble is that the selected regions may not accurately identify differences in the underlying preferences.² The method proposed in the following makes it possible to estimate the range in prejudicial attitudes without making any assumptions about the sorting that results from attitudinal variation.

The second link between neighborhood ethnicity and house values reflects our nation’s history. Because of past discrimination and the resulting disparities in wealth and other factors that influence housing choices, historically disadvantaged minority groups tend to cluster in neighborhoods with poor amenities, even controlling for income (Deng, Ross, and Wachter 2003). This type of clustering may be magnified by housing market institutions. Ondrich, Ross, and Yinger (2003) find that real estate brokers steer blacks toward neighborhoods with low average house values or high average house ages compared to the neighborhoods shown to equally qualified white customers. Without extensive controls for neighborhood characteristics, therefore, a negative impact of minority concentration on housing prices may be overstated.³

To address this issue, the regressions in this article include many neighborhood characteristics, as well as a variable for houses located in Cleveland’s black “ghetto,” defined as a census tract with more than 80 percent black residents clustered with other tracts that have a similar concentration. As shown in figure 1, two areas in eastern Cleveland and neighboring suburbs meet this definition. About 60 percent of the majority-black neighborhoods are located in this ghetto. These areas are direct descendants of the ghetto that developed in the years after the World War I when tens of thousands of blacks migrated to Cleveland from the South. Indeed, between 1910 and 1970, Cleveland’s black population grew by more than 300,000 people and most of these people settled on Cleveland’s east side (Cutler, Glaeser, and Vigdor 1999). Cleveland has no comparable areas of Hispanic concentration. Figure 1 also highlights the correlation between neighborhood characteristics and ethnicity by plotting the locations with both property and violent crime above the 95th percentile for the Cleveland area (and indicating neighborhoods within one mile of the center of these locations). These crime “hot spots” overlap with the black ghetto on the city’s east side but also can be found on the city’s largely white west side.

Figure 1.

The black ghetto and crime hot spots in Cleveland, 2000.

The third possibility is that households in certain ethnic groups may face discrimination in obtaining housing or mortgages. Recent housing audit studies find evidence of continuing discrimination against blacks and Hispanics (Choi, Ondrich, and Yinger 2005; Ross and Turner 2005; Zhao, Ondrich, and Yinger 2006; Ihlanfeldt and Mayock 2009; Hanson and Hawley 2011; Turner et al. 2013). Although housing discrimination has declined over time, it is still statistically significant and may have a large impact in some places. Definitive evidence about discrimination in mortgage markets is not available, but it may exist, as well (Ross and Yinger 2002; Ross et al. 2008). By limiting minority access to housing in some locations through steering, withholding information, or denial, discrimination may drive up the price of housing where those minority groups tend to live. This type of impact was dramatic in the past. “In 1918,” Cutler, Glaeser, and Vigdor (1999, 491) report, “the Cleveland Chamber of Commerce estimated that blacks paid 65 percent more than whites for equivalent housing.”⁴ The “ghetto” variable discussed earlier tests whether this impact lingered in 2000.

The fourth link between neighborhood ethnicity and housing prices arises through expectations. Many scholars have found that housing prices reflect anticipated changes in neighborhood ethnic composition (Zabel 2008). A white neighborhood into which blacks are starting to or expected to move may experience a temporary decline in housing prices, for example, as prejudiced whites flee.⁵ I test for this possibility by including a variable to indicate neighborhoods that are near Cleveland’s black ghetto.

Deriving the Ethnicity Envelope

To estimate the impact of neighborhood ethnicity on housing prices, this article draws on Yinger (2013), who brings together the standard hedonic model (Rosen 1974) with well-known theories of local public finance (reviewed in Ross and Yinger 1999). This new approach to hedonics sheds light on the demand for neighborhood ethnicity and on the way ethnic preferences affect household sorting across neighborhoods. In addition, new analysis in this article shows that information about the distribution of attitudes toward neighborhood ethnicity can be extracted from simple or complex hedonic regressions.

The Rosen framework for a multi-attribute commodity, such as housing, indicates that each type of household has a family of bid functions for each attribute. Each bid function describes price-attribute combinations that yield a given level of utility. The observed market price function, or hedonic, is the envelope of the underlying bid functions. In other words, the envelope consists of the winning bids at each value for the attribute.⁶ The theory of local public finance applies this logic to public services and neighborhood amenities. Households’ bids for housing in a given location depend on the quality of the public services and neighborhood amenities there. Moreover, different household types sort across locations according to the slopes of their bid functions. One theorem (called the sorting theorem in this article) is that households with steeper bid functions, that is, with a greater marginal willingness to pay (MWTP) for a particular amenity, win the competition for the locations where the amenity is higher.

This conceptual literature is accompanied by an empirical literature on “hedonic regressions.” Some of this literature focuses on the hedonic envelope. Many studies explore the impact of school quality on house values, for example (Nguyen-Hoang and Yinger 2011). Other studies follow a recommendation in Rosen by estimating the envelope as a first step and then estimating a demand function for a given housing attribute as a second step. This two-step procedure relies on the fact that each point on the envelope is tangent with an underlying bid function; that is, each household sets its own MWTP for a housing attribute equal to the “implicit price” indicated by the slope of the hedonic. The second-step demand function for a sample of households can therefore be specified as the amount of the attribute as a function of the implicit price, household income, and other demand traits. With a nonlinear hedonic, a household simultaneously chooses the attribute and its implicit price. This leads to an endogeneity problem in the second-step regression that has proven to be difficult to solve. See Taylor (2008).

Most studies of attribute demand (a) estimate the first step with a general form, such as a Box-Cox, (b) use the derivatives of that form as the implicit prices, and (c) estimate the second-step demand equations with a simple specification, such as a double-log.⁷ As shown by Yinger (2013), however, the forms used in the first and second steps are sometimes inconsistent.

Yinger (2013) derives and estimates the hedonic envelope based on assumptions about household preferences and the sorting equilibrium. This approach (a) allows for a general treatment of household heterogeneity, (b) obtains demand elasticities from the first-step regression thereby avoiding the endogeneity problem in the Rosen two-step procedure, (c) eliminates inconsistency between the forms of the envelope and the demand equations, and (d) allows for the possibility that an amenity has a positive value for some households and a negative value for others. The last point is particularly important in studying neighborhood ethnicity.

