_14_ from existing consumers or expanding market share and risking price competition. Our main result is that we are more likely to observe higher enrollment in treated schools in the _L_ arm and higher quality (and increased fees) in the _H_ arm. Moreover, private profits will be higher for _L_<sup>_t_</sup> schools. Although, conceptually, a test of the theory can be based on variation in the size of the uncovered market and the cost of quality investments, these are not observed in the data. Therefore, we focus attention in our empirical results on the di↵erence in impact between low and high-saturation villages.

# **III. Experiment, Data and Empirical Methods**

# _A._ **_Experiment_**

Our intervention tests the impact of increasing financial access for schools for outcomes guided by theory (revenue, expenditures, enrollment, fees and quality captured as test scores) and assesses whether this impact varies by the degree of financial saturation in the market. Our intervention has three features: (i) it is carried out only with private schools where all decisions are made at the level of the school;<sup>19</sup> (ii) we vary financial saturation in the market by comparing villages where only one (private) school receives a grant ( _L_ arm) versus villages where all (private) schools receive grants ( _H_ arm); and (iii) we never vary the grant amount at the school level, which remains fixed at Rs.50,000.

_Randomization Sample and Design.—_ Our sampling frame is defined as all villages in the district of Faisalabad in Punjab province with at least 2 private or NGO schools; 42 percent (334 out of 786) of villages in the district fall in this category. Based on power calculations using longitudinal LEAPS data, we sampled 266 villages out of the 334 eligible villages with a total of 880 schools, of which 855 (97%) agreed to participate in the study.

Table 1 presents summary statistics from our sample at the village (Panel A) and the private school level (Panel B). The median village has 2 public schools, 3 private schools and 416 children enrolled in private schools. The median private school has 140 enrolled children, charges Rs. 201 in monthly fees, and reports a monthly revenue of Rs. 26,485. Monthly variable costs are Rs. 16,200 and annual fixed costs are Rs. 33,000, for an annual profit of Rs. 90,420. The range of outcome variables is quite large. Relative to a mean of 164 students, the 5th percentile of enrollment is 45 compared to 353 at the 95th percentile of the distribution. Similarly, fees range from Rs. 81 (5th percentile) to Rs. 503 (95th percentile) and monthly revenues from Rs. 4,943 to Rs. 117,655. The kurtosis, a measure of the density at the tails, is 17 for annual fixed expenses and 51 for revenues relative to a kurtosis of 3 for a standard normal distribution. Our decision to include all schools in the market provides external validity, but has implications for precision and mean imbalance, both of which we discuss.

> 19This excludes public schools, which cannot charge fees and lack control over hiring and pedagogic decisions. In Andrabi et al. (2018), we study the impact of a parallel experiment with public schools between 2004 and 2011. It also excludes 5 (out of close to 900) private schools that were part of a larger school chain with schooling decisions taken at the central office rather than within each school.