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Econometric Reviews

ISSN: 0747-4938 (Print) 1532-4168 (Online) Journal homepage: http://www.tandfonline.com/loi/lecr20

Residential Mobility, Neighborhood Effects, andEducational Attainment of Blacks and Whites

Yan Dong , Li Gan & Yingning Wang

To cite this article: Yan Dong , Li Gan & Yingning Wang (2015) Residential Mobility,Neighborhood Effects, and Educational Attainment of Blacks and Whites, Econometric Reviews,34:6-10, 763-798, DOI: 10.1080/07474938.2014.956586

To link to this article: http://dx.doi.org/10.1080/07474938.2014.956586

Published online: 17 Dec 2014.

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Econometric Reviews, 34(6–10):763–798, 2015Copyright © Taylor & Francis Group, LLCISSN: 0747-4938 print/1532-4168 onlineDOI: 10.1080/07474938.2014.956586

Residential Mobility, Neighborhood Effects, andEducational Attainment of Blacks and Whites

Yan Dong1, Li Gan2, and Yingning Wang3

1Research Institute of Economics and Management, Southwestern University of Financeand Economics, Chengdu, China

2Department of Economics, Texas A&M University, College Station, Texas, USA3Institute of Health and Aging, University of California San Francisco, San Francisco,

California, USA

This paper proposes a new model to identify if and how much the educational attainmentgap between blacks and whites is due to the difference in their neighborhoods. In thismodel, individuals belong to two unobserved types: the endogenous type, which may movein response to the neighborhood effect on their education; or the exogenous type, which maymove for reasons unrelated to education. The Heckman sample selection model becomes aspecial case of the current model in which the probability of one type of individuals is zero.Although we cannot find any significant neighborhood effect in the usual Heckman sampleselection model, we do find heterogeneous effects in our two-type model. In particular, thereis a substantial neighborhood effect for the movers who belong to the endogenous type.No significant effects exist for other groups. We also find that the endogenous type hasmore education and moves more often than the exogenous type. On average, we find thatthe neighborhood variable, the percentage of high school graduates in the neighborhood,accounts for about 28.96% of the education gap between blacks and whites.

Keywords Educational attainment; Neighborhood effects; Residential mobility.

JEL Classification I2; R2; J7.

1. INTRODUCTION

The education gap between blacks and whites is substantial in the United States.According to the 2000 census, the percentage of whites graduating from high school is18% more than that of blacks, while the percentage of whites with bachelor degrees istwice as much as that of blacks. The difference in returns to education between blacksand whites is often considered to be one of the reasons for the education gap. However,

Address correspondence to Li Gan, Department of Economics, Texas A&M University, College Station,TX 77843-4228, USA; E-mail: gan@econmail.tamu.edu

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lecr.

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Neal and Johnson (1996) and O’Neil (1990) argue that the returns to education betweenblacks and whites have been converging over the last twenty years, but the educationdisparity has remained the same (Couch and Daly, 2002). Similarly, the widespreadresidential segregation of blacks from whites in metropolitan areas also remains (Cutleret al., 1999). Segregation has declined in the cities but has increased in suburbia, resultingin little net change. Wide racial segregation indicates that blacks and whites have differentneighborhoods (Ananat, 2007). For example, the percentage of high school graduates inthe black neighborhoods is only 59.9% of that in the white neighborhoods (see Table1) in our sample. A growing literature claims that neighborhoods and peer groupscan be important in determining education outcomes (Durlauf, 2002; Manski, 1993).However, it is difficult to empirically identify the neighborhood effect on educationbecause individuals may move in response to the impact of the neighborhood on theireducation outcomes. Although this type of moving may have significant effects, it is onlyone of many reasons people may move. Individuals may choose to move for several otherreasons which are independent of the neighborhood effect on education.

This paper argues that moving because of various reasons actually provides anopportunity to reveal individuals’ preferences about neighborhoods and to help identifythe neighborhood effect. In particular, we suggest that there are two unobserved typesof individuals: the endogenous type and the exogenous type. For the endogenous type,moving is for better education, while for the exogenous type, moving has nothing to do

TABLE 1Data Description—County-Level Variables

Variables White Black All

Percentage high school graduates 51.01 45.15 49.39(10.68) (10.97) (10.97)

Percentage high school graduates (race specific) 53.68 32.13 46.21(11.36) (10.61) (15.33)

Crime rate (per 100,000) 4,949 5,833 5395(3154) (3769) (3693)

Mortality rate (per 100,000) 89.21 161.98 109.78(69.00) (150.34) (105.50)

Percentage employed in the education institution 7.97 7.33 7.82(2.70) (1.78) (2.53)

Per capita income (in $) 4,362 4,293 4,345(873) (954) (896)

Percentage of population is black 8.900 25.40 13.67(10.05) (14.24) (13.55)

Civil unemployment rate 4.51 4.63 4.61(1.75) (1.92) (1.82)

Percentage of population being urban 69.29 74.07 71.41(27.60) (29.67) (28.06)

Number of observations 2,461 1,045 3,686

Note: Numbers in parentheses are standard deviations.

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with education. Although the types are unobserved, it is possible to assign a probabilitythat each household belongs to one of the two types. The usual Heckman sample selectionmodel becomes a special case of this model in which the probability of falling into one ofthe two types equals zero or one.

A specification test rejects the Heckman model and favors our two-type model.Although we cannot find any significant neighborhood effect in the usual Heckmansample selection model, we do find different neighborhood effects for different types ofpeople in the model. In particular, there is a substantial neighborhood effect for moverswho belong to the endogenous type. No significant effects exist for the other type. Onaverage, we find that the neighborhood effect accounts for about 28.96% of the educationgap between blacks and whites. In addition, we find that the endogenous type would havetaken significantly more education and moves more often than the exogenous type.

Neighborhood effects on educational attainment have been widely studied. Earlierstudies such as the Coleman Report (Coleman et al., 1979) find that the socioeconomiccomposition of students has significant effects on the unequal academic attainments ofwhite and black children. Crane’s (1991) test supports the existence of neighborhoodeffects by examining the pattern of neighborhood effects on dropout rates and teenagechildbearing. Aaronson (1998) also finds children with more exposure to neighborhoodpoverty had lower rates of high school and college completion. Cutler and Glaeser(1997) and Ananat (2007) studied racial segregation and find that African-Americans whoreside in highly segregated metropolitan areas have lower educational attainment, worselabor market outcomes, and often end up with single parenthood. Card and Rothstein(2007) also find they have lower standardized test scores. However, other scholars findmixed evidence or an insignificant effect of neighborhoods on educational attainment(Brooks-Gunn et al., 1997; Datcher, 1982; Duncan, 1994; Duncan et al., 1997; Lillard,1993; Plotnick and Hoffman, 1999). The neighborhood variables in these studies includeeconomic conditions, occupational composition, racial characteristics, poverty status, anddemographic composition.

According to Ginther et al. (2000), the inconsistency of neighborhood effects oneducation actually implies that the research of neighborhood effects could be subject toomitted variable or selection biases. The difficulty in identifying neighborhood effects iswell known within the literature and has thus received extensive attention. This difficultyarises because nonrandom self-selection generates the correlation between individual andgroup attributes, some of which are likely to be unobservable, resulting in biases in theestimation of group effects on group members’ behaviors.

One approach to solve this problem is to randomize housing subsidies to encouragemoving to better neighborhoods. However, results from these experiments are mixed.Early results from the Gautreaux program imply that outcomes for parents and childrenwere markedly better for those who moved to the less-segregated suburbs (Popkin et al.,1993). However, Kling and Votruba (2001) find that the placement assignments in theGautreaux program were not entirely random. Moving to Opportunity (MTO) uses a

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randomized design and finds that randomly selected families who move from deprivedareas to more affluent neighborhoods have less violent criminal behavior by teens, betterhealth care and child care, and better mental and physical health. However, the differencein welfare participation, employment, and child test scores is much less than what is foundin the Gautreaux studies (Hanratty et al., 1998; Katz et al., 2001; Kling et al., 2007;Ladd and Ludwig, 1997; Ludwig et al., 2001). Similarly, Oreopolous (2003) and Jacob(2004) study the impact of public housing projects in Toronto and Chicago and findno significant differences in test scores and dropout rates. Finally, Gibbons (2002) findsthat educational attainment is slightly higher for those from neighborhoods with aboveaverage educated households by using data from contrasting council tenant housing inthe United Kingdom. However, his result is not robust to random housing assignment.

The above results from social experiments suggest that the significance ofneighborhood effects on education is sensitive to whether or not projects have randomdesigns. Significant neighborhood effects on education are only found in experimentswhere housing assignment is not totally random. This implies that whether the residentialmobility is endogenous is strongly related with the extent of neighborhood effects oneducation.

Social experiments, although very insightful, are limited in scope. Another broadapproach is to pursue various identification strategies. One of the best known strategiesis to look at a higher level of aggregation where there is less opportunity for sorting.For example, Cutler and Glaeser (1997), Card and Rothstein (2008), and Ananat(2007) study the racial segregation by examining the effect of across metropolitan areavariation, and Ross (1998) and Weinberg (2000, 2004) examine the effect of accessto employment or the spatial mismatch hypothesis. On the other hand, instead ofaggregating to the higher level of neighborhood, Bayer et al. (2008) and Grinblatt etal. (2007) disaggregate the neighborhood by assuming that strategically sorting intoparticular streets or blocks is not possible due to a thin housing market. The third strategyis to apply instrumental variable strategy; Cutler and Glaeser (1997) and Ananat (2007)isolate the causal impact of segregation by instrumenting for segregation with historicalmeasures of metropolitan structure, number of jurisdictions, and railroad networks. Thefourth strategy is identifying the model by controlling for neighborhood fixed effects.(Weinberg et al., 2002; Glaeser and Mare, 2001). Ross (2011) provides a more completereview of various identification strategies. Lastly, Ioannides and Zabel (2008) suggestan identification strategy by taking housing demand and neighborhood choice as jointdecisions in the presence of neighborhood effects.