The first main assumption in the Yinger (2013) approach is that the underlying demand functions for both the amenity, A, and housing services, H, have a constant elasticity form. The term underlying is key here, because these demand functions are not directly observed. The amenity demand function shows how much A a household would demand if it faced price W:

A = K_{A} N^{δ} Y^{θ} W^{μ},

where K_A is a constant, Y is income, and N is a vector of preference and other variables that influence the demand for A.⁸ The demand function for housing is

H = K_{H} M^{ρ} Y^{γ} (P {A} (1 + τ^{*}))^{ν} = K_{H} M^{ρ} Y^{γ} {(\hat{P} {A})}^{ν},

where K_H is a constant, M is a set of variables that influence housing demand, and P{A}, the price of H, is a function of A. The first version of equation (2) includes property taxes. A household’s property tax payment is τ multiplied by its house value, V = PH/r, where r is a discount rate; to account for property taxes, the price per unit of H must be multiplied by (1+ τ/r) = (1+ τ*). Because property taxes are not the focus here, the following analysis is based on the second version with before-tax price,

\hat{P}

, not after-tax price, P. Demand functions with these forms can be derived from a model of “incomplete” demand, in which one set of commodities (Z) is not observed but affects the observed commodities (A and H) through a price index, which appears in K_A and K_H (LaFrance 1986).

In the standard local public finance model (Ross and Yinger 1999), households maximize utility over a public service or amenity, A, housing services, H, and a composite good, subject to a budget constraint in which housing cost is P{A}H. The condition for locational equilibrium is that household are compensated for a change in A through a change in P; more specifically, P′{A} = MB_A/H, where MB_A is inverse demand function for A. With the forms in equations (1) and (2), the solution to this differential equation, which is the bid function for a single household type, is

\hat{P} {A} = {((1 + ν) (C + (\frac{ψ μ}{1 + μ}) A^{(1 + μ) / μ}))}^{1 / (1 + ν)},

where C is a constant of integration and

ψ = {({(K_{A} N^{δ})}^{1 / μ} K_{H} M^{ρ} Y^{(θ / μ) + γ})}^{- 1} .

One might think that this system of bid functions could be estimated by introducing interactions between the demand variables, such as Y, and the amenity, A. In fact, however, the housing prices, amenities, and demand traits one observes at a given location are simultaneous outcomes of the process that sorts different types of households into different locations. Any attempt to estimate this system of bid functions, therefore, is subject to severe endogeneity bias.

A key feature of equation (3) is that ψ provides a comprehensive measure of household heterogeneity that is, ψ contains all the information that identifies the relative slope of the bid function for a given household type. At a point where the bid functions of two household types cross, the two types share values for A and $\hat{P} {A}$ , so values of ψ, which obviously can differ across types, determine which type has the steeper bid function. According to the sorting theorem, the type with the steeper bid function (i.e., the higher value of ψ) will win the competition for housing in the location with the higher value of A. Thus, the equilibrium sorting outcome can be expressed by writing A as a monotonically increasing function of ψ.

The form of this equilibrium depends on the distributions of ψ and A and on the way these two variables are matched through sorting. Yinger focuses on one-to-one matching, which arises when each household type, identified by a value of ψ, has a unique value of A. He shows that if the distribution of A can be transformed to have the same distribution as ψ (or vice versa), then the form of the sorting equilibrium depends only on the nature of the transformation, not on the distributions themselves. Suppose, for example, that both ψ and A have normal distributions with different means and standard deviations. Because a linear transformation can convert a normal distribution with one set of parameters into a normal distribution with any other set of parameters, the sorting equilibrium in this case is A as a linear function of ψ (or vice versa). To capture a range of underlying distributions, Yinger specifies the equilibrium using the following generalization of a linear equation with parameters to be estimated:

A {ψ} = (σ_{1} + σ_{2} ψ)^{σ_{3}} .

Finally, Yinger combines equations (3), (5), and the definition of an envelope to derive the hedonic:

{({\hat{P}}^{E})}^{(λ_{1})} = C_{0}^{'} - \frac{σ_{1}}{σ_{2}} A^{(λ_{2})} + \frac{1}{σ_{2}} A^{(λ_{3})},

where

λ_{1} = 1 + ν; λ_{2} = (1 + μ) / μ; λ_{3} = λ_{2} + 1 / σ_{3}; X^{(λ)} = (X^{λ} - 1) / λ i f λ \neq 0; X^{(λ)} = ln {X}

if λ = 0; and the “E” superscript stands for “envelope.” These terms in equation (6) are examples of the Box-Cox transformation. A regression using this (nonlinear) form yields estimates of μ and the σs.

Equation (6) has two key implications. First, most functional forms in the literature are special cases of equation (6). The left-hand side reduces to $ln {{\hat{P}}^{E}}$ when ν = −1, for example, and the right-hand side reduces to a quadratic form when μ = −∞ and σ₃ = 1. As shown in the following, this quadratic form provides a simple way to study attitudes toward neighborhood ethnicity. Second, according to equation (5), an equilibrium relationship between A and ψ does not exist (so the sorting theorem does not hold) unless 0 < σ₃ < ∞. With the assumptions in this article, a hedonic specification without a second term (the term that includes σ₃) implicitly rules out sorting.

This result can be generalized to many amenities and public services (both identified with an A), and introduced into a standard house value equation, V = PH/r (Yinger 2013). If β is the degree of tax capitalization, X is structural housing characteristics, and ∊ is a random error, then

V = \frac{P^{E} H {X} e^{ϵ}}{r} = \frac{{\hat{P}}^{E} {A_{1}, A_{2}, \dots, A_{n}} H {X} e^{ϵ}}{(r + β τ)} .

This equation can be estimated in log form with H{X} as a multiplicative function.

One striking feature of equation (6) is that a neighborhood trait can be an amenity for some households and a disamenity for others. To be specific, equation (5) implies that a household’s MWTP for A, which is proportional to ψ, is negative if the sorting theorem holds and $(σ_{1})^{σ_{3}} > A$ . This type of household heterogeneity is therefore revealed by estimating the σ parameters. This possibility makes this method ideal for studying preferences for neighborhood ethnicity. The survey evidence makes it clear that some households prefer black neighborhoods, for example, while other households prefer white neighborhoods. The resulting differences in bid functions for share nonblack could lead to some portions of the hedonic envelope that are downward-sloping and other portions that are upward-sloping.

