Does School Choice Lead to Sorting? Evidence from Tiebout ...msu2101/Urquiola(2005).pdf · Does...

Does School Choice Lead to SortingEvidence from Tiebout Variation

By MIGUEL URQUIOLA

Two issues dominate the school choice de-bate whether competition would make schoolsmore productive and whether choice would re-sult in sorting or stratification In trying to an-swer these questions economists have generallyfocused on the consequences of voucher sys-tems yet inter-district or Tiebout choice is andis likely to remain the main form of schoolchoice in the United States Surprisingly weknow comparatively little about its effects

This paper focuses on whether inter-districtchoice leads to sorting an issue on whichthere is no consensus In recent work forinstance Charles T Clotfelter (1999) arguesthat district availability does influence chil-drenrsquos peer groups but Alberto Alesina et al(2002) suggest this finding reflects a failure toconsider within-district sorting via attendanceareas

The issue is difficult to settle because districtconcentration may be correlated with unob-served factors that affect outcomes of interestTo address this problem this study uses a re-search design that builds from an Alesina andEnrico Spolaore (1997)ndashtype model It startswith the observation that metropolitan areas infact contain two education markets one at theprimary and one at the secondary level and thatthese often contain different numbers of dis-tricts It is natural to motivate such differencesas reflecting the presence of higher fixed costs atthe secondary level and the paper presents sub-stantial prima facie evidence consistent withthis possibility

Differences in the number of primary andsecondary districts make it possible to identifythe effects of changes in district availabilityusing between-level within-area changes in dis-trict concentration Two factors underlie thisdesignrsquos contribution (a) the use of within-areavariation allows significant controls for unob-served heterogeneity across markets and (b) theapproach takes advantage of education levelndashspecific data which allows one to control forsystematic and significant differences betweenthe primary and secondary sectors One mustbear in mind however that both the presenceand the magnitude of between-level differencesare not randomly assigned although these doseem to be significantly less correlated withobservable metropolitan area (MA) characteris-tics than are measures of aggregate districtconcentration

The results suggest that increases in districtavailability do affect childrenrsquos district- andschool-level peer groups (with respect to bothrace and parental education) and that theyreduce private enrollment Thus district con-centration seems to affect both the distribu-tion and the composition of the students in thepublic sector These findings are informativeas regards some of the mechanisms that drivestratification in the United States For instancethey are consistent with Steven G Rivkinrsquos(1994) finding that inter-district choice haslimited the success of past racial integrationefforts Additionally they are relevant to avariety of analyses that relate variation inschool district availability to educationaloutcomes1

The paper proceeds as follows Section I dis-cusses some background and introduces the re-search design and Section II describes the dataused Section III presents results and SectionIV concludes

School of International and Public Affairs and Depart-ment of Economics Columbia University 1402B Interna-tional Affairs Building New York NY 10027 (e-mailmsu2101columbiaedu) For generous feedback I am in-debted to Timothy Besley David Card Kenneth ChayStephen Coate Chang-Tai Hsieh Darren Lubotsky RandallReback Jesse Rothstein David Stern and three anonymousreferees Earlier versions of this paper circulated as ldquoDe-mand Matters School District Concentration Compositionand Educational Expenditurerdquo and ldquoSchool Choice andSchool Productivity What Can Tiebout Really Revealrdquo

1 For instance Dennis Epple and Richard E Romano(2003) illustrate how sorting is relevant to a number ofanalyses of school choice particularly if peer effects exist

1310

I Background and Research Design

In analyzing the effects of school choice it isrelevant to consider why households value theability to select schools for their children Tothe extent that parents choose schools based ontheir productivity one might expect that schoolchoice would improve school productivity sub-stantially On the other hand Jesse Rothstein(2003) illustrates that parental concern for peergroups if significant might blunt these compet-itive effects

The empirical literature does not reveal muchabout the extent to which choice leads to sort-ing Most work focuses on comparing the out-comes of private and public schools andassessing the impact of vouchers its method-ological emphasis is on approximating experi-mental conditions2 By its very nature suchresearch is not informative as to sorting effectssince few children change schools as a result ofthe interventions studied

Rather to learn about the effects of schoolchoice on sorting one needs to look at situa-tions in which there is substantial variation inthe degree of choice observed across educa-tional markets3 Inter-district or Tieboutchoice in the United States provides such anopportunity since the number of school dis-tricts in metropolitan areas ranges from 1 toover 200

Past work has not reached a consensus onwhether district availability affects the peergroups children encounter at school Clot-felter (1999) suggests that it does but Alesinaet al (2000) and Caroline M Hoxby (2000)argue this reflects a failure to consider within-district sorting via attendance areas4 theyconclude that it is these ldquojurisdictionsrdquo withinjurisdictions and not districts that determinepeer groups5

A A New Research Design

In part these disagreements reflect that dis-trict concentration may be endogenous In orderto deal with this complication this paper notesthat many MAs have more primary than sec-ondary districts which may reflect the presenceof higher fixed costs at the secondary level Tomotivate this it follows Alesina and Spolaore(1997) modeling jurisdictional creation as atrade-off between the benefits of large jurisdic-tions and the costs of heterogeneity in largepopulations6

To illustrate their approach consider an aream that has population Z and contains T typesof individuals These individuals desire a publicgood g and the issue is how many local juris-dictions should be created for its provision In-dividuals of different types are located at adistance h from each other where this capturesheterogeneity the greater h the more differentindividuals are along a given dimension Eachtype has a mass equal to so Z T Eachperson has a utility function Ui g(A li) y ti where g 0 0 A 0 y is incomeand ti and li are respectively the tax paid byindividual i and his distance from the publicgood

In the case of education the issue of interestis the number of school districts into which anarea splits In the model one school and twoborders characterize a district The cost of eachschool is k k k1S where S is each districtrsquospopulation and k and k1 are fixed and variablecosts respectively The social plannerrsquos solu-tion is to locate the school in the middle of eachdistrict and to create equally sized districts inthe amount N (T2)(ghk) Indexing areasby m this suggests a reduced form expressionfor district availability

2 See Helen F Ladd (2002) Derek Neal (2002) andPatrick J McEwan (2004) for reviews of the literature onvouchers

3 For instance Chang-Tai Hsieh and Urquiola (2003)consider Chilersquos nationwide voucher program under whichthe private enrollment share ranges from 0 to about 60percent across municipalities

4 These arise when a district operating many schoolsexplicitly ties the attendance at a given school to a givenresidential area

5 In other work Randall W Eberts and Timothy J Gron-berg (1981) and Amy B Schmidt (1992) present results

that although generally consistent with the possibility thatTiebout choice leads to sorting are not always significantW Norton Grubb (1982) studies whether districts becomerelatively more homogeneous over time His results onincome are consistent with this but those on racial structureare not For background on how district-based residentialsorting has limited the effects of desegregation policies seealso Gary Orfield and Frank Monfort (1992) and Rivkin(1994)

