Vouchers for Private Schooling in Colombia: Evidence from aRandomized Natural Experiment

By JOSHUA ANGRIST, ERIC BETTINGER, ERIK BLOOM, ELIZABETH KING,

AND MICHAEL KREMER*

Colombia used lotteries to distribute vouchers which partially covered the cost ofprivate secondary school for students who maintained satisfactory academicprogress. Three years after the lotteries, winners were about 10 percentage pointsmore likely to have finished 8th grade, primarily because they were less likely torepeat grades, and scored 0.2 standard deviations higher on achievement tests.There is some evidence that winners worked less than losers and were less likely tomarry or cohabit as teenagers. Benefits to participants likely exceeded the $24 perwinner additional cost lo the government of supplying vouchers instead of public-school places. (JEL 122, J13, 128)

While the academic controversy over schoolproviders and school vouchers has raged mostintensely in the United States, private schoolsaccount for only about 11 percent of U.S. en-rollment (U.S. Department of Education. 1998).Moreover, over half of American parents reportthat they are very satisfied with the publicschools their children attend. In the developingworld, in contrast, private enrollment as a pro-

* Angrist: Deparlmeni of Economics, MIT, 50 MemorialDrive. Cambridge. MA 02142: Beitinger: Department ofEcononiifs. Weacherhead School of Management. CaseWestern Reserve University. Cleveland. Ohio 44106:Bloom: Asian Development Bank. 6 ADB Avenue. Man-daluyong City, MM 0401. Philippines: King: DevelopmentResearch Group, The World Bank. 181 S^H Sireel NW,Washington. DC 2043.'̂ : Kremer: Department of Econom-ics. Harvard University. Littauer Center 207. Cambridge.MA 02138. Special thanks go to the survey and field teamin Bogota: Claudia Gonzalez. Marcela Monsalvo, Ana G6me:?:,and a dedicated team of interviewers from Javeriana Uni-versity: in the United States, we had the help of EmilyConover. Helen Lee, Brian Pasquinelli, and especiallyCristina Estrada. We are also grateful to Jorge Estrada forhelp interpreting Colombian ID numbers, and lo Jose Uribefor arranging for use of a testing site. Finally, thanks go tothe World Bank and the National Institutes of Health forfunding, and to Alberto Abadie. Jere Behrman. AdrianaKugler. David Levine. Lant Pritchett. Petia Topalova. andseminar participants at Banco de la Republica. University ofCaiifomia-Berkeley. Harvard University. MIT. the NBER.Northwestern University, and Princeton University for com-ments. This document does not necessarily reflect the posi-tion of the Asian Development Bank or the World Bank.

portion of total enrollment is 2-3 times higherthan in industrialized nations (Estelle James,1993). Problems with public schools are usuallymore severe in low-income countries, since thequality and integrity of public sector servicedelivery is highly correlated with income levels(James E. Rauch and Peter B. Evans, 2000). InIndian schools, for example, a recent studyfound that one-third of headmasters were absentat the time of the researchers' visit (PROBETeam, 1999), while in Kenya, Paul Glewwe etal. (2000) found that teachers were absent 28percent of the time. The view that privateschools function better than public schools inthe developing world ha.s prompted calls forgovernments in poor countries to experimentwith demand-side financing programs such asvouchers (e.g.. George Psacharopolous et al.,1986).

This paper presents evidence on the impact ofone of the largest school voucher programs todate, the Programa de Ampliacion de Coberturade la Educacion Secundaria (PACES), a Colom-bian initiative that provided over 125,000 pupilswith vouchers covering somewhat more thanhalf the cost of private secondary school.Vouchers were renewable as long as studentsmaintained satisfactory academic performance.Since many vouchers were awarded by lottery,we use a quasi-experimental research designcomparing educational and other outcome.s oflottery winners and losers. Subject to a variety

1535

1536 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

of caveats, the resulting estimates provide evi-dence on program effects thai are similar tothose arising from a randomized trial. As far aswe know, ours is the first study of a private-school voucher program in a developing coun-try to take advantage of randomly assignedtreatment.'

A survey of three applicant cohorts shows nosignificant differences between lottery winnersand losers in enrollment three years after appli-cation, with most pupils in both the winner andloser groups still in school. But lottery winnerswere 15 percentage points more likely to attendprivate schools rather than public schools.Moreover, lottery winners had completed anadditional 0.1 years of school and were about 10percentage points more likely than losers tohave completed eighth grade, primarily becausethey repeated fewer grades. Although high ratesof grade repetition are a widely recognized prob-lem in Latin America (see, e.g., Fsacharopoulosand Eduardo Velez, 1993; Hanan Jacoby, 1994),reduced repetition need not indicate greaterlearning. We therefore administered achieve-ment tests to a subset of the pupils surveyed.The test results suggest that, on average, lotterywinners scored about 0.2 standard deviationshigher than losers, a large but only marginallysignificant difference. The effect on girls islarger and more precisely estimated than theeffect on boys.

' U.S. studies in this moid include Jay Green et al f 1996)and Cecilia Elena Rouse (1998). who evaluated a voucherlottery in Milwaukee. Rouse's estimates, which control forattrition, show modest increases in math scores amongvoucher recipients. Other U.S. studies include William G.Howell et al. (2000). Bettinger (2001a). and Daniel Mayeret al. (20021. who evaluate various private scholarship pro-grams. Chang-Tai Hsieh and Miguel Urquiola (2002) ex-amine a large-scale voucher program in Chile but do nottake adviintage of random assignment. Rosemary Bellewand King (1993) assess a smaller program in Bangladesh.The literature on public/private comparisons in the UnitedStates is exten.sive. See, e.g.. William N. Evans and RobenM.Schwab (1995) and Derek NeaM 1997). Donald Cox andEmmanuel Jimenez (1990) compare public and privateschools in Colombia and Tanzania, and Jimenez et al.(1991) summarize comparisons in live countries. See alsothe Harry A. Patrinos and David L. Ariasiiigham (1997)survey of demand-side financing in poor countries. JereBehrman et al (2000) and Glewwe ei al. (2000) use ran-domization to examine other educational interventions indeveloping countries.

In addition to increased educational attain-ment and academic achievement, there is alsosome evidence that the voucher program af-fected noneducational outcomes. In particular,lottery winners were less likely to be married orcohabiting and worked about 1.2 fewer hoursper week (again, mostly a difference for girls).Both of these results suggest an increased focuson schooling among lottery winners.

While comparisons between winners and los-ers provide a simple strategy for assessing pro-gram impact, our survey indicates that onlyabout 90 percent of lottery winners had everused the voucher or any other type of scholar-ship, while 24 percent of losers received schol-arships from other sources. It therefore seemsreasonable to think of lottery win/loss status asan instrument for scholarship receipt in a two-stage least-squares (2SLS) setup. There is astrong first stage here, though the relationshipbetween voucher status and scholarship use isnot deterministic, instrumenting for scholarshipuse with lottery win/loss status suggests that.scholarship use generated effects on grade com-pletion and test scores that are roughly 50 per-cent larger than the reduced-form effect ofwinning the lottery.

The last part of the paper presents a fiscal andcost-benefit analysis of the voucher program.Most lottery winners would have attended pri-vate school anyway, at least for a few years, andtherefore reduced their educational expenditurein response to the program. On the other hand,voucher winners who were induced to switchfrom public to private schools greatly increasedtheir educational expenditure, since the vouchercovered only about half the cost of privateschool. On balance, winners* gross school feesexceeded those of losers by about 70 percent ofthe amount they received from the voucher.Winners paid greater fees because they weremore likely to go to private schools, and be-cause some winners who would have goneto private schools anyway switched to moreexpensive private schools. Moreover, lotterywinners worked less, so that, on balance, house-holds winning the lottery actually devoted moreresources to education than the voucher facevalue. We also estimate that the voucher pro-gram cost the government about $24 more perwinner than the cost of creating a public schoolplacement. These costs to participants and the

VOL 92 NO. 5 ANGRIST ET AL: VOUCHERS FOR PRIVATE SCHOOUNG 1537

government are likely to have been more thanoutweighed by the benefits of the voucher toparticipants—in the form of the economic re-turn to increased educational attainment and testscores.

A number of channels could potentially ac-count for the PACES program's effects on par-ticipants. The program clearly shifted someparticipants from public to private school, andpupils who shifted may have benefitted from theopportunity to attend private schools. There isalso evidence that some pupils who would haveattended private school anyway were able toattend more expensive private schools. Finally,voucher recipients may have had greater incen-tives to focus on school because vouchers couldonly be renewed for those pupils who did notrepeat grades.

The paper is organized as follows. Section Iprovides background on education in Colombiaand describes the PACES program in more de-tail. Section II discusses data and presents de-scriptive statistics from our survey. Section IIIdiscusses the effect of the program on schoolchoice and basic educational outcomes. SectionIV reports the effect of winning a voucher ontest scores and noneducation outcomes. SectionV discusses the use of lottery win/loss status asan instrument to identify the causal effect ofreceiving a scholarship. Einally, Section VIlooks at the effect of the program on householdand government expenditure, and comparesprogram costs with the benefits to participants.Section VII concludes the paper.

I. Background

The Colombian government established thePACES program in late 1991 as part of a widerdecentralization effort and in an attempt to ex-pand private provision of public services (Kinget al., 1997). The program, which was partlyfunded by the World Bank, was also motivatedas an effort to quickly expand school capacityand to raise secondary-school enrollment rates(King et al., 1998).' Although 89 percent of

•PACES was launched in November 1991 with adver-tisements in print and on radio soliciting applicants inparticipating cities (Alberto Calderon, 1996). A Worid Bankreport (1993) on Colombian secondiiry schools notes thatmost schools operated two or three shifts and that some

Colombia's primary-school age children wereenrolled in 1993, only 75 percent of the eli-gible population was enrolled in secondaryschools. Among children of eligible age in thepoorest quintile of the population, 78 percentwere enrolled in primary school, but only 55percent were enrolled in secondary school(Fabio Sanchez and Jairo Mendez, 1995; notethat secondary school covers grades 6-11 inColombia).

