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Essays in Empirical Auctions and Partially Identified Econometric Models

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Chapter 1: (Bounds on the Counterfactual Revenue Distributions in Auctions with Reserve Prices) In first-price auctions with interdependent bidder values, the distributions of private signals and values cannot be uniquely recovered from bids in Bayesian Nash equilibria. Non-identification invalidates structural analyses that rely on exact identification of the model primitives. In this paper I introduce tight, informative bounds on the distribution of revenues in counterfactual first- and second-price auctions with binding reserve prices. These robust bounds are identified from distributions of equilibrium bids in first-price auctions under minimal restrictions where I allow for affiliated signals and both private- and common-value paradigms. The bounds can be used to compare auction formats and to select optimal reserve prices. I propose consistent nonparametric estimators of the bounds. I extend the approach to account for observed heterogeneity across auctions, as well as endogenous participation due to binding reserve prices. I use a recent data of 6,721 first-price auctions of U.S. municipal bonds to estimate bounds on counterfactual revenue distributions. I then bound optimal reserve prices for sellers with various risk attitudes. Chapter 2: (Semiparametric Estimation of Binary Response Models under Inequality Quantile Restrictions) In this paper I study the estimation of a class of binary response models where conditional medians of disturbances are bounded between known functions of regressors. This class of models incorporates several interesting micro-econometric sub-models with wide empirical applications. These include binary response with interval data on regressors, simultaneous discrete games with incomplete information, and Markovian binary choice processes. I characterize the identification region of linear coefficients in payoff functions, and give fairly general restrictions on the distribution of regressors that are sufficient for point identification. I also show how these restrictions are satisfied by primitive conditions in some of the motivating sub-models. I then define a two-step extreme estimator, and show it is consistent regardless of point identification, and converges to a normal distribution at the rate of √n under point identification. This is possible because point identification can be attained even when the regressors have bounded supports. Monte Carlo evidence on the estimator's performance in finite samples when the model is partially identified is reported. Chapter 3: (Identification of Dynamic Binary Choice Processes) In this paper, we study the identification of structural parameters in a class of dynamic binary choice processes where transitions to future states are independent from unobservable disturbances conditional on current actions and observable states. We give a full characterization of the set of single-period payoffs and disturbance distributions that generate the same choice probabilities as observed in a given process. We show with knowledge of the disturbance distribution, the differences in payoffs from two trivial policies of choosing the same action forever can be uniquely recovered from choice probabilities. Furthermore, we analyze the identifying power of various stochastic restrictions such as the statistical independence and conditional symmetry of the disturbance distributions. For models with finite spaces of observable states, we characterize the identification region of single-period payoffs under these restrictions by checking the feasibility of a system of linear equations in the nuisance parameters, subject to inequality constraints implied by observational equivalence and the restrictions imposed. This approach of identification through linear programming can be readily extended to cases where single-period payoffs are known to satisfy any form of restrictions

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  • 09/19/2018
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