1 The Causal Question

Do private-school vouchers improve educational outcomes for poor children? The question is among the most contested in the economics of education, and most evidence is hopelessly confounded: families who choose private schools differ from those who do not in motivation, income, and a hundred unmeasured ways. A simple comparison of voucher users and non-users measures selection as much as it measures schooling.

Colombia's Programa de Ampliación de Cobertura de la Educación Secundaria (PACES) handed researchers something rare: a setting in which the confounding was switched off by administrative necessity. Between 1991 and 1997 the programme distributed over 125,000 vouchers covering more than half the cost of private secondary school to children from poor neighbourhoods. Because demand exceeded the budget, many municipalities allocated vouchers by lottery. Angrist et al. [2002] recognised this for what it was a randomised natural experiment and used it to estimate the causal effect of voucher receipt on schooling, achievement, and behaviour.

2 The Identification Strategy

The lottery is the whole game. Among applicants in over-subscribed municipalities, voucher receipt was determined by a random draw, so lottery winners and losers are, in expectation, identical in every pre-treatment characteristic. The difference in their later outcomes is therefore a clean estimate of the intention-to-treat (ITT) effect of winning a voucher:

Winning a voucher is not the same as using one, nor as attending private school: some winners never enrolled, and some losers attended private school by other means. To recover the effect of using the voucher, Angrist et al. [2002] treat lottery status as an instrument and estimate the local average treatment effect (LATE) by two-stage least squares,

which scales the ITT by the first-stage jump in voucher use. Under random assignment, the exclusion restriction (winning affects outcomes only through schooling), and monotonicity,

τ_LATE is the effect for compliers children who used a voucher because they won one [Imbens and Angrist, 1994]. Because assignment was random, the instrument is unimpeachable, and the analysis is as close to an experiment as observational education research gets.

3 Data and Setting

PACES targeted students entering grade 6 (the start of secondary school) in low-income urban neighbourhoods. Vouchers were renewable conditional on satisfactory academic progress a feature that, by design, gave recipients an incentive to advance rather than repeat grades. Angrist et al. [2002] combined application records with a follow-up survey of Bogotá applicants conducted about three years after the lotteries, measuring grade completion, repetition, achievement on a purpose-built test, and a range of non-schooling behaviours. A companion study, Angrist et al. [2006], linked the original lottery records to centralised administrative data on the national college-entrance examination (the ICFES), enabling the team to follow the same children years later without the attrition that plagues survey follow-ups.

4 Key Findings

The short-run results were striking and consistent across outcomes:

• Grade progression. Three years on, lottery winners were about 10 percentage points more likely to have finished eighth grade, an effect driven largely by reduced grade repetition rather than reduced dropout.
• Achievement. Winners scored roughly 0.2 standard deviations higher on the achievement tests administered by the study a sizeable effect for a partial-cost voucher.
• Behaviour. Winners worked less during the school years and were less likely to marry or cohabit as teenagers, consistent with the voucher pulling children more fully into schooling and away from the labour market.
• Cost-effectiveness. Because the renewal incentive cut repetition, the additional public cost of supplying a voucher over a public-school place was modest on the order of $24 per winner so the programme's social benefits plausibly exceeded its costs.

The long-run administrative follow-up reinforced the picture. Angrist et al. [2006] found that voucher winners were about 5 to 7 percentage points more likely to take the college-entrance examination- proxy for high-school completion against a base completion rate of roughly 25 to 30 percent, and scored modestly higher on it. The effects of a three-year, half-cost subsidy thus persisted into the threshold of higher education.

Limitations and What We Learn

No design is bulletproof, and the authors are candid about the caveats. First, the LATE in equation (2) is a complier effect: it speaks to families on the margin of using a voucher in over-subscribed Colombian municipalities in the 1990s, not to the average effect of vouchers everywhere. Whether the result travels to other countries, other programme designs, or universal (non-rationed) voucher schemes is a question of external validity the lottery cannot answer.

Second, the renewal-conditional-on-progress feature means PACES bundled a price subsidy with a performance incentive. The estimated effect is the effect of this package; a pure unconditional voucher might do less. Third, the achievement test in the short-run study was administered to a non-random subset of applicants who could be located and agreed to sit it, raising the possibility of differential follow-up a concern the administrative-records strategy of Angrist et al. [2006] was specifically designed to overcome.

The methodological lesson outlasts the policy verdict. PACES is a textbook illustration of how rationing under a binding budget constraint can generate experimental variation, and of the disciplined two-step that turns it into evidence: estimate the ITT from the lottery, then instrument to recover the effect of treatment on compliers. The same template lottery-based admission as an instrument now underpins causal work on charter schools, housing assistance, and public-sector hiring. When governments cannot afford to serve everyone and resort to a fair draw, they are, often unwittingly, running the cleanest experiment an economist could ask for.

References

1. Angrist, J., Bettinger, E., Bloom, E., King, E., and Kremer, M. (2002). Vouchers for private schooling in Colombia: evidence from a randomized natural experiment. American Economic Review, 92(5), 1535-1558.
2. Angrist, J., Bettinger, E., and Kremer, M. (2006). Long-term educational consequences of secondary school vouchers: evidence from administrative records in Colombia. American Economic Review, 96(3), 847-862.
3. Imbens, G. W., and Angrist, J. D. (1994). Identification and estimation of local average treatment effects. Econometrica, 62(2), 467-475.