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Ethnic diversity and neighborhood house prices
Ethnic Diversity and Neighborhood House Prices Qiang Li PII: DOI: Reference:
S0166-0462(14)00042-8 doi: 10.1016/j.regsciurbeco.2014.04.007 REGEC 3052
To appear in:
Regional Science and Urban Economics
Received date: Revised date: Accepted date:
21 December 2011 17 April 2014 22 April 2014
Please cite this article as: Li, Qiang, Ethnic Diversity and Neighborhood House Prices, Regional Science and Urban Economics (2014), doi: 10.1016/j.regsciurbeco.2014.04.007
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Ethnic Diversity and Neighborhood House Prices Qiang Li1
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Department of Real Estate, School of Design and Environment, National University of Singapore, 4 Architecture Drive, Singapore 117566
Abstract
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In recent decades, the large inux of immigrants to the U.S. and other developed countries has made cities in these countries more ethnically diverse. In this paper, I aim to understand whether and how ethnic diversity a¤ects communities in these cities. A general equilibrium model is built in which people of many ethnic groups interact in the housing market through both price signals and non-market mechanisms. An endogenous correlation between neighborhood house price and the Her ndahl index of ethnic concentration arises because of social interactions. After addressing the endogeneity issue, I nd that neighborhoods with more homogeneous minority populations command higher prices using a dataset of housing transactions and neighborhood socio-economic characteristics in Vancouver, Canada. This and other ndings support the notion that non-market social interactions inuence peoples preference and behavior. Key words: Ethnic diversity, housing, neighborhood choice
1 Email: [email protected]. This paper is a revision of Chapter 3 of my PhD dissertation submitted to the University of British Columbia. I am indebted to my supervisor Bob Helsley for his encouragement and guidance. My dissertation committee members Keith Head, Sanghoon Lee, and Tsur Somerville provided valuable inputs. The comments by Danny Ben-Shahar, Lu Han, Haifeng Huang, Dean Lacy, Charles Leung, Katherine ORegan, Kuzey Yilmaz, and audiences at NUS, 2009 AREAUA International, 2009 NARSC, 2011 Urban Economics Association, and 2012 AREAUA Annual meetings are greatly appreciated. I also thank the editor and two anonymous referees for valuable comments that improve the paper substantially. Financial support by Neville Gibson and Grosvenor Scholarship at UBC Sauder is greatly appreciated. This research is also sponsored by Shanghai Pujiang Program. All errors are mine.
Preprint submitted to Elsevier
April 17, 2014
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1. Introduction
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In recent decades, immigration to advanced economies has dramatically changed their ethnic landscapes. For example, only 4.7% of the U.S. population were born in a foreign country in 1970, while the same statistic jumped to approximately 13% in 2000 and remained at this level until 2010. Among immigrants in 1970, approximately 60% were born in Europe, 19% in Latin America, and 9% in Asia. In 2010, the share in European countries decreased to 12%, while the shares in Latin American and Asian countries increased signi cantly to 53% and 28%, respectively. To a lesser extent, Canada and European countries have experienced similar changes, i.e., higher ethnic diversity. How do changes in ethnic landscapes a¤ect urban neighborhoods, residents housing and neighborhood choices, and housing market outcomes? To answer these questions, I perform three sequential tasks. First, I build a general equilibrium model to tie all of the above factors together. Speci cally, the allocation of multiple ethnic groups across neighborhoods results from choices made by individuals. Moreover, both housing prices and ethnic composition directly a¤ect individuals decisions in the rst place.2 As a result, housing prices closely depend on the ethnic composition of neighborhoods. Many papers employ the hedonic methodology of Rosen (1974) to regress housing prices on measures of ethnic composition and hope to reveal peoples preferences for group composition through these estimates.3 Hedonic methods require the housing market to be in equilibrium and to o¤er a continuum of choices of neighborhood characteristics, including shares of ethnic groups. However, theoretical models of ethnic segregation, such as Schelling (1969, I assume that people can freely choose communities. Peoples preference for ethnic composition in a multiethnic context can be quite complicated, as illustrated by Clark (1992), who nds that individuals seem to have a optimum racial mix in mind and do not always prefer more of their own group. 3
Zabel (2008) reviews the literature using hedonic regressions to test whether minorities pay higher housing prices (evidence of discrimination or centralized racism) and whether people pay more for larger share of their own group (evidence for prejudice or decentralized racism). An incomplete list includes earlier papers, such as King and Mieszkowski (1973) and Yinger (1978), and recent studies, such as Kiel and Zabel (1996) and Cutler et al. (1999). A related line of research directly estimates whether ethnic composition is capitalized into house prices. These papers are summarized later in the introduction.
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1971), OSullivan (2009), and Zhang (2011), and those of race and housing markets, such as the border models of Bailey (1959) and Rose-Ackerman (1975) and the amenity model of Yinger (1976), predict complete segregation as the most probable equilibrium.4 Apparently, such an equilibrium cannot generate a continuum of group shares; therefore, the hedonic method is not consistent with these models. The general equilibrium model o¤ers a solution. I build on the work of Miyao (1978) by adding a housing market to relate housing price to ethnic composition. Two key results are obtained. Firstly, if people indeed have a preferred ethnic composition, neighborhood housing prices can be expressed as a continuous function of some measures of ethnic composition. Secondly, racially mixed neighborhoods can be stable if preference for living with certain groups is not too strong. Consequently, we can observe a full spectrum of group distribution in the data as long as the number of neighborhoods is su¢ciently large. Additionally, this theoretical framework ts the analysis of ethnic diversity very well because it allows many ethnic groups, in contrast to the white-black or native-immigrant dichotomy often assumed by previous researchers. My second task is to derive a parametric model of housing price determination with a focus on the role of ethnic composition. Speci c microfoundations are needed to make such connection more concrete. People may prefer to live close to people from the same group to enjoy better social interactions. Evidence in support of this mechanism is provided by Marmaros and Sacerdote (2006), who show that geographic proximity and within-race a¢nity can explain many friendships between individuals. Given this mechanism, I obtain a straightforward parametric relationship between housing price and a natural measure of ethnic composition in a multiethnic context, namely, the Her ndahl index Hj : Hj =
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(skj )2 ; for all j = 1; :::; J;
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where K denotes the number of ethno-linguistic groups and J denotes the number of neighborhoods in a city. skj is the population share of group k in neighborhood j. This index can be interpreted as the probability that two 4
In some cases, these models also admit racially mixed neighborhoods. However, such neighborhoods are often considered as exceptions rather than likely outcomes.
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randomly selected persons belong to the same group and is thus a measure of ethnic concentration.5 Therefore, to test whether people care about ethnic composition is reduced to testing whether housing price is correlated with the Her ndahl index. Further analysis shows that income and preference heterogeneity can hinder the interpretation of the correlation. In these cases, it is important to separate the e¤ect of the majority share from that of the overall Her ndahl index. My last task involves devising an identi cation strategy to estimate this correlation. The theory demonstrates an empirical challenge in that housing prices and ethnic composition are simultaneously determined. Intuitively, ethnic composition is endogenous in the determination of housing price because many unobservable neighborhood and personal characteristics inuence both at the same time. I address this endogeneity problem by constructing a panel of housing transactions as well as census tract characteristics in the metropolitan area of Vancouver, Canada. Here, census tracts correspond to neighborhoods in the theory. The panel structure enables me to account for time-invariant unobservable neighborhood characteristics that may be correlated with ethnic composition. The dataset covers four census years: 1986, 1991, 1996, and 2001. Employing standard xed e¤ects regressions, we can consistently estimate the endogenous correlation under standard identifying assumptions. The panel structure also enables the implementation of an alternative identi cation strategy, the conditional di¤erence-in-di¤erences method proposed by Heckman et al. (1998). This approach combines propensity score matching (Rosenbaum and Rubin, 1983) with the di¤erence-in-di¤erences method to estimate the treatment e¤ect of a policy change or a social program that may be endogenous. The treatment in this papers context is de ned as an increase in ethnic concentration.6 The key to applying this method is nding a matching pair: one with treatment and one without 5
The Her ndahl index is closely related to the ethno-linguistic fractionalization (ELF) index commonly used in the large literature on ethnic diversity and economic performance, reviewed by Alesina and LaFerrara (2005). The fractionalization index equals one minus the Her ndahl index exactly. Therefore, ELF is a measure of diversity, while Hj is a measure of concentration. 6 Two de nitions of treatment are implemented: (1) an increase in absolute value in the Her ndahl; (2) an increase relative to the overall change in the Her ndahl for the metropolitan area.
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treatment. The criterion in determining the pair is the propensity score or predicted probability of treatment generated in a model of treatment. Another approach is to select neighboring tracts. Here, we implicitly assume that some unobserved neighborhood attributes are shared by neighboring communities.7 After we obtain the pair, a di¤erence-in-di¤erences estimator is created to represent the treatment e¤ect. This method imposes no parametric restriction on the housing price equation. In addition, it employs di¤erent identifying assumptions from those of xed e¤ects models.8 All in all, these new results can corroborate the xed e¤ects models. All methods yield essentially the same results. The overall ethno-linguistic concentration index has mostly insigni cant, but negative, e¤ects on housing prices. However, if we control for the majority share, the sign changes from negative to positive. Meanwhile, the minority Her ndahl index, excluding the English-speaking group, has a strong positive e¤ect. Fixed e¤ects models also indicate that the correlation is nonlinear, but a precise identi cation of this relation is infeasible due to data limitations. Other measures of ethnicity, such as place of birth, ethnic origin, and religion, are found to have no signi cant e¤ect on housing prices. In summary, the empirical results support the notion that non-market interactions have a substantial inuence on peoples decisions. This paper is most closely related to the literature on the capitalization of ethnic composition into housing prices. Examples are Coulson and Bond (1990), Bajari and Kahn (2005), and Fu (2005), who use cross-sectional data, and Macpherson and Sirmans (2001), Clapp et al. (2008), and Saiz and Wachter (2011), who use panel data. As these papers employ the hedonic method, my model provides theoretical support for these empirical studies. In addition, my empirical analysis di¤ers from these papers in the following ways: (1) I ask the question in a multi-ethnic context and (2) the data enable me to implement both the xed e¤ects and the conditional di¤erencein-di¤erences methods. 7
This method is therefore similar in spirit to Black (1999) and Bayer and McMillan (2008), who use boundary xed e¤ects to identify the e¤ect of their variables of interest. It is also related with di¤erence-in-di¤erences analysis at border areas such as Dhar and Ross (2012) and Dachis et al. (2012). I should note that there are no clear policy variations across neighborhoods in my analysis, but rather variations over time of ethnic composition. 8 For details about the identifying assumptions, see Section 4.4.1 or Heckman et al. (1998).
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My theory resembles the discrete choice models of Bayer et al. (2004), Bayer and Timmins (2005), Bayer et al. (2007), Bayer and Timmins (2007), and Wong (2013). Their approach is more general because they model preference for ethnic composition as well as other factors. I am able to derive a reduced form relationship between housing price and the Her ndahl index in a simpler model. An empirical test of such a relationship follows. In contrast, they aim to estimate the structural parameters of the utility function directly. These two approaches should complement each other. In the next section, I present a general equilibrium theory of neighborhood choice with multiple ethnic groups. Several examples are shown to lead to a correlation between housing price and ethnic diversity. Section 3 describes the housing transaction data and the census data. Section 4 reports the main results using various methods. Finally, I conclude and discuss the key ndings in Section 5.
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2. A Model of Ethnic Diversity and Neighborhood Choice
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2.1. Model Setup: Ethnicity, Neighborhood, and Utility Maximization In a closed city, each individual from K ethnic groups chooses one and only one neighborhood to live in. The population size of each ethnic group is xed, denoted by Lk (k 2 f1; 2; :::; Kg). There are J neighborhoods in the city, where J is much larger than K. Each neighborhood has a xed housing supply of Sj (j 2 f1; 2; :::; Jg): Housing is perfectly divisible. The utility of an individual i of group k that lives in neighborhood j is equal to Vikj (rj ; y k ; qjk ) v kj (rj ; y k ; qjk ) + "ij max u(z; h; qjk ) + "ij subject to z + rj h = y k : z;h
(1)
Vikj (rj ; y k ; qjk ) is composed of two additively separable components: the indirect or representative utility v kj (rj ; y k ; qjk ) and an independent and identically distributed amenity shock "ij for each individual and every neighborhood.9 9
The i.i.d. assumption about "ij is restrictive yet necessary to simplify my analysis. An identical distribution means that people of di¤erent groups only di¤er in terms of their evaluations of ethnic composition. Independence implies that unobservable neighborhood attributes are not correlated across neighborhoods.
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In the budget constraint, rj denotes the housing price in neighborhood j, and y k denotes the common income level within group k.10 The direct utility function u(z; h; qjk ) depends on the consumption of both composite good z and housing h and the quality of the neighborhood qjk : Assume that @u=@z > 0; @u=@h > 0; and @u=@q > 0. Ethnic composition determines the quality of a neighborhood. Formally, k k qj = q k (n1j ; n2j ; :::; nK j ); where nj is the population of group k in neighborhood j: Notice that quality is in the eye of the beholder, i.e., people of di¤erent groups assign di¤erent quality indices for the same neighborhood. In addition, the formulation of qjk can accommodate many types of preferences. For example, if individuals of group k like to live with people of group h, then @qjk =@nhj > 0; for h 2 f1; :::; Kg: If individuals care the size of the neighP k borhood, then @qjk =@ k nj Q 0: Preference for ethnic diversity can be P P 2 k < 0, where k (skj )2 measures ethnic concenmodeled by @qj =@ k (skj ) tration. To facilitate further analysis, I assume that the city is a pure exchange economy. Formally,
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y k = rwk and
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where wk = (w0k ; w1k ; w2k ; :::; wJk )0 0 is a strictly positive vector of endowments in the composite good (denoted by w0k ) and housing assets (denoted by wjk ), and r = (1; r1 ; :::; rJ ) is the corresponding price vector. In an exchange economy, individuals obtain income from their endowments. Furthermore, the total housing supply Sj equals the total endowments of housing in each neighborhood. The neighborhood choice problem for an individual involves two steps. First, she chooses a consumption plan given a hypothetical choice of a neighborhood. Second, she compares utilities across neighborhoods and chooses the neighborhood that o¤ers the highest utility. Let P kj denote the probability that an individual of group k chooses neighborhood j. De ne Nj 10
I implicitly assume that no discrimination exists in the housing market and that no within-group heterogeneity in income exists. Any residual individual heterogeneity is absorbed by "ij : In addition, any additional heterogeneity does not violate the i.i.d. requirement.
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"il > v kl
v kj ] for all l 6= j 2 f1; :::; Jg:
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P kj = Pr["ij
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(n1j ; n2j ; :::; nK j ) or the vector of population distribution in neighborhood j. Utility maximization implies that
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Note that v kj = v kj (rj ; y k ; qjk ) = v kj (r; Nj ; wk ), where I substitute rwk for y k and q k (Nj ) for qjk to obtain the second equality. If we specify a probability distribution for ("i1 ; :::; "iJ ), we can then express the choice probability P kj as a function of the house price vector r and a vector of inter-neighborhood group allocation N (N1 ; N2 ; :::; NJ ). In addition, P kj must satisfy the following two conditions: J X
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(2) (3)
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2.2. Equilibrium: Existence and Uniqueness of Neighborhood House Prices In contrast to the model by Miyao (1978), housing prices play a key role in this paper. This extension enables me to analyze housing price and ethnic composition at the same time. In the present context, an equilibrium is de ned as an ethnic allocation N and a price vector r that satisfy the following: (1) the housing markets in all neighborhoods clear and (2) the allocation N is consistent with utility maximization for all. Once r is known, we can solve for consumption of housing fhkj ; 8k; jg and composite good fz k ; 8kg: Let the demand for housing be hkj (rj ; y k ; Nj ) = hkj (r; Nj ) for an individual of group k in neighborhood j: The housing market clearing conditions are K K X X k kj kj L P (r; N)h (r; Nj ) Lk wjk = 0; where j 2 f1; 2; :::; Jg: k=1
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The left-hand side can be expressed as a vector e(r; N), an excessive demand function.11 The above equation system is equivalent to e(r; N) = 0; 11
(4)
In the above equation system, the market clearing condition for the composite good z is not included because I have normalized the price of z to one, i.e., it is the numeraire good. This normalization does not a¤ect the generality of the results. I could prove all propositions by including a market clearing condition for the numeraire good.
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P kj (v k1 (r; N1 ); :::; v kJ (r; NJ ))Lk = 0; 8k; j;
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fjk (r; N) nkj
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J where r 2 R++ is a strictly positive vector, N 2 fnkj j0 nkj Lk ; 8j; kg 2 KJ R ; and is a closed rectangular region. If people maximize utility, then the selection probability P kj must equal the actual proportion of group k choosing neighborhood j; or nkj =Lk :
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P such that Jj=1 nkj = Lk for all k; and fjk (r; N) is the k j th element of the vector function f (r; N) of dimension K J. Solving the system of equations (4) and (5) is rather di¢cult. I solve the problem in two steps. First, I solve Equation (4) for the price vector r conditional on N; i.e., taking N as exogenous variables. If such a price vector exists, I then characterize conditions under which r can be expressed as a function of N. In the second step, I search for a solution N to the equation f (r; N) = 0 under the condition that r is indeed a function of N. The second step involves the search for a xed point for the mapping P kj (N)Lk from N 2 to itself.
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Proposition 1. 12 If the utility function u(z; h; Nj ) is continuous, strictly quasi-concave, and strictly increasing in h, and P kj (v k1 ; :::; v kJ ) is continuous in v k1 ; :::; v kJ for all k, a strictly positive price vector r exists to clear all of the neighborhood housing markets conditional on a population distribution N. Proposition 1 shows that a price vector exists, but it does not rule out multiple equilibria. Multiple equilibria often make comparative statics analysis problematic. The gross substitute property, de ned below, is utilized to establish the uniqueness and stability of the price vector. De nition 1. The excess demand function e(r; N) has the gross substitute property if whenever r0 and r are such that, for some j, rj0 > rj and rl0 = rl for l 6= j, we have el (r0 ; N) > el (r; N). Proposition 2. If the excess demand function e(r; N) is continuously di¤erJ entiable in r 2 R++ and satis es the gross substitute property, then e(r; N) = 0 has a unique solution r conditional on N. Additionally, the solution r is 12
The proofs of this and other propositions can be found in the Appendix.
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stable given the following dynamic adjustment process when r( ) at time is out of equilibrium: (6)
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rj ( + 1) = rj ( ) + dj ej ( ); where dj > 0; 8j 2 f1; :::; Jg;
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and ej ( ) denotes the jth element of the excess demand function e(r; N):
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Are these conditions in Proposition 2 restrictive? Continuous di¤erentiability is satis ed when the utility function and the distribution functions of ("i1 ; :::; "iJ ) behave nicely. The gross substitute property is very restrictive. It implies that excess demand increases as housing prices in other neighborhoods increase. However, we can con rm that both conditions are satis ed if the utility function is Cobb-Douglas and the choice probability is based on the logit model of McFadden (1974). I should note that these conditions are su¢cient but not necessary, so there may exist cases when uniqueness and stability hold even though these conditions are violated. The results in Proposition 2 are useful to empirical researchers. Because of uniqueness, researchers do not have to worry about multiple equilibria in testing the comparative statics implied by their theoretical models. Because hedonic regressions implicitly require that housing markets are in a long-run equilibrium, the global stability of the equilibrium justi es the estimation of the hedonic price of ethnic composition. Proposition 3. If the excess demand function e(r; N) is continuously differentiable in r N and satis es the gross substitute property and a reguJ larity condition, then there exists a unique function g : ! R++ such that e(g(N); N) = 0 for all N2 and g(N) is continuously di¤erentiable on : The result in Proposition 3 is useful to solve the xed-point problem in the next section. The classical implicit function theorem is of limited help because it only ensures the local solvability of r in terms of N. A global implicit function theorem (Sandberg, 1981, Corollary 1) is hence used to establish the global solvability of r: The additional regularity condition required in this proposition is explained in the Appendix. Roughly speaking, it requires that as nkj approaches the boundary of ; rj also approaches its boundary. In the next section, the properties of g(N) are used to prove the existence and stability of an equilibrium that admits ethnically diverse neighborhoods. 10
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Proposition 3 goes further than Proposition 2 by showing that housing price is a continuous function of all group population sizes N. In empirical applications, we could adopt a more parsimonious speci cation that con nes to group sizes in the same neighborhood Nj :
P kj (v k1 (g(N); N1 ); :::; v kJ (g(N); NJ ))Lk = 0; 8k; j:
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2.3. Equilibrium: Existence and Stability of Group Allocation Given the result in Proposition 3, Equation (5) can be rewritten as:
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My objective is to nd a xed point for P kj Lk ; a problem already solved by Miyao (1978).
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Proposition 4. If the following conditions are satis ed: (1) All conditions in Proposition 3 hold, (2) v kj (r; N1 ) is continuous in nkj for 0 nkj L PK k kj k1 kJ kj for all k 2 f1; :::; Kg k=1 L ; and (3) P (v ; :::; v ) is continuous in v and j 2 f1; :::; Jg; then there exists an equilibrium distribution of the population N .
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Next, I establish conditions under which such an equilibrium is unique and stable. Following Miyao (1978), I de ne stability as whether the following dynamic adjustment process converges over time: nkj ( + 1) = P kj (v k1 (g(N( )); N1 ( )); :::; v kJ (g(N( )); NJ ( )))Lk ;
(7)
where denotes the time. In other words, there is a one-period lag for individuals to adjust their behavior to the desired choice. Proposition 5. If the following conditions are satis ed: (1) All conditions in Proposition 3 hold, (2) v kj (r; Nj ) is di¤erentiable in nhj ; (3) P kl (v k1 ; :::; v kJ ) is di¤erentiable in v kj and @P kl =@v kj 0 for all l 6= j; (4) v kj (g(N); Nj ) is di¤erentiable in r; and ! K J X X 1 @P kl @v kj Lk < ; for all j; l 2 f1; :::; Jg and k; h 2 f1; :::; Kg; h kj @v 2 @nl j=1 k=1 (8)
then the equilibrium solution N is unique and globally stable.
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Proposition 5 shows that the equilibrium is unique and globally stable if kj h the marginal e¤ect of population size on utility or @v =@nl is su¢ciently small, i.e., if peoples preference for or aversion to certain groups is not too strong. A similar point was made by Miyao (1978).13 In fact, my model o¤ers an even more optimistic view because of the addition of the price mechanism. This point is best illustrated by expanding the total derivative of v kj (g(N); Nj ) with respect to nhl or @v kj =@nhl :
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@v kj @v kj (g(N); Nj ) @v kj @gj (N) X @v kj @gj 0 (N) = + + ; @gj (N) @nhl @gj 0 (N) @nhl @nhl @nhl 0 6=j j | {z } | {z } | {z } Own Price E¤ect
Income E¤ect
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Direct E¤ect
(9)
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where gj (N) = rj : This seemingly complicated expression has an intuitive interpretation. The rst term represents the direct e¤ect of population size on utility, the only e¤ect analyzed by Miyao (1978). This study includes two new e¤ects: the own price e¤ect and the income e¤ect. The two additional e¤ects tend to counterbalance the direct e¤ect. Take @v kj =@nkj as an example. Suppose utility to group k increases with its own size in neighborhood j; or @v kj (g(N); Nj )=@nkj > 0. A positive migration shock of group k to neighborhood j is likely to attract even more people from group k: If housing prices in neighborhood j increase so that @gj (N)=@nkj > 0; the own price e¤ect becomes negative because @v kj =@gj (N) < 0. The income e¤ect is also negative because people obtain income from their endowments. Their income and utility increase with housing prices in other neighborhoods, so @v kj =@gj 0 (N) > 0. However, @gj 0 (N)=@nkj < 0 because an increase in nkj reduces housing demand in other neighborhoods and hence lowers prices.14 Therefore, Proposition 5 provides additional assurance to the practice of regressing housing prices on measures of ethnic composition. However, such 13
See also Anas (1988) for a discussion of the stability of equilibrium and taste heterogeneity. 14 Di¤erent combinations of v kj and nhl are listed as follows: (1) j = l; k = h; (2) j = l; k 6= h; (3) j 6= l; k = h; (4) j 6= l; k 6= h: Case (1) is discussed in the main text. For cases (3) and (4), no direct e¤ect exists, and the other two e¤ects are small. Case (2) is more complicated. If @v kj =@nhj > 0, an increase in nhj increases nkj , so the own price e¤ect is likely to be negative, thus canceling the direct e¤ect. If @v kj =@nhj < 0; an increase in nhj decreases nkj , so the own price e¤ect is ambiguous or negative but smaller and thus the net e¤ect is unknown. The income e¤ect is mostly negative for all scenarios. Therefore, the net e¤ect is ambiguous. As long as these e¤ects are small, stability is still present.
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regressions su¤er from the endogeneity problem. Section 4 develops identi cation strategies to resolve this issue, while Section 2.4 derives a parametric housing price equation using additional assumptions.
