Residential Location Choice: The Role of a Taste for Similarity

This paper examines the importance of social interactions on a household's location decision. The theory argues that individuals' utility will be greater when socially interacting with similar others. The hypothesis that a household desires to find a good community match is tested through the application of a discrete residential location choice model. In addition, this paper also tests Tiebout's hypothesis that households search for a community where their benefits from local public goods will exceed their local tax costs. The findings tend to support both hypotheses, indicating that a household prefers neighbors with a similar socio-economic background and somewhat larger houses.


Introduction
For many households, purchasing a home is one of the most significant economic decisions that they will make. The choice of an optimal level of housing consumption requires that a household gather information regarding the features of potential residences. The characteristics of the housing structure itself will be an important determinant of a household's choice of residence (Quigley, 1976), but other factors also will influence this decision, such as households' individual characteristics (Gabriel and Rosenthal, 1989), and neighborhood's quality (Friedman, 1980;Quigley, 1985;and Nechyba & Strauss, 1997). All of these additional determinants have been verified to be significant in a household's location choice. For example, Nechyba and Strauss (1997) showed that an individual household's location decision is significantly affected by community attributes. The findings of Gabriel and Rosenthal (1989) indicate the influential impact of household socioeconomic and demographic characteristics on community choice. Previous studies in this literature place emphasis on the impact of households' characteristics and neighborhood's attributes on residence choice respectively and/or jointly. There is no research taking into account of the influence of the overall match of a community and a household on the household's community choice. This effect cannot be simply captured by a cross effect. It involves how the degree of match is measured. maintaining the independence of irrelevant alternatives (IIA) assumption (Note 7) within each group. Suppose, then, the J alternatives can be divided into L subgroups such that the choice set can be written as , ⋯ , | , ⋯ , | , ⋯ , | , ⋯ , | , ⋯ , | , ⋯ , | with a choice of subgroups indexed by l=1,2,⋯L, and alternatives j=1,2,⋯,Jl in subgroup l. Logically, the choice process can be thought as that of choosing among the L choice sets and then making the specific choice within the chosen set. One way to express the utility that a household derives from choosing a location j in subgroup l is to use the random utility model (RUM). It is defined as: ( 1) where represents a household's conditional utility function (conditional on the decision) in choosing location j in subgroup l, is the deterministic component of the household's conditional utility, and is the random element due to unobserved attributes.
If the household is rational, the location he/she choses must have maximized his/her utility. Therefore, becomes the unconditional utility function: Consequently, the probability of an individual choosing community j among the total available alternatives Jl in choice set l is, Equation (3) means that the conditional probability of alternative j being chosen given choice set l is equal to the probability that the utility obtained by the individual from option j exceeds the utility obtained from any of the other alternatives in the given choice set. Substitution of (1) into (3) For estimation purpose, we further assume that the deterministic component of the total utility, , has a linear form as, , where denotes the vector of observed attributes of choice | , , represents the vector of observed attributes of the choice set l, α and β are the vectors of the unknown parameters.
Substitution of (5) into (4) yields where log ∑ exp is defined as an inclusive value for nest l, which is the expected utility for the choice of alternatives within nest l. The probability of choosing nest l is derived as, ∑ where, 1 is a measure of the correlation in unobserved factors within nest l. (Note 9) By the law of probability, the unconditional probability of the observed choice made by a household has the form of