The PACES program targeted low-incomefamilies by offering vouchers only to childrenresiding in neighborhoods classified as fallinginto the two lowest socioeconomic strata (out ofsix possible strata). Applicants had to submit autility bill to establish residential location andvoucher eligibility. Targeting was enhanced byrestricting vouchers to children who attendedpublic primary schools. Almost half of childrenfrom the richest income quintile attendedprivate primary schools. Studies by PatriciaMorales-Cobo (1993) and Roci'o Ribero andJaime Tenjo (1997) suggests that the targetingwas largely effective in Bogota.

PACES vouchers were worth only aboutUS$190 at the time of our survey. The maxi-mum voucher value was set initially to corre-spond to the average tuition of low-to-middlecost private schools in Colombia's three largestcities. Schools charging less than the vouchers'face value received only their usual tuition.PACES vouchers became less generous overtime because they did not keep up with infla-tion, and hence recipients had to supplementvouchers with additional payments to coverschool fees. Our survey data show matriculationand monthly fees for private schools attendedby voucher applicants in 1998 averaged about$340, so most voucher recipients supplementedthe voucher with private funds. By way of com-parison, the average annual per-pupil public ex-penditure in Colombia's public secondary-school system in 1995 was just over $350

towns have little room tor additional pupils in spite oi'projected enrollment growth. Other problems mentioned inthe repon include poor primary-school preparation, weakschool management, lack of teacher preparedness, lack oftextbooks, and shonages of other supplemental materials.The early 199O's was a general period of refonii and liber-alization in Colombia; see, for example, Adriana D. Kugler(1999)-

I53H THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

(DNP, 1999), and public-school parents in oursample typically paid tuition or fees of roughly$58. Per capita GNP in Colombia is around$2,280 (World Bank, 1999).

To qualify for a voucher, applicants musthave been entering the Colombian secondary-school cycle which begins with grade 6, and beaged 15 or under. Prior to applying, studentsmust already have been admitted to a partici-pating secondary school (i.e.. one that wouldaccept the voucher)."^ Participating schools hadto be located in participating towns, which in-cluded all of Colombia's largest cities. Just un-der half of private schools in the ten largestcities accepted vouchers in 1993.

Participating schools tended to serve lower-income pupils, and to have lower tuition thannonparticipating private schools. Schools with avocational cumculum were also overrepre-sented among those in the program. Participat-ing private schools included for-profit schools,religious-affiliated schools, and schools run bycharitable foundations. Initially, vouchers couldbe used at both for-profit and nonprofit schools,but after 1996, for-profit schools were excluded.'̂The number of vouchers in use in any one yearpeaked at roughly 90,000 in 1994 and 1995. Therewere approximately 3.1 million secondary-schoolpupils in Colombia in 1995. 37 percent of whomattended private schools. In Bogota, roughly 58percent of 567,000 secondary-school pupils at-tended private school.

Test-score comparisons reported by King etal. (1997) show achievement levels in partici-pating private schools were very close to thosein public schools, though significantly belowachievement levels in nonparticipating privateschools. Pupil-teacher ratios and facilities weresimilar in public and participating privateschools, and many of the teachers in the privateschools most likely to participate in the PACESprogram were moonlighting or retired public-school teachers. Nonparticipating private schools

•* Background infonnation in this section is taken fromCalderon (1996), King et al. (1997). and unpublished ICE-TEX documents.

"* This was due largely to reported problems with low-quality for-profit schools created to exploit the vouchers.Calder6ii (1996) notes that even before the nonprofit restric-tion was imposed, only 15 percent of Bogota's voucherstudents attended such inslitutions.

had lower pupil-teacher ratios and better facilities.Clearly, then, relatively elite private schoolsopted out of the PACES program. Reasons forthis may include delays in payment of voucherfunds to schools and bureaucracy in the Colom-bian Institute for Education, Credit and TrainingAbroad (ICETEX), which ran the program.Moreover, vouchers were insufficient to covermuch of the tuition at more expensive schools,and some school managers probably viewed theprospect of an infiux of pupils from low-incomebackgrounds as undesirable. On the other hand,many private schools in Colombia serving low-income populations apparently welcomed thePACES program.

Voucher recipients were eligible for auto-matic renewal through eleventh grade, whenColombian high school ends, provided the re-cipient's academic performance warranted pro-motion to the next grade. Students failing agrade were supposed to be dropped from thePACES program. Figures from Calderon (1996)show that, on average. 77 percent of recipientsrenewed their vouchers, and estimates from ourdata are similar. By way of comparison, thenational high-school promotion rate was about70 percent. Students who transferred from oneparticipating private school to another could, inprinciple, transfer the voucher to the newschool. In practice, however, our survey sug-gests many students who transferred after win-ning lost their vouchers.

Cities and towns used lotteries to allocatevouchers when demand exceeded supply. Mu-nicipal governments paid 20 percent of thevoucher cost, while the central government paid80 percent. Each municipality decided howmany vouchers to fund, subject to a maximumallocated to tovras by the central government.This allocation was determined by estimatingthe shortfall between primary-school enroll-ment and the available space in public second-ary schools. Voucher award rates thereforevaried considerably by city and year, dependingon the ratio of applicants to available vouchers.Regional ICETEX offices worked with individ-ual municipalities to determine the number ofvouchers to be funded, to check school require-ments for participation, and to monitor imple-mentation of the program. The Bogota ICETEXoffice provided software and instructions to re-gional offices for the purposes of random selec-

VOL 92 NO. 5 ANGRIST ET AL: VOUCHERS FOR PRIVATE SCHOOLING 1539

tion of applicants in cases of oversubscription.We obtained copies of lists of lottery winnersand losers from ICETEX offices.^

II. The Applicant Survey

A. Descriptive Statistics

Beginning in the summer of 1998, we inter-viewed roughly 1,600 PACES applicants, strat-ifying to obtain approximately equal numbersof winners and losers. Interviewing was limitedto the 1995 and 1997 applicant cohorts fromBogota and the 1993 applicant cohort fromJamundi, a suburb of Cali. These years andcities were chosen for a combination of scien-tific and practical reasons. The largest andlongest-mnning voucher program was in Bogota,and our survey team was based there. Cali isColombia's second-largest city and thereforealso important, but almost no Cali applicantsreported phone numbers, so we concentrated ona suburb. Jamtjndi. Telephones were used forthe majority of interviews, primarily to reducecosts, but also because of interviewer safety andlogistical considerations. In principle, the lot-tery was random within localities and condi-tional on whether households had access to atelephone. The results should therefore yieldinternally valid estimates of the causal effect ofthe program on voucher applicants with accessto a telephone in surveyed cities. Over 80 per-cent of applicants had access to a phone, and inthe Bogota 1995 cohort. 88 percent had accessto a phone, possibly via a neighbor.

Table I reports descriptive statistics for thesampling frame, attempted contacts, and com-pleted interviews.'' There were 6,156 applicantsin the three applicant cohorts of interest. Weattempted to interview almost 3.000 applicants,obtaining an overall response rate of 54 percentand a response rate of almost 61 percent for the1997 Bogota lottery. The higher respon.se rate inthe most recent lottery is not surprising sincecontact infonnation for 1997 apphcants is more

' In a tew cities, the local ICETEX office assignedvouchers based on pupils' primary-school performance in-stead of randomly.

''The Data Appendix in our working paper (Angrist etah. 2001) provides additional informaiion ahout the survey.

recent. Interviews were completed with 55 per-cent of lottery winners and 53 percent of lotterylosers. Although this response rate is far fromideal., the fact that winners and losers werealmost equally likely to be interviewed is en-couraging because the question of sample selec-tion bias turns on whether voucher status iscorrelated with response probabilities (see. e.g.,Angrist, 1997). Because response probabilitiesare virtually uncorrelated with voucher status,there should be little bias from our failure tointerview all applicants.^

The typical applicant was about 13 years oldat the time of application, while average age onthe survey date varied from 13 for 1997 appli-cants to 17 for 1993 applicants. About half ofthe applicants were male. Roughly 85 percent ofapplicants were still in school, enrolled ingrades ranging from sixth for the 1997 cohort toeighth or ninth for the 1993 cohort. Cohortsadvance less than one grade per year because ofrepetition. The descriptive statistics also showthat almost 90 percent of the applicants weinterviewed started sixth grade in privateschool. This refiects the fact that eligibility forPACES vouchers was conditional on admissionto a participating private school. Thus, mostlottery losers went to private school anyway, alleast for one year. On the other hand, only 63percent of applicants were still in private schoolas of the survey date.

B. Personal Characteristics andVoucher Status

There is little evidence of any associationbetween win/loss status and the individual

' The va.st majority of nonresponders were people wecould not reach hy telephone, either because they hadmoved or because the telephone number we had no longerworked. Roughly 3 percent of families contacied refused toanswer. The only significant difference in response rates hywin/loss status is for the Jamundi cohort. In what follows,we present results for the Bogota 1995 cohort and thecombined cohons separately. Complete follow-up is theholy grail of education research. Even careful evaluationstudies using randomized and quasi-randomized designs(e.g.. Rouse. 1998: Alan B. Knieger and Diane M. Whitmore.2001) are hased on samples with substantial loss t() follow-up. Similarly. Howell et al. {20001 report follow-up ratessimilar to ours for U.S. voucher trials in three cities.

1540 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

TABLE 1—SAMPLE DESIGN AND SURVEY RESPONSE DATA

Variable

A. Population: j

NPercentage awarded vouchers

B. Attempted Interviews:

NPercentage awarded vouchersResponse rateWinner rateLoser rate

C. Completed Interviews:

NPercentage awarded vouchersHousehold visitAge at time of application

Age on stirvey date (firomsurvey data)

MaleStarted 6th grade in privateStarted 7th grade in privateCurrently in private schoolHighest grade completed

Currently in school

Bogota1995

4.04458.8

2.24950.0

0.5230.5280.518

1.17650.4

0.05412.6(1.3)15.0(1.3)0.5100.9100.7630.618

7.6(0.940)0.836

Bogotd1997

1,77084.7

45751.6

0.6060.6190.593

27752.7

0.00412.4(1.4)13.1(1.4)0.4950.8800.7310.738

6.0(0.480)0.957

Jamundi1993

34250.0

27950.2

0.5910.6500.532

16555.2

0.78212.5(1.9)16.9(!.5)0.4240.6690.6260.506

8.6(l.l)0.778

Combinedsample

6.15665.8

O,' ' :

2,98550.3

0.5420.5530.531

1.61851.3

0.12012.6(1.4)14.9(1.7)0.4990.8800.7440.628

7.4(I.I)0.85!

