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Teachers College Record Volume 123, 020305, February 2021, 30 pages Copyright © by Teachers College, Columbia University 0161-4681

A Spatial Analysis on Charter School Access in the New York Metropolitan Area

JIN LEE

University of Louisiana at Lafayette

CHRISTOPHER A. LUBIENSKI

Indiana University, Bloomington

Background: Extant literature has consistently indicated that access to charter school markets is shaped by social geography. Given interest in location shown by charter schools and parents, estimating potential spatial access to charter schools has become instrumental in understanding equal opportunities for charter school enrollment in metropolitan areas with preexisting residential segregation.

Purpose: By considering the increasing significance of sociogeography, this article asks wheth- er students have equal opportunities for potential spatial access to charter schools across com- munities and how disparities in charter school access are related to housing patterns.

Setting: This study focuses on 122 charter schools in the New York metropolitan region, a highly segregated metropolitan area in the United States where charter schools are a primary component of education reform.

Research Design: The first part of this study illustrates patterns of spatial accessibility of the area’s charter schools, within a 20-minute commuting time, to students aged 5–13 years by employing the enhanced two-step floating catchment area method using a Gaussian function. The next part of the study tests the hypothesis that students are able to access charter schools equitably and irrespective of their place of residence. The spatial lag regression model is used to compare distributions of potential spatial accessibility with 15 demographic and socioeconomic variables.

Findings: Even after controlling for disproportionate population sizes by census tract, the potential need for charter schools is matched inequitably with the supply of educational service providers. The spatial lag regression results indicate that children in areas less accessible to charter schools within a convenient travel period tend to be exposed to communities with more populations of color, higher unemployed groups, and less expensive housing.

Conclusions: The findings offer empirical evidence that access to charter school differs depending on demographic and socioeconomic attributes, in significant combination with geography, illuminating charter school location strategies in real-world contexts. Though charter schools have been promoted as a vehicle to offer significant equity advantages across

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politically designed and strictly operated school attendance boundaries, charter schools in metropolitan New York exercise a distinct and profound form of pseudo-zoning by use of location strategies to exclude certain children who may be considered less desirable.

In the United States, students typically attend public schools based on their home address. This approach assigns children to schools within specific zones designated by residence. Given that U.S. residential pat- terns are relatively segregated, students are often grouped into schools with other children of similar socioeconomic backgrounds. Most parents send their school-age children to tax-operated schools without having to shoulder transportation costs or research effort. However, because school attendance zones often mirror geographical segregation by race, ethnic- ity, income, and education (Denton, 1995; The Equity and Excellence Commission, 2013; Mitchell et al., 2010), residence-based enrollment schemes constraining school options have raised questions about unequal access to education. This widely used method of school assignment and enrollment has provoked calls for school choice alternatives that offer the freedom to leave an assigned school and to opt for another school, irrespective of one’s place of residence (Brunner et al., 2012; Henig & Sugarman, 1999). Among various school choice initiatives, charter schools have received considerable attention as a vehicle for equal opportunities because they can admit students from across school district boundaries based on the consumer-style choices of parents. Drawing on recent find- ings and implications (e.g., Frankenberg et al., 2011; Glomm et al., 2005; Kotok et al., 2017), this article examines the promising notion that charter schools can deliver equal education opportunities for education because they are not bound by district-imposed geographical restrictions. To clarify the empirical relationship between residential patterns and charter school markets, this study uses thematic maps of charter school catchment areas based on the concept of potential spatial accessibility. Then, the spatial patterns are integrated with data on population distributions according to socioeconomic status indicators. This article’s findings provide detailed information on whether charter schools alleviate or reinforce existing in- equalities and offer insights into access to diverse educational options in real-world contexts.

PROXIMITY IN CHARTER SCHOOL MARKETS

U.S. housing markets have historically been shaped by institutional and structural attributes such as race, ethnicity, education level, income, and occupation (Lichter et al., 2015; Massey & Mullan, 1984). In particular, Tiebout’s sorting mechanism of people voting with their feet (i.e., local

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residents efficiently sort themselves across locations in accordance with their interests and needs) and the ability to pay for higher local taxes and housing prices have not only exemplified vast disparities, evident in fi- nancing across communities, but also served as invisible barriers to entry to other neighborhoods (Nechyba, 2010; Tiebout, 1956). Much research on the spatial distribution of public services such as medical care, play- grounds, parks, and preschools has provided evidence that varying levels in potentiality of access to publicly available activities or facilities are inter- connected with a range of social and economic factors (e.g., Neuman & Celano, 2001; Nicholls, 2001; Oh & Jeong, 2007; Talen & Anselin, 1998). The practice of assigning students to schools based on catchment areas has been also criticized for exacerbating inequitable educational opportu- nities in divided communities (Frankenberg et al., 2018; Richards, 2014; Siegel-Hawley, 2013).

