Vouchers for Private Schooling in Colombia

Vouchersfor Private Schooling in Colombia: Evidence from a RandomizedNatural Experiment

By JOSHUA ANGRIST, ERIC BETTINGER, ERIK BLOOM, ELIZABETH KING, AND MICHAEL KREMER*

Colombiaused lotteries to distribute vouchers which partially covered the cost of privatesecondary school for students who maintained satisfactory academic progress.Three years after the lotteries, winners were about 10 percentage points morelikely to have nished8th grade, primarily because they were less likely to repeatgrades, and scored 0.2 standard deviations higher on achievement tests. Thereis some evidence that winners worked less than losers and were less likely to marryor cohabitas teenagers.Bene ts to participants likely exceeded the $24 per winneradditional cost to the government of supplying vouchers instead of public- schoolplaces. (JEL I22,J13, I28)

Whilethe academic controversy over school portionof total enrollment is 2– 3 timeshigher providersand school vouchers has raged most thanin industrialized nations (Estelle James, intenselyin the United States, private schools 1993).Problems with public schools are usually accountfor onlyabout 11 percent of U.S. en- moresevere in low-incomecountries, since the rollment(U.S. Departmentof Education,1998). qualityand integrity of public sector service Moreover,over half of Americanparents report deliveryis highlycorrelated with income levels thatthey are very satis ed with the public (James E.Rauchand Peter B. Evans,2000). In schoolstheir children attend. In the developing Indianschools, for example,a recentstudy world,in contrast, private enrollment as a pro- foundthat one-third of headmasters were absent atthe time of the researchers’ visit (PROBE Team,1999), while in Kenya, Paul Glewwe et *Angrist:Department ofEconomics, MIT, 50 Memorial al.(2000) found that teachers were absent28 Drive,Cambridge, MA 02142;Bettinger: Department of percentof the time. The view that private Economics,Weatherhead School of Management, Case schoolsfunction better than public schools in Western Reserve University,Cleveland, Ohio 44106; thedeveloping world has prompted calls for Bloom:Asian DevelopmentBank, 6 ADBAvenue,Man- governmentsin poor countries to experiment daluyongCity, MM 0401,Philippines; King: Development Research Group,The World Bank, 1818 H Street NW, withdemand-side nancingprograms such as Washington,DC 20433;Kremer: Department ofEconom- vouchers(e.g., George Psacharopolous et al., ics, HarvardUniversity, Littauer Center 207,Cambridge, 1986). MA02138.Special thanks go tothesurvey and eldteam Thispaper presents evidence on theimpact of inBogota ´:ClaudiaGonzalez, Marcela Monsalvo,Ana Go´mez, anda dedicatedteam ofinterviewers from Javeriana Uni- oneof the largest school voucher programs to versity;in the United States, we hadthe help of Emily date,the Programa de AmpliaciońdeCobertura Conover,Helen Lee, BrianPasquinelli, and especially delaEducaciońSecundaria(PACES), aColom- CristinaEstrada. We are alsograteful to Jorge Estrada for bianinitiative that provided over 125,000 pupils helpinterpreting Colombian ID numbers,and to Jose Úribe withvouchers covering somewhat more than forarranging for use ofatestingsite. Finally, thanks go to theWorld Bank and the National Institutes of Health for halfthe cost of private secondary school. funding,and to Alberto Abadie, Jere Behrman,Adriana Voucherswere renewableas long as students Kugler,David Levine, Lant Pritchett, Petia Topalova,and maintainedsatisfactory academic performance. seminar participantsat Bancode la Repu´blica,University of Sincemany vouchers were awardedby lottery, California–Berkeley, Harvard University, MIT, the NBER, NorthwesternUniversity, and Princeton University for com- we usea quasi-experimentalresearch design ments.This document does not necessarily reect theposi- comparingeducational and other outcomes of tionof theAsian DevelopmentBank or theWorld Bank. lotterywinners and losers. Subject to a variety 1535 1536 THEAMERICANECONOMIC REVIEW DECEMBER2002 ofcaveats, the resulting estimates provide evi- Inaddition to increased educational attain- denceon program effects that are similar to mentand academic achievement, there is also thosearising from arandomizedtrial. As far as someevidence that the voucher program af- we know,ours is the rst studyof a private- fectednoneducational outcomes. In particular, schoolvoucher program in a developingcoun- lotterywinners were lesslikely to be married or tryto take advantage of randomly assigned cohabitingand worked about 1.2 fewer hours treatment.1 perweek (again, mostly a differencefor girls). Asurveyof three applicant cohorts shows no Bothof these results suggest an increasedfocus signicant differences between lottery winners onschooling among lottery winners. andlosers in enrollmentthree years after appli- Whilecomparisons between winners and los- cation,with most pupils in boththe winner and ers providea simplestrategy for assessingpro- losergroups still in school. But lottery winners gramimpact, our survey indicates that only were 15percentagepoints more likely to attend about90 percent of lottery winners had ever privateschools rather than public schools. usedthe voucher or any other type of scholar- Moreover,lottery winners had completed an ship,while 24 percentof losersreceived schol- additional0.1 years of schooland were about10 arshipsfrom othersources. It therefore seems percentagepoints more likely than losers to reasonableto think of lotterywin/ lossstatus as havecompleted eighth grade, primarily because aninstrument for scholarshipreceipt in a two- theyrepeated fewer grades.Although high rates stageleast-squares (2SLS) setup.There is a ofgrade repetition are a widelyrecognized prob- strong rst stagehere, though the relationship lemin LatinAmerica (see, e.g., Psacharopoulos betweenvoucher status and scholarship use is andEduardo Ve ´lez,1993; Hanan Jacoby, 1994), notdeterministic. Instrumenting for scholarship reducedrepetition need not indicate greater usewith lottery win/ lossstatus suggests that learning.We thereforeadministered achieve- scholarshipuse generated effects on gradecom- menttests to a subsetof the pupils surveyed. pletionand test scores that are roughly 50 per- Thetest results suggest that, on average,lottery centlarger than the reduced-form effect of winnersscored about 0.2 standard deviations winningthe lottery. higherthan losers, a largebut only marginally Thelast part of thepaper presents a scaland signicant difference. The effect on girls is cost-benet analysisof the voucher program. largerand more precisely estimated than the Mostlottery winners would have attended pri- effecton boys. vateschool anyway, at least for afew years,and thereforereduced their educational expenditure inresponse to the program. On the other hand, voucherwinners who were inducedto switch 1 U.S.studies in this mold include Jay Green et al.(1996) from publicto private schools greatly increased andCecilia ElenaRouse (1998), who evaluated a voucher theireducational expenditure, since the voucher lotteryin Milwaukee. Rouse’ s estimates, whichcontrol for attrition,show modest increases inmath scores among coveredonly about half the cost of private voucherrecipients. Other U.S. studies include William G. school.On balance, winners’ gross school fees Howellet al.(2000), Bettinger (2001a), and Daniel Mayer exceededthose of losersby about70 percentof et al.(2002), who evaluate variousprivate scholarship pro- theamount they received from thevoucher. grams. Chang-TaiHsieh andMiguel Urquiola (2002) examine alarge-scale voucherprogram in Chile but do not Winnerspaid greater fees becausethey were take advantageof random assignment. Rosemary Bellew morelikely to go to private schools, and be- andKing (1993) assess asmaller programin Bangladesh. causesome winners who would have gone Theliterature on public/ privatecomparisons in the United toprivate schools anyway switched to more States isextensive. See, e.g.,William N. Evansand Robert expensiveprivate schools. Moreover, lottery M.Schwab(1995) and Derek Neal (1997).Donald Cox and Emmanuel Jimenez (1990)compare publicand private winnersworked less, so that, on balance,house- schoolsin Colombia and Tanzania, and Jimenez et al. holdswinning the lottery actually devoted more (1991)summarize comparisonsin vecountries. See also resourcesto education than the voucher face theHarry A.Patrinosand David L. Ariasingham(1997) value.We alsoestimate that the voucher pro- surveyof demand-side nancingin poor countries. Jere Behrman et al (2000)and Glewwe et al.(2000) use ran- gramcost the government about $24 more per domizationto examine othereducational interventions in winnerthan the cost of creatinga publicschool developingcountries. placement.These costs to participants and the VOL. 92 NO. 5 ANGRISTET AL.:VOUCHERS FOR PRIVATE SCHOOLING 1537 governmentare likely to have been more than Colombia’s primary-schoolage children were outweighedby the bene ts of the voucher to enrolledin 1993, only 75 percent of the eli- participants—in the form ofthe economic re- giblepopulat ionwas enrolledin secondar y turnto increasededucational attainment and test schools.Among children of eligible age in the scores. poorestquintile of the population, 78 percent Anumberof channels could potentially ac- were enrolledin primary school, but only 55 countfor thePACES program’s effectson par- percentwere enrolledin secondar yschool ticipants.The program clearly shifted some (FabioSa ńchezand Jairo Me ńdez,1995; note participantsfrom publicto private school, and thatsecondary school covers grades 6 –11in pupilswho shifted may have bene tted from the Colombia). opportunityto attend private schools. There is ThePACES programtargeted low-income alsoevidence that some pupils who would have familiesby offering vouchers only to children attendedprivate school anyway were ableto residingin neighborhoods classi ed as falling attendmore expensive private schools. Finally, intothe two lowest socioeconomic strata (out of voucherrecipients may have had greater incen- sixpossible strata). Applicants had to submit a tivesto focus on schoolbecause vouchers could utilitybill to establish residential location and onlybe renewed for thosepupils who did not vouchereligibility. Targeting was enhancedby repeatgrades. restrictingvouchers to children who attended Thepaper is organized as follows. Section I publicprimary schools. Almost half of children providesbackground on educationin Colombia from therichest income quintil eattended anddescribes the PACES programin more de- privateprimary schools. Studies by Patricia tail.Section II discussesdata and presents de- Morales-Cobo(1993) and Roc ´‡oRiberoand scriptivestatistics from oursurvey. Section III JaimeTenjo (1997) suggests that the targeting discussesthe effect of the program on school was largelyeffective in Bogota ´. choiceand basic educational outcomes. Section PACES voucherswere worthonly about IVreportsthe effect of winning a voucheron US$190at the time of our survey. The maxi- testscores and noneducation outcomes. Section mumvoucher value was setinitially to corre- Vdiscussesthe use of lotterywin/ lossstatus as spondto the average tuition of low-to-middle aninstrument to identify the causal effect of costprivate schools in Colombia’ s threelargest receivinga scholarship.Finally, Section VI cities.Schools charging less than the vouchers’ looksat theeffect of the program on household facevalue received only their usual tuition. andgovernment expenditure, and compares PACES vouchersbecame less generous over programcosts with the bene ts to participants. timebecause they did not keep up with in a- SectionVII concludesthe paper. tion,and hence recipients had to supplement voucherswith additional payments to cover I.Background schoolfees. Our surveydata show matriculation andmonthly fees for privateschools attended TheColombian government established the byvoucher applicants in 1998 averaged about PACES programin late 1991 as part of awider $340,so mostvoucher recipients supplemented decentralizationeffort and in an attempt to ex- thevoucher with private funds. By way of com- pandprivate provision of publicservices (King parison,the average annual per-pupil public ex- etal., 1997). The program, which was partly penditurein Colombia’ s publicsecondary- fundedby theWorld Bank, was alsomotivated schoolsystem in 1995 was justover $350 asan effort to quickly expand school capacity andto raise secondary-school enrollment rates 2 (Kinget al., 1998). Although89 percent of townshave little room for additional pupils in spite of projectedenrollment growth. Other problems mentioned in thereport include poor primary-school preparation, weak 2 PACESwas launchedin November 1991 with adver- schoolmanagement, lack ofteacher preparedness,lack of tisements inprint and on radio soliciting applicants in textbooks,and shortages of other supplemental materials. participatingcities (AlbertoCaldero ń,1996).A WorldBank Theearly 1990’s was ageneralperiod of reform andliber- report(1993) on Colombian secondary schools notes that alizationin Colombia; see, forexample, Adriana D. Kugler mostschools operated two or three shiftsand that some (1999). 1538 THEAMERICANECONOMIC REVIEW DECEMBER2002