Test-takers

——

47353.9

0.5980.6240.571

1

28355.6

0.09312.6(1.2)15.6(1.2)0.5110.8320.7310.6987.7

(0.910)0.841

Notes: Standard deviations for nonbinary variables are shown in parentheses. Sample sizesmay differ across rows. Data are from 1998 household surveys. "Age at time of application"is imputed from ihe National Identification number reported on the application.

characteristics measured in our data fromBogota, although winners and losers are lesscomparable in the 1993 Jamundi cohort. Thiscan be seen in Table 2, which reports means anddifferences by win/los.s status for all applicantsin the study population, for sampled applicants,and for the sample of completed surveys. Thesampling process began with lists showing ap-plicant ID numbers, names, addresses, andphone numbers, separately for winners andlosers. To obtain demographic characteristicsfor all applicants, whether surveyed or not, wecoded sex from names and itnputed ageusing ID numbers (which incorporate birth-days). Imputed age is subject to error since 13percent of applicants have invalid ID numbersas determined by the ID number control digit.We excluded observations in which the appli-cant was younger than 9 or older than 25. Inpractice, this restriction affected only two ob-

servations. We used first names to assign sexfor about 80 percent of the applicants. A finalvariable from the applicant record is a dummyfor whether the applicant reported a phonenumber.

Winners and losers have similar telephoneaccess, age, and sex mix in the 1995 and 1997Bogota data. As a further check on randomness,we compared win rates by school in schoolswith more than 20 applicants to city averages inthe Bogota data from 1995. No school had a winrate that differed significantly from the city av-erage. In the Jamundi-93 sample, however,there are significant differences in average ageand gender by win/loss status. Because the dif-ferences between winners and losers in theJamundi lottery may indicate nonrandom as-signment of vouchers, and because the 1997Bogota cohort is too recent for a good readingon some outcomes, we present results from the

VOL 92 NO. 5

Dependent v;iriable

ANGRIST ET AL: VOUCHERS FOR PRIVATE SCHOOUNG

TABLt; 2—PERsoNAt. CHARACTERISTICS AND VOUCHER STATUS

Bogoti 1995

Losermeans

A. Delia from PACES Appliculiori:

Has phone

Age al time of application

Male

A'

0.882

12.7(1.3J0.493

1.519

B. Data for All Attempted Contacts:

Has phone

Age at time of application

Male

N

C. Survey Data:

Age at time of survey

Male

Mother's highe.st gradecompleted

Father's highest gradecompleted

Mother's age

Father's age

Father's wage ( > 2 minwage)

N

1

12.8(1.3)0.500

1.035

15.0(1.4)0.501

5.9(2.7)

5.9(2.9)

40.7(7.3)

44.4(8.1)0.100

583

Wonvoucher

0.009(0.011)

- 0 . 0 8 6(0.045)0.013

(0.017)3,661

—

- 0 . 1 1 8(0.060)

- 0 . 0 0 7(0.022)2,067

-0 .013(0.078)0.004

(0.029)- 0 . 0 7 9(0.166)

-0 .431(0.199)

- 0 . 0 2 7(0.426)0.567

(0.533)O.(K)5

(0.021)1.176

Bogotd 1997

Losermeans

0.828

12.7(1.5)0.484

256

1

12.6(1.5)0.488

212

13.2(1.4)0.527

5.9(2.7)5.5

(2.5)38.7(6.6)

41.9(7.3)0.088

131

Wonvoucher

0.029(0.025)

-0 .227(0.102)0.007

(0.044)1.736

—

- 0 . 1 9 3(0.136)

- 0 . 0 2 0(0.048)448

- 0 . 2 5 9(0.I7I)

- 0 . 0 4 7(0.061)0.654

(0.371)0.929

(0.388)- 0 . 1 4 6(0.808)0.265

(0.973)- 0 . 0 0 8

(0.043)277

Jamundi 1993

Losermeans

().3{)l

12.7(1.5)0.386

166

0.370

12.8(1.6)0.372

135

17.2(1.4)0.365

4.4(2.7)5.2

(2.9)43.6(8.8)

45.5(9.1)0.133

74

Wonvoucher

0.068(0.052)

- 0 . 3 8 3(0.162)0.114

(0.055)334

0.082(0.059)

- 0 . 5 9 5(0.183)0.102

(0.061)272

- 0 . 3 7 5(0.217)O.IIO

(0.077)1.46

(0.494)0.737

(0.640)- 0 . 7 3 6(1.42)

1.92(1.61)

- 0 . 0 9 2(0.056)

165

Combinedsample

Losermeans

0.825

12.7(1.4)0.483

i.941

0.938

12.7(1.4)0.486

1.382

14.9(1.7)0.492

5.8(2.7)5.8

(2.9)40.6(7.4)44.1(8.1)0.101

788

Wonvoucher

0.017(0.010)

- 0 . 1 3 3(0.040)0.019

(0.015)5,731

0.008(0.006)

- 0 . 1 7 7(0.052)0.001

(0.019)2.787

- 0 . 1 0 7(0-068)0.008

(0.025)0.183

(0.144)- 0 . 0 4 2(0.170)

- 0 . 0 7 6(0.362)0.537

(0.453)-0 .003(0.018)1,618

1541

Test-takers

Losermeans

.—.

—

—

.

—

14.9(1.4)0.447

5.5(2.9)4.0

(3.3)40.3(6.6)

43.5(7.7)0.052

(0.222)124

Wonvoucher

—

—

—

- 0 . 1 6 0(0.162)0.053

(0.060)- 0 . 2 7 7(0.351)

-0 .171(0.392)0.459

(0.811)1.18

(1.06)0.083

(0.039)283

Notes: The table reports voucher losers' means and the estimated ellect of winning a voucher. Numbers in parentheses arestandard deviations in columns of means and .standard errors in colurrms of estimated voucher effects. Models used for theestimates in Panels A and B include control for city and year of application; ihose for Panel C add controls for type of surveyand itistrument. neighborhood of residence, and monlh of interview. Sample size varies by row. The maximum sample sizeis .shown in each panel. The sample for the outcome "Age at time of application" is restricted to applicants 9 -25 years old.

Bogota-95 sample separately from the resultsfor the pooled sample including ail threecohorts.

III. Impact on Scholarship Use,School Choice, and Schooling

Our estimates of lottery effects are based onthe following regression model:

(I) e,.

where y,,. is the dependent variable for child /from application cohort c (defined by city andyear); X, represents a vector of individual andsurvey characteristics like age, sex. and whetherthe survey was telephone or in person; Z,. is anindicator for whether child / won the voucher

1542 THE AMERICAN ECONOMIC REVIEW

TARt.E 3—EDUCATIONAL OtjicoMES AND VoucHt!R STATUS

Dependent variable

Using any .scholar.shipin .survey year

Ever used a scholarship

Started 6th grade inprivate

Started 7th grade inprivate

Currently in privateschool

Highest gradecompleted

Currently in school

Finished 6th grade

Finished 7th grade(excludes Bogota 97)

Finished 8th grade(excludes Bogota 97)

Repetitions of 6lh grade

Ever repeated afterlottery

Total repetitions sincelottery

Years in school sincelottery

Sample size

Losermeans

(1)

0.057(0.232)0.243

(0.430)0.877

(0.328)0.673

(0.470)0.539

(0.499)7.5

(0.960)0.831

(0.375)0.943

(0.232)0.847

(0.360)0.632

(0.483)0.194

(0.454)0.224

(0.417)0.254

(0.508)3.7

(0.951)

562

Bogoti 1995

Nocontrols

(2)

0.509(0.023)0.672

(0.021)0.063

(0.017)0.174

(0.025)0.160

(0.028)0.164

(0.053)0.019

(0.022)0.026

(0.012)0.040

(0.020)0.112

(0.027)-0.066(0.024)

-0.060(0.023)

-0.073(0.028)0.058

(0.052)

Basiccontrols

(3)

0.504(0.023)0.663

(0.022)0.057

(0.017)0.168

(0.025)0.153

(0.027)0.130

(0.051)0.007

(0.020)0.023

(0.012)0.031

(0.019)0.100

(0.027)-0.059(0.024)

-0.055(0.023)

-0.067(0.027)0.034

(0.050)

1.147

Basic + 19barrio

controls(4)

0.505(0.023)0.662

(0.022)0.058

(0.017)0.I7I

(0.024)0.156

(0.027)0.120

(0.051)0.007

(0.020)0.021

(0.011)0.029

(0.019)0.094

(0.027)-0.059(0.024)

-0.051(0.023)

-0.064(0.027)0.031

(0.050)

DECEMBER 2002

Combined sample

Basiccontrols

(5)

0.526(0.019)0.636

(0.019)0.066

(0.016)0.170

(0,021)0.152

(0.023)0.085

(0.041)-0.002(0.016)0.014

(0.011)0.027

(0.018)0.077

(0.024)-0.049(0.019)

-0.055(0.019)

-0.058(0.022)0.015

(0.044)

1

Basic -M9barrio

controls(6)

0.521(0.019)0.635

(0.019)0.067

(0.016)0.173

(0.021)0.154

(0.023)0.078

(0.041)-0.002 •(0.016)0.012

(0.010)0.025

10.018)0.074

(0.024)-0.049(0.019)

-0.053(0.019)

-0.057 ' ., ,(0.022) , ,0.012

(0.043)

577

Noti-'.s': The table reports voucher losers' means and the estimated effect of winning a voucher.Numbers in parentheses are standard deviations in the column of means and standard errorsin columns of estimated voucher effects. The samples used to estimate 7th- and 8th-gradecompletion effects exclude Bogota 1997. The sample size for these outcomes is 1.304 incolumns (5) and (6). The regression estimates are from models that include controls for city,year of application, phone access, age, type of survey and instrument, strata of residence, andmonth of interview.

lottery; and 8^ is an applicant cohort effect tocontrol for the fact that the probability of win-ning varied by city and year. The coefficient ofinterest is a,,. We estimate (1) using three setsof control variables: "no controls," i.e.. exclud-ing the X, variables; "basic controls" includingthe X; variables; and "basic plus barrio con-trols" which includes the X̂ variables plus 19neighborhood dummies in the Bogota-95sample.**

' Neighborhoods in this case are large areas or districts.

