also interviewed from each school. Students were randomly selected from Senior 1 and 2 classes. In cases where there were not enough students from these two grades, Senior 3 students were interviewed. In total, 944 and 801 students were selected from treatment and control schools, respectively.

Follow-up unannounced surveys were administered at three different points in time (subsequently referred to as _checks_ 1, 2 and 3). Check 1 was administered in July 2011 in 96 schools, during the second school term. Check 2 was administered in September 2011 in 94 schools, during the third term of the school year. Check 3 was administered in 95 schools in February 2012, during the first term of the new school year, prior to the expansion of the program to the control schools. Check 3 also included student interviews with 1,467 and 1,261 students in treatment and control schools, respectively. The variation in number of schools covered in each check is linked to the inability of reach certain schools at certain times of the year. Some common reasons for not reaching schools were weather conditions leading to lack of access or school closure. In addition, some schools closed permanently, an outcome we examine explicitly in the results.

In addition to surveys designed by the research team, the study partnered with the Uganda National Examinations Bureau (UNEB) to measure student performance. UNEB conducts an annual standardized assessment in a nationally representative sample of 500 schools called the National Assessment of Progress in Education (NAPE). This mid-year assessment measures student proficiency in English, Mathematics and Biology for a group of 30 randomly selected students in Senior 2. In July 2011 and 2012, UNEB included the list of 100 schools from the study in addition to their national sample and administered the three assessments. In addition, UNEB administered an additional Mathematics test (“Math independent”), which the research team adapted from TIMSS, an international test,<sup>9</sup> through discussions with psychometricians in Uganda. The independent test was included to detect real gains in achievement using an alternative to the official test (NAPE), which may be subject to “teaching to the test”. NAPE data were collected in 2011 for 1,230 students from 48 treatment schools and 1,126 from 45 control schools, and in 2012 for 1,268 students from 48 treatment schools and 990 from 45 control schools.

# b. Empirical Strategy

The research team performed the phase-in lottery in December 2010. Treatment is defined as formal notification that the private school is a part of the PPP program. All treatment schools received this notification of acceptance into the PPP program in February 2011 and none of the control schools did. In this respect, compliance to randomized design was close to 100%.

However, actual transfer of resources under the PPP program was slower and compliance was less than perfect. Consequently, we are estimating two models: an intent-to-treat model, ITT (based on the lottery assignment) and an instrumental variable (IV) design that uses actual program implementation, as reported by the schools.

The ITT model is based on two main specifications. In the first model, the outcome variable _Y_ of student (grade and gender) _i_ in school _s_ at time _t,_ is regressed against a dummy variable indicating random assignment to treatment ( _T_ , 1=treatment; 0=control).

> 9 <mark>The Trends in International Mathematics and Science Study (TIMSS) is a series of international assessments of the mathematics and science knowledge of students around the world. For this research, we used a balanced selection of openly available questions from Grade 4 TIMSS Mathematics tests across specified learning domains.</mark>

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