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2.4. House Prices and Ethnic Diversity: The Role of Social Interactions People care about neighborhood ethnic composition for many reasons. I provide below an example that illustrates how social interactions can a¤ect peoples locational choices. This idea dates back at least to Beckman (1976). Recent research provides some empirical support for this idea. For example, Currarini et al. (2009) and Marmaros and Sacerdote (2006) have shown that people tend to form social ties with people who are from the same group and who reside nearby. Additional examples with di¤erent mechanisms are included in Appendix B. People consume three goods: the numeraire good z, housing h, and social interactions q(t), which depends on the time t spent in interactions. Note that q(t) is now speci ed as the quantity of social interactions, while Equation (1) only vaguely states that it is related to the quality of the neighborhood. People have di¤erent incomes and opportunity costs of time across groups. They maximize a Cobb-Douglas utility function:
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max Az h q(t)1 z;h;t
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where ck is the opportunity cost of time. To simplify, an individual of ethnic group k consumes a xed quantity qk of social interactions, where qk = tk + bk (s1j ; :::; sKj ):
The rst term tk denotes the time spent on phone calls, internet socializing, and so on, while the latter term bk (s1j ; :::; sKj ) is the quantity of social interactions from living in the neighborhood itself. It is free because it comes from random meetings, except that the individual must rent a house to live there. Consequently, this term depends on the ethnic composition or group shares fskj g for all k. A neighborhood is more desirable to an individual if its bk (s1j ; :::; sKj ) is larger because he will save on time spent on social interactions. Housing supply is linear in population size, i.e., Sj = Nj .15 15
This assumption removes the supply e¤ect because the per capita housing supply is a constant everywhere. As a result, in-migration to a neighborhood does not necessarily generate upward pressure on price.
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bk (s1j ; :::; sKj ) = b0 skj + ab0 (1
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2.4.1. Constant Bene ts The simplest case involves constant but di¤erent bene ts from intra-group and inter-group interactions. I assume that each intra-group meeting generates a bene t of b0 , while each inter-group meeting gives a payo¤ b0 a. The parameter a captures the di¤erence. These bene ts do not vary across groups. Therefore, the expected bene t from these random meetings is skj ) = ab0 + b0 skj (1
a),
(10)
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where skj is the probability of meeting a person from the same group, while 1 skj is the probability of meeting a person from another group. If a < 1, higher group share increases the bene ts of random meetings and thus lowers the individuals time spent on other types of interactions. She can a¤ord more expenditures on housing. Thus, individual housing demand increases with her group share. In turn, the housing price that equalizes demand and supply is ( ) X X rj = y k + ck ab0 qk skj + (1 a) b0 ck s2kj :
(a + ) k k
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Proposition 6. If income y k , the opportunity cost of time ck , and the xed amount of required social interactions qk are equal across all groups, then the neighborhood housing price will be increasing in the Her ndahl index of ethnic group composition. Proof. If y k = y, ck = c, and qk = q for all k, the rst summation P becomes 2 becomes c(1 a)b y + c(ab0 q) and the second summation 0 k (skj ) : As P 2 long as a < 1, rj will be increasing in k (skj ) . Proposition 6 implies that a parametric model can be used to test whether people value ethnic composition. Note that social interactions have no e¤ect on housing prices if a = 1 or if there is no ine¢ciency for inter-group interactions. Holding other variables constant, a positive correlation between the Her ndahl index and the neighborhood housing price represents evidence for inter-group communication ine¢ciencies. A negative correlation, on the other hand, signi es a positive bene t for inter-group communications. If y k ; ck ; and qk are not homogeneous across groups, the correlation becomes less straightforward. The case of three groups is analyzed with an assumption that ck = c for all k. Because s1j + s2j + s3j = 1 and 14
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P Hj 3k=1 (skj )2 , we have two degrees of freedom in the set fs1j ; s2j ; s3j ; Hj g. For example, I can vary Hj and s1j independently, but not all of Hj ; s1j ; and s2j . I solve for s2j and s3j as a function of Hj and s1j , which I use to denote the share of the majority group: i 1h 2 1=2 1 s1j 2Hj (1 s1j ) s2j ; s3j = : 2
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( + ) 2 (2Hj (1 s1j ) )1=2
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Proposition 7. Suppose there are three ethnic groups. If the net income q k of the second largest group is higher than that of the third largest y k c group, the neighborhood house price will be increasing in the Her ndahl index Hj . Otherwise, as long as the bene t from social interactions b0 is large enough or the ine¢ciency from inter-group interactions 1 a is large enough, the neighborhood house price will be increasing in the Her ndahl index Hj . Proof. Both claims are directly implied by Equation (11). As long as the condition for the rst claim is satis ed, both terms on the left-hand side of Equation (11) are positive. The condition in the second claim can be (y 3 c q 3 ) (y 2 c q2 ) expressed more formally as 2(2H (1 s )2 )1=2 < c(1 a)b0 . The right-hand side j 1j of the inequality is always positive, while the left-hand side can be positive or negative. Therefore, the scale of b0 and 1 a are important determinants of the sign of the price derivative. The key point of Proposition 7 is that the correlation between the housing price and the ethnic diversity index can be distorted by income and preference heterogeneity in the population. In these cases, it is important to control the share of one group to identify @rj =@Hj in a regression analysis. Proposition 7 also shows that the sign of @rj =@Hj is intricately related with the more fundamental preference parameter a. For cases with more than three groups, closed-form solutions for @rj =@Hj are unlikely. However, the intuition in this simple three-group case should be applicable to the more general cases.
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2.4.2. Diminishing Bene ts from Intra-group Interactions Wong (2013) showed that preference with respect to ones own groups share people exihibits an inverted-U-shape. The next example illustrates how such a preference can result from diminishing bene ts from intra-group interactions. To make the model tractable, I abstract away from inter-group income variation and other dimensions of heterogeneity. Suppose the bene t from intra-group interactions is b0 + b1 skj , where b1 < 0. Consequently, the expected bene t from random meetings is ab0 + b0 skj (1
a) + b1 s2kj :
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a) This function achieves its maximum at b0 (1 . Because skj 2 (0; 1), 2b1 k b (s1j ; :::; sKj ) is always decreasing in skj if a > 1, while it is always increasing in skj if a < 1 + 2bb01 : If a 2 (1 + 2bb01 ; 1); the preference will be unimodal. The three parameters a; b0 , and b1 ; characterize the type of preference people have for social interactions and hence the equilibrium housing price: ( ) X X rj = ! + (1 a) b0 c s2kj + b1 c s3kj ; (12)
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where ! = y + c (ab0 q) : Similar to the results in Proposition 6, housing price is increasingP in the Her ndahl index as long as a < 1. However, an additional term k s3kj emerges due to the diminishing e¤ects. One special case is when only the majority group has diminishing bene ts from intra-group interactions, in which case Equation (12) simpli es to ( ) X ! + (1 a) b0 c s2kj + cb1 s31j : (13) rj =
( + ) k We can con rm that housing price is increasing in the overall Her ndahl index and decreasing in the majority share. Equation (13) shows that we need to separate the e¤ects of the majority from that of the Her ndahl index, even if the population is homogeneous. In an empirical analysis, we have to control the majority share if we believe that the majority group is satiable with respect to its group share. Alternatively, if minority individuals have satiable preferences, the housing price becomes ( ) X X rj = ! + (1 a) b0 c s2kj + b1 c s3kj : (14)
( + ) k k6=1 16
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in the neighborhood is
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As a result, the housing price ( rj = ! + (1
( + ) ( = ! + (1
( + ) +cs1j b1 s21j (1
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2.4.3. Diminishing Bene ts and Distinction among Majority, Own Group, and All Other Groups The rst two examples assume that individuals treat people from all other groups the same. In reality, a minority individual may receive additional bene ts from interactions with people from the majority group because such interactions provide better job information and better chances of assimilation (Patacchini and Zenou, 2012; Zenou, 2013). On the other hand, such interactions may be deemed undesirable by his culture and hence less valuable. I distinguish among three types of interactions faced by a minority individual: those with the majority population, those within his own group, and those with all other groups.16 The bene t function simpli es to b0 skj + a1 b0 s1j + ab0 (1 s1j skj ) for k 6= 1 k b (s1j ; :::; sKj ) = : (a1 b0 + b1 s1j ) s1j + ab0 (1 s1j ) for k = 1
a) b0 c
X
s2kj + cs1j b1 s21j + b0 (a1
X
s2kj
k6=1
a) b0 c
k=1
a)b0 s1j + b0 (a1
a)
:
) a) (15)
(16)
The above equations include some additional terms, such as cb1 s31j ; b0 (a1 a)cs1j ; and c(1 a)b0 s21j . The importance of controlling for the majority share in a regression of housing price on the Her ndahl index is shown once again. These new terms reect the di¤erent valuations people place on various types of interactions. Although housing price is still increasing in the overall Her ndahl index as well as the minority Her ndahl index, it may increase or decrease with the majority share due to these additional terms.
2.5. Empirical Implications of the Theory Both the general model and the examples have implications for the empirical analysis. First, the model shows quite clearly that housing prices and 16
We can in principle generalize this by allowing bene ts to di¤er for every grouppair. We may even allow asymmetry for the bene ts experienced by the two persons in a meeting. I leave those generalizations for future research.
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neighborhood ethnic composition are simultaneously determined. In other words, a simple regression of neighborhood house prices on ethnic composition is unlikely to produce consistent estimates. Resolving the endogeneity problem will be the focus of my empirical analysis. Speci cally, I exploit variations in the time dimension and use panel data techniques to address the problem. Second, the general model also assures researchers that we can run hedonic regressions to estimate the e¤ect of ethnic composition on housing price. As shown by Propositions 3 and 5, the observed neighborhood con gurations can be considered to be in a long-run equilibrium as long as preference for ethnicity is not too strong and neighborhoods are substitutes for one another. In contrast, most models of ethnic segregation in the spirit of Schelling (1969) do not admit ethnically mixed neighborhoods. Therefore, my theory provides a new justi cation for the hedonic analysis of ethnicity and housing price. Next, the examples in the previous section imply a straightforward relationship between housing price and the Her ndahl index. In fact, restrictive assumptions on preference are made to arrive at this parametric model. I have also shown that di¤erent formulations of peoples preferences lead to di¤erent parametric speci cations. As demonstrated by Clark (1992), peoples preferences for ethnic composition can be quite complicated. I certainly cannot exhaust all possibilities, so future research is needed. Finally, the examples show that correlation between price and the Her ndahl index reveals information about peoples preferences. A positive correlation suggests greater bene ts from intra-group interactions, and vice versa. However, income heterogeneity across groups and diminishing bene ts from intra-group interactions can complicate the interpretation. It is hence necessary to include the majority share in a housing price regression. In addition, we can construct a Her ndahl index for minority groups and include this measure and the majority share in the regression. 3. Data I combine housing transaction data and census data for the metropolitan area of Vancouver, Canada.17 The census data are the 1986, 1991, 1996, and 2001 Canadian Census Pro le Tables at the census tract level. The data 17
Details about the data sources can be found in the Appendix.
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include a self-reported housing price and other neighborhood characteristics. The census tract is an appropriate unit of measurement because it closely corresponds to our concept of a neighborhood.18 I construct a balanced panel of census tracts using the Census Tract Correspondence Files for various years.19 Table 1 summarizes the neighborhood characteristics. From 1986 to 1996, the average housing value in Vancouver more than doubled. However, the housing value dropped from 1996 to 2001. The city became more diverse, as measured by the overall Her ndahl index of home language, mother tongue, ethnic origin, and place of birth. At the same time, the concentration within minority groups increased, as reected by the higher minority Her ndahl index (home language). The unemployment rate dropped, while the average household income, population density, share of people with bachelors degrees, and new immigrants were on the rise. Variables that were relatively stable include home ownership rate, the share of migrants, and the average number of rooms per dwelling. In general, Vancouver has experienced steady growth from 1986 to 2001. The housing transaction data are from the British Columbia Assessment Authority (BCAA). I focus primarily on single-family homes.20 The data contain information on a houses attributes and its transaction price. I include only the transactions in the years 1986, 1991, 1996, and 2001 for which I could associate the transaction with a census tract. The geocoding procedure is explained in more detail in the Appendix. Table 2 lists the summary statistics for the transaction dataset. The average transaction prices are somewhat higher than the average estimated According to Statistics Canada, "Census tracts (CTs) are small, relatively stable geographic areas that usually have a population of 2,500 to 8,000. They are located in census metropolitan areas and in census agglomerations with an urban core population of 50,000 or more in the previous census. A committee of local specialists (for example, planners, health and social workers, and educators) initially delineates census tracts in conjunction with Statistics Canada. Once a census metropolitan area (CMA) or census agglomeration (CA) has been subdivided into census tracts, the census tracts are maintained, even if the urban core population subsequently declines below 50,000." 19 Details concerning the construction of this dataset and the description of the variables can be found in the Appendix. 20 Because single-family houses and condominiums di¤er in many attributes that are di¢cult to quantify, I avoid the omitted variables problem by dropping condominiums from the analysis.
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housing values shown in Table 1, but the general time trend is similar. The transacted houses shown here are slightly newer than the overall housing stock. The numbers of rooms in a dwelling are similar across the two datasets. These similarities suggest that the results based on the self-reported housing values should not di¤er considerably from those based solely on real transactions.
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4. Ethno-Linguistic Diversity and House Prices
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My primary goal is to test whether there is a structural relationship between housing price and ethnic concentration. To achieve this objective, the endogeneity issue must be resolved. Speci cally, there are two sources of the endogeneity problem. First, some unobservable neighborhood characteristics, such as natural amenities, are valued di¤erently across groups. These characteristics thus a¤ect both housing prices and ethnic compositions. If these characteristics are relatively stable over time, we can employ panel xed e¤ects models. Second, some neighborhood characteristics describe the attributes of its residents, e.g., average income, average education, and cultural background. Ethnic composition belongs to this category. If some resident characteristics are unobservable and vary over time and are also correlated with ethnic composition, we can no longer use xed e¤ects to address the endogeneity issue. In this case, conditional di¤erence-in-di¤erence (Heckman et al., 1998) o¤ers an alternative solution.21 4.1. Fixed E¤ects Models: Self-Reported Housing Value In this section, the average self-reported housing value HV aljt in neighborhood j and census year t is modeled as a function of neighborhood characteristics: ln HV aljt = f (Hjt ; HMjt ; s1jt ; ) + Zjt + Mjt + j + t + "jt ;
(17)
where f (Hjt ; HMjt ; s1jt ; ) is a function of the overall ethno-linguistic diversity index Hjt , the diversity index for minority groups HMjt , and the share of majority group s1jt . Zjt is a vector of socio-economic characteristics; Mjt is a vector of characteristics of the housing stock; j denotes an individual 21
Details about the identifying assumptions for the xed e¤ects and conditional di¤erence-in-di¤erence methods are explained later.
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census tract xed e¤ect; t denotes the census-year dummies, and "jt is an i.i.d. error term. All of the variables are measured at the census tract level and obtained from the census data. The average self-reported housing values are based on all housing units in the census tract but are subject to measurement errors. The identifying assumption is that the included regressors are not correlated with "jt . The assumption is violated in two cases. First, we may parameterize f (Hjt ; HMjt ; s1jt ; ) incorrectly, giving rise to the omitted variable problem. Second, unobservable characteristics that vary over time may be correlated with the included regressors. In these cases, the xed e¤ects model in Equation (17) no longer ensures identi cation. To address the misspeci cation problem, I specify a variety of parameterizations for f (Hjt ; HMjt ; s1jt ; ). To solve the second problem, we must resort to a di¤erent method later in this paper. Table 3 shows the results for the xed e¤ects model. All of the ethnicityrelated variables are based on home languages. Model RE (1) includes neighborhood characteristics but not census tract xed e¤ects. The identi cation comes from both cross-sectional and time-series variations. The coe¢cient before the overall He ndahl index is negative and signi cant, i.e., more ethnically diverse neighborhoods have higher house prices on average. However, estimates in RE (1) are unlikely to be reliable because ethnic composition and other neighborhood characteristics are endogenous in price determination. In addition, we need to control for the majority group share because group heterogeneity in income and preference complicates the correlation between housing price and the Her ndahl index.22 Models FE (1) to (4) show the results when the above issues are addressed. In fact, the coe¢cient estimates dropped for most control variables. This suggests that residential sorting along these variables is likely. In other words, unobserved neighborhood characteristics a¤ect peoples choices and the price at the same time. FE (1) to (4) achieve identi cation from time-series variations in the data. Although FE (1) demonstrates a negative relationship between housing price and the overall Her ndahl index, FE (2) shows a positive relationship. FE (2) is preferred because it addresses group heterogeneity and more complex preferences by holding the majority share constant. The positive coe¢cient before the Her ndahl index indicates 22
See the discussions after Propositions 7 and Sections 2.4.2 and 2.4.3 for details.
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ine¢ciency from inter-group interactions according to Proposition 7. The negative coe¢cient before the majority share reects the group heterogeneity in income and other personal attributes, the more complicated preferences analyzed in Sections 2.4.2 and 2.4.3, or both. FE (3) and FE (4) circumvent group heterogeneity by examining the e¤ect of minority concentration. Both FE (3) and FE (4) allow the Her ndahl index of minority concentration to freely vary from 0 to 1. FE (4) includes the majority share as one additional control and is thus comparable to FE (2). In general, FE (3) and FE (4) provide similar results to FE (2), i.e., more ethnically homogeneous communities experience greater price appreciation once the majority share is controlled for. Models FE (5) to FE (7) test for nonlinearities. These models allow very exible function forms for f (Hjt ; HMjt ; s1jt ; ): The speci cations are not motivated by theoretical analysis in Sections 2.4.2 and 2.4.3. Instead, these speci cations aim to capture the non-linear interactions between the Her ndahl index and the majority share because of group heterogeneity. FE (5) shows that housing price decreases with Hjt and achieves its minimum when Hjt = 0:82: Because Hjt > 0:82 only if the majority share is above 0.9, the housing price is decreasing in Hjt in most of its range. FE (6) shows that housing price is decreasing in Hjt if the majority share is below 55%, but increasing in Hjt if the majority share is above 55%. The di¤erence lies in the inclusion of majority share in FE (6). FE (7) accounts for all of the second-order terms, but the coe¢cients are no longer statistically signi cant, possibly due to an insu¢cient number of data points to identify these e¤ects. In FE (8) and FE (9), I attempt to test the implications of my analysis P 3 in Sections 2.4.2 using the sign patterns of Hjt and K s . k=1 kj FE (9) is the preferred speci cation. The regressors are no longer statistically signi cant. This result is not consistent with diminishing bene ts higher group PK from 3 share for all groups because the coe¢cient before k=1 skj is positive and insigni cant. However, the negative coe¢cient before the majority share is consistent with the notion that the majority group has an inverted-Ushaped preference for its own group share. However, this evidence is not conclusive. To answer this question more concretely, more data and analyses are necessary. 4.2. Fixed E¤ects Models: Individual Housing Transaction Price In this section, housing transaction and census data are combined. Individual housing transaction prices are modeled as a function of the individual 22
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housing characteristics Xit and neighborhood characteristics: ln Pijt = Xit + f (Hjt ; HMjt ; s1jt ; ) + Zjt + j + t + "ijt ;
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where Pijt denotes the price of transaction i in neighborhood j at time t, and Xit corresponds to the variables reported in Table 2. The remaining f (Hjt ; HMjt ; s1jt ; ); Zjt ; j ; t are as described earlier. "ijt is an i.i.d. error term, which is assumed to be uncorrelated with all regressors once we allow the xed e¤ects j to be potentially correlated with other regressors. Although the data only include housing units transacted over this period, the prices are measured more precisely. Moreover, the precise measurement of housing attributes allows more precise identi cation of price variations across neighborhoods. Table 4 reports the results. The speci cations listed in Table 3 are all reported here. All of the results are similar as well. FE (2) and FE (4) show that housing price is positively correlated with the Her ndahl index, overall and minority. This correlation can be interpreted as before. The interpretation of FE (5) to FE (9) is also similar. Nonlinearity exists in the relationship between housing price and the Her ndahl index. Finally, it is di¢cult to disentangle the diminishing e¤ects using the sign patterns in FE (8) and (9). 4.3. Fixed E¤ects Models: Repeat-Sale Housing Price Index In this section, the combined housing transaction and census data are used again. However, the housing transaction prices are transformed into housing price indices for every census tract and each census year. The method of Case and Shiller (1989) is employed to create this repeat-sale index. Census tracts with fewer than 100 pairs of repeat sales are dropped to ensure the reliability of the estimate. Next, the housing price index HP Ijt ; expressed in levels, is regressed on neighborhood characteristics: ln HP Ijt = f (Hjt ; HMjt ; s1jt ; ) + Zjt + j + t + "jt ;
(18)
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units in the neighborhood. However, the results in Table 5 do not di¤er signi cantly from those in Tables 3 and 4. Table 3, Table 4, and Table 5 use di¤erent samples, di¤erent sets of housing attributes, and di¤erent measures of housing prices, but they provide essentially the same results. Housing price is positively related to the overall concentration of ethnic groups after conditioning on the majority share. In addition, the housing price increases with the minority concentration index. All of these ndings support the existence of a material e¤ect of social interactions on housing market outcomes.
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4.4. Conditional Di¤erence-in-Di¤erences Method 4.4.1. Research Design and Identi cation In this section, I adopt the conditional di¤erence-in-di¤erences method proposed by Heckman et al. (1998). The empirical question becomes whether neighborhoods that become more ethnically homogenous, de ned as the treated group, experience higher price appreciation compared with the control group of neighborhoods. This method combines propensity score matching (Rosenbaum and Rubin, 1983) with the di¤erence-in-di¤erences method. The method suits my analysis well. First, it is non-parametric; thus, it relaxes the restrictive parametric assumptions on the housing price equation. Second, the method requires a di¤erent set of identifying assumptions and can thus o¤er corroboration to the results of xed e¤ects models.23 Treatment is de ned in two ways. First, the more straightforward de nition is an increase in the Her ndahl index, either overall or minority only. The second de nition is based on relative changes in ethnic concentration. If the change in the Her ndahl index for a neighborhood exceeds that for the metropolitan area, this neighborhood is considered to be treated, and vice versa. I prefer the second de nition. Because both absolute changes in ethnic composition and housing prices are subject to time trends, the correlation between them can be spurious. Table 1 shows that Vancouver became more ethnically diverse and more expensive during this period. Even if these two phenomena are entirely unrelated, we could still nd a signi cant relationship between them. Relative changes, however, are detrended, so the correlation is less likely to be spurious. 23
Heckman et al. (1998) describe the technical details of these assumptions. A nontechnical description is provided later in this section.
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Changes in ethnic composition are clearly endogenous to neighborhood changes because residential sorting by income or unobservable individual characteristics a¤ects both housing prices and ethnic composition. The conditional di¤erence-in-di¤erences method is designed to address this problem. Figure 1 illustrates the key concept. The squares represent neighborhoods or census tracts. Suppose that tract A is treated, while B, C, and D are not. The color represents the propensity scores, with lighter colors indicating higher scores. The score equals the predicted treatment probability from a parametric probit model.24 According to the estimated scores, tracts B and D are better matches. Suppose D has the propensity score closest to A. The "best match" method will select D as the comparison unit. The "n best matches" will select a group of tracts as the comparison. If n = 2, the selected tracts will be B and D. The method of matching assumes that house price in tract D can act as an estimate of the counterfactual outcome for tract A had A experienced no treatment. Consequently, a consistent estimate of the treatment e¤ect equals the price di¤erential between A and D. However, the housing price in D may not be a good proxy for the counterfactual outcome in A. The conditional di¤erence-in-di¤erences method assumes instead that the bias or the approximation error of using the housing price in D to proxy the counterfactual for A remains xed over time. Consequently, a consistent estimate of the treatment e¤ect is the di¤erence-in-di¤erences estimator (t0 > t): (HV alA;t0 HV alA;t ) (HV alD;t0 HV alD;t ) :25 I also modify the matching method by focusing on neighboring tracts. Tracts that are neighbors can share some common unobservable time-varying neighborhood characteristics. Matching based on both geographic proximity and propensity score therefore relies on weaker identifying assumptions. In Figure 1, the "neighbor and the best match" method selects tract B as the comparison, although its propensity score is slightly further from A than 24
The probit model includes all neighborhood characteristics except the Her ndahl index as independent variables. Due to space limitations, these estimates are not reported, but are available from the author upon request. 25 Note that the expression equals (HV alA;t0 HV alD;t0 ) (HV alA;t HV alD;t ), where HV alA;t HV alD;t is the bias from the approximation at time t because both tracts are not treated yet. Therefore, HV alD;t0 + (HV alA;t HV alD;t ) is a good proxy for the counterfactual for A at t0 as long as the bias is the same in both periords.
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that of D. The "average of all neighbors" method selects both B and C as the comparison, which is no longer conditional di¤erence-in-di¤erences but rather a simple di¤erence-in-di¤erences strategy.