A. Effects on Scholarship Useand School Choice

We begin with a simple analysis of the effectof winning the lottery on private-school schol-arsliip receipt and the choice between publicand private school. The most immediate effectof the lottery was to increase the likelihood ofreceiving a private-school scholarship. This canbe seen in the first row of Table 3. which showsthat at the time of our survey, voucher winnerswere 51 percentage points more likely than los-ers to have been using some kind of scholarship

VOL 92 NO. 5 ANGRIST ET AL: VOUCHERS FOR PRIVATE SCHOOUNG 1543

(including non-PACES scholarships). Not allwinners were using their PACES vouchers inthe survey year. This is because 15 percent ofwinners were not in school at all, and another 16percent were in public schools, and thereforeineligible for scholarships. Some lottery win-ners also lost their voucher after repeating agrade (7 percent), while 5 percent switched tononparticipating private schools or failed tocomplete the paperwork for a transfer. Othersattended schools that stopped accepting vouch-ers or lost their vouchers for unreported reasons.Just as nol all winners were using a scholarship,some losers obtained scholarships from pro-grams other than PACES and one loser wasawarded a PACES voucher after reapplying thefollowing year.

At the time of the survey, enrollment rateswere 0.83 for losers and 0.85 for winners in theBogota-95 sample, an insignificant difference.The estimates in Table 3 also show that mostPACES applicants entered sixth grade in a pri-vate secondary school, and most finished sixthgrade whether or not they won a voucher. Butlottery winners were 6-7 percentage pointsmore likely than losers to have begun sixthgrade in private school, and 15-16 percentagepoints more likely to be in private school at thetime of our survey. The effect of winning thePACES lottery on the probability of private-school attendance was even larger in seventhgrade, probably because losers were more likelyto have left private school by then.

These results suggest the decision betweenpublic and private school was sensitive to vari-ation in the price of private school induced bythe program, while the decision whether to at-tend school was not.^ This is consistent with amodel in which tho.se households most willingand able to pay for education aitend privateschool; a middle group attends public school;and those least willing or able to pay do notattend at all. In this case, no one is on theprivate-school/no-school margin, and so small

^ We can convert the private-school enrollment effects toan elasticity as follows. PACES vouchers redueed the mar-ginal cost of private-school attendance by about 50 percentwhile vouchers increased private-school enrollment in sev-enth grade by about 17 percent. The implied elasticity ofprivate enrollment with respect to marginal cost is therefore0.34.

subsidies to private education do not directlyincrease overall enrollment.'" However, sincemany public secondary schools in Colombiawere turning away applicants due to overcrowd-ing, PACES is likely to have opened up placesin public school for other pupils by reducingpubhc-school queuing.

B. Effects on Schooling

Lottery winners completed more schoolingthan losers, and were less likely to repeatgrades. For example, lottery losers had com-pleted 7.5 years of schooling at the time of oursurvey, but winners in the 1995 Bogota samplecompleted an additional 0.12-0.16 years (0.8years in the full sample). As noted earlier, therewas no statistically significant effect on enroll-ment. The effect on years of schooling and thelack of an effect on enrollment is primarily theresult of a reduced probability of grade repeti-tion for winners. This is reflected in a sharpincrease in the likelihood lottery winners hadfinished eighth grade as of the survey date, witha smaller impact on seventh-grade completion.In the Bogota-95 sample, over 20 percent oflosers had repeated a grade since beginningsixth grade, and almost 20 percent repealedsixth grade. But the probability of grade repeti-tion was reduced by 5-6 percentage points forlottery winners.

The estimates of a,, change little as the list ofcontrol variables changes, a result to be ex-pected since the voucher lottery was random.The estimation results are also similar in theBogota-95 and full samples, and are largelyinvariant to the inclusion of neighborhood ef-fects. Estimates and standard errors for theBogota-95 sample also change little in modelswith school effects.

Sepaiate results by sex, reported in Ta-ble 4, show moderately larger effects on educa-tional attainment for girls, though the pattern ofsex differences in the effects on private-schoolenrollment are not clear-cut. Results for theBogota-95 sample show male lottery winners

'" PACES subsidies were initiaUy large enough to coverthe entire cost of private school, and may have shiftedrecipients from no school to private school when the pro-gram staned. However, the voucher value was later erodedby inflation.

1544 THE AMERICAN ECONOMIC REVIEW

TABLt; 4—EDUCATIONAL OtiTCOMEs AND VOUCHHR STATKS.

1.4. " u 1 ,

• .

Dependent variable

Started 6th grade inprivate

Started 7th grade inprivate

Currently in privateschool

Highest gradecompleted

Currently in school

Finished 6lh grade

Finished 7th grade

Finished 8th grade

Repetitions of 6th grade

Ever repeated afterlottery

Total repetitions sincelottery

Calendar years inschool since lottery

Sample size

Coefficient on

Bogotd

Male

Losermeans

0.857(0.351)0.646

(0.479)0.543

(0.499)7.4

(0.990)0.843

(0.365)0.932

(0.252)0.825

(0.380)0.589

(0.493)0.229

(0.506)0.254

(0.436)0.296

(0.550)3.7

(0.962)280

Basiccontrols

0.082(0.025)0.187

(0.035)0.136

(0.039)0.124

(0.076)-0.020(0.029)0.014

(0.018)0.026

(0.029)0.095

(0.039)-0.087(0.037)

-0.083(0.034)

-0.101(0.042)

-0.029(0.077)575

1995

BY GEt̂ JER

voucher status

Female

Losermeans

0,897(0.304)0.699

(0.460)0.535

(0.500)7.6

(0.934)0.819

(0.386)0.954

(0.210)0.869

(0.338)0.674

(0.470)0.160

(0.395)0.195

(0.370)0.213

(0.459)3.6

(0.941)282

Basiccontrols

0.027(0.021)0.143

(0.033)0.171

(0.039)0.140

(0.065)0.035

(0.027)0.032

(0,013)0.041

(0.025)0.105

(0.036)-0.036(0.030)

-0.029(0.031)

-0.031(0.033)0.091

(0.063)572

Combined

Male

Basiccontrols

0.058(0.023)0.166

(0.031)0.124

(0.033)0.056

(0.062)-0.026(0.024)0.003

(0.017)-0.003(0.024)0.066

(0.030)-0.070(0.031)

-0.076(0.028)

-0.079(0.035)

-0.041(0.067)779

DECEMBER 2002

sample

Female 'f • • •

Basiccontrols

0.077(0.021)0.177

(0.029)0.182

(0.033)0.122

(0.052)0.029

(0.022)0.027

(0.012)0.022

(0.020)0.078

(0.027)-0.033(0.023)

-0.035(0.025) ' •

-0.037(0.026)0.081

(0.055)798

Notes: The table reports voucher lo.sers' means and the estimated effect of winning a voucher.Numbers in parentiieses are standard deviations in columns of means and standard errors incolumns of estimated voucher effects. The regression estimates are from models that includecontrols for city, year of application, whether applicant has phone, age, type of survey andinstrument, strata of residence, and month of interview.

with an insignificant 0.12 more years of school-ing while female lottery winners obtained 0.14years more of schooling, a statistically signifi-cant effect. Differences by sex are more pro-nounced in the full sample, with an insignificant0.06 more years of schooling for boys, and astatistically significant 0.12 more years ofschooling for girls. It should also be noted thatwhile effects for boys are almost entirely due tograde repetition, the effects for girls appear tocome from both reduced grade repetition andadditional time spent in school."

' ' There is little evidence that the effect of winning thevoucher varied with applicants' .socioeconomic strata ofresidence or parents' education. However, estimates forsubgroups are imprecise.

The greater probability of eighth-grade com-pletion and lower repetition rates for lotterywinners seem like desirable outcomes. In fact,high rates of grade repetition in Latin Americaare widely seen as symptomatic of poorly func-tioning public schools. But the interpretationof these effects is complicated by the fact thatpupils who failed a grade were supposed toforfeit PACES vouchers. Private schools maytherefore have had an incentive to promote pu-pils with vouchers even if their performance didnot meet normal promotional standards. To ex-

'- For example, R. W. Harbison and Eric A. Hanu.shek(1992) and Psacharopolous and V6lez (1993) use repetitionrates as a measure of school quality in Colombia and Brazil.

VOL 92 NO. 5 ANGRIST ET AL: VOUCHERS FOR PRIVATE SCHOOUNG 1545

plore this possibility, we look at effects on testscores and noneducational outcomes in the nextsection.

rv. Effects on Test Scores andNoneducation Outcomes

A. Effects on Test Scores

We tested children from the 1995 applicantcohort in three Bogota neighborhoods. Theseneighborhoods were chosen because they hadrelatively large numbers of winners and losers.and because of the availability of suitable (andsafe) testing sites. The tests were administeredin 1999. approximately one year after ourhousehold survey and three years after the chil-dren applied for the program. The test samplewas drawn from applicants for whom we hadsurvey data. Participants were solicited by tele-phone, followed by hand delivery of letters de-scribing the purpose of the test and invitingpupils to be tested. Those who failed to appearon the test day were invited again for a secondtesting, except at the last sitting. To encourageparticipation, refreshments were provided ateach site, and each test concluded with the raffleof a bicycle and other prizes. Pupils were alsogiven 5,000 or 10.000 pe.sos (U.S. $3.23 or$6.45) to cover travel costs. The invitation letternoted the offer of refreshments, travel reim-bursement, and raffle. See the Data Appendixfor additional details on the testing, available at(http://www.aeaweb.org/aer/contents/).