A negatively sloped envelope is not entirely consistent, however, with the theory that leads to equation (6). The nonprice terms in the demand functions, equations (1) and (2), are all positive, but according to equation (4), a negative ψ implies that one of these terms must be negative for some households. A partial solution to this inconsistency is to select the definition of A most likely to minimize the negatively sloped segment of the envelope. Because most households in the Cleveland area are white and non-Hispanic who are likely to prefer whiter neighborhoods, I specify the two neighborhood ethnicity as share nonblack and share non-Hispanic. Estimated envelopes are virtually the same, however, using share black and share Hispanic.

A more complete solution is to define A* as the minimum point on the envelope and then to define the amenity as (A − A*)², where A* is a parameter to be estimated.⁹ With this approach, the amenity, neighborhood ethnicity, is at a minimum when A = A*, and increases when A diverges from A* in either direction. According to the sorting theorem, households with a positive MWTP for share nonblack (or share non-Hispanic) will sort into locations above A*, whereas households with a positive MWTP for share black (or share Hispanic) will locate below A*. If households of both types live in the area, then the resulting hedonic envelope will be U-shaped, with a minimum at A*. This approach, which is consistent with the theory behind equation (6), is implemented subsequently. Unlike previous approaches, this approach is not based on assumptions about the pattern of segregation and it does not assume that all households in an exogenously determined set of neighborhoods have the same ethnic attitudes.

Finally, equations (1) and (2) often perform well in empirical applications, and one could interpret them as approximations to the true demand functions.¹⁰ Under some assumptions, however, they have a more formal interpretation and can be used for welfare calculations. LaFrance (1986) shows that the key assumptions are that either all observed commodities have the same income elasticity or else some of these commodities have a zero income elasticity while others have a unitary income elasticity and that all observed commodities have cross-price elasticities equal to zero. Using the terms from equations (1) and (2), these assumptions are that θ = γ (or each elasticity equals either 0 or 1), W is not an element of M, and $\hat{P}$ is not an element of N. The last two requirements rule out any interactions between amenities in the hedonic regression.

These assumptions are not very restrictive. The income elasticity assumption has no impact on the estimation of the hedonic equation because the term in which it appears, ψ, is integrated out. Moreover, many different values for the income elasticities satisfy the LaFrance conditions. The zero-cross-price elasticity assumption also is not as restrictive, as it would be in a standard application because public services and some amenities (both called amenities for short) are determined at the community level. Thus, nonzero cross-price elasticities can be introduced indirectly whenever a household predicts the level of an amenity that is likely to persist in the long run based on the community traits that help to determine it. In other words, community-level determinants of demand for amenity i can be included in the demand function for amenity j (through the N term) without violating the LaFrance conditions.

This approach is tested subsequently. After estimating the hedonic, I find the associated values for ψ for my two neighborhood ethnicity variables and then estimate the quasi-demand function, equation (4). One hypothesis is that the willingness of prejudiced whites to pay for a largely white neighborhood depends on the quality of neighborhood schools, which is determined by both supply and demand factors. Many studies have shown that a higher share of children from poor families (measured here by the share of students from families receiving welfare) raises education costs (e.g., Duncombe and Yinger 2005), and several other studies have shown that higher educational costs lower the demand for education (e.g., Duncombe and Yinger 1998). Many studies (including the one just cited) have also found that the demand for education depends on the tax price, which is a voter’s share of the increment in property taxes that is needed for an increment in educational quality and is measured here by the residential share of property value. These two variables can be used to test the hypotheses that predictions of future school quality influence the demand for neighborhood ethnicity, without introducing a direct interaction between ethnicity and school quality into the hedonic regression.¹¹

An alternative approach to estimating neighborhood ethnic preferences is in Bayer, Ferreira, and McMillan (2007).¹² Using data from the Oakland–San Francisco area, they estimate a multinomial logit model in which household i selects the house, h, that maximizes $U_{h}^{i} = α_{X}^{i} X_{h} - α_{V}^{i} V_{h} + ϵ_{h}^{i}$ , where U is indirect utility, X is housing traits and amenities (including ethnicity), V is house value, and ∊ is a random error.¹³ They allow the αs to vary with household traits such as ethnicity and income. They find that white households place a negative value on an increase in a neighborhood’s percentage black, but that this sign reverses for black households.

The Bayer, Ferreira, and McMillan (2007) approach has different strengths and weaknesses than the method in this article. First, their model makes it possible to test the hypothesis that black and white households have different preferences for neighborhood ethnicity. I cannot test this hypothesis directly, but the hedonic I estimate allows for this possibility and, unlike Bayer, Ferreira, and McMillan, it does not restrict variation in preferences for neighborhood ethnicity within each ethnic group.

Second, the two approaches make different assumptions about amenity demand. A bid function is defined as the amount a household will pay for housing at different levels of an amenity and a given utility. The bid function associated with the preceding utility function can be found by holding U constant and solving for V. The resulting bid function for, say, X,¹ is linear, because U and the other X’s are held constant. According to equation (6), a linear bid function assumes that the price elasticity of demand for the amenity equals ∞, which corresponds to a horizontal demand curve. No such restriction is imposed here.

Estimation Strategy

My strategy is to first estimate equation (7) in log-linear form for a sample of house sales with housing traits and neighborhood fixed effects on the right-hand side. A neighborhood is defined as a census block group (CBG), and all sales in block groups with at least two sales are included. The error term is assumed to be independent and identically distributed (IID). The coefficient of each fixed effect measures neighborhood quality from all sources, observed and unobserved (Deng, Ross, and Wachter 2003).

The second stage uses these coefficients as the dependent variable to estimate equation (6), expanded to include many amenities and an error term, for the sample of CBGs. An extensive set of public service, tax, and neighborhood amenity variables are included as explanatory variables. The dependent variable in this second stage is $ln {{\hat{P}}^{E}}$ which, according to equation (6), requires the assumption that ν = −1. I make this assumption to start and then test it. As is well known, the errors in this second stage are heteroscedastic (Goldhaber and Brewer 1997). This two-stage estimation of the hedonic facilitates the consideration of functional forms for the bid-function envelope.¹⁴ The initial and “split” specifications for the ethnicity variables, for example, can each be estimated with no need to reconsider structural housing characteristics.