6 Alesina et al (2000) similarly analyze the availabilityof local functional jurisdictions

1311VOL 95 NO 4 URQUIOLA DOES SCHOOL CHOICE LEAD TO SORTING

(1) Nm fhm gm m k m

The key predictions are (Nk) 0 districtavailability decreases with the fixed costs in-curred in setting up a district and (Nh) 0it increases with heterogeneity

The emphasis on fixed costs is appropriategiven evidence that is consistent with theexistence of economies of scale in the schoolsector For instance Lawrence W Kenny andSchmidt (1994) document that the number ofschool districts in the United States hasdropped from 50000 to 15000 in the pastdecades and a significant reason for this ap-pears to be the exploitation of economies ofscale The second implication that heteroge-neity leads to greater demand for schools anddistricts is relevant to the extent that house-holds wish to separate themselves fromhouseholds with different preferences andorcharacteristics

To build a research design let MAs stand forthe areas m and note that in fact they containtwo educational levels which we can index l p s for primary and secondary respectively7

Note also that MAs often contain different num-bers of districts at each level for exampleSanta Cruz California has 11 districts that op-erate primary schools but only four that operatesecondary ones

To understand the origins of such differencesa first aspect to note is that primary andsecondary schools in some sense have differ-ent technologies Primary instruction is rela-tively simple and easy to replicate A first-grade teacher for instance can carry out mostinstruction in a single simply equipped class-room In contrast secondary subjects likephysics and athletics require specialized in-structors and infrastructure giving rise tohigher fixed costs This suggests that in equi-librium primary schools should be smallerFigure 1 panel A shows that enrollment is anexcellent predictor of school availability atthe MA level and as expected the number of

primary schools increases much faster withenrollment

If fixed costs are higher at the secondarylevel k sm kpm and if one thinks of theselevels as distinct markets and allows for theexistence of districts that specialize in onelevel then one would expect that MAs willhave more primary than secondary districtsNpm Nsm8

As usual things are more complicated than amodel would suggest Figure 2 shows twohypothetical MAs that are representative ofthe type of district structure observed in manyMAs Area A has four districts that operate atboth education levels ie they run both pri-mary and secondary schools Area B containssuch districts as well (5 and 6) but also hasfive primary-only and two secondary-onlydistricts The primary-only districts will typ-ically ldquofeedrdquo their students to the secondary-only ones9

Despite these complications Figure 1shows that while enrollment does not predictdistrict as well as school availability (panelsA and B) it is the case that among areas withbetween-level differences in district concen-tration the number of primary districts in-creases faster with enrollment than thenumber of secondary districts (panel C) Thiswithin-area between-level variation in dis-trict availability provides a strategy to studythe effects of district concentration For anexample consider a reduced-form regressionof private enrollment Pm

(2) Pm 0 1 Nm 2 Xm m

where Nm is a measure of district concentrationand Xm is a vector of MA characteristics Onemight expect 1 to be negative since both produc-tivity improvements and greater stratificationmean that as their number increases at least somedistricts become more attractive relative to the

7 In this paper the primary level will be understood asgrades 1 to 8 (and ages 6 to 13) and the secondary level asgrades 9 to 12 (and ages 14 to 18) This is also the officialdefinition in manymdashthough not allmdashstates an issue wereturn to below

8 There is evidence that market participants do makedistinctions between levels For instance Anthony S Bryket al (1993) report that Catholic primary schools are gen-erally smaller and run by parishes while Catholic highschools are larger and typically administered by religiousorders or archdioceses

9 In California for instance the name of each districtindicates its type Districts like 7 are called elementarythose like 10 are labeled union high school and those like5 are called unified

1312 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2005

private sector10 Nonetheless cross-sectional esti-mates could be biased for example if there is

variation in unobserved preferences for religiousinstruction Some indication of this is found in theprevious literature which has produced mixedfindings on whether district availability reducesprivate enrollment1110 Theoretically though the direction of the effect is not

clear One might expect that increased district availabilitywould reduce private enrollment and perhaps raise publicschool expenditure but as Epple and Romano (1996) andThomas J Nechyba (2003) illustrate there are general equi-librium and potential feedback effects to consider

11 For instance Jorge Martinez-Vasquez and Bruce ASeaman (1985) relate district concentration and private en-

Primary

Primary

Secondary

Secondary

FIGURE 1 SCHOOL AND SCHOOL DISTRICT AVAILABILITY IN MAS

Notes These figures use the Common Core of Data (CCD) for 1990 In panels A B and C the lines are predicted values ofregressions of the number of schools and districts on enrollment Panel C refers to MAs with different numbers of districts at theprimary and secondary levels Panel D plots the density of MA-level observations of the ratio of the total number of districtsoperating at the primary level to the total number of districts operating at the secondary level for all MAs

FIGURE 2 HYPOTHETICAL SCHOOL DISTRICT STRUCTURE


Using between-level differences in districtconcentration however one can introduce adummy Zm for each MA resulting in a fixedeffectsndashtype specification

(3) Plm 0 1 Nlm m 2

M

m Zm lm

This requires that both outcomes and districtavailability be measured with level-specific in-formation and has the advantage of controllingfor MA characteristics including those unob-served by the researcher which are constantacross levels

B Sorting between and within Districts

In short the motivation is that by looking atMAs that have a different number of districts ateach educational level one can observe the be-havior of the same set of households when itfaces different opportunities to sort out To clar-ify how such differential choice may arise notethat a household moving into an MA will typi-cally find (often through information provideddirectly by realtors) that the purchase of a givenresidence entitles it to attend a given set ofprimary schools and a given set of secondaryschools In cases in which there are more dis-tricts at the primary level households will findthat conditional on settling in a given secondarydistrict they will be able to choose (via thechoice of residence) between multiple primarydistricts At such a juncture they will poten-tially have a greater degree of influence over thepeer groups their children encounter in the pri-mary grades12

Alesina et al (2000) emphasize that sortingcan also occur within districts via catchmentareas13 In fact they suggest that it is the num-ber of schools rather than the number of dis-

tricts that influences how homogeneouschildrenrsquos peer groups are Although their anal-ysis does not distinguish between education lev-els this point is relevant because evenhouseholds moving into a larger district thatoffers all grades will often find greater choicebetween schools at the primary level This isbecause as shown below it is common forK-12 districts to contain a single high schooland several primary schools To the extent thatthe latter have separate catchment areas fami-lies will again have a greater chance to selectpeer groups at the primary level14 To accountfor this the regressions below will includeschool availability measured at the relevantlevel

C Possible Sources of Bias

By exploiting within-MA between-level dif-ferences in district availability the strategy pro-posed here has the advantage of implicitlycontrolling for unobserved heterogeneity acrossMAs This approach is not without potentiallimitations however A central one is that thepresence and the magnitude of these differencesmay themselves be endogenous and it is there-fore relevant to discuss where they originate