Some scholars and policy makers advancing market logics of choice and competition in the education sector have proposed school choice as a way to dilute the strong relationship between residential patterns and school access (Chubb & Moe, 1990). For the last two decades, neoliberal theorists around the globe have advanced market metaphors as plausible explana- tions for how empowering parents with consumer-style choice in educa- tion markets can reduce or eliminate geographical barriers to equal access to better and more diverse schools (J. T. Scott & Wells, 2013). This po- tential of school choice policies to satisfy concerns for democratic equity has encouraged the establishment of charter schools, which are generally prohibited from drawing school zone lines or using a distance criterion as a prerequisite for admission. Supporters of charter schools have main- tained that parents, dissatisfied with the academic performance at local schools, would be willing to transfer their children to schools outside their assigned attendance zones—as has indeed often been the case (Finn et al., 2001; Gill et al., 2001).

Contrary to the theoretical expectation that market-oriented approach- es weaken the prominent role of home address in access to schools, extant literature has consistently indicated that access to school choice, includ- ing access to charter school markets, is still shaped by social geography (Goyette, 2008; Koller & Welsch, 2017; Taylor, 2001). Many parents, al- though eligible to opt out of their assigned zones, prefer to enroll their children in a neighborhood school rather than in a more distant school (Burgess et al., 2015; Hastings et al., 2005). Along with the relative paucity of accurate information on more distant school options, the financial bur- den of traveling farther away discourages many students from leaving their current school (Fast, 2020; Reay & Lucey, 2003; Urban Institute, 2017). Most families rarely move into a new community for better access to other

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schools (Renzulli & Evans, 2005; Rhodes & DeLuca, 2014). Therefore, previous studies have noted that simply breaking down political bound- aries and offering the right to choose a charter school in the market does not lead to an automatic right to service (Gibson & Asthana, 2000; Lubienski, 2005; Makarewicz, 2013). In light of the importance of prox- imity in schooling (Gibbons & Vignoles, 2012; Hamnett & Butler, 2013), it is not surprising that charter schools serve students from a similar geo- graphic enrollment pool to the one served by nearby traditional schools in segregated areas (N. Jacobs, 2013; Wamba & Ascher, 2003).

Because parental decisions on charter school enrollment are closely tied to students’ residential locations (Bell, 2007, 2009), charter schools often use location-friendly strategies to respond to competitive incentives in market hierarchies. A number of charter schools open and move into school districts with high expenditures per pupil and high teacher sala- ries, or into neighborhoods with a high proportion of college-educated and employed adults and fewer members of underrepresented communi- ties (Bifulco & Buerger, 2012; Glomm et al., 2005; Gulosino & Lubienski, 2011; Saultz & Yaluma, 2017). Some charter schools in Detroit, New Orleans, and Washington, DC, for instance, implicitly shape their appli- cant pools by marketing to populations with fewer socioeconomic needs or students associated with lower costs (Lubienski et al., 2009). A recent study has similarly revealed that several charter schools under competi- tive pressure to renew charters and improve academic performance only disseminated marketing materials to parents with certain backgrounds in given areas (Jabbar, 2016). In light of the findings that access to competi- tive school markets becomes geographically stratified as a wide variation of communities reproduce dissimilarities among schools and school dis- tricts (Goyette, 2008; Müller, 2011), interest in location shown by charter schools and parents necessitates more sophisticated research into spatial access in competitive charter school markets.

POTENTIAL SPATIAL ACCESS TO CHARTER SCHOOLS

Given that parents place great emphasis on proximity when choosing schools and that this preference often influences school behaviors with regard to student recruitment, spatial access to charter schools in com- petitive markets deserves additional scrutiny (Gulosino & d’Entremont, 2011; Lauder & Hughes, 1999; Lubienski et al., 2009). On the grounds that racially and socioeconomically segregated landscapes have increased the risk of uneven geographical arrangement of public service providers (K. Jacobs & Manzi, 2013; Nicholls, 2001; Ryan, 2010; Williams & Wang, 2014), prior research has examined the association between spatial access

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to charter schools and residential patterns through an analysis of aggre- gated charter school enrollment and census data (e.g., Archbald et al., 2018; Frankenberg et al., 2011; Rapp & Eckes, 2007; Renzulli & Evans, 2005). However, numerous studies that reveal unique student body com- positions in charter schools have offered incomplete information about potential spatial access to these schools. Because population data sets demonstrate which students of color are more or less likely to exercise the right to choose charter schools and to what extent families with a cer- tain socioeconomic background are over- or underrepresented in char- ter schools, enrollment patterns refer only to realized access to charter schools through actual usage (Andersen et al., 1983; Joseph & Phillips, 1984). Furthermore, data on this revealed access do not typically distin- guish spatial elements, such as the geographic distribution of schools or travel barriers resulting from nonspatial factors, including income and race (Khan & Bhardwaj, 1994; Schuurman et al., 2010).