The data for this study are built on all the house sales in the Cleveland area in 2000. The basic data set, which was collected by David Brasington (see Brasington 2007; Brasington and Haurin 2006), includes sales price, structural housing characteristics, house location, census block traits, school district traits, crime rates, and air quality, among other things. I supplemented this data set with additional neighborhood amenities. See tables A1 and A2.

Results

The first-stage regression was estimated using the Stata “areg” command with 22,800 observations (= house sales) and 1,665 neighborhood fixed effects. The explanatory variables are housing characteristics and within-neighborhood locational differences. Almost all the variables are statistically significant with the expected signs. The R² is .793. See table A1.

The second-stage regression is carried out using the 1,665 CBGs as observations and the fixed effects from the first stage as the dependent variable. Robust standard errors are used to account for heteroscedasticity.¹⁵ A few key results are discussed here, all explanatory variables are listed in table A2, and additional results are in Yinger (2013). School districts with the highest high school passing rate on state tests have housing prices that are 30.0 percent above the price of those with a very low rate. Houses in tracts with high property and violent crime sell for 8.7 percent less than houses in tracts with low crime of both types. Moreover, houses located within one-half mile of a crime “hot spot” (a tract with property and violent crime in the 95th percentile as in figure 2), sell for 20.3 percent less than houses far from such a location.

Figure 2.

Hedonic envelopes for neighborhood ethnicity.

Initial results for the neighborhood ethnicity variables are presented in table 1. The three columns refer to regressions with linear, quadratic, and cubic specifications, respectively, for the two ethnicity variables. The other variables are listed in the appendix. The first column indicates that for both ethnicity measures the estimated coefficient is positive, indicating that, on average, housing prices increase with percentage nonminority. As explained earlier, however, this specification is inconsistent with both the survey evidence and sorting theory. The second column presents results for a quadratic specification, which, as shown earlier, corresponds to an infinite price elasticity of amenity demand. This hedonic is U-shaped for both ethnicity measures, although the coefficients are not significant for share non-Hispanic. As illustrated in figure 2, the minimum points on the hedonics are at 25.8 percent for share nonblack and 25.3 percent for share non-Hispanic. In the case of share nonblack, the hedonic has a negative slope for the 219 CBGs with at least 75 percent black. All of the CBGs in the sample have a non-Hispanic share above 25.3 percent, however, so this hedonic has a positive slope everywhere. A Wald test indicates that adding cubic terms is warranted, but none of the individual cubic terms in column three is significant. Adding the cubic term has little impact on the shape of the hedonic for share nonblack but raises the minimum for share non-Hispanic to 50.0 percent.¹⁶ The slope of this hedonic is negative for the 14 CBGs that are more than half-Hispanic. See figure 2, panel B. In short, these results support the view that some households prefer neighborhoods with high minority concentrations, whereas others prefer neighborhoods that are mostly nonminority.

Table 1.

Results for Polynomial Envelope Specifications.

Variable	Linear	Quadratic	Cubic
Share nonblack in CBG
Linear term	0.2633*** (0.0291)	−0.2120* (0.1247)	−0.1795 (0.2724)
Squared term	—	0.4114*** (0.1031)	0.3615 (0.5174)
Cubed term			0.0188 (0.2959)
Share non-Hispanic in CBG
Linear term	0.4849*** (0.0656)	−0.2440 (0.4306)	−3.9180 (2.7120)
Squared term	—	0.4832* (0.2871)	5.6436 (3.7788)
Cubed term			−2.3011 (1.6829)
Number of observations	1,665	1,665	1,665
R ²	.7046	.7156	.7197
SSE	34.7383	33.4405	32.9601
F test for significant compared to previous column
Wald statistic	N.A.	6.890	2.780
Significance level	N.A.	0.000	0.007

Note: The dependent variable is log{P} in the census block group (CBG). Parentheses contain t-statistics based on robust standard errors (using the hc3 option in Stata). *, **, and *** indicate statistical significance at the 10, 5, and 1 percent levels, respectively. The regressions also include the variables in table A2. The quadratic and cubic specifications apply to the school variables. The degrees of freedom for the F tests are 7 and 1,592 in the second column and 7 and 1,585 in the third.

Table 2 presents results for the parameters in equation (6), namely, the σs, which describe the sorting equilibrium, and µ, the price elasticity of amenity demand. The first column treats share nonminority as the amenity. Share minority yields virtually identical results. Except for μ for share nonblack, all the estimated coefficients are significant. The positive, significant values for σ₂ support the sorting theorem. As shown in figure 2, the shape of the envelope for share nonblack is about the same as the shape with a quadratic. In the case of share non-Hispanic, this nonlinear envelope has approximately the same minimum as the cubic envelope, but it also has a steeper slope in the CBGs with the lowest observed non-Hispanic shares.

Table 2.

Results for Theoretically Derived Envelopes.

Variable	Nonlinear estimation of equation (6)	Nonlinear estimation of equation (6) with split ethnicity variables	Nonlinear estimation of equation (6) with split ethnicity variables and constraint
Share nonblack in CBG
σ¹	0.2494*** (0.0940)	0.0132** (0.0066)	0.0136 (0.0544)
σ²	1.2571***	3.4246***	2.6556*
	(0.3476)	(1.0927)	(1.4193)
μ	−34.6629 (605.0691)	−0.7578*** (0.1177)	−0.8915* (0.5300)
A^M	N.A.	0.2478*** (0.0135)	0.2554** (0.1193)
Share non-Hispanic in CBG
σ¹	0.5001*** (0.0211)	0.0004 (0.0043)	0.0014 (0.0076)
σ²	0.8544*** (0.2590)	3.260* (1.9070)	3.9924 (3.4529)
μ	−0.3773*** (0.1406)	−0.6632*** (0.1093)	−0.6273*** (0.1558)
A^M	N.A.	0.5067*** (0.0269)	0.5277*** (0.0330)
Number of observations	1,665	1,665	1,665
R ²	.7167	.7188	.7169
SSE	33.3169	33.0632	33.2932

Note: The dependent variable is log{P} in the CBG. The specification, equation (6), is estimated with NLLS assuming σ₃ = 1. Parentheses contain t-statistics based on robust standard errors using the hc3 option in Stata. *, **, and *** indicate statistical significance at the 10,5, and 1 percent levels, respectively. The regressions also include the variables in tables A2. Equation (6) applies to the school variables, without the “split” component.