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4.4.2. Results The dataset is the panel constructed for use in sections 4.1 and 4.3. Table 6 reports the estimated average treatment e¤ect on the treated group for di¤erent de nitions of treatment. There are four de nitions in total: (1) an increase in the absolute values of the overall Her ndahl index; (2) an increase relative to the change in the city-wide overall Her ndahl index; (3) an increase in the absolute values of the minority Her ndahl index; (4) an increase relative to the change in the city-wide minority Her ndahl index. The latter two are reported to better separate the e¤ect of majority share from that of the Her ndahl index. All of the Her ndahl indices are based on home language. Because multiple before-after observations are included, i.e., 1986-1991, 1991-1996, and 1996-2001, we have to assume that these before-after pairs are independent over time to aggregate them into a result for all periods.26 We report the estimated treatment e¤ects for each period and the overall average, shown in the column labeled "All Years". Two matching methods, namely the "best match" and "10 best matches", are reported in this table. I measure housing price movement using both the self-reported housing values (Panels A.1 and A.2) and the repeat-sale price indices (Panels B.1 and B.2). Because the results are similar, I focus on summarizing the results in Panels A.1 and A.2. In Panel A.1, the "best match" method shows that neighborhoods that become more homogeneous overall experience lower price appreciation. The estimate is -3.8% using all of the before-after observations. However, those neighborhoods that become more homogeneous in minority composition experience higher price appreciation. The positive estimate of 2.4% is statistically signi cant. The estimates based on the "10 best matches" are similar. Panel A.2 shows a slightly di¤erent picture. We observe mixed results as to how overall ethnic diversity a¤ects housing price movement. The e¤ect of minority concentration, however, is still a positive 2.9% and statistically signi cant. After subtracting a city-wide trend in ethnic composition move26
The assumptions made here are formally presented in Miquel (2003).
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ment, Panel A.2 provides a more reliable estimate of the treatment e¤ect than Panel A.1. Similarly, Panel B.2 is preferred to Panel B.1. A robust nding in this table is the positive relationship between minority concentration and house price appreciation. Table 7 reports the same set of results as that in Table 6. The "neighbor and best match" method conditions the matching on both the propensity score and whether the treatment and the control tracts are, in fact, neighboring. The "average of all neighbors" method is only based on geographic proximity; thus, it is the di¤erence-in-di¤erences estimator. Again, Panels A.2 and B.2 are preferred to Panels A.1 and Panel B.1, respectively, because the former two de ne treatment by a detrended change in ethnic composition. The results are essentially the same as those in Table 6. The results in Tables 6 and 7 are consistent with previous results from the xed e¤ects models. The e¤ect of the overall concentration is mostly negative but not very strong. The concentration of minority groups has a strong and statistically signi cant positive e¤ect. In light of my theory of social interactions and housing price determination, these results suggest that intra-group interactions generate greater bene ts for the individuals.
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4.5. Other Measures of Ethnic Diversity There are alternative measures of ethnicity in the data, including places of birth or origin, ethnic origins, and religious a¢liations. These attributes may a¤ect peoples neighborhood choices and hence housing prices. I redo the conditional di¤erence-in-di¤erences exercise for these measures of ethnic diversity. Table 8 de nes treatment in the relative sense, i.e., an increase in ethnic concentration relative to a city-wide change.27 Columns 2-3 report the results for ethnic composition as measured by mother tongue. All of the census year pairs (1986-1991, 1991-1996, and 1996-2001) are available for this measurement. However, I report only the aggregated results due to space limitations. The results are basically the same as those based on home language. The overall concentration index has a negative but sometimes insigni cant e¤ect, while the minority concentration index has a positive and signi cant e¤ect. 27
Details concerning the construction of these other ethnicity-related variables are contained in the Appendix. The results based on absolute changes in ethnic composition are similar to those for relative changes. Fixed e¤ects models are also run for these measures. The results are similar to the conditional di¤erence-in-di¤erences results.
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Columns 4-9 show additional results based on other de nitions of ethnic groups. These de nitions include ethnic origins (available for 1996-2001 and 1991-1996), places of birth (available only for 1996-2001), and religious a¢liations (available only for 1991-2001). Most of the estimates are insignificant, and no clear pattern is detected. These results could be due to the small sample sizes. It is also possible that these measures do not in fact have signi cant e¤ects on peoples choices and thus do not a¤ect house prices. Ethno-linguistic measures appear to be the only factors that matter in the housing market, at least in the metropolitan area of Vancouver. Further studies are certainly required to test whether this is generally true.
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5. Conclusion
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In this paper, I build a general equilibrium model in which housing prices and the distribution of ethnic groups across neighborhoods are endogenously determined. Under certain conditions, the coexistence of several groups in the same neighborhood can be sustained in the long-term. Such an equilibrium is often implicitly required by hedonic regressions of housing price on continuous measures of ethnic composition. In other words, ethnically diverse neighborhoods have to be stable for the hedonic regression to work. Moreover, I analyze neighborhood choices in the context of multiple groups. This is an improvement over traditional models that assume a white-black or native-immigrant dichotomy. Using additional assumptions of peoples preferences for social interactions, I derive in equilibrium an endogenous correlation between house prices and the Her ndahl index of ethnic composition. This correlation is positive conditional on the share of the majority group. A test of this theory is then carried out using panel data constructed for the metropolitan area of Vancouver, Canada. Both the xed e¤ects models and the conditional di¤erence-in-di¤erences method provide the same results. Conditional on the majority share, an increase in the concentration of ethnic groups positively a¤ects housing price in a neighborhood. However, more data and analyses are needed to test the social interactions mechanism against its alternatives. More realistic formulations of peoples behavior and preferences along the lines of Clark (1992) will be interesting extensions. The relationship between housing price and ethnic composition is found to exist only when we measure ethnicity by linguistic origin. Further investigation in di¤erent cities and countries is warranted to assess whether 28
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and how linguistic characteristics di¤er from other measures of ethnic identity.
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A. Proof of Propositions
ej (r) =
K X
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A.1. Proof Proposition 1 The proof is analogous to the standard proof for the existence of the Walrasian equilibrium such as Proposition 17.C.1 of Mas-Colell et al. (1995). In this model, the excess demand e(r) (e1 (r); :::; eJ (r)) di¤ers slightly from that in Proposition 17.C.1 of Mas-Colell et al. (1995). Here, an element of e(r) or ej (r) contains an additional term P kj (v k1 (r; N1 ); :::; v kJ (r; NJ )) that depends on r: Lk P kj (v k1 (r; N1 ); :::; v kJ (r; NJ ))hkj (r; Nj )
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Lk wjk :
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To prove the proposition, we have to check whether the excess demand e(r) satis es the following conditions (see Proposition 17.B.2 of Mas-Colell et al. (1995)). They are: (1) e(r) is continuous; (2) e(r) is homogeneous of degree zero; (3) e(r) satis es the Walras law or r e(r) = 0 for all r; (4) There is an s > 0 such that ej (r) > s for every neighborhood j and all r; (5) If rn ! r, where r 6= 0 and rj = 0 for some j, then maxfe1 (rn ); :::; eJ (rn )g ! 1. Once these conditions are satis ed by the excess demand function e(r), we can directly apply Proposition 17.C.1. We can show that both v kj (r; Nj ) and hkj (r; Nj ) are continuous and homogeneous of degree zero in r under the conditions on the utility function u(:): Since P kj is continuous in v k1 ; :::; v kJ ; P kj is also continuous in r because continuity is preserved under function composition. We can also con rm that P kj is also homogeneous of degree zero given that v kj (r; Nj ) is homogeneous of degree zero. Consequently, ej (r) is both continuous in r and homogeneous of degree zero. Walras law is satis ed because of the strict monotonicity of the utility function. Condition (4) follows from the fact that both P kj and hk must be nonnegative. Condition (5) is satis ed as long as hkj increase to positive in nity as housing price rj approaches zero while r 6= 0, which is a mild restrictions on hkj . A.2. Proof of Proposition 2 Propositions 17.F.3 and 17.H.1 of Mas-Colell et al. (1995) directly imply Proposition 2.
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A.3. Proof of Proposition 3 I apply a global implicit function theorem by Sandberg (1981) (Corollary 1). There are three conditions to be checked: (1) for some N0 2 , there is J exactly one r0 2 R++ , such that e(r0 ; N0 ) = 0; (2) e(r; N) = 0 is locally solvable; (3) (See Sandberg, 1980, for more details) De ne A and B as open rectangular regions such that A = fN 2 : 0 < Ni < i ; for all i 2 J f1; :::; K Jgg and B = fr 2 R++ : 0 < rl < 'l ; for all l 2 f1; :::; Jgg: (j) 1 For each sequence fN g1 A such that for some index i we have either (j) (j) Ni ! 0 or Ni ! i as j ! 1; there is an index l such that either gl (N(j) ) ! 0 or gl (N(j) ) ! 'l as j ! 1. The rst two conditions are implied directly by Proposition 2 given that e is continuously di¤erentiable and sastis es the gross substitute property. The third condition is the regularity condition required in the proof of this proposition. Because e(r; N) is homogeneous of degree zero, we can restrict J : our analysis of the price vector in the unit simplex in R++ X J B = fr 2 R++ : rj = 1g: j
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Therefore, condition (3) can be rewritten as follows: for each sequence fN(j) g1 1 (j) (j) k A such that for some index i we have either Ni ! 0 or Ni ! L as j ! 1; there is an index l such that either rl = gl (N(j) ) ! 0 or gl (N(j) ) ! 1 as j ! 1 respectively. Roughly speaking, this condition requires that as some component of N approaches zero, some component of r approaches zero as well, while as some component of N approaches Lk , some component of r approaches 1. As long as this condition is satis ed, we can apply Corrollary 1 of Sandberg (1981) to prove the uniqueness and continuous di¤erentiability of g(:) . A.4. Proof of Proposition 4 This proof closely follows the proof of Theorem 1 in Miyao (1978). Each k nj is an element of the following simplex nkj
0 and
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It is well known that a simplex is nonempty, compact, and convex and hence satis es the requirement for applying Brouwers xed point theorem. 34
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The function f (:) maps from the above simplex to itself. The continuity of the mapping P kj and hkj can be con rmed. Because continuity is preserved under the functional composition, f (:) is continuously in N for all N 2 .
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A.5. Proof of Proposition 5 The proof is analogous to the proofs of Theorems 2 and 4 by Miyao (1978). h The di¤erences are two fold: (1) @v kj =@n contains two additional terms PJ @P kl @vl kj @P kl @v kl as shown in Equation (9); (2) j=1 @vkj @nh takes the place of @vkl @nh l
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= 0 for all j 6= l in the model by Miyao (1978). Our proof P kl @v kj simply repeats the steps of Miyao (1978) by substituting Jj=1 @P for @v kj @nh l @P kl @v kl everywhere the latter term appears. For details, see the proofs by @v kl @nh l Miyao (1978) and the comment by Papageorgiou (1982). because
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B.1. Ethnic Good Better access to ethnic goods can be another mechanism. It is possible that certain ethnic goods are better or less expensive in ethnic neighborhoods. These goods can be ethnic groceries, food services, and religious services. The utility function is again Cobb-Douglas with one new component, the xed consumption in ethnic good xk : 1 max Az h xk s.t. z + rh + xk pk (skj ) = y k ; z;h
where pk (skj ) is the price of ethnic good k in neighborhood j. More speci cally pk (skj ) = p 1 skj + 2 (skj )2 ;
where p > 1 > 0 and 12 1 2 0: If 2 = 0, the price is a linear function of skj . If 2 > 0, the price of the ethnic good is strictly decreasing and convex in skj . The parameter p measures the price of the ethnic good when the share of the group is zero. Again, housing demand is increasing in group share skj due to the income e¤ect. Again, Sj = Nj . The housing market clearing condition implies that ) ( X X X y k xk p skj + xk 1 (skj )2 xk 2 (skj )3 : rj =
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If the price of the ethnic good is a convex function of group share, i.e., the housing price will depend on both the Her ndahl index and P2 > 0, then 3 (s ) : Clearly, the Her ndahl index represents the rst order e¤ect of the kj k group shares, while the cubic term represents the second-order e¤ect. Again, income and preference heterogeneity can distort the correlation between the housing price and ethnic composition.
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B.2. Social Capital and Local Public Good The utility function is a Cobb-Douglas function with a public good A(gj ); where gj is the average spending per person in neighborhood j and A0 (gj ) > 0: max A(gj )z h s.t. z + rh + gjik = y k ;
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where gjik is the contribution by an individual i of group k to the public good in neighborhood j. I assume that gjik is chosen from outside of the above maximization problem. Following Vigdor (2002), I assume
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k where k > 0; k + k > 0; and E("ik j ) = 0: The zero-share contribution is the contribution by an individual to the community if she were the only member of group k living in the neighborhood. The within-group a¢nity parameter k is the additional amount that an individual would be willing to pay if her group was the only ethnic group in the neighborhood.28 The parameter "ik j is a mean-zero individual heterogeneity. Therefore, the per capita spending on public goods in neighborhood j is X X k skj + k (skj )2 : gj = k
k
Housing demand decreases with the contribution to the community due to the income e¤ect. Again, I assume that skj = Nj . The housing market clearing condition then implies that ) ( X X rj = y k k skj k (skj )2 : ( + ) k k 28
These two terms are borrowed from Vigdor (2002).
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It is surprising to see that the utility of a worker increases with the Her ndahl index Hj while the housing price decreases with Hj : This is because no supply e¤ect exists. This e¤ect is turned o¤ because I assume per capita housing supply is a constant . The fact more people coming to the neighborhood does not necessarily drive up the price. Instead, because people contribute more to the public good when their group has a higher population share, they are left with less money to spend on housing. The per capita housing demand decreases as Hj increases. Because the per capita housing supply is xed at , house prices must fall. Another reason for this surprising result is the lack of productivity e¤ect of the public good. A formulation of the positive productivity e¤ect is:29 X X yjk = yk + gj = yk + k skj + k (skj )2 ; k
k
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where > 0. Note that yk is the income when social capital in the neighborhood is zero and is the marginal e¤ect of social capital on the income of an individual. Consequently, the housing market clearing condition implies that ( ) X X X 2 3 yk k skj + k k (skj ) + rj = k (skj ) ( + ) k k k The above equation shows that the correlation between the housing price and the Her ndahl index can be decomposed into two e¤ects. They are the positive productivity e¤ect and the negative within-group a¢nity e¤ect k . It is positive as long as the former dominates the latter. In addition, if we are going to separate the a¢nity e¤ect P from 3the productivity e¤ect, we must include higher-order terms such as k (skj ) : When income and preference are heterogeneous across groups, it is important to consider the majority share as a separate factor. 29
The opposite argument that ethnic diversity should be positively related to productivity can be easily incorporated into the model. In that case, the parameter should be negative. More complicated speci cations can also be accommodated.
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C. Construction of the Dataset
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C.1. Geocoding of the Housing Transactions The pro le tables of the census tracts of the Vancouver Census Metropolitan Area are retrieved using the Canadian Census Analyzer provided by the CHASS Data Centre at the University of Toronto. These pro le tables were originally provided by Statistics Canada for release with other Census products. I choose the census years 1986, 1991, 1996, and 2001 because the reported language variables, including mother tongue and home languages, have only been reported in detail since 1986.30 The BCAA housing transaction data are provided by the Centre for Urban Economics and Real Estate at the Sauder School of Business at the University of British Columbia. The data contain all residential real estate transactions in greater Vancouver and in the lower mainland region of the province of British Columbia. The data cover the period from 1986 to 2001. I restrict my analysis to single family housing units, though the data also include condominiums and townhouses. The data report detailed structural and other characteristics. The data that I use to link a street address with a particular census tract are the Block-Face Data File for the 1996 Canadian Census.31 A block-face is the smallest available geographic entity available from Statistics Canada. The block-face information includes street name (including street type and direction), address range, geographic codes, longitude and latitude coordinates for a representative point and the 1996 population and dwelling counts. The geocoding procedure involves the following steps. First, I construct street address variables such as street name, street type, street direction, and the address range, based on address information already in the BCAA housing transaction data. Some errors in coding are found in both the housing data and the block-face data. These errors are corrected. Second, within a census subdivision (a municipality), if a housing transactions address falls into the address range in the block-face data, and the other street address variables match between the two addresses, I can associate the transaction with a unique representative point of a block-face. This representative point 30
For more details about the language variables and other socio-economic variables, see the next section. 31 The Block-Face Data File was discontinued in 2001.
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also has unique longitude and latitude coordinates. Third, I use GIS software (GRASS) to overlay these representative points onto a 2001 map of the Vancouver census tracts. Therefore, I can associate each housing transaction with a unique census tract as de ned by the 2001 Canadian Census. Lastly, each transaction is linked with socio-economic variables at the census tract level according to the year in which the transaction took place. A balanced panel of census tracts based on the de nition of census tracts in 2001 is used in this process. The construction of this panel is explained in the next section.
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C.2. Construction of a Panel of Census Tracts in Vancouver: 1986-2001 For the Census Metropolitan Area of Vancouver, the de nition of the census tracts changed over this period. I must therefore choose a consistent de nition for the census tracts. In this paper, I adopt the 2001 de nition. Statistics Canada provides the Census Tract Correspondence Files for various years (2001-1996, 1996-1991, and 1991-1986). These les are then used to link census tracts over time. Because most changes are splits of old tracts into smaller tracts, I use the characteristics of the old tract as the common characteristics of the several smaller tracts created by these splits. Historical maps of the census tracts are checked to verify the linking procedure. C.3. Construction of Variables The BCAA housing transaction data contain primarily structural and other housing characteristics. Almost all the variables have self-explanatory names. They are shown in Table 2. The neighborhood characteristics at the census tract level are constructed from the census pro le tables mentioned previously. These variables require detailed explanations. Ethno-linguistic variables include three variables, namely the Her ndahl index of all language groups, the Her ndahl index of minority language groups, and the population share of the English-speaking group. These variables can be based on either mother tongue or language spoken at home. A consistent categorization of language groups is based on the language groups reported in 1986. There are 20 groups: English, French, Aboriginal languages, Italian, Portugese, Spanish, German, Yiddish, Dutch, Ukrainian, Russian, Polish, Finnish, Hungarian, Greek, Arabic, Punjabi, Chinese, Vietnamese, and Tagalog (Filipino). Only single responses are used to calculate
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the above indices. The Her ndahl index of all language groups Hj is calculated as K X Hj = (skj )2 ; for all j = 1; :::; J; k=1
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where j indexes the census tracts, k indexes the language groups, and skj denotes the share of group k living in census tract j. The Her ndahl index of minority language groups HMj is calculated as (~ skj )2 ; for all j = 1; :::; J;
k=2
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where s~kj denotes the fraction of group k within the total minority population. The total minority population excludes the English-speaking group, which is denoted by k = 1. The population share of the English-speaking group s1j is simply the share of the English-speaking group in census tract j. These three variables are available for the census years 1986, 1991, 1996, and 2001. Other ethnic diversity measures include those that are based on ethnic origin, religious a¢liation, and place of birth. A consistent categorization of ethnic origins is based on the 1991 de nition, which includes 31 groups.32 In calculating the overall Her ndahl index, I use this 1991 categorization. However, I consider those who report Canadian, English, Scottish, and other British origins as belonging to the majority group. The Her ndahl index of minority groups is calculated by excluding the previous four groups instead of just one group. These variables are available only for the years 1991, 1996, and 2001. A consistent categorization of religious a¢liation is based on the 1991 de nition. There are 21 di¤erent categories.33 I consider all the Protestant 32
The groups are French, English, Scottish, Irish, Other British, German, Canadian, Italian, Chinese, Aboriginal origins, Ukrainian, Dutch (Netherlands), East Indian n.i.e., Polish, Portuguese, Jewish, Black origins, Filipino, Greek, Hungarian (Magyar), Vietnamese, Spanish, Lebanese, Norwegian, Japanese, Yugoslav n.i.e., Korean, Swedish, Croatian, Danish, and Finnish. 33 The religions are Roman Catholic, Ukrainian Catholic, Protestant - United Church, Protestant - Anglican, Protestant - Baptist, Protestant - Presbyterian, Protestant Lutheran, Protestant - Pentecostal, Protestant - Mennonite, Protestant - Jehovahs Witnesses, Protestant - Reformed Bodies, Protestant - Salvation Army, Protestant - Latter-day
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denominations as belonging to the majority group. The diversity measures and the majority share are calculated as those that are based on ethnic origins. Variables based on religious a¢liation are available only for the years 1991 and 2001 because they are reported every 10 years in the Canadian Census. The place of birth categorization is based on the 1996 de nition. There are 51 categories.34 I consider the non-immigrant group as the majority group. The same set of variables is similarly constructed. The variables are available for the census years 1996 and 2001 because the data before 1991 are not available at the country-level and were heavily aggregated.35 Details concerning how the di¤erent categorizations of the language, ethnic origin, place of birth, and religion over time are treated are available from the author upon request. The rest of the neighborhood characteristics can be divided into two subgroups. The rst group of the control variables is the socio-economic characteristics of the neighborhood. The population density is the population of a census tract divided by its land area (in km2 ). The share of retirees equals the population fraction of people of 65 years age and older in a census tract. The unemployment rate is the fraction of unemployed workers. The share of new immigrants equals the people who immigrated during the last 10 years, as a fraction of the total immigrant population. The share of migrants equals the fraction of people who are migrants, or people who moved to the current place of residency within the last 5 years, in the total population ve years old and older. The share of university graduates equals the share of people with a bachelors degree in a census tract. The average household income is the average household-level income in a particular neighborhood. The second group of variables are characteristics of the housing stock. The average housing value equals the average of the self-estimated housing Saints (Mormons), other Protestant, Eastern Orthodox, Jewish, Islam, Buddhist, Hindu, Sikh, and no religious a¢liation. 34 These categories include the Non-immigrant population, United Kingdom, Italy, United States, Hong Kong, India, China, Poland, Philippines, Germany, Portugal, Viet Nam, Netherlands, Jamaica, Greece, Guyana, Sri Lanka, Lebanon, France, Trinidad and Tobago, Yugoslavia, Hungary, Haiti, Taiwan, Iran, Romania, Korea South, Ukraine, Pakistan, El Salvador, Egypt, Croatia, Russian Federation, Ireland, South Africa, Mexico, Austria, Chile, Belgium, Fiji, Morocco, Denmark, Czechoslovakia n.i.e., Malaysia, Cambodia, Switzerland, Tanzania, Kenya, Iraq, Somalia, and Israel. 35 There were 10 regions of birth in 1991 and 7 regions in 1986. These regions are not very useful for constructing meaningful ethnic groups.
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values for all of the owner-occupiers. The share of apartments equals the total share of apartments, including duplex, 5-story and higher, and less than 5 stories, in the housing stock. The ownership rate equals the share of owneroccupied dwellings in the neighborhood. The average age of dwellings equals the weighted average of the dwellings age. This variable is constructed using the counts of dwellings built during various periods of time. The average number of rooms equals the average number of rooms in a dwelling in the neighborhood, which is a proxy for the average dwelling size. There is also information about the quality/condition of the housing stock, but this information is not available for earlier years; thus, I do not include these variables in the analysis.