This paper contributes to the econometric solution to the neighborhood effect problemby focusing on the residential mobility. The coefficients for the inverse mills ratios in theHeckman sample selection model are significant for non-movers but not significant formovers. To reconcile this heterogeneity, we suggest that the population may consist oftwo types of people: the endogenous type and the exogenous type. Accordingly, a newmodel to account for two types is proposed. In this new model, individuals are assumed

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to belong to one of the two types: an endogenous type whose moving decisions andeducation decisions are jointly determined, and an exogenous type whose decisions aboutmoving and education are determined independently. Because the type is unobserved,it can only be determined with a probability. Following the typical approach in theliterature to model the unobserved types, we use a mixture density to characterize theunobserved types.

Another difficulty in modeling residential mobility is that we only observe individuals’final residences but no alternative choices. Ignoring this problem will lead to inconsistentestimation. We solve this problem by choosing the average of characteristics within thegroup of counties that are spatially adjacent to the county where individuals reside asinstrumental variables (Ioannides and Zanella, 2007).

Empirically, this paper has two main findings. First, the paper provides strongevidences of two unobserved types. The estimation in the paper is conducted allowingthe possibilities of either one type or two types. Clearly, the two-type model matcheswith the data better than the one-type model. In addition, this paper finds that peoplefrom different types do behave differently. The endogenous type would have taken 5.603years of extra schooling after compulsory education, much more than the 3.653 years ofextra schooling taken by the exogenous type. Overall, 78.73% of people belong to theendogenous type. In addition, the endogenous type would be more likely to move thanthe exogenous type.

Second, this paper finds a strong neighborhood effect for the people who areendogenous movers, despite no statistically significant effects in the one-type Heckmansample selection model. This result suggests the importance of two-type model. Inparticular, the paper finds that if a black who belongs to the endogenous type movesto a white neighborhood, his education would increase by 0.86 years because of theneighborhood effect. Overall, the difference in the percentage of high school graduatescan explain about 28.96% of the gap in education between blacks and whites.

These results are consistent with studies using social experiments in residentialmobility. Public school choice lottery results (Hastings et al., 2006) also show that thegains of students’ test scores after attending their chosen school depends on the weightthat their parents’ preference for academic quality carries in their choices, indicating thatneighborhood effects may be different for different types of people who have differentweights on the education when choosing neighborhood.

The individual and household level data in this paper comes from the NationalLongitudinal Surveys of Youth 1979 (NLSY79). The majority of county level informationis from NLSY79; we supplement that data with county level information derived fromeither the U.S. Census or from Centers for Disease Control and Prevention (CDC). Thekey neighborhood characteristic variable used in the paper is the race-specific county leveleducation.

The remainder of the paper is organized as follows: Part II is the data description.Part III first estimates the Heckman sample selection model, then introduces the two-type

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model, and proposes a solution to the endogeneity of the neighborhood variable. PartIV estimates the model and presents the main empirical results of this paper, and Part Vconcludes the paper with a discussion of the future research.

2. DATA AND DESCRIPTIVE STATISTICS

The data for the analysis are primarily from NLSY79, supplemented by the 5% censussample in 1980, CDC’s Compressed Mortality Files, the Geographic Information System(GIS)-based census data, and residential segregation indexes from the census. TheNLSY79 includes a representative sample of 12,686 individuals. These individuals were14–22 years old when they were first interviewed in 1979, which was also the time for themto choose whether or not they would need to acquire post-compulsory education. Theseindividuals were interviewed annually through 1994 and on a biennial basis until 2000.NLSY79 includes individual, family, and some county (neighborhood) characteristicsdata.

2.1. Key Variables

The key individual level variables in this paper include the highest grade completed foran individual after compulsory schooling years and his/her moving status between 1979and 1982. The individual schooling years after compulsory schooling are constructed byusing the highest grade completed minus compulsory schooling. We use school yearsbeyond compulsory schooling since this represents educational attainment determined bythe individual. We assume that in 1979 individuals make two decisions: years of schoolingafter compulsory education, and whether they want to change their neighborhoods ornot. To exclude the residential mobility resulting from entering college, we restrict thesample to individuals between the ages of 14 and 171. Individuals who drop out of schoolsbefore they finish their compulsory education are also excluded from our sample. Keaneand Wolpin (1997) use the schooling years after age 16 as a proxy for schooling beyondcompulsory years when they study the schooling and career choices for young men.

Compulsory schooling years are derived from compulsory attendance laws and childlabor laws. Compulsory attendance laws specify a minimum and maximum age betweenwhich attendance is required and the minimum period of attendance. The child laborlaw regulates the employment of minors and the minimum of age to work. Thoselaws differ across states, and child labor laws and compulsory attendance laws havedifferent requirements for leaving school. Following Lleras-Muney (2005), we constructtwo measurements for schooling years: work permit age minus entrance age, and leavingage minus entrance age. We choose the minimum requirement of these as our variablefor compulsory schooling years. The years of compulsory schooling vary from six years

1In the data, only one person went to college before age 14.

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TABLE 2Data Description—Individual Variables

Variables White Black All

Schooling years beyond compulsory schooling 5.3149 4.9301 5.1880(2.7780) (2.3929) (2.6755)

Move dummy (1 if moved in 1979 and 1982) 0.1682 0.1244 0.1533(0.3741) (0.3302) (0.3603)

Age 15.61 15.60 15.60(1.06) (1.06) (1.06)

Mom highest grade (total years of education) 10.92 10.75 10.73(3.08) (2.46) (3.05)

Dad highest grade (total years of education) 11.23 10.23 10.83(3.66) (2.90) (3.54)

The oldest sibling’s highest grade 11.85 11.81 11.81(2.52) (3.08) (3.01)

Family size 4.96 5.62 5.19(1.78) (2.31) (2.01)

Family income (in $) 18,671 10,876 16,087(12,243) (8,585) (11,665)

Safe feeling about the school (1 if feel safe) 0.5924 0.5368 0.5724(0.4915) (0.4989) (0.4948)

Religion Degree 0.4039 0.4201 0.4102(0.4908) (0.4938) (0.4919)

Urban (1 if living in urban) 0.74 0.7856 0.7653(0.44370) (0.4106) (0.4239)

Family poverty (1 if in poverty) 0.2239 0.5005 0.3125(0.4169) (0.5002) (0.4636)

Living with parents until age 18 (1 if yes) 0.6270 0.4584 0.5754(0.4837) (0.4985) (0.4943)

Multi move in 1979 and 1982 (1 if yes) 0.0707 0.0507 0.0638(0.2564) (0.2195) (0.2443)

Living with parents at age 14 (1 if yes) 0.7217 0.4469 0.6381(0.4483) (0.4974) (0.4806)

Married (1 if never married) 0.9825 0.9971 0.9872(0.1311) (0.0535) (0.1122)

Black (1 if black) 0 1 0.28350 0 (0.4508)

Male (1 if male) 0.4835 0.5005 0.4891(0.4998) (0.5002) (0.5000)

Note: Numbers in parentheses are standard deviations.

to ten years.2 In Table 2, the average additional schooling years are 5.315 for whites and4.930 for blacks.

In the 1979, 1980, 1982, and 2000 interviews, information from individuals’ five mostrecent moves and residences was collected in NLSY79 at the county level. An individualis defined as a mover if his county of residence in 1979 is different from his county of

2Oregon, South Dakota, Tennessee, Vermont, and Washington have six years of compulsory schooling,while Ohio has ten years of compulsory schooling.

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770 Y. DONG ET AL.

residence in 1982; otherwise, he is defined as a non-mover. We do not have informationon people who moved within a county. People who moved away first and then movedback to the same county are categorized as non-movers. In our sample, 22.21% of whites,16.90% of blacks, and 14.77% of other races are movers.

Defining the neighborhood of an individual is very difficult. This paper uses the countyin which the individual resides and the individual’s racial group as his neighborhood, fortwo main reasons. First is the data availability. The most detailed data we can obtainfrom NLSY is at county level. Second, a substantial residential segregation betweenblacks and whites in metropolitan areas and counties has been well documented in theliterature. Blacks are very likely to live in neighborhoods with few whites (Massey andDenton, 1989). Since the focus of this paper is the neighborhood effect on the highestgrade completed, the ideal neighborhood variable would be average schooling years atthe neighborhood level. However, data on the percentage of the population who finishhigh school and college are available only by county. We expect that those percentagevariables are highly related to average schooling years. Therefore, the key neighborhoodvariable in this article is the percentage of population finishing high school.

However, only the overall percentage of high school graduates at the county levelis available in the NLSY. To construct race-specific high school graduates at thecounty level, we use the 1980 Integrated Public Used Micro data Series (IPUMS) 5%census samples to construct two data series: the metropolitan level percentage of highschool graduates (SM ) and the metropolitan level race-specific percentage of high schoolgraduates (SM−Black and SM−White). Let the county-level percentage of high school graduatesbe SC . Then the county-level race specific percentages of high school graduates (SC−Black

and SC−White) can be obtained as follows:

SC−Black = SM−Black

SM· SC , and SC−White = SM−White

SM· SC �

The above strategy assumes that the ratio for the percentage of high school graduatesis the same for the county and the metropolitan area.

Figure 1 shows a positive relationship between the individual education and theneighborhood variables, i.e., the county-level race specific percentages of high schoolgraduates, for both movers and non-movers. The slope is larger for the mover groupthan for the non-mover group, suggesting that moving may induce a difference in theneighborhood effect. The simple regression results, listed in Fig. 1, reveal the samerelationship. The slope estimates are statistically significant at 0.0297 for the movers and0.0210 for the non-movers.