Though a growing body of charter school research has examined their underlying contexts, because of practical difficulties in defining catch- ment areas for each charter school, little progress has been made to mea- sure this crucial factor. To model spatial access to charter schools, scholars have estimated charter schools’ service areas by using traditional boundar- ies, such as school districts and attendance zones, or by relying on a single statistical geographic unit to which the charter school belongs (such as a census unit; e.g., Ritter et al., 2016; Saporito & Sohoni, 2006, 2007). Alternatively, by considering parental preference for proximity as a con- venience factor, researchers have estimated potential catchment areas as a circular buffer within a given radius of a charter school (e.g., Bell, 2009; Burgess et al., 2011). However, although recent technical approaches have led to remarkable advances in understanding the significance of charter school locations, previous studies have faced clear limitations in the ways that they account for inequitable geographic access to charter schools. Unlike with traditional public schools, where spatial access has been estab- lished through the boundary lines of school districts, states allow children to enroll in any charter school in that state—or, in the case of Washington, DC, within that jurisdiction (Orfield, 2014; Siegel-Hawley, 2014). This fea- ture of charter schools suggests that simply drawing circles with a pair of compasses tends to oversimplify charter schools’ surroundings by ignor- ing geographic opportunities and constraints, such as transportation sys- tems and social barriers. Additionally, census tracts or block groups, which have been widely used as geographic units in recent research on charter schools because of analytical convenience, may only represent a small part of a region that is accessible to a charter school (Gulosino & d’Entremont, 2011; Lee et al., 2008). Thus, the use of researcher-designed or established

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school attendance areas can undercut examinations of spatial access to charter schools by overlooking the lack of residency requirements for charter school enrollment.

Because access to charter schools can be constrained, though not deter- mined, by proximity (Burgess et al., 2015; Hastings et al., 2005), estimating potential spatial access to charter schools becomes instrumental in under- standing equal opportunities for charter school enrollment in metropoli- tan areas with preexisting residential segregation. New research is required to address the need for more precise representation of possible accessible charter schools, which can be done by incorporating data on spatial interac- tion with charter schools as service vendors within a range of reachable op- tions for parents. Researchers in a number of disciplines, including health, environment, and transportation, have paid attention to spatial accessibility in the multidimensional concept of access (Cromley & McLafferty, 2011; Hansen, 1959; Khan & Bhardwaj, 1994; Penchansky & Thomas, 1981). Differentiated from spatial availability, which represents the number of ser- vices that a client can choose from in a certain area, spatial accessibility, as a precondition for the actual use of a service, is defined as “the spatial distri- bution of potential destinations, the ease of reaching each destination, and the magnitude, quality and character of the activities found there” (Handy & Niemeier, 1997, p. 1175). Where charter schools are nonrandomly clus- tered in metropolitan areas with well-developed transportation systems and a high population density (Frankenberg et al., 2011; Saultz et al., 2015), a measure of potential spatial accessibility can provide accurate and mean- ingful information about equitable access to charter schools by integrating geographical proximity with geographic information.

DATA AND METHODS

Parental preference for proximity has suggested that charter school ac- cess becomes linked—for better or worse—to geographies constructed by demographic features, social capital, and economic characteristics. Yet, prior research has delivered limited information about spatial access to charter schools because of its reliance on geographical factors in inad- equately defined catchment areas. This study explores the spatial equity of potential accessibility to primary charter schools through an examination of the New York metropolitan region, a highly segregated metropolitan area in the United States where charter schools are a primary component of education reform. The first part of this study illustrates patterns of spa- tial accessibility of the area’s charter schools, which do not require proof of residence in the NY metropolitan area for enrollment. This analysis subdivides a geographically continuous area according to estimated values

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of potential spatial accessibility. The next part of the study tests the hy- pothesis that students are able to access charter schools equitably, and irrespective of their place of residence, by comparing housing patterns in the research area with distributions of potential spatial accessibility.

CHARTER SCHOOLS IN NEW YORK

Since New York passed the charter school law in 1998 and the first 10 char- ter schools in the state opened in 2001, the New York charter school law has limited the total number of charter schools across the state. However, high demand for charter schools has increased the cap on the number of charter schools from 100 to 460. All 460 charter schools are authorized by the Board of Regents of the University of the State of New York and the Board of Trustees of the State University of New York, but the conver- sion of an existing public school to a charter school is not subject to the cap policy. New York contains a sizable number of charter schools run by either for-profit or nonprofit education management organizations (EMOs). Among the 209 New York charter schools that were operational in the 2012–13 school year, about 10% were run by a for-profit EMO, and about 30% were operated by nonprofit charter management organiza- tions (Miron & Gulosino, 2013).

Because geographic divides in U.S. metropolitan areas are not simply distinctions between affluent suburbs and poor cities, this study extends the research area to an entire metropolitan area. Among the 209 New York charter schools, 164 are located in the New York metropolitan area, stretching out across seven counties (Bronx, Kings, Nassau, New York, Queens, Richmond, and Westchester). To clarify the spatial relationship between accessibility variations and housing patterns, this research focus- es on 122 charter schools in which the highest grade offered is lower than Grade 9, serving students aged 5–13 years. Restricting attention to the primary-grade charter schools in the New York metropolitan area allows this research to draw significant conclusions about potential spatial ac- cessibility to charter schools by controlling for the effects of small school reforms that mainly offer choice to high school students at large, lower performing schools in less advantaged areas. The physical locations of charter school campuses, excluding network headquarters and adminis- tration offices, are extracted from the school directories of state and lo- cal governments, from charter school websites, and from the Common Core Data of the National Center for Education Statistics for the 2012–13 school year. These locations are geocoded in ArcGIS 10.3, and the geo- coded addresses are then assigned to a Metropolitan Statistical Area from the 2010 TIGER/Line shapefile of the U.S. Census Bureau.