(DNP, 1999),and public-school parents in our hadlower pupil– teacher ratios and better facilities. sampletypically paid tuition or fees ofroughly Clearly,then, relatively elite private schools $58.Per capitaGNP inColombia is around optedout of the PACES program.Reasons for $2,280(World Bank, 1999). thismay include delays in payment of voucher Toqualify for avoucher,applicants must fundsto schools and bureaucracy in theColom- havebeen entering the Colombian secondary- bianInstitute for Education,Credit and Training schoolcycle which begins with grade 6, andbe Abroad(ICETEX), whichran the program. aged15 or under. Prior toapplying, students Moreover,vouchers were insufcient to cover mustalready have been admitted to a partici- muchof the tuition at more expensive schools, patingsecondary school (i.e., one that would andsome school managers probably viewed the acceptthe voucher). 3 Participatingschools had prospectof anin ux of pupilsfrom low-income tobe located in participating towns, which in- backgroundsas undesirable.On the other hand, cludedall of Colombia’s largestcities. Just un- manyprivate schools in Colombiaserving low- derhalf of private schools in the ten largest incomepopulations apparently welcomed the citiesaccepted vouchers in 1993. PACES program. Participatingschools tended to serve lower- Voucherrecipients were eligiblefor auto- incomepupils, and to have lower tuition than maticrenewal through eleventh grade, when nonparticipatingprivate schools. Schools with a Colombianhigh school ends, provided the re- vocationalcurriculum were alsooverrepre- cipient’s academicperformance warranted pro- sentedamong those in the program. Participat- motionto the next grade. Students failing a ingprivate schools included for-pro t schools, gradewere supposedto be dropped from the religious-afliated schools, and schools run by PACES program.Figures from Calderoń(1996) charitablefoundations. Initially, vouchers could showthat, on average, 77 percent of recipients beusedat both for-pro t andnonpro t schools, renewedtheir vouchers, and estimates from our butafter 1996, for-pro t schoolswere excluded. 4 dataare similar. By way of comparison, the Thenumber of vouchers in use in any one year nationalhigh-school promotion rate was about peakedat roughly 90,000 in 1994 and 1995. There 70percent. Students who transferred from one were approximately3.1 million secondary-school participatingprivate school to another could, in pupilsin Colombia in 1995, 37 percent of whom principle,transfer the voucher to the new attendedprivate schools. In Bogota ´,roughly58 school.In practice, however, our survey sug- percentof 567,000 secondary-school pupils at- gestsmany students who transferred after win- tendedprivate school. ninglost their vouchers. Test-scorecomparisons reported by King et Citiesand towns used lotteries to allocate al.(1997) show achievement levels in partici- voucherswhen demand exceeded supply. Mu- patingprivate schools were veryclose to those nicipalgovernments paid 20 percent of the inpublic schools, though signi cantly below vouchercost, while the central government paid achievementlevels in nonparticipating private 80percent. Each municipality decided how schools.Pupil– teacher ratios and facilities were manyvouchers to fund, subject to a maximum similarin public and participating private allocatedto towns by the central government. schools,and many of the teachers in the private Thisallocation was determinedby estimating schoolsmost likely to participate in thePACES theshortfall between primary-school enroll- programwere moonlightingor retired public- mentand the available space in public second- schoolteachers. Nonparticipating private schools aryschools. Voucher award rates therefore variedconsiderably by cityand year, depending ontheratio of applicantsto available vouchers. 3 Backgroundinformation in this section is takenfrom RegionalICETEX ofces worked with individ- Calderoń(1996),King et al.(1997), and unpublished ICE- ualmunicipalities to determine the number of TEXdocuments. vouchersto befunded, to checkschool require- 4 Thiswas duelargely to reported problems with low- mentsfor participation,and to monitor imple- qualityfor-pro t schoolscreated toexploit the vouchers. Calderoń(1996)notes that even before the nonpro t restric- mentationof the program. The Bogota ÍCETEX tionwas imposed,only 15 percent of Bogota ´’svoucher ofce provided software and instructions to re- studentsattended such institutions. gionalof ces for thepurposes of randomselec- VOL. 92 NO. 5 ANGRISTET AL.:VOUCHERS FOR PRIVATE SCHOOLING 1539 tionof applicants in cases of oversubscription. recent.Interviews were completedwith 55 per- We obtainedcopies of lists of lottery winners centof lotterywinners and 53 percentof lottery andlosers from ICETEX ofces. 5 losers.Although this response rate is far from ideal,the fact that winners and losers were almostequally likely to be interviewed is en- II.The ApplicantSurvey couragingbecause the question of sampleselec- tionbias turns on whether voucher status is A. DescriptiveStatistics correlatedwith response probabilities (see, e.g., Angrist,1997). Because response probabilities Beginningin the summer of 1998, we inter- arevirtually uncorrelated with voucher status, viewedroughly 1,600 PACES applicants,strat- thereshould be little bias from ourfailure to ifyingto obtain approximately equal numbers interviewall applicants. 7 ofwinnersand losers. Interviewing was limited Thetypical applicant was about13 years old tothe 1995 and 1997 applicant cohorts from atthetime of application,while average age on Bogotaándthe 1993 applicant cohort from thesurvey date varied from 13for 1997appli- Jamundi,a suburbof Cali. These years and cantsto 17 for 1993applicants. About half of citieswere chosenfor acombinationof scien- theapplicants were male.Roughly 85 percentof tic andpractical reasons. The largest and applicantswere stillin school, enrolled in longest-runningvoucher program was inBogota ´, gradesranging from sixthfor the1997 cohort to andour survey team was basedthere. Cali is eighthor ninth for the1993 cohort. Cohorts Colombia’s second-largestcity and therefore advanceless than one grade per year because of alsoimportant, but almost no Cali applicants repetition.The descriptive statistics also show reportedphone numbers, so we concentratedon thatalmost 90 percent of the applicants we asuburb,Jamundi. Telephones were usedfor interviewedstarted sixth grade in private themajority of interviews, primarily to reduce school.This re ects the fact that eligibility for costs,but also because of interviewersafety and PACES voucherswas conditionalon admission logisticalconsiderations. In principle, the lot- toa participatingprivate school. Thus, most terywas random within localitiesand condi- lotterylosers went to privateschool anyway, at tionalon whether households had access to a leastfor oneyear. On the other hand, only 63 telephone.The results should therefore yield percentof applicants were stillin private school internallyvalid estimates of thecausal effect of asof the survey date. theprogram on voucher applicants with access toa telephonein surveyed cities. Over 80per- centof applicantshad access to aphone,and in B. PersonalCharacteristics and theBogota ´1995cohort, 88 percent had access VoucherStatus toa phone,possibly via a neighbor. Table1 reportsdescriptive statistics for the Thereis little evidence of any association samplingframe, attemptedcontacts, and com- betweenwin/ lossstatus and the individual pletedinterviews. 6 Therewere 6,156applicants inthe three applicant cohorts of interest. We attemptedto interviewalmost 3,000 applicants, 7 Thevast majority of nonresponders were peoplewe obtainingan overallresponse rate of 54percent couldnot reach bytelephone, either because theyhad anda responserate of almost61 percentfor the movedor because thetelephone number we hadno longer 1997Bogota ´lottery.The higherresponse rate in worked.Roughly 3 percentof families contactedrefused to themost recent lottery is not surprising since answer. Theonly signi cant difference inresponse rates by win/lossstatus is for the Jamundi cohort. In what follows, contactinformation for 1997applicants is more we presentresults for the Bogota ´1995cohort and the combinedcohorts separately. Complete follow-up is the holygrail of education research. Evencareful evaluation 5 Ina few cities, thelocal ICETEX of ce assigned studiesusing randomized and quasi-randomized designs vouchersbased on pupils’ primary-school performance in- (e.g.,Rouse, 1998; Alan B. Krueger and Diane M.Whitmore, stead ofrandomly. 2001)are basedon samples withsubstantial loss to follow- 6 TheData Appendixin our working paper (Angrist et up.Similarly, Howell et al.(2000) report follow-up rates al.,2001) provides additional information about the survey. similar toours for U.S. voucher trials inthree cities. 1540 THEAMERICANECONOMIC REVIEW DECEMBER2002

TABLE 1—SAMPLE DESIGN AND SURVEY RESPONSE DATA

Bogota´ Bogota´ Jamundi Combined Variable 1995 1997 1993 sample Test-takers A. Population: N 4,0441,770 342 6,156 — Percentage awarded vouchers58.8 84.7 50.0 65.8 —

B. AttemptedInterviews: N 2,249457 279 2,985 473 Percentage awarded vouchers50.0 51.6 50.2 50.3 53.9 Responserate 0.5230.606 0.591 0.542 0.598 Winner rate 0.5280.619 0.650 0.553 0.624 Loser rate 0.5180.593 0.532 0.531 0.571