Table 1 lists the county-level overall percentages of high school graduates for bothwhites and blacks, as well as the race-specific percentages of high school graduates forboth whites and blacks. Overall, blacks live in counties that have lower percentages ofhigh school graduates. The difference is even larger if it is race-specific, indicating thatblack neighborhoods have an even lower percentage of high school graduates.

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FIGURE 1 The relationship between the individual schooling years and the county-level race-specificpercentages of highs school graduates.

2.2. Data Imputation and Sample Size

A substantial number of county and individual variables are involved in this article. Asa result, the intersection of nonmissing values of all these variables is a rather smallsample size. NLSY79 includes 4,963 individuals who were between the ages of 14 and 17,with positive schooling years and a nonmissing record for their residences in 1979–1982.However, the intersection of all nonmissing variables reduces the sample size to 918.3

Therefore, it is necessary to impute missing variables to preserve the sample size to someextent.

3The estimation of the type model with 918 individuals leads to similar conclusion, but the resultsoverestimate the neighborhood effects.

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We use the mean imputation method that applies the means of nonmissing values toimpute the missing values. We have three levels of variables: individual level, county level,and state and metropolitan level. The following imputation rule is adopted: (1) for theindividual level data, we use the race-specific national means; (2) for the county level data,we use race-specific state means; and (3) for the state level or metropolitan level data, weuse race-specific national means. In addition to imputation, we also construct a missingdummy variable for each variable with missing observations. The variable takes on thevalue of one if an observation is missing, and zero otherwise. Among the total 4,963observations, 3,686 observations remain in the sample after imputation. The rest of theobservations are not used in our analysis due to at least one of the other variables beingmissing. Table A1 presents the data statistics before imputation and after imputation. Thesample means before and after the imputation are very close to each other.

2.3. Other Variables

Table 2 lists other individual characteristics variables, including race, gender, age,residence (at the county level), religion (1 if religion frequency is more than once perweek), and feelings about the safety of school (1 if the individual feels safe). Variablesabout family background include mother and father’s education, family size, the oldestsibling’s highest grade completed, family income, whether or not the individual lived withhis parents until the age of 18, and family poverty status. From the table, whites are fromricher families, with a smaller family size and a better educated father than blacks.

In addition to the individual and family background, Table 1 presents a set of countycharacteristics as county level control variables. These variables are referred in Manski(1993) as contextual variables. These variables include the race-specific mortality risks,obtained from the CDC. In particular, the external mortality rate for ages 15 to 34 isused, under the assumptions that a huge disparity of mortality risks between black andwhite teenagers is due to external reasons such as homicide and that the peer group forteenagers is the young group with similar ages. During this time period, blacks’ externalmortality rate is about 162 per 100,000 people, while whites’ is only 89.2 per 100,000people.

Other county characteristics variables include the percentage of blacks in thepopulation, the percentage of people living in urban areas, arrest rates, employment ratein the education institution, and the overall unemployment rate. Table 1 lists the meansand standard deviations for the key variables for the whole population and by race.Neighborhood variables also differ significantly. Blacks also have a much higher crimerate; theirs is 5,833 per 100,000 people versus the white crime rate of 4,949 per 100,000.

Table 3 presents differences in county-level variables between movers and non-moversin 1979 (before moving) and 1982 (after moving) by race. The number in the table is thepercentage difference between movers and non-movers. For example, for the mortalityrate, the number in column (1) is −1�1298, indicating that black movers’ county mortality

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TABLE 3Percentage Difference between Movers and Non-movers

Blacks Whites

Before move After move Before move After move

% diff. % diff. % diff. % diff.

Mortality rate −1�1298 −10�8796 2�3601 −6�7735Percentage employed rate in education 2�8601 27�8552 3�6462 25�5653Per capita income −1�9702 0�7241 −0�5589 −0�7654Percentage of black −2�3586 −16�0754 −8�4888 −3�5056Crime rate −4�1961 −0�0259 −5�6378 3�7392Percentage of high school graduates −0�9830 9�3583 0�4812 3�4753Percentage of urban −6�8416 −1�2992 −6�4887 −2�2933Civil unemployment rate 2�3718 −9�4775 −1�4453 −0�9936

Note: (1) Because 1982 data are not available in IPUMS, we could not impute county level race-specificpercentage of high school graduates here.

(2) A negative number in the table indicates that the county variable for movers is less than that for thenon-movers.

rate is 1.1298% lower than the black non-movers county mortality rate. Since the numberin column (2) (after they move) for mortality risk is −10�8796%, blacks move fromcounties with slightly low mortality risks to counties with significant lower mortality risks.In other words, compared with black non-movers, black movers move to counties withlower external mortality rates. The difference between the two columns for blacks and thedifference between the two columns for whites are the difference-in-difference estimator,with the treatment group being the movers’ group, and the control group being the non-movers’ group.

It is obvious from Table 3 that moving has substantially changed movers’neighborhood characteristics. In most cases, people move to relatively betterneighborhoods. Both blacks and whites move to counties with lower mortality risksand higher percentages of high school graduates. In addition, both blacks and whitesmove to counties with relatively higher percentages of people live in urban areas, andcounties with higher percentages of people employed in education, as well as countieswith lower percentages of blacks in the population. The difference between blacks andwhites, however, is that the changes in neighborhood characteristics are often larger forblacks than for whites. Another difference between blacks and whites is that blacks moveto counties with higher per capita income and much lower unemployment rates, whilewhites do not. Finally, it is worth noting that both blacks and whites move to countieswith higher crime rates. This is likely due to the fact that both blacks and whites movefrom less urban areas to more urban areas where crime rates are often higher.4

4According to Duhart (2000), from 1993 to 1998, violent crime rate in urban areas was about 74% higherthan the rural rate and 37% higher than the suburban rate.

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3. THE MODEL

3.1. Choice of Schooling Years

Suppose that individual i be a member of group g. He (with his parents) choosesthe schooling years Si after his compulsory schooling. Let Si be linearly related tothe following control variables: (i) individual level characteristics Xi; (ii) group levelvariables that are predetermined at the time that choices are made, Zg; (iii) an individual’sperception of the average choice of others, Sg; and (iv) unobserved individual and groupattributes vi and �g , which make up the error term. According to Manski (1993), (ii) arethe contextual effects, (iii) are the endogenous effects, and (iv) are the correlated effects.Therefore, the basic equation of school years can be written as

Si = �1Xi + �2Zg + �3Sg + vi + �g� (1)

Nonrandom sorting processes may create correlation between Sg and the error term vi.For example, those people with positive vi are likely to move to areas or neighborhoodswith high quality schools. This may create a correlation between the observed groupcharacteristics such as percentage of high school graduates enrolling in colleges.

3.2. Residential Mobility Choice

The residential mobility choice model in this paper is given by

movei = 1(�oLog + �dLdg + �1Xi + ei > 0) ≡ 1(zig� + ei

), (2)

where movei = 1 if individual i’s location at 1979 is different from his location at 1982,and movei = 0 otherwise. The moving decision depends on the individual characteristicsXi, the contextual variables, that is, group level variables as we mentioned above in theoriginal location Log , and the destination Ldg . In this article, the original location, o, is thecounty where the individual resided in 1979, and the destination, d, is the county wherehe resided in 1982.

Moving can be driven by a multitude of reasons: convenience, cost saving, or randomshocks to the family or the job. This paper investigates the relationship between themoving and education investment decisions; therefore, children’s welfare is assumed to beone of the factors the parents consider when they choose their location.

Since we can only observe whether an individual moves and information on theorigin and destination, and no information on the steps involved in search is observed,without strong assumption, the estimation of the above equation for alternativelocation is impossible. However, ignoring those alternatives may cause the estimationto be inconsistent. Following Ioannides and Zanella (2007), we choose the area-levelcharacteristics of spatially adjacent counties as instrumental variables. There are two

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RESIDENTIAL MOBILITY, NEIGHBORHOOD EFFECTS 775

reasons to use these variables as instruments. First, if different areas are characterizedby different distributions, Weitzman (1979) shows that the optimal search strategy is thenested strategy in which people search among areas first and then search within the area.This type of search strategy suggests that average characteristics of adjacent countieswould be correlated with the own-county characteristics. Moreover, even if a person’ssearch strategy is not the nested strategy of Weitzman (1979), it is still appropriate touse the adjacent counties as instruments as long as these instruments are well correlatedwith the own-county characteristics, and are uncorrelated with the error term of the mainequation. It is worth noting here that the instrumental regression does not require that wecorrectly specify the relationship between the instrumental variables and the endogenousvariable; it only requires a correlation between these variables.

The construction of the instrumental variables in this article is slightly differentfrom Ioannides and Zanella (2007). They choose the averages of the characteristicswithin the entire group of spatially adjacent census tracts, including the census tractwhere households reside as their instrumental variables. Including the location where thehousehold resides could introduce some correlation between the instrument variables andthe error term. Therefore, in calculating the spatially adjacent county means, we excludethe individual’s county of residence.

3.3. Joint Decisions of Mobility and Schooling

Here we allow the schooling decision and residential mobility to be jointly determined.The residential mobility decision is described in Eq. (2). The schooling-choice model (1)with mobility is assumed to be as follows:

Si = �1Xi + �2Zog + �3Sog + �4Sog∗moveig + vi + �g� (3)

In Eq. (3), we allow the neighborhood effect of original location, o, to affect theschooling choice. Sog is the average education attainment in the original neighborhood,i.e., percentage of high school graduates in the neighborhood in the paper. Zog is othergroup level variables in the original neighborhood. Figure 1 suggests that movers andnon-movers may differ in their responses to the neighborhood variable. This differencemay arise from the fact that those who move are more sensitive to the neighborhood thanthose who do not move. The parameter �4 captures the differential effect of Sog on moversand non-movers We use the 1979 values in this equation.

