Abstract
Recent evidence suggests that market participants make mistakes (even) in a strategically straightforward environment but seldom with significant payoff consequences. Uncertainties arising from the use of lotteries or other sources increase payoff consequences of certain mistakes, and force participants to take care to avoid them. Consequently, uncertainties limit the extent to which certain mistakes are made, thus making it possible for one to infer some preference relations reliably. We propose a novel method of exploiting the uncertainties present in a matching environment to systematically and robustly infer student preferences over schools based on their rank-order lists data. Our method consists of three steps: (i) simulating the underlying structure of uncertainties present in the environment, (ii) extracting preference relations revealed under the simulated uncertainties, and then (iii) extending the revealed preference relations via the axiom of transitivity. Depending on the type of uncertainties present, the method rationalizes a variety of procedures, ranging from truthful-reporting assumption at one extreme (full-support uncertainty) to the stability assumption at the other extreme (when there is little uncertainty). Further, we refine our method to strengthen the robustness of the revealed preferences in the presence of participants making even some payoff-relevant mistakes, and explore ways to optimally balance the tradeoff between robustness and efficiency in preference estimation. We apply our methods to estimate student preferences through a Monte Carlo analysis capturing canonical school choice environment with single tie-breaking lotteries. Finally, we apply our methods as well as other existing methods to New York City high school assignment data to explore their implications for preference estimation and counterfactual analysis under a possible policy intervention.
Joint work with Yeon-Koo Che, Dong Woo Hahm.