Model Parameterization
In order to parameterize the nested logit model, further assumptions about the form of the underling indirect utility function are required. Specifically, a household allocates its income between non-housing and housing consumptions, as well as deciding the community to achieve the maximum level of utility. If we describe the direct utility a household receives by choosing to live in a particular community as a function of housing consumption, non-housing consumption, and his/her tastes, the indirect utility of household i in choosing community jl (i.e., community j in subgroup l) can be written in the following form: (Note 10) , , where denotes household i's demographic characteristics which determine the individual's preferences, represents individual i's income, , is the non-housing consumption of household i in community jl, (Note 11) , is the housing services consumed by household i in community jl, and , denotes household i's housing expenditure in community jl. (Note 12) Because the housing expenditure in community jl can be artificially decomposed into two categories including the spending on housing structural attributes, , (where is the composite price of housing structure bundle, and is the vector of housing structural variables), and the spending on community characteristics, , (where is the composite price of community feature bundle, and is the vector of community variables, which includes both the specific attributes relevant to community j, and the common attributes relevant to subgroup l), (Note 13) the utility function can therefore be written as, where is household i's consumption bundle of the housing structural attributes, denotes community jl's attributes, such as local public service, socio-economic characteristics composition, median income and so on.
To maximize its utility, household i can choose the quantity of , , the value of , and the value of the product of and , but not the quantity of . This is because the value of is constant for all households who choose community jl in which to reside. Therefore household i's budget constraint is rewritten as, , , The available income that household i can allocate between non-housing consumption and housing structure bundle is the difference of real income and the expenditure on community attributes of location jl.
After maximizing direct utility subject to the budget constraint, and substituting the derived demand functions into the direct utility function, the indirect utility function can be expressed as, (Note 14) , , where is the product of and (expenditure on the community attributes), , denotes the random component of the total utility, and , is the deterministic component of the total utility, which has a linear function form according to the assumption for equation (5).
The community variables, , entering the indirect utility function through the product of and , include both community amenities and socio-economic composition of the neighborhood.
The economic interpretation of the relevance of neighbors' socio-economic characteristics comes from the independent preferences suggested by Pollak (1976). (Note 15) This is the so called exogenous or contextual effect (Manski, 1993) in the neighborhood effects literature, and was used to estimate households' demand in some previous studies.
While the inclusion of in the indirect utility function reveals the role that is played by the potential neighbors' characteristics on the household's total utility, it does not describe household's preference for homogeneous neighbors. If the household values a homogenous community, the homogeneity of the community can be thought as a special good that should also be priced. Consequently, the price of homogeneity should also enter the household's utility function. However, this paper takes a different approach than pricing homogeneity as a special good; rather, it tests a household's preference for a homogeneous community directly through the inclusion of dissimilarity in the household's utility function. (Note 16) Specially, the amount of dissimilarity is included in the utility function to indicate the disutility of a household resulting from living with heterogeneous neighbors. The quantity of dissimilarity is measured by the absolute difference between the household's and the neighbors' amount of a particular characteristics. The utility function (10) is extended as following,   ,  ,   , , , , ,  ,  ,  , , , where represents community jl's demographic characteristics, represents community jl's median income level, is household i's house value, is community jl's median house value. Thus, denotes the absolute difference of household i's demographic characteristics and the median characteristics of the neighbors in community jl, denotes the absolute difference of household i's income and the median income of the neighbors in community jl, denotes the absolute difference of household i's house value and the median value of the houses in community jl, and denotes the difference of household i's house value and the median value of the houses in community jl.
Three absolute difference terms are created to test a household's preferences for similarity. The use of them captures the desires of a household to match the neighborhood in multiple dimensions. The absolute values of the differences are constructed for the purpose of avoiding the confusion arising from the signs of the estimated coefficients. This study focuses on households' preferences over similarity, therefore; only the absolute value of the difference of a household and its neighbors is relevant for this paper.
Tiebout's hypothesis is tested by including , the difference of household i's house value and the median house value in community jl. The smaller the value of is, the more likely that household i has a relatively smaller house than most of the houses in community jl. If the estimated coefficient of has a negative sign, Tiebout's hypothesis is confirmed. In other words, households prefer to live in an affluent community. (Note 17) The probability of choosing community jl can be computed for the NL model by substituting the linear function of , , which is indicated by equation (11), into equation (8). Because , , and are constant across alternative communities, they will no longer remain in the probability function. Therefore, the vector of the explanatory attributes in the probability function is composed of , , , , , and .
The community entry price, , in the indirect utility function needs to be constructed for each community in the choice set. The hedonic house price estimation method is employed to handle this issue (Rosen, 1974).