C. CompletedInterviews: N 1,176277 165 1,618 283 Percentage awarded vouchers50.4 52.7 55.2 51.3 55.6 Householdvisit 0.0540.004 0.782 0.120 0.093 Age at time ofapplication12.6 12.4 12.5 12.6 12.6 (1.3)(1.4) (1.9) (1.4) (1.2) Age onsurveydate (from 15.0 13.1 16.9 14.9 15.6 surveydata) (1.3) (1.4) (1.5) (1.7) (1.2) Male 0.5100.495 0.424 0.499 0.511 Started6th grade in private 0.910 0.880 0.669 0.880 0.832 Started7th grade in private 0.763 0.731 0.626 0.744 0.731 Currentlyin private school 0.618 0.738 0.506 0.628 0.698 Highestgrade completed 7.6 6.0 8.6 7.4 7.7 (0.940)(0.480) (1.1) (1.1) (0.910) Currentlyin school 0.8360.957 0.778 0.851 0.841

Notes: Standarddeviations for nonbinary variables are shownin parentheses. Sample sizes may differacross rows.Data are from1998 household surveys. “ Age at time ofapplication” isimputed from the National Identi cation number reported on the application. characteristicsmeasured in our data from servations.We used rst namesto assign sex Bogota´,althoughwinners and losers are less for about80 percent of the applicants. A nal comparablein the 1993 Jamundi cohort. This variablefrom theapplicant record is a dummy canbe seenin Table2, whichreports means and for whetherthe applicant reported a phone differencesby win/ lossstatus for allapplicants number. inthestudy population, for sampledapplicants, Winnersand losers have similar telephone andfor thesample of completed surveys. The access,age, and sex mix in the 1995 and 1997 samplingprocess began with lists showing ap- Bogota´data.As afurthercheck on randomness, plicantID numbers,names, addresses, and we comparedwin rates by school in schools phonenumbers, separately for winnersand withmore than 20 applicantsto city averages in losers.To obtain demographic characteristics theBogota ´datafrom 1995.No school had a win for allapplicants, whether surveyed or not, we ratethat differed signi cantly from thecity av- codedsex from namesand imputed age erage.In the Jamundi-93 sample, however, usingID numbers(which incorporate birth- thereare signi cant differences in average age days).Imputed age is subject to error since13 andgender by win/ lossstatus. Because the dif- percentof applicants have invalid ID numbers ferencesbetween winners and losers in the asdetermined by the ID numbercontrol digit. Jamundilottery may indicate nonrandom as- We excludedobservations in which the appli- signmentof vouchers, and because the 1997 cantwas youngerthan 9 orolder than 25. In Bogota´cohortis too recent for agoodreading practice,this restriction affected only two ob- onsome outcomes, we presentresults from the VOL. 92 NO. 5 ANGRISTET AL.:VOUCHERS FOR PRIVATE SCHOOLING 1541

TABLE 2—PERSONAL CHARACTERISTICSAND VOUCHER STATUS

Combined Bogota´1995Bogota ´1997Jamundi 1993 sample Test-takers Loser Won Loser Won Loser Won Loser Won Loser Won Dependentvariable means voucher means voucher means voucher means voucher means voucher A. Datafrom PACES Application: Has phone 0.8820.009 0.828 0.029 0.301 0.068 0.825 0.017 — — (0.011) (0.025) (0.052) (0.010) Age at time ofapplication 12.7 20.086 12.7 20.227 12.7 20.383 12.7 20.133 — — (1.3)(0.045) (1.5) (0.102) (1.5) (0.162) (1.4) (0.040) Male 0.4930.013 0.484 0.007 0.386 0.114 0.483 0.019 — — (0.017) (0.044) (0.055) (0.015) N 1,5193,661 256 1,736 166 334 1,941 5,731 — —

B. Datafor All Attempted Contacts: Has phone 1 — 1 —0.3700.082 0.938 0.008 — — (0.059) (0.006) Age at time ofapplication 12.8 20.118 12.6 20.193 12.8 20.595 12.7 20.177 — — (1.3)(0.060) (1.5) (0.136) (1.6) (0.183) (1.4) (0.052) Male 0.500 20.007 0.488 20.0200.372 0.102 0.486 0.001 — — (0.022) (0.048) (0.061) (0.019) N 1,0352,067 212 448 135 272 1,382 2,787 — —

C. Survey Data: Age at time ofsurvey 15.0 20.013 13.2 20.259 17.2 20.375 14.9 20.107 14.9 20.160 (1.4)(0.078) (1.4) (0.171) (1.4) (0.217) (1.7) (0.068) (1.4) (0.162) Male 0.5010.004 0.527 20.0470.365 0.110 0.492 0.008 0.447 0.053 (0.029) (0.061) (0.077) (0.025) (0.060) Mother’s highestgrade 5.9 20.0795.9 0.654 4.4 1.46 5.8 0.183 5.5 20.277 completed (2.7)(0.166) (2.7) (0.371) (2.7) (0.494) (2.7) (0.144) (2.9) (0.351) Father’s highestgrade 5.9 20.4315.5 0.929 5.2 0.737 5.8 20.042 4.0 20.171 completed (2.9)(0.199) (2.5) (0.388) (2.9) (0.640) (2.9) (0.170) (3.3) (0.392) Mother’s age 40.7 20.027 38.7 20.146 43.6 20.736 40.6 20.07640.3 0.459 (7.3)(0.426) (6.6) (0.808) (8.8) (1.42) (7.4) (0.362) (6.6) (0.811) Father’s age 44.40.567 41.9 0.265 45.5 1.92 44.1 0.537 43.5 1.18 (8.1)(0.533) (7.3) (0.973) (9.1) (1.61) (8.1) (0.453) (7.7) (1.06) Father’s wage ( .2min0.100 0.005 0.088 20.008 0.133 20.092 0.101 20.0030.052 0.083 wage) (0.021) (0.043) (0.056) (0.018)(0.222) (0.039) N 5831,176 131 277 74 165 788 1,618 124 283

Notes: Thetable reports voucher losers’ means andthe estimated effect ofwinning a voucher.Numbers inparentheses are standarddeviations in columns of means andstandard errors incolumnsof estimated vouchereffects. Modelsused for the estimates inPanels A andB includecontrol for city and year ofapplication;those for Panel C addcontrols for type of survey andinstrument, neighborhood of residence, andmonth of interview.Sample size varies byrow.The maximum sample size isshownin each panel.The sample forthe outcome “ Age at time ofapplication”is restricted toapplicants 9 –25years old.

Bogota´-95sample separately from theresults (1) yic 5 X9ib 0 1 a0 Zi 1 dc 1 «ic for thepooled sample including all three cohorts. where yic isthe dependent variable for child i III.Impacton ScholarshipUse, from applicationcohort c (dened by city and SchoolChoice, and Schooling year); Xi representsa vectorof individual and surveycharacteristics like age, sex, and whether Our estimatesof lottery effects are based on thesurvey was telephoneor inperson; Zi is an thefollowing regression model: indicatorfor whetherchild i wonthe voucher 1542 THEAMERICANECONOMIC REVIEW DECEMBER2002

TABLE 3—EDUCATIONAL OUTCOMES AND VOUCHER STATUS

Bogota´1995 Combinedsample Basic 119 Basic 119 Loser No Basic barrio Basic barrio means controls controls controls controls controls Dependentvariable (1) (2) (3) (4) (5) (6) Usingany scholarship 0.057 0.509 0.504 0.505 0.526 0.521 insurveyyear (0.232) (0.023) (0.023) (0.023) (0.019) (0.019) Everused a scholarship0.243 0.672 0.663 0.662 0.636 0.635 (0.430) (0.021) (0.022) (0.022) (0.019) (0.019) Started6th grade in 0.877 0.063 0.057 0.058 0.066 0.067 private (0.328) (0.017) (0.017) (0.017) (0.016) (0.016) Started7th grade in 0.673 0.174 0.168 0.171 0.170 0.173 private (0.470) (0.025) (0.025) (0.024) (0.021) (0.021) Currentlyin private 0.539 0.160 0.153 0.156 0.152 0.154 school (0.499) (0.028) (0.027) (0.027) (0.023) (0.023) Highestgrade 7.5 0.164 0.130 0.120 0.085 0.078 completed (0.960) (0.053) (0.051) (0.051) (0.041) (0.041) Currentlyin school 0.831 0.019 0.007 0.007 20.002 20.002 (0.375) (0.022) (0.020) (0.020) (0.016) (0.016) Finished6th grade 0.943 0.026 0.023 0.021 0.014 0.012 (0.232) (0.012) (0.012) (0.011) (0.011) (0.010) Finished7th grade 0.847 0.040 0.031 0.029 0.027 0.025 (excludesBogota ´97) (0.360) (0.020) (0.019) (0.019) (0.018) (0.018) Finished8th grade 0.632 0.112 0.100 0.094 0.077 0.074 (excludesBogota ´97) (0.483) (0.027) (0.027) (0.027) (0.024) (0.024) Repetitionsof 6thgrade 0.194 20.066 20.059 20.059 20.049 20.049 (0.454) (0.024) (0.024) (0.024) (0.019) (0.019) Everrepeated after 0.224 20.060 20.055 20.051 20.055 20.053 lottery (0.417) (0.023) (0.023) (0.023) (0.019) (0.019) Totalrepetitions since 0.254 20.073 20.067 20.064 20.058 20.057 lottery (0.508) (0.028) (0.027) (0.027) (0.022) (0.022) Years inschool since 3.7 0.058 0.034 0.031 0.015 0.012 lottery (0.951) (0.052) (0.050) (0.050) (0.044) (0.043) Sample size 562 1,147 1,577

Notes: Thetable reports voucher losers’ means andthe estimated effect ofwinninga voucher. Numbers inparentheses are standarddeviations in the column of means andstandard errors incolumns of estimated vouchereffects. Thesamples usedto estimate 7th-and 8th-grade completioneffects excludeBogota ´1997.The sample size forthese outcomesis 1,304 in columns(5) and (6). The regression estimates are frommodels that include controls for city, year ofapplication,phone access, age,type of surveyand instrument, strata ofresidence, and monthof interview.