The endogenous moving process means that unobserved factors driving individuals’moving also have impacts on individual’ schooling choices. If the moving decision ismodeled as in (2), then the error term ei in Eq. (2) is correlated with the error term vi inEq. (3). Assuming that Corr(vi, ei) = �, and taking the conditional expectation for movers

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776 Y. DONG ET AL.

and non-movers, we have

E(Sig | moveig = 1

) = �1Xi + �2Zog + (�3 + �4) Sog + �

(� (Z�)

(Z�)

)� (4.1)

E(Sig | moveig = 0

) = �1Xi + �2Zog + �3Sog + �

( −� (Z�)

1 − (Z�)

)� (4.2)

Equations (4.1) and (4.2) are the Heckman sample selection model. Equation (4.1) isfor the movers, and Eq. (4.2) is for the non-movers. Testing the statistical significance ofthe coefficient � in Eq. (4.1) using the subsample of movers is a test for the endogeneityof the moving decision. Similarly, one can use the subsample of non-movers to test thestatistical significance of the coefficient estimate of � in Eq. (4.2).

A less-discussed implication of (4.1) and (4.2), however, is that the coefficient for theHeckman correction term (z�)/(z�) for movers is the same as the coefficient for theterm −(z�)/(1 − (z�)) for non-movers. Therefore, testing the equality of these twocoefficients can serve as a specification test of the model.5

We use the two-step Heckman method to estimate the model. In the first step,we estimate the residential mobility choice model described in Eq. (2).6 The estimatedcoefficients, �, are used to construct the inverse mills ratio term �

(z�

)/

(z�

)for the

mover subsample and the term −�(

z�)

/(

1 − (

z�))

for the non-mover subsample.Table 4 lists the estimation results for the Heckman sample selection models for bothmovers and non-movers. For comparison purposes, the OLS results are also presented inTable 4 for both movers and non-movers.

It is clear from Table 4 that the coefficients between movers and non-movers aredifferent, while the coefficients between the OLS and the Heckman sample selectionmodel are only marginally different. It is important to point out that the coefficientsfor the neighborhood variable—the county level race-specific percentages of high schoolgraduates—are insignificant for both the mover subsample and the non-mover subsamplein the Heckman model. The Heckman sample selection test rejects the OLS model fornon-mover subsample but not for mover subsample. Therefore, despite an unconditionalpositive relationship between the percentage of high school graduates and schooling yearsillustrated in Fig. 1, this neighborhood variable does not have any effect on schoolingyears after controlling for other variables in the Heckman sample selection model.

More importantly, the Heckman sample selection test exhibits inconsistent results fromtwo subsamples. As discussed earlier, the coefficients from the inverse mills ratios shouldbe the same for both subsamples. For the non-mover group, the coefficient estimate for

5In fact, the coefficient of Xi should also be the same for both equations. Testing the equality of thecoefficient � can also serve as a specification test. The specification test suggests we reject the equality of thecoefficient � at 1% level of significance.

6The estimation procedure and the results for the residential mobility model are discussed in detail insection IV-A.

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RESIDENTIAL MOBILITY, NEIGHBORHOOD EFFECTS 777

TABLE 4OLS and Heckman Estimation for Movers and Non-movers

Movers Non-movers

Variables OLS Heckman OLS Heckman

Predicted percentage high school −0.0171 −0.0135 0.00179 0.00393graduates(race specific) (0.01203) (0.01222) (0.00511) (0.00527)Religion degree 0.966156∗∗∗ 1.001621∗∗∗ 0.516738∗∗∗ 0.504357∗∗∗

(0.214219) (0.21652) (0.087316) (0.086957)Family size −0.1174∗∗∗ −0.12117∗∗∗ −0.07311∗∗∗ −0.07122∗∗∗

(0.01848) (0.01954) (0.01864) (0.02005)Family poverty −1.53884∗∗∗ −1.59188∗∗∗ −0.89755∗∗∗ −0.97936∗∗∗

(0.25881) (0.261855) (0.098021) (0.098306)Mom went to college (1 if yes) 1.9273∗∗∗ 1.9248∗∗∗ 2.1579∗∗∗ 1.9811∗∗∗

(0.2679) (0.2702) (0.1049) (0.1125)Mortality rate 0.000562 0.000521 −4.7E-05 −0.00035

(0.001076) (0.001089) (0.00043) (0.000437)Crime rate −4.6E-05 −4.6E-05 −6.8E-06 −1.5E-05

(3.08E-05) (0.000031) (1.21E-05) (1.37E-05)Civil unemployment rate −0.00175 −0.00115 0.01253∗∗∗ 0.01338∗∗∗

(0.005034) (0.00509) (0.00243) (0.00247)Percentage employed in education 0.002699 0.001699 −0.00105 −0.00294

(0.003794) (0.003836) (0.001922) (0.00193)Percentage of being urban 0.001135∗∗ 0.001342 0.000614∗∗∗ 0.001045∗∗∗

(0.000554) (0.000564) (0.000174) (0.000194)Percentage of blacks −0.00051∗∗ 6.86E-05 −2.6E-05 0.000537

(0.00027) (0.000306) (0.000314) (0.000354)Per capita income 0.000159 7.68E-05 −0.00015 −0.00027∗∗∗

(0.000159) (0.000161) (5.45E-05) (5.71E-05)Constant 5.605963∗∗∗ 5.627543∗∗∗ 4.892277∗∗∗ 5.121283∗∗∗

(0.108947) (0.1167) (0.150718) (0.170126)Inverse Mills Ratio 0.8043 1.2323∗∗

(0.5435) (0.6373)R square 0.0573 0.1376# observations 4,929 4,550 4,771 4,163

Note: (1) The estimation includes dummy variables for missing values of imputed variables.(2) Robust standard errors in parentheses: ∗∗∗p < 0�01, ∗∗p < 0�05, ∗p < 0�1.(3) Equation 4.1 is the estimated equation for Heckman movers.(4) Equation 4.2 is the estimated equation for Heckman non-movers.(5) Sig = �1Xi + �2Zog + �3Sog is the estimated equation for OLS.

the inverse of mills ratio is a statistically significant value of 1.23 (0.637), suggestingthat the neighborhood choice is endogenous. However, if we use the mover group, thecoefficient estimate for inverse mills ratio is statistically insignificant at the value of 0.804(0.543), suggesting that the moving decision is exogenous. This difference could suggestthe possibility that the population may be heterogeneous in its motivations for moving.7

7Other reasons such as the model misspecification could also result in the difference.

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778 Y. DONG ET AL.

In the next subsection, we consider an extension of the current model in which boththe endogenous moving decisions and the exogenous moving decisions to the schoolingchoices may simultaneously exist in the population.

3.4. A Model of Heterogeneous Motivation in Moving

People move for multiple reasons. For example, they may move for better economicprospects. Bowles (1970) finds that economic incentives affect geographic mobility ofworkers. By estimating a dynamic model of search, Kennan and Walker (2006) concludethat differences in expected returns are important in driving migrations across the UnitedStates. Borjas et al. (1992) also make a similar conclusion. Other papers suggest thatmobility may be driven by the individual taste and characteristics. For example, college-educated couples usually locate in larger cities to pursue more job opportunities, betterquality of life, and a business environment (Chen and Rosenthal, 2006; Costa andKahn, 2000). There are also Schelling-type motives (Schelling, 1971); i.e., white Americanfamilies tend to move out of areas where the share of minorities is above a critical point—tipping point (Card et al., 2008).

Therefore, it is possible that some residential mobility may be exogenous while othersmay be endogenous to the schooling choice. We assume there are two types of people:one is the endogenous type and another is the exogenous type. Because these two types ofpeople may have different preferences, it is possible that their neighborhood effects mayaffect their schooling choices differently. Consider the following extensions of Eq. (3):

Si = �11Xi + �12Zog + �13Sog + �14Sog∗movei + v1i + �o� (5.1)

Si = �01Xi + �02Zog + �03Sog + �04Sog∗movei + v0i + �o� (5.2)

For Eqs. (5.1) and (5.2), the coefficients for Xi, Zog , Sog are allowed to be different tocapture the possible behavioral differences for the two types of individuals. Without lossof generality, we let the moving decision for type 1 in Eq. (5.1) be endogenous, and let themoving decisions for type 0 in Eq. (5.2) be exogenous. Given that the moving decision ismodeled in Eq. (2), we have

Corr(v1i, ei) = �, and Corr(v0i, ei) = 0� (6)

Further, suppose that an unobserved variable Ti governs individual i’s type: When Ti =0, individual i is type 0 (exogenous type); when Ti = 1, individual i is type 1 (endogenoustype). Therefore, the observed education Si can be written as

Si = (1 − Ti)S0i + TiS1i, (7)

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RESIDENTIAL MOBILITY, NEIGHBORHOOD EFFECTS 779

where S0i is the exogenous type’s schooling years and S1i refers to the schooling years ofthe endogenous type.