Our evaluation used La Prueba de Realiza-cion, a grade-specific multiple-choice achieve-ment test for native Spanish speakers, publishedby Riverside. We administered only the mathe-matics, reading, and writing subtests. each tak-ing about 30 minutes. This test was chosenbecause Colombian educators participated intest development and the test had been usedpreviously in Colombia (Nancy S. Cole et al..1993). The Appendix to our working paper(Angrist et al., 2001) compares test results fromthe Hispanic-American test-norming popula-tions for grades 9 and 10 with the results fromour test. Colombian ninth-graders in our samplescored lower than American pupils in mathe-matics, but they had reading skills slightly bet-ter than American tenth-graders. The average

Colombian writing score was close to the aver-age score for American tenth graders.

The Test Sample.—Of ihe 1.176 Bogota 1995applicants surveyed, 473 were invited for test-ing. Statistics for pupils invited and tested ap-pear in the last column of Table I. Of the 473invited, 283 were tested, an overall responserate of about 60 percent. The test-response rateis about 5 percent higher for winners, but thedifference in response rates by voucher status isnot statistically significant. The personal char-acteristics of those tested are generally similarto those of the full Bogota-95 sample. Alsoencouraging is the fact that, conditional on tak-ing the test, there is little evidence of differ-ences in personal characteristics betweenvoucher winners and losers. This comparisoncan be seen in the last column of Table 2.

Test Results.—Table 5 reports estimates ofthe effect of winning the voucher lottery on testscores. Columns (I) and (2) of Table 5 showresults from models with and without covari-ates.'-* Columns (3) and (4) present the resultsof estimating a single voucher coefficient forstacked subject results, in models with a pupilrandom effect. That is, we estimated

(2)

where v,̂ is pupil /'s score in subject .v, and 5,is a random effect used to adjust standard errorsfor the fact that there is likely to be within-pupilcorrelation across subjects. Note that test-scoreresults are reported in standard deviation units.

Lottery winners scored just over 0.2 standarddeviations more than lottery losers, though thisdifference is (not surprisingly, given the smalltest sample) only marginally significant. Ac-cording to U.S. norms for La Prueba, two-tenthsof a standard deviation is roughly the score gainassociated with one additional school year(Cole et al, 1993). This effect should probably

'•^The results in columns (1) and (3) are from modelsthat include site dummies only. The results in columns (2)and (4) are from models that include controls for age. sex,parents' schooling, strata of residence, type of interview,and survey form.

1546 ••• ^ THE AMERICAN ECONOMIC REVIEW

1

Variable

A. Al! Applicants:

Total points

Math scores " '

Reading scores • ,"

Writing scores

Pooled test scores

Math and reading scores

B. Female Applicants:

Total points

Madi scores

Reading scores

Math and reading scores

C. Male Applicants:

Total points

Math scores

Reading scores

Math and reading scores

TABt.E

OLSresults

(1)

0.211(0.116)0.178

(0.120)0.204

(0.115)0.126

(0.116)

• . 1 .

• '

0.199(0.162)0.292

(0.145)0.117

(0.158)

0.204(0.169)0.010

(0.178)0.276

(0.183)

5-TBSTRes

OLSresultswith

covariates(2)

0.205(0.108)0.153

(0.114)0.203

(0.114)0.128

(0.105)

0.263(0.126)0.346

(0.141)0.152

(0.136)

1

0.170(0.189)0.004

(0.187)0.220

(0.190)

RE(3)

0.170(0.095)0.192

(0.101)

0.204(0.130)

0.143(0.160)

RE withcovariates

(4)

0.148(0.088)0.162

(0.096)

*

. • • ' . . ( •

0.235(0.117)

' '• i r ' •

, . , .

0.087(0.160)

DECEMBER 2002

Samplesize(5)

282

283

846

568

. 1* • . / '

m293

m

268

Notes: Robust standard erTors are reported in parentheses. Standard errors in columns (1) and(2) are corrected for within-school-of-application clustering. Test scores are in standarddeviation units. The estimates in columns (2) and (4) are from models that include controlsfor applicant's age. gender, parents' schooling, strata of residence, and type of survey andinstrument. Columns (3) and (4) models include random effects (RE) for each test subject.The sample for "Pooled test scores" includes three observations per student (one for eachsubject) while "Math and reading scores" includes two observations per student.

be seen as large, since subjects were tested threeyears after applying to the program. Lotterywinners also scored higher on all subtests,though the only significant difference is forreading scores (t = 1.8). The results for thestacked subjects, reported in columns (3) and(4), also show marginally significantly higher

scores for lottery winners, with the largest ef-fects for models that stack math and readingscores only.

Models estimated separately for boys andgirls generate larger and more precise effects forgirls than boys. For example, the estimated ef-fect on total points for girls, reported in column

VOL 92 NO. 5 ANGRIST ET AL: VOUCHERS FOR PRIVATE SCHOOUNG 1547

(2) of Panel B for models with covariates, is0.26 (SE = 0.13). The corresponding estirnatefor boys, reported in Panel C, is 0.17 (SE =0.19). The finding of a stronger effect on girlsechoes some of the survey results.

Earlier we noted that reduced grade repetitionatnong lottery winners could theoretically havebeen caused by a reduction in promotion stan-dards for lottery winners, as well as by in-creased learning or a change in school quality.Comparing the test scores of winners and loserswho were promoted provides evidence that thegrade-repetition results are not due solely toschools' lowering ihe bar for promotion of win-ners. If the program itself did not affect achieve-ment, but did lead schools to relax promotionsstandards for winners, then average test scoresfor lottery winners who were promoted shouldbe lower than average test scores for lotterylosers who were promoted.'** In fact, the com-posite test scores of winners who were pro-moted are about 0.14 standard deviationsgreater than the scores of promoted losers, al-though the difference is not significant.

Another possible channel through which theprogram could have reduced grade repetition isincreased effort by voucher recipients in orderto avoid failing a grade and losing Iheir vouch-ers. In this scenario, the program would havebeen just as successful if ii had made paymentto students conditional on satisfactory academicperformance, with no element of school choice.This would imply that the primary incentiveeffect should be on those who are near themaigin for passing on to the next grade. How-ever, quantile regression estimates (not reportedhere) suggest that the increase in test scores isnot confined to low quantiles of the score dis-tribution. For reading and writing, there is nostrong pattern of differential effects acrossquantiles, while for math, the effects are, if

'^ Suppose schools promote if a random variable x,representing the school's internal assessment of the student,is greater than a cutoff c. which takes on two values, t ^ forwinners and CL for losers. Suppose c^ < LL. but test scores.T. and the variable x are unaffected by winning the lottery.Then the expected test score for lottery losers who arepromoted is E{T\x > c\). Tlie expected score for winnerswill be a weighted average of this and £(7'|c^ < .v < Ci_).Average scores for promoted losers will therefore exceedaverage scores for promoted winners as long as EiT\x) isincreasing in .v.

anything, larger at the top of the distribution.Standard errors for these estimate are, of course,large, given the small sample.

B. Other Outcomes

Table 6 reports estimates of the effect ofwinning the lottery on noneducational out-comes. Approximately 1.6 percent of lotterylosers from Bogota were married or living witha companion, a low proportion consistent withthe fact that the average age of survey respon-dents was about 15. Since this outcome is rare,we estimated probit models as well as linearprobability models.

Both probit marginal effects and ordinaryleast-squares (OLS) estimates suggest that mar-riage and cohabitation were reduced for lotteiywinners, a marginally significant effect. There issome evidence from the pooled sample thatlottery winners were less likely to be workingthan losers, with the largest effects in BogotlThere is also a significant difference in hoursworked. In particular, lottery winners worked1.2 fewer hours per week than losers. This ef-fect is larger and more precisely estimated forgirls. The reduction in work may be due toincome effects for the household, the greatertime demands of private school relative to pub-lic school, or increased incentives for lotterywinners to spend time studying so as to avoidfailing a grade and losing the PACES voucher.

V. Instrumental Variables Estimates ofScholarship Effects

The analysis so far focuses on reduced-formeffects of winning the lottery. In the discussionof Table 3, however, we noted that some lotterylosers were awarded other scholarships, whilesome winners failed to use or retain theirPACES scholarships. This section discussestwo-stage least-square (2SLS) estimates of theeffect of ever receiving any scholarship usingvoucher win/loss status as an instrumental vari-able (IV). While only 6 percent of lottery losersused a scholarship at the time of the survey, 24percent had used a scholarship at some point. Incontrast. 90 percent of winners used a scholar-ship at some time. The 2SLS estimates based onthis difference are necessarily larger than thereduced-form effects of winning the lottery

I54S

TABLI= f

> ' i ' . •

Dependent variable

A. Male and Female:

Married or livingwith companion

Has child

Applicant isworking

Number of hoursworking

Sample size

B. Male:

Married or livingwith companion

Applicant isworking

Number of hoursworking

Sample size

C. Female: ' " '

Married or livingwith companion

Pregnant or haschild

Applicant isworking

Number of hoursworking

Sample size

THE AMERICAN ECONOMIC REVIEW

1—NONEDUCATtONAL OUTCOMES AND VOUCHER STATUS

Lo.sermeans

(I)

0.0160(0.1256)0.0338

(0.1809)0.1690

(0.3751)4.881

(12.3)562

0.0036(0.0598)0.2321

(0.4230)6.421

(13.69)280

0.0284(0.1663)0.0603

(0.2384)0.1064

(0.3089)3.351

(10.57)282

Coefficient on voucher .status

Bogotd 1995

Basiccontrols

(2)

-0.0087(0.0059)

-0.0103(0.0096)

-0.0297(0.0205)

-1.222(0.6441)1,147

-0.0039(0.0038)

-0.0366(0.0331)

-0.6376(1.072)

575

' ' I

-0.0100(0.0113)

-0.0151(0.0179)

-0.0314(0.0235)

-2.116(0.6527)

572

Probit withbasic

controls(3)

-0.0066(0.0038)

-0.0079(0.0075)

-0.0299(0.0184)

——

1.147

——

-0.0336(0.0324)

——575

-0.0112(0.0078)

-0.0155(0.0138)

-0.0262(0.0189)

——

572

DECEMBER 2002

Combined sample

Losermeans

(4)

0.0171(0.1297)0.0303

(0.1714)0.1616

(0.3684)4.417

(11.60)760

0.0027(0.0518)0.2252

(0.4183)6.198

(13.31)373

0.0309(0.1733)0.0541

(0.2266)0.1005

(0.3011)2.704

(9.36)388

Basiccontrols

(5)

-0.0094(0.0056)

-0.0069(0.0079)

-0.02651(0.0171)

-0.8699(0.5235)

1,577

-0.0027(0.0026)

-0.0283(0.0278)

-0.6231(0.8859)

779

-0.0113(0.0109)

-0.0092(0.0147)

-0.0317(0.0196)

-1.499(0.5240)

798

Probit withbasic

controls(6)

-0.0065(0.0034)

-0.0055(0.0062)

-0.0254(0.0153)

—

1,577

——

-0.0294(0.026t)

——778

-0.0114(0.0068)

-0.0119(0.0110)

-0.0240(0.0156)

——798

Notes: Numbers in parentheses are standard deviations in columns of means and standarderrors in columns of estimated voucher effects. Results are for samples with nonmlssingnoneducational and educational outcomes. Columns (2) and (3) show results from models thatcontrol for whether applicants had access to a phone, age, gender, type of survey andInstrument, strata of residence, and month of interview. Columns (5) and (6) also includecontrols for city and year of application.

since winning the lottery is only imperfectlycorrelated with receiving a scholarship.