lottery;and dc isan applicant cohort effect to A. Effectson Scholarship Use controlfor thefact that the probability of win- andSchool Choice ningvaried by city and year. The coef cient of interest is a0.We estimate(1) usingthree sets We beginwith a simpleanalysis of the effect ofcontrolvariables: “ nocontrols,” i.e., exclud- ofwinning the lottery on private-school schol- ing the Xi variables;“ basiccontrols” including arshipreceipt and the choice between public the Xi variables;and “ basicplus barrio con- andprivate school. The most immediate effect trols”which includes the Xi variablesplus 19 ofthe lottery was toincrease the likelihood of neighborhooddummies in the Bogota ´-95 receivinga private-schoolscholarship. This can sample.8 beseenin the rst row ofTable3, whichshows thatat the time of oursurvey, voucher winners were 51percentagepoints more likely than los- 8 Neighborhoodsin this case are large areas ordistricts. ers tohave been using some kind of scholarship VOL. 92 NO. 5 ANGRISTET AL.:VOUCHERS FOR PRIVATE SCHOOLING 1543

(includingnon-PACES scholarships). Not all subsidiesto private education do not directly winnerswere usingtheir PACES vouchersin increaseoverall enrollment. 10 However,since thesurvey year. This is because 15 percent of manypublic secondary schools in Colombia winnerswere notinschoolat all,and another 16 were turningaway applicants due to overcrowd- percentwere inpublic schools, and therefore ing,PACES islikely to have opened up places ineligiblefor scholarships.Some lottery win- inpublic school for otherpupils by reducing nersalso lost their voucher after repeating a public-schoolqueuing. grade(7 percent), while 5 percentswitched to nonparticipatingprivate schools or failed to B. Effectson Schooling completethe paperwork for atransfer.Others attendedschools that stopped accepting vouch- Lotterywinners completed more schooling ers orlosttheir vouchers for unreportedreasons. thanlosers, and were lesslikely to repeat Justas not all winners were usinga scholarship, grades.For example,lottery losers had com- somelosers obtained scholarships from pro- pleted7.5 years of schoolingat thetime of our gramsother than PACES andone loser was survey,but winners in the 1995 Bogota ´sample awardeda PACES voucherafter reapplying the completedan additional 0.12– 0.16 years (0.8 followingyear. yearsin the full sample). As notedearlier, there At thetime of the survey, enrollment rates was nostatistically signi cant effect on enroll- were 0.83for losersand 0.85 for winnersin the ment.The effect on years of schooling and the Bogota´-95sample, an insigni cant difference. lackof aneffect on enrollment is primarilythe Theestimates in Table 3 alsoshow that most resultof a reducedprobability of grade repeti- PACES applicantsentered sixth grade in a pri- tionfor winners.This is re ected in a sharp vatesecondary school, and most nishedsixth increasein the likelihood lottery winners had gradewhether or not they won a voucher.But nishedeighth grade as ofthesurvey date, with lotterywinners were 6–7percentagepoints asmallerimpact on seventh-grade completion. morelikely than losers to have begun sixth Inthe Bogota ´-95sample, over 20 percent of gradein private school, and 15– 16 percentage losershad repeated a gradesince beginning pointsmore likely to be inprivate school at the sixthgrade, and almost 20 percent repeated timeof our survey. The effect of winning the sixthgrade. But the probability of graderepeti- PACES lotteryon the probability of private- tionwas reducedby 5– 6 percentagepoints for schoolattendance was evenlarger in seventh lotterywinners. grade,probably because losers were morelikely Theestimates of a0 changelittle as the list of tohave left private school by then. controlvariables changes, a resultto be ex- Theseresults suggest the decision between pectedsince the voucher lottery was random. publicand private school was sensitiveto vari- Theestimation results are also similar in the ationin the price of private school induced by Bogota´-95and full samples, and are largely theprogram, while the decision whether to at- invariantto the inclusion of neighborhood ef- tendschool was not. 9 Thisis consistent with a fects.Estimates and standard errors for the modelin which those households most willing Bogota´-95sample also change little in models andable to pay for educationattend private withschool effects. school;a middlegroup attends public school; Separateresults by sex, reported in Ta- andthose least willing or able to pay do not ble4, showmoderately larger effects on educa- attendat all. In this case, no one is on the tionalattainment for girls,though the pattern of private-school/no-schoolmargin, and so small sexdifferences in the effects on private-school enrollmentare not clear-cut. Results for the Bogota´-95sample show male lottery winners 9 We can convertthe private-school enrollment effects to anelasticity as follows.PACES vouchers reduced the mar- ginalcost of private-school attendance by about 50 percent 10 PACESsubsidies were initiallylarge enoughto cover whilevouchers increased private-schoolenrollment in sev- theentire cost of private school, and may haveshifted enthgrade by about 17 percent. The implied elasticity of recipientsfrom no school to private school when the pro- privateenrollment with respect tomarginalcost is therefore gram started.However, the voucher value was later eroded 0.34. byin ation. 1544 THEAMERICANECONOMIC REVIEW DECEMBER2002

TABLE 4—EDUCATIONAL OUTCOMES AND VOUCHER STATUS, BY GENDER

Coefcient on voucher status Bogota´1995 Combinedsample Male Female Male Female Loser Basic Loser Basic Basic Basic Dependentvariable means controls means controls controls controls Started6th grade in 0.857 0.082 0.897 0.027 0.058 0.077 private (0.351) (0.025) (0.304) (0.021) (0.023) (0.021) Started7th grade in 0.646 0.187 0.699 0.143 0.166 0.177 private (0.479) (0.035) (0.460) (0.033) (0.031) (0.029) Currentlyin private 0.543 0.136 0.535 0.171 0.124 0.182 school (0.499) (0.039) (0.500) (0.039) (0.033) (0.033) Highestgrade 7.4 0.124 7.6 0.140 0.056 0.122 completed (0.990) (0.076) (0.934) (0.065) (0.062) (0.052) Currentlyin school 0.843 20.020 0.819 0.035 20.026 0.029 (0.365) (0.029) (0.386) (0.027) (0.024) (0.022) Finished6th grade 0.932 0.014 0.954 0.032 0.003 0.027 (0.252) (0.018) (0.210) (0.013) (0.017) (0.012) Finished7th grade 0.825 0.026 0.869 0.041 20.003 0.022 (0.380) (0.029) (0.338) (0.025) (0.024) (0.020) Finished8th grade 0.589 0.095 0.674 0.105 0.066 0.078 (0.493) (0.039) (0.470) (0.036) (0.030) (0.027) Repetitionsof 6thgrade 0.229 20.087 0.160 20.036 20.070 20.033 (0.506) (0.037) (0.395) (0.030) (0.031) (0.023) Everrepeated after 0.254 20.083 0.195 20.029 20.076 20.035 lottery (0.436) (0.034) (0.370) (0.031) (0.028) (0.025) Totalrepetitions since 0.296 20.101 0.213 20.031 20.079 20.037 lottery (0.550) (0.042) (0.459) (0.033) (0.035) (0.026) Calendaryears in 3.7 20.029 3.6 0.091 20.041 0.081 schoolsince lottery (0.962) (0.077) (0.941) (0.063) (0.067) (0.055) Sample size 280575 282 572 779 798

Notes: Thetable reports voucher losers’ means andthe estimated effect ofwinninga voucher. Numbers inparentheses are standarddeviations in columns of means andstandard errors in columnsof estimated vouchereffects. Theregression estimates are frommodels that include controlsfor city, year ofapplication, whether applicant has phone,age, type of surveyand instrument,strata ofresidence, andmonth of interview. withan insignicant 0.12 more years of school- Thegreater probability of eighth-gradecom- ingwhile female lottery winners obtained 0.14 pletionand lower repetition rates for lottery yearsmore of schooling, a statisticallysigni - winnersseem like desirable outcomes. In fact, canteffect. Differences by sex are more pro- highrates of graderepetition in Latin America nouncedin the full sample, with an insignicant arewidely seen as symptomaticof poorlyfunc- 0.06more years of schooling for boys,and a tioningpublic schools. 12 Butthe interpretation statisticallysigni cant 0.12 more years of ofthese effects is complicated by the fact that schoolingfor girls.It should also be noted that pupilswho failed a gradewere supposedto whileeffects for boysare almost entirely due to forfeitPACES vouchers.Private schools may graderepetition, the effects for girlsappear to thereforehave had an incentive to promote pu- comefrom bothreduced grade repetition and pilswith vouchers even if theirperformance did additionaltime spent in school. 11 notmeet normal promotional standards. To ex-

11 There islittleevidence that the effect ofwinningthe vouchervaried with applicants’ socioeconomic strata of 12 Forexample, R. W.Harbisonand Eric A.Hanushek residence orparents’ education. However, estimates for (1992)and Psacharopolous and Ve ´lez (1993)use repetition subgroupsare imprecise. rates as ameasure ofschoolquality in Colombia and Brazil. VOL. 92 NO. 5 ANGRISTET AL.:VOUCHERS FOR PRIVATE SCHOOLING 1545 plorethis possibility, we lookat effects on test Colombianwriting score was closeto the aver- scoresand noneducational outcomes in thenext agescore for Americantenth graders. section. TheTest Sample. —Of the1,176 Bogota ´1995 applicantssurveyed, 473 were invitedfor test- IV.Effectson Test Scores and ing.Statistics for pupilsinvited and tested ap- NoneducationOutcomes pearin the last column of Table 1. Of the473 invited,283 were tested,an overall response A. Effectson Test Scores rateof about60 percent. The test-response rate isabout 5 percenthigher for winners,but the We testedchildren from the1995 applicant differencein responserates by voucherstatus is cohortin three Bogota ´neighborhoods.These notstatistically signi cant. The personal char- neighborhoodswere chosenbecause they had acteristicsof those tested are generally similar relativelylarge numbers of winners and losers, tothose of the full Bogota ´-95sample. Also andbecause of the availability of suitable (and encouragingis the fact that, conditional on tak- safe) testingsites. The tests were administered ingthe test, there is little evidence of differ- in1999, approximately one year after our encesin personal characteristics between householdsurvey and three years after the chil- voucherwinners and losers. This comparison drenapplied for theprogram. The test sample canbe seen in the last column of Table2. was drawnfrom applicantsfor whomwe had surveydata. Participants were solicitedby tele- TestResults. —Table5 reportsestimates of phone,followed by handdelivery of lettersde- theeffect of winning the voucher lottery on test scribingthe purpose of the test and inviting scores.Columns (1) and(2) ofTable 5 show pupilsto be tested. Those who failed to appear resultsfrom modelswith and without covari- onthe test day were invitedagain for asecond ates.13 Columns(3) and(4) presentthe results testing,except at the last sitting. To encourage ofestimating a singlevoucher coef cient for participation,refreshments were providedat stackedsubject results, in models with a pupil eachsite, and each test concluded with the raf e randomeffect. That is, we estimated ofa bicycleand other prizes. Pupils were also given5,000 or 10,000 pesos (U.S. $3.23or (2) y is 5 X9ib 0 1 a0 Zi 1 di 1 «is $6.45)to cover travel costs. The invitation letter notedthe offer ofrefreshments, travel reim- where yis is pupil i’sscorein subject s, and di bursement,and raf e. See the Data Appendix isarandomeffect used to adjuststandard errors for additionaldetails on thetesting, available at for thefact that there is likelyto bewithin-pupil http://www.aeaweb.org/aer/contents/ . correlationacross subjects. Note that test-score Our evaluationused LaPrueba de Realiza- resultsare reported in standard deviation units. cio´n, agrade-specic multiple-choiceachieve- Lotterywinners scored just over 0.2 standard menttest for nativeSpanish speakers, published deviationsmore than lottery losers, though this byRiverside.We administeredonly the mathe- differenceis (not surprisingly, given the small matics,reading, and writing subtests, each tak- testsample) only marginally signi cant. Ac- ingabout 30 minutes. This test was chosen cordingto U.S. normsfor La Prueba, two-tenths becauseColombian educators participated in ofa standarddeviation is roughly the score gain testdevelopment and the test had been used associatedwith one additional school year previouslyin Colombia (Nancy S. Coleet al., (Coleet al., 1993). This effect should probably 1993).The Appendix to our working paper (Angristet al.,2001) compares test results from theHispanic-American test-norming popula- tionsfor grades9 and10 with the results from 13 ourtest. Colombian ninth-graders in our sample Theresults in columns (1) and (3) are frommodels thatinclude site dummies only.The results in columns (2) scoredlower than American pupils in mathe- and(4) are frommodels that include controls for age, sex, matics,but they had reading skills slightly bet- parents’schooling, strata ofresidence, typeof interview, terthan American tenth-graders. The average andsurvey form. 1546 THEAMERICANECONOMIC REVIEW DECEMBER2002