Hedonic Price Function
According to Rosen, the conceptual form of the hedonic function is a relationship between the bidding function from consumers and the offering function from the suppliers in the housing market. In other words, consumers bid for structural components of housing units and packages of neighborhood amenities in order to maximize their utility; suppliers maximize their profits by offering different housing unit packages to the market. Considering the market process described above, the variation in transaction prices can be explained as a function of property characteristics. In this paper, the structural characteristics of housing units, neighborhood socioeconomic attributes, community features and public services enter the hedonic price function: (Note 18) , , , where is a dummy variable indicating school district j, reflects the transaction price (Note 19) of household i's house, is the vector of the community variables (Note 20), is the vector of the structural attributes of household i's house, and represents the independent and identically distributed (IID) random error term. (Note 21) Due to the durability and the fixed position of a house, it has been broadly accepted in the housing literature that the geographic location of a house has nontrivial impact on its economic value. The inclusion of and is to test for capitalization of the geographic locations on house values. According to Can (1992), (Note 22) the elements of that denote the neighbors' socio-economic characteristics test for the capitalization of the adjacency effects. Neighbors' socio-economic characteristics can be interpreted as the signals of maintenance decisions that may affect the market value of a given house. Other elements of and variable , capture the neighborhood effects of a house's geographic location. www.ccsenet.org/ijef International Journal of Economics and Finance Vol. 4, No. 9;2012 To parameterize the hedonic function, (Note 23) a linear form is assumed and equation (12) is rewritten as, ∑ , where, , , , and are the coefficients to be estimated, while we use , , , and to indicate the estimated coefficients.
The hedonic regression reveals the marginal price of each attribute given the linear hedonic form, but tells nothing about the demand function or the supply function; therefore, it is only a market clearing function determined by the equilibrium market-clearing price.

Hedonic Price Index
Upon the selection of the functional form and the appropriate determinants of housing values, the hedonic function is estimated, and the estimated coefficients are applied to construct the house price index for each school district. The price index is, where denotes the price index of school district j, (Note 24) and ̅ is the average of neighborhood characteristics in community j.
In this formulation, the price index, , reflects spending on community attributes, which is one part of the entire expenditure on the house. This corresponds to the community premium denoted before. The price index defined in this paper is different from the conventional ones, because it excludes the spending on the constant-quality housing structures. The reason for making this change is to be consistent with the input element in the indirect utility function. Because the excluded part of the conventional price index is a constant number, using instead of the standard measure in the NL model does not make any difference to the results.