As explained earlier, this specification is not completely consistent with the theory because it implies that the “amenity,” percentage nonminority, is measured by a positive number for some households and a negative number by others. To address this problem, I estimate a “split” envelope in which the amenity is defined as (A – A*)², where A is the share minority and A* is a parameter to be estimated.¹⁷ To avoid adding still more parameters, the values of σ₁, σ₂, and μ are assumed to be the same on each side of A*. The results appear in the second column of table 2. The estimated values of A*, 24.8 percent for share nonblack and 50.7 percent for share non-Hispanic, are highly significant and are similar to the minimum points obtained with other methods (excluding linear and, for Hispanics, quadratic). The estimated price elasticities, −0.76 for share nonblack and −0.66 for share non-Hispanic, are highly significant.

Although this approach appears promising, it has one flaw, namely, that it yields unreasonable values for the envelope near A*. As shown earlier, an envelope described by equation (6) has a negative slope whenever $A < σ_{1}^{σ_{3}}$ . This is, of course, the property that leads to the U-shape for the envelope estimated in column 1 of table 2. In this case, however, the condition becomes $(A - A *)^{2} < σ_{1}^{σ_{3}}$ , which inevitably holds for values of A close to A*, a positive σ₁, and σ₃ = 1, which is the assumption in these estimations.¹⁸ When such values exist, therefore, this form leads to a W-shaped envelope with a very large peak in the middle. This peak makes no conceptual sense. People with very steep bid functions will win the competition for housing at extreme values of A, not at an intermediate value such as A*.

One possibility is to drop the observations with value of A so close to A* that they have the “wrong” slope. For the regression in the second column of table 2, the number of observations that fall into this category is sixty-three for share nonblack and two for share non-Hispanic. A more compelling approach is to prevent the troubling change in the sign of the envelope slope close to A* by holding the envelope height constant between its minimum points on either side of A*; namely, $A = A * - \sqrt{σ_{1}}$ and $A = A * + \sqrt{σ_{1}}$ . This constraint leads to an envelope with a flat section between these two values of A. This region can be interpreted as an integrated zone within which variations in ethnic composition are perceived to be insignificant. The boundaries of this zone are estimated, but the flatness of the bid function within the zone is imposed by the constraint. The results for this constrained model (in the third column of table 2) are similar in magnitude to those in column 2, except that σ₁ and σ₂ are no longer significant and the price elasticity for share nonblack is now only significant at the 9 percent level. The envelopes implied by these estimates are presented in figure 2. The integrated region extends from 14.1 percent to 37.1 percent nonblack and from 49.3 to 56.2 percent non-Hispanic. Except for the flat sections, the shapes of these envelopes are similar to those based on column 1 and column 2.

Overall, these results provide strong support for the notion that the he-donic envelopes for key types of neighborhood ethnicity are U-shaped. With the constrained, split envelope, the price of housing is 25.1 percent higher at 100 percent white (and 7.5 percent higher at 100 percent black) than in the integrated zone. Compared to the integrated zone for Hispanics, the price of housing is 34.1 percent higher at 100 percent white and 21.0 percent higher at 63.3 percent Hispanic. Precise estimate of all the underlying structural parameters remains elusive, however, and further research on this topic is needed. Despite its theoretical inconsistency, the nonsplit envelope provides a close approximation to the envelope from a model that is theoretically consistent. At the current time, therefore, any of the approaches in table 2, including the simplest, can be used to approximate the shape of this envelope.

As discussed earlier, Rosen (1974) shows that an estimated hedonic price function reveals a household’s MWTP at the level of the attribute it consumes. This logic applies to amenities, so the slope of the hedonic at a given level of an amenity describes the MWTP of the household in the associated neighborhood. Even without estimates of underlying bid functions, therefore, hedonic regressions provide information about preferences for neighborhood ethnicity. First, they indicate how many people live in neighborhoods that attract homebuyers with different types of ethnic preferences. When the slope of the hedonic for share nonblack is positive in a given neighborhood, the people moving into that neighborhood have a positive MWTP for an increase in share nonblack; that is, they prefer a whiter neighborhood. Thus, we can determine the share of people in different ethnic groups who live in neighborhoods that attract people with different ethnic preferences. The results are shown in table 3.

Table 3.

Ethnic Groups and Ethnic Preferences.

Household ethnicity	Share of ethnic group living in CBGs in which the value homebuyers place on an increase in
	Share nonblack	Share non-Hispanic
	Is positive (percentage)
All	89.21	99.27
Black	36.31	99.32
Hispanic	97.17	87.86
White	99.04	99.73
	Is zero (percentage)
All	2.91	0.12
Black	14.17	0.12
Hispanic	1.25	1.72
White	0.77	0.05
	Is negative (percentage)
All	7.88	0.61
Black	49.52	0.56
Hispanic	1.58	10.42
White	0.18	0.22

Note: These calculations are based on the regression in the third column of table 2. They indicate the share of all households living in neighborhoods identified by the sign of the MWTP of homebuyers in that neighborhood.

The first column of table 3 indicates that about half of the black population in the Cleveland area lives in a neighborhood attracting homebuyers who, at the margin, would pay for an increase in the neighborhood’s black share (i.e., a decrease in share nonblack).¹⁹ Another 36.3 percent of the black population lives where the MWTP for more white neighbors is positive. The rest of the black population (14.2 percent) lives in an integrated area where the MWTP for more black (or white) neighbors is constrained to be zero. Similar results arise from the other envelopes in panel A of figure 2; the MWTP is close to zero, for example, in these integrated neighborhoods even with a quadratic specification. This column also indicates that most white and Hispanic households live where homebuyers’ MWTP for black neighbors is negative. The second column of this table describes a similar but weaker pattern for Hispanics. Only 10.4 percent of Hispanics live where the MWTP for Hispanic neighbors is positive.

Second, the results in tables 1 or 2 can be used to determine the most extreme expressions of neighborhood ethnic preferences in the Cleveland area. The Rosen MWTP analysis applies at every observed point on the envelope, including at the extreme values of ethnic composition, where the slopes of the U-shaped envelopes are highest. The highest MWTP for a black neighborhood is therefore revealed by the slope at the left-most point on a hedonic envelope in panel A of figure 2, whereas the highest MWTP for a nonblack neighborhood is revealed by the slope of the right-most point. These slopes indicate the highest MWTP in the current equilibrium, of course, not the highest possible MWTP for households in Cleveland.