The assumption that a scholarship usedummy satisfies the exclusion restriction in aninstrumental variables (IV) setup motivates2SLS estimation of the equation:

(3)

where s, is a dummy for scholarship use, and X,

is the vector of "basic controls" used in previoustables. The associated first-stage relationshipusing Z, as an instrument is

(4)

The estimate of TT is about 0.66 (SE = 0.021) sothe second-stage estimates can be expected tobe about 50 percent larger than the correspond-ing reduced-form estimates. The interpretation

VOL 92 NO. 5 ANGRIST ETAL: VOUCHERS FOR PRIVATE SCHOOUNG 1549

TABLE 7—OLS AND 2SLS ESTIMATES OF THE EFFECT OF EVER USING

A PRIVATE SCHOOL SCHOLARSHIP

Dependent variable

Highest gradecompleted

In school

Total repetitions sincelottery

Finished 8th grade

Test scores (totalpoints)

Married or living withcompanion

N

Coefficient on "Ever used a private-school scholarship"

Lo.sermeans

7.5(0.965)0.831

(0.375)0.254

(0.508)0.632

(0.483)-0.099(1.0)0.016

(0.126)

5fi2

Bogota 1995

OLS

0.167(0.053)0.021

(0.021)-0.077(0.029)0.114

(0.028)0.379

(0.111)-0.009(0.006)

1.147

2SLS

0.196(0.078)0.010

(0.031)-0.100(0.042)0.151

(0.041)0.291

(0.153)-0.013(0.009)

Combined sample

OLS

0.141(0.042)0.033

(0.017)-0.069(0.023)0.108

(0.025)—

-0.010(0.006)

2SLS

0.134(0.065)

-0.003(0.026)

-0.091(0.035)0.127

(0.038)—

-0.014(0.009)

1..577

Notes: The table reports loser means and OLS and 2SLS estimates of the effect of ever havingused a private-school scholarship. Results are from models that control for city, year ofapplication, whether applicant had access to a phone, age. type of survey and instrument,strata of residence, and month of interview. Robust standard errors are reported in parenthe-ses. Data for the outcome "Finished 8th grade" in the combined sample does not includeapplicants to the Bogota-1997 voucher lottery. For the outcome "Test scores (total points)."the sample is restricted to those individuals who took the exam. In the 2SLS specification, theendogenous regressor used scholarship is instrumented with voucher status.

of a, in this case is as an approximate effect oftreatment on the subset of scholarship users whowould not have used a scholarship withoutPACES (Guido W. Imbens and Angrist,1994).'^

The 2SLS estimate of the effect of scholar-ship use on highest grade completed is about 0.2in the Bogotd-95 sample and 0.13 in the fullsample. These estimates are reported in Ta-ble 7. Two-stage least-squares estimates ofvoucher effects on the probability of finishingeighth grade are 13-15 percentage points,nearly a 25-percent increase in completionrates. This seems to be in the ballpark of SusanM. Dynarski's (2001) estimated completion

'^ At first blush, private-sclioo! attendance might appearto be the appropriate endogenous regressor for a 2SLSsetup. But this seems unlikely to satisfy the required exclu-sion restriction since increased effort and increased schoolquality probably also mediate the effects of the voucher.Consistent with this, in practice. 2SLS estimates treatingprivate-school attendance as an endogenous regressor gen-erate estimates that are implausibly large.

elasticities with respect to U.S. financial aid forcollege students, though obviously not directlycomparable. Another interesting result is the2SLS estimate of the effect on test scores, 0.29,somewhat smaller than the corresponding OLSestimate. The 2SLS estimates are likely to bemore useful for predicting the impact of schol-arship programs on new scholarship recipientsthan are the reduced-form effects, which arediluted by take-up rates less than one and theavailability of alternative financing.

VI. Impact on Household andGovernment Expenditure

This section discusses the impact of the pro-gram on household and government budgets.We begin by showing that approximately 70percent of voucher funds flowed to increasededucation expenditures, with the remainder go-ing to educational spending thai householdswould have made without the voucher. Takinginto account the reduction in work by lotterywinners suggests that winning the lottery induced

1550 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

TABLE 8- -MATRtCULATION, TirtTiON FEES, AND VOUCHER STATUSRiK B(XiOTA 1995 APPLICANTS

Variable

Using any scholarship insurvey year

Currently in private school

Currently in public school

Scholarship valtie

Scholarship value(conditional on >0)

Gross school fees

Net school fees

Gross school fees forpublic schools

Currently using scholai'shipfrom the private school

Sample size

Full sample

Losermeans

(!)

0.054(0.227)0.530

(0.500)0.290

(0.454)16.0

(64.2)199.0

(122.4)191.5

(188.3)175.9

(185.6)54.6

(109.4)0.031

(0.173)534

Nocontrols

(2)

0.497(0.023)0.156

(0.029)-0.140(0.025)74.3(5.4)

-13.3(19.1)52.3

(10.2)-22.0(11.5)

3.2(13.4)-0.008(0.011)1.085

Basiccontrols

(3)

0.494(0.023)0.152

(0.028)-0.146(0.025)72.6(5.4)

-11.3(18.5)48.1

(11.0)-24.5

(9.9)1.0

(13.8)-0.010(0.012)1.085

Conditional on private-school

Losermeans

(4)

0.085(0.279)1

0

29.8(85.8)211.1

(118.2)332.2

(133.6)302.4

(154.3)—

0.059(0.235)283

attendance

Nocontrols

(5)

0.709(0.027)

—

—

101.8(7.6)

-25.5(19.1)11.0

(10.7)-90.7(11.6)

—

-0.026(0.019)661

Basiccontrols

(6)

0.696(0.028)

—

—

98.1(7.9)

-22.0(18.5)

9.8(10.7)

-88.2(11.7)

—

-0.031(0.020)664

Notes: The table reports voucher losers* means and the estimated effect of winning a voucher.Numbers in parentheses are standard deviations in columns of means and standard errors incolumns of estimated voucher effects. Sample sizes differ from other tables because ofmissing fee data. The sample sizes differ slightly across rows because of missing data for"Currently using scholarship from the private school" and the outcomes with the morecomprehensive fee measure. The regression estimates in columns (3) and (6) are from modelsthat include controls for whether applicants had access to a phone, age, type of survey andinstrument, strata of residence, and month of interview.

households to devote more net resources to ed-ucation. The higher fees paid by voucher win-ners are due primarily to winners' greaterlikelihood of attending private school. How-ever, there is also some evidence that appli-cants who would have attended privateschools anyway traded up to tiiore expensiveprivate schools in response to winning thevoucher. Since the voucher did nol reduce thecost of private school at the margin, this resultweighs against the simplest models of educationas human-capital investment without creditconstraints.

The results in subsection B suggest that itcost the government about $24 more per lotterywinner to provide school places throughPACES than through the public system. Finally,subsection C aggregates the impact on house-holds, schools, and the government budget, ar-

guing that the total social costs of providingadditional school places through the PACESvoucher system were small, and thereforedwarfed by the benefits of the program to par-ticipants. The analysis in this section uses datafor the 1995 Bogota applicant cohort only.

A. Impact on HouseholdEducational Expenditure

Three years after the 1995 lottery in Bogota,about 55 percent of winners and 5 percent oflosers were still receiving scholarships (a resultfrom Table 3 repeated in the first row of Table8 for the sample of observations with usable feedata). In this sample, 53 percent of losers werestill in private school in the survey year, withthe private-school enrolhnent rate 15.2 percenthigher for winners after control for covariates.

VOL 92 NO. 5 ANGRIST ET AL: VOUCHERS FOR PRIVATE SCHOOUNG 1551

Among applicants to the Bogota-95 lottery,winners received an average of $74 more inscholarship aid than losers, a result reported inthe fourth row of Table 8. Conditional on re-ceiving a scholarship, scholarship amounts weresimilar for winners and losers, at roughly $200.The estimates in Table 8 also show gross ma-triculation and tuition fees were S52 greater forlottery winners than losers. Thus, the 1998voucher expenditures of $74 per winner causedan increase of $52 in gross fees for winners,about 70 percent of the extra amount receivedby winners on average. The remaining $22 ofvoucher funds presumably increased noneduca-lional expenditures by lottery winners.'^

Aside from paying for school fees, house-holds bear the opportunity cost of the effortstudents devote to education. The estimates fornoneducational outcomes in Table 6 suggestlottery winners spent 1.2 fewer hours workingeach week. According to our survey data, theaverage hourly wage was 71 cents.'^ Assumingthat students work 48 weeks per year, this re-duction corresponds to an opportunity cost of1.2 X $.71 X 48 weeks, approximately $41.Combining the increase of $52 in expenditureson fees and the $41 of lost earnings, we estimatethat PACES lottery winners devoted $93 moreto education than losers in the survey year, or126 percent of the $74 in extra scholarshipassistance they received.