The type variable Ti is assumed to be determined by a vector of family and individualcharacteristics variables, denoted as wi:

Ti = 1(wi� + �i > 0) where �i ∼ N (0, 1)� (8)

We assume that covariances between v and � in these two pairs, (v0i, �i) and (v1i, �i), arezero in this analysis. After plugging S0 and S1 into the Si in Eq. (3), we have the followingmodel on schooling choice:

Si = T(�11 − �01)Xi + T(�12 − �02)Zo + T(�13 − �03)So + T(�14 − �04)So∗movei

+ �01Xi + �02Zo + �03Soi + �04So∗movei

+ i + �o + �io,

where i = Tv1i + (1 − T)v0i.Because only type 1 individuals are assumed to engage in endogenous moving

while type 0 individuals are assumed to move for exogenous factors, the expectationsconditioning on types and moves are given by

E(vi | movei, type = 1) = �

[(1 − movei)

−�(z�)

1 − (z�)+ movei

�(z�)

(z�)

]

E(vi | movei, type = 0) = 0�

Since types are unobserved, the expectations conditioning on moves only are given by

E(Si | move = 1) = E(S1i | move = 1, T = 1) Pr(T = 1 | move = 1)

+ E(S0i | move = 1, T = 0) Pr(T = 0 | move = 1)

E(Si | move = 0) = E(S1i | move = 0, T = 1) Pr(T = 1 | move = 0)

+ E(S0i | move = 0, T = 0) Pr(T = 0 | move = 0)�

Therefore,

E(Si | move = 1) = ��11Xi + (�12) Zo + (�13 + �14) So� (�i�)

+ ��01Xi + (�02) Zo + (�03 + �04) So� (1 − (�i�))

+ �

[�(z�)

(z�)

](�i�) + �o, (9.1)

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780 Y. DONG ET AL.

E(Si | move = 0) = (�11Xi + �12Zo + �13So) (�i�)

+ (�01Xi + �02Zo + �03So) (1 − (�i�))

+ �

[ −�(z�)

1 − (z�)

](�i�) + �o� (9.2)

Equations (9.1) and (9.2) together describe our two-type model. Comparing Eq. (9.1)with the Heckman sample selection model of (4.1), and (9.2) with Eq. (4.2), we find thatour model is reduced to the Heckman model in two circumstances. First, if there is onlyone type of individuals, our model becomes the Heckman sample selection model. In thecase that all individuals belong to the exogenous type, Pr(Ti = 0) = 1, i.e., (wi�) = 0,(9.1) and (9.2) become (4.1) and (4.2) without the Heckman sample correction term. In thecase that all individuals belong to the endogenous type, Pr(Ti = 1) = 1, i.e., (wi�) = 1,(9.1) and (9.2) become (4.1) and (4.2) with the Heckman sample correction term. Second,when the coefficients of two types are the same; i.e., the behavior or the responses ofthe two types of individuals are the same, and Eqs. (9.1) and (4.1) only differ by theprobability term (wi�). This is intuitive since the model assumes that only part ofthe people belong to the endogenous type. The probability term (wi�) precisely givesthe proportion of people who are endogenous. Estimates using (4.1) may overestimate thecoefficient for the Heckman sample correction term.

The two-type model suggested in this paper belongs to the family of the mixture densitymodels. The mixture density models have been widely used in the literature to modelunobserved types. For example, Feinstein (1990) proposes and estimates a mixture densitythat considers the unobserved violations and the observed detections of violations of lawsand regulations. Keane and Wolpin (1997) model five different unobserved types in abilityendowment using a mixture density model. Knittel and Stango (2003) estimate a mixturedensity model using state-mandated price ceilings as focal points for unobserved tacitcollusions of credit card companies. When modeling the default probability of consumercredit cards, Gan and Mosquera (2008) suggest that different types of consumers maycome from the heterogeneity in consumers’ time discount rates, and/or the heterogeneityin their risk aversion. A model with unobserved types would lead to better out-of-samplepredictions in default probability. Identification of this type of model, however, dependson the assumptions of the distribution. Here we assume that error distributions arenormal since there are no compelling reasons to assume any other distributions.

The type-consistent model also relates to the literature on correlated randomcoefficients (the treatment effects are heterogenous by selection types). Instrumentalvariable estimation is probably most notable strategy for the treatment of correlatedrandom coefficient models. Heckman and Vitlacyl (1998) and Wooldridge (2003) provideidentifying assumptions for it. However, this model is different from or is a special case ofthe correlated random coefficient model in the following two points: first, the treatmenteffects in the model are heterogeneous by selection types instead of individually. Second,there is a presence of endogenous binary variables in the model.

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RESIDENTIAL MOBILITY, NEIGHBORHOOD EFFECTS 781

Estimation of (9.1) and (9.2) requires two steps. First, we estimate the residentialmobility model to obtain the inverse mills ratio term. The results of this estimation arelisted in Table 5. In the second step, we estimate both (9.1) and (9.2) simultaneously. Theparameters to be estimated include parameters from the schooling choice models, �, andthe parameters from the type determination model, �. Nonlinear least squares is appliedto Eq. (9.1) for movers and (9.2) for non-movers simultaneously.

Since the two-type model is highly nonlinear, it is useful to understand its small sampleproperties. In the Appendix B, we conduct a simulation study with sample sizes of 100,500, 1,000, and 3,000. It is shown that, when the sample size is below 1,000, large biasesmay occur and estimates are no longer reliable. When the sample size is 1,000, some biasesmay occur, and estimates must be taken with caution. The estimates are very close to thetrue values when the sample size is 3,000.

TABLE 5Results for IV Probit for the Moving Decision

Variables IV Probit Std. Err.

Individual variables Mom’s highest grade 0.0311∗∗∗ 0.0108Dad’s highest grade 0.0193∗∗ 0.0088Family size −0.0436∗∗∗ 0.0133Age 2.8030∗∗∗ 0.8050Age squared −0.0844∗∗∗ 0.0257Black (1 if black) −0.0975 0.0659Male (1 if male) −0.0442 0.0488Urban (1 if living in Urban) −0.0162 0.1210

The destination Percentage urban 0.025∗∗∗ 0.005Percentage female head 0.021 0.031Crime rate 6.81e-05∗∗∗ 2.45e-05Percentage college graduates 0.0888∗∗∗ 0.014Civil unemployment rate∗ −0.353∗∗∗ 0.137Civil employment −1.32e-07 1.57e-07Per capita income −0.0013∗∗∗ 0.0004

The origin Percentage urban −0.026∗∗∗ 0.006Percentage female head −0.034 0.035Crime rate −5.28e-05∗∗ 2.45e-05Percentage college graduates −0.028 0.017Civil unemployment rate∗ 0.354∗∗∗ 0.135Civil employment −1.32e-06 1.57e-06Per capita income∗ 0.0013∗∗∗ 0.0004Constant −24.5800∗∗∗ 6.29

No. of observations 4,817

Note: (1) This is the estimation results for Eq. (2) in the paper.(2) Robust standard errors in parentheses: ∗∗∗p < 0�01, ∗∗p < 0�05, ∗p < 0�1.(3) Variables with superscript ∗ are endogenous and the predicted values used here.(4) Instrument variables for those variables are the mean values of adjacent counties excluding the

residence.(5) The estimation also includes dummy variables for missing values of imputed variables.

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782 Y. DONG ET AL.

3.5. Endogeneity of the Neighborhood Variable and Its Instrumental Variables

In the education demand equation, the perceived neighborhood education variable So ispossibly related to the error term �o; thus, we must find appropriate instrument variables.The paper uses instruments similar to those used in Ioannides and Zabel (2008): thecounty means of the inverse mills ratios. The county means of the inverse mills ratiosare constructed from county variables and derived from the econometric assumption.Therefore, the county inverse mills ratio will not be correlated with unobserved countycharacteristics, and it is a valid instrumental variable.

Another source of instruments is the racial residential segregation indexes. Theseindexes are calculated at the metropolitan level. Residential segregation indexes usuallymeasure the degree of racial segregation in terms of residence in five dimensions: evenness,exposure, concentration, centralization, and clustering. The maintained assumption in thispaper is that a black’s neighborhood would be the black population in the county wherehe resides, and a white’s neighborhood would be the white population in the county wherehe resides. However, the degrees of residential segregation may be different not onlyacross the counties, but also within the counties. Therefore, our neighborhood variablecan only be a proxy of the true neighborhood variable. In other words, our neighborhoodvariable is a measure of the true neighborhood variable with measurement errors, causingan endogeneity problem. To mitigate this problem, we use the segregation indexes asinstrumental variables, which should mitigate these biases. Obviously, the segregationindexes would be correlated with our neighborhood variable, but there is no reason tobelieve that these variables would have an effect on schooling in addition to their effect onthe neighborhood variable. This article uses seven different measures of the segregationindexes as instrumental variables for our key neighborhood variable, the race-specificpercentage of high school graduates. These seven measures capture all five dimensions ofsegregation. Table A2-1 describes these seven indexes in detail, and Table A2-2 lists theirsummary statistics. All these indexes are directly obtained from the Census Bureau.

We use a weak identification test to test the above sets of instruments, and the Cragg–Donald test statistic is 95.43, much larger than the Stock–Yogo weak IV test criticalvalues for 5% relative bias (20.53) and 10% size (36.19). Therefore, we reject the nullhypotheses of weak identification. Table 6 lists the first stage results for the percentage ofhigh school graduates.

4. ESTIMATION RESULTS

The estimation involves several stages. First, we estimate a probit model for the movingdecision (Eq. 2) by using the adjacent county means as instrumental variables. Second,using the county mean inverse mills ratio derived from the moving estimation andsegregation indexes as IVs for the endogenous neighborhood variable, we get thepredicted race-specific percentage of high school graduates at county level. Third, the

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RESIDENTIAL MOBILITY, NEIGHBORHOOD EFFECTS 783

TABLE 6Estimation for the County High School Graduates

Variables Coefficient Std. Err.

County mean inverse mills ratio −0.7217∗∗∗ 0.2511Absolute Centralization Index (ACE) −9.6376 6.7710Absolute Clustering Index (ACL) −25.6396∗∗∗ 5.6340Atkinson Index with b=#1 (A1) −11.7859 19.4012Entropy Index (H) 87.1056∗∗∗ 19.4236Gini Index (G) −44.6909∗∗∗ 9.8105Relative Centralization Index (RCE) 5.3356 5.2515Relative Concentration Index (RCO) −13.1328∗∗ 5.2579Inverse mills ratio 0.8593∗∗∗ 0.2883Religion degree −0.5298∗∗ 0.2536Family poverty −0.0986 0.4005Mom highest grade 0.3348∗∗∗ 0.0709Mortality rate 0.0026 0.0029Crime rate −0.0002 0.0001Civil unemployment rate 0.3859 0.3149Employment in education institution 1.0655∗∗∗ 0.1803Percentage being urban 0.0744∗∗∗ 0.0258Percentage being black −0.1806∗∗∗ 0.0417Per capita income 0.0080∗∗∗ 0.0008Constant 2.7008 4.4166Observations 4,100R2 0.851

Note: (1) The estimation includes dummy variables for missing values ofimputed variables.