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Figure 1: Illustration of the Conditional Di¤erence-in-Di¤erence Method
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N 386 363 386 385 386 386 386 386 386 386 386 386 386 386 386 386 386 386 386 386
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1996 Mean 313,383 1.174 0.711 0.459 0.805 0.568 0.116 0.498 8.694 56,475 3,488 0.117 0.49 0.31 0.17 17.869 0.544 0.636 25.129 6.191
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N 386 363 386 377 386 386 386 386 386 386 386 386 386 385 386 386 386 386 386 386 386
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2001 Mean 292,135 1.198 0.751 0.572 0.828 0.544 0.124 0.47 0.225 7.337 65,568 3,857 0.122 0.391 0.241 0.219 17.869 0.53 0.647 27.186 6.34
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Variable Name Average Housing Value ($) Log Repeat Sale Housing Price Index Her ndahl Ind of All - Home Language Her ndahl Ind of Minorities - Home Lang. Share of Majority - Home Language Her ndahl Ind of All - Mother Tongue Her ndahl Ind of All - Ethnic Origin Her ndahl Ind of All - Place of Birth Her ndahl Ind of All - Religion Unemployment Rate Average Household Income ($) Population Density (persons/km 2 ) Share of People above Age 65 Share of New Immigrants Share of Migrants in the Last 5 Years Share of University Graduates Distance to CBD (km) Share of Detached Housing Units Home Ownership Rate Average Age of the Dwelling (yrs) Average No of Rooms per Dwelling
PT
Table 1: Characteristics of Census Tracts in Vancouver: 1986-2001 1991 Mean 238,851 0.801 0.782 0.408 0.863 0.654 0.177 0.181 9.247 52,672 3,300 0.119 0.301 0.336 0.137 17.869 0.587 0.625 24.212 6.311
N 386 363 386 384 386 386 386 386 386 386 386 386 386 386 386 386 386 386 386 386
1986 Mean 123,459 0 0.846 0.348 0.908 0.706 11.834 37,654 2,702 0.116 0.191 0.26 0.111 17.869 0.615 0.623 23.946 6.011
N 386 363 386 382 386 386 386 386 386 386 386 386 386 386 386 386 386 386
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1991 Mean N 223,413 37,111 21.311 37,111 2,278 37,039 10,164 37,106 17.529 37,029 1.374 37,039 3.88 37,026 2.093 37,111 1.283 37,111 0.665 37,111 0.032 37,111 0.17 37,079 0.076 37,111 0.003 37,111 0 37,111 0.021 37,111 0.01 37,111 0.01 37,111 0.127 37,111 0.028 37,111
NU
SC
RI
1996 Mean N 333,941 24,202 21.689 24,202 2,402 24,139 10,382 24,191 19.673 24,131 1.444 24,139 3.966 24,128 2.293 24,202 1.348 24,202 0.669 24,202 0.036 24,202 0.163 24,122 0.072 24,202 0.002 24,202 0 24,202 0.021 24,202 0.014 24,202 0.01 24,202 0.112 24,202 0.03 24,202
MA
2001 Mean N 330,683 22,371 20.408 22,371 2,343 22,305 46,675 22,365 25.62 22,300 1.401 22,304 3.963 22,275 2.25 22,371 1.297 22,371 0.699 22,371 0.036 22,371 0.188 22,314 0.069 22,371 0.003 22,371 0 22,371 0.021 22,371 0.012 22,371 0.011 22,371 0.067 22,371 0.041 22,371
AC CE P
TE
Variable Name Transaction Price ($) Distance to CBD (km) Floor Area (sq feet) Lot Size (sq feet) Age of the Dwelling (yrs) Number of Stories Number of Bedrooms Number of Bathrooms Number of Parking Space With a Deck With a Pool With a Basement Suite On a Cornerlot On a Waterfront Lot On a Water Lot Prime View Good View Fair View New Property Transaction Is a Duplex
PT
Table 2: Summary Statistics of Housing Transactions in Vancouver: 1986-2001
45
1986 Mean N 113,544 26,299 21.066 26,299 2,147 26,269 48,454 26,295 15.024 26,259 1.313 26,271 3.74 26,263 1.955 26,299 1.195 26,299 0.666 26,299 0.037 26,299 0.157 26,283 0.07 26,299 0.003 26,299 0 26,299 0.02 26,299 0.009 26,299 0.008 26,299 0.118 26,299 0.024 26,299
46
FE (1) -0.275 a (0.060)
FE (2) 0.474 a (0.108) -0.976 a (0.118)
0.001 (0.001) 0.009 a (0.002) 1.220 a (0.041) -0.040 a (0.006) 1.856 a (0.107) 0.651 a (0.054) 0.346 a (0.076) 0.233 b (0.097) Yes Yes -0.952 b (0.400) 1541 0.011 a (0.002) 0.253 a (0.044) -0.070 a (0.019) 0.699 a (0.142) -0.074 (0.053) 0.016 (0.074) 0.115 (0.122) Yes Yes 9.263 a (0.462) 1541 0.951
0.010 a (0.002) 0.282 a (0.043) -0.071 a (0.018) 0.733 a (0.138) -0.050 (0.052) 0.024 (0.072) 0.143 (0.119) Yes Yes 9.098 a (0.450) 1541 0.953
0.109 a (0.023)
FE (3)
0.011 a (0.002) 0.239 a (0.044) -0.069 a (0.019) 0.627 a (0.144) 0.027 (0.048) 0.033 (0.075) 0.048 (0.124) Yes Yes 9.138 a (0.469) 1528 0.950
0.010 a (0.002) 0.298 a (0.044) -0.089 a (0.018) 0.668 a (0.140) -0.120 b (0.050) 0.015 (0.073) 0.113 (0.121) Yes Yes 9.128 a (0.457) 1528 0.953
0.009 a (0.002) 0.254 a (0.043) -0.066 a (0.018) 0.773 a (0.139) -0.035 (0.052) 0.007 (0.073) 0.148 (0.120) Yes Yes 9.649 a (0.456) 1541 0.953
1.150 a (0.164)
FE (5) -1.888 a (0.237)
0.010 a (0.002) 0.277 a (0.043) -0.069 a (0.018) 0.758 a (0.138) -0.043 (0.052) 0.017 (0.072) 0.155 (0.119) Yes Yes 9.399 a (0.469) 1541 0.953
0.723 b (0.326)
FE (6) -0.403 (0.411) -1.091 a (0.129)
0.010 a (0.002) 0.275 a (0.043) -0.070 a (0.018) 0.755 a (0.138) -0.036 (0.052) 0.019 (0.072) 0.147 (0.119) Yes Yes 9.231 a (0.529) 1541 0.954
0.875 (0.943) -0.616 (1.754) 0.063 (1.094)
FE (7) -0.346 (0.414) -0.533 (0.740)
0.010 a (0.002) 0.280 a (0.043) -0.071 a (0.018) 0.741 a (0.138) -0.050 (0.052) 0.025 (0.072) 0.149 (0.119) Yes Yes 9.202 a (0.484) 1541 0.953
0.223 (0.383)
FE (9) 0.158 (0.553) -0.972 a (0.119)
PT
RI
0.010 a (0.002) 0.249 a (0.044) -0.069 a (0.019) 0.714 a (0.142) -0.075 (0.053) 0.018 (0.074) 0.126 (0.123) Yes Yes 9.452 a (0.497) 1541 0.951
0.411 (0.394)
FE (8) -0.851 (0.555)
SC
NU
MA
-0.497 a (0.065) 0.079 a (0.022)
FE (4)
D
TE
AC CE P
RE (1) -0.471 a (0.053)
The dependent variable is the logarithm of average self-reported housing values by census tracts. All variables about ethnic composition are based on home language. The housing attributes at census tracts level include share of detached housing units, home ownership rate, average age of dwelling, age squared, and average number of rooms per dwelling. RE(1) is a random e¤ect model and the rest are xed e¤ects models. Standard errors are in parentheses. a , b , and c represent signi cance levels 1%, 5%, and 10% respectively.
N R-Squared
Housing Attributes Year Dummies Constant
Share of University Grads
Share of Migrants
Share of New Immigrants
Share of Above Age 65
Log Population Density
Log AVG Household Income
Unemployment Rate
Distance to CBD (km)
3 k=1 skj
PK
Squared Majority Share s2j1
Interaction Hj sj1
Hj2
Minority Her ndahl Ind HMj
Share of Majority sj1
Overall Her ndahl Ind Hj
Table 3: Ethno-Linguistic Diversity and Self-Reported Housing Value: Fixed E¤ects Models
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FE (1) -0.016 (0.058)
FE (2) 0.544 a (0.115) -0.755 a (0.131)
-0.009 a (0.001) -0.008 a (0.003) 0.046 (0.039) 0.019 a (0.006) 1.005 a (0.103) -0.194 a (0.060) -0.070 (0.057) 1.978 a (0.084) Yes Yes No 7.654 a (0.468) 109,447 0.828
-0.010 a (0.003) 0.001 (0.002) 0.056 (0.044) -0.014 (0.019) -0.121 (0.155) 0.063 (0.043) 0.161 a (0.062) 0.358 a (0.108) Yes Yes Yes 7.765 a (0.449) 109,447 0.849
-0.010 a (0.003) 0.000 (0.002) 0.118 a (0.039) -0.019 (0.017) -0.061 (0.143) 0.094 b (0.041) 0.115 b (0.057) 0.330 a (0.105) Yes Yes Yes 7.394 a (0.425) 109,447 0.849
-0.010 a (0.003) 0.000 (0.002) 0.064 (0.042) -0.016 (0.020) -0.153 (0.157) 0.057 (0.043) 0.177 a (0.062) 0.333 a (0.109) Yes Yes Yes 7.672 a (0.456) 108,776 0.848
-0.010 a (0.003) -0.000 (0.002) 0.112 a (0.038) -0.016 (0.017) -0.013 (0.136) 0.109 a (0.041) 0.104 c (0.056) 0.350 a (0.105) Yes Yes Yes 7.918 a (0.414) 109,447 0.849
1.278 a (0.316)
FE (6) -1.027 b (0.460) -0.931 a (0.121)
-0.010 a (0.003) -0.001 (0.002) 0.110 a (0.038) -0.015 (0.017) -0.016 (0.135) 0.120 a (0.041) 0.110 b (0.055) 0.337 a (0.105) Yes Yes Yes 7.489 a (0.453) 109,447 0.849
1.574 c (0.922) -1.004 (1.600) -0.2 16 (1.163)
FE (7) -0.891 b (0.402) 0.333 (0.618)
0.654 (0.411) -0.010 a (0.003) 0.000 (0.002) 0.113 a (0.038) -0.018 (0.017) -0.040 (0.141) 0.096 b (0.041) 0.117 b (0.057) 0.350 a (0.105) Yes Yes Yes 7.691 a (0.434) 109,447 0.849
FE (9) -0.385 (0.649) -0.743 a (0.140)
PT
0.801 c (0.462) -0.010 a (0.003) 0.001 (0.002) 0.052 (0.043) -0.013 (0.019) -0.093 (0.152) 0.066 (0.043) 0.162 a (0.061) 0.382 a (0.108) Yes Yes Yes 8.122 a (0.433) 109,447 0.849
FE (8) -1.143 c (0.661)
RI
SC
NU
-0.010 a (0.003) -0.001 (0.002) 0.094 b (0.041) -0.012 (0.018) -0.008 (0.135) 0.115 a (0.041) 0.115 b (0.056) 0.356 a (0.105) Yes Yes Yes 7.945 a (0.423) 109,447 0.849
1.211 a (0.124)
FE (5) -1.726 a (0.186)
MA
-0.010 a (0.003) -0.000 (0.002) 0.106 b (0.043) -0.026 (0.019) -0.082 (0.145) 0.001 (0.046) 0.160 a (0.061) 0.350 a (0.108) Yes Yes Yes 7.532 a (0.458) 108,776 0.849
-0.229 a (0.067) 0.043 b (0.019)
FE (4)
D
0.056 a (0.019)
FE (3)
TE
AC CE P
RE (1) -0.357 a (0.042)
The dependent variable is log housing price. All variables about ethnic composition are based on home language. The housing attributes included are log oor area, log lot size, number of stories, number of bedrooms, number of bathrooms, number of parking space, age of the house, squared house age, a dummy for the presence of a pool, a deck, or a basement, a dummy for whether it is on a waterfront lot, a water lot, or a corner lot, transaction type dummy, whether the house is a duplex, and dummies indicating the view of the house. Standard errors are in parentheses and clustered by Census Tracts. a , b , and c represent signi cance levels 1%, 5%, and 10% respectively.
N R-Squared
Housing Attributes Year Dummies Census Tract Dummies Constant
Share of University Grads
Share of Migrants in Recent 5 Yrs
Share of New Immigrants
Share of Above Age 65
Log Population Density
Log AVG Household Income
Unemployment Rate
Distance to CBD (km)
3 k=1 skj
PK
Squared Majority Share s2j1
Interaction Hj sj1
Hj2
Minority Her ndahl Ind HMj
Share of Majority sj1
Overall Her ndahl Ind Hj
Table 4: Ethno-Linguistic Diversity and Individual Transaction Price: Fixed E¤ects Models
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FE (2) 0.405 b (0.190) -0.512 b (0.207)
FE (3)
-0.003 (0.003) 0.336 a (0.079) 0.320 a (0.027) 0.203 (0.283) 0.111 (0.095) 0.310 b (0.121) 0.313 (0.225) Yes -5.973 a (0.848) 1308 0.931
-0.003 (0.003) 0.370 a (0.080) 0.316 a (0.027) 0.240 (0.282) 0.131 (0.095) 0.284 b (0.121) 0.311 (0.225) Yes -6.174 a (0.850) 1308 0.932
-0.003 (0.003) 0.337 a (0.078) 0.312 a (0.027) 0.124 (0.285) 0.070 (0.087) 0.319 a (0.122) 0.295 (0.227) Yes -5.927 a (0.855) 1298 0.931
-0.004 (0.003) 0.357 a (0.081) 0.307 a (0.027) 0.157 (0.287) 0.042 (0.092) 0.310 b (0.122) 0.311 (0.227) Yes -5.991 a (0.858) 1298 0.931
D
-0.112 (0.120) 0.080 b (0.041)
FE (4)
TE
0.087 b (0.040)
AC CE P
FE (1) 0.017 (0.107)
1.259 c (0.695) -0.003 (0.003) 0.363 a (0.080) 0.318 a (0.027) 0.284 (0.283) 0.132 (0.095) 0.285 b (0.121) 0.355 (0.226) Yes -5.614 a (0.903) 1308 0.932
FE(9) -1.387 (1.008) -0.481 b (0.207)
PT
RI
1.393 b (0.694) -0.003 (0.003) 0.330 a (0.079) 0.322 a (0.027) 0.254 (0.283) 0.113 (0.095) 0.309 b (0.121) 0.362 (0.226) Yes -5.367 a (0.899) 1308 0.932
FE (8) -1.940 b (0.981)
SC
-0.003 (0.003) 0.370 a (0.080) 0.318 a (0.027) 0.300 (0.283) 0.127 (0.096) 0.266 b (0.122) 0.360 (0.226) Yes -5.183 a (0.979) 1308 0.932
-1.172 (1.712) 2.166 (3.164) 1.290 (1.968)
FE (7) -0.862 (0.749) -2.551 b (1.292)
NU
-0.004 (0.003) 0.368 a (0.080) 0.319 a (0.027) 0.277 (0.283) 0.143 (0.095) 0.271 b (0.121) 0.335 (0.225) Yes -5.804 a (0.879) 1308 0.932
0.961 (0.593)
FE (6) -0.766 (0.746) -0.663 a (0.227)
MA
-0.004 (0.003) 0.354 a (0.079) 0.322 a (0.027) 0.260 (0.283) 0.142 (0.095) 0.283 b (0.121) 0.332 (0.225) Yes -5.848 a (0.847) 1308 0.932
0.722 b (0.293)
FE (5) -0.999 b (0.427)
The dependent variable is the logarithm of a repeat sale housing price index by Census Tracts. All variables about ethnic composition are based on home language. No housing attribute is included. Standard errors are in parentheses. a , b , and c represent signi cance levels 1%, 5%, and 10% respectively.
N R-Squared
Year Dummies Constant
Share of University Grads
Share of Migrants
Share of New Immigrants
Share of Above Age 65
Log Population Density
Log AVG Household Income
Unemployment Rate
3 k=1 skj
PK
Squared Majority Share s2j1
Interaction Hj sj1
Hj2
Minority Her ndahl Ind HMj
Share of Majority sj1
Overall Her ndahl Ind Hj
Table 5: Ethno-Linguistic Diversity and Repeat-Sale Housing Price Index: Fixed E¤ects Models
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PT
RI
SC
NU
MA
sale housing price index. Standard errors are in parentheses.
a, b,
and
c
represent signi cance levels 1%, 5%, and 10% respectively.
types of housing price appreciation are reported (Panels A.1 and A.2 versus Panels B.1 and B.2): the self-reported housing value and the repeat
groups, while columns 6-9 corresponding to changes in the concentration index of minority groups only. Panel A.2 and Panel B.2 de ne treatment as an increase in the group concentration index relative to the change in the MSA-wide concentration index. Columns 2-5 and Columns 6-9 have similar representations as those in Panels A.1 and B.1. Two methods of matching are shown: best match and the average of 10 best matches. Two
The reported values are treatment e¤ects of changes in ethnic concentration on log housing values by census tracts. Panel A.1 and Panel B.1 de ne treatment as an increase in the group concentration index, with columns 2-5 corresponding to changes in the overall concentration of all language
D
TE
AC CE P
Table 6: Treatment E¤ects: Conditional Di¤erence-in-Di¤erences Estimates Overall Conentration Index Minority Conentration Index All Years 1986-1991 1991-1996 1996-2001 All Years 1986-1991 1991-1996 1996-2001 Panel A.1: Average Self-Reported Housing Value: Absolute Change in Concentration as Treatment Best Match -0.038a -0.063b -0.035 -0.033a 0.024a 0.011 0.030a 0.030b (0.010) (0.026) (0.028) (0.012) (0.006) (0.010) (0.010) (0.012) 10 Best Matches -0.036a -0.050b -0.034 -0.034a 0.031a 0.020b 0.037a 0.035a (0.008) (0.022) (0.031) (0.008) (0.005) (0.008) (0.007) (0.009) Number of Obs. 418 69 48 301 770 239 235 296 Panel A.2: Average Self-Reported Housing Value: Relative Change in Concentration as Treatment Best Match 0.019b 0.015 0.042b -0.017 0.029a 0.028b 0.021 0.034a (0.009) (0.012) (0.017) (0.019) (0.007) (0.012) (0.014) (0.012) 10 Best Matches -0.015b -0.005 -0.033a -0.002 0.029a 0.021b 0.019b 0.042a (0.007) (0.009) (0.012) (0.013) (0.006) (0.009) (0.009) (0.010) Number of Obs. 631 239 253 139 609 208 158 243 Panel B.1: Repeat Sale Housing Price Index: Absolute Change in Concentration as Treatment Best Match -0.047a -0.059 -0.030 -0.047a 0.013 0.026 0.012 0.003 (0.014) (0.042) (0.037) (0.015) (0.011) (0.023) (0.018) (0.018) 10 Best Matches -0.031a -0.048 -0.037 -0.026b 0.010 0.036c 0.019 -0.018 (0.010) (0.030) (0.023) (0.011) (0.008) (0.019) (0.013) (0.012) Number of Obs. 382 65 41 276 695 216 215 264 Panel B.2: Repeat Sale Housing Price Index: Relative Change in Concentration as Treatment Best Match -0.006 -0.019 -0.012 0.026 0.044a 0.067b 0.050b 0.020 (0.012) (0.023) (0.014) (0.026) (0.013) (0.027) (0.022) (0.020) 10 Best Matches -0.030a -0.057a -0.034a 0.027 0.031a 0.048b 0.034b 0.016 (0.009) (0.017) (0.011) (0.019) (0.010) (0.021) (0.017) (0.014) Number of Obs. 573 218 231 124 551 186 150 215
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PT
RI
SC
NU
MA
housing value and the repeat sale housing price index. Standard errors are in parentheses. respectively.
a, b,
and
c
represent signi cance levels 1%, 5%, and 10%
groups, while columns 6-9 corresponding to changes in the concentration index of minority groups only. Panel A.2 and Panel B.2 de ne treatment as an increase in the group concentration index relative to the change in the MSA-wide concentration index. Columns 2-5 and Columns 6-9 have similar representations as those in Panels A.1 and B.1. Two methods of matching are shown: neighbor and best match and the average of all nontreated neighbors. Two types of housing price appreciation are reported (Panels A.1 and A.2 versus Panels B.1 and B.2): the self-reported
The reported values are treatment e¤ects of changes in ethnic concentration on log housing values by census tracts. Panel A.1 and Panel B.1 de ne treatment as an increase in the group concentration index, with columns 2-5 corresponding to changes in the overall concentration of all language
D
TE
AC CE P
Table 7: Treatment E¤ects: Spatial Conditional Di¤erence-in-Di¤erences Estimates Overall Conentration Index Minority Conentration Index All Yrs 1986-1991 1991-1996 1996-2001 All Yrs 1986-1991 1991-1996 1996-2001 Panel A.1: Average Self-Reported Housing Value: Absolute Change in Concentration as Treatment Neighbor and Best Match -0.035a -0.049c -0.027 -0.032b 0.024a 0.007 0.027b 0.037a (0.013) (0.025) (0.034) (0.016) (0.008) (0.013) (0.013) (0.014) Average of Neighbors -0.022c -0.036c 0.011 -0.025c 0.030a 0.029b 0.029b 0.032b (0.012) (0.020) (0.029) (0.015) (0.007) (0.013) (0.012) (0.013) Number of Obs. 305 63 46 196 577 184 187 206 Panel A.2: Average Self-Reported Housing Value: Relative Change in Concentration as Treatment Neighbor and Best Match -0.012 -0.006 -0.031c -0.003 0.025a 0.023c 0.017 0.033b (0.009) (0.014) (0.016) (0.018) (0.008) (0.013) (0.015) (0.013) Average of Neighbors -0.011 -0.010 -0.025 -0.0004 0.033a 0.040a 0.024c 0.032a (0.008) (0.013) (0.015) (0.014) (0.007) (0.013) (0.013) (0.012) Number of Obs. 364 121 111 132 526 168 150 208 Panel B.1: Repeat Sale Housing Price Index: Absolute Change in Concentration as Treatment Neighbor and Best Match -0.012 -0.016 -0.022 -0.008 0.005 0.020 0.004 -0.006 (0.019) (0.061) (0.038) (0.019) (0.011) (0.025) (0.019) (0.016) Average of Neighbors -0.027c -0.073b -0.046 -0.007 0.002 0.013 0.016 -0.021 (0.014) (0.036) (0.028) (0.017) (0.010) (0.022) (0.015) (0.015) Number of Obs. 239 54 35 150 488 154 162 172 Panel B.2: Repeat Sale Housing Price Index: Relative Change in Concentration as Treatment Neighbor and Best Match -0.044a -0.087a -0.050b -0.002 0.033a 0.069b 0.044b -0.004 (0.015) (0.032) (0.021) (0.023) (0.012) (0.029) (0.019) (0.015) Average of Neighbors -0.041a -0.091a -0.050a 0.010 0.024b 0.062b 0.040b -0.019 (0.013) (0.029) (0.018) (0.019) (0.011) (0.026) (0.017) (0.014) Number of Obs. 306 99 94 113 445 140 132 173
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51
PT
RI
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NU
MA
Standard errors are in parentheses.
a, b,
and
c
represent signi cance levels 1%, 5%, and 10% respectively.
1996-2001, 1991-1996, and 1986-1991), ethnic origin (aggregation of 1996-2001 and 1991-1996), place of birth (1996-2001), and religious a¢liation (1991-2001), compared with MSA-wide changes in the corresponding indices. Two sets of results are reported: the results for the overall Her ndahl index and those for the minority Her ndahl index. Four methods of matching are employed. Best match and 10 best matches are reported in Panel A and Panel B. Neighbor and best match and the average of all nontreated neighbors are reported in Panel C and Panel D. Panel A and Panel C use the self-reported housing values as the outcome variable, while Panel B and Panel D use the repeat-sale price index as the outcome variable.
when treatment is de ned as a relative increase in terms of a Census tracts Her ndahl Indices that are based on mother tongue (aggregation of
The reported values are treatment e¤ects of changes in ethnic concentration on log housing values by census tracts. Columns 2-9 reports results
D
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Table 8: Other Ethnic Diversity Measures: Conditional Di¤erence-in-Di¤erences Estimates Mother Tongue Ethnic Origin Birthplace Religion Overall Minority Overall Minority Overall Minority Overall Minority Panel A: Average Self-Reported Housing Value - Propensity Score Best Match -0.016b 0.007 0.035a -0.027a 0.017 0.004 0.008 0.029c (0.008) (0.008) (0.012) (0.010) (0.012) (0.014) (0.017) (0.015) 10 Best Matches -0.011c 0.026a 0.021b -0.027a 0.005 0.006 0.010 0.024b (0.006) (0.007) (0.008) (0.008) (0.010) (0.010) (0.012) (0.012) Number of Obs. 736 518 324 429 219 203 232 247 Panel B: Repeat Sale Housing Price Index - Propensity Score Best Match -0.019c 0.044a 0.006 0.028b 0.009 -0.019 -0.034 0.011 (0.010) (0.013) (0.017) (0.013) (0.017) (0.024) (0.021) (0.020) 10 Best Matches -0.041a 0.036a 0.012 0.017c 0.017 0.023c -0.017 0.011 (0.009) (0.011) (0.013) (0.010) (0.013) (0.013) (0.015) (0.015) Number of Obs. 675 472 286 381 199 181 209 223 Panel C: Average Self-Reported Housing Value - Score and Neighbor Neighbor and Best Match -0.007 0.037a 0.016 -0.008 0.012 0.026c 0.018 0.023 (0.009) (0.009) (0.012) (0.010) (0.016) (0.015) (0.017) (0.016) Average of Neighbors -8.74e-5 0.034a 0.013 -0.014 0.017 0.003 0.021 0.014 (0.008) (0.008) (0.010) (0.009) (0.014) (0.012) (0.016) (0.015) Number of Obs. 406 420 301 340 188 187 193 188 Panel D: Repeat Sale Housing Price Index - Score and Neighbor Neighbor and Best Match -0.002 0.038a 0.022 0.013 0.017 -0.006 -0.009 0.015 (0.015) (0.013) (0.014) (0.012) (0.018) (0.017) (0.019) (0.021) Average of Neighbors -0.008 0.043a 0.013 0.006 0.011 -0.021 0.004 0.016 (0.013) (0.012) (0.012) (0.011) (0.016) (0.015) (0.018) (0.018) Number of Obs. 322 353 243 283 159 155 157 154
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Highlights I analyze the effect of ethnic diversity on neighborhood house prices.