The resulting maximum values for MWTP are shown in table 4. The first panel indicates that, regardless of specification, households in all-black neighborhoods would pay about 2 percent more to avoid a 10 percentage point decrease in the black population. Moreover, households in all-white neighborhoods would pay about 6 percent less if they experienced a 10 percentage point increase in the black population. The second panel indicates more variation in the maximum MWTP for a decrease in the Hispanic share; the estimates range from −22.2 percent with the simple nonlinear envelope to −5.4 percent with the split, constrained envelope. In contrast, the estimates of MWTP for the households with the strongest preference for non-Hispanic neighborhoods equal about 5 percent in all three columns.

Table 4.

Percent Change in Bid with 10 Percentage Point Change in Ethnicity.

	Polynomial (percentage)	Nonlinear envelope (percentage)	Split envelope (percentage)
Share nonblack in CBG
Households with strongest preference for black neighborhoods
Impact of move from 100 to 90 percent black	−2.11	−2.41	−1.70
Households with strongest preference for nonblack neighborhoods
Impact of move from 100 to 90 percent nonblack	−6.11	−5.97	−5.43
Share non-Hispanic in CBG
Households with strongest preference for Hispanic neighborhoods
Impact of move from 37 to 27 percent Hispanic	−7.05	−22.20	−4.59
Households with strongest preference for non-Hispanic neighborhoods
Impact of move from 100 to 90 percent non-Hispanic	−4.66	−5.85	−5.08

Note: The entries in this table are the estimated percentage change in housing bid, P, at the lowest and highest values of the neighborhood ethnicity variables. The Polynomial column is based on the quadratic formulation for share nonblack and the cubic formulation for share non-Hispanic.

These models also include the “ghetto” and “near ghetto” variables, which always have small, insignificant coefficients. The results for “ghetto” suggest that neither omitted neighborhood traits nor ongoing housing discrimination affect housing prices, or else the effects of these two factors offset each other. This result is consistent with the rapid decline in segregation in the Cleveland area between 1980 and 2000, which suggests that housing discrimination no longer constrains black households to ghetto locations. This result does not prove, of course, that discrimination no longer exists; instead, it indicates that any remaining discrimination does not have a systematic impact on housing prices. The results for “near ghetto” suggest that anticipated neighborhood change near the ghetto also did not affect house values.

Black buyers might face price discrimination, which would have a larger impact on housing prices in places with a larger black population share. Using data from Florida, Ihlanfeldt and Mayock (2009) find that blacks pay about 1 percent more than the price paid by whites (when buying from whites), all else equal. Hispanics do not face this type of discrimination. However, they also “found no evidence of price discrimination in majority black neighborhoods” (p. 136). Based on these results, the downward sloping portions of the envelopes in figure 2 do not appear to be explained by price discrimination.

Table 5 presents estimates of the quasi-demand function, equation (4), which is analogous to Rosen’s second step. Three hypotheses are tested. The first is that neighborhood ethnicity exhibits “normal” sorting in which higher-income households sort into locations with higher amenities. This hypothesis can be tested using the coefficient of Y in equation (4), which is positive if normal sorting exists (Yinger 2013). A test for normal sorting is direct if it controls for other determinants of sorting and indirect if it leaves out these other determinants so that, to the extent they are correlated with income, their impact on sorting shows up in the Y coefficient. The second hypothesis is that bid functions for neighborhood ethnicity are influenced by variables that predict school quality, namely, the percentage of a school district’s students from families on welfare and the residential share of property value. The third is whether the results of these tests differ in largely nonminority and largely minority neighborhoods.

Table 5.

Tests for “Normal” Sorting and Indirect Attribute Interactions.

	Share nonblack		Share non-Hispanic
	CBGs > 37.1% nonblack	CBGs > 37.1% or < 14.1% nonblack	CBGs > 56.2% non-Hispanic	CBGs > 56.2% or < 49.3% non-Hispanic
Indirect test
Income	0.3820***	0.3412***	0.2890***	0.2918***
(Standard Error)	(0.0528)	(0.0564)	(0.0397)	(0.0395)
Income × Largely minority		−0.2430***		−0.3760***
(Standard Error)		(0.0055)		(0.0140)
R²	.0296	.6070	.0334	.3273
Observations	1,415	1,602	1,649	1,662
Direct test
Income	0.4159*	0.3652***	−0.0233	−0.0266
(Standard error)	(0.8059)	(0.0977)	(0.0583)	(0.0585)
Income × Largely minority		−0.3611***		0.1421
(Standard Error)		(0.0470)		(4.0956)
Welfare in school district	−0.0024*	−0.0030**	−0.0058***	−0.0058***
(Standard error)	(0.0013)	(0.0012)	(0.0011)	(0.0011)
Welfare × Largely minority		0.0180***		−0.0531
(Standard Error)		(0.0055)		(0.3383)
Percent residential in SD	−0.0025	−0.0029	−0.0049***	−0.0048***
(Standard error)	(0.0018)	(0.0018)	(0.0012)	(0.0012)
Resid. × Largely minority		0.0143**		−0.0127
(Standard Error)		(0.0056)		(0.3824)
R²	.2109	.6704	.4349	.5963
Observations	1,415	1,602	1,649	1,662

Note: Tests are conducted with ordinary least squares (OLS) using robust standard errors from the hc3 option in Stata. The dependent variable in all cases is log{ψ} based on column 3 of table 2. Income is the log of median owner income in the CBG. In addition to the variables listed previously, direct tests control for the CBG's percent of households that have children, are headed by a married couple, speak English at home, are Asian, are headed by an elderly person; five education categories for adults (all for the CBG), and the share of households in the tract that moved during the last year. Most of these variables are significant at the 5 percent level. Results are similar using other sets of controls or the results in the other columns of table 2. *, **, and *** indicate statistical significance at the 10, 5, and 1 percent level, respectively.