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The New York state government encourages the establishment of charter schools with the purpose of providing better learning opportunities, par- ticularly for students at risk of academic failure in the current public school system (NY CLS Educ, Title II, Art. 56). Thus, as illustrated in Figure 1, the 122 charter schools serving K–8 students are concentrated in particular regions such as New York (Manhattan) and Kings Counties. In addition, the previous New York City mayor’s strong commitment to charter schools, with support from national and local philanthropic organizations, has boosted the establishment of charter schools in New York City, particularly in Harlem and the South Bronx (Fullan & Boyle, 2014; Mader et al., 2018). When the number of applicants for charter school enrollment exceeds ca- pacity, the New York State charter school law allows schools to give enroll- ment priority to students whose siblings are already enrolled in the school or to students who reside in the school district where that charter school is located. Charter school students in New York are not eligible for public assistance with transportation, but it is possible for a school district to enter into a contract with charter schools for related transportation services.

Figure 1. Charter school locations in the New York metropolitan area

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ESTIMATING POTENTIAL SPATIAL ACCESSIBILITY

This study identifies an area as having low charter school accessibility if school-age children cannot easily reach charter schools as a result of dis- tance or travel time based on street networks or if there are no enrollment openings. Here, the selection of an empirical parameter for the commut- able distance and time required of school-age children plays a critical role in estimating the value of potential spatial accessibility. The measure of ac- cessibility for job opportunities and healthcare providers for adults often relies on public transit (Ding & Bagchi-Sen, 2019; Hu, 2014). However, American parents increasingly prefer to drop their children off at school by using private vehicles for the sake of convenience (Schlossberg et al., 2006; Sirard & Slater, 2008; U.S. Department of Transportation, 2019; Yang et al., 2012). Therefore, the patterns and trends in students’ travel to charter schools are influenced more by commuting time than by physical distance, taking into account street conditions and multiple routes in met- ropolitan areas (Helbich et al., 2016). In general, participation in choice programs requires additional commuting efforts, such as longer drives to school and correspondingly greater demand on cars (District of Columbia Public Charter School Board, 2015; Steiner et al., 2006). This willingness to travel to a remote school, in combination with the parental preference for proximity, indicates that a scenario of maximum potential accessibil- ity is not necessarily dependent on a well-integrated regional public tran- sit system. Guided by the latest evidence (Bragg et al., 2018; Corcoran, 2018), this study sets the limit of accessibility to a car-based driving time of 20 minutes for students aged 5–13 years, which is longer than the limit for students of neighborhood schools. Each charter school catchment area within a 20-minute commuting time is constructed with the Network Analyst extension tool in ArcGIS Desktop 10.3 on the basis of a road-based network distance. By working with a compiled map data set that includes street conditions such as speed limits, one-way restrictions, and signpost information, this method can minimize a false representation of potential accessibility on the basis of Euclidean linear distance.

Once accessible areas within a given travel time are rendered, this study calculates accessibility through employing the enhanced two-step floating catchment area model developed by Radke and Mu (Dai, 2011; Luo & Qi, 2009). A basic floating catchment area model involves a ratio of schools to students within an area centered at a school location. The enhanced two- step floating catchment area method can differentiate accessibility with- in a catchment area by multiplying the weights of accessibility measures (Dai, 2010; Kwan, 1998; Luo & Qi, 2009). This enhanced two-step floating catchment area method, incorporating a Gaussian function that accounts

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for the continuous and incremental decay, is estimated as Equation 1 (see details in Appendix):

(1) where AiEFCA is the accessibility at census tract i, charter school j falls within the travel-time-based catchment area centered at census tract i, tij is the travel time between i and j, Rj is the school enrollment-to-student number ratio of charter school j, and Wij is the time weight when charter school j falls within the catchment area centered at census tract i. A large value of AiEFCA indicates that location i has better accessibility. The distribution of potential spatial accessibility values, distinct from demand (school-age children) and supply (charter schools) density maps, can suggest more ac- curate information on the geographic variation of access to charter school.

SPATIAL REGRESSION ANALYSIS

Given spatial patterns of segregation and stratification in U.S. metropolitan areas, a value observed in a given census tract tends to be strongly related to the values observed in neighboring tracts. In other words, a variable in census tract i is under the influence of the selective variables in both cen- sus tract i and its neighboring tracts. When spatial characteristics are likely to be clustered or dispersed in a given space, spatial autocorrelation not only violates independence between variables observed for residential pat- terns but also fails to satisfy the underlying assumptions of linear regression analysis. Therefore, sociogeographic research, such as the research in this study, requires a test of spatial autocorrelation by feature in adjoining ar- eas. This process checks whether the errors are uncorrelated and whether the variables are independent before statistical analyses are conducted. The spatial autocorrelation for residuals of accessibility is tested through the use of Moran’s I statistics (Fotheringham & Rogerson, 2009).

After statistically significant spatial autocorrelation is detected, this study employs the spatial lag regression model rather than the ordi- nary least squares regression model to investigate the relation between gaps in spatial access to charter schools and uneven residential patterns (Fotheringham & Rogerson, 2009; Voss et al., 2006; Ward & Gleditsch, 2008). The spatial lag model yields statistical inference along with spatial dependency, as shown in Equation 2:

(2)

where y is the accessibility in a census tract, β is the coefficient of the select- ed variables, ρ is the spatial coefficient, Wy is the spatially lagged accessibility using the first-order queen contiguity weights matrix, and ε is the errors.