(2) Robust standard errors in parentheses: ∗∗∗p < 0�01, ∗∗p < 0�05, ∗p < 0�1.

predicted county education level is used to estimate the two-type model (Eqs. 9.1 and 9.2).In particular, we simultaneously estimate the type determination equation (Eq. 8) and theneighborhood effects on the education equations for the two types.

4.1. Residential Mobility Choice Estimation

The residential mobility choice is modeled in Eq. (2). The contextual variables for boththeir current location Yog and their destination Ydg used in this article include percentageof population living in urban areas, percentage of households with a female as thehousehold head, the crime level, percentage of high school graduates, percentage ofcollege graduates, the unemployment rate, the total employment, and per capita income.All variables are at the county level. The individual and family background variablesinclude the father and mother’s highest grades achieved, family size, age and age squared,a dummy for blacks, a dummy for male, and a dummy for living in an urban area. If avariable has missing values, we construct a missing dummy for those observations withmissing values.

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784 Y. DONG ET AL.

As discussed earlier, the contextual variables are potentially endogenous. The strategy isto employ the mean value of adjacent counties (excluding the county where the individualresides8) as instrumental variables. This instrument choice may have the following concerns:First, if observed county and adjacent counties area are correlated, then unobservableterms could also be related with the adjacent counties as well. Secondly, the individualunobservables may also be correlated with the instruments. For the first concern, thecorrelation between the instruments and the unobservable county characteristics is cross-correlation, since variables at the county and area level are either observable for both orunobservable for both. In terms of cross-correlation, if the area has enough heterogeneityacross counties, then such correlation will be negligible (Ioannides and Zanella, 2007).According to the pairwise correlations between all contextual variables in a county andits adjacent counties (not including itself), we find that the median of correlation is 0.359and the mean of the correlation is 0.202. Those numbers suggest that the area has enoughheterogeneity. As for the correlation between individual unobservable characteristics andinstruments, we can assume that it is very small. For example, a household may move to acertain area closer to friends or family, but where exactly they choose to move may dependon completely different considerations, unrelated to the presence of friends and family inthe larger area. Therefore, the individual unobservable characteristics that affect whether ornot to move to the destination can, in principle, be assumed to be independent of averagearea level characteristics.

To test the endogeneity of the contextual variables, the Rivers and Vuong (1988) two-stage procedure is implemented. First, we run each neighborhood characteristic variableon its instruments (the mean of adjacent counties) and get residuals; second, we run theprobit model with individual variables, all the neighborhood characteristic variables, andall the residuals from the first stage. If the coefficients before the residuals are significant,then corresponding variables are endogenous; otherwise, they are exogenous. The secondstage results are presented in Table 7. From this table, only the civil unemployment ratesat the origin and the destination and the per capita income at the origin are endogenous.Therefore, we only instrument for these three endogenous variables in our estimation. Theestimation results are presented in Table 5.

Before we discuss the estimation results, we follow Ioannides and Zanella (2007) tolabel a variable as an “attractor” if its coefficient is negative for the current county, andpositive for the destination county. Similar, a variable is labeled as a “repeller” if itscoefficient is positive for the current county, and negative for the destination county. Weexpect that for the same variable the coefficients for the origin and the destination willhave opposite signs and the same absolute value:

H1 : sgn(�o,j) = −sgn(�d,j) for all j;

H2 : �o,j = −�d,j for all j�

8The adjacent counties for each county are found from GIS programming, and we thank Ms. Yige Gao’shelp and guide in our GIS programming.

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TABLE 7Second Stage Results for Rivers and Vuong Procedure

Variables Estimation

Destination Error for percentage urban −9.13E-06(0.0016)

Error for percentage female head −0.0024(0.0111)

Error for the crime rate −1.01e-05(0.0001)

Error for percentage college graduates −0.0097(0.0091)

Error for unemployment rate 0.0198∗∗

(0.0098)Error for civil employment −9.72E-07

−6.81E-07Error for per capita income 0.0003

−0.0003Origin Error for percentage urban 0.0020

−0.0019Error for percentage female head 0.0100

−0.0112Error for the crime rate −7.06E-05

−9.25E-05Error for percentage college graduates 0.0142

−0.0099Error for unemployment rate −0.0168∗

−0.0091Error for civil employment 4.78E-07

−8.07E-07Error for per capita income −0.0006∗∗

−0.0003

Note: (1) This procedure is to justify the endogeneity of variables in Eq. (2).(2) Only the estimations for the error terms presented here.(3) Robust standard errors in parentheses: ∗∗∗p < 0�01, ∗∗p < 0�05, ∗p < 0�1.

In Table 5, we find that percentage of urban population, crime rate, percentage of highschool graduates, unemployment rate, and per capita income have significant impacts onpeople’s moving decision. Among the above variables, the percentage of urban populationand the percentage of college graduates are attractors in individuals’ moving decision.People would like to stay in places with a high percentage of urban population and ahigh education level. On the other hand, the unemployment rate acts as a repeller. Peoplewould like to move away from places with high unemployment rates and move to placeswith high employment rates. The estimation results show that low crime rates and highper capita income will increase the probability of moving out. The estimation result forthe crime rate is consistent with the fact that movers move to the residence with highcrime rate (see Table 3) because people move from less urban areas to more urban areas

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786 Y. DONG ET AL.

with higher crime rates. In terms of per capita income, black movers move to the locationwith higher per capita income, while white movers do not. The estimation result for percapita income reflects that on the average movers move to the location with low per capitaincome because we have more whites than blacks in the sample.

In addition, Table 5 also shows that the inclination of moving also differs acrossfamilies. It is related to parents’ education background and family size. In most cases,moving is easier for the smaller families and for highly educated parents. The coefficientestimate is positive for age but negative for age squared, suggesting that moving happensmore frequently before individuals are 16.6 years old and becomes less when individualsare older than 16.6 years. Finally, there is no statistically significant difference betweenblacks and other races in their moving probabilities.

4.2. Results From the Two-Type Model

In Subsection 2C, we discuss the Heckman sample selection model for movers and non-movers and present the estimation results in Table 4. We show that the Heckman sampleselection model produces inconsistent results for the mover group and the non-movergroup. In this section, we estimate our two-type model. To be more general, we allow bothtypes to be potentially endogenous. By doing this, we can test if one type is exogenouswhile another type is endogenous. In particular, we rewrite (6)

Corr(v1i, ei) = �1, and Corr(v0i, ei) = �0� (10)

A specification test of our two-type model is that �1 �= 0 and �0 = 0. Alternatively,a specification test for the Heckman sample selection is that �1 = �0 = �. In addition,it is entirely possible that �1 �= �0, and neither one of them equals zero. This suggeststhe existence of two endogenous types. These two types may exhibit different behaviorin their education equations. With this setup, Eqs. (9.1) and (9.2) are modified in thefollowing way:

E(Si | move = 1) =[�11Xi + (�12) Zo + (�13 + �14) So + �1

�(z�)

(z�)

](�i�)

+[�01Xi + (�02) Zo + (�03 + �04) So + �0

�(z�)

(z�)

](1− (�i�)) � (11.1)

E(Si | move = 0) =(

�11Xi + �12Zo + �13So + �1−�(z�)

1 − (z�)

)(�i�)

+(

�01Xi + �02Zo + �03So + �0−�(z�)

1 − (z�)

)(1 − (�i�)) � (11.2)

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RESIDENTIAL MOBILITY, NEIGHBORHOOD EFFECTS 787

In both equations, So instead of So is used where So the predicted value from theinstrumental variable regression. As discussed earlier, the instrumental variables areaverages of the inverse mills ratios and segregation index. Since the parameters � and� are the same for both equations, it is necessary to simultaneously estimate both Eqs.(11.1) and (11.2). The nonlinear least squares method is applied to estimate this model.

Tables 8 and 9 present the estimation results. Table 8 reports the type estimationresults, where the basic type determination model is described in Eq. (8). The coefficientsreported from this table are similar to those from a binary probit-type of model. Apositive coefficient of a variable indicates a positive marginal effect of that variable’scontribution toward the endogenous type. Different from a regular binary probit model,here the types are unobserved.

We do not have strong priors ex ante on variables that may help identifying types ofindividuals. So here we can only offer some ex post intuitions. First, the estimation resultsshow that endogenous type people are more likely to be those who are from a largerfamily and whose father went to college. Meanwhile the oldest sibling’s education andfamily income have positive contribution to be of the endogenous type. Males are morelikely to belong to the endogenous type than females.

Table 9 reports the estimation results for the schooling equations for both types. Thefirst row in Table 9 reports the covariance between the error ei (from moving equation)

TABLE 8Two-Type Model Regression Results for Type Determination

Variables Coef. Std. Err.