The results in the first and third columns of table 5 refer only to upward-sloping portions of the constrained split envelopes in figure 2. The results in the second and third columns include all observations with a positive or a negative slope in these figures, with interactions to determine whether the income, percent welfare, or percent residential variables have different coefficients in largely minority or largely white neighborhoods.²⁰ In terms of the first hypothesis, table 5 indicates that neighborhood ethnicity is characterized by normal sorting, but only in neighborhoods that are not predominantly minority.²¹ One exception is that the direct test for Hispanics finds no evidence of normal sorting in any neighborhoods. Column 3 supports the second hypothesis for share non-Hispanic; the MWTP for share non-Hispanic goes down when the factors that predict poorer schools (more welfare and more residential property) go up. Column 1 does not support a similar conclusion for blacks. In columns 2 and 4, however, this welfare result is supported in largely nonblack and largely non-Hispanic neighborhoods. The results in column 2 also indicate a sign reversal in largely black neighborhoods; that is, the predictors of poor schools lead to a higher preference for largely black school districts. This result likely reflects unique events in the two lowest-performing school districts: households had access to vouchers and charter schools in Cleveland, and East Cleveland was given a huge state grant for capital improvements (Yinger 2013).

Conclusion

This article uses a new method to study the impact of neighborhood ethnicity on housing prices. This method makes it possible to estimate the range in preferences concerning neighborhood ethnicity in an urban area and the impact of those preferences on both housing prices and household sorting across neighborhoods. An application to the Cleveland area in 2000 indicates that some households prefer largely minority neighborhoods whereas others prefer largely nonminority neighborhoods. The dividing point between these two groups of households in the sorting equilibrium is about 25 percent for share nonblack and about 50 percent for share non-Hispanic. Some households are willing to pay about 2 percent more for housing in a neighborhood that is 100 percent black than in one that is 90 percent black, whereas others are willing to pay about 5 percent more at 100 than at 90 percent white. The regressions in the article find no signs in housing prices of ethnic discrimination, omitted neighborhood variables in ghetto areas, or anticipated ethnic transition, but the tests are not strong enough to rule out any of these phenomena.

The results also indicate that houses in all-white neighborhoods may have housing prices up to one-third higher than houses in integrated neighborhoods, all else equal. Appraisers or assessors who do not account for this possibility are likely to have inaccurate estimates of house values—and to place buyers or taxpayers in integrated neighborhoods at a disadvantage.

The methods proposed here have strengths but need further investigation. The basic estimations provide statistically significant results for the preceding preference patterns for both the black and Hispanic shares of neighborhood population, but they strain some model assumptions. Two more theoretically precise approaches are also explored, both of which support these patterns. Unfortunately, one leads to extreme values for the hedonic envelope for a few observations in integrated neighborhoods and the other yields insignificant coefficients for the sorting parameters. The good news is that the first and third of these approaches lead to envelopes with very similar shapes, so the relatively simple first approach appears to provide a good approximation to the envelope. Further research is needed to identify a fourth method with theoretical rigor that yields significant estimates of all the model’s structural parameters.

Footnotes

Appendix

Table A2.

Additional Explanatory Variables in Second-stage Regression.

School and tax variables	Amenity variables
Relative elementary score	Population of city (if CBG in a city)
High school passing rate	Distance to air pollution cluster
Elementary value added	Distance to hazardous waste site
Share minority teachers	Distance to Lake Erie
Dummy for Cle. & E. Cle. school districts	Location in “Snow Belt”
Relative elementary score in Cle. & E. Cle	CBG in the black ghetto
Distance to nearest elementary school	CBG within 5 miles of ghetto center
Distance to nearest private school	Distance to Cleveland Airport
School district income tax rate	No. of parks, golf courses, rivers, or lakes within ¼ mile of CBG
School district effective property tax rate	CBG within ¼ mile of freeway
Effective city property tax rate beyond school tax	CBG within ¼ mile of railroad
Exemption rate for city property tax	CBG within 1 mile of shopping center
Dummy: No A/V data	CBG within 1 mile of hospital
CBG not in a city	CBG within 1 mile of small airport
Worksite and crime variables	CBG within 1 mile of regional park
Job-weighted distance to worksites	CBG within an historic district
Low property, high violent crime	CBG within ½ mile of elderly public housing
High property, low violent crime	CBG within ½ mile of small family public housing
High property and violent crime	CBG within ½ mile of large family public housing (>200 units)
CBG within ½ mile of crime hot spot	Fixed effects for 5 worksites
CBG ½ to 1 mile from crime hot spot	Fixed effects for counties
CBG 1 to 2 miles from crime hot spot
CBG 2 to 5 miles from crime hot spot
CBG receives police from a village
CBG receives police from a township
CBG receives police from a county

Note: These variables are included, along with measures of neighborhood ethnicity in table 1 or 2, in the second-stage regressions with the first-stage CBG fixed effects as the dependent variable. Detailed definitions, complete specifications, descriptive statistics, and estimation results for these variables can be found in Yinger (2013).

Acknowledgment

The author is grateful for helpful comments from Jan Ondrich, two anonymous referees, and participants in the Maxwell Research Symposium, “Housing Issues in the 21st Century,” Syracuse University, September 21–22, 2012.

Author’s Note

The data for this project and a data-collection appendix are available on the author’s web page ().

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

References

Bajari

Patrick

Kahn

Matthew E.

. 2005. “Estimating Housing Demand with an Application to Explaining Racial Segregation in Cities.” Journal of Business and Economic Statistics 23:20–33.

Bayer

Patrick

Ferreira

Fernando

McMillan

Robert

. 2007. “A Unified Framework for Measuring Preferences for Schools and Neighborhoods.” The Journal of Political Economy 115:558–638.

Brasington

David M.

2007. “Private Schools and the Willingness to Pay for Public Schooling.” Education Finance and Policy 2:152–74.

Brasington

David M.

Haurin

Donald R.

. 2006. “Educational Outcomes and House Values: A Test of the Value-added Approach.” Journal of Regional Science 46:245–68.

Charles

Camille Zubrinsky

. 2006. Won’t You be my Neighbor? Race, Class, and Residence in Los Angeles. New York: Russell Sage Foundation.

Choi

Seok Joon

Ondrich

Jan

Yinger

John

. 2005. “Do Rental Agents Discriminate against Minority Customers? Evidence from the 2000 Housing Discrimination Study.” Journal of Housing Economics 14:1–26.

Cutler

David M.

Glaeser

Edward L.

Vigdor

Jacob L.

. 1999. “The Rise and Decline of the American Ghetto.” The Journal of Political Economy 107:455–506.