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A general equilibrium model with multiple groups and the housing market is presented.
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Ethnic composition is capitalized into house prices, supporting the existence of non-
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market social interactions.
S0166-0462(14)00042-8 doi: 10.1016/j.regsciurbeco.2014.04.007 REGEC 3052
To appear in:
Regional Science and Urban Economics
Received date: Revised date: Accepted date:
21 December 2011 17 April 2014 22 April 2014
Please cite this article as: Li, Qiang, Ethnic Diversity and Neighborhood House Prices, Regional Science and Urban Economics (2014), doi: 10.1016/j.regsciurbeco.2014.04.007
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Ethnic Diversity and Neighborhood House Prices Qiang Li1
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Department of Real Estate, School of Design and Environment, National University of Singapore, 4 Architecture Drive, Singapore 117566
Abstract
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In recent decades, the large inux of immigrants to the U.S. and other developed countries has made cities in these countries more ethnically diverse. In this paper, I aim to understand whether and how ethnic diversity a¤ects communities in these cities. A general equilibrium model is built in which people of many ethnic groups interact in the housing market through both price signals and non-market mechanisms. An endogenous correlation between neighborhood house price and the Her ndahl index of ethnic concentration arises because of social interactions. After addressing the endogeneity issue, I nd that neighborhoods with more homogeneous minority populations command higher prices using a dataset of housing transactions and neighborhood socio-economic characteristics in Vancouver, Canada. This and other ndings support the notion that non-market social interactions inuence peoples preference and behavior. Key words: Ethnic diversity, housing, neighborhood choice
1 Email: [email protected]. This paper is a revision of Chapter 3 of my PhD dissertation submitted to the University of British Columbia. I am indebted to my supervisor Bob Helsley for his encouragement and guidance. My dissertation committee members Keith Head, Sanghoon Lee, and Tsur Somerville provided valuable inputs. The comments by Danny Ben-Shahar, Lu Han, Haifeng Huang, Dean Lacy, Charles Leung, Katherine ORegan, Kuzey Yilmaz, and audiences at NUS, 2009 AREAUA International, 2009 NARSC, 2011 Urban Economics Association, and 2012 AREAUA Annual meetings are greatly appreciated. I also thank the editor and two anonymous referees for valuable comments that improve the paper substantially. Financial support by Neville Gibson and Grosvenor Scholarship at UBC Sauder is greatly appreciated. This research is also sponsored by Shanghai Pujiang Program. All errors are mine.
Preprint submitted to Elsevier
April 17, 2014
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1. Introduction
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In recent decades, immigration to advanced economies has dramatically changed their ethnic landscapes. For example, only 4.7% of the U.S. population were born in a foreign country in 1970, while the same statistic jumped to approximately 13% in 2000 and remained at this level until 2010. Among immigrants in 1970, approximately 60% were born in Europe, 19% in Latin America, and 9% in Asia. In 2010, the share in European countries decreased to 12%, while the shares in Latin American and Asian countries increased signi cantly to 53% and 28%, respectively. To a lesser extent, Canada and European countries have experienced similar changes, i.e., higher ethnic diversity. How do changes in ethnic landscapes a¤ect urban neighborhoods, residents housing and neighborhood choices, and housing market outcomes? To answer these questions, I perform three sequential tasks. First, I build a general equilibrium model to tie all of the above factors together. Speci cally, the allocation of multiple ethnic groups across neighborhoods results from choices made by individuals. Moreover, both housing prices and ethnic composition directly a¤ect individuals decisions in the rst place.2 As a result, housing prices closely depend on the ethnic composition of neighborhoods. Many papers employ the hedonic methodology of Rosen (1974) to regress housing prices on measures of ethnic composition and hope to reveal peoples preferences for group composition through these estimates.3 Hedonic methods require the housing market to be in equilibrium and to o¤er a continuum of choices of neighborhood characteristics, including shares of ethnic groups. However, theoretical models of ethnic segregation, such as Schelling (1969, I assume that people can freely choose communities. Peoples preference for ethnic composition in a multiethnic context can be quite complicated, as illustrated by Clark (1992), who nds that individuals seem to have a optimum racial mix in mind and do not always prefer more of their own group. 3
Zabel (2008) reviews the literature using hedonic regressions to test whether minorities pay higher housing prices (evidence of discrimination or centralized racism) and whether people pay more for larger share of their own group (evidence for prejudice or decentralized racism). An incomplete list includes earlier papers, such as King and Mieszkowski (1973) and Yinger (1978), and recent studies, such as Kiel and Zabel (1996) and Cutler et al. (1999). A related line of research directly estimates whether ethnic composition is capitalized into house prices. These papers are summarized later in the introduction.
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1971), OSullivan (2009), and Zhang (2011), and those of race and housing markets, such as the border models of Bailey (1959) and Rose-Ackerman (1975) and the amenity model of Yinger (1976), predict complete segregation as the most probable equilibrium.4 Apparently, such an equilibrium cannot generate a continuum of group shares; therefore, the hedonic method is not consistent with these models. The general equilibrium model o¤ers a solution. I build on the work of Miyao (1978) by adding a housing market to relate housing price to ethnic composition. Two key results are obtained. Firstly, if people indeed have a preferred ethnic composition, neighborhood housing prices can be expressed as a continuous function of some measures of ethnic composition. Secondly, racially mixed neighborhoods can be stable if preference for living with certain groups is not too strong. Consequently, we can observe a full spectrum of group distribution in the data as long as the number of neighborhoods is su¢ciently large. Additionally, this theoretical framework ts the analysis of ethnic diversity very well because it allows many ethnic groups, in contrast to the white-black or native-immigrant dichotomy often assumed by previous researchers. My second task is to derive a parametric model of housing price determination with a focus on the role of ethnic composition. Speci c microfoundations are needed to make such connection more concrete. People may prefer to live close to people from the same group to enjoy better social interactions. Evidence in support of this mechanism is provided by Marmaros and Sacerdote (2006), who show that geographic proximity and within-race a¢nity can explain many friendships between individuals. Given this mechanism, I obtain a straightforward parametric relationship between housing price and a natural measure of ethnic composition in a multiethnic context, namely, the Her ndahl index Hj : Hj =
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(skj )2 ; for all j = 1; :::; J;
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where K denotes the number of ethno-linguistic groups and J denotes the number of neighborhoods in a city. skj is the population share of group k in neighborhood j. This index can be interpreted as the probability that two 4
In some cases, these models also admit racially mixed neighborhoods. However, such neighborhoods are often considered as exceptions rather than likely outcomes.
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randomly selected persons belong to the same group and is thus a measure of ethnic concentration.5 Therefore, to test whether people care about ethnic composition is reduced to testing whether housing price is correlated with the Her ndahl index. Further analysis shows that income and preference heterogeneity can hinder the interpretation of the correlation. In these cases, it is important to separate the e¤ect of the majority share from that of the overall Her ndahl index. My last task involves devising an identi cation strategy to estimate this correlation. The theory demonstrates an empirical challenge in that housing prices and ethnic composition are simultaneously determined. Intuitively, ethnic composition is endogenous in the determination of housing price because many unobservable neighborhood and personal characteristics inuence both at the same time. I address this endogeneity problem by constructing a panel of housing transactions as well as census tract characteristics in the metropolitan area of Vancouver, Canada. Here, census tracts correspond to neighborhoods in the theory. The panel structure enables me to account for time-invariant unobservable neighborhood characteristics that may be correlated with ethnic composition. The dataset covers four census years: 1986, 1991, 1996, and 2001. Employing standard xed e¤ects regressions, we can consistently estimate the endogenous correlation under standard identifying assumptions. The panel structure also enables the implementation of an alternative identi cation strategy, the conditional di¤erence-in-di¤erences method proposed by Heckman et al. (1998). This approach combines propensity score matching (Rosenbaum and Rubin, 1983) with the di¤erence-in-di¤erences method to estimate the treatment e¤ect of a policy change or a social program that may be endogenous. The treatment in this papers context is de ned as an increase in ethnic concentration.6 The key to applying this method is nding a matching pair: one with treatment and one without 5
The Her ndahl index is closely related to the ethno-linguistic fractionalization (ELF) index commonly used in the large literature on ethnic diversity and economic performance, reviewed by Alesina and LaFerrara (2005). The fractionalization index equals one minus the Her ndahl index exactly. Therefore, ELF is a measure of diversity, while Hj is a measure of concentration. 6 Two de nitions of treatment are implemented: (1) an increase in absolute value in the Her ndahl; (2) an increase relative to the overall change in the Her ndahl for the metropolitan area.
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treatment. The criterion in determining the pair is the propensity score or predicted probability of treatment generated in a model of treatment. Another approach is to select neighboring tracts. Here, we implicitly assume that some unobserved neighborhood attributes are shared by neighboring communities.7 After we obtain the pair, a di¤erence-in-di¤erences estimator is created to represent the treatment e¤ect. This method imposes no parametric restriction on the housing price equation. In addition, it employs di¤erent identifying assumptions from those of xed e¤ects models.8 All in all, these new results can corroborate the xed e¤ects models. All methods yield essentially the same results. The overall ethno-linguistic concentration index has mostly insigni cant, but negative, e¤ects on housing prices. However, if we control for the majority share, the sign changes from negative to positive. Meanwhile, the minority Her ndahl index, excluding the English-speaking group, has a strong positive e¤ect. Fixed e¤ects models also indicate that the correlation is nonlinear, but a precise identi cation of this relation is infeasible due to data limitations. Other measures of ethnicity, such as place of birth, ethnic origin, and religion, are found to have no signi cant e¤ect on housing prices. In summary, the empirical results support the notion that non-market interactions have a substantial inuence on peoples decisions. This paper is most closely related to the literature on the capitalization of ethnic composition into housing prices. Examples are Coulson and Bond (1990), Bajari and Kahn (2005), and Fu (2005), who use cross-sectional data, and Macpherson and Sirmans (2001), Clapp et al. (2008), and Saiz and Wachter (2011), who use panel data. As these papers employ the hedonic method, my model provides theoretical support for these empirical studies. In addition, my empirical analysis di¤ers from these papers in the following ways: (1) I ask the question in a multi-ethnic context and (2) the data enable me to implement both the xed e¤ects and the conditional di¤erencein-di¤erences methods. 7
This method is therefore similar in spirit to Black (1999) and Bayer and McMillan (2008), who use boundary xed e¤ects to identify the e¤ect of their variables of interest. It is also related with di¤erence-in-di¤erences analysis at border areas such as Dhar and Ross (2012) and Dachis et al. (2012). I should note that there are no clear policy variations across neighborhoods in my analysis, but rather variations over time of ethnic composition. 8 For details about the identifying assumptions, see Section 4.4.1 or Heckman et al. (1998).
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My theory resembles the discrete choice models of Bayer et al. (2004), Bayer and Timmins (2005), Bayer et al. (2007), Bayer and Timmins (2007), and Wong (2013). Their approach is more general because they model preference for ethnic composition as well as other factors. I am able to derive a reduced form relationship between housing price and the Her ndahl index in a simpler model. An empirical test of such a relationship follows. In contrast, they aim to estimate the structural parameters of the utility function directly. These two approaches should complement each other. In the next section, I present a general equilibrium theory of neighborhood choice with multiple ethnic groups. Several examples are shown to lead to a correlation between housing price and ethnic diversity. Section 3 describes the housing transaction data and the census data. Section 4 reports the main results using various methods. Finally, I conclude and discuss the key ndings in Section 5.
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2. A Model of Ethnic Diversity and Neighborhood Choice
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2.1. Model Setup: Ethnicity, Neighborhood, and Utility Maximization In a closed city, each individual from K ethnic groups chooses one and only one neighborhood to live in. The population size of each ethnic group is xed, denoted by Lk (k 2 f1; 2; :::; Kg). There are J neighborhoods in the city, where J is much larger than K. Each neighborhood has a xed housing supply of Sj (j 2 f1; 2; :::; Jg): Housing is perfectly divisible. The utility of an individual i of group k that lives in neighborhood j is equal to Vikj (rj ; y k ; qjk ) v kj (rj ; y k ; qjk ) + "ij max u(z; h; qjk ) + "ij subject to z + rj h = y k : z;h
(1)
Vikj (rj ; y k ; qjk ) is composed of two additively separable components: the indirect or representative utility v kj (rj ; y k ; qjk ) and an independent and identically distributed amenity shock "ij for each individual and every neighborhood.9 9
The i.i.d. assumption about "ij is restrictive yet necessary to simplify my analysis. An identical distribution means that people of di¤erent groups only di¤er in terms of their evaluations of ethnic composition. Independence implies that unobservable neighborhood attributes are not correlated across neighborhoods.
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In the budget constraint, rj denotes the housing price in neighborhood j, and y k denotes the common income level within group k.10 The direct utility function u(z; h; qjk ) depends on the consumption of both composite good z and housing h and the quality of the neighborhood qjk : Assume that @u=@z > 0; @u=@h > 0; and @u=@q > 0. Ethnic composition determines the quality of a neighborhood. Formally, k k qj = q k (n1j ; n2j ; :::; nK j ); where nj is the population of group k in neighborhood j: Notice that quality is in the eye of the beholder, i.e., people of di¤erent groups assign di¤erent quality indices for the same neighborhood. In addition, the formulation of qjk can accommodate many types of preferences. For example, if individuals of group k like to live with people of group h, then @qjk =@nhj > 0; for h 2 f1; :::; Kg: If individuals care the size of the neighP k borhood, then @qjk =@ k nj Q 0: Preference for ethnic diversity can be P P 2 k < 0, where k (skj )2 measures ethnic concenmodeled by @qj =@ k (skj ) tration. To facilitate further analysis, I assume that the city is a pure exchange economy. Formally,
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y k = rwk and
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where wk = (w0k ; w1k ; w2k ; :::; wJk )0 0 is a strictly positive vector of endowments in the composite good (denoted by w0k ) and housing assets (denoted by wjk ), and r = (1; r1 ; :::; rJ ) is the corresponding price vector. In an exchange economy, individuals obtain income from their endowments. Furthermore, the total housing supply Sj equals the total endowments of housing in each neighborhood. The neighborhood choice problem for an individual involves two steps. First, she chooses a consumption plan given a hypothetical choice of a neighborhood. Second, she compares utilities across neighborhoods and chooses the neighborhood that o¤ers the highest utility. Let P kj denote the probability that an individual of group k chooses neighborhood j. De ne Nj 10
I implicitly assume that no discrimination exists in the housing market and that no within-group heterogeneity in income exists. Any residual individual heterogeneity is absorbed by "ij : In addition, any additional heterogeneity does not violate the i.i.d. requirement.
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"il > v kl
v kj ] for all l 6= j 2 f1; :::; Jg:
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(n1j ; n2j ; :::; nK j ) or the vector of population distribution in neighborhood j. Utility maximization implies that
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Note that v kj = v kj (rj ; y k ; qjk ) = v kj (r; Nj ; wk ), where I substitute rwk for y k and q k (Nj ) for qjk to obtain the second equality. If we specify a probability distribution for ("i1 ; :::; "iJ ), we can then express the choice probability P kj as a function of the house price vector r and a vector of inter-neighborhood group allocation N (N1 ; N2 ; :::; NJ ). In addition, P kj must satisfy the following two conditions: J X
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(2) (3)
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2.2. Equilibrium: Existence and Uniqueness of Neighborhood House Prices In contrast to the model by Miyao (1978), housing prices play a key role in this paper. This extension enables me to analyze housing price and ethnic composition at the same time. In the present context, an equilibrium is de ned as an ethnic allocation N and a price vector r that satisfy the following: (1) the housing markets in all neighborhoods clear and (2) the allocation N is consistent with utility maximization for all. Once r is known, we can solve for consumption of housing fhkj ; 8k; jg and composite good fz k ; 8kg: Let the demand for housing be hkj (rj ; y k ; Nj ) = hkj (r; Nj ) for an individual of group k in neighborhood j: The housing market clearing conditions are K K X X k kj kj L P (r; N)h (r; Nj ) Lk wjk = 0; where j 2 f1; 2; :::; Jg: k=1
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The left-hand side can be expressed as a vector e(r; N), an excessive demand function.11 The above equation system is equivalent to e(r; N) = 0; 11
(4)
In the above equation system, the market clearing condition for the composite good z is not included because I have normalized the price of z to one, i.e., it is the numeraire good. This normalization does not a¤ect the generality of the results. I could prove all propositions by including a market clearing condition for the numeraire good.
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P kj (v k1 (r; N1 ); :::; v kJ (r; NJ ))Lk = 0; 8k; j;
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fjk (r; N) nkj
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J where r 2 R++ is a strictly positive vector, N 2 fnkj j0 nkj Lk ; 8j; kg 2 KJ R ; and is a closed rectangular region. If people maximize utility, then the selection probability P kj must equal the actual proportion of group k choosing neighborhood j; or nkj =Lk :
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P such that Jj=1 nkj = Lk for all k; and fjk (r; N) is the k j th element of the vector function f (r; N) of dimension K J. Solving the system of equations (4) and (5) is rather di¢cult. I solve the problem in two steps. First, I solve Equation (4) for the price vector r conditional on N; i.e., taking N as exogenous variables. If such a price vector exists, I then characterize conditions under which r can be expressed as a function of N. In the second step, I search for a solution N to the equation f (r; N) = 0 under the condition that r is indeed a function of N. The second step involves the search for a xed point for the mapping P kj (N)Lk from N 2 to itself.
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Proposition 1. 12 If the utility function u(z; h; Nj ) is continuous, strictly quasi-concave, and strictly increasing in h, and P kj (v k1 ; :::; v kJ ) is continuous in v k1 ; :::; v kJ for all k, a strictly positive price vector r exists to clear all of the neighborhood housing markets conditional on a population distribution N. Proposition 1 shows that a price vector exists, but it does not rule out multiple equilibria. Multiple equilibria often make comparative statics analysis problematic. The gross substitute property, de ned below, is utilized to establish the uniqueness and stability of the price vector. De nition 1. The excess demand function e(r; N) has the gross substitute property if whenever r0 and r are such that, for some j, rj0 > rj and rl0 = rl for l 6= j, we have el (r0 ; N) > el (r; N). Proposition 2. If the excess demand function e(r; N) is continuously di¤erJ entiable in r 2 R++ and satis es the gross substitute property, then e(r; N) = 0 has a unique solution r conditional on N. Additionally, the solution r is 12
The proofs of this and other propositions can be found in the Appendix.
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stable given the following dynamic adjustment process when r( ) at time is out of equilibrium: (6)
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Are these conditions in Proposition 2 restrictive? Continuous di¤erentiability is satis ed when the utility function and the distribution functions of ("i1 ; :::; "iJ ) behave nicely. The gross substitute property is very restrictive. It implies that excess demand increases as housing prices in other neighborhoods increase. However, we can con rm that both conditions are satis ed if the utility function is Cobb-Douglas and the choice probability is based on the logit model of McFadden (1974). I should note that these conditions are su¢cient but not necessary, so there may exist cases when uniqueness and stability hold even though these conditions are violated. The results in Proposition 2 are useful to empirical researchers. Because of uniqueness, researchers do not have to worry about multiple equilibria in testing the comparative statics implied by their theoretical models. Because hedonic regressions implicitly require that housing markets are in a long-run equilibrium, the global stability of the equilibrium justi es the estimation of the hedonic price of ethnic composition. Proposition 3. If the excess demand function e(r; N) is continuously differentiable in r N and satis es the gross substitute property and a reguJ larity condition, then there exists a unique function g : ! R++ such that e(g(N); N) = 0 for all N2 and g(N) is continuously di¤erentiable on : The result in Proposition 3 is useful to solve the xed-point problem in the next section. The classical implicit function theorem is of limited help because it only ensures the local solvability of r in terms of N. A global implicit function theorem (Sandberg, 1981, Corollary 1) is hence used to establish the global solvability of r: The additional regularity condition required in this proposition is explained in the Appendix. Roughly speaking, it requires that as nkj approaches the boundary of ; rj also approaches its boundary. In the next section, the properties of g(N) are used to prove the existence and stability of an equilibrium that admits ethnically diverse neighborhoods. 10
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Proposition 3 goes further than Proposition 2 by showing that housing price is a continuous function of all group population sizes N. In empirical applications, we could adopt a more parsimonious speci cation that con nes to group sizes in the same neighborhood Nj :
P kj (v k1 (g(N); N1 ); :::; v kJ (g(N); NJ ))Lk = 0; 8k; j:
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2.3. Equilibrium: Existence and Stability of Group Allocation Given the result in Proposition 3, Equation (5) can be rewritten as:
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Proposition 4. If the following conditions are satis ed: (1) All conditions in Proposition 3 hold, (2) v kj (r; N1 ) is continuous in nkj for 0 nkj L PK k kj k1 kJ kj for all k 2 f1; :::; Kg k=1 L ; and (3) P (v ; :::; v ) is continuous in v and j 2 f1; :::; Jg; then there exists an equilibrium distribution of the population N .
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Next, I establish conditions under which such an equilibrium is unique and stable. Following Miyao (1978), I de ne stability as whether the following dynamic adjustment process converges over time: nkj ( + 1) = P kj (v k1 (g(N( )); N1 ( )); :::; v kJ (g(N( )); NJ ( )))Lk ;
(7)
where denotes the time. In other words, there is a one-period lag for individuals to adjust their behavior to the desired choice. Proposition 5. If the following conditions are satis ed: (1) All conditions in Proposition 3 hold, (2) v kj (r; Nj ) is di¤erentiable in nhj ; (3) P kl (v k1 ; :::; v kJ ) is di¤erentiable in v kj and @P kl =@v kj 0 for all l 6= j; (4) v kj (g(N); Nj ) is di¤erentiable in r; and ! K J X X 1 @P kl @v kj Lk < ; for all j; l 2 f1; :::; Jg and k; h 2 f1; :::; Kg; h kj @v 2 @nl j=1 k=1 (8)
then the equilibrium solution N is unique and globally stable.
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Proposition 5 shows that the equilibrium is unique and globally stable if kj h the marginal e¤ect of population size on utility or @v =@nl is su¢ciently small, i.e., if peoples preference for or aversion to certain groups is not too strong. A similar point was made by Miyao (1978).13 In fact, my model o¤ers an even more optimistic view because of the addition of the price mechanism. This point is best illustrated by expanding the total derivative of v kj (g(N); Nj ) with respect to nhl or @v kj =@nhl :
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Income E¤ect
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Direct E¤ect
(9)
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where gj (N) = rj : This seemingly complicated expression has an intuitive interpretation. The rst term represents the direct e¤ect of population size on utility, the only e¤ect analyzed by Miyao (1978). This study includes two new e¤ects: the own price e¤ect and the income e¤ect. The two additional e¤ects tend to counterbalance the direct e¤ect. Take @v kj =@nkj as an example. Suppose utility to group k increases with its own size in neighborhood j; or @v kj (g(N); Nj )=@nkj > 0. A positive migration shock of group k to neighborhood j is likely to attract even more people from group k: If housing prices in neighborhood j increase so that @gj (N)=@nkj > 0; the own price e¤ect becomes negative because @v kj =@gj (N) < 0. The income e¤ect is also negative because people obtain income from their endowments. Their income and utility increase with housing prices in other neighborhoods, so @v kj =@gj 0 (N) > 0. However, @gj 0 (N)=@nkj < 0 because an increase in nkj reduces housing demand in other neighborhoods and hence lowers prices.14 Therefore, Proposition 5 provides additional assurance to the practice of regressing housing prices on measures of ethnic composition. However, such 13
See also Anas (1988) for a discussion of the stability of equilibrium and taste heterogeneity. 14 Di¤erent combinations of v kj and nhl are listed as follows: (1) j = l; k = h; (2) j = l; k 6= h; (3) j 6= l; k = h; (4) j 6= l; k 6= h: Case (1) is discussed in the main text. For cases (3) and (4), no direct e¤ect exists, and the other two e¤ects are small. Case (2) is more complicated. If @v kj =@nhj > 0, an increase in nhj increases nkj , so the own price e¤ect is likely to be negative, thus canceling the direct e¤ect. If @v kj =@nhj < 0; an increase in nhj decreases nkj , so the own price e¤ect is ambiguous or negative but smaller and thus the net e¤ect is unknown. The income e¤ect is mostly negative for all scenarios. Therefore, the net e¤ect is ambiguous. As long as these e¤ects are small, stability is still present.
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regressions su¤er from the endogeneity problem. Section 4 develops identi cation strategies to resolve this issue, while Section 2.4 derives a parametric housing price equation using additional assumptions.