Spatially Autocorrelated Error Terms in the Hedonic Regression
The precision of the price indices can be affected by a number of factors, such as the functional form of the hedonic regression and the set of influential explanatory variables excluded from the function. This section addresses the issue of the spatially dependent error terms in order to achieve more efficient coefficient estimates and unbiased estimates of the standard errors. The IID assumption ofthe stochastic error term in the hedonic function does not hold because of the possibility of measurement errors and omitted variables.
Among the determinants of house values, housing structure variables are usually measured with little error, but it is likely that many of them are omitted. The location variables may not be fully observed, and even they can be observed, some measurement errors are likely to occur, which will leave the residuals produced by the hedonic equations spatially correlated. It is reasonable to expect that the correlation between residuals are determined by the proximity of observations, given that nearby house units share the same neighborhood, which tend to create similar errors in measuring the attributes of the neighborhood. The strength of the relationship diminishes as the distance between the observations increases. To address this problem, this study models the spatial correlation of the error terms explicitly through the use of a geostatistical model (Dubin, 1988). The covariance matrix of the error terms is defined as, , where K is the correlation matrix, and Ω is the covariance matrix with nonzero off-diagonal elements.
To estimate the covariance matrix, Ω, a semivariogram model can be employed, which expresses the variance of the difference between the values of the regionalized variables as a function of separation distance. The process is, where , denoting the location of property i ( indicates the latitude, and indicates the longitude of property i), , denoting the covariance of residual and residual , and 0 denotes the variance.
To explicitly model the semivariogram process, the functional form of the semivariogram needs to be specified. This paper applies the spherical model, which is, Grandview heights school district 5 Hamilton local school district 6 Gahanna Jefferson city school district 7 Groveport Madison local school district 8 Plain local school district 9 Reynoldsburg city school district 10 Hilliard city school district 11 Southwestern city school district 12 Upper Arlington city school district 13 Dublin city school district 14 Westerville city school district 15 Whitehall city school district 16 Worthington city school district Although Franklin County contains 16 major school districts, (Note 29) only 11 of them have sufficient observations to be used for the estimation of the residential location choices. These eleven school districts are: the Bexley city school district, the Columbus city school district, the Gahanna Jefferson city school district, the Groveport Madison local school district, the Reynoldsburg city school district, the Hilliard city school district, the Southwestern city school district, the Upper Arlington city school district, the Dublin city school district, the Westerville city school district, and the Worthington city school district. Consistent estimates are still available according to McFadden (1978). (Note 30) See Figure (1) for the map of Franklin County indexed by school districts. A legend for the index numbers is reported in Table (1).
The data set that is used to estimate the NL model contains 1,467 observations in total. (Note 31) The definitions and statistical descriptions of the variables in the estimation of the location choice model are provided in Table  (2) and Table (3). Table (2) contains some community variables as well as the set of price indices constructed from ML estimates (GEOPIND). These estimates were constructed from the hedonic regression, which is explained in detail in Appendix A2. Table (3) displays the key variables of this study, representing the dissimilarity of a household and its neighbors. A household's preference over a homogenous community is studied through five categories: (Note 32) the difference in education background, the difference in number of children, the difference in race, the difference in income, and the difference in house value. (Note 33) The indicators of dissimilarity are used to measure how different a household is from its neighbors. If households prefer to group themselves into homogenous neighborhoods, the signs of those coefficients on these indicators are expected to be negative. The coefficient on DFMASTER measures how the location decision of a household with a Masters degree is affected by the percentage of households whose highest level of education is not a Masters degree. The variable DFCHILD is included to test whether a household with children is more attracted to a community where most of his/her neighbors also have children. The variable DFINC gives a measure of the dissimilarity of household and its neighbors in regards to income. In the same vein, the coefficients on DFWHITE and on DFBLACK capture the disutility caused by moving into a community where the composition of ethnicities is different from a household's own race.
In order to distinguish the hypothesis of households' preferences for similarity from Tiebout's hypothesis that households prefer to live in a community with large houses, a pair of variables are created: DFHVAL and DFHVALTIE. The former is the absolute difference of a household's house value and its median neighbor's, while the latter is the simple difference of house values. A negative sign of DFHVAL is expected if households have a preference for similarity. According to Tiebout (1956) and Hamilton (1975), households prefer to buy a small house in a community with many relatively large houses, for the purpose of capturing a fiscal surplus. The variable DFHVALTIE is expected to have a negative sign because positive values of DFHVALTIE imply the household would be subsidizing others in the neighborhood through property tax payments. Because of the high correlation of DFINC and DFHVAL (rich households intend to purchase more expensive houses, while poor households can only afford cheap houses), we expect it be difficult to separate the effects of these two variables. (a) A household's highest education achievement is categorized into less than high school, high school, some college degree, bachelor's degree, and master's degree. For whatever level of education the household achieves, we subtract the percentage of the population with that level from 1 and assign it to the household. All others are assigned zero. For instance, if a household has attained some college, and 45% of the population has this level, the DFCOLLEGE will be assigned .55, while DFLESSHS, DFHS, DFBACHELOR and DFMASTER will be assigned zero. By construction, these variables are always between zero and one.
(b) For a household that has children, DFICHILD is the absolute difference of one and the percentage of households that have children in the school district. For a household that has no children, DFCHILD is zero.
(c) For a white household, DFWHITE is the difference between 1 and the percentage population that is white in the neighborhood and DFBLACK is zero; for a black household, n DFBLACK is the difference between 1 and the percentage of population who is black and DFWHITE is zero.
(d) DFINC is the absolute value of the income difference between the household's and the median neighbor's (scaled by $10,000), and is always positive.
(e) DFHVAL is always positive, but DFHVALTIE can be negative or positive.
The mean values of community attributes and selected dissimilarity variables (Note 34) of each school district are plotted in Figure (   Another competing hypothesis is that homogeneity is due to income segregation, which is predicted by urban economic models. This hypothesis predicts that households with similar incomes tend to group together, but it predicts nothing about their preferences along the other socio-economic dimensions. If the hypothesis of similarity search is corroborated in more than just income dimension, then the income segregation hypothesis does not completely describe the results. If black households select to live with other black households, it either suggests the pure preferences of blacks for black culture, or it might be caused by a constrained choice set faced by black households, due to racial discrimination. For example, Yinger (1998) documents real estate agents engage in racial steering. This study cannot separate discrimination from preferences as the cause of racial segregation.