Disaggregating Effects on Fees.—-Whilewinning households spent about $52 more onschool fees, this average conceals importantheterogeneity. Since vouchers covered only partof the cost of private school, families with chil-dren who were induced to switch to privateschool increased their educational expendituresharply. However, most of the applicants wholost the lottery started private school in sixthgrade anyway, and over half were still in private

'* The estimated displacement of private expenditure iseven lower when a more comprehensive expenditure mea-sure is used. Lottery winners repon an estimated $84 morein comprehensive scholarship assistance (i.e.. including ex-penditure on uniforms and textbooks) and an extra $74 morein comprehensive educational expenditure.

'^ Conditional on working, the average daily wage in oursample was $5.71. We estimated tiie hourly wage assuminga seven-hour work day.

school in the survey year. So most voucherswere received by applicants who would haveattended private school without the vouchers.

Simple tnodels of education as human-capitalinvestment with perfect credit markets suggestthat since PACES vouchers were worth only$190 per year, while most private schoolscost over $300 per year, vouchers were infra-marginal. In other words, vouchers were notlarge enough to have cau.sed households toincrease educational spending by choosing amore expensive private school.'^ On the otherhand, winning the voucher could have ledhouseholds to choose more expensive privateschools if educational spending is limited bycredit constraints or if education has consump-tion value as well as investment value.

In a noncausal, purely accounting sense, the$52 of increased expenditure by winners onschool fees can be decomposed into the effectsof increased private-school enrollment, and aswitch to more expensive private schools bywinners. Let Z be a dummy for lottery win/lossstatus as before, except we now drop "/''' sub-scripts to sitnplify notation. Also, let R denotetype of school attended (I for private. 0 forpublic) and let F denote education expenditure.Gross school fees conditional on lottery win/loss status (i.e., fees paid by pupils withoutsubtracting voucher amounts) are equal to

E[F\Z] = E[F\Z, R = 1 ]P[R = 1 |Z]

+ E[F\Z, R = O]P[R = 0|Z].

The overall change in fees is a linear combina-tion of changes in public/private enrollment andchanges in fees charged by school type. We cansimplify the fee contrast between winners andlosers using the fact that public-school feeschanged little and overall school enrollment wasalso affected little, so that P[R = l|Z = 1] -P[R = 1|Z = 01 - -{P[R = 0|Z = n - P[R =0[Z = 0 ] } . Then we have the following ac-counting relationship:

"*To see this, note that if education is pure human-capital investment, people choose schools so that a schoolcosting one dollar more generates exactly one more dollarof present di.scounted earnings. For people who would inany case have attended a school costing more than $ 190. thevoucher does not affect this first-order condition.

THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

(5) E[F\Z= 1] - E[F\Z= 0 ]

= {E[F\Z = \,R= \]- E[F\Z - 1, ;? - 0]}

X{P[R= i | Z = \]- P[R^ 1 | Z - O ] }

-F p[/; = i|z-o]{£;[F|z= 1,;? - I] • i-

- E[F\Z=O,R= I ] ) .

In words, the overall fee increase is caused bythe private-public fee difference for winners,times private-school enrollment effects of theprogram, plus the win/loss contrast in fees forprivate-school pupils.''' The right-hand-sidecomponents of (5) are as follows:

P[R = 1] - P[R = l\Z= 0] = 0.15

E[F\Z= I , /? = I ] - E[F\Z = 1 . ^ - 0 ]

= 3 4 3 - 5 8 = 2 8 5 • i -

E[F\Z= \,R= []

- E[f\Z = 0, R = i ] = I I

P[R= 1|Z = 0] = 0.53.

This implies a total effect of $49, which is lessthan $52 because of the approximation used tosimplify (5), with $43 due to school switching.Thus, in an accounting sense, the bulk of thechange in household expenditure can be attrib-

. • • , , • • - r ' '

'^ Without simplification the comparison is

E[F\Z= 1] - E[F\Z= 0]

= P [ R = 1|Z = OJ ' ' '

X{E[F\Z= l.R= I] ~ E[F\Z = Q. R = 1]}

+ E[F\Z= l . f t = 1] . ,• _,(-

X {P[R ^ \\Z = \1 - P[R = 1\Z ^ 0]} '• '"••

+ P[R = O\Z = (}]

X {E[F\Z = 1, R = 0] - E[F\Z = 0. R = 0]}

+ E[F\Z= i,R = O]

X {P[R = 0\Z = \] - P[R = 0\Z = 0]}. I .

uted to increased private-school enrollment.However, for reasons discussed below, this de-composition provides an incomplete picture ofthe causal effect of the program on the feedistribution.

Causal effects on fees for families who wouldhave sent their children to private school any-way are difficult to measure since we do notknow who these families are. Simply comparingfees by win/loss status conditional on private-school attendance [the second term in (5),above] leads to a biased estimate that is almostcertainly too low. To see this, let FQ be thepublic or private fee a pupil would pay if he orshe loses the lottery and let F, be the pubhc orprivate fee he or she would pay if he or shewins, and let /?(j and /?, denote private-schoolattendance if a pupil loses or wins the lotteryrespectively. Similarly, let /o be the private-school fee a pupil would pay if he or she losesthe lottery and let/, be the private-school fee apupil would pay if he or she wins. Thus f^ =FQRQ and/I = F ,^ i . We imagine that thesevariables are defined for every pupil, though inpractice, we can only observe Fy, /?„. and/j, forlosers and F, , ^ | , and/, for winners. £•[/, —/ol/f) > 01 is the effect on fees for those whowould attend private school even if they were tolose the lottery. The observed contrast in fees forprivate-school pupils can be written as follows:

(6) £ [ F | Z = \, R = 1] - F [F |Z= 0, i? = 1]

The term in braces refiects selection bias in theconditional-on-positive contrast. Under mild as-sumptions, this tenn is negative.^" Assuming, as

is easy lo show in a model where/, = h(fo)for any increasing transformation. More generally, win-ners who attend private school only if they win probablyattend cheaper private schools than those who attendregardless. Suppose, for example, that school qualitycomplements ability and higher-quality schools are moreexpensive. Then low-ability children attend publicschools if they lose the lottery and attend cheap privateschoois if they win the lottery, while high-ability childrenattend expensive private schools whether or not they wina voucher. Alternatively, consider a model with creditconstraints in which the poor attend public school; the

VOL 92 NO. 5 ANGRIST ET AL: VOUCHERS FOR PRIVATE SCHOOUNG 1553

seems likely, that / , > /(,, the left-hand sidetherefore is a lower bound on the causal effect.

The parameter £•[/, — folfo > 0] is notidentified without further assumptions (see e.g.,Gary Chamberlain, 1986), though the previousdiscussion suggests we can treat the observedcontrast in fees for private-school students as alower bound. Under mild assumptions, we canobtain a reasonably tight upper bound on this anda related family of parameters: E[f\ - /o[/o >/»o(6)l where mo(fl) is the 0-quantile of the losers*fee distribution. By choosing *n(,(0) == 0, webound E[fi — ^ | ^ > 0]. while picking points athigher quantiles, we measure the effect on thosewho would have spent more on private schoolingin the absence of the lottery. For example, we canbound the effect of winning the lottery on private-school fees for those who would have spent morethan the voucher amount ($190) on private-schoolfees in the absence of the lottery. This result isstated formally below.

PROPOSITION: Suppose that F, > F,,. UtmQ(B) be the 6 quantile of the distribution of Ffor losers, withmi(B) defined similarly for win-ners. Then

(7)

^ P[R = O,

PROOF:Define F ^ = o , , ^

FoKFo > mo(0), Ro = 0) + F,l(Fo >m,,(0), ffo ^ n . Note that F^ = F, forhouseholds above the quantile who would haveattended private schools anyway. Otherwise,

= F,j. Thus, F , > Let> mo(0)]. Then

rich attend private school: and the very rich attend ex-pensive private schools. Then lottery winners who wouldhave attended public school if they lost the lottery willattend cheaper schools than lottery winners who wouldhave attended private school even if they lost.

Note that

= 0].

Therefore,

= I].

Since /() = ^^, this implies

which is the quantity we seek to bound. Also,since Fj >: F ^ ^ /̂ o for all applicants,

|> and we have

By randomization, E[Fi\F^ >E[F\Z = I, F > mi(0)] and o | om,,(0)] = £[F|Z = 0, F > mo(B)] and /J,, =P[R = l|Z = 0, F > m,,(0)l. which implies(7) and completes the proof.

To see why the upper bound works in thecase where B = 0, note that E(FM - Eft) is theaverage difference between winners* and losers'fees due to households who would have at-tended private schools in any case trading up tomore expensive private schools. This is lessthan the observed difference in total fee pay-ments by win/loss status, E(Fi - F,,). Econo-metric intuition for this result comes from thefact that in parametric sample selection models.

1554 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

TABLE 9—LOWER/UPPER BOUNDS OF VOUCHER EFFECTS ON MATRICULATION AND TumoNFOR BOGOTA 1995 APPLICANTS WHO WOULD HAVE AITENDED PRIVATE SCHOOL

AND PAID MORE THAN CtrrorF FEES

Dollarcutoff

190.0

283.2

335.8

370.1

427.0

Correspondingquantiie ofloser fee

distribution

52nd percentile

60th percentile

70th percentile

80th percentiie

90th pereentile

Loser averagefee abovequantile

370.5(104.7)396.7(94.4)424.8(92.7)460.2(96.0)523.3

(101.0)

Loserprobability of

private-school

attendance

0.973(0.163)0.981

(0.136)0.981

(0.136)0.972

(0.167)0.943

(0.233)

Loser averageprivate-school

fee abovecutoff

368.1(95.1)392.5(83.0)419.3(78.7)452.8(78.3)511.9(74.5)

Upperbotind

38.4(9.5)31.4(9.7)32.1

(11.3)36.5(9.3)48.3

(16.8)

1

Lowerbound

2.9(8.9)

9.2(8.8)17.7

(10.0)14.0

(12.3)27.7

(18.3)

Notes: The upper bound above a given percentile is computed in a two-step process. First, weestimate the difference between winners' and losers' matriculation fees conditional on beinggreater than the given quantile in tlieir respective distributions. Second, we divide this differenceby the probability that losers above the given percentile attend private school. The lower boundabove a cutoff is computed by difterencing winners' and losers' fees conditional on private-schoolattendance and conditional on being greater than the cutoD. See lext for further details.

controlling for the probability of sample selec-tion eliminates selection bias. Comparing win-ners and losers at the same quantiles equalizesthe "probability of selection" if F, = h(F^^) forsome monotone increasing transformation, h. Infact, with no public-school fees, the bound isexact when F, = /?(F(,). More generally, dividingby P[/? = 1 |Z = 0, F > Wo(e)] corrects for the factthat some of those with positive fees were attend-ing public school, and the bound applies evenwithout a deterministic link between FQ and F,.