TABLE 5—TEST RESULTS

OLS results OLS with RE with Sample results covariates RE covariates size Variable (1) (2) (3) (4) (5) A. AllApplicants: Totalpoints 0.217 0.205 282 (0.116)(0.108) Math scores 0.178 0.153 282 (0.120)(0.114) Readingscores 0.204 0.203 283 (0.115)(0.114) Writingscores 0.126 0.128 283 (0.116)(0.105) Pooledtest scores 0.170 0.148 846 (0.095)(0.088) Mathand reading scores 0.192 0.162 568 (0.101)(0.096)

B. Female Applicants: Totalpoints 0.199 0.263 146 (0.162)(0.126) Math scores 0.292 0.346 146 (0.145)(0.141) Readingscores 0.117 0.152 147 (0.158)(0.136) Mathand reading scores 0.204 0.235 293 (0.130)(0.117)

C. MaleApplicants: Totalpoints 0.204 0.170 134 (0.169)(0.189) Math scores 0.010 0.004 134 (0.178)(0.187) Readingscores 0.276 0.220 134 (0.183)(0.190) Mathand reading scores 0.143 0.087 268 (0.160)(0.160)

Notes: Robuststandard errors are reportedin parentheses. Standard errors incolumns (1) and (2)are corrected forwithin-school-of-application clustering. Test scores are instandard deviationunits. The estimates incolumns(2) and (4) are frommodels that include controls forapplicant’ s age,gender, parents’ schooling, strata ofresidence, andtype of survey and instrument.Columns (3) and (4) models include random effects (RE)for each test subject. Thesample for“ Pooledtest scores”includes three observationsper student (one for each subject)while “ Mathand reading scores” includes two observations per student.

beseenas large,since subjects were testedthree scoresfor lotterywinners, with the largest ef- yearsafter applying to the program. Lottery fectsfor modelsthat stack math and reading winnersalso scored higher on all subtests, scoresonly. thoughthe only signi cant difference is for Modelsestimated separately for boysand readingscores ( t 5 1.8).Theresults for the girlsgenerate larger and more precise effects for stackedsubjects, reported in columns (3) and girlsthan boys. For example,the estimated ef- (4),also show marginally signi cantly higher fecton totalpoints for girls,reported in column VOL. 92 NO. 5 ANGRISTET AL.:VOUCHERS FOR PRIVATE SCHOOLING 1547

(2) ofPanel B for modelswith covariates, is anything,larger at the top of the distribution. 0.26 (SE 5 0.13).The corresponding estimate Standarderrors for theseestimate are, of course, for boys,reported in Panel C, is0.17 (SE 5 large,given the small sample. 0.19).The ndingof a strongereffect on girls echoessome of the survey results. B. OtherOutcomes Earlierwe notedthat reduced grade repetition amonglottery winners could theoretically have Table6 reportsestimates of the effect of beencaused by a reductionin promotion stan- winningthe lottery on noneducational out- dardsfor lotterywinners, as well as by in- comes.Approximately 1.6 percent of lottery creasedlearning or a changein school quality. losersfrom Bogota´were marriedor livingwith Comparingthe test scores of winnersand losers acompanion,a lowproportion consistent with whowere promotedprovides evidence that the thefact that the average age of survey respon- grade-repetitionresults are not due solely to dentswas about15. Since this outcome is rare, schools’lowering the bar for promotionof win- we estimatedprobit models as well as linear ners.If theprogram itself did not affect achieve- probabilitymodels. ment,but did lead schools to relax promotions Bothprobit marginal effects and ordinary standardsfor winners,then average test scores least-squares(OLS) estimatessuggest that mar- for lotterywinners who were promotedshould riageand cohabitation were reducedfor lottery belower than average test scores for lottery winners,a marginallysigni cant effect. There is loserswho were promoted. 14 Infact, the com- someevidence from thepooled sample that positetest scores of winners who were pro- lotterywinners were lesslikely to be working motedare about 0.14 standard deviations thanlosers, with the largest effects in Bogota ´. greater thanthe scores of promoted losers, al- Thereis also a signicant difference in hours thoughthe difference is not signi cant. worked.In particular, lottery winners worked Anotherpossible channel through which the 1.2fewer hoursper week than losers. This ef- programcould have reduced grade repetition is fectis larger and more precisely estimated for increasedeffort by voucher recipients in order girls.The reduction in work may be due to toavoidfailing a gradeand losing their vouch- incomeeffects for thehousehold, the greater ers.In this scenario, the program would have timedemands of privateschool relative to pub- beenjust as successful if it had made payment licschool, or increased incentives for lottery tostudentsconditional on satisfactoryacademic winnersto spend time studying so as to avoid performance,with no elementof schoolchoice. failinga gradeand losing the PACES voucher. Thiswould imply that the primary incentive effectshould be on those who are near the V.InstrumentalVariables Estimates of marginfor passingon to the next grade. How- ScholarshipEffects ever,quantile regression estimates (not reported here)suggest that the increase in test scores is Theanalysis so far focuseson reduced-form notcon ned to low quantiles of the score dis- effectsof winningthe lottery. In the discussion tribution.For readingand writing, there is no ofTable3, however,we notedthat some lottery strongpattern of differential effects across loserswere awardedother scholarships, while quantiles,while for math,the effects are, if somewinners failed to use or retain their PACES scholarships.This section discusses two-stageleast-square (2SLS) estimatesof the 14 Supposeschools promote if a randomvariable x, effectof ever receiving any scholarship using representingthe school’ s internalassessment ofthestudent, voucherwin/ lossstatus as an instrumental vari- isgreater thana cutoff c,whichtakes ontwovalues, c for W able(IV). Whileonly 6 percentof lottery losers winners and cL forlosers. Suppose cW , cL,buttest scores, T,andthe variable x are unaffectedby winning the lottery. useda scholarshipat thetime of the survey, 24 Thenthe expected test score forlottery losers whoare percenthad used a scholarshipat somepoint. In promoted is E(Tzx . cL).Theexpected score forwinners contrast,90 percent of winners used a scholar- willbe aweightedaverage ofthisand E(TzcW , x , cL). Average scores forpromoted losers willtherefore exceed shipat some time. The 2SLS estimates based on average scores forpromoted winners as longas E(Tzx) is thisdifference are necessarily larger than the increasingin x. reduced-formeffects of winning the lottery 1548 THEAMERICANECONOMIC REVIEW DECEMBER2002

TABLE 6—NONEDUCATIONAL OUTCOMES AND VOUCHER STATUS

Coefcient on voucherstatus Bogota´1995 Combinedsample Probit with Probit with Loser Basic basic Loser Basic basic means controls controls means controls controls Dependentvariable (1) (2) (3) (4) (5) (6) A. Maleand Female: Marriedor living 0.0160 20.0087 20.0066 0.0171 20.0094 20.0065 withcompanion (0.1256) (0.0059) (0.0038) (0.1297) (0.0056) (0.0034) Has child 0.0338 20.0103 20.0079 0.0303 20.0069 20.0055 (0.1809) (0.0096) (0.0075) (0.1714) (0.0079) (0.0062) Applicantis 0.1690 20.0297 20.0299 0.1616 20.02651 20.0254 working (0.3751) (0.0205) (0.0184) (0.3684) (0.0171) (0.0153) Numberof hours 4.881 21.222 — 4.417 20.8699 — working (12.3) (0.6441) — (11.60) (0.5235) — Sample size 5621,147 1,147 760 1,577 1,577

B. Male: Marriedor living 0.0036 20.0039 — 0.0027 20.0027 — withcompanion (0.0598) (0.0038) — (0.0518) (0.0026) — Applicantis 0.2321 20.0366 20.0336 0.2252 20.0283 20.0294 working (0.4230) (0.0331) (0.0324) (0.4183) (0.0278) (0.0261) Numberof hours 6.421 20.6376 — 6.198 20.6231 — working (13.69) (1.072) — (13.31) (0.8859) — Sample size 280575 575 373 779 778

C. Female: Marriedor living 0.0284 20.0100 20.0112 0.0309 20.0113 20.0114 withcompanion (0.1663) (0.0113) (0.0078) (0.1733) (0.0109) (0.0068) Pregnantor has 0.0603 20.0151 20.0155 0.0541 20.0092 20.0119 child (0.2384) (0.0179) (0.0138) (0.2266) (0.0147) (0.0110) Applicantis 0.1064 20.0314 20.0262 0.1005 20.0317 20.0240 working (0.3089) (0.0235) (0.0189) (0.3011) (0.0196) (0.0156) Numberof hours 3.351 22.116 — 2.704 21.499 — working (10.57) (0.6527) — (9.36) (0.5240) — Sample size 282572 572 388 798 798