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This study identifies 15 demographic and socioeconomic variables from the voluminous literature on area-based socioeconomic measures (e.g., Darden & Kamel, 2000; Gulosino & Lubienski, 2011; Reardon & Bischoff, 2011; M. R. Scott & Marshall, 2019; Wilson, 2012). Each variable is derived from the 2009–2013 American Community Survey 5-Year Estimates from the U.S. Census Bureau. (See Table 1.)

Table 1. Description of the Variables

M SD Min. Max.

Potential Spatial Accessibility 2.10 1.59 0.00 5.29

Proportion of African American, but not Hispanic, population

0.22 0.28 0.00 1.00

Proportion of population with Hispanic or Latinx origin

0.24 0.22 0.00 1.00

Median earning in the past 12 months for population 16 years and over

37,306.00 16,892.80 0.00 97,500.00

Proportion of population below poverty level in the past 12 months

0.17 0.14 0.00 1.00

Proportion of households with public assis- tance income (PAI) in the past 12 months

0.04 0.04 0.00 0.30

Gini index of income inequality 0.43 0.09 0.00 0.69

Proportion of population 5–64 years who do not speak English well or at all

0.09 0.10 0.00 0.58

Proportion of population 18–24 years who do not graduate high schools (including equivalency)

0.14 0.13 0.00 1.00

Proportion of population 25 years and over who do not hold at least associate’s degree

0.58 0.21 0.00 1.00

Proportion of females 16–59 years and males 16–64 years unemployed in civilian labor force

0.10 0.07 0.00 1.00

Proportion of vacant housing units 0.08 0.06 0.00 0.69

Proportion of housing units with more than 1.01 occupants per room

0.08 0.07 0.00 0.53

Median value of owner-occupied housing units

408.40 5,157.14 0.00 99,400.00

Median contract rent of renter-occupied housing units

1,156.80 418.19 0.00 2,001.00

Proportion of housing units without car ownership

0.41 0.27 0.00 1.00

Note. Total census tracts = 2,666.

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FINDINGS

UNEVEN POTENTIAL SPATIAL ACCESS TO CHARTER SCHOOLS

In view of the relationship between supply and demand in markets, char- ter schools tend to be clustered in locations with high prospective de- mand. Highly populated urban regions, such as New York City in Figure 2, are remarkably gradated in dark colors to represent a high degree of ac- cessibility to charter schools, whereas the values of accessibility tend to decrease dramatically at the fringes of the New York metropolitan area. It is therefore not surprising to observe that the geographic pattern of po- tential accessibility to primary-grade charter schools presented in Figure 2 corresponds closely to the distribution of physical availability of those charter schools shown in Figure 1. However, this correspondence should be interpreted with caution. This research calculates potential spatial accessibility to charter schools on the basis of demand (the size of the school-age population) and supply (the number of charter schools), not by the manner of simply plotting charter school locations, as in Figure 1 (Page et al., 2018). This measure of charter school access from a distinct standpoint of spatial relation can offer appropriate information about variations in accessibility across a space.

In Figure 2, the uneven pattern of potential spatial accessibility to charter schools suggests that even after controlling for disproportionate population sizes by census tract, the potential need for charter schools is matched in- equitably with the supply of educational service providers. Children who re- side in New York City have a greater likelihood of accessing a charter school within a convenient travel period in comparison with children in other areas. The degrees of accessibility are also likely to decline incrementally toward the three regions adjacent to New York City. Specifically, the par- ticular regions of Bronx County in the North, Kings County in the South, and Queens County in the East, closely neighboring New York City, pres- ent high accessibility values. Children in the southern Bronx area, which is adjacent to northern Manhattan, have greater access to charter schools in comparison with children in other surrounding regions. Similarly, the western Queens County, which is across the East River from Manhattan, shows a high degree of accessibility to charter schools, likely because young school-age children are less likely to cross bridges and railroads for school commutes (Collins & Kearns, 2001; Stewart, 2010). Despite well-developed commuting systems and probable demand for charter schools, spatial access to charter school markets is not evenly distributed across the New York met- ropolitan area, suggesting that accessibility to charter schools in the New York metropolitan area is dependent on residential location.

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Figure 2. The geographic distribution of potential accessibility to charter schools in the New York metropolitan area

GEOGRAPHIC RESTRICTION OF CHARTER SCHOOL ACCESS

In a similar manner to residential patterns across the New York metropoli- tan area, the higher values of accessibility centered in several regions af- firm a strongly positive spatial autocorrelation for residuals using Moran’s I statistic (Moran’s I = .840; p < .001). Given that nonrandom patterns and clustering in sociogeographies across the New York metropolitan area generate inaccurate coefficients due to spatial dependencies, the presence of spatial autocorrelation indicates that the application of tradi- tional statistical tests to this study would yield biased and misleading coef- ficient inferences. Table 2 presents the results of the spatial lag regression; the spatial lag parameter, which presents a statistically significant value

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(ρ = 0.792; p < .001), justifies the power of proximity in accounting for ac- cessibility to charter schools. This suggests that a high value of accessibility in a given census tract is determined by the selected values of nearby cen- sus tracts and the geographic attributes at the given census tract. The geo- graphic distribution of potential accessibility to primary charter schools in the New York metropolitan area can be adequately examined with a spa- tial regression model that controls for spatial autocorrelation and involves a spatially lagged dependent variable.