Table 1 contains descriptive statistics Ta-ble 2 columns 1 and 2 present logit regres-sions that relate the presence of across-leveldifferences in the number of districts to ob-servable MA characteristics A salient fact isthat these are less likely to be observed insouthern states which partly reflects that thepresence of such differences is frequently dueto past institutional development In southernstates county governmentsrsquo responsibilitieshave historically included education (thereare county-wide school districts) and there isno scope for specializing districts In otherstates the emergence of secondary-only dis-tricts seems to have been encouraged by taxlimitations that made it difficult for singledistricts to fund complete K-12 educationrollment in 75 large MAs They obtain mixed results de-

pending on the concentration measure In contrast Schmidt(1992) finds the expected relationship

12 At greater cost households can of course also switchdistricts once they are in a given area

13 This type of sorting which gives rise to ldquoneighbor-hood schoolsrdquo should be distinguished from the district-wide ldquoopen enrollmentrdquo policies that are in place in somedistricts Epple and Romano (2003) contrast the implicationof both types of choice See also Randall Reback (2002) foran analysis of much less extended choice programs that

allow children to enroll in school districts different fromthose in which they live

14 Sandra E Black (1999) shows that movements acrosscatchment area borders are associated with discrete changesin housing prices She attributes this to the capitalization ofschool quality which can of course encompass peer groupcomposition


programs particularly as initially low enroll-ment rates grew in the upper reaches of thisrange15 Such limitations seem to have beenmore common in western states and indeedcolumn 1 suggests differences are more com-mon in the West as well as in the Northeast16

Column 5 shows that among the MAs that dodisplay between-level differences in districtavailability the magnitude of these does notseem to be strongly correlated with observableMA traits For instance it is not significantlycorrelated with median income the proportion

Catholic population density or poverty On theother hand it is significantly correlated with theproportion black (negatively) and the propor-tion Hispanic (positively) This is in contrastwith the significantly stronger correlation thatsuch observables display with the number ofdistricts in an area as described in column 6Columns 3 and 4 present similar evidence inregression form showing that once one controlsfor their presence the magnitude of between-level differences (as measured by the ratio ofthe total number of primary to secondary dis-tricts in an MA) is not significantly higher inany given census region This again is in con-trast with what one observes concerning thenumber of districts

Despite this evidence between-level differ-ences are of course not randomly assigned andmay additionally be related to unobservables In

15 See American Association of School AdministratorsCommission on District Reorganization (1958)

16 For further illustration Table A1 in the Appendixpresents a sample of real MAs including areas like A and B(Figure 2) and describes the total number of districts oper-ating at each level

TABLE 1mdashDESCRIPTIVE STATISTICS

School-level data District-level data MA-level data

Mean Std dev N Mean Std dev N Mean Std dev N

Racial heterogeneitya 285 213 48075 218 192 5555 351 170 333Racial heterogeneity relative to

own MA694 558 48075 559 471 5555

Racial heterogeneity relative toown district

909 498 48075

Educational heterogeneitya 660 95 5554 721 24 318Educational heterogeneity

relative to MA910 131 5554

Number of districtsb 434 466 51518 505 492 5555 188 243 333Log of the number of districtsb 32 06 51518 348 100 5555 23 12 333Number of districts operating

primary schools178 222 333

Number of districts operatingsecondary schools

141 164 333

Number of primary schools 72 172 5555 1332 1771 333Number of secondary schools 15 33 5555 284 333 333Proportion of hhlds heads

with a college degree028 006 51518 028 006 5555 027 007 331

Proportion Catholicc 021 011 51518 023 012 5555 021 012 333Proportion poor 012 004 51518 012 004 5555 013 005 333Median income 32 064 51518 32 065 5555 30 063 333Proportion of hhlds on welfare 007 003 51518 007 003 5555 007 003 333Proportion of hhlds that own

their home049 004 51518 049 004 5555 049 005 333

Proportion of hhldslinguistically isolated

004 005 51518 004 005 5555 003 004 333

a This is the probability (in percentage terms) that two randomly selected individuals are from different racial oreducational groups

b For MAs the entries indicate the number of districts operating within the MA For districts and schools these are thecorresponding figures for their respective districts or MAs

c The proportion Catholic is proxied using the proportion of individuals of French French-Canadian Irish Italian PolishPortuguese and Spanish ancestry The proportion Hispanic enters as a separate control


particular estimates from specifications like (3)might be biased if the correlation between unob-served characteristics and district concentrationwere to differ between levels For example house-holds in a given MA might have a strong prefer-ence for private schooling (relative to householdsin other MAs) at the primary level but a weakerrelative preference at the secondary level

A final issue is that the motivation abovesuggests that when between-level differences indistrict availability arise this should be because

there are more districts at the primary level Infact this is not always the case While in thecomplete sample roughly 40 percent of MAshave more districts at the primary level about 9percent have more secondary districts In thelatter cases however the differences are signif-icantly smaller Specifically among the 29 MAswith more secondary districts the ratio of thetotal number of primary to secondary districtshas an average of 091 (with a standard devia-tion of 005 and a minimum of 080) In con-

TABLE 2mdashDISTRICT-AVAILABILITY AND BETWEEN-LEVEL DIFFERENCES

Dependent variable Correlation coefficients

Dummy for between-level differences

Ratio of primaryto secondary

districtsNo of

districts


districtsNo of

districts

(1) (2) (3) (4) (5) (6)

Census region Northeast 08 06 01 32(035) (06) (01) (48)

Census region South 11 04 01 116(03) (5) (01) (30)

Census region West 07 07 02 74(04) (05) (01) (28)

Percent pop black 17 00 120 018 000(27) (06) (157)

Percent pop Hispanic 42 08 404 017 005(30) (06) (184)

Pct hhlds linguistically isolated 180 54 1669 011 012(126) (26) (670)

Percent adults with college degree 11 02 147 001 015(37) (09) (177)

Percent pop Catholic 02 02 104 007 016(20) (04) (130)

Percent pop poor 100 34 231 003 019(81) (16) (471)

Median income 00 00 00 008 033(00) (00) (00)

Percent hhlds on welfare 255 59 1423 021 007(111) (44) (538)

Pct hhlds that own their home 31 07 305 008 007(30) (05) (217)

Population 13 02 176 003 067(03) (01) (37)

Population density 00 00 00 006 030(00) (00) (00)

Percent pop immigrants 75 48 158 022 026(69) (18) (505)

Number of districts 01 00 014(00) (00)

Dummy for MAs withbetween-level differences

02(01)

R2 0102 0340 0390 0566N (districts) 331 331 331 331 138 331

Notes and indicate significance at the 10- 5- and 1-percent level respectively Observations are at the MA levelColumns 1 and 2 are logit regressions and columns 3 and 4 use OLS Columns 5 and 6 present simple correlation coefficients


trast among the 138 MAs with more districts atthe primary level the mean value of this ratio is165 (with a standard deviation of 085 and amaximum of 675)17 Figure 1 panel D de-scribes the cross-MA distribution of this ratio

II Data and Measures

This study uses two central data sources theCommon Core of Data (CCD) and the SchoolDistrict Data Book (SDDB) both for 199018