Notes: Numbers inparentheses are standarddeviations in columns of means andstandard errors incolumns of estimated vouchereffects. Resultsare forsamples withnonmissing noneducationaland educational outcomes. Columns (2) and (3) show results from models that controlfor whether applicants had access toa phone,age, gender, type of survey and instrument,strata ofresidence, andmonth of interview. Columns (5) and (6) also include controlsfor city and year ofapplication. sincewinning the lottery is only imperfectly isthevectorof “basiccontrols” used in previous correlatedwith receiving a scholarship. tables.The associated rst-stagerelationship Theassumption that a scholarshipuse using Zi asan instrument is dummysatis es the exclusion restriction in an instrumentalvariables (IV) setupmotivates (4) si 5 X9ig 1 pZi 1 hi. 2SLSestimation of the equation: Theestimate of p isabout0.66 (SE 5 0.021) so (3) yi 5 X9ib 1 1 a1 si 1 ji thesecond-stage estimates can be expected to beabout50 percent larger than the correspond- where si isadummyfor scholarshipuse, and Xi ingreduced-form estimates. The interpretation VOL. 92 NO. 5 ANGRISTET AL.:VOUCHERS FOR PRIVATE SCHOOLING 1549

TABLE 7—OLS AND 2SLS ESTIMATESOF THE EFFECT OF EVER USING A PRIVATE SCHOOL SCHOLARSHIP

Coefcient on “ Everused a private-schoolscholarship” Bogota´1995 Combinedsample Loser Dependentvariable means OLS 2SLS OLS 2SLS Highestgrade 7.5 0.167 0.196 0.141 0.134 completed (0.965) (0.053) (0.078) (0.042) (0.065) In school 0.831 0.021 0.010 0.033 20.003 (0.375) (0.021) (0.031) (0.017) (0.026) Totalrepetitions since 0.254 20.077 20.100 20.069 20.091 lottery (0.508) (0.029) (0.042) (0.023) (0.035) Finished8th grade 0.632 0.114 0.151 0.108 0.127 (0.483) (0.028) (0.041) (0.025) (0.038) Test scores (total 20.099 0.379 0.291 — — points) (1.0) (0.111) (0.153) Marriedor livingwith 0.016 20.009 20.013 20.010 20.014 companion (0.126) (0.006) (0.009) (0.006) (0.009) N 562 1,147 1,577

Notes: Thetable reports loser means andOLS and 2SLS estimates oftheeffect ofever having useda private-schoolscholarship. Results are frommodels that control for city, year of application,whether applicant had access toa phone,age, type of survey and instrument, strata ofresidence, andmonth of interview.Robust standard errors are reportedin parentheses. Data forthe outcome “ Finished8th grade” in the combined sample doesnot include applicantsto the Bogota ´-1997voucher lottery. For the outcome “ Test scores (totalpoints),” thesample is restricted tothose individuals who took the exam. Inthe 2SLS speci cation, the endogenousregressor usedscholarship isinstrumentedwith voucher status.

of a1 inthiscase is as anapproximateeffect of elasticitieswith respect to U.S. nancialaid for treatmenton thesubset of scholarshipusers who collegestudents, though obviously not directly wouldnot have used a scholarshipwithout comparable.Another interesting result is the PACES (GuidoW. Imbensand Angrist, 2SLSestimate of the effect on testscores, 0.29, 1994).15 somewhatsmaller than the corresponding OLS The2SLS estimate of the effect of scholar- estimate.The 2SLS estimates are likely to be shipuse on highestgrade completed is about0.2 moreuseful for predictingthe impact of schol- inthe Bogota ´-95sample and 0.13 in the full arshipprograms on new scholarship recipients sample.These estimates are reported in Ta- thanare the reduced-form effects, which are ble7. Two-stage least-squares estimates of dilutedby take-up rates less than one and the vouchereffects on the probability of nishing availabilityof alternative nancing. eighthgrade are 13– 15 percenta gepoints, nearlya 25-percentincrease in completion VI.Impacton Householdand rates.This seems to be inthe ballpark of Susan GovernmentExpenditure M.Dynarski’s (2001)estimated completion Thissection discusses the impact of thepro- gramon household and government budgets. 15 At rst blush, private-schoolattendance mightappear We beginby showing that approximately 70 tobe the appropriate endogenous regressor fora 2SLS percentof voucher funds owedto increased setup.But this seems unlikelyto satisfy the required exclu- educationexpenditures, with the remainder go- sionrestriction since increased effortand increased school ingto educational spending that households qualityprobably also mediate theeffects ofthe voucher. Consistentwith this, in practice, 2SLSestimates treating wouldhave made without the voucher. Taking private-schoolattendance as anendogenous regressor gen- intoaccount the reduction in work by lottery erate estimates thatare implausiblylarge. winnerssuggests that winning the lottery induced 1550 THEAMERICANECONOMIC REVIEW DECEMBER2002

TABLE 8—MATRICULATION , TUITION FEES, AND VOUCHER STATUS FOR BOGOTA´ 1995 APPLICANTS

Conditionalon private-school Full sample attendance Loser No Basic Loser No Basic means controls controls means controls controls Variable (1)(2) (3) (4) (5) (6) Usingany scholarship in 0.054 0.497 0.494 0.085 0.709 0.696 survey year (0.227) (0.023) (0.023) (0.279) (0.027) (0.028) Currentlyin private school 0.530 0.156 0.152 1 — — (0.500) (0.029) (0.028) Currentlyin public school 0.290 20.140 20.146 0 — — (0.454) (0.025) (0.025) Scholarshipvalue 16.0 74.3 72.6 29.8 101.8 98.1 (64.2) (5.4) (5.4) (85.8) (7.6) (7.9) Scholarshipvalue 199.0 213.3 211.3 211.1 225.5 222.0 (conditionalon .0) (122.4) (19.1) (18.5) (118.2) (19.1) (18.5) Gross schoolfees 191.5 52.3 48.1 332.2 11.0 9.8 (188.3) (10.2) (11.0) (133.6) (10.7) (10.7) Net schoolfees 175.9 222.0 224.5 302.4 290.7 288.2 (185.6) (11.5) (9.9) (154.3) (11.6) (11.7) Gross schoolfees for 54.6 3.2 1.0 — — — publicschools (109.4) (13.4) (13.8) Currentlyusing scholarship 0.031 20.008 20.010 0.059 20.026 20.031 fromthe private school (0.173) (0.011) (0.012) (0.235) (0.019) (0.020) Sample size 5341,085 1,085 283 661 664

Notes: Thetable reports voucher losers’ means andthe estimated effect ofwinninga voucher. Numbers inparentheses are standarddeviations in columns of means andstandard errors in columnsof estimated vouchereffects. Sample sizes differfrom other tables because of missingfee data.The sample sizes differslightly across rowsbecause ofmissing data for “Currentlyusing scholarship from the private school” and the outcomes with the more comprehensivefee measure. Theregression estimates incolumns (3) and (6) are frommodels thatinclude controls for whether applicants had access toa phone,age, type of survey and instrument,strata ofresidence, andmonth of interview. householdsto devote more net resources to ed- guingthat the total social costs of providing ucation.The higher fees paidby voucher win- additionalschool places through the PACES nersare due primarily to winners’ greater vouchersystem were small,and therefore likelihoodof attending private school. How- dwarfedby the bene ts of the program to par- ever,there is also some evidence that appli- ticipants.The analysis in this section uses data cantswho would have attended private for the1995 Bogota ´applicantcohort only. schoolsanyway traded up to more expensive privateschools in response to winning the A. Impacton Household voucher.Since the voucher did not reduce the EducationalExpenditure costof private school at the margin, this result weighsagainst the simplest models of education Threeyears after the 1995 lottery in Bogota ´, ashuman-ca pitalinvestme ntwithout credit about55 percent of winners and 5 percentof constraints. loserswere stillreceiving scholarships (a result Theresults in subsection B suggestthat it from Table3 repeatedin the rst row ofTable costthe government about $24 more per lottery 8for thesample of observationswith usable fee winnerto provide school places through data).In this sample, 53 percent of loserswere PACES thanthrough the public system. Finally, stillin private school in the survey year, with subsectionC aggregatesthe impact on house- theprivate-school enrollment rate 15.2 percent holds,schools, and the government budget, ar- higherfor winnersafter control for covariates. VOL. 92 NO. 5 ANGRISTET AL.:VOUCHERS FOR PRIVATE SCHOOLING 1551

Amongapplicants to the Bogota ´-95lottery, schoolin the survey year. So most vouchers winnersreceived an average of $74 more in were receivedby applicants who would have scholarshipaid than losers, a resultreported in attendedprivate school without the vouchers. thefourth row ofTable 8. Conditional on re- Simplemodels of education as human-capital ceivinga scholarship,scholarship amounts were investmentwith perfect credit markets suggest similarfor winnersand losers, at roughly$200. thatsince PACES voucherswere worthonly Theestimates in Table 8 alsoshow gross ma- $190per year, while most private schools triculationand tuition fees were $52greater for costover $300 per year, vouchers were infra- lotterywinners than losers. Thus, the 1998 marginal.In other words, vouchers were not voucherexpenditures of $74per winner caused largeenough to have caused households to anincrease of $52 in gross fees for winners, increaseeducational spending by choosing a about70 percent of the extra amount received moreexpensive private school. 18 On the other bywinners on average. The remaining $22 of hand,winning the voucher could have led voucherfunds presumably increased noneduca- householdsto choose more expensive private tionalexpenditures by lottery winners. 16 schoolsif educational spending is limited by Asidefrom payingfor schoolfees, house- creditconstraints or if education has consump- holdsbear the opportunity cost of the effort tionvalue as well as investment value. studentsdevote to education. The estimates for Ina noncausal,purely accounting sense, the noneducationaloutcomes in Table 6 suggest $52of increased expenditure by winners on lotterywinners spent 1.2 fewer hoursworking schoolfees canbe decomposed into the effects eachweek. According to our survey data, the ofincreased private-school enrollment, and a averagehourly wage was 71cents. 17 Assuming switchto more expensive private schools by thatstudents work 48 weeks per year, this re- winners.Let Z beadummyfor lotterywin/ loss ductioncorresponds to an opportunity cost of statusas before, except we nowdrop “ i” sub- 1.2 3 $.71 3 48weeks, approximately $41. scriptsto simplify notation. Also, let R denote Combiningthe increase of $52 in expenditures typeof school attended (1 for private,0 for onfees andthe $41of lostearnings, we estimate public)and let F denoteeducation expenditure. thatPACES lotterywinners devoted $93 more Gross schoolfees conditionalon lottery win/ toeducation than losers in the survey year, or lossstatus (i.e., fees paidby pupils without 126percent of the $74 in extra scholarship subtractingvoucher amounts) are equal to assistancethey received. E@FzZ# 5 E@FzZ, R 5 1#P@R 5 1zZ# DisaggregatingEffects on Fees. —While winninghouseholds spent about $52 more on 1 E@FzZ, R 5 0#P@R 5 0zZ#. schoolfees, this average conceals important heterogeneity.Since vouchers covered only part Theoverall change in fees isalinearcombina- ofthecost of privateschool, families with chil- tionof changes in public/privateenrollment and drenwho were inducedto switch to private changesin fees chargedby schooltype. We can schoolincreased their educational expenditure simplifythe fee contrast between winners and sharply.However, most of the applicants who losersusing the fact that public-school fees lostthe lottery started private school in sixth changedlittle and overall school enrollment was gradeanyway, and over half were stillin private alsoaffected little, so that P[R 5 1zZ 5 1] 2 P[R 5 1zZ 5 0] ’ 2{P[R 5 0zZ 5 1] 2 P[R 5 0zZ 5 0]}.Thenwe havethe following ac- countingrelationship: 16 Theestimated displacementof private expenditure is evenlower when a more comprehensiveexpenditure measure is used.Lottery winners report an estimated $84more incomprehensivescholarship assistance (i.e.,including ex- 18 Tosee this,note that if education is pure human- penditureon uniforms and textbooks) and an extra $74more capital investment,people choose schools so that a school incomprehensiveeducational expenditure. costingone dollar more generates exactlyone more dollar 17 Conditionalon working, the average dailywage inour ofpresent discounted earnings. For people who would in sample was $5.71.We estimated thehourly wage assuming anycase haveattended a schoolcosting more than$190, the aseven-hourwork day. voucherdoes not affect this rst-ordercondition. 1552 THEAMERICANECONOMIC REVIEW DECEMBER2002