Estimation: Results
In   Vol. 4, No. 9;2012 Recall that when the IV parameter is 1 a nested logit model becomes a conditional logit model. The estimated IV parameters of the NL model found in Table ( In column I of Table (4), more than half of the dissimilarity variables perform well with the expected negative sign, which confirms the hypotheses in this paper and suggests that households are more attracted to a similar neighborhood. The community variables also perform well. Other estimation results are consistent with previous studies.

Preference on the Similarity of Education Background
Among the five categories of education levels, the dissimilarity measures of the two highest education level, DFMASTER and DFBACHELOR have the expected negative coefficients, but the other three have significant positive estimates. The negative signs of DFMASTER and DFBACHELOR suggest that a household with a master's degree or a bachelor's degree tends to group with others who have a similar educational background, while the positive signs of DFLESSHS, DFHS, and DFCOLLEGE indicate that a household without a bachelor's degree would be discouraged in living with someone else who is equally educated as he/she is. The former finding is consistent with the hypothesis in this paper. But the latter one seems to contradict the similarity hypotheses. To test whether the households in the three lower level educational categories would prefer an educationally heterogeneous neighborhood or would be more interested in choosing better educated neighbors because of the positive externality of education, two other variables that indicate the neighborhood education level (variable SDBA is the percentage of the population in the school district that has a Bachelor's Degree and the variable SDMA is the percentage of the population in the school district that has a Master's Degree) are added in the NL model. After the inclusion of these two new variables, DFLESSHS, DFHS, and DFCOLLEGE are no longer significant, while SDBA, and SDMA are significantly positive, and DFMASTER and DFBACHELOR keep their negative signs. These new results suggest that a household is in general more attracted by a better educated neighborhood, but discouraged by a poorly educated one, no matter whether he/she is well educated or not. Additionally the unchanged negative coefficients on DFMASTER and DFBACHELOR suggest that the general preference of a household over a better educated neighborhood does not dominate the preference of a highly educated household over a residency with homogenously educated residents. In other words, a household with a bachelor's degree or a master's degree is not only attracted by a well educated neighborhood area, but also interested in living with others who are equally educated as he/she is, while a household with little education would prefer to choose better educated neighbors.
For those well educated households, similar high education background implies more common interests for those residents, which in turn creates a more interactive community. These households enjoy a higher utility in a highly interactive community in contrast to a segmented one. In contrast, relatively poorly educated households, appear to prefer trading a homogenous neighborhood for a positive externality flow of education.

Preference for Households with Children
The negative sign of the coefficient on DFCHILD indicates that a household that has children is less likely to choose a community with few children per household. (

Preference for the Similarity of Income
The negative sign of the coefficient on DFINC is consistent with the hypothesis that households prefer to group themselves within a neighborhood of similar income households. Because income works as a signal, indicating hobbies and interests of households, seeking similar income neighbors is another way to approximate an interactive community and therefore create greater gains from the social interaction in the neighborhood.