The CCD which is based mainly on adminis-trative information contains data on districtsrsquolocation their grade levels of operation andvarious characteristics of their schools and stu-dents The SDDB consists of district-level tab-ulations of the Census with the key advantagethat data for districts like 5 in Figure 2 can beextracted using appropriate age ranges For in-stance it is possible to determine how manychildren aged 6 to 13mdashthe standard primaryagemdashattend private school This procedure al-lows one not only to obtain level-specific databut also to deal with the problem of geographicoverlap posed by districts like 7 and 10

In view of this the dependent variables forprivate enrollment were constructed using theSDDB The dependent variables for sortingwere created from the SDDB and CCD fordistrict- and school-level analyses respectively(the SDDB does not contain school informa-tion)19 The key independent variables the mea-sures of district and school availability wereconstructed using the CCD

The sorting analyses focus on stratification byracial and parental education groups For race thegroups considered are Asian black Hispanicwhite Native American and other and were con-structed using data on students For schooling thegroups are no high school high school degreesome college and Bachelorrsquos degree or higher

and were constructed using data for householdheads The results use the heterogeneity measurein Alesina et al (2002) For illustration considerr 1 R racial groups and let Srm be group rrsquosshare in the population of MA m The basic het-erogeneity measure used is Hm 1 yenr1

R Srm2

and is interpreted as the probability that two indi-viduals selected at random belong to two differentracial groups20

III Results

Introducing the results on sorting Figure 3presents the distribution of this heterogeneitymeasure for race and parental education PanelsA and B show that among MAs there is sub-stantially more variation in racial than in edu-cational heterogeneity although as thedescriptive statistics in Table 1 illustrate thereis less racial heterogeneity overall The proba-bility that two randomly selected people in anMA are from different racial groups has a meanof 035 and a standard deviation of 019 theaverage probability that they are from differenteducational groups is 072 with a standard de-viation of only 002 Panels C and D presentdistrict-level distributions and show that muchmore sorting into districts occurs for race thanfor education Moving from MAs to districtsreduces the mean racial heterogeneity measurefrom 035 to 021 for education the mean fallsfrom 072 to 066 Further the coefficient ofvariation for parental schooling remains sub-stantially lower

A Sorting

Table 3 presents regression evidence on theimpact of district availability on district heter-ogeneity For comparability with earlier workit uses a relative sorting measure as the depen-dent variable namely the ratio between dis-trictsrsquo heterogeneity measures and those of theirrespective MAs21 This captures that a given17 This reflects that differences in favor of the number of

secondary districts mainly arise when there are one or twosecondary-only districts operating alongside a much largernumber of districts that operate at both levels ScrantonndashWilkes Barre Pennsylvania for instance has 33 districtsthat operate at both levels and two that are secondary-only

18 The analyses based on the CCD were reproducedusing 1999 data with no changes in the key conclusions

19 For many of the district-level analyses it is possible touse the SDDB or the CCD data The figures and regressionsbelow occasionally use them interchangeably Not surpris-ingly the results are very similar

20 One can also use the ldquoexposurerdquo measures describedin Clotfelter (1999) which can be decomposed to determinethe portions of stratification that are due to within- andbetween-district sorting The qualitative conclusions theseproduce are similar to those presented below and are omit-ted for brevity

21 The conclusions using absolute heterogeneity mea-sures are quite similar and are omitted


MArsquos heterogeneity limits that which can bedisplayed on average by its component dis-tricts Further for comparability with Alesina etal (2002) the key independent variable is thelog of the number of districts in the MA22 Alltables also include results using the absolutenumber of districts23

Columns 1 and 2 present simple cross-sectional

results In panel A the simplest specification sug-gests that districts in areas with greater districtavailability are more racially homogeneous withrespect to their MAs The initial point estimatessuggest that doubling the number of districts in adistrictrsquos MA would move it about 15 percent of astandard deviation in the distribution of relativesorting Nonetheless the addition of controls (col-umn 2) renders the key coefficient insignificantThis is consistent with earlier work

Columns 3 to 5 use what we will label level-specific data which is necessary to implementthe research design introduced above Specif-ically there are two observations for districtsthat operate at both levels For example anarea like B in Figure 2 would supply sevenobservations at the primary level and four atthe secondary level with the district avail-ability measures also calculated for eachlevel Column 5 includes MA dummies and

22 Alesina et al do not discuss why they use this trans-formation but it may be appropriate because of the nonlin-earity in the relation between heterogeneity and districtconcentration To illustrate Figure A1 in the Appendixshows that districtsrsquo (relative) heterogeneity is more nega-tively related to district availability when MAs have fewdistricts This is consistent with the possibility that parentscare about peer groups along dimensions such as race andeducation and that this is one of the first dimensions alongwhich districts differentiate

23 Regressions using the number of districts per studentyield similar results

FIGURE 3 HETEROGENEITY AMONG MAS AND DISTRICTS

Notes The graphs are densities of the absolute heterogeneity measure described in the data section Panels A and B containMA-level observations and C and D are at the district level All data are for 1990 Panels B and D use SDDB data and PanelsA and C use CCD school data aggregated up to the MA and district level respectively (Using SDDB data produces similarresults)


thus implements the full designmdashthe effectsof district availability are identified usingonly within-MA between-level variation indistrict concentration The results are nowuniformly significant and somewhat larger inmagnitude Panel B presents similar results onthe schooling of household heads These sug-

gest that despite the fact that households areless sorted out on schooling than on race(Figure 3) increases in district availabilityare also associated with greater stratificationalong this characteristic

To summarize although there is no clear apriori expectation on the direction of bias these

TABLE 3mdashDOES DISTRICT AVAILABILITY AFFECT DISTRICT-LEVEL PEER GROUPS(Dependent variable Districtsrsquo heterogeneity relative to that in their MA)

Cross-sectional data Level-specific data

(1) (2) (3) (4) (5)

Panel A Race

Log of the number of districts 71 19 88 99 102

(11) (30) (11) (19) (27)[015] [004] [019] [021] [022]

R2 0023 0070 0030 0049 0164Controlsa N Y N Y NMA dummies N N N N YN (districts) 5555 5555 9452 9452 9452MAs covered 318 318 318 318 318

Number of districts 011 002 02 02 01(003) (006) (00) (01) (01)

[011] [002] [021] [021] [010]R2 0014 0071 0019 0042 0162Controlsa N Y N Y NMA dummies N N N N YN (districts) 5555 5555 9452 9452 9452MAs covered 318 318 318 318 318

Panel B Education

Log of the number of districts 21 29 21 26 63(03) (05) (03) (03) (08)




Notes and indicate significance at the 10- 5- and 1-percent level respectively All regressions adjust for clusteringat the MA level The controls are the number of schools in districtsrsquo respective MAs median income a cubic of populationand the proportion of the population with college degree Catholic poor on welfare and linguistically isolated The numbersin brackets indicate the proportion of a standard deviation change in the dependent variable induced by increasing the log ofthe number of districts by one or increasing the number of districts by one standard deviation The dependent variable is basedon SDDB data and the district availability measures come from the CCD

a The regressions in column 5 contain one control variable that varies within MAs across education levels the number ofschools operating at each level Removing this variable has only a minmal effect on the coefficients of interest


regressions suggest that the cross-sectional co-efficient on the effect of district availability onsorting is biased toward zero The results usingthe full research design which suggest that all-else-equal districts are more homogeneouswhere there are more of them are in line withthe usual expectation in the literature

