Estimating an Equilibrium Model of Horizontal Competition in Education

Study Design and Findings

A student who knows calculus will not benefit from remedial math instruction, no matter how well taught. Similarly, a student who has never learned fractions is unlikely to benefit from calculus. A growing literature shows that the match between a student’s instructional needs and a school’s instructional level is an important determinant of learning. Given the importance of this match, instructional level may be misallocated, with students attending schools whose instruction is not well-matched to their needs. Yet little is known about the extent of this misallocation, how schools choose their instructional level, and how their choices of instructional level respond to competition.

Indeed, competition may increase the misallocation of instructional level. Private schools do not typically provide the socially optimal quality, and if increased competition causes the marginal consumer’s preferences to be further from those of the average consumer, competition may reduce welfare. These distortions may be exacerbated if students have limited information about schools’ instructional levels. Given extremely high rates of private schooling, low levels of learning, and the frequency of a single teacher teaching all the students in a grade in low-income countries, understanding how instructional match interacts with private schools’ competitive incentives may be crucial for improving students’ outcomes. The increasing popularity of policies that incentivize school competition in low-income countries further underscores the importance of understanding the interaction between match-specific quality and competition.

To evaluate the importance of instructional match and how it interacts with competition, I develop a novel, equilibrium model. In this model, private schools choose their instructional levels strategically to maximize profits in response to competitive incentives, rich and poor students have different optimal instructional levels, and students choose schools based on their characteristics to maximize their perceived utilities. I estimate both the demand and supply-sides of this model using data from a particularly relevant context, Pakistan’s rural private schooling market. As in many low-income countries, private school enrollment in Pakistan is large and fast-growing.