With regard to the relationship between housing patterns and accessi- bility distributions, a high or low accessibility value in a given census tract is affected to some extent by patchiness in housing attributes. The spatial lag model reveals the positive relation between areas with rich spatial ac- cessibility and areas with larger Hispanic or Latinx populations. In the same fashion as the generally known racial disproportionality in charter school enrollment (Frankenberg et al., 2017; Vasquez Heilig et al., 2019), access to charter schools is more likely to be offered to primary school stu- dents who reside in areas with larger Hispanic or Latinx populations. Still, a higher proportion of a population aged 5–64 years with limited or no English has a strong negative correlation with potential spatial accessibil- ity to New York metropolitan charter schools. Given the disproportion of Hispanic or Latinx populations across the New York metropolitan region, residing in neighborhoods isolated from English speakers is associated with a decreased likelihood of charter school access, even when all oth- er factors are equal. Notably, this finding that communities with a larger English-speaking population have more access to charter schools suggests that the chance of attending charter schools may not be offered equitably to all minority communities in a diverse metropolitan region.

In Table 2, the estimates from the spatial lag model indicate that hous- ing values of only owner-occupied units show a statistically significant difference at a selected significance level of .05. The findings of the spatially lagged regression model indicate a small, but still significant, positive connection between the logged median housing price and the level of accessibility to charter schools. Children aged 5–14 years in ar- eas with lower monthly rents are less likely to live within a convenient travel time for charter school enrollment, even though the estimate from the spatial lag model is statistically insignificant at a .05 significance level (p = .084). These findings lend partial support to previous research find- ings that some families are willing to pay more for housing when it is ac- companied by access to certain schools with particular features (Black, 1999; Dougherty et al., 2009).

Interestingly, this uneven accessibility pattern, in combination with the nonspatial variables, is repeatedly simulated across neighborhoods with

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preexisting inequality, including New York City. In general, the bulk of research on large metropolitan areas defines an urban community as a space with disproportionately large populations from disadvantaged back- grounds (Clark et al., 2015; Frey, 2011; Sandoval, 2011). Since the 2008 economic recession, many city cores have been unable to supply afford- able housing units with a sufficient number of bedrooms for school-age children (Lipman & Hursh, 2007). Therefore, less affordable neighbor- hoods associated with higher housing and rent prices have discouraged the provision of equal access to charter schools. Considering that the mis- match between the supply and demand of housing is portrayed in the concentration of low-income populations and unaffordable housing in urban areas, the higher values of accessibility in New York City (Figure 2) reflect the growing inequality and the spatial polarization of potential ac- cess to charter schools. Additionally, a high percentage of households with no vehicle and a large number of overcrowded housing units have led to considerable variations in accessibility.

The spatial lag regression model in Table 2 indicates that the greater the proportion of people with no higher education experience in an area, the higher the spatial barrier to charter schools. While the acquisition of a high school diploma or alternative certificate does not account for greater charter school accessibility, the presence of more individuals with a higher level of experience of higher education in a given census tract is likely to produce significantly positive change in the level of potential accessibility in the census tract. Children aged 5–13 years in census tracts with higher employment rates are more likely to live within a viable travel time to charter schools, albeit at a low significance level (p = .081). Simply stated, areas with a more educated and more employed population are likely to have better charter school accessibility, but this increase in ac- cessibility is unrelated to the median earning levels in census tracts. In light of the close relationship between educational attainment, occupa- tional hierarchy, and income distribution, the statistics from the spatial lag model demand future attention to detailed socioeconomic background factors, such as education level, employment status, and occupation, in a given census tract. Most notably, charter school access in the New York metropolitan area is not dependent on the presence of a population with higher paid professional occupations.

Although the spatial lag model in Table 2 raises concerns about the im- pacts of nonspatial features on potential spatial access to charter schools, the results of this study indicate that only a few variables cause statistically notable differences in accessibility. In particular, income-related attributes (e.g., the proportion of economically disadvantaged families and the Gini index) have no significant effect on spatial access to charter schools.

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These results partly challenge previous findings arguing that census tracts with fewer economically disadvantaged populations enjoy better access to charter schools.

Table 2. Spatial Lag Regression for Potential Accessibility

Coefficient SE p

Intercept -0.059 0.096 0.538

African American 0.071 0.061 0.249

Hispanic or Latinx 0.480 0.087 0.000

Logged median earning -0.003 0.014 0.857

Below poverty -0.216 0.182 0.236

PAI -0.159 0.463 0.732

Gini coefficient -0.257 0.233 0.272

No college degree -0.273 0.106 0.010

High school dropout -0.083 0.124 0.500

Unemployment -0.431 0.247 0.081

Vacancy 0.273 0.228 0.230

Overcrowdedness 0.518 0.253 0.041

Logged median housing value 0.016 0.005 0.001

Logged median rent 0.023 0.013 0.084

Poor English -0.699 0.212 0.001

No car ownership 1.049 0.090 0.000

Spatial lag (ρ) 0.792 0.000

Log likelihood -2811.3

AIC 5658.6

Note. Cells are shaded if a p value is less than .05.