Constant 2.615948 3.534404Family size 0.05062∗∗∗ 0.015393Living with parents until age 18 0.071706 0.046645Black (1 if black) 0.022895 0.077242Male (1 if male) 0.23189∗∗∗ 0.073712Urban (1 if living in urban) −0.20102 0.139263Move multiple times (1 yes) 0.048057 0.068428Family poverty −0.1244 0.176474the oldest sibling highest grade 0.064349∗∗∗ 0.018465Dad went to college or not (1 yes) 0.523928∗∗∗ 0.154174Living with parents at age 14 (1 yes) 0.009633 0.045448Married (1 if never married) 0.253372 0.163534Family income (in US $) 1.21E-05∗∗∗ 4.11E-06Age −0.42282 0.462966Age squared 0.01427 0.014908Feel safe about the school (1 if yes) 0.2104∗∗∗ 0.053399

Note: (1) The estimation includes dummy variables for missing values of imputed variables.(2) Robust standard errors in parentheses: ∗∗∗p < 0�01, ∗∗p < 0�05, ∗p < 0�1.(3) Equation 8 is the estimated equation.

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TABLE 9Two-Type Model Regression Results for School Equation

Exogenous Endogenous

Variables Coefficient Coefficient

Zeta 0.2400 −0.4916∗∗

(0.4820) (0.2805)Predicted percentage high school graduates (race specific) −0.0447 0.02863

(0.02889) (0.01855)Predicted percentage high school graduates (race specific)∗move −0.0268 0.04035∗∗∗

(0.02094) (0.00901)Crime −0.0001 5.93E-05

(7.37E-05) (4.94E-05)Mortality rate 6.67E-05 0.003491∗∗∗

(0.001422) (0.001201)Civil unemployment rate 0.027846∗∗∗ 0.008593

(0.009354) (0.007861)Family poverty 0.5981 −0.2609

(0.7067) (0.5377)Religion degree 0.5373∗∗ 0.5037∗∗∗

(0.3125) (0.2059)Mom went to college or not (1 yes) 0.2901 1.1471∗∗∗

(0.7946) (0.2853)Per capita income 0.000809∗∗ −0.00035

(0.000438) (0.000261)Percentage black −0.00176 0.00251∗∗

(0.002051) (0.001342)Employment in education institution 0.019873∗∗ −0.00548

(0.009535) (0.005715)Percentage urban 0.001104 0.00086

(0.001165) (0.000764)Constant −3.73456 5.558276∗∗∗

(2.315014) (1.434037)

Note: (1) The estimation includes dummy variables for missing values of imputed variables.(2) Robust standard errors in parentheses: ∗∗∗p < 0�01, ∗∗p < 0�05, ∗p < 0�1.(3) Equations 7, 9.1, and 9.2 are the estimated equations.

and the error vis (from the schooling equation for type s). The covariance �1 is estimatedto be −0.49 (0.28), with a p-value of 0.08, and the covariance �0 is insignificant (pointestimate is 0.24, and the standard error is 0.48). This result suggests the existence of boththe exogenous type (type 0) and the endogenous type (type 1).

To understand the intuition of a negative �1, consider a negative shock to the movingequation in (1). This negative shock could be a result of a change of the instructor, forexample. Because of the negative correlation between ei and vi, the probability of movingwould increase. Alternatively, consider a positive shock in the moving Eq. (2). An exampleof a positive shock is a job offer from a different location. Because of the negative �1, themoving probability would be less than if there were no correlation between ei and vi.

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The table also shows that the neighborhood effects are different for different types ofhouseholds. The key neighborhood variable in this paper is the race-specific percentageof high school graduates at the county level. The only statistically significant effect isfor the movers who belong to the endogenous type. The coefficient estimate for theinteraction term between percentage high school graduates and moving dummy is 0.04(0.009). Compared with the Heckman model in Table 4, not only is the estimate inthe two-type model statistically significant while the estimates in Heckman models arenot, but also the magnitude from the two-type is much larger than estimates from theHeckman models.

From Table 1, we know that the mean difference in percentage of high graduatesbetween white neighborhoods and black neighborhoods is 21.5%. Therefore, if anendogenous type person moved from an average black neighborhood to an averagewhite neighborhood, his education level would increase by 0�04∗21�5% = 0�86 years. Forthe exogenous type person, the proportion of high school graduates does not haveany significant impacts on his educational attainment. The result suggests that theneighborhood effect is concentrated on the movers who belong to the endogenous type.

Furthermore, individual, family background variables, and other county variables alsoshow different impacts for different types. For the endogenous type, religion has a positiveimpact on educational attainment. Religious people will choose higher education levels.For the endogenous type, the percentage of blacks and the mortality rate also havepositive impacts on educational attainment.

For the exogenous type, the unemployment rate has a positive impact on educationalattainment. One plausible explanation is that the high unemployment rate will giveindividuals more incentive to study hard, since higher education lowers their risk ofbecoming unemployed. Another possible reason is the high unemployment rate makesfinding work difficult, so people stay in school longer than they would have whenunemployment rate was low.

In conclusion, the above results imply that neighborhood effects have differentialeffects on educational attainment. If the location choice is endogenous, there isa substantial neighborhood effect for movers. However, no statistically significantneighborhood effect exists if the location choice is exogenous. Furthermore, the two typesof people behave differently. Some characteristics may affect the education choice for onetype of people but not for the others. Given the fact that Table 4, based on the Heckmanselection model, shows no statistically significant neighborhood effect, it is important toaccount for the heterogeneity. It is worth pointing out here that our conclusions areconsistent with what social experiments have found.

Based on the estimation results from Tables 8 and 9, Table 10 calculates the numbersof endogenous types and exogenous types for movers and non-movers. Among the 3,121non-movers, 77.67% (or 2,424) belong to the endogenous type. For the 565 movers, thepercentage of belonging to the endogenous type is slightly higher, at 84.60% (or 478).Overall, 78.73% of the sample belongs to the endogenous type. It is interesting to note

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790 Y. DONG ET AL.

TABLE 10Education Level across the Type and the Move

Type Non-movers Movers Total

Exogenous Type 3.7202 3.1149 3.6531(2.1783) (2.3695) (2.2069)

Observations 697 87 784Endogenous Type 5.3993 6.633891 5.6027

(2.5331) (2.918506) (2.6400)Observations 2,424 478 2,902Total 5.0244 6.0920 5.1880

(2.5555) (3.1106) (2.6755)Observations 3,121 565 3,686

Note: The number in the bracket is the standard deviation.

that 16.47% of the endogenous type is movers, while only 11.10% of the exogenous typeis movers.

Table 10 lists the average years of schooling by type and moving status. Overall,movers have 6.092 years of additional schooling, more than 5.024 years of schoolingthan non-movers. More importantly, the endogenous type has 5.603 years of additionalschooling, 1.95 years or 53.38% more education beyond compulsory schooling than theexogenous type. For the movers, the difference is even more striking. The endogenoustype would take 6.634 years of education, 113% more schooling years than the exogenous

TABLE 11Observed and Predicated Education Level by Type and Race

Type White Black Other Total

Panel A: Expected schooling years

Exogenous type 3.3778 3.8486 3.8489 3.6012(0.8802) (0.7754) (0.8210) (0.8674)

Endogenous type 5.7091 5.3696 5.5614 5.6167(1.3084) (1.0078) (0.9869) (1.2356)

Total 5.3188 4.9271 4.9144 5.1880(1.5207) (1.1714) (1.2448) (1.4290)

Panel B: Observed schooling years

Exogenous type 3.3786 3.9934 3.7941 3.6531(2.2131) (2.1061) (2.4099) (2.2070)

Endogenous type 5.7042 5.3144 5.6518 5.6027(2.7168) (2.3987) (2.6191) (2.6400)

Total 5.3149 4.9301 4.9500 5.1880(2.7780) (2.3929) (2.6913) (2.6755)

Note: The number in the bracket is the standard deviation.

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RESIDENTIAL MOBILITY, NEIGHBORHOOD EFFECTS 791

type at 3.114 years. This large difference in education between the two types is consistentwith the notion that the types identify two distinct groups of people.

Table 11 lists the observed and predicted education level by type and race. Panel B hasthe observed schooling years, while panel A presents the predicted the schooling years. Itis clear from the table that the two-type model predicts schooling years at the mean levelquite well. The largest difference is about 3.76% for the blacks who are exogenous type.

As discussed earlier, if we let endogenous black movers have whites’ neighborhoodvalue where the percentage of high school graduates is 21.5 percentage points higher,these black movers’ education level would increase by 0.86 years. Table 10 shows thatmovers account for 15.33% of population and that endogenous type accounts for 84.60%of all movers. Therefore, the average gains if blacks have the same neighborhood variablewould be 0.1115 (0�86∗84�60%∗15�33% = 0�1115) years, which is 28.96% of the overalldifference at 0.385 years between blacks and whites in sample. Therefore, we concludethat the neighborhood effect accounts for 28.96% of the overall education differencebetween blacks and whites.

5. CONCLUSIONS

This article makes three main contributions to the neighborhood effect literature. First,it contributes to the econometric solution to the neighborhood effect by proposing a newmodel to identify the neighborhood effect. The key feature of the proposed model isits identification of the unobserved types. The article presents two reasons to justify itsassumption of unobserved types. The first reason is more theoretical. The article arguesthat people move for different reasons. One reason is to search for neighborhoods thatmay help education. In this case, the moving decision is endogenous. However, it is alsotypical for people to move for reasons that are independent to education choice. In thiscase, the moving decision is potentially exogenous. The second reason is empirical. Thetest based on Heckman sample selection model shows that coefficients for inverse millsratio are different between the mover group and the non-mover group.

Second, this article provides strong evidences of the existence of the two unobservedtypes. The estimation is conducted by allowing possibilities of both the one-type modeland the two-type model. The data supports the two-type model. In addition, peoplefrom different types exhibit different behaviors. The endogenous type has 53.42% moreschooling years (beyond the compulsory schooling) than the exogenous type.

Third, introducing the two unobserved types of individuals helps us to identify theneighborhood effect. When we use the Heckman sample selection model, we do not findany statistically significant neighborhood effects. However, the two-type model shows thatthe neighborhood effect only shows up for the endogenous mover group. Therefore, it isnot surprising that the effect is not seen for the population with one-type model. We findthat neighborhood difference between blacks and whites is an important factor affectingtheir educational gap. In particular, we find that the county-level race specific percentage

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792 Y. DONG ET AL.

of high school graduates can explain 28.96% of education difference between blacks andwhites.