Preference for the Similarity of Races
The coefficient on DFBLACK is negative and significant, which implies that a black household is more likely to live with blacks. The coefficient on DFWHITE is negative but not significant, which implies that white households do not have a particular preference regarding their neighbors' races. The insignificance of DFWHITE www.ccsenet.org/ijef International Journal of Economics and Finance Vol. 4, No. 9;2012 might result from the approximation of the percentages of white households across the sample school districts. (Note 41) These results are partially consistent with the hypothesis of searching for similarities.
The negative coefficient on DFBLACK may suggest another explanation for the racial segregation phenomenon. Given results of previous studies that suggested black households' preference over racially integrated neighborhoods, the findings in this paper point to another possible explanation. The segregation of black households and white households might be not caused by racial discrimination, but households' own preferences over the neighbors' ethnicities. This self-selection might result from comfort with the culture, which implies that a racially segregated community is more interactive than an integrated one for the members in it. Of course, black households' choice might not necessarily suggest their preference, but their inability to locate in a white neighborhood, which is caused by racial discrimination. Both of the explanations are consistent with the findings in this paper, thus further study will be required.

Preference on the Community Attributes
All of the community variables have the expected significant signs. The positive sign of the coefficient on PUPILEXP suggests the greater educational expenditures per pupil; the more attractive is a community. The positive sign of AVGSC9 implies that the better the scholarly performance of students, the more desirable is a community. For parents who have children, greater school spending and a high proficiency score signal better student performance. For households without school age children, greater school spending and high proficiency score imply a better investment value of houses in the school district. (Note 42) The negative coefficients on TAX, CRIME and GEOPIND indicate that high tax rate, high crime rate, or high entry price of a school district make a community less attractive. The positive sign of MHVALUE suggests that households are attracted to a community with a relatively high median house value, which is consistent with Tiebout's hypothesis. The coefficient on CBD is not significant, implying the distance between the property and the CBD does not affect a household`s choice.
The fact that the coefficients of DFMASTER, DFBACHELOR, DFCHILD, and DFBLACK are significant even when DFINC is included in the regression suggests that a household's preference toward neighborhood with a similar socio-economic background is not swamped by housing affordability. The high correlation between income and education/ethnicity/age might suggest that the observed homogeneous neighborhood (i.e., similar education background/ethnic group/family structure) is likely the result of households with similar income and therefore can afford houses in the same neighborhood. Our regression result indicates that households' preference for similarity persists when income level is controlled. In other words, though households with similar income can afford houses in the similar price range, because of their preference for similarity they do not necessarily end up buying houses in the same community.
Column II of Table (4) provides the results of complete model that includes the house value differences variables, most of which are consistent with the results in column I of Table (4), except some variables that are no longer significant. This is partially because of the reduced sample size. Another reason is that the variable DFHVAL picks up the effects of DFINC and DFMASTER. Because households' income differences and education differences are highly correlated to their house value differences, it is not surprising to see that the coefficients of DFINC and DFMASTER are no more significant after the inclusion of DFHVAL. The negative coefficient on DFHVAL confirms the similarity hypothesis, while the negative sign of DFHVALTIE confirms Tiebout's hypothesis. If household i's house value, , is greater than the average house value in the community jl, , $10,000 increase of will decrease i's total utility by 0.61. (Note 43) If household i's house value, , is less than the average house value in the community jl, , $10,000 increase of will decrease i's total utility by 0.31. (Note 44) The dominant effect of DFHVALTIE suggests that a household would always like to buy a cheaper house than his/her neighbors' house values. This effect adds to the effect of a household's preference on similarities, which creates an asymmetry of preferences for downward deviations over upward deviations from the average house value in the neighborhood. This finding extracts the influence of DFHVAL from the prominent influence of DFHVALTIE.