DISCUSSION

The quantity and quality of public services and facilities have been shaped in different manners by human and monetary resources at the local level (Briffault, 1996; Owens & Candipan, 2019; Ryan, 2010). Previous research has argued that an increase in the percent of poor populations and the pro- portion of families who are provided with cash payments affects a decrease in young children’s access to charter schools in a given census tract. This study, which measures potential spatial accessibility to charter schools in a census tract by employing the spatially lagged regression model, also ob- serves that a child’s place of residence shapes potential spatial accessibility to charter schools. Specifically, children in areas with less access to charter

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schools tend to be from communities with a greater Hispanic or Latinx population, fewer individuals with college degrees, more housing units in which children do not have their own bedrooms, more non-native-English speakers, and more families without vehicles. Also, families in neighbor- hoods with less expensive housing values have fewer viable opportunities to access charter schools in the New York metropolitan area. Therefore, the findings of this study, which take into account access to charter schools in relation to children aged 5–13 years, present empirical evidence of the connection between spatial access to charter schools and nonspatial so- cioeconomic features. This analysis parallels a body of research on geo- graphical advantages and disadvantages that shape diverse educational opportunities, or missed opportunities, with regard to charter school ac- cess. In addition, this study raises the possibility that some parents may be incentivized to pay a premium for charter school access by moving into areas with dissimilar backgrounds and higher housing values, in the same manner that a desire for access to better schools can lead to increases in housing prices under traditional zoning policies (Black, 1999; Imberman et al., 2015; LaFleur, 2016). Leaving aside questions about charter school outcomes, charter schools as a means of promoting better learning op- portunities under the law are spatially inaccessible to underserved fami- lies. Because geographical factors for charter school enrollment are inter- connected with the fragmentation of U.S. metropolitan regions by race, ethnicity, income, and education level, the findings of this study offer a glimpse into how demographic and socioeconomic characteristics might be considered transformative assets and resources for attracting charter schools to an area (Phillippo & Griffin, 2016; Shapiro, 2004).

Along with these familiar, nonspatial features of charter school access, this research provides a more elaborate approach to investigating access to charter school markets. The close relationship between spatial access to charter schools and housing features explored in plentiful literature has been derived from predesigned catchment areas of charter schools, which pay less attention to accessible travel times and potential opportunities. Potential spatial access to charter schools in the New York metropolitan area is less likely to be explained by residential characteristics when con- trolling for the effect of proximity. In other words, the geographic varia- tion in access to charter schools moderately depends on demographic characteristics and socioeconomic attributes, in combination with geo- graphic proximity. Considering that the emergent results highlight signifi- cant but small effects of the selected residential attributes on accessibility under the spatial lag regression model, the main conclusion of this study is that geographic proximity accounts for the level of charter school acces- sibility in highly fragmented metropolitan areas.

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In the United States, the paradigm of school assignment has evolved from a focus on diversity through a court-ordered desegregation plan to proximity on the basis of enrollment in neighboring schools (Ayscue et al., 2018). This latter model, which emphasizes the significant effect of housing on school access, has been criticized for reproducing educational inequality through differences in housing prices, demographic compo- sitions, and academic performances (Black, 1999; Gibbons et al., 2013; Holme et al., 2016). In the context of geographical discontinuity shaped by attendance zones, the rise of neoliberal policies that encourage pa- rental choice and school competition has been expected to improve ac- cess to quality schools beyond political barriers (Friedman, 2005; Greene, 2000). Charter schools, simply because they are purportedly open to all students irrespective of geographic constraints, have been promoted as a vehicle to offer significant equity advantages across politically designed and strictly operated school attendance boundaries, especially for disad- vantaged communities. This promising potential has substantially boosted the number of charter schools in the United States. However, as is the case with similar plans in other contexts (Lubienski et al., 2013), charter schools in metropolitan New York exercise a distinct and profound form of pseudo-zoning by use of location strategies to exclude certain children who may be considered less desirable. This research, which focuses on the geographic aspect of access and examines inequality of opportunity through the example of charter schools, suggests the presence of a discon- nect between theory and practice.

In light of the complexity of defining a neighborhood, communities are created on myriad considerations beyond simple physical proximity (Coulton et al., 2011, 2013). Thus, residential location may play a crucial but incomplete role in accessing school options (Lubienski et al., 2012; Schneider & Buckley, 2002). For instance, parents and policy makers may also value information about a disproportionate composition in student enrollment, which is not within the scope of this geospatial analysis, so that this can simulate a distinct geographical arrangement of charter schools. Nonetheless, given that unequal access to education has been a substantial problem besetting American education for decades, a lack of access to charter schools, even when other factors are equal, functions as an obstacle to equal and equitable educational opportunity. In light of the contribution of this research highlighting the possibility that injustice is reproduced spatially (Dikec, 2001; Soja, 2011; Tate, 2008), potential un- equal access to charter schools necessitates further research on its links with actual access to charter schools. This would, in turn, help to create a better understanding of how parents respond to competitive markets with geographic preferences and restrictions.