As indicated there is more controversy onwhether district availability also affects school-level peer groups Clotfelter (1999) suggeststhat it does but Hoxby (2000) finds that theracial heterogeneity of a studentrsquos peers is re-lated to the number of schools but not to thenumber of districts in his or her MA where theargument is that such sorting takes place withindistricts One can consider this issue for race(although not for parental schooling) becausethe CCD provides information on schoolsrsquo ra-cial composition24

As an introduction Figure 4 panel A showsthat within-district sorting is indeed empiricallyrelevant The figure plots unweighted smoothedvalues of schoolsrsquo heterogeneity relative to thatof the district to which they belong against thenumber of schools in their respective districtwith a clear negative relation Panel B plotsschoolsrsquo heterogeneity relative to their MAagainst the number of schools in their MA andshows a similar finding25

The question at hand however is whetherschool-level heterogeneity is affected notonly by school but also by district availabil-ity Panel C presents evidence consistent withthis Here schoolsrsquo heterogeneity (relative totheir respective MAs) is related to the totalnumber of districts in their respective MAsand again there is a negative relation al-though this does not control for the number ofschools or any other variable The regressionevidence is in Table 4 where the unit ofobservation is now the school Columns 1 to 3contain cross-sectional data With these thesimplest specification does suggest that in-creased district availability makes schoolsmore homogeneous The addition of schoolavailability as a control reduces the magni-tude of the effect but it is still negative and

significant In column 3 the addition of fur-ther controls renders them both insignificant

Columns 4 to 6 again turn to level-specificdata26 The coefficient on the district availa-bility measure is now significant throughoutmdashmost importantly in column 6 where theinclusion of MA dummies means that the ef-fect is identified using within-MA between-level variation in district and school availabilityNote also that the effect of school availabilityapproaches zero and is no longer significantThis is to be expected given Figure 1 whichshows that the number of schools in an MA islargely a function of its total enrollment As thisimplies there is much more variation (acrossMAs) in the ratio of primary to secondary dis-tricts than in the ratio of primary to secondaryschools

In short these results suggest that districtavailability affects not only districtsrsquo composi-tion but also the peer groups children encounterat school One possible reason for this is thatmost districts simply do not have a large num-ber of schools Table A2 in the Appendixshows that the median district (among those inMAs) has fewer than four schools Among dis-tricts that operate primary schools 50 percenthave three or fewer Among those that operatesecondary schools more than 70 percent haveonly one This may in turn partially accountfor why many schools are simply not that muchmore racially homogeneous than their respec-tive districts as shown in Figure 4 panel D

B Interpretation

These results suggest that on the marginparentsrsquo choices regarding districts of resi-dence do affect their childrenrsquos peer groups Itis important to be clear however that thesorting effects identified may not be duesolely to school choice since they could alsoreflect the interaction between residential ra-cial segregation patterns potentially unrelatedto school choice and the division of an urbanarea into jurisdictions tied to specific sets ofschools

24 It is possible to construct level-specific school mea-sures using information on schoolsrsquo grades of operation

25 Both results are highly statistically significant in re-gression specifications

26 The slight increase in sample sizes reflects that thereare now two observations for schools that operate at bothlevels almost always those that span K to 12 As describedbelow such schools are rare


To illustrate assume that districts 7 8 and9 (in Figure 2) feed their students to district10 and that they share the same geographicarea with it What results like those in Table 3tell us is that there is more segregation by raceand parental schooling at the primary level(districts 7 to 9) than at the secondary level(district 10) One cannot rule out that thismerely reflects that households in this area arespatially distributed in a certain way that hap-pens to be associated with school districtboundaries27

Nonetheless it is likely that these results atleast partially reflect parental preferences re-

garding school peer groups for two reasonsFirst as Table 4 shows district boundaries alsoseem to affect the school-level (rather than justdistrict-level) peer groups that students experi-ence Second the next set of results shows thatit also affects private enrollment One would notexpect these results (particularly the second) ifthe placement of district boundaries was orthog-onal to factors that affect parentsrsquo choice ofschools

C Results on Private Enrollment

As stated the previous literature is not clearon whether increased district availability re-duces private enrollment To present evidenceon this Table 5 switches to MAs as the unit ofanalysis since private enrollment rates areproperly viewed as a market-level outcomeThe table again begins with cross-sectional

27 Because of such issues disentangling the causes ofsorting ultimately benefits from a general equilibrium ap-proach For an interesting example see Patrick Bayer et al(2004)

FIGURE 4 RACIAL HETEROGENEITY IN SCHOOLS AND MAS

Notes Figures based on the CCD 1990 Panels A to C plot unweighted smoothed values of schoolsrsquo relative heterogeneitymeasures (with a bandwidth of 010 in all cases) Panel A uses schoolsrsquo respective districts as the benchmark and panels Band C use their respective MAs Panel D describes the density of schoolsrsquo heterogeneity relative to that observed in theirrespective districts


evidence the dependent variable is the ag-gregate private enrollment rate in the MAwithout distinguishing between educationallevels and the independent variable is basedon the total number of districts in each MAColumn 1 shows that the cross-sectional evi-dence runs contrary to the usual expectationColumn 2 adds a number of controls includ-ing the number of schools in the MA renderingthe coefficient on the number of districtsinsignificant

Columns 3 to 6 use level-specific informa-tion they incorporate two observations for eachMA one at each education level with eachregressed on a measure of the number of dis-tricts operating at the corresponding level28

Columns 3 and 4 replicate the previous speci-fications and again the coefficient on district

availability is not robust In such analyses how-ever one should control for the fact that asFigure 5 panel A shows private enrollment issignificantly higher at the primary level In factpanel B suggests that conditional on districtavailability MAs display a roughly constantdifference in private enrollment between thesetwo levels What may account for this differ-ence As discussed average costs and thereforeaverage tuition are higher at the secondarylevel Additionally other aspects of secondaryeducation may lower parentsrsquo propensity to useprivate schools For instance in the secondarygrades schools intensify the separation of stu-dents into ldquotracksrdquo (eg advanced placementversus vocational education) To the extent thatthese procedures separate students by socioeco-nomic characteristics this may satisfy parentaldemand for sorting

Regression 5 of Table 5 introduces a roughcontrol for such factors by including a dummyfor observations at the secondary level Its co-efficient is highly significant and in results notpresented here is also very stable across re-

28 That is two measurements of private enrollment arecalculated for each MA one for children in the primary agerange and one for children in the secondary range Theindependent variable is based on the number of districtsoperating at the respective educational level

TABLE 4mdashRACE DOES DISTRICT AVAILABILITY AFFECT SCHOOL-LEVEL PEER GROUPS(Dependent variable Schoolsrsquo racial heterogeneity relative to their respective MAs)


(1) (2) (3) (4) (5) (6)

Log of the number of districts 61 31 16 64 53 82(13) (14) (13) (13) (13) (16)