Estimation: Discussion
A case study of the Columbus city school district provides more insight about the estimated results. This case study is based on the NL results in column I of Table (4). To aid in interpretation of the findings, Table (5) contains the estimated marginal effects on the probabilities with respect to the explanatory variables in the Columbus city school district, while Table (6) reports the elasticity effects on the probabilities with respect to the explanatory variables in the Columbus city school www.ccsenet.org/ijef International Journal of Economics and Finance Vol. 4, No. 9;2012 district. (Note 45) All marginal effects and elasticity effects are evaluated for each individual household separately, and then averaged across all households of the appropriate subgroup.  The own marginal effect of locating in the Columbus city school district for the attribute DFCHILD is negative and has the largest absolute value among all the dissimilarity variables, which implies that households are more responsive to the change of DFCHILD than the other difference variables. This is also confirmed by the elasticity of DFCHILD. Because per pupil expenditure can be used to measure school quality, the large value of the own marginal effect of PUPILEXP implies households' concern for school quality is a major determinant of location choice when they migrate.

Conclusions
The focus of this paper has been to test the effects of dissimilarity on households' residential location choice. This was tested by a two step procedure. First a location choice model requires inclusion of a house price index and thus the construction of an estimate of that index. Next, with an estimate of the house price index in hand, we estimate a nested logit regression model. Several data sets containing both households' characteristics and community attributes are utilized. The location decision of a household is modeled as a searching process for a matching community along the dimensions of households' socio-economic characteristics. The dissimilarity variables have been grouped into five categories: educational background, with school age children or not, race, income, and house value.
The findings reveal that a household prefers neighbors who are like herself/himself with the exception that poorly educated households prefer better educated neighbors. It is hypothesized that the reason for these preferences over similarity comes from the desirability of social interaction, while the preferences of households www.ccsenet.org/ijef International Journal of Economics and Finance Vol. 4, No. 9;2012 50 with little education over better educated neighbors suggests the positive externality flow of education. The revealed preference of white households in our sample suggests that they are indifferent about their neighbors' races, which might be explained by the small variations on the percentages of white households across the sample school districts. These results suggest an alternative explanation for the widely observed phenomena of homogeneous communities. The concentration of like households in many communities may be the result of the households' own volunteer selection for the purpose of beneficial social interactions among neighbors.
The introduction of households' preferences on similarities in this study raises additional questions, whcih provides fertile ground for future research. For example, in this paper, the preferences for similarity are tested along the dimensions that are constrained by the data in hand. The similarity of households can also be measured on other charateristics, such as religion, and social-political attitude. Furthermore, the analysis here is based on the benificial social interactions that are derived from similar individuals. An extension of of current study is to introduce heterogeneous preference structures among like households, allowing beneficial social interactions to arise from individuals with complementary needs in addition to individuals with similar characteristics. There may exist variations of households' utility determination processes based upon on their characteristics. Some households gain positive utility from bounded heterogeneous communities, whereas others lose utility on that. For instance, better educated households may respond differently than less educated households to a racially homogeneous community. The possible findings based on alternative preference settings might strengthen the robustness of the resutls in this paper and provide suggestions on policies about neighborhood integration.
In addition, Tiebout's hypothesis has been tested and has been corroborated by the data in this paper. Households would like to buy a somewhat cheaper house as compared with the values of the neighbors' houses in order to gain a fiscal surplus. Meanwhile, the house values difference of a household and his/her neighbors' should be small enough for the household to stay in a relatively homogeneous community.  and improve the precision of the predictions. The values of the estimated parameters of the spherical semivariogram function ( and ) using the method of moment estimation are very close to the values of the estimates using the ML method. This fact validates the robustness of the ML estimates. The chi-square value of 18.58 in Table (9) indicates that the geostatistical model is superior to the OLS model. (Note 49) Because the indices created from OLS are so close to the indices created from ML, we do not expect that the results of the discrete choice model will be will significantly different using OLS indices or ML indices. Only the ML price indices (Note 50) are reported in Table (10).