Several school districts use assignment systems that give students an incentive to misrepresent their preferences. We find evidence consistent with strategic behavior in Cambridge. Such strategizing can complicate preference analysis. This paper develops empirical methods for studying random utility models in a new and large class of school choice mechanisms. We show that preferences are nonparametrically identified under either sufficient variation in choice environments or a preference shifter. We then develop a tractable estimation procedure and apply it to Cambridge. Estimates suggest that while 83% of students are assigned to their stated first choice, only 72% are assigned to their true first choice because students avoid ranking competitive schools. Assuming that students behave optimally, the Immediate Acceptance mechanism is preferred by the average student to the Deferred Acceptance mechanism by an equivalent of 0.08 miles. The estimated difference is smaller if beliefs are biased, and reversed if students report preferences truthfully.

Several school districts use assignment systems that give students an incentive to misrepresent their preferences. We find evidence consistent with strategic behavior in Cambridge. Such strategizing can complicate preference analysis. This paper develops empirical methods for studying random utility models in a new and large class of school choice mechanisms. We show that preferences are non-parametrically identified under either sufficient variation in choice environments or a preference shifter. We then develop a tractable estimation procedure and apply it to Cambridge. Estimates suggest that while 82% of students are assigned to their stated first choice, only 72% are assigned to their true first choice because students avoid ranking competitive schools. Assuming that students behave optimally, the Immediate Acceptance mechanism is preferred by the average student to the Deferred Acceptance mechanism by an equivalent of 0.08 miles. The estimated difference is smaller if beliefs are biased, and reversed if students report truthfully.

We develop a model for studying dynamic competition in environments with frictions that lead to partial lock-in of customers to products. The dynamic aspects associated with customer retention and acquisition introduce pricing incentives that do not exist in more traditional, static product markets. The proposed model, while highly stylized, maintains certain symmetry properties that allow us to obtain equilibrium existence and uniqueness. We then study the comparative statics of the model and derive a closed-form relationship between average equilibrium markups and the Herfindahl index. We illustrate how the model can be used by analyzing mergers in such a dynamic environment.

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