[011] [006] [003] [011] [009] [015]Log of the number of schools 50 105 17 06

(21) (35) (13) (06)R2 0018 0022 0046 0019 0020 0085Controls N N Y N N NMA dummies N N N N N YN (districts) 48075 48075 48075 50224 50224 50224MAs covered 313 313 313 313 313 313

Number of districts 02 01 00 02 02 01(00) (00) (00) (00) (01) (00)

[017] [008] [004] [017] [017] [008]Number of schools 00 00 00 00


Notes and indicate significance at the 10- 5- and 1-percent level respectively All regressions adjust for clusteringat the MA level The controls are median income population and the proportion of the population with college degreeCatholic poor on welfare and linguistically isolated The numbers in brackets indicate the proportion of a standard deviationchange in the dependent variable induced by increasing the log of the number of districts by one or increasing the numberof districts by one standard deviation All data come from the CCD for 1990


gional samples Further its inclusion improvesthe fit significantly the R2 now exceeds 06 inboth specifications Finally column 6 imple-ments the full research design by adding adummy for each MA so that the effect of vari-ations in district concentration is identified onlyusing differences between levels within MAsThis produces statistically significant resultswhich suggest that doubling the number of dis-tricts would reduce private enrollment by one-fifth of a standard deviation29

IV Conclusion

An important question in the school choicedebate is whether greater choice would result instratification that might adversely affect somechildren Inter-district choice provides a fruitfulsetting to look at this issue not least because itis probably the most prevalent form of schoolchoice in the United States This paper relies onwithin-MA between-level variation in districtstructure to suggest that increased districtavailability indeed affects childrenrsquos districtand school-level peer groups and that it re-duces private enrollment ie district concen-tration seems to affect both the distributionand the composition of the students in thepublic sector

The empirical strategy used to produce thesefindings has the advantage of introducing sub-stantial controls for MA-level heterogeneity andof using level-specific information At the same

29 If parents value school choice another testable impli-cation arises because one would expect that between-leveldifferences in district concentration might be correlatedwith intercity migration patterns depending on the age ofhouseholdsrsquo children An analysis using the Census PUMSdata for 106 MAs however did not provide evidence ofthis This might reflect that other considerations (eg theemployment outlook or weather) overwhelm the availabilityof school districts when households make decisions onwhere to live

TABLE 5mdashDOES DISTRICT AVAILABILITY AFFECT PRIVATE ENROLLMENT LEVELS(Dependent variable MA-level private enrollment rates)


(1) (2) (3) (4) (5) (6)

Log of the number of districts 11 02 13 09 00 10(02) (03) (02) (02) (03) (05)[024] [004] [028] [020] [001] [022]

Log of the number of schools 10 37 05 03(07) (02) (05) (06)

Secondary level dummy 58 63(07) (09)

R2 0070 0458 0067 0570 0618 0952Controls N Y N Y Y NMA dummies N N N N N YN 291 291 582 582 582 582MAs covered 291 291 291 291 291 291

Number of districts 007 002 009 002 00 003(001) (002) (001) (002) (00) (001)[037] [011] [038] [009] [001] [013]

Number of schools 002 002 00 000(001) (000) (00) (00)



Notes and indicate significance at the 10- 5- and 1-percent level respectively The controls are median incomepopulation and the proportion of the population with college degree Catholic poor on welfare and linguistically isolatedThe numbers in brackets indicate the proportion of a standard deviation change in the dependent variable induced byincreasing the log of the number of districts by one or increasing the number of districts by one standard deviation The dataon private enrollment come from the SDDB and the data on district and school availability from the CCD


time one must bear in mind that both the pres-ence and the magnitude of between-level differ-ences are not randomly assigned (althoughthese do seem to be significantly less correlatedwith observable MA characteristics than aremeasures of aggregate district concentration)Aside from leaving open the potential for biasthis means that one cannot be certain that the in-troduction of additional districts or of between-level differences would have similar effectselsewhere Finally note that the sorting identi-

fied may not be due solely to school choicesince it could also reflect the interaction be-tween residential segregation patterns (poten-tially unrelated to schooling) and school districtboundaries

Despite these caveats these results are infor-mative as to some of the mechanisms that drivestratification in the United States and are rele-vant to a variety of analyses that relate variationin school district availability to educationaloutcomes

APPENDIX

TABLE A1mdashSCHOOL DISTRICTS OF DIFFERENT TYPES IN SELECTED MAS

Metropolitcanarea State

Primary onlydistricts

(1)

Secondary onlydistricts

(2)

Consolidateddistricts

(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)

Kenosha WI 10 2 1 11 3 367Yuma AZ 7 2 0 7 2 350Portsmouth NH-ME 20 1 8 28 9 311Altantic City NJ 26 4 8 34 12 283Santa Cruz CA 8 1 3 11 4 275Joliet IL 26 6 8 34 14 243San Diego CA 27 5 12 39 17 229Burlington VT 12 2 6 18 8 225Victoria TX 2 0 2 4 2 200Nashville TN 3 0 8 11 8 136Vancouver WA 2 0 7 9 7 129Nassau-Suffolk NY 31 3 96 127 99 128Springfield MA 11 4 22 33 26 127Altoona PA 0 0 7 7 7 100Baltimore MD 0 0 7 7 7 100Bradenton FL 0 0 1 1 1 100Bristol CT 0 0 4 4 4 100Clarksville TN-KY 0 0 2 2 2 100

Source Common Core of Data 1990

Secondary

Secondary

PrimaryPrimary

FIGURE 5 PRIMARY AND SECONDARY PRIVATE ENROLLMENT RATES

Notes Based on calculations using the SDDB and the CCD both for 1990 Observations areat the MA level Panel A contains densities of the private enrollment rate (in percentages)Panel B plots two observations for each MAmdashthe primary and secondary private enrollmentratesmdashboth against the number of districts in the MA


REFERENCES

Alesina Alberto and Spolaore Enrico ldquoOn theNumber and Size of Nationsrdquo Quarterly Jour-nal of Economics 1997 112(4) pp 1027ndash56

Alesina Alberto Baqir Reza and Hoxby CarolineldquoPolitical Jurisdictions in Heterogeneous Com-munitiesrdquo National Bureau of Economic Re-search Inc NBER Working Papers No 78592000

American Association of School AdministratorsCommission on School District ReorganizationSchool district organization WashingtonDC American Association of School Admin-istrators 1958

Bayer Patrick McMillan Robert and Rueben KimldquoResidential Segregation in General Equilib-riumrdquo National Bureau of Economic ResearchInc NBER Working Papers No 11095 2004

Black Sandra E ldquoDo Better Schools MatterParental Valuation of Elementary Educa-tionrdquo Quarterly Journal of Economics 1999114(2) pp 577ndash99

Bryk Anthony S Lee Valerie E and Holland Peter

B Catholic schools and the common good Cam-bridge MA Harvard University Press 1993

Clotfelter Charles T ldquoPublic School Segrega-tion in Metropolitan Areasrdquo Land Econom-ics 1999 75(4) pp 487ndash504

