Introducing Prices to Public School Assignment: The Tradeoff between Quality and Equal Access [Job Market Paper]

Market incentives have been introduced in many school systems around the world, with goals such as promoting school quality and equalizing student access. One of these policies is to allow public schools to offer priced admission options. From the supply perspective, allowing schools to charge tuitions may create incentives for improvements in school quality. From the demand perspective, the availability of priced admission options may allow students, who have heterogeneous talents, to better express their preferences over price and quality. However, such a policy may undermine the general goal of equal access to good schools. I study a high school market of a large city in China which introduced a policy that allows individual public schools to offer both free and priced admission options, where students can apply for both, within a centralized school assignment mechanism. I address four questions using data from this market. Does the policy indeed lead to an increase in teaching quality? Are students’ preferences heterogenous across talents? Why do different schools choose different levels of teaching quality? And finally, what are the sources of quality gain and how can one address the impact on equal access?

 

Using a data set of high school entry and exit exam scores that I collect, a value-added regression shows that this policy leads to an increase in teaching quality measured by value-added. However, a difference-in-difference regression shows that such increase in quality is not distributed equally among schools. Top tier high schools with better ability to attract students and to collect tuition are more likely to have a larger increase in their qualities.

 

On the demand side, I estimate an empirical model of school choice by students. I collect data of students' reports of school preferences. Students are allowed to rank a limited number of schools of their choice in a report that they must file before taking the entrance exam. They are then admitted through a variation of serial dictatorship mechanism. Thus, students need to be strategic, and consider not only their true preferences, but also their beliefs about admission probabilities based on a noisy signal of their test scores. I use such reported preferences to estimate students’ true school preferences and beliefs about admission probabilities. The spread of the characteristics between the first and last reported schools is useful to identify the variance of the noisy signal. The interaction between student and school characteristics helps to identify important utility parameters. I estimate the parameters using simulated moments, together with an algorithm I propose to find optimal reports for individual students. Results show that students prefer quality and dislike price. More importantly, students with higher scores, when compared to students with lower scores, care more about quality and less about price.

 

On the supply side, I model schools to care about a weighted average between profit and its quality, so as to incorporate the facts that schools may want to keep excess demand in the market. To better understand schools’ choice of quality, I explicitly model schools' marginal costs of producing quality as being quadratic in quality. I combine such models of school competition with the demand side to estimate the model. Results show that better schools have lower marginal cost of producing quality and will choose a higher level of teaching quality.

 

The counterfactual analysis shows that introducing subsidies to low income students while keeping the current priced admission options would give students more equal access to better schools, while keeping the quality gain brought by market incentives. Another counterfactual analysis shows that the quality gain brought by market incentives are driven by more funds to improve quality and schools’ preference for quality.

Second-Price Auctions with Participation Costs (with Jose-Antonio Espin-Sanchez and Alvaro Parra)

We study equilibria and efficiency in second-price auctions with public participation costs. We generalize previous results by allowing arbitrary heterogeneity in bidders' distributions of valuations and in their participation costs. We develop the notion of bidder strength, defined as the best response of a bidder when all of her opponents play the same strategy as her. We then show that a herculean equilibrium in which stronger bidders have a lower participation threshold than weaker bidders exists in general environments. In other words, the order of bidders given by their strength, which is a non-equilibrium concept and can be easily calculated for each bidder using only one equation, predicts the order of the participation threshold in a certain equilibrium which exists in general. Combining with a sufficient condition for equilibrium uniqueness that we further provide, bidders’ strength points out the direction for finding and simplifies the formulation of the equilibrium. Furthermore, even though all equilibria are ex-post inefficient, an ex-ante efficient equilibrium always exists. Therefore, under the uniqueness condition, the herculean equilibrium is the unique equilibrium of the game and is ex-ante efficient.

Entry Games under Private Information (with Jose-Antonio Espin-Sanchez and Alvaro Parra)

We study market entry decisions when firms have private information about their profitability. We generalize current models by allowing unrestricted forms of market competition and heterogeneous firms that self-select when entering the market. Post-entry profits depend on market structure, and on the identities and the private information of the entering firms. We introduce a notion of firm's strength and show that an equilibrium where players' strategies are ranked by their strength, or herculean equilibrium, always exists. Moreover, when profits are elastic enough with respect to the firm's private information, the herculean equilibrium is the unique equilibrium of the game.