(5) E@FzZ 5 1# 2 E@FzZ 5 0# utedto increased private-school enrollment. However,for reasonsdiscussed below, this de- 5 $E@FzZ 5 1, R 5 1# 2 E@FzZ 5 1, R 5 0#% compositionprovides an incomplete picture of thecausal effect of the program on the fee 3 $P@R 5 1zZ 5 1# 2 P@R 5 1zZ 5 0#% distribution. Causaleffects on fees for familieswho would 1 P@R 5 1zZ 5 0#$E@FzZ 5 1, R 5 1# havesent their children to private school any- wayare dif cult to measure since we donot 2 E@FzZ 5 0, R 5 1#}. knowwho these families are. Simply comparing fees bywin/ lossstatus conditional on private- Inwords, the overall fee increase is caused by schoolattendance [the second term in (5), theprivate– public fee difference for winners, above]leads to a biasedestimate that is almost timesprivate-school enrollment effects of the certainlytoo low. To see this, let F0 be the program,plus the win/ losscontrast in fees for publicor privatefee a pupilwould pay if he or 19 private-schoolpupils. Theright-hand-side sheloses the lottery and let F1 bethe public or componentsof (5) areas follows: privatefee he or she would pay if he or she wins,and let R0 and R1 denoteprivate-school P@R 5 1zZ 5 1# 2 P@R 5 1zZ 5 0# 5 0.15 attendanceif a pupilloses or wins the lottery respectively.Similarly, let f0 bethe private- E@FzZ 5 1, R 5 1# 2 E@FzZ 5 1, R 5 0# schoolfee a pupilwould pay if he or sheloses thelottery and let f1 betheprivate-school fee a 5 343 2 58 5 285 pupilwould pay if he or she wins. Thus f0 5 F0R0 and f1 5 F1R1.We imaginethat these E@FzZ 5 1, R 5 1# variablesare de ned for everypupil, though in practice,we canonly observe F0, R0, and f0 for 2 E@FzZ 5 0, R 5 1# 5 11 losers and F1, R1, and f1 for winners. E[ f1 2 f0zf0 . 0]isthe effect on fees for thosewho P@R 5 1zZ 5 0# 5 0.53. wouldattend private school even if they were to losethe lottery. The observed contrast in fees for Thisimplies a totaleffect of $49,which is less private-schoolpupils can be written as follows: than$52 because of theapproximation used to simplify(5), with $43 due to school switching. (6) E@FzZ 5 1, R 5 1# 2 E@FzZ 5 0, R 5 1# Thus,in an accounting sense, the bulk of the changein household expenditure can be attrib- 5 E@f1 2 f0zf0 . 0#

1 $E@f1zf1 . 0# 2 E@f1zf0 . 0#%. 19 Withoutsimpli cation the comparison is Theterm in braces re ects selection bias in the E@FzZ 5 1# 2 E@FzZ 5 0# conditional-on-positivecontrast. Under mild as- 20 5 P@R 5 1zZ 5 0# sumptions,this term is negative. Assuming,as

3 $E@FzZ 5 1, R 5 1# 2 E@FzZ 5 0, R 5 1#% 20 Thisis easy toshow in a modelwhere f 1 5 h( f 0) 1 E@FzZ 5 1, R 5 1# forany increasing transformatio n.More generally, winners whoattend private school only if theywin probably 3 $P@R 5 1zZ 5 1# 2 P@R 5 1zZ 5 0#% attendcheaper privateschools than those who attend regardless. Suppose,for example, thatschool quality 1 P@R 5 0zZ 5 0# complements abilityand higher-qual ityschools are more expensive.Then low-ability children attend public 3 $E@FzZ 5 1, R 5 0# 2 E@FzZ 5 0, R 5 0#% schoolsif they lose the lottery and attend cheap private schoolsif theywin the lottery, while high-abilit ychildren 1 E@FzZ 5 1, R 5 0# attendexpensive private schools whether or notthey win avoucher.Alternatively ,considera modelwith credit 3 $P@R 5 0zZ 5 1# 2 P@R 5 0zZ 5 0#%. constraintsin which the poor attend public school; the VOL. 92 NO. 5 ANGRISTET AL.:VOUCHERS FOR PRIVATE SCHOOLING 1553

seemslikely, that f1 $ f0,theleft-hand side E@FMzF0 . m0 ~u!# 2 E@F0zF0 . m0 ~u!# thereforeis a lowerbound on the causal effect,

E[ f1 2 f0z f0 . 0]. 5 $pu E@F1zF0 . m0 ~u!, R0 5 1# Theparameter E[ f1 2 f0z f0 . 0] is not identied withoutfurther assumptions (see e.g., 1 ~1 2 pu !E@F0zF0 . m0 ~u!, R0 5 0#} Gary Chamberlain,1986), though the previous discussionsuggests we cantreat the observed 2 E@F0zF0 . m0 ~u!#. contrastin fees for private-schoolstudents as a lowerbound. Under mild assumptions, we can Note that obtaina reasonablytight upper bound on this and arelatedfamily of parameters: E[ f1 2 f0z f0 . E@F0zF0 . m 0 ~u!# m0(u)] where m0(u) is the u-quantileof the losers’ feedistribution. By choosing m0(u) 5 0, we 5 pu E@F0zF0 . m0 ~u!, R0 5 1# bound E[ f1 2 f0z f0 . 0],while picking points at higherquantiles, we measurethe effect on those 1 ~1 2 pu !E@F0zF0 . m0 ~u!, R0 5 0#. whowould have spent more on private schooling inthe absence of the lottery. For example,we can Therefore, boundthe effect of winning the lottery on private- schoolfees for thosewho would have spent more E@FMzF0 . m0 ~u!# 2 E@F0zF0 . m0 ~u!# thanthe voucher amount ($190) on private-school feesin the absence of the lottery. This result is 5 pu E@F1 2 F0zF0 . m0 ~u!, R0 5 1#. statedformally below. Since f0 5 R0F0,thisimplies PROPOSITION: Supposethat F 1 $ F0. Let m0(u ) be the u quantileof thedistribution of F $E@FMzF0 . m0 ~u!# 2 E@F0zF0 . m0 ~u!%/pu forlosers, with m 1(u ) dened similarly for winners. Then 5 E@f1 2 f0z f0 . m0 ~u!#

(7) E@f 1 2 f0z f0 . m 0 ~u!# whichis the quantity we seekto bound. Also, since F1 $ FM $ F0 for allapplicants, # $E@FzZ 5 1, F . m1 ~u!# E[F1zF1 . m1(u )] $ E[F1zF0 . m0(u )] $ E[FMzF0 . m0(u )],andwe have 2 E@FzZ 5 0, F . m0 ~u!#} E@F1zF1 . m 1 ~u!# 2 E@F0zF 0 . m 0 ~u!# 4 P@R 5 1zZ 5 0, F . m0 ~u!#. $ E@FMzF0 . m0 ~u!# 2 E@F0zF0 . m0 ~u!#. PROOF: De ne FM 5 F01(F0 # m0(u )) 1 Byrandomization, E[F1zF1 . m1(u )] 5 F01(F0 . m0(u ), R0 5 0) 1 F11(F0 . E[FzZ 5 1, F . m1(u )] and E[F0zF0 . m0(u ), R0 5 1).Notethat FM 5 F1 for m0(u )] 5 E[FzZ 5 0, F . m0(u )] and pu 5 householdsabove the quantile who would have P[R 5 1zZ 5 0, F . m0(u )],whichimplies attendedprivate schools anyway. Otherwise, (7) andcompletes the proof. FM 5 F0. Thus, F1 $ FM $ F0. Let pu 5 Tosee why the upper bound works in the P[R0 5 1zF0 . m0(u )]. Then case where u 5 0, note that E(FM 2 F0) is the averagedifference between winners’ and losers’ fees dueto households who would have attendedprivate schools in any case trading up to moreexpensive private schools. This is less richattend private school; and the very rich attend ex- thanthe observed difference in total fee pay- pensiveprivate schools. Then lottery winners who would haveattended public school if they lost the lottery will mentsby win/ lossstatus, E(F1 2 F0). Econo- attendcheaper schoolsthan lottery winners who would metricintuition for thisresult comes from the haveattended private school even if they lost. factthat in parametric sample selection models, 1554 THEAMERICANECONOMIC REVIEW DECEMBER2002

TABLE 9—LOWER/UPPER BOUNDS OF VOUCHER EFFECTS ON MATRICULATIONAND TUITION FEES FOR BOGOTA´ 1995 APPLICANTS WHO WOULD HAVE ATTENDED PRIVATE SCHOOL AND PAID MORE THAN CUTOFF FEES