Estimates of the right-hand size of (7) arereported in Table 9, along with a lower boundusing tbe biased comparison for quantiles anal-ogous to (6); this is, £[F|Z = 1, /? = 1, F >mo(9)l - E\F\Z - 0, /? = 1, F > mo(B)\.As noted earlier, this is a plausible lower boundbecause of negative selection bias. Note alsothat any reasonable behavioral model wouldpredict that a family that spent less than thevoucher amount on private school without avoucher would spend more after the voucher.We therefore focus on bounding effects that areconditional on paying pre-voucher fees equal toat least the voucher amount, roughly $190.

Among losers paying at least $190 in fees,the average fee was $371. Almost all of thesepupils were in private school (in fact, some

reports of public-school fees above $190 areprobably in error; others refer to a handful ofelite public schools that charge significant fees).The lower bound on £ [ / , - /o[/n > 190] isabout $3, but the upper bound is $38. Thevoucher amount of $190 is the 0.52 quantile ofthe fee distribution. Above this amount, thebounds are tighter. The estimated upper boundsabove 0.6 range from $31 to $48. while thelower bounds range from $9 to $28. The lower-bound estimates are not significantly differentfrom zero at the 5-percent level. In some cases,however, the lower bounds are close to a 10-percent significance level, while the upperbounds allow for effects on the order of 10percent of fee costs and 20 percent of thevoucher value. Thus, it seems likely that win-ners in the upper half of the fee distributionspent 5-10 percent more on private schools thanthey otherwise would have. This implies thatthe marginal propensity to spend voucher in-come on more expensive private schools wasnontrivial, counter to a simple mode! of human-capital investment without credit constraints.

Price Discrimination by Private Schools.—Another potential source of increased expen-diture on fees by winners is price discrimina-

VOL 92 NO. 5 ANGRIST ETAL: VOUCHERS EOR PRIVATE SCHOOUNG 1555

tion. There is little evidence that private .schoolsdiscriminated by charging more to applicantswith PACES scholarships. The easiest way forschools to price discriminate was to offer schol-arships to those less likely to be able to affordeducation at the full price (i.e., applicants with-out PACES vouchers). In practice, however, wefound little evidence of price discrimination.Our survey indicates that roughly 6 percent oflosers in private school received a school schol-arship, while 3 percent of winners in privateschool received a school scholarship. This is asmall and insignificant difference. Per lotterywinner (i.e., without conditioning on attendingprivate school), the difference is only about 1percent.

B. Impact on the Government Budget

The PACES program was established in partto expand secondary-school enrollment withoutusing the public system. We estimate that theprogram increased public educational expendi-ture by about $24 per lottery winner, relative tothe cost of accommodating these pupils in pub-lic school. As discussed in Section III, winnerswere no more likely than losers to attend school,but the program probably did expand overallschool enrollment by freeing up places in publicschools as lottery winners transferred to privateschools.

To see where the $24 figure comes from, notethat the probability of attending public school,reported in Table 8, fell by 0.14 for lotterywinners. The average per-pupil cost of a publicsecondary-school slot was about $350, exclud-ing implicit rental for school facilities. In theshort run, the marginal cost of public-schoolslots may differ from the average cost, but in thelong run, it seems reasonable to assume mar-ginal and average costs will be similar. Assum-ing the marginal cost of providing public-schoolplaces equals the average cost, adding schoolspaces through PACES reduced long-run ex-penditure on public schools by 14 percent of$350 or roughly $50 per winner, so the extrapublic educational expenditure per lottery win-ner is about $74 (to pupils) -$50 (in reducedpublic-school costs) = $24. Moreover, allowingthe marginal cost to differ from average cost by$100 either way still leads to voucher programcosts in the $10-$40 range.

C. Overall Cost and Benefits

The extra society-wide educational resourcecost per lottery winner differs from the roughly$24 of extra public-education expenditure, sincehouseholds used part of the voucher funds tooffset education costs they would have incurredprivately, and lost income from their children'swork. The average lottery winner received $74more than the average loser in scholarship as-sistance, but spent only $52 more on grossschool fees. Lottery winners earned $41 lessthan losers through work. Winning households'net resource contribution was therefore $52 (ad-ditional school fees) + $4! (reduced earn-ings) - $74 (voucher) = $19. This implies thatthe society-wide additional educational resourcecost per lottery winner was approximately $24(government) + $19 (households) = $43.

The comparison of costs and benefits shouldtake account of the fact that three years of costswere incurred prior to our survey. The total costof the program can therefore be estimated bymultiplying the annual resource cost times theroughly three years winners received vouchers,for a total of about 3 X 24 = $72 in additionalpublic-educational expenditure and 3 X $43 —$129 in total societal resource cost. Actual costsare probably somewhat higher, however, sincevoucher take-up rates declined over time, with88 percent of winners having ever used avoucher, and only 49 percent using it in thesurvey year. Multiplying costs by 88 percent/49percent for the first and second years yields anupper bound on the three-year cost of the pro-gram of about $195 using the $43/year figurefor social costs.

These costs are likely to have been smallrelative to the benefits for participants. Al-though lottery winners gave up current eam-ing.s, they completed an additional 0.12 to 0.16grades and scored approximately 0.2 standarddeviations higher on tests. Among U.S. His-panic students who took the same test, the dif-ference in test scores between seventh- andeighth-graders, or between eighth- and ninth-graders, was also about 0.2 standard deviations,so the achievement gain from winning the lot-tery may be as large as that associated with afull year of schooling. Our estimates using arecent Colombian labor-force survey show re-turns to a year of schooling of about 10 percent.

7556 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

If the gain from the program is solely the eco-nomic return to an additional 0.12 years ofschooling, the program raised winners' wagesby 1.2 percent per year, whereas if it is equal tothat from a full year of schooling it raised wagesby 10 percent. Annual earnings of parents in oursample were about $2,400 per worker, andPACES applicants should be able to earn more,since the average parent had only 5.9 years ofeducation while the average applicant had al-ready completed 7.5 years and was still inschool at the time of our survey. We thereforeassume the expected earnings of applicants are$3,000. Thus, PACES seems very likely to raiselottery winners' wages by $36 per year, andmight raise wages by as much as $300 per yearif higher test scores have a grade-equivalentpayoff. Discounted over applicants workinglives, these benefits easily outweigh the socialcosts of the voucher program, which are prob-ably no more than $195.

A more complete cost-benefit analysis wouldtake into account the program's effects on non-participants. Pupils left behind in public schoolsmay have been hurt by the departure of moti-vated classmates for private schools, as arguedby Hsieh and Urqiola (2001), or alternatively,public schools may have responded positivelyto increased competition, a possibility consideredby Caroline M. Hoxby (2000) and Bettinger(2001b). Such general-equilibrium effects can-not be assessed by comparing lottery winnersand losers. But since the partial-equilibriumcost-benefit analysis is clear-cut, and since only15 percent of winners moved from public toprivate schools, any negative external effects onnonparticipants would have to bave been ex-traordinarily large to outweigh program benefits.

VII. Summary and Conclusions

Governments in many developing countriesare increasingly willing to experiment withdemand-side subsidies and public-private part-nerships to meet basic education needs. Theimpact of these programs and policy innova-tions is an open question. Colombia's PACESprogram provides an unusual opportunity to as-sess the effect of demand-side education financ-ing in a Latin American country where privateschools educate a substantial fraction of pupils.

The PACES program is of special interest be-cause many vouchers were assigned by lottery,so program effects can be reliably assessed. Ourresults suggest that lottery winners benefittedfrom higher educational attainment, primarilyas a consequence of reduced grade repetition, aswell as from higher test scores and a lowerprobability of teen cohabitation or employment.Our estimates of the economic benefits to par-ticipants far exceed the estimated costs. Most ofthe results suggest PACES vouchers had astronger effect on the education of girls than onthe education of boys.

Our findings suggest that demand-side pro-grams like PACES can be a cost-effective wayto increa.se educational attainment and aca-demic achievement, at least in countries likeColombia with a weak public-school infrastruc-ture and a well-developed private-educationsector. A number of channels could account forthe impact of PACES vouchers. Eirst, lotterywinners were more likely to have attended par-ticipating private schools, and these schoolsmay be better than public schools. Second,vouchers allowed some pupils who would haveattended private schools anyway to attend moreexpensive schools. Finally, because voucher re-cipients who failed a grade risked losing vouch-ers, lottery winners had an incentive to devotemore effort to school. The net effect is such thatthe benefit of voucher awards were more thanenough to offset the costs. In work in progress,we are assessing longer-term consequences ofvoucher receipt. Preliminary results indicatethat the program increased secondary-schoolcompletion rates, and that college-entrance testscores were higher for lottery winners than los-ers. These results are indicative of greater learn-ing and seem unlikely to be due solely to greaterincentives for PACES recipients to avoid graderepetition.

REFERENCES

Angrist, Joshua D. "Conditional Independencein Sample Selection Models."' EconomicsLetters. February 1997, 54(2), pp. 103-12.

Angrist, Joshua; Bettinger, Eric; Bloom, Erik;King, Elizabeth and Kremer, Michael."Vouchers for Private Schooling in Colom-bia: Evidence from a Randomized NaturalExperiment." National Bureau of Economic

VOL 92 NO. 5 ANGRIST ET AL: VOUCHERS FOR PRIVATE SCHOOUNG 1557

Research (Cambridge, MA) Working PaperNo. 8343, June 2001.

Behrman, Jere; Sengupta. Piyali and Todd, Petra.•'Progressing through PROGRESA: An Im-pact Assessment of Mexico's School SubsidyExperiment." Working paper. University ofPennsylvania and the International Food Pol-icy Research Institute, 2000.

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