2003; MacLeod and Urquiola, 2012). Evidence exists for Pakistan on the relative effectiveness of private versus government schools. Using an instrumental-variables approach, Andrabi et al. (2010) find that lowcost private schools in rural Punjab have large, positive effects on test scores and civic knowledge among primary-school students. They attribute this to the fact that private schools adjust their inputs to meet local conditions, whereas government schools do not. In the same setting, Andrabi et al. (2011) also examine the effects of enrollment in low-cost private schools on test scores, based on data for students who switch from government to private schools, and vice versa. They find that students who move from government to private schools see a large gain in test scores shortly after moving, while those who move from private to government schools see a large decline. The estimated effects from these studies may, however, be biased due to demand-side selection into private schools by households and supply-side selection of students by schools. These forms of selection make it difficult to disentangle the effect of school effectiveness from that of the composition of students in terms of ability.

An important source of rigorous evidence on private-school effectiveness comes from studies of privateschool voucher programs in developing countries. Based on vouchers offered through lotteries to low-income, government-school students for private secondary schooling in Colombia, Angrist et al. (2002) find positive effects of private-school enrollment on several outcomes, including grade progression and test scores. However, these effects potentially reflect both private-school effectiveness and incentivized student effort.<sup>8</sup> Randomly assigning vouchers at the village and household levels to government-school students for private primary schooling in India, Muralidharan and Sundararaman (2015) find that private schools are highly cost-effective in raising test scores. They also find that private schools are more responsive in terms of matching what’s taught to household demand, reallocating time away from subjects such as reading and mathematics, towards English, Hindi, science, and social studies.<sup>9</sup> In addition, the study did not find spillover effects on governmentschool students who were not assigned vouchers, nor students initially enrolled in private schools, in program villages.

This study is also linked to the literature on PPP programs in education (Patrinos, Barrera-Osorio, and Guáqueta, 2009). Although these programs share many of the theoretical justifications discussed in the private-school voucher literature (for example, private-school effectiveness, market competition), they differ in important ways. Most conspicuously, PPPs enable higher-quality education for beneficiary students through the terms of the contract between the program school and the government, with some programs regulating school inputs (including teachers), and others selecting program schools based on measures of

> 8In addition to enabling private-school enrollment, the program stipulated that students would lose their vouchers if their grades fell below a certain level.

> 9Test scores for Telugu and mathematics remained the same, despite significantly less time being spent on these topics; while time allocated towards other topics yielded test-score improvements.

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