Loser Corresponding probabilityof Loseraverage quantile of Loseraverage private- private-school Dollar loser fee fee above school fee above Upper Lower cutoff distribution quantile attendance cutoff bound bound 190.052nd percentile 370.5 0.973 368.1 38.4 2.9 (104.7) (0.163) (95.1)(9.5) (8.9) 283.260th percentile 396.7 0.981 392.5 31.4 9.2 (94.4) (0.136) (83.0)(9.7) (8.8) 335.870th percentile 424.8 0.981 419.3 32.1 17.7 (92.7) (0.136) (78.7)(11.3) (10.0) 370.180th percentile 460.2 0.972 452.8 36.5 14.0 (96.0) (0.167) (78.3)(9.3) (12.3) 427.090th percentile 523.3 0.943 511.9 48.3 27.7 (101.0) (0.233) (74.5)(16.8) (18.3)

Notes: Theupper bound above a givenpercentile is computedin a two-stepprocess. First, we estimate thedifference between winners’and losers’ matriculation fees conditionalon being greater thanthe given quantile in their respective distributions.Second, we dividethis difference bythe probability that losers above the given percentile attend private school. The lower bound abovea cutoffis computed by differencing winners’ and losers’ fees conditionalon private-school attendanceand conditional on being greater thanthe cutoff. See textfor further details. controllingfor theprobability of sample selec- reportsof public-school fees above$190 are tioneliminates selection bias. Comparing win- probablyin error; others refer toa handfulof nersand losers at the same quantiles equalizes elitepublic schools that charge signi cant fees). the“ probabilityof selection” if F1 5 h(F0) for Thelower bound on E[ f1 2 f0zf0 . 190] is somemonotone increasing transformation, h. In about$3, but the upper bound is $38. The fact,with no public-school fees, the bound is voucheramount of $190is the 0.52 quantile of exact when F1 5 h(F0). Moregenerally, dividing thefee distribution. Above this amount, the by P[R 5 1zZ 5 0, F . m0(u)] correctsfor thefact boundsare tighter. The estimated upper bounds thatsome of those with positive fees were attend- above0.6 range from $31to $48, while the ingpublic school, and the bound applies even lowerbounds range from $9to $28. The lower- withouta deterministiclink between F0 and F1. boundestimates are not signi cantly different Estimatesof the right-hand size of (7) are from zeroat the5-percent level. In some cases, reportedin Table 9, along with a lowerbound however,the lower bounds are close to a 10- usingthe biased comparison for quantilesanal- percentsigni cance level, while the upper ogousto (6); this is, E[FzZ 5 1, R 5 1, F . boundsallow for effectson the order of 10 m0(u )] 2 E[FzZ 5 0, R 5 1, F . m0(u )]. percentof fee costs and 20 percent of the As notedearlier, this is aplausiblelower bound vouchervalue. Thus, it seems likely that win- becauseof negative selection bias. Note also nersin the upper half of the fee distribution thatany reasonable behavioral model would spent5– 10 percent more on privateschools than predictthat a familythat spent less than the theyotherwise would have. This implies that voucheramount on private school without a themarginal propensity to spend voucher in- voucherwould spend more after the voucher. comeon more expensive private schools was Wethereforefocus on boundingeffects that are nontrivial,counter to asimplemodel of human- conditionalon payingpre-voucher fees equalto capitalinvestment without credit constraints. atleast the voucher amount, roughly $190. Amonglosers paying at least $190 in fees, PriceDiscrimination by Private Schools. theaverage fee was $371.Almost all of these —Anotherpotential source of increasedexpen- pupilswere inprivate school (in fact, some ditureon fees bywinners is price discrimina- VOL. 92 NO. 5 ANGRISTET AL.:VOUCHERS FOR PRIVATE SCHOOLING 1555 tion.There is littleevidence that private schools C. OverallCost and Bene ts discriminatedby charging more to applicants withPACES scholarships.The easiest way for Theextra society-wide educational resource schoolsto price discriminate was tooffer schol- costper lottery winner differs from theroughly arshipsto those less likely to be able to afford $24of extrapublic-education expenditure, since educationat thefull price (i.e., applicants with- householdsused part of the voucher funds to outPACES vouchers).In practice, however, we offseteducation costs they would have incurred foundlittle evidence of price discrimination. privately,and lost income from theirchildren’ s Our surveyindicates that roughly 6 percentof work.The average lottery winner received $74 losersin privateschool received a schoolschol- morethan the average loser in scholarship as- arship,while 3 percentof winners in private sistance,but spent only $52 more on gross schoolreceived a schoolscholarship. This is a schoolfees. Lottery winners earned $41 less smalland insigni cant difference. Per lottery thanlosers through work. Winning households’ winner(i.e., without conditioning on attending netresource contribution was therefore$52 (ad- privateschool), the difference is only about 1 ditionalschool fees) 1 $41(reduced earn- percent. ings) 2 $74(voucher) 5 $19.This implies that thesociety-wide additional educational resource B. Impacton the Government Budget costper lottery winner was approximately$24 (government) 1 $19(households) 5 $43. ThePACES programwas establishedin part Thecomparison of costsand bene ts should toexpandsecondary-school enrollment without takeaccount of thefact that three years of costs usingthe public system. We estimatethat the were incurredprior to our survey. The total cost programincreased public educational expendi- ofthe program can therefore be estimated by tureby about$24 per lottery winner, relative to multiplyingthe annual resource cost times the thecost of accommodatingthese pupils in pub- roughlythree years winners received vouchers, licschool. As discussedin Section III, winners for atotalof about3 3 24 5 $72in additional were nomorelikely than losers to attendschool, public-educationalexpenditureand 3 3 $43 5 butthe program probably did expand overall $129in total societal resource cost. Actual costs schoolenrollment by freeingup places in public areprobably somewhat higher, however, since schoolsas lotterywinners transferred to private vouchertake-up rates declined over time, with schools. 88percent of winners having ever used a Toseewhere the $24 gurecomes from, note voucher,and only 49 percent using it in the thatthe probability of attending public school, surveyyear. Multiplying costs by 88 percent/49 reportedin Table 8, fell by 0.14 for lottery percentfor the rst andsecond years yields an winners.The average per-pupil cost of apublic upperbound on the three-year cost of the pro- secondary-schoolslot was about$350, exclud- gramof about $195 using the $43/ year gure ingimplicit rental for schoolfacilities. In the for socialcosts. shortrun, the marginal cost of public-school Thesecosts are likely to have been small slotsmay differ from theaverage cost, but in the relativeto the bene ts for participants.Al- longrun, it seems reasonable to assume mar- thoughlottery winners gave up current earn- ginaland average costs will be similar.Assum- ings,they completed an additional 0.12 to 0.16 ingthe marginal cost of providingpublic-school gradesand scored approximately 0.2 standard placesequals the average cost, adding school deviationshigher on tests. Among U.S. His- spacesthrough PACES reducedlong-run ex- panicstudents who took the same test, the dif- penditureon public schools by 14 percent of ferencein test scores between seventh- and $350or roughly $50 per winner, so the extra eighth-graders,or between eighth- and ninth- publiceducational expenditure per lottery win- graders,was alsoabout 0.2 standard deviations, neris about $74 (to pupils) 2$50(in reduced sothe achievement gain from winningthe lot- public-schoolcosts) 5 $24.Moreover, allowing terymay be as large as that associated with a themarginal cost to differfrom averagecost by fullyear of schooling. Our estimatesusing a $100either way still leads to voucher program recentColombian labor-force survey show re- costsin the $10 – $40range. turnsto ayearof schoolingof about10 percent. 1556 THEAMERICANECONOMIC REVIEW DECEMBER2002

If thegain from theprogram is solely the eco- ThePACES programis of special interest be- nomicreturn to an additional 0.12 years of causemany vouchers were assignedby lottery, schooling,the program raised winners’ wages soprogrameffects can be reliablyassessed. Our by1.2percent per year, whereas if itisequalto resultssuggest that lottery winners bene tted thatfrom afullyear of schoolingit raised wages from highereducational attainment, primarily by10percent. Annual earnings of parents in our asaconsequenceof reducedgrade repetition, as samplewere about$2,400 per worker, and wellas from highertest scores and a lower PACES applicantsshould be ableto earnmore, probabilityof teencohabitation or employment. sincethe average parent had only 5.9 years of Our estimatesof the economic bene ts to par- educationwhile the average applicant had al- ticipantsfar exceedthe estimated costs. Most of readycompleted 7.5 years and was stillin theresults suggest PACES vouchershad a schoolat the time of our survey. We therefore strongereffect on theeducation of girlsthan on assumethe expected earnings of applicants are theeducation of boys. $3,000.Thus, PACES seemsvery likely to raise Our ndingssuggest that demand-side pro- lotterywinners’ wages by $36 per year, and gramslike PACES canbe a cost-effectiveway mightraise wages by asmuchas $300per year toincrease educational attainment and aca- ifhigher test scores have a grade-equivalent demicachievement, at least in countries like payoff.Discounted over applicants working Colombiawith a weakpublic-school infrastruc- lives,these bene ts easily outweigh the social tureand a well-developedprivate-education costsof the voucher program, which are prob- sector.A numberof channels could account for ablyno more than $195. theimpact of PACES vouchers.First, lottery Amorecomplete cost-bene t analysiswould winnerswere morelikely to have attended par- takeinto account the program’ s effectson non- ticipatingprivate schools, and these schools participants.Pupils left behind in public schools maybe better than public schools. Second, mayhave been hurt by the departure of moti- vouchersallowed some pupils who would have vatedclassmates for privateschools, as argued attendedprivate schools anyway to attend more byHsieh and Urqiola (2001), or alternatively, expensiveschools. Finally, because voucher re- publicschools may have responded positively cipientswho failed a graderisked losing vouch- toincreased competition, a possibilityconsidered ers,lottery winners had an incentive to devote byCaroline M. Hoxby(2000) and Bettinger moreeffort to school.The net effect is suchthat (2001b).Such general-equilibrium effects can- thebene t ofvoucher awards were morethan notbe assessed by comparing lottery winners enoughto offset the costs. In work in progress, andlosers. But since the partial-equilibrium we areassessing longer-term consequences of cost-benet analysisis clear-cut, and since only voucherreceipt. Preliminary results indicate 15percent of winners moved from publicto thatthe program increased secondary-school privateschools, any negative external effects on completionrates, and that college-entrance test nonparticipantswould have to have been ex- scoreswere higherfor lotterywinners than los- traordinarilylarge to outweigh program bene ts. ers.These results are indicative of greaterlearn- ingand seem unlikely to be due solely to greater incentivesfor PACES recipientsto avoid grade VII.Summary and Conclusions repetition.

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