Davidson

Russell

MacKinnon

James G.

. 2004. Econometric Theory and Methods. New York: Oxford University Press.

Deng

Yongheng

Ross

Stephen L.

Wachter

Susan M.

. 2003. “Racial Differences in Homeownership: The Effect of Residential Location.” Regional Science and Urban Economics 33:517–56.

10.

Duncombe

William D.

Yinger

John

. 1998. “School Finance Reform: Aid Formulas and Equity Objectives.” National Tax Journal 51:239–62.

11.

Duncombe

William D.

Yinger

John

. 2005. “How Much More does a Disadvantaged Student Cost?” Economics of Education Review 24:513–32.

12.

Epple

Dennis

Romer

Thomas

Sieg

Holger

. 2000. “Interjurisdictional Sorting and Majority Rule: An Empirical Analysis.” Econometrica 69:1437–65.

13.

Epple

Dennis

Sieg

Holger

. 1999. “Estimating Equilibrium Models of Local Jurisdictions.” The Journal of Political Economy 107:645–81.

14.

Goldhaber

Dan D.

Brewer

Dominic J.

. 1997. “Why Don't Schools and Teachers Seem to Matter? Assessing the Impact of Unobservables on Educational Productivity.” The Journal of Human Resources 32:505–23.

15.

Hanson

Andrew

Hawley

Zackary

. 2011. “Do Landlords Discriminate in the Rental Housing Market? Evidence from an Internet Field Experiment in U.S. Cities.” Journal of Urban Economics 70:99–114.

16.

Iceland

John

Weinberg

Daniel H.

Erika

Steinmetz

. 2002. Racial and Ethnic Residential Segregation in the United States: 1980-2000. Census 2000 Special Report CENSR-3. Washington, DC: U. S. Bureau of the Census.

17.

Ihlanfeldt

Keith R.

Mayock

Tom

. 2009. “Price Discrimination in the Housing Market.” Journal of Urban Economics 66:125–40.

18.

Ihlanfeldt

Keith R.

Scafidi

Benjamin

. 2004. “Whites’ Neighbourhood Racial Preferences and Neighbourhood Racial Composition in the United States: Evidence from the Multi-city Study of Urban Inequality.” Housing Studies 19:325–59.

19.

Krysan

Maria

Couper

Mick P.

Farley

Reynolds

Forman

Tyrone A.

. 2009. “Does Race Matter in Neighborhood Preferences? Results from a Video Experiment.” American Journal of Sociology 115:527–59.

20.

LaFrance

Jeffrey T.

1986. “The Structure of Constant Elasticity Demand Models.” American Journal of Agricultural Economics 68:543–52.

21.

Nguyen-Hoang

Phuong

Yinger

John

. 2011. “The Capitalization of School Quality into House Values: A Review.” Journal of Housing Economics 20:30–48.

22.

Ondrich

Jan

Ross

Stephen L.

Yinger

John

. 2003. “Now You See It, Now You Don’t: Why Do Real Estate Agents Withhold Available Houses from Black Customers.” The Review of Economics and Statistics 85:854–73.

23.

Rosen

Sherwin

. 1974. “Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition.” The Journal of Political Economy 82:34–55.

24.

Ross

Stephen L.

Turner

Margery A.

. 2005. “Housing Discrimination in Metropolitan America: Explaining Changes between 1989 and 2000.” Social Problems 52:152–80.

25.

Ross

Stephen L.

Turner

Margery A.

Godfrey

Erin

Smith

Robin R.

. 2008. “Mortgage Lending in Chicago and Los Angeles: A Paired Testing Study of the Pre-application Process.” Journal of Urban Economics 63:902–19.

26.

Ross

Stephen L.

Yinger

John

. 1999. “Sorting and Voting: A Review of the Literature on Urban Public Finance.” In Handbook of Urban and Regional Economics (Volume 3), Applied Urban Economics, edited by Cheshire

Paul

Mills

Edwin S.

, 2001–60. Amsterdam, The Netherlands: North-Holland.

27.

Ross

Stephen L.

Yinger

John

. 2002. The Color of Credit: Mortgage Lending Discrimination, Research Methodology, and Fair-lending Enforcement. Cambridge, MA: MIT Press.

28.

Taylor

Laura O.

2008. “Theoretical Foundations and Empirical Developments in Hedonic Modeling.” In Hedonic Methods in Housing Markets: Pricing Environmental Amenities and Segregation, edited by Baranzini

Andrea

Ramirez

José

Schaerer

Caroline

Thalmann

Philippe

, 15–59. New York: Springer.

29.

Turner

Margery A.

Santos

Rob

Levy

Diane K.

Wissoker

Doug

Aranda

Claudia

Pitingolo

Rob

. 2013. Housing Discrimination against Racial and Ethnic Minorities 2012. Washington, DC: US Department of Housing and Urban Development, Office of Policy Development and Research.

30.

Yinger

John

. 1978. “The Black White Price Differential in Housing: Some Further Evidence.” Land Economics 54:187–206.

31.

Yinger

John

. 1979. “Prejudice and Discrimination in the Urban Housing Market.” In Current Issues in Urban Economics, edited by Mieszkowski

Peter

Straszheim

Mahlon

, 430–68. Baltimore, MD: Johns Hopkins University Press.

32.

Yinger

John

. 1995. Closed Doors, Opportunities Lost: The Continuing Costs of Housing Discrimination. New York: Russell Sage Foundation.

33.

Yinger

John

. 2013. “Implicit Prices and Explicit Demands: Bid Function Envelopes for Public Services and Neighborhood Amenities.” Syracuse University Working Paper, Syracuse, NY.

34.

Zabel

Jeffrey E.

2004. “The Demand for Housing Services.” Journal of Housing Economics 13:16–35.

35.

Zabel

Jeffrey E.

2008. “Using Hedonic Models to Measure Racial Discrimination and Prejudice in the U. S. Housing Market.” In Hedonic Methods in Housing Markets: Pricing Environmental Amenities and Segregation, edited by Baranzini

Andrea

Ramirez

José

Schaerer

Caroline

Thalmann

Philippe

, 177–201. New York: Springer.

36.

Zhao

Ondrich

Jan

Yinger

John

. 2006. “Why Do Real Estate Brokers Continue to Discriminate? Evidence from the 2000 Housing Discrimination Study.” Journal of Urban Economics 59:394–419.