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2.4. House Prices and Ethnic Diversity: The Role of Social Interactions People care about neighborhood ethnic composition for many reasons. I provide below an example that illustrates how social interactions can a¤ect peoples locational choices. This idea dates back at least to Beckman (1976). Recent research provides some empirical support for this idea. For example, Currarini et al. (2009) and Marmaros and Sacerdote (2006) have shown that people tend to form social ties with people who are from the same group and who reside nearby. Additional examples with di¤erent mechanisms are included in Appendix B. People consume three goods: the numeraire good z, housing h, and social interactions q(t), which depends on the time t spent in interactions. Note that q(t) is now speci ed as the quantity of social interactions, while Equation (1) only vaguely states that it is related to the quality of the neighborhood. People have di¤erent incomes and opportunity costs of time across groups. They maximize a Cobb-Douglas utility function:
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max Az h q(t)1 z;h;t
s.t. z + rh + ck t = y k ;
where ck is the opportunity cost of time. To simplify, an individual of ethnic group k consumes a xed quantity qk of social interactions, where qk = tk + bk (s1j ; :::; sKj ):
The rst term tk denotes the time spent on phone calls, internet socializing, and so on, while the latter term bk (s1j ; :::; sKj ) is the quantity of social interactions from living in the neighborhood itself. It is free because it comes from random meetings, except that the individual must rent a house to live there. Consequently, this term depends on the ethnic composition or group shares fskj g for all k. A neighborhood is more desirable to an individual if its bk (s1j ; :::; sKj ) is larger because he will save on time spent on social interactions. Housing supply is linear in population size, i.e., Sj = Nj .15 15
This assumption removes the supply e¤ect because the per capita housing supply is a constant everywhere. As a result, in-migration to a neighborhood does not necessarily generate upward pressure on price.
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bk (s1j ; :::; sKj ) = b0 skj + ab0 (1
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2.4.1. Constant Bene ts The simplest case involves constant but di¤erent bene ts from intra-group and inter-group interactions. I assume that each intra-group meeting generates a bene t of b0 , while each inter-group meeting gives a payo¤ b0 a. The parameter a captures the di¤erence. These bene ts do not vary across groups. Therefore, the expected bene t from these random meetings is skj ) = ab0 + b0 skj (1
a),
(10)
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where skj is the probability of meeting a person from the same group, while 1 skj is the probability of meeting a person from another group. If a < 1, higher group share increases the bene ts of random meetings and thus lowers the individuals time spent on other types of interactions. She can a¤ord more expenditures on housing. Thus, individual housing demand increases with her group share. In turn, the housing price that equalizes demand and supply is ( ) X X rj = y k + ck ab0 qk skj + (1 a) b0 ck s2kj :
(a + ) k k
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Proposition 6. If income y k , the opportunity cost of time ck , and the xed amount of required social interactions qk are equal across all groups, then the neighborhood housing price will be increasing in the Her ndahl index of ethnic group composition. Proof. If y k = y, ck = c, and qk = q for all k, the rst summation P becomes 2 becomes c(1 a)b y + c(ab0 q) and the second summation 0 k (skj ) : As P 2 long as a < 1, rj will be increasing in k (skj ) . Proposition 6 implies that a parametric model can be used to test whether people value ethnic composition. Note that social interactions have no e¤ect on housing prices if a = 1 or if there is no ine¢ciency for inter-group interactions. Holding other variables constant, a positive correlation between the Her ndahl index and the neighborhood housing price represents evidence for inter-group communication ine¢ciencies. A negative correlation, on the other hand, signi es a positive bene t for inter-group communications. If y k ; ck ; and qk are not homogeneous across groups, the correlation becomes less straightforward. The case of three groups is analyzed with an assumption that ck = c for all k. Because s1j + s2j + s3j = 1 and 14
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P Hj 3k=1 (skj )2 , we have two degrees of freedom in the set fs1j ; s2j ; s3j ; Hj g. For example, I can vary Hj and s1j independently, but not all of Hj ; s1j ; and s2j . I solve for s2j and s3j as a function of Hj and s1j , which I use to denote the share of the majority group: i 1h 2 1=2 1 s1j 2Hj (1 s1j ) s2j ; s3j = : 2
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Without loss of generality, I assume that group 2 is larger in size than group 3. We obtain the following result: " # 2 2 3 3 (y c q ) (y c q ) @rj = + c(1 a)b0 (11) 2 @Hj s1j
( + ) 2 (2Hj (1 s1j ) )1=2
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Proposition 7. Suppose there are three ethnic groups. If the net income q k of the second largest group is higher than that of the third largest y k c group, the neighborhood house price will be increasing in the Her ndahl index Hj . Otherwise, as long as the bene t from social interactions b0 is large enough or the ine¢ciency from inter-group interactions 1 a is large enough, the neighborhood house price will be increasing in the Her ndahl index Hj . Proof. Both claims are directly implied by Equation (11). As long as the condition for the rst claim is satis ed, both terms on the left-hand side of Equation (11) are positive. The condition in the second claim can be (y 3 c q 3 ) (y 2 c q2 ) expressed more formally as 2(2H (1 s )2 )1=2 < c(1 a)b0 . The right-hand side j 1j of the inequality is always positive, while the left-hand side can be positive or negative. Therefore, the scale of b0 and 1 a are important determinants of the sign of the price derivative. The key point of Proposition 7 is that the correlation between the housing price and the ethnic diversity index can be distorted by income and preference heterogeneity in the population. In these cases, it is important to control the share of one group to identify @rj =@Hj in a regression analysis. Proposition 7 also shows that the sign of @rj =@Hj is intricately related with the more fundamental preference parameter a. For cases with more than three groups, closed-form solutions for @rj =@Hj are unlikely. However, the intuition in this simple three-group case should be applicable to the more general cases.
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2.4.2. Diminishing Bene ts from Intra-group Interactions Wong (2013) showed that preference with respect to ones own groups share people exihibits an inverted-U-shape. The next example illustrates how such a preference can result from diminishing bene ts from intra-group interactions. To make the model tractable, I abstract away from inter-group income variation and other dimensions of heterogeneity. Suppose the bene t from intra-group interactions is b0 + b1 skj , where b1 < 0. Consequently, the expected bene t from random meetings is ab0 + b0 skj (1
a) + b1 s2kj :
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a) This function achieves its maximum at b0 (1 . Because skj 2 (0; 1), 2b1 k b (s1j ; :::; sKj ) is always decreasing in skj if a > 1, while it is always increasing in skj if a < 1 + 2bb01 : If a 2 (1 + 2bb01 ; 1); the preference will be unimodal. The three parameters a; b0 , and b1 ; characterize the type of preference people have for social interactions and hence the equilibrium housing price: ( ) X X rj = ! + (1 a) b0 c s2kj + b1 c s3kj ; (12)
( + ) k k
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where ! = y + c (ab0 q) : Similar to the results in Proposition 6, housing price is increasingP in the Her ndahl index as long as a < 1. However, an additional term k s3kj emerges due to the diminishing e¤ects. One special case is when only the majority group has diminishing bene ts from intra-group interactions, in which case Equation (12) simpli es to ( ) X ! + (1 a) b0 c s2kj + cb1 s31j : (13) rj =
( + ) k We can con rm that housing price is increasing in the overall Her ndahl index and decreasing in the majority share. Equation (13) shows that we need to separate the e¤ects of the majority from that of the Her ndahl index, even if the population is homogeneous. In an empirical analysis, we have to control the majority share if we believe that the majority group is satiable with respect to its group share. Alternatively, if minority individuals have satiable preferences, the housing price becomes ( ) X X rj = ! + (1 a) b0 c s2kj + b1 c s3kj : (14)
( + ) k k6=1 16
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in the neighborhood is
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As a result, the housing price ( rj = ! + (1
( + ) ( = ! + (1
( + ) +cs1j b1 s21j (1
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2.4.3. Diminishing Bene ts and Distinction among Majority, Own Group, and All Other Groups The rst two examples assume that individuals treat people from all other groups the same. In reality, a minority individual may receive additional bene ts from interactions with people from the majority group because such interactions provide better job information and better chances of assimilation (Patacchini and Zenou, 2012; Zenou, 2013). On the other hand, such interactions may be deemed undesirable by his culture and hence less valuable. I distinguish among three types of interactions faced by a minority individual: those with the majority population, those within his own group, and those with all other groups.16 The bene t function simpli es to b0 skj + a1 b0 s1j + ab0 (1 s1j skj ) for k 6= 1 k b (s1j ; :::; sKj ) = : (a1 b0 + b1 s1j ) s1j + ab0 (1 s1j ) for k = 1
a) b0 c
X
s2kj + cs1j b1 s21j + b0 (a1
X
s2kj
k6=1
a) b0 c
k=1
a)b0 s1j + b0 (a1
a)
:
) a) (15)
(16)
The above equations include some additional terms, such as cb1 s31j ; b0 (a1 a)cs1j ; and c(1 a)b0 s21j . The importance of controlling for the majority share in a regression of housing price on the Her ndahl index is shown once again. These new terms reect the di¤erent valuations people place on various types of interactions. Although housing price is still increasing in the overall Her ndahl index as well as the minority Her ndahl index, it may increase or decrease with the majority share due to these additional terms.
2.5. Empirical Implications of the Theory Both the general model and the examples have implications for the empirical analysis. First, the model shows quite clearly that housing prices and 16
We can in principle generalize this by allowing bene ts to di¤er for every grouppair. We may even allow asymmetry for the bene ts experienced by the two persons in a meeting. I leave those generalizations for future research.
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neighborhood ethnic composition are simultaneously determined. In other words, a simple regression of neighborhood house prices on ethnic composition is unlikely to produce consistent estimates. Resolving the endogeneity problem will be the focus of my empirical analysis. Speci cally, I exploit variations in the time dimension and use panel data techniques to address the problem. Second, the general model also assures researchers that we can run hedonic regressions to estimate the e¤ect of ethnic composition on housing price. As shown by Propositions 3 and 5, the observed neighborhood con gurations can be considered to be in a long-run equilibrium as long as preference for ethnicity is not too strong and neighborhoods are substitutes for one another. In contrast, most models of ethnic segregation in the spirit of Schelling (1969) do not admit ethnically mixed neighborhoods. Therefore, my theory provides a new justi cation for the hedonic analysis of ethnicity and housing price. Next, the examples in the previous section imply a straightforward relationship between housing price and the Her ndahl index. In fact, restrictive assumptions on preference are made to arrive at this parametric model. I have also shown that di¤erent formulations of peoples preferences lead to di¤erent parametric speci cations. As demonstrated by Clark (1992), peoples preferences for ethnic composition can be quite complicated. I certainly cannot exhaust all possibilities, so future research is needed. Finally, the examples show that correlation between price and the Her ndahl index reveals information about peoples preferences. A positive correlation suggests greater bene ts from intra-group interactions, and vice versa. However, income heterogeneity across groups and diminishing bene ts from intra-group interactions can complicate the interpretation. It is hence necessary to include the majority share in a housing price regression. In addition, we can construct a Her ndahl index for minority groups and include this measure and the majority share in the regression. 3. Data I combine housing transaction data and census data for the metropolitan area of Vancouver, Canada.17 The census data are the 1986, 1991, 1996, and 2001 Canadian Census Pro le Tables at the census tract level. The data 17
Details about the data sources can be found in the Appendix.
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include a self-reported housing price and other neighborhood characteristics. The census tract is an appropriate unit of measurement because it closely corresponds to our concept of a neighborhood.18 I construct a balanced panel of census tracts using the Census Tract Correspondence Files for various years.19 Table 1 summarizes the neighborhood characteristics. From 1986 to 1996, the average housing value in Vancouver more than doubled. However, the housing value dropped from 1996 to 2001. The city became more diverse, as measured by the overall Her ndahl index of home language, mother tongue, ethnic origin, and place of birth. At the same time, the concentration within minority groups increased, as reected by the higher minority Her ndahl index (home language). The unemployment rate dropped, while the average household income, population density, share of people with bachelors degrees, and new immigrants were on the rise. Variables that were relatively stable include home ownership rate, the share of migrants, and the average number of rooms per dwelling. In general, Vancouver has experienced steady growth from 1986 to 2001. The housing transaction data are from the British Columbia Assessment Authority (BCAA). I focus primarily on single-family homes.20 The data contain information on a houses attributes and its transaction price. I include only the transactions in the years 1986, 1991, 1996, and 2001 for which I could associate the transaction with a census tract. The geocoding procedure is explained in more detail in the Appendix. Table 2 lists the summary statistics for the transaction dataset. The average transaction prices are somewhat higher than the average estimated According to Statistics Canada, "Census tracts (CTs) are small, relatively stable geographic areas that usually have a population of 2,500 to 8,000. They are located in census metropolitan areas and in census agglomerations with an urban core population of 50,000 or more in the previous census. A committee of local specialists (for example, planners, health and social workers, and educators) initially delineates census tracts in conjunction with Statistics Canada. Once a census metropolitan area (CMA) or census agglomeration (CA) has been subdivided into census tracts, the census tracts are maintained, even if the urban core population subsequently declines below 50,000." 19 Details concerning the construction of this dataset and the description of the variables can be found in the Appendix. 20 Because single-family houses and condominiums di¤er in many attributes that are di¢cult to quantify, I avoid the omitted variables problem by dropping condominiums from the analysis.
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housing values shown in Table 1, but the general time trend is similar. The transacted houses shown here are slightly newer than the overall housing stock. The numbers of rooms in a dwelling are similar across the two datasets. These similarities suggest that the results based on the self-reported housing values should not di¤er considerably from those based solely on real transactions.
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4. Ethno-Linguistic Diversity and House Prices
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My primary goal is to test whether there is a structural relationship between housing price and ethnic concentration. To achieve this objective, the endogeneity issue must be resolved. Speci cally, there are two sources of the endogeneity problem. First, some unobservable neighborhood characteristics, such as natural amenities, are valued di¤erently across groups. These characteristics thus a¤ect both housing prices and ethnic compositions. If these characteristics are relatively stable over time, we can employ panel xed e¤ects models. Second, some neighborhood characteristics describe the attributes of its residents, e.g., average income, average education, and cultural background. Ethnic composition belongs to this category. If some resident characteristics are unobservable and vary over time and are also correlated with ethnic composition, we can no longer use xed e¤ects to address the endogeneity issue. In this case, conditional di¤erence-in-di¤erence (Heckman et al., 1998) o¤ers an alternative solution.21 4.1. Fixed E¤ects Models: Self-Reported Housing Value In this section, the average self-reported housing value HV aljt in neighborhood j and census year t is modeled as a function of neighborhood characteristics: ln HV aljt = f (Hjt ; HMjt ; s1jt ; ) + Zjt + Mjt + j + t + "jt ;
(17)
where f (Hjt ; HMjt ; s1jt ; ) is a function of the overall ethno-linguistic diversity index Hjt , the diversity index for minority groups HMjt , and the share of majority group s1jt . Zjt is a vector of socio-economic characteristics; Mjt is a vector of characteristics of the housing stock; j denotes an individual 21
Details about the identifying assumptions for the xed e¤ects and conditional di¤erence-in-di¤erence methods are explained later.
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census tract xed e¤ect; t denotes the census-year dummies, and "jt is an i.i.d. error term. All of the variables are measured at the census tract level and obtained from the census data. The average self-reported housing values are based on all housing units in the census tract but are subject to measurement errors. The identifying assumption is that the included regressors are not correlated with "jt . The assumption is violated in two cases. First, we may parameterize f (Hjt ; HMjt ; s1jt ; ) incorrectly, giving rise to the omitted variable problem. Second, unobservable characteristics that vary over time may be correlated with the included regressors. In these cases, the xed e¤ects model in Equation (17) no longer ensures identi cation. To address the misspeci cation problem, I specify a variety of parameterizations for f (Hjt ; HMjt ; s1jt ; ). To solve the second problem, we must resort to a di¤erent method later in this paper. Table 3 shows the results for the xed e¤ects model. All of the ethnicityrelated variables are based on home languages. Model RE (1) includes neighborhood characteristics but not census tract xed e¤ects. The identi cation comes from both cross-sectional and time-series variations. The coe¢cient before the overall He ndahl index is negative and signi cant, i.e., more ethnically diverse neighborhoods have higher house prices on average. However, estimates in RE (1) are unlikely to be reliable because ethnic composition and other neighborhood characteristics are endogenous in price determination. In addition, we need to control for the majority group share because group heterogeneity in income and preference complicates the correlation between housing price and the Her ndahl index.22 Models FE (1) to (4) show the results when the above issues are addressed. In fact, the coe¢cient estimates dropped for most control variables. This suggests that residential sorting along these variables is likely. In other words, unobserved neighborhood characteristics a¤ect peoples choices and the price at the same time. FE (1) to (4) achieve identi cation from time-series variations in the data. Although FE (1) demonstrates a negative relationship between housing price and the overall Her ndahl index, FE (2) shows a positive relationship. FE (2) is preferred because it addresses group heterogeneity and more complex preferences by holding the majority share constant. The positive coe¢cient before the Her ndahl index indicates 22
See the discussions after Propositions 7 and Sections 2.4.2 and 2.4.3 for details.
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ine¢ciency from inter-group interactions according to Proposition 7. The negative coe¢cient before the majority share reects the group heterogeneity in income and other personal attributes, the more complicated preferences analyzed in Sections 2.4.2 and 2.4.3, or both. FE (3) and FE (4) circumvent group heterogeneity by examining the e¤ect of minority concentration. Both FE (3) and FE (4) allow the Her ndahl index of minority concentration to freely vary from 0 to 1. FE (4) includes the majority share as one additional control and is thus comparable to FE (2). In general, FE (3) and FE (4) provide similar results to FE (2), i.e., more ethnically homogeneous communities experience greater price appreciation once the majority share is controlled for. Models FE (5) to FE (7) test for nonlinearities. These models allow very exible function forms for f (Hjt ; HMjt ; s1jt ; ): The speci cations are not motivated by theoretical analysis in Sections 2.4.2 and 2.4.3. Instead, these speci cations aim to capture the non-linear interactions between the Her ndahl index and the majority share because of group heterogeneity. FE (5) shows that housing price decreases with Hjt and achieves its minimum when Hjt = 0:82: Because Hjt > 0:82 only if the majority share is above 0.9, the housing price is decreasing in Hjt in most of its range. FE (6) shows that housing price is decreasing in Hjt if the majority share is below 55%, but increasing in Hjt if the majority share is above 55%. The di¤erence lies in the inclusion of majority share in FE (6). FE (7) accounts for all of the second-order terms, but the coe¢cients are no longer statistically signi cant, possibly due to an insu¢cient number of data points to identify these e¤ects. In FE (8) and FE (9), I attempt to test the implications of my analysis P 3 in Sections 2.4.2 using the sign patterns of Hjt and K s . k=1 kj FE (9) is the preferred speci cation. The regressors are no longer statistically signi cant. This result is not consistent with diminishing bene ts higher group PK from 3 share for all groups because the coe¢cient before k=1 skj is positive and insigni cant. However, the negative coe¢cient before the majority share is consistent with the notion that the majority group has an inverted-Ushaped preference for its own group share. However, this evidence is not conclusive. To answer this question more concretely, more data and analyses are necessary. 4.2. Fixed E¤ects Models: Individual Housing Transaction Price In this section, housing transaction and census data are combined. Individual housing transaction prices are modeled as a function of the individual 22
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housing characteristics Xit and neighborhood characteristics: ln Pijt = Xit + f (Hjt ; HMjt ; s1jt ; ) + Zjt + j + t + "ijt ;
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where Pijt denotes the price of transaction i in neighborhood j at time t, and Xit corresponds to the variables reported in Table 2. The remaining f (Hjt ; HMjt ; s1jt ; ); Zjt ; j ; t are as described earlier. "ijt is an i.i.d. error term, which is assumed to be uncorrelated with all regressors once we allow the xed e¤ects j to be potentially correlated with other regressors. Although the data only include housing units transacted over this period, the prices are measured more precisely. Moreover, the precise measurement of housing attributes allows more precise identi cation of price variations across neighborhoods. Table 4 reports the results. The speci cations listed in Table 3 are all reported here. All of the results are similar as well. FE (2) and FE (4) show that housing price is positively correlated with the Her ndahl index, overall and minority. This correlation can be interpreted as before. The interpretation of FE (5) to FE (9) is also similar. Nonlinearity exists in the relationship between housing price and the Her ndahl index. Finally, it is di¢cult to disentangle the diminishing e¤ects using the sign patterns in FE (8) and (9). 4.3. Fixed E¤ects Models: Repeat-Sale Housing Price Index In this section, the combined housing transaction and census data are used again. However, the housing transaction prices are transformed into housing price indices for every census tract and each census year. The method of Case and Shiller (1989) is employed to create this repeat-sale index. Census tracts with fewer than 100 pairs of repeat sales are dropped to ensure the reliability of the estimate. Next, the housing price index HP Ijt ; expressed in levels, is regressed on neighborhood characteristics: ln HP Ijt = f (Hjt ; HMjt ; s1jt ; ) + Zjt + j + t + "jt ;
(18)
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units in the neighborhood. However, the results in Table 5 do not di¤er signi cantly from those in Tables 3 and 4. Table 3, Table 4, and Table 5 use di¤erent samples, di¤erent sets of housing attributes, and di¤erent measures of housing prices, but they provide essentially the same results. Housing price is positively related to the overall concentration of ethnic groups after conditioning on the majority share. In addition, the housing price increases with the minority concentration index. All of these ndings support the existence of a material e¤ect of social interactions on housing market outcomes.
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4.4. Conditional Di¤erence-in-Di¤erences Method 4.4.1. Research Design and Identi cation In this section, I adopt the conditional di¤erence-in-di¤erences method proposed by Heckman et al. (1998). The empirical question becomes whether neighborhoods that become more ethnically homogenous, de ned as the treated group, experience higher price appreciation compared with the control group of neighborhoods. This method combines propensity score matching (Rosenbaum and Rubin, 1983) with the di¤erence-in-di¤erences method. The method suits my analysis well. First, it is non-parametric; thus, it relaxes the restrictive parametric assumptions on the housing price equation. Second, the method requires a di¤erent set of identifying assumptions and can thus o¤er corroboration to the results of xed e¤ects models.23 Treatment is de ned in two ways. First, the more straightforward de nition is an increase in the Her ndahl index, either overall or minority only. The second de nition is based on relative changes in ethnic concentration. If the change in the Her ndahl index for a neighborhood exceeds that for the metropolitan area, this neighborhood is considered to be treated, and vice versa. I prefer the second de nition. Because both absolute changes in ethnic composition and housing prices are subject to time trends, the correlation between them can be spurious. Table 1 shows that Vancouver became more ethnically diverse and more expensive during this period. Even if these two phenomena are entirely unrelated, we could still nd a signi cant relationship between them. Relative changes, however, are detrended, so the correlation is less likely to be spurious. 23
Heckman et al. (1998) describe the technical details of these assumptions. A nontechnical description is provided later in this section.
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Changes in ethnic composition are clearly endogenous to neighborhood changes because residential sorting by income or unobservable individual characteristics a¤ects both housing prices and ethnic composition. The conditional di¤erence-in-di¤erences method is designed to address this problem. Figure 1 illustrates the key concept. The squares represent neighborhoods or census tracts. Suppose that tract A is treated, while B, C, and D are not. The color represents the propensity scores, with lighter colors indicating higher scores. The score equals the predicted treatment probability from a parametric probit model.24 According to the estimated scores, tracts B and D are better matches. Suppose D has the propensity score closest to A. The "best match" method will select D as the comparison unit. The "n best matches" will select a group of tracts as the comparison. If n = 2, the selected tracts will be B and D. The method of matching assumes that house price in tract D can act as an estimate of the counterfactual outcome for tract A had A experienced no treatment. Consequently, a consistent estimate of the treatment e¤ect equals the price di¤erential between A and D. However, the housing price in D may not be a good proxy for the counterfactual outcome in A. The conditional di¤erence-in-di¤erences method assumes instead that the bias or the approximation error of using the housing price in D to proxy the counterfactual for A remains xed over time. Consequently, a consistent estimate of the treatment e¤ect is the di¤erence-in-di¤erences estimator (t0 > t): (HV alA;t0 HV alA;t ) (HV alD;t0 HV alD;t ) :25 I also modify the matching method by focusing on neighboring tracts. Tracts that are neighbors can share some common unobservable time-varying neighborhood characteristics. Matching based on both geographic proximity and propensity score therefore relies on weaker identifying assumptions. In Figure 1, the "neighbor and the best match" method selects tract B as the comparison, although its propensity score is slightly further from A than 24
The probit model includes all neighborhood characteristics except the Her ndahl index as independent variables. Due to space limitations, these estimates are not reported, but are available from the author upon request. 25 Note that the expression equals (HV alA;t0 HV alD;t0 ) (HV alA;t HV alD;t ), where HV alA;t HV alD;t is the bias from the approximation at time t because both tracts are not treated yet. Therefore, HV alD;t0 + (HV alA;t HV alD;t ) is a good proxy for the counterfactual for A at t0 as long as the bias is the same in both periords.
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that of D. The "average of all neighbors" method selects both B and C as the comparison, which is no longer conditional di¤erence-in-di¤erences but rather a simple di¤erence-in-di¤erences strategy.