One of the limitations of this paper is the definition of neighborhood. This article usesthe county as the neighborhood. If we were able to use a sufficiently narrower geographicdefinition (census tract or zip code, or perhaps some information about individuals’ socialcircle), it is possible that the magnitude of neighborhood effects would be larger. Here,still because of the limited information we have, we cannot make a formal comparison byusing different definitions of neighborhood. However, it is likely that our results providelower bounds of the true neighborhood effect.

APPENDIX A

TABLE A1Data Statistics Before and After Imputation Comparison

Before After

Variables Obs. Mean Obs. Mean

Mom highest grade 5,128 10.8181 5,451 10.8120(3.0866) (2.9985)

Dad highest grade 4,631 10.9581 5,448 10.9032(3.8101) (3.5286)

The oldest sibling’s highest grade 3,945 11.8063 5,446 11.8251(3.1702) (2.6991)

Family size 5,454 5.1459 5,454 5.1459(1.9937) (1.9937)

Family income 4,498 16,095.06 5,444 16,107.60(12,371.00) (11,326.28)

Safe feeling about the school (1 if feel safe) 4,982 0.6200 5,451 0.5667(0.4854) (0.4956)

Crime rate 5,444 5,419.8330 5,444 5,419.8330(3,786.1470) (3,786.1470)

Mortality rate 4,979 107.0678 5,383 109.8763(103.1462) (103.0561)

Employment in the education institution 5,408 7.8425 5,408 7.8425(2.5455) (2.5455)

Per capita income 5,452 4,396.2320 5,452 4,396.2320(903.9928) (903.9928)

% black 5,452 13.4507 5,452 13.4507(13.9422) (13.9422)

Civil unemployment rate 5,452 4.5879 5,452 4.5879(1.7735) (1.7735)

% urban 5,452 71.9662 5,452 71.9662(28.2481) (28.2481)

Note: The number in the bracket is the standard deviation.

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TABLE A2-1Segregation Indexes Definition

VariableDimension ofsegregation Explanation

AbsoluteCentralizationIndex (ACE)

Measures ofcentralization

Examines only the distribution of the minority grouparound the center and varies between −1�0 and 1.0.Positive values indicate a tendency for minority groupmembers to reside close to the city center, while negativevalues indicate a tendency to live in outlying areas. Ascore of 0 means that a group has a uniform distributionthroughout the metropolitan area.

RelativeCentralizationIndex (RCE)

Measures ofcentralization

The relative share of the minority population that wouldhave to change their area of residence to match thecentralization of the majority. The index varies between−1�0 and 1.0 with positive values indicating thatminority members are located closer to the center thanmajority, and negative values the reverse. An index of0.0 indicates that the two groups have the same spatialdistribution around the center.

AbsoluteClustering Index(ACL)

Measures ofclustering

Expresses the average number of minority members innearby area units as a proportion of the total populationin those nearby area units, where distances between areaunits are measured from their centroids. It varies from0.0 to 1.0.

Atkinson Indexwith b=#1 (A1)

Measurement ofinequality

The Atkinson index allows the researcher to differentiallyweight area units at different points along the Lorenzcurve. The shape parameters 0.1 means minorities are"underrepresented" and this area units will contributemore to segregation index.

Entropy Index(H)

Measurement ofevenness

Measures the weighted average deviation of each areaunit from the metropolitan area’s "entropy" or racial andethnic diversity. It varies between 0.0 (when all areashave the same composition as the entire metropolitanarea) and 1.0 (when all areas contain one group only).

Gini Index (G) Measurement ofevenness

Derived from the Lorenz curve, and varies between 0.0and 1.0, with 1.0 indicating maximum segregation.

RelativeConcentrationIndex (RCO)

Measurement ofsimilarly

Takes account of the distribution of the majority groupas well. This measure varies from −1�0 to 1.0. A score of0.0 means that the minority and majority groups areequally concentrated. An index of −1�0 means that theconcentration of the majority exceeds that of theminority to the maximum extent, and an index of 1.0 thereverse.

Source: http://www.census.gov/hhes/www/housing/housing_patterns/app_b.html

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794 Y. DONG ET AL.

TABLE A2-2Segregation Indexes Statistics

Variables Statistics

Absolute Centralization Index (ACE) 0.2549(0.3692)

Absolute Clustering Index (ACL) 0.1263(0.2013)

Atkinson Index with b = 0.1 (A1) 0.0728(0.1164)

Entropy Index (H) 0.1697(0.2573)

Gini Index (G) 0.2771(0.4009)

Relative Centralization Index (RCE) 0.1090(0.1877)

Relative Concentration Index (RCO) 0.2178(0.3394)

Note: The number in the bracket is the standard deviation.

APPENDIX B

This appendix studies the small sample properties of the two-type model using simulatedsamples. The data generating process is given as

(1) The main behavior equations for the two different types are given by

yi = 0�3 − 0�5x1i + 0�26 x2i + 0�34 x2i∗mi + u1i if type = 1

yi = 0�5 − 0�12x1i + 0�6 x2i − 0�24 x2i∗mi + u0i if type = 0

(2) The dummy variable mi is generated by

mi = 1 (−0�1 + 0�01x1i + 0�15x2i + 0�03x3i − 0�032x4i + vi > 0) �

(3) The yi equation and the dummy mi equation have the following relationship:

cov(u0i, vi) = 0, cov(u1i, vi) = 0�6�

(4) Type T is determined by Ti = 1 (0�003 + 1�1z1i + �i > 0).

The variables used in the simulation are independently drawn with following distribution:

vi ∼ N (0, 1); �i ∼ N (0, 1); u0i ∼ N (0, 1); u1i ∼ N (0, 1);

�i ∼ N (0, (1 − 0�642)),

and all other variables x1, x2, x3, x4, y0, y1, z1 ∼ N (0, 1).

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RESIDENTIAL MOBILITY, NEIGHBORHOOD EFFECTS 795

TABLE B1Small Sample Bias of the Two-Type Model

Heckman Model Two-type

True Subsample mi = 0 Subsample mi = 1 Model

Coef. Value Obs. Bias Bias Bias

�11 −0�5 100 −0�3890 −0�3747 0.3254�11 0�26 100 0�4734 0.6299�11 + �12 0�6 100 −0�2616 0.0276� 0�6 100 −0�3615 −0�2616 0.0082�1 0�3 100 −0�4213 1�4392 0.1877�01 −0�12 100 1�5460 1�6054 1.3851�01 0�6 100 −0�3615 0.2625�01 + �22 0�36 100 0�2306 0.1120�0 0�5 100 −0�6528 0�4635 0.0945�11 −0�5 500 −0�3751 −0�3594 0.0472�11 0�26 500 0�5744 0.1691�11 + �12 0�6 500 −0�2362 0.0498� 0�6 500 −0�3178 −0�2362 0.0021�1 0�3 500 −0�0752 0�7036 0.0553�01 −0�12 500 1�6039 1�6691 0.2226�01 0�6 500 −0�3178 0.0588�01 + �22 0�36 500 0�2731 0.0636�0 0�5 500 −0�4451 0�0222 0.0376�11 −0�5 1,000 −0�3834 −0�3894 0.0164�11 0�26 1,000 0�5996 0.0355�11 + �12 0�6 1,000 −0�2175 0.0032� 0�6 1,000 −0�3069 −0�2175 0.0045�1 0�3 1,000 −0�1095 0�7190 0.0086�01 −0�12 1,000 1�5692 1�5441 0.0467�01 0�6 1,000 −0�3069 0.0087�01 + �22 0�36 1,000 0�3042 0.0150�0 0�5 1,000 −0�4657 0�0314 0.0098�11 −0�5 3,000 −0�3821 −0�3761 0.0033�11 0�26 3,000 0�6289 0.0015�11 + �12 0�6 3,000 −0�2015 0.0010� 0�6 3,000 −0�2941 −0�2015 0.0000�1 0�3 3,000 0�1251 0�3489 0.0064�01 −0�12 3,000 1�5748 1�5996 0.0059�01 0�6 3,000 −0�2941 0.0052�01 + �22 0�36 3,000 0�3308 0.0062�0 0�5 3,000 −0�3250 −0�1907 0.0053

We are mainly interested in the estimation bias under different sample sizes. In thesimulation, we consider four different sample sizes: 3,000, 1,000, 500, and 100. Foreach sample size, we simulate a sample according to above setup and estimate boththe Heckman model and the two-type model. The difference between the estimated

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coefficients and the true values is the bias. This process is repeated 500 times for eachsample size. Table B1 reports the average biases from the 500 processes.

In Table B1, it is clear that coefficient estimates using the Heckman sample selectionmodel have large biases, regardless if the mi = 1 subsample or the mi = 0 subsample isused, and regardless of the sample size. This is not surprising since the data is simulatedaccording to the two-type model. For the two-type model, however, coefficient estimatesare very close to the true values when the sample size is 3,000. When the sample size is1,000, the largest bias is 38.9% of the true value, occurring at �01 (true value is −0�12,bias is 0.0467). The bias for the parameter �11 is 13.7% (true value is 0.26, bias is 0.0355).The biases for all other parameters are lower than 5% of the true values. Therefore, onehas to be cautious when the sample size is around 1,000.

When sample size is 500, the estimation bias is too large to be useful. For example, for�01, the bias is 185.5% of the true value (the true value is −0�12, while the bias is 0.2226).For �11, the bias is 65.0% of the true value (the bias is 0.1691, while the true value is 0.26).Therefore, using the two-type model when sample size is 500 is problematic. When samplesize is 100, estimates are clearly no longer reliable.

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