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metropolitan Baton Rouge, Louisiana 1990–2010. Urban Geography, 35, 1066–1083. Wilson, W. J. (2012). The truly disadvantaged: The inner city, the underclass, and public policy.

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school commuting: A case study of a middle-sized school district in Oregon. Environment and Planning A, 44, 1856–1874.

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APPENDIX

Spatial Accessibility

Measuring spatial accessibility has largely depended on gravity-based mod- els, also known as a spatial interaction model (Hu, 2014; Luo & Wang, 2003; Schuurman et al., 2010). Gravity models estimate the value of the potential interaction between population points and service points within a given distance, often equivalent to the distance decay. In developing a measure of accessibility using gravity models, the key component is to decompose the attraction factors affecting the spatial separation between students and schools. The gravity-based accessibility model is presented as follows (Hansen, 1959):

where Aiv is the accessibility in location i by transportation mode v, Sj is the number of school enrollments at location j, Pjm is the prospective demand in location j using transportation mode m, tijv is the time between location i and location j by mode, and β is the exponent describing the spatial sepa- ration (Shen, 1998). Despite the complete concept of gravity models for measuring accessibility, it is not easy to interpret, and various data sources are needed to calculate it (Luo & Qi, 2009). Specifically, β as a negative exponential distance friction is derived from actual distances and times between choosers and charter schools through empirical research, but these data are generally not available (Wan et al., 2012). For this reason, many researchers use arbitrarily determined coefficients.

The enhanced two-step floating catchment area method is developed to minimize uncertainties of gravity models (Luo & Qi, 2009; Radke & Mu, 2000). At the first step of the method, each school has the school enrollment-to-student number ratio within a threshold travel time from the school. In the left example of Figure A1, one school has the ratio of school capacity to the number of children in five census tracts. At the sec- ond step, accessibility at an individual census tract is estimated as the sum of the ratios within threshold travel time or distance. Because the acces- sible area of one census tract includes two schools in the right example of Figure A1, its accessibility is the sums of ratios of two schools, as calculated in the first step. Potential accessible zones in real life may be represented in Figure A2, on the basis of street networks, including actual streets, bus stops, bus routes, rail stops, and rail lines.

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Figure A1. The sample accessible areas for the enhanced two-step floating catchment area method

Figure A2. The real-life example of accessible areas for the enhanced two-step floating catchment area method

Though a value of accessibility at each geographic unit, such as census tract and block group, is estimated by setting a threshold time or distance, there exist differences of travel impedance even within catchment areas. In addition to a dichotomous measure of either inside or outside catch- ment areas, accessibility within one catchment can be differently measured by the time (or distance) weight from the centroids of individual census tracts. Prior research has introduced diverse methods for the estimation of the weight, including the inverse power and negative exponential (Dai, 2010, 2011; Kwan, 1998). Those methods following “clear-cut neighbor- hood boundaries” commonly divide one catchment area into several sub- zones and then employ discrete zonal weighted methods, as shown on the left in Figure A3. Geographies in metropolitan regions with highly developed transportation systems are continuously spread rather than sharply separated, as presented on the right in Figure A3. Thus, current

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research on spatial accessibility has measured spatial accessibility based on a Gaussian function that accounts for the continuous and incremental decay (Dai, 2010, 2011; Langford et al., 2012; Salze et al., 2011).

Figure A3. The comparison of travel impedance methods

Taken together, the enhanced two-step floating catchment area method using a Gaussian function is estimated as follows:

where Wkj is the time weight when charter school j falls within the catch- ment area centered at census tract k, Rj is the school enrollment-to-stu- dent number ratio of charter school j, Sj is the number of charter school enrollments within a threshold travel time from charter school j, k is all census tracts within a threshold travel time from location j, tkj is the travel time between k and j, t0 is a threshold travel time, and Pk is the number of children in census tract k; and

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where AiEFCA is the accessibility at census tract i, charter school j falls within the catchment area of travel time centered at census tract i, tij is the travel time between i and j, and Wij is the time weight when charter school j falls within the catchment area centered at census tract i.

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JIN LEE is an assistant professor in the Department of Educational Foundations and Leadership at the University of Louisiana at Lafayette. Her research focuses on school choice programs and urban school re- forms. Her current work examines neighborhood effects on equity and access, including racial disproportionality in school discipline and lo- cal market responses to competitive environments. She has published journal articles in Journal of Education Policy, Education and Urban Society, and Geographical Research.

CHRISTOPHER A. LUBIENSKI is a professor of education policy at Indiana University. He is also a fellow with the National Education Policy Center at the University of Colorado and a visiting professor at East China Normal University in Shanghai, and he was previously Sir Walter Murdoch Visiting Professor at Murdoch University in Western Australia. His re- search focuses on education policy, reform, and the political economy of education, with a particular concern for issues of equity and access. His 2019 book, Learning to Teach in an Era of Privatization: Global Trends in Teacher Preparation (coedited with T. James Brewer), was named a winner of the 2020 AESA Critic’s Choice Book Award.