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4.4.2. Results The dataset is the panel constructed for use in sections 4.1 and 4.3. Table 6 reports the estimated average treatment e¤ect on the treated group for di¤erent de nitions of treatment. There are four de nitions in total: (1) an increase in the absolute values of the overall Her ndahl index; (2) an increase relative to the change in the city-wide overall Her ndahl index; (3) an increase in the absolute values of the minority Her ndahl index; (4) an increase relative to the change in the city-wide minority Her ndahl index. The latter two are reported to better separate the e¤ect of majority share from that of the Her ndahl index. All of the Her ndahl indices are based on home language. Because multiple before-after observations are included, i.e., 1986-1991, 1991-1996, and 1996-2001, we have to assume that these before-after pairs are independent over time to aggregate them into a result for all periods.26 We report the estimated treatment e¤ects for each period and the overall average, shown in the column labeled "All Years". Two matching methods, namely the "best match" and "10 best matches", are reported in this table. I measure housing price movement using both the self-reported housing values (Panels A.1 and A.2) and the repeat-sale price indices (Panels B.1 and B.2). Because the results are similar, I focus on summarizing the results in Panels A.1 and A.2. In Panel A.1, the "best match" method shows that neighborhoods that become more homogeneous overall experience lower price appreciation. The estimate is -3.8% using all of the before-after observations. However, those neighborhoods that become more homogeneous in minority composition experience higher price appreciation. The positive estimate of 2.4% is statistically signi cant. The estimates based on the "10 best matches" are similar. Panel A.2 shows a slightly di¤erent picture. We observe mixed results as to how overall ethnic diversity a¤ects housing price movement. The e¤ect of minority concentration, however, is still a positive 2.9% and statistically signi cant. After subtracting a city-wide trend in ethnic composition move26
The assumptions made here are formally presented in Miquel (2003).
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ment, Panel A.2 provides a more reliable estimate of the treatment e¤ect than Panel A.1. Similarly, Panel B.2 is preferred to Panel B.1. A robust nding in this table is the positive relationship between minority concentration and house price appreciation. Table 7 reports the same set of results as that in Table 6. The "neighbor and best match" method conditions the matching on both the propensity score and whether the treatment and the control tracts are, in fact, neighboring. The "average of all neighbors" method is only based on geographic proximity; thus, it is the di¤erence-in-di¤erences estimator. Again, Panels A.2 and B.2 are preferred to Panels A.1 and Panel B.1, respectively, because the former two de ne treatment by a detrended change in ethnic composition. The results are essentially the same as those in Table 6. The results in Tables 6 and 7 are consistent with previous results from the xed e¤ects models. The e¤ect of the overall concentration is mostly negative but not very strong. The concentration of minority groups has a strong and statistically signi cant positive e¤ect. In light of my theory of social interactions and housing price determination, these results suggest that intra-group interactions generate greater bene ts for the individuals.
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4.5. Other Measures of Ethnic Diversity There are alternative measures of ethnicity in the data, including places of birth or origin, ethnic origins, and religious a¢liations. These attributes may a¤ect peoples neighborhood choices and hence housing prices. I redo the conditional di¤erence-in-di¤erences exercise for these measures of ethnic diversity. Table 8 de nes treatment in the relative sense, i.e., an increase in ethnic concentration relative to a city-wide change.27 Columns 2-3 report the results for ethnic composition as measured by mother tongue. All of the census year pairs (1986-1991, 1991-1996, and 1996-2001) are available for this measurement. However, I report only the aggregated results due to space limitations. The results are basically the same as those based on home language. The overall concentration index has a negative but sometimes insigni cant e¤ect, while the minority concentration index has a positive and signi cant e¤ect. 27
Details concerning the construction of these other ethnicity-related variables are contained in the Appendix. The results based on absolute changes in ethnic composition are similar to those for relative changes. Fixed e¤ects models are also run for these measures. The results are similar to the conditional di¤erence-in-di¤erences results.
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Columns 4-9 show additional results based on other de nitions of ethnic groups. These de nitions include ethnic origins (available for 1996-2001 and 1991-1996), places of birth (available only for 1996-2001), and religious a¢liations (available only for 1991-2001). Most of the estimates are insignificant, and no clear pattern is detected. These results could be due to the small sample sizes. It is also possible that these measures do not in fact have signi cant e¤ects on peoples choices and thus do not a¤ect house prices. Ethno-linguistic measures appear to be the only factors that matter in the housing market, at least in the metropolitan area of Vancouver. Further studies are certainly required to test whether this is generally true.
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5. Conclusion
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In this paper, I build a general equilibrium model in which housing prices and the distribution of ethnic groups across neighborhoods are endogenously determined. Under certain conditions, the coexistence of several groups in the same neighborhood can be sustained in the long-term. Such an equilibrium is often implicitly required by hedonic regressions of housing price on continuous measures of ethnic composition. In other words, ethnically diverse neighborhoods have to be stable for the hedonic regression to work. Moreover, I analyze neighborhood choices in the context of multiple groups. This is an improvement over traditional models that assume a white-black or native-immigrant dichotomy. Using additional assumptions of peoples preferences for social interactions, I derive in equilibrium an endogenous correlation between house prices and the Her ndahl index of ethnic composition. This correlation is positive conditional on the share of the majority group. A test of this theory is then carried out using panel data constructed for the metropolitan area of Vancouver, Canada. Both the xed e¤ects models and the conditional di¤erence-in-di¤erences method provide the same results. Conditional on the majority share, an increase in the concentration of ethnic groups positively a¤ects housing price in a neighborhood. However, more data and analyses are needed to test the social interactions mechanism against its alternatives. More realistic formulations of peoples behavior and preferences along the lines of Clark (1992) will be interesting extensions. The relationship between housing price and ethnic composition is found to exist only when we measure ethnicity by linguistic origin. Further investigation in di¤erent cities and countries is warranted to assess whether 28
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and how linguistic characteristics di¤er from other measures of ethnic identity.
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A. Proof of Propositions
ej (r) =
K X
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A.1. Proof Proposition 1 The proof is analogous to the standard proof for the existence of the Walrasian equilibrium such as Proposition 17.C.1 of Mas-Colell et al. (1995). In this model, the excess demand e(r) (e1 (r); :::; eJ (r)) di¤ers slightly from that in Proposition 17.C.1 of Mas-Colell et al. (1995). Here, an element of e(r) or ej (r) contains an additional term P kj (v k1 (r; N1 ); :::; v kJ (r; NJ )) that depends on r: Lk P kj (v k1 (r; N1 ); :::; v kJ (r; NJ ))hkj (r; Nj )
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Lk wjk :
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To prove the proposition, we have to check whether the excess demand e(r) satis es the following conditions (see Proposition 17.B.2 of Mas-Colell et al. (1995)). They are: (1) e(r) is continuous; (2) e(r) is homogeneous of degree zero; (3) e(r) satis es the Walras law or r e(r) = 0 for all r; (4) There is an s > 0 such that ej (r) > s for every neighborhood j and all r; (5) If rn ! r, where r 6= 0 and rj = 0 for some j, then maxfe1 (rn ); :::; eJ (rn )g ! 1. Once these conditions are satis ed by the excess demand function e(r), we can directly apply Proposition 17.C.1. We can show that both v kj (r; Nj ) and hkj (r; Nj ) are continuous and homogeneous of degree zero in r under the conditions on the utility function u(:): Since P kj is continuous in v k1 ; :::; v kJ ; P kj is also continuous in r because continuity is preserved under function composition. We can also con rm that P kj is also homogeneous of degree zero given that v kj (r; Nj ) is homogeneous of degree zero. Consequently, ej (r) is both continuous in r and homogeneous of degree zero. Walras law is satis ed because of the strict monotonicity of the utility function. Condition (4) follows from the fact that both P kj and hk must be nonnegative. Condition (5) is satis ed as long as hkj increase to positive in nity as housing price rj approaches zero while r 6= 0, which is a mild restrictions on hkj . A.2. Proof of Proposition 2 Propositions 17.F.3 and 17.H.1 of Mas-Colell et al. (1995) directly imply Proposition 2.
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A.3. Proof of Proposition 3 I apply a global implicit function theorem by Sandberg (1981) (Corollary 1). There are three conditions to be checked: (1) for some N0 2 , there is J exactly one r0 2 R++ , such that e(r0 ; N0 ) = 0; (2) e(r; N) = 0 is locally solvable; (3) (See Sandberg, 1980, for more details) De ne A and B as open rectangular regions such that A = fN 2 : 0 < Ni < i ; for all i 2 J f1; :::; K Jgg and B = fr 2 R++ : 0 < rl < 'l ; for all l 2 f1; :::; Jgg: (j) 1 For each sequence fN g1 A such that for some index i we have either (j) (j) Ni ! 0 or Ni ! i as j ! 1; there is an index l such that either gl (N(j) ) ! 0 or gl (N(j) ) ! 'l as j ! 1. The rst two conditions are implied directly by Proposition 2 given that e is continuously di¤erentiable and sastis es the gross substitute property. The third condition is the regularity condition required in the proof of this proposition. Because e(r; N) is homogeneous of degree zero, we can restrict J : our analysis of the price vector in the unit simplex in R++ X J B = fr 2 R++ : rj = 1g: j
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Therefore, condition (3) can be rewritten as follows: for each sequence fN(j) g1 1 (j) (j) k A such that for some index i we have either Ni ! 0 or Ni ! L as j ! 1; there is an index l such that either rl = gl (N(j) ) ! 0 or gl (N(j) ) ! 1 as j ! 1 respectively. Roughly speaking, this condition requires that as some component of N approaches zero, some component of r approaches zero as well, while as some component of N approaches Lk , some component of r approaches 1. As long as this condition is satis ed, we can apply Corrollary 1 of Sandberg (1981) to prove the uniqueness and continuous di¤erentiability of g(:) . A.4. Proof of Proposition 4 This proof closely follows the proof of Theorem 1 in Miyao (1978). Each k nj is an element of the following simplex nkj
0 and
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It is well known that a simplex is nonempty, compact, and convex and hence satis es the requirement for applying Brouwers xed point theorem. 34
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The function f (:) maps from the above simplex to itself. The continuity of the mapping P kj and hkj can be con rmed. Because continuity is preserved under the functional composition, f (:) is continuously in N for all N 2 .
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A.5. Proof of Proposition 5 The proof is analogous to the proofs of Theorems 2 and 4 by Miyao (1978). h The di¤erences are two fold: (1) @v kj =@n contains two additional terms PJ @P kl @vl kj @P kl @v kl as shown in Equation (9); (2) j=1 @vkj @nh takes the place of @vkl @nh l
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= 0 for all j 6= l in the model by Miyao (1978). Our proof P kl @v kj simply repeats the steps of Miyao (1978) by substituting Jj=1 @P for @v kj @nh l @P kl @v kl everywhere the latter term appears. For details, see the proofs by @v kl @nh l Miyao (1978) and the comment by Papageorgiou (1982). because
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B.1. Ethnic Good Better access to ethnic goods can be another mechanism. It is possible that certain ethnic goods are better or less expensive in ethnic neighborhoods. These goods can be ethnic groceries, food services, and religious services. The utility function is again Cobb-Douglas with one new component, the xed consumption in ethnic good xk : 1 max Az h xk s.t. z + rh + xk pk (skj ) = y k ; z;h
where pk (skj ) is the price of ethnic good k in neighborhood j. More speci cally pk (skj ) = p 1 skj + 2 (skj )2 ;
where p > 1 > 0 and 12 1 2 0: If 2 = 0, the price is a linear function of skj . If 2 > 0, the price of the ethnic good is strictly decreasing and convex in skj . The parameter p measures the price of the ethnic good when the share of the group is zero. Again, housing demand is increasing in group share skj due to the income e¤ect. Again, Sj = Nj . The housing market clearing condition implies that ) ( X X X y k xk p skj + xk 1 (skj )2 xk 2 (skj )3 : rj =
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If the price of the ethnic good is a convex function of group share, i.e., the housing price will depend on both the Her ndahl index and P2 > 0, then 3 (s ) : Clearly, the Her ndahl index represents the rst order e¤ect of the kj k group shares, while the cubic term represents the second-order e¤ect. Again, income and preference heterogeneity can distort the correlation between the housing price and ethnic composition.
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B.2. Social Capital and Local Public Good The utility function is a Cobb-Douglas function with a public good A(gj ); where gj is the average spending per person in neighborhood j and A0 (gj ) > 0: max A(gj )z h s.t. z + rh + gjik = y k ;
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where gjik is the contribution by an individual i of group k to the public good in neighborhood j. I assume that gjik is chosen from outside of the above maximization problem. Following Vigdor (2002), I assume
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k where k > 0; k + k > 0; and E("ik j ) = 0: The zero-share contribution is the contribution by an individual to the community if she were the only member of group k living in the neighborhood. The within-group a¢nity parameter k is the additional amount that an individual would be willing to pay if her group was the only ethnic group in the neighborhood.28 The parameter "ik j is a mean-zero individual heterogeneity. Therefore, the per capita spending on public goods in neighborhood j is X X k skj + k (skj )2 : gj = k
k
Housing demand decreases with the contribution to the community due to the income e¤ect. Again, I assume that skj = Nj . The housing market clearing condition then implies that ) ( X X rj = y k k skj k (skj )2 : ( + ) k k 28
These two terms are borrowed from Vigdor (2002).
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It is surprising to see that the utility of a worker increases with the Her ndahl index Hj while the housing price decreases with Hj : This is because no supply e¤ect exists. This e¤ect is turned o¤ because I assume per capita housing supply is a constant . The fact more people coming to the neighborhood does not necessarily drive up the price. Instead, because people contribute more to the public good when their group has a higher population share, they are left with less money to spend on housing. The per capita housing demand decreases as Hj increases. Because the per capita housing supply is xed at , house prices must fall. Another reason for this surprising result is the lack of productivity e¤ect of the public good. A formulation of the positive productivity e¤ect is:29 X X yjk = yk + gj = yk + k skj + k (skj )2 ; k
k
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where > 0. Note that yk is the income when social capital in the neighborhood is zero and is the marginal e¤ect of social capital on the income of an individual. Consequently, the housing market clearing condition implies that ( ) X X X 2 3 yk k skj + k k (skj ) + rj = k (skj ) ( + ) k k k The above equation shows that the correlation between the housing price and the Her ndahl index can be decomposed into two e¤ects. They are the positive productivity e¤ect and the negative within-group a¢nity e¤ect k . It is positive as long as the former dominates the latter. In addition, if we are going to separate the a¢nity e¤ect P from 3the productivity e¤ect, we must include higher-order terms such as k (skj ) : When income and preference are heterogeneous across groups, it is important to consider the majority share as a separate factor. 29
The opposite argument that ethnic diversity should be positively related to productivity can be easily incorporated into the model. In that case, the parameter should be negative. More complicated speci cations can also be accommodated.
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C. Construction of the Dataset
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C.1. Geocoding of the Housing Transactions The pro le tables of the census tracts of the Vancouver Census Metropolitan Area are retrieved using the Canadian Census Analyzer provided by the CHASS Data Centre at the University of Toronto. These pro le tables were originally provided by Statistics Canada for release with other Census products. I choose the census years 1986, 1991, 1996, and 2001 because the reported language variables, including mother tongue and home languages, have only been reported in detail since 1986.30 The BCAA housing transaction data are provided by the Centre for Urban Economics and Real Estate at the Sauder School of Business at the University of British Columbia. The data contain all residential real estate transactions in greater Vancouver and in the lower mainland region of the province of British Columbia. The data cover the period from 1986 to 2001. I restrict my analysis to single family housing units, though the data also include condominiums and townhouses. The data report detailed structural and other characteristics. The data that I use to link a street address with a particular census tract are the Block-Face Data File for the 1996 Canadian Census.31 A block-face is the smallest available geographic entity available from Statistics Canada. The block-face information includes street name (including street type and direction), address range, geographic codes, longitude and latitude coordinates for a representative point and the 1996 population and dwelling counts. The geocoding procedure involves the following steps. First, I construct street address variables such as street name, street type, street direction, and the address range, based on address information already in the BCAA housing transaction data. Some errors in coding are found in both the housing data and the block-face data. These errors are corrected. Second, within a census subdivision (a municipality), if a housing transactions address falls into the address range in the block-face data, and the other street address variables match between the two addresses, I can associate the transaction with a unique representative point of a block-face. This representative point 30
For more details about the language variables and other socio-economic variables, see the next section. 31 The Block-Face Data File was discontinued in 2001.
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also has unique longitude and latitude coordinates. Third, I use GIS software (GRASS) to overlay these representative points onto a 2001 map of the Vancouver census tracts. Therefore, I can associate each housing transaction with a unique census tract as de ned by the 2001 Canadian Census. Lastly, each transaction is linked with socio-economic variables at the census tract level according to the year in which the transaction took place. A balanced panel of census tracts based on the de nition of census tracts in 2001 is used in this process. The construction of this panel is explained in the next section.
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C.2. Construction of a Panel of Census Tracts in Vancouver: 1986-2001 For the Census Metropolitan Area of Vancouver, the de nition of the census tracts changed over this period. I must therefore choose a consistent de nition for the census tracts. In this paper, I adopt the 2001 de nition. Statistics Canada provides the Census Tract Correspondence Files for various years (2001-1996, 1996-1991, and 1991-1986). These les are then used to link census tracts over time. Because most changes are splits of old tracts into smaller tracts, I use the characteristics of the old tract as the common characteristics of the several smaller tracts created by these splits. Historical maps of the census tracts are checked to verify the linking procedure. C.3. Construction of Variables The BCAA housing transaction data contain primarily structural and other housing characteristics. Almost all the variables have self-explanatory names. They are shown in Table 2. The neighborhood characteristics at the census tract level are constructed from the census pro le tables mentioned previously. These variables require detailed explanations. Ethno-linguistic variables include three variables, namely the Her ndahl index of all language groups, the Her ndahl index of minority language groups, and the population share of the English-speaking group. These variables can be based on either mother tongue or language spoken at home. A consistent categorization of language groups is based on the language groups reported in 1986. There are 20 groups: English, French, Aboriginal languages, Italian, Portugese, Spanish, German, Yiddish, Dutch, Ukrainian, Russian, Polish, Finnish, Hungarian, Greek, Arabic, Punjabi, Chinese, Vietnamese, and Tagalog (Filipino). Only single responses are used to calculate
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the above indices. The Her ndahl index of all language groups Hj is calculated as K X Hj = (skj )2 ; for all j = 1; :::; J; k=1
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where j indexes the census tracts, k indexes the language groups, and skj denotes the share of group k living in census tract j. The Her ndahl index of minority language groups HMj is calculated as (~ skj )2 ; for all j = 1; :::; J;
k=2
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where s~kj denotes the fraction of group k within the total minority population. The total minority population excludes the English-speaking group, which is denoted by k = 1. The population share of the English-speaking group s1j is simply the share of the English-speaking group in census tract j. These three variables are available for the census years 1986, 1991, 1996, and 2001. Other ethnic diversity measures include those that are based on ethnic origin, religious a¢liation, and place of birth. A consistent categorization of ethnic origins is based on the 1991 de nition, which includes 31 groups.32 In calculating the overall Her ndahl index, I use this 1991 categorization. However, I consider those who report Canadian, English, Scottish, and other British origins as belonging to the majority group. The Her ndahl index of minority groups is calculated by excluding the previous four groups instead of just one group. These variables are available only for the years 1991, 1996, and 2001. A consistent categorization of religious a¢liation is based on the 1991 de nition. There are 21 di¤erent categories.33 I consider all the Protestant 32
The groups are French, English, Scottish, Irish, Other British, German, Canadian, Italian, Chinese, Aboriginal origins, Ukrainian, Dutch (Netherlands), East Indian n.i.e., Polish, Portuguese, Jewish, Black origins, Filipino, Greek, Hungarian (Magyar), Vietnamese, Spanish, Lebanese, Norwegian, Japanese, Yugoslav n.i.e., Korean, Swedish, Croatian, Danish, and Finnish. 33 The religions are Roman Catholic, Ukrainian Catholic, Protestant - United Church, Protestant - Anglican, Protestant - Baptist, Protestant - Presbyterian, Protestant Lutheran, Protestant - Pentecostal, Protestant - Mennonite, Protestant - Jehovahs Witnesses, Protestant - Reformed Bodies, Protestant - Salvation Army, Protestant - Latter-day
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denominations as belonging to the majority group. The diversity measures and the majority share are calculated as those that are based on ethnic origins. Variables based on religious a¢liation are available only for the years 1991 and 2001 because they are reported every 10 years in the Canadian Census. The place of birth categorization is based on the 1996 de nition. There are 51 categories.34 I consider the non-immigrant group as the majority group. The same set of variables is similarly constructed. The variables are available for the census years 1996 and 2001 because the data before 1991 are not available at the country-level and were heavily aggregated.35 Details concerning how the di¤erent categorizations of the language, ethnic origin, place of birth, and religion over time are treated are available from the author upon request. The rest of the neighborhood characteristics can be divided into two subgroups. The rst group of the control variables is the socio-economic characteristics of the neighborhood. The population density is the population of a census tract divided by its land area (in km2 ). The share of retirees equals the population fraction of people of 65 years age and older in a census tract. The unemployment rate is the fraction of unemployed workers. The share of new immigrants equals the people who immigrated during the last 10 years, as a fraction of the total immigrant population. The share of migrants equals the fraction of people who are migrants, or people who moved to the current place of residency within the last 5 years, in the total population ve years old and older. The share of university graduates equals the share of people with a bachelors degree in a census tract. The average household income is the average household-level income in a particular neighborhood. The second group of variables are characteristics of the housing stock. The average housing value equals the average of the self-estimated housing Saints (Mormons), other Protestant, Eastern Orthodox, Jewish, Islam, Buddhist, Hindu, Sikh, and no religious a¢liation. 34 These categories include the Non-immigrant population, United Kingdom, Italy, United States, Hong Kong, India, China, Poland, Philippines, Germany, Portugal, Viet Nam, Netherlands, Jamaica, Greece, Guyana, Sri Lanka, Lebanon, France, Trinidad and Tobago, Yugoslavia, Hungary, Haiti, Taiwan, Iran, Romania, Korea South, Ukraine, Pakistan, El Salvador, Egypt, Croatia, Russian Federation, Ireland, South Africa, Mexico, Austria, Chile, Belgium, Fiji, Morocco, Denmark, Czechoslovakia n.i.e., Malaysia, Cambodia, Switzerland, Tanzania, Kenya, Iraq, Somalia, and Israel. 35 There were 10 regions of birth in 1991 and 7 regions in 1986. These regions are not very useful for constructing meaningful ethnic groups.
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values for all of the owner-occupiers. The share of apartments equals the total share of apartments, including duplex, 5-story and higher, and less than 5 stories, in the housing stock. The ownership rate equals the share of owneroccupied dwellings in the neighborhood. The average age of dwellings equals the weighted average of the dwellings age. This variable is constructed using the counts of dwellings built during various periods of time. The average number of rooms equals the average number of rooms in a dwelling in the neighborhood, which is a proxy for the average dwelling size. There is also information about the quality/condition of the housing stock, but this information is not available for earlier years; thus, I do not include these variables in the analysis.