Eberts Randall W and Gronberg Timothy JldquoJurisdictional Homogeneity and the TieboutHypothesisrdquo Journal of Urban Economics1981 10(2) pp 227ndash39

Epple Dennis and Romano Richard E ldquoEndsagainst the Middle Determining Public Ser-vice Provision when There Are Private Al-ternativesrdquo Journal of Public Economics1996 62(3) pp 297ndash325

Epple Dennis and Romano Richard ldquoNeighbor-hood Schools Choice and the Distribution ofEducational Benefitsrdquo in Caroline M Hoxbyed The economics of school choice Chi-cago University of Chicago Press 2003

Grubb W Norton ldquoThe Dynamic Implications ofthe Tiebout Model The Changing Compositionof Boston Communities 1960ndash1970rdquo PublicFinance Quarterly 1982 10(1) pp 17ndash38

Hoxby Caroline M ldquoDoes Competition among

TABLE A2mdashDISTRIBUTION OF SCHOOL DISTRICTS BY THE NUMBER OF SCHOOLS THEY CONTAIN

Percentage of districts with

Total Primary Secondary

1 school 153 218 7312 schools 288 383 8513 schools 430 511 9084 schools 537 612 9365 schools 629 691 95310 schools 830 853 982

Notes Based on CCD data for 1990 The columns that refer to primary and secondary includeonly districts with positive numbers of each type of school

FIGURE A1 DISTRICT AVAILABILITY AND DISTRICTSrsquo RELATIVE HETEROGENEITY

Notes Calculations based on the CCD 1990 The lines plot unweighted smoothed values ofdistrictsrsquo heterogeneity relative to that of their respective MAs (in both cases the bandwidthis equal to 005)


Public Schools Benefit Students and Taxpay-ersrdquo American Economic Review 200090(5) pp 1209ndash38

Hsieh Chang-Tai and Urquiola Miguel ldquoWhenSchools Compete How Do They CompeteAn Assessment of Chilersquos NationwideSchool Voucher Programrdquo National Bureauof Economic Research Inc NBER WorkingPapers No 10008 2003

Kenny Lawrence W and Schmidt Amy B ldquoTheDecline in the Number of School Districts inthe US 1950ndash1980rdquo Public Choice 199479(1ndash2) pp 1ndash18

Ladd Helen F ldquoSchool Vouchers A CriticalViewrdquo Journal of Economic Perspectives2002 16(4) pp 3ndash24

Martinez-Vasquez Jorge and Seaman Bruce AldquoPrivate Schooling and the Tiebout Hypoth-esisrdquo Public Finance Quarterly 1985 13(3)pp 293ndash318

McEwan Patrick J ldquoThe Potential Impact ofVouchersrdquo Peabody Journal of Education2004 79(3) pp 57ndash80

Neal Derek ldquoHow Vouchers Could Change theMarket for Educationrdquo Journal of EconomicPerspectives 2002 16(4) pp 25ndash44

Nechyba Thomas J ldquoCentralization Fiscal Federal-

ism and Private School Attendancerdquo Interna-tional Economic Review 2003 44(1) pp 179ndash204

Orfield Gary and Monfort Frank ldquoStatus ofSchool Desecration The Next Generationrdquo Alex-andria Council of Urban Boards of EducationNational School Boards Association 1992

Reback Randall ldquoCapitalization under PublicSchool Choice Are the Winners Really theLosersrdquo National Center for the Study ofPrivatization in Education Occasional PaperNo 66 2002

Rivkin Steven G ldquoResidential Segregation andSchool Integrationrdquo Sociology of Education1994 67(4) pp 279ndash92

Rothstein Jesse ldquoGood Principals or GoodPeers Parental Valuation of School Charac-teristics Tiebout Equilibrium and the Effectsof Inter-District Competitionrdquo National Bu-reau of Economic Research Inc NBERWorking Papers No 10666 2004

Schmidt Amy B ldquoPrivate School Enrollment inMetropolitan Areasrdquo Public Finance Quar-terly 1992 20(3) pp 298ndash320

Tiebout Charles M ldquoA Pure Theory of LocalExpendituresrdquo Journal of Political Economy1956 64(5) pp 416ndash24


I Background and Research Design

In analyzing the effects of school choice it isrelevant to consider why households value theability to select schools for their children Tothe extent that parents choose schools based ontheir productivity one might expect that schoolchoice would improve school productivity sub-stantially On the other hand Jesse Rothstein(2003) illustrates that parental concern for peergroups if significant might blunt these compet-itive effects

The empirical literature does not reveal muchabout the extent to which choice leads to sort-ing Most work focuses on comparing the out-comes of private and public schools andassessing the impact of vouchers its method-ological emphasis is on approximating experi-mental conditions2 By its very nature suchresearch is not informative as to sorting effectssince few children change schools as a result ofthe interventions studied

Rather to learn about the effects of schoolchoice on sorting one needs to look at situa-tions in which there is substantial variation inthe degree of choice observed across educa-tional markets3 Inter-district or Tieboutchoice in the United States provides such anopportunity since the number of school dis-tricts in metropolitan areas ranges from 1 toover 200

Past work has not reached a consensus onwhether district availability affects the peergroups children encounter at school Clot-felter (1999) suggests that it does but Alesinaet al (2000) and Caroline M Hoxby (2000)argue this reflects a failure to consider within-district sorting via attendance areas4 theyconclude that it is these ldquojurisdictionsrdquo withinjurisdictions and not districts that determinepeer groups5

A A New Research Design

In part these disagreements reflect that dis-trict concentration may be endogenous In orderto deal with this complication this paper notesthat many MAs have more primary than sec-ondary districts which may reflect the presenceof higher fixed costs at the secondary level Tomotivate this it follows Alesina and Spolaore(1997) modeling jurisdictional creation as atrade-off between the benefits of large jurisdic-tions and the costs of heterogeneity in largepopulations6

To illustrate their approach consider an aream that has population Z and contains T typesof individuals These individuals desire a publicgood g and the issue is how many local juris-dictions should be created for its provision In-dividuals of different types are located at adistance h from each other where this capturesheterogeneity the greater h the more differentindividuals are along a given dimension Eachtype has a mass equal to so Z T Eachperson has a utility function Ui g(A li) y ti where g 0 0 A 0 y is incomeand ti and li are respectively the tax paid byindividual i and his distance from the publicgood

In the case of education the issue of interestis the number of school districts into which anarea splits In the model one school and twoborders characterize a district The cost of eachschool is k k k1S where S is each districtrsquospopulation and k and k1 are fixed and variablecosts respectively The social plannerrsquos solu-tion is to locate the school in the middle of eachdistrict and to create equally sized districts inthe amount N (T2)(ghk) Indexing areasby m this suggests a reduced form expressionfor district availability

2 See Helen F Ladd (2002) Derek Neal (2002) andPatrick J McEwan (2004) for reviews of the literature onvouchers

3 For instance Chang-Tai Hsieh and Urquiola (2003)consider Chilersquos nationwide voucher program under whichthe private enrollment share ranges from 0 to about 60percent across municipalities

4 These arise when a district operating many schoolsexplicitly ties the attendance at a given school to a givenresidential area

5 In other work Randall W Eberts and Timothy J Gron-berg (1981) and Amy B Schmidt (1992) present results

that although generally consistent with the possibility thatTiebout choice leads to sorting are not always significantW Norton Grubb (1982) studies whether districts becomerelatively more homogeneous over time His results onincome are consistent with this but those on racial structureare not For background on how district-based residentialsorting has limited the effects of desegregation policies seealso Gary Orfield and Frank Monfort (1992) and Rivkin(1994)

6 Alesina et al (2000) similarly analyze the availabilityof local functional jurisdictions


(1) Nm fhm gm m k m










(2) Pm 0 1 Nm 2 Xm m










Primary

Primary

Secondary

Secondary






(3) Plm 0 1 Nlm m 2

M

m Zm lm

























own MA694 558 48075 559 471 5555


909 498 48075






141 164 333




their home049 004 51518 049 004 5555 049 005 333


004 005 51518 004 005 5555 003 004 333












districtsNo of

districts


districtsNo of

districts

(1) (2) (3) (4) (5) (6)









Percent pop poor 100 34 231 003 019(81) (16) (471)

Median income 00 00 00 008 033(00) (00) (00)



Population 13 02 176 003 067(03) (01) (37)





02(01)

R2 0102 0340 0390 0566N (districts) 331 331 331 331 138 331










R Srm2


III Results


A Sorting






















(1) (2) (3) (4) (5)

Panel A Race


(11) (30) (11) (19) (27)[015] [004] [019] [021] [022]




Panel B Education















B Interpretation























(1) (2) (3) (4) (5) (6)










IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




REFERENCES






































(1) Nm fhm gm m k m










(2) Pm 0 1 Nm 2 Xm m










Primary

Primary

Secondary

Secondary






(3) Plm 0 1 Nlm m 2

M

m Zm lm

























own MA694 558 48075 559 471 5555


909 498 48075






141 164 333




their home049 004 51518 049 004 5555 049 005 333


004 005 51518 004 005 5555 003 004 333












districtsNo of

districts


districtsNo of

districts

(1) (2) (3) (4) (5) (6)









Percent pop poor 100 34 231 003 019(81) (16) (471)

Median income 00 00 00 008 033(00) (00) (00)



Population 13 02 176 003 067(03) (01) (37)





02(01)

R2 0102 0340 0390 0566N (districts) 331 331 331 331 138 331










R Srm2


III Results


A Sorting






















(1) (2) (3) (4) (5)

Panel A Race


(11) (30) (11) (19) (27)[015] [004] [019] [021] [022]




Panel B Education















B Interpretation























(1) (2) (3) (4) (5) (6)










IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




REFERENCES










































Primary

Primary

Secondary

Secondary






(3) Plm 0 1 Nlm m 2

M

m Zm lm

























own MA694 558 48075 559 471 5555


909 498 48075






141 164 333




their home049 004 51518 049 004 5555 049 005 333


004 005 51518 004 005 5555 003 004 333












districtsNo of

districts


districtsNo of

districts

(1) (2) (3) (4) (5) (6)









Percent pop poor 100 34 231 003 019(81) (16) (471)

Median income 00 00 00 008 033(00) (00) (00)



Population 13 02 176 003 067(03) (01) (37)





02(01)

R2 0102 0340 0390 0566N (districts) 331 331 331 331 138 331










R Srm2


III Results


A Sorting






















(1) (2) (3) (4) (5)

Panel A Race


(11) (30) (11) (19) (27)[015] [004] [019] [021] [022]




Panel B Education















B Interpretation























(1) (2) (3) (4) (5) (6)










IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




REFERENCES







































(3) Plm 0 1 Nlm m 2

M

m Zm lm

























own MA694 558 48075 559 471 5555


909 498 48075






141 164 333




their home049 004 51518 049 004 5555 049 005 333


004 005 51518 004 005 5555 003 004 333












districtsNo of

districts


districtsNo of

districts

(1) (2) (3) (4) (5) (6)









Percent pop poor 100 34 231 003 019(81) (16) (471)

Median income 00 00 00 008 033(00) (00) (00)



Population 13 02 176 003 067(03) (01) (37)





02(01)

R2 0102 0340 0390 0566N (districts) 331 331 331 331 138 331










R Srm2


III Results


A Sorting






















(1) (2) (3) (4) (5)

Panel A Race


(11) (30) (11) (19) (27)[015] [004] [019] [021] [022]




Panel B Education















B Interpretation























(1) (2) (3) (4) (5) (6)










IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




REFERENCES
















































own MA694 558 48075 559 471 5555


909 498 48075






141 164 333




their home049 004 51518 049 004 5555 049 005 333


004 005 51518 004 005 5555 003 004 333












districtsNo of

districts


districtsNo of

districts

(1) (2) (3) (4) (5) (6)









Percent pop poor 100 34 231 003 019(81) (16) (471)

Median income 00 00 00 008 033(00) (00) (00)



Population 13 02 176 003 067(03) (01) (37)





02(01)

R2 0102 0340 0390 0566N (districts) 331 331 331 331 138 331










R Srm2


III Results


A Sorting






















(1) (2) (3) (4) (5)

Panel A Race


(11) (30) (11) (19) (27)[015] [004] [019] [021] [022]




Panel B Education















B Interpretation























(1) (2) (3) (4) (5) (6)










IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




REFERENCES













































districtsNo of

districts


districtsNo of

districts

(1) (2) (3) (4) (5) (6)









Percent pop poor 100 34 231 003 019(81) (16) (471)

Median income 00 00 00 008 033(00) (00) (00)



Population 13 02 176 003 067(03) (01) (37)





02(01)

R2 0102 0340 0390 0566N (districts) 331 331 331 331 138 331










R Srm2


III Results


A Sorting






















(1) (2) (3) (4) (5)

Panel A Race


(11) (30) (11) (19) (27)[015] [004] [019] [021] [022]




Panel B Education















B Interpretation























(1) (2) (3) (4) (5) (6)










IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




REFERENCES













































R Srm2


III Results


A Sorting






















(1) (2) (3) (4) (5)

Panel A Race


(11) (30) (11) (19) (27)[015] [004] [019] [021] [022]




Panel B Education















B Interpretation























(1) (2) (3) (4) (5) (6)










IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




REFERENCES




















































(1) (2) (3) (4) (5)

Panel A Race


(11) (30) (11) (19) (27)[015] [004] [019] [021] [022]




Panel B Education















B Interpretation























(1) (2) (3) (4) (5) (6)










IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




REFERENCES













































B Interpretation























(1) (2) (3) (4) (5) (6)










IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




REFERENCES























































(1) (2) (3) (4) (5) (6)










IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




REFERENCES







































IV Conclusion






(1) (2) (3) (4) (5) (6)














APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




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APPENDIX




(1)


(2)


(3)

Totalprimary

(4)

Totalsecondary

(5)

Ratio(4)(5)

(6)



Secondary

Secondary

PrimaryPrimary




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