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Figure 1: Illustration of the Conditional Di¤erence-in-Di¤erence Method
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N 386 363 386 385 386 386 386 386 386 386 386 386 386 386 386 386 386 386 386 386
RI
1996 Mean 313,383 1.174 0.711 0.459 0.805 0.568 0.116 0.498 8.694 56,475 3,488 0.117 0.49 0.31 0.17 17.869 0.544 0.636 25.129 6.191
SC
N 386 363 386 377 386 386 386 386 386 386 386 386 386 385 386 386 386 386 386 386 386
NU
2001 Mean 292,135 1.198 0.751 0.572 0.828 0.544 0.124 0.47 0.225 7.337 65,568 3,857 0.122 0.391 0.241 0.219 17.869 0.53 0.647 27.186 6.34
MA
Variable Name Average Housing Value ($) Log Repeat Sale Housing Price Index Her ndahl Ind of All - Home Language Her ndahl Ind of Minorities - Home Lang. Share of Majority - Home Language Her ndahl Ind of All - Mother Tongue Her ndahl Ind of All - Ethnic Origin Her ndahl Ind of All - Place of Birth Her ndahl Ind of All - Religion Unemployment Rate Average Household Income ($) Population Density (persons/km 2 ) Share of People above Age 65 Share of New Immigrants Share of Migrants in the Last 5 Years Share of University Graduates Distance to CBD (km) Share of Detached Housing Units Home Ownership Rate Average Age of the Dwelling (yrs) Average No of Rooms per Dwelling
PT
Table 1: Characteristics of Census Tracts in Vancouver: 1986-2001 1991 Mean 238,851 0.801 0.782 0.408 0.863 0.654 0.177 0.181 9.247 52,672 3,300 0.119 0.301 0.336 0.137 17.869 0.587 0.625 24.212 6.311
N 386 363 386 384 386 386 386 386 386 386 386 386 386 386 386 386 386 386 386 386
1986 Mean 123,459 0 0.846 0.348 0.908 0.706 11.834 37,654 2,702 0.116 0.191 0.26 0.111 17.869 0.615 0.623 23.946 6.011
N 386 363 386 382 386 386 386 386 386 386 386 386 386 386 386 386 386 386
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1991 Mean N 223,413 37,111 21.311 37,111 2,278 37,039 10,164 37,106 17.529 37,029 1.374 37,039 3.88 37,026 2.093 37,111 1.283 37,111 0.665 37,111 0.032 37,111 0.17 37,079 0.076 37,111 0.003 37,111 0 37,111 0.021 37,111 0.01 37,111 0.01 37,111 0.127 37,111 0.028 37,111
NU
SC
RI
1996 Mean N 333,941 24,202 21.689 24,202 2,402 24,139 10,382 24,191 19.673 24,131 1.444 24,139 3.966 24,128 2.293 24,202 1.348 24,202 0.669 24,202 0.036 24,202 0.163 24,122 0.072 24,202 0.002 24,202 0 24,202 0.021 24,202 0.014 24,202 0.01 24,202 0.112 24,202 0.03 24,202
MA
2001 Mean N 330,683 22,371 20.408 22,371 2,343 22,305 46,675 22,365 25.62 22,300 1.401 22,304 3.963 22,275 2.25 22,371 1.297 22,371 0.699 22,371 0.036 22,371 0.188 22,314 0.069 22,371 0.003 22,371 0 22,371 0.021 22,371 0.012 22,371 0.011 22,371 0.067 22,371 0.041 22,371
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Variable Name Transaction Price ($) Distance to CBD (km) Floor Area (sq feet) Lot Size (sq feet) Age of the Dwelling (yrs) Number of Stories Number of Bedrooms Number of Bathrooms Number of Parking Space With a Deck With a Pool With a Basement Suite On a Cornerlot On a Waterfront Lot On a Water Lot Prime View Good View Fair View New Property Transaction Is a Duplex
PT
Table 2: Summary Statistics of Housing Transactions in Vancouver: 1986-2001
45
1986 Mean N 113,544 26,299 21.066 26,299 2,147 26,269 48,454 26,295 15.024 26,259 1.313 26,271 3.74 26,263 1.955 26,299 1.195 26,299 0.666 26,299 0.037 26,299 0.157 26,283 0.07 26,299 0.003 26,299 0 26,299 0.02 26,299 0.009 26,299 0.008 26,299 0.118 26,299 0.024 26,299
46
FE (1) -0.275 a (0.060)
FE (2) 0.474 a (0.108) -0.976 a (0.118)
0.001 (0.001) 0.009 a (0.002) 1.220 a (0.041) -0.040 a (0.006) 1.856 a (0.107) 0.651 a (0.054) 0.346 a (0.076) 0.233 b (0.097) Yes Yes -0.952 b (0.400) 1541 0.011 a (0.002) 0.253 a (0.044) -0.070 a (0.019) 0.699 a (0.142) -0.074 (0.053) 0.016 (0.074) 0.115 (0.122) Yes Yes 9.263 a (0.462) 1541 0.951
0.010 a (0.002) 0.282 a (0.043) -0.071 a (0.018) 0.733 a (0.138) -0.050 (0.052) 0.024 (0.072) 0.143 (0.119) Yes Yes 9.098 a (0.450) 1541 0.953
0.109 a (0.023)
FE (3)
0.011 a (0.002) 0.239 a (0.044) -0.069 a (0.019) 0.627 a (0.144) 0.027 (0.048) 0.033 (0.075) 0.048 (0.124) Yes Yes 9.138 a (0.469) 1528 0.950
0.010 a (0.002) 0.298 a (0.044) -0.089 a (0.018) 0.668 a (0.140) -0.120 b (0.050) 0.015 (0.073) 0.113 (0.121) Yes Yes 9.128 a (0.457) 1528 0.953
0.009 a (0.002) 0.254 a (0.043) -0.066 a (0.018) 0.773 a (0.139) -0.035 (0.052) 0.007 (0.073) 0.148 (0.120) Yes Yes 9.649 a (0.456) 1541 0.953
1.150 a (0.164)
FE (5) -1.888 a (0.237)
0.010 a (0.002) 0.277 a (0.043) -0.069 a (0.018) 0.758 a (0.138) -0.043 (0.052) 0.017 (0.072) 0.155 (0.119) Yes Yes 9.399 a (0.469) 1541 0.953
0.723 b (0.326)
FE (6) -0.403 (0.411) -1.091 a (0.129)
0.010 a (0.002) 0.275 a (0.043) -0.070 a (0.018) 0.755 a (0.138) -0.036 (0.052) 0.019 (0.072) 0.147 (0.119) Yes Yes 9.231 a (0.529) 1541 0.954
0.875 (0.943) -0.616 (1.754) 0.063 (1.094)
FE (7) -0.346 (0.414) -0.533 (0.740)
0.010 a (0.002) 0.280 a (0.043) -0.071 a (0.018) 0.741 a (0.138) -0.050 (0.052) 0.025 (0.072) 0.149 (0.119) Yes Yes 9.202 a (0.484) 1541 0.953
0.223 (0.383)
FE (9) 0.158 (0.553) -0.972 a (0.119)
PT
RI
0.010 a (0.002) 0.249 a (0.044) -0.069 a (0.019) 0.714 a (0.142) -0.075 (0.053) 0.018 (0.074) 0.126 (0.123) Yes Yes 9.452 a (0.497) 1541 0.951
0.411 (0.394)
FE (8) -0.851 (0.555)
SC
NU
MA
-0.497 a (0.065) 0.079 a (0.022)
FE (4)
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RE (1) -0.471 a (0.053)
The dependent variable is the logarithm of average self-reported housing values by census tracts. All variables about ethnic composition are based on home language. The housing attributes at census tracts level include share of detached housing units, home ownership rate, average age of dwelling, age squared, and average number of rooms per dwelling. RE(1) is a random e¤ect model and the rest are xed e¤ects models. Standard errors are in parentheses. a , b , and c represent signi cance levels 1%, 5%, and 10% respectively.
N R-Squared
Housing Attributes Year Dummies Constant
Share of University Grads
Share of Migrants
Share of New Immigrants
Share of Above Age 65
Log Population Density
Log AVG Household Income
Unemployment Rate
Distance to CBD (km)
3 k=1 skj
PK
Squared Majority Share s2j1
Interaction Hj sj1
Hj2
Minority Her ndahl Ind HMj
Share of Majority sj1
Overall Her ndahl Ind Hj
Table 3: Ethno-Linguistic Diversity and Self-Reported Housing Value: Fixed E¤ects Models
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FE (1) -0.016 (0.058)
FE (2) 0.544 a (0.115) -0.755 a (0.131)
-0.009 a (0.001) -0.008 a (0.003) 0.046 (0.039) 0.019 a (0.006) 1.005 a (0.103) -0.194 a (0.060) -0.070 (0.057) 1.978 a (0.084) Yes Yes No 7.654 a (0.468) 109,447 0.828
-0.010 a (0.003) 0.001 (0.002) 0.056 (0.044) -0.014 (0.019) -0.121 (0.155) 0.063 (0.043) 0.161 a (0.062) 0.358 a (0.108) Yes Yes Yes 7.765 a (0.449) 109,447 0.849
-0.010 a (0.003) 0.000 (0.002) 0.118 a (0.039) -0.019 (0.017) -0.061 (0.143) 0.094 b (0.041) 0.115 b (0.057) 0.330 a (0.105) Yes Yes Yes 7.394 a (0.425) 109,447 0.849
-0.010 a (0.003) 0.000 (0.002) 0.064 (0.042) -0.016 (0.020) -0.153 (0.157) 0.057 (0.043) 0.177 a (0.062) 0.333 a (0.109) Yes Yes Yes 7.672 a (0.456) 108,776 0.848
-0.010 a (0.003) -0.000 (0.002) 0.112 a (0.038) -0.016 (0.017) -0.013 (0.136) 0.109 a (0.041) 0.104 c (0.056) 0.350 a (0.105) Yes Yes Yes 7.918 a (0.414) 109,447 0.849
1.278 a (0.316)
FE (6) -1.027 b (0.460) -0.931 a (0.121)
-0.010 a (0.003) -0.001 (0.002) 0.110 a (0.038) -0.015 (0.017) -0.016 (0.135) 0.120 a (0.041) 0.110 b (0.055) 0.337 a (0.105) Yes Yes Yes 7.489 a (0.453) 109,447 0.849
1.574 c (0.922) -1.004 (1.600) -0.2 16 (1.163)
FE (7) -0.891 b (0.402) 0.333 (0.618)
0.654 (0.411) -0.010 a (0.003) 0.000 (0.002) 0.113 a (0.038) -0.018 (0.017) -0.040 (0.141) 0.096 b (0.041) 0.117 b (0.057) 0.350 a (0.105) Yes Yes Yes 7.691 a (0.434) 109,447 0.849
FE (9) -0.385 (0.649) -0.743 a (0.140)
PT
0.801 c (0.462) -0.010 a (0.003) 0.001 (0.002) 0.052 (0.043) -0.013 (0.019) -0.093 (0.152) 0.066 (0.043) 0.162 a (0.061) 0.382 a (0.108) Yes Yes Yes 8.122 a (0.433) 109,447 0.849
FE (8) -1.143 c (0.661)
RI
SC
NU
-0.010 a (0.003) -0.001 (0.002) 0.094 b (0.041) -0.012 (0.018) -0.008 (0.135) 0.115 a (0.041) 0.115 b (0.056) 0.356 a (0.105) Yes Yes Yes 7.945 a (0.423) 109,447 0.849
1.211 a (0.124)
FE (5) -1.726 a (0.186)
MA
-0.010 a (0.003) -0.000 (0.002) 0.106 b (0.043) -0.026 (0.019) -0.082 (0.145) 0.001 (0.046) 0.160 a (0.061) 0.350 a (0.108) Yes Yes Yes 7.532 a (0.458) 108,776 0.849
-0.229 a (0.067) 0.043 b (0.019)
FE (4)
D
0.056 a (0.019)
FE (3)
TE
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RE (1) -0.357 a (0.042)
The dependent variable is log housing price. All variables about ethnic composition are based on home language. The housing attributes included are log oor area, log lot size, number of stories, number of bedrooms, number of bathrooms, number of parking space, age of the house, squared house age, a dummy for the presence of a pool, a deck, or a basement, a dummy for whether it is on a waterfront lot, a water lot, or a corner lot, transaction type dummy, whether the house is a duplex, and dummies indicating the view of the house. Standard errors are in parentheses and clustered by Census Tracts. a , b , and c represent signi cance levels 1%, 5%, and 10% respectively.
N R-Squared
Housing Attributes Year Dummies Census Tract Dummies Constant
Share of University Grads
Share of Migrants in Recent 5 Yrs
Share of New Immigrants
Share of Above Age 65
Log Population Density
Log AVG Household Income
Unemployment Rate
Distance to CBD (km)
3 k=1 skj
PK
Squared Majority Share s2j1
Interaction Hj sj1
Hj2
Minority Her ndahl Ind HMj
Share of Majority sj1
Overall Her ndahl Ind Hj
Table 4: Ethno-Linguistic Diversity and Individual Transaction Price: Fixed E¤ects Models
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FE (2) 0.405 b (0.190) -0.512 b (0.207)
FE (3)
-0.003 (0.003) 0.336 a (0.079) 0.320 a (0.027) 0.203 (0.283) 0.111 (0.095) 0.310 b (0.121) 0.313 (0.225) Yes -5.973 a (0.848) 1308 0.931
-0.003 (0.003) 0.370 a (0.080) 0.316 a (0.027) 0.240 (0.282) 0.131 (0.095) 0.284 b (0.121) 0.311 (0.225) Yes -6.174 a (0.850) 1308 0.932
-0.003 (0.003) 0.337 a (0.078) 0.312 a (0.027) 0.124 (0.285) 0.070 (0.087) 0.319 a (0.122) 0.295 (0.227) Yes -5.927 a (0.855) 1298 0.931
-0.004 (0.003) 0.357 a (0.081) 0.307 a (0.027) 0.157 (0.287) 0.042 (0.092) 0.310 b (0.122) 0.311 (0.227) Yes -5.991 a (0.858) 1298 0.931
D
-0.112 (0.120) 0.080 b (0.041)
FE (4)
TE
0.087 b (0.040)
AC CE P
FE (1) 0.017 (0.107)
1.259 c (0.695) -0.003 (0.003) 0.363 a (0.080) 0.318 a (0.027) 0.284 (0.283) 0.132 (0.095) 0.285 b (0.121) 0.355 (0.226) Yes -5.614 a (0.903) 1308 0.932
FE(9) -1.387 (1.008) -0.481 b (0.207)
PT
RI
1.393 b (0.694) -0.003 (0.003) 0.330 a (0.079) 0.322 a (0.027) 0.254 (0.283) 0.113 (0.095) 0.309 b (0.121) 0.362 (0.226) Yes -5.367 a (0.899) 1308 0.932
FE (8) -1.940 b (0.981)
SC
-0.003 (0.003) 0.370 a (0.080) 0.318 a (0.027) 0.300 (0.283) 0.127 (0.096) 0.266 b (0.122) 0.360 (0.226) Yes -5.183 a (0.979) 1308 0.932
-1.172 (1.712) 2.166 (3.164) 1.290 (1.968)
FE (7) -0.862 (0.749) -2.551 b (1.292)
NU
-0.004 (0.003) 0.368 a (0.080) 0.319 a (0.027) 0.277 (0.283) 0.143 (0.095) 0.271 b (0.121) 0.335 (0.225) Yes -5.804 a (0.879) 1308 0.932
0.961 (0.593)
FE (6) -0.766 (0.746) -0.663 a (0.227)
MA
-0.004 (0.003) 0.354 a (0.079) 0.322 a (0.027) 0.260 (0.283) 0.142 (0.095) 0.283 b (0.121) 0.332 (0.225) Yes -5.848 a (0.847) 1308 0.932
0.722 b (0.293)
FE (5) -0.999 b (0.427)
The dependent variable is the logarithm of a repeat sale housing price index by Census Tracts. All variables about ethnic composition are based on home language. No housing attribute is included. Standard errors are in parentheses. a , b , and c represent signi cance levels 1%, 5%, and 10% respectively.
N R-Squared
Year Dummies Constant
Share of University Grads
Share of Migrants
Share of New Immigrants
Share of Above Age 65
Log Population Density
Log AVG Household Income
Unemployment Rate
3 k=1 skj
PK
Squared Majority Share s2j1
Interaction Hj sj1
Hj2
Minority Her ndahl Ind HMj
Share of Majority sj1
Overall Her ndahl Ind Hj
Table 5: Ethno-Linguistic Diversity and Repeat-Sale Housing Price Index: Fixed E¤ects Models
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sale housing price index. Standard errors are in parentheses.
a, b,
and
c
represent signi cance levels 1%, 5%, and 10% respectively.
types of housing price appreciation are reported (Panels A.1 and A.2 versus Panels B.1 and B.2): the self-reported housing value and the repeat
groups, while columns 6-9 corresponding to changes in the concentration index of minority groups only. Panel A.2 and Panel B.2 de ne treatment as an increase in the group concentration index relative to the change in the MSA-wide concentration index. Columns 2-5 and Columns 6-9 have similar representations as those in Panels A.1 and B.1. Two methods of matching are shown: best match and the average of 10 best matches. Two
The reported values are treatment e¤ects of changes in ethnic concentration on log housing values by census tracts. Panel A.1 and Panel B.1 de ne treatment as an increase in the group concentration index, with columns 2-5 corresponding to changes in the overall concentration of all language
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Table 6: Treatment E¤ects: Conditional Di¤erence-in-Di¤erences Estimates Overall Conentration Index Minority Conentration Index All Years 1986-1991 1991-1996 1996-2001 All Years 1986-1991 1991-1996 1996-2001 Panel A.1: Average Self-Reported Housing Value: Absolute Change in Concentration as Treatment Best Match -0.038a -0.063b -0.035 -0.033a 0.024a 0.011 0.030a 0.030b (0.010) (0.026) (0.028) (0.012) (0.006) (0.010) (0.010) (0.012) 10 Best Matches -0.036a -0.050b -0.034 -0.034a 0.031a 0.020b 0.037a 0.035a (0.008) (0.022) (0.031) (0.008) (0.005) (0.008) (0.007) (0.009) Number of Obs. 418 69 48 301 770 239 235 296 Panel A.2: Average Self-Reported Housing Value: Relative Change in Concentration as Treatment Best Match 0.019b 0.015 0.042b -0.017 0.029a 0.028b 0.021 0.034a (0.009) (0.012) (0.017) (0.019) (0.007) (0.012) (0.014) (0.012) 10 Best Matches -0.015b -0.005 -0.033a -0.002 0.029a 0.021b 0.019b 0.042a (0.007) (0.009) (0.012) (0.013) (0.006) (0.009) (0.009) (0.010) Number of Obs. 631 239 253 139 609 208 158 243 Panel B.1: Repeat Sale Housing Price Index: Absolute Change in Concentration as Treatment Best Match -0.047a -0.059 -0.030 -0.047a 0.013 0.026 0.012 0.003 (0.014) (0.042) (0.037) (0.015) (0.011) (0.023) (0.018) (0.018) 10 Best Matches -0.031a -0.048 -0.037 -0.026b 0.010 0.036c 0.019 -0.018 (0.010) (0.030) (0.023) (0.011) (0.008) (0.019) (0.013) (0.012) Number of Obs. 382 65 41 276 695 216 215 264 Panel B.2: Repeat Sale Housing Price Index: Relative Change in Concentration as Treatment Best Match -0.006 -0.019 -0.012 0.026 0.044a 0.067b 0.050b 0.020 (0.012) (0.023) (0.014) (0.026) (0.013) (0.027) (0.022) (0.020) 10 Best Matches -0.030a -0.057a -0.034a 0.027 0.031a 0.048b 0.034b 0.016 (0.009) (0.017) (0.011) (0.019) (0.010) (0.021) (0.017) (0.014) Number of Obs. 573 218 231 124 551 186 150 215
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housing value and the repeat sale housing price index. Standard errors are in parentheses. respectively.
a, b,
and
c
represent signi cance levels 1%, 5%, and 10%
groups, while columns 6-9 corresponding to changes in the concentration index of minority groups only. Panel A.2 and Panel B.2 de ne treatment as an increase in the group concentration index relative to the change in the MSA-wide concentration index. Columns 2-5 and Columns 6-9 have similar representations as those in Panels A.1 and B.1. Two methods of matching are shown: neighbor and best match and the average of all nontreated neighbors. Two types of housing price appreciation are reported (Panels A.1 and A.2 versus Panels B.1 and B.2): the self-reported
The reported values are treatment e¤ects of changes in ethnic concentration on log housing values by census tracts. Panel A.1 and Panel B.1 de ne treatment as an increase in the group concentration index, with columns 2-5 corresponding to changes in the overall concentration of all language
D
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Table 7: Treatment E¤ects: Spatial Conditional Di¤erence-in-Di¤erences Estimates Overall Conentration Index Minority Conentration Index All Yrs 1986-1991 1991-1996 1996-2001 All Yrs 1986-1991 1991-1996 1996-2001 Panel A.1: Average Self-Reported Housing Value: Absolute Change in Concentration as Treatment Neighbor and Best Match -0.035a -0.049c -0.027 -0.032b 0.024a 0.007 0.027b 0.037a (0.013) (0.025) (0.034) (0.016) (0.008) (0.013) (0.013) (0.014) Average of Neighbors -0.022c -0.036c 0.011 -0.025c 0.030a 0.029b 0.029b 0.032b (0.012) (0.020) (0.029) (0.015) (0.007) (0.013) (0.012) (0.013) Number of Obs. 305 63 46 196 577 184 187 206 Panel A.2: Average Self-Reported Housing Value: Relative Change in Concentration as Treatment Neighbor and Best Match -0.012 -0.006 -0.031c -0.003 0.025a 0.023c 0.017 0.033b (0.009) (0.014) (0.016) (0.018) (0.008) (0.013) (0.015) (0.013) Average of Neighbors -0.011 -0.010 -0.025 -0.0004 0.033a 0.040a 0.024c 0.032a (0.008) (0.013) (0.015) (0.014) (0.007) (0.013) (0.013) (0.012) Number of Obs. 364 121 111 132 526 168 150 208 Panel B.1: Repeat Sale Housing Price Index: Absolute Change in Concentration as Treatment Neighbor and Best Match -0.012 -0.016 -0.022 -0.008 0.005 0.020 0.004 -0.006 (0.019) (0.061) (0.038) (0.019) (0.011) (0.025) (0.019) (0.016) Average of Neighbors -0.027c -0.073b -0.046 -0.007 0.002 0.013 0.016 -0.021 (0.014) (0.036) (0.028) (0.017) (0.010) (0.022) (0.015) (0.015) Number of Obs. 239 54 35 150 488 154 162 172 Panel B.2: Repeat Sale Housing Price Index: Relative Change in Concentration as Treatment Neighbor and Best Match -0.044a -0.087a -0.050b -0.002 0.033a 0.069b 0.044b -0.004 (0.015) (0.032) (0.021) (0.023) (0.012) (0.029) (0.019) (0.015) Average of Neighbors -0.041a -0.091a -0.050a 0.010 0.024b 0.062b 0.040b -0.019 (0.013) (0.029) (0.018) (0.019) (0.011) (0.026) (0.017) (0.014) Number of Obs. 306 99 94 113 445 140 132 173
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Standard errors are in parentheses.
a, b,
and
c
represent signi cance levels 1%, 5%, and 10% respectively.
1996-2001, 1991-1996, and 1986-1991), ethnic origin (aggregation of 1996-2001 and 1991-1996), place of birth (1996-2001), and religious a¢liation (1991-2001), compared with MSA-wide changes in the corresponding indices. Two sets of results are reported: the results for the overall Her ndahl index and those for the minority Her ndahl index. Four methods of matching are employed. Best match and 10 best matches are reported in Panel A and Panel B. Neighbor and best match and the average of all nontreated neighbors are reported in Panel C and Panel D. Panel A and Panel C use the self-reported housing values as the outcome variable, while Panel B and Panel D use the repeat-sale price index as the outcome variable.
when treatment is de ned as a relative increase in terms of a Census tracts Her ndahl Indices that are based on mother tongue (aggregation of
The reported values are treatment e¤ects of changes in ethnic concentration on log housing values by census tracts. Columns 2-9 reports results
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Table 8: Other Ethnic Diversity Measures: Conditional Di¤erence-in-Di¤erences Estimates Mother Tongue Ethnic Origin Birthplace Religion Overall Minority Overall Minority Overall Minority Overall Minority Panel A: Average Self-Reported Housing Value - Propensity Score Best Match -0.016b 0.007 0.035a -0.027a 0.017 0.004 0.008 0.029c (0.008) (0.008) (0.012) (0.010) (0.012) (0.014) (0.017) (0.015) 10 Best Matches -0.011c 0.026a 0.021b -0.027a 0.005 0.006 0.010 0.024b (0.006) (0.007) (0.008) (0.008) (0.010) (0.010) (0.012) (0.012) Number of Obs. 736 518 324 429 219 203 232 247 Panel B: Repeat Sale Housing Price Index - Propensity Score Best Match -0.019c 0.044a 0.006 0.028b 0.009 -0.019 -0.034 0.011 (0.010) (0.013) (0.017) (0.013) (0.017) (0.024) (0.021) (0.020) 10 Best Matches -0.041a 0.036a 0.012 0.017c 0.017 0.023c -0.017 0.011 (0.009) (0.011) (0.013) (0.010) (0.013) (0.013) (0.015) (0.015) Number of Obs. 675 472 286 381 199 181 209 223 Panel C: Average Self-Reported Housing Value - Score and Neighbor Neighbor and Best Match -0.007 0.037a 0.016 -0.008 0.012 0.026c 0.018 0.023 (0.009) (0.009) (0.012) (0.010) (0.016) (0.015) (0.017) (0.016) Average of Neighbors -8.74e-5 0.034a 0.013 -0.014 0.017 0.003 0.021 0.014 (0.008) (0.008) (0.010) (0.009) (0.014) (0.012) (0.016) (0.015) Number of Obs. 406 420 301 340 188 187 193 188 Panel D: Repeat Sale Housing Price Index - Score and Neighbor Neighbor and Best Match -0.002 0.038a 0.022 0.013 0.017 -0.006 -0.009 0.015 (0.015) (0.013) (0.014) (0.012) (0.018) (0.017) (0.019) (0.021) Average of Neighbors -0.008 0.043a 0.013 0.006 0.011 -0.021 0.004 0.016 (0.013) (0.012) (0.012) (0.011) (0.016) (0.015) (0.018) (0.018) Number of Obs. 322 353 243 283 159 155 157 154
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Highlights I analyze the effect of ethnic diversity on neighborhood house prices.
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A general equilibrium model with multiple groups and the housing market is presented.
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Ethnic composition is capitalized into house prices, supporting the existence of non-
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market social interactions.