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Identification, Estimation and Testing of Auction Models

  • Author(s): Wei, Jie
  • Advisor(s): Ullah, Aman
  • Malueg, David
  • et al.
Abstract

The first chapter establishes a way of inferring risk aversion in a first-price auction (FPA) model when an entry decision is endogenous. Bidders' risk aversion is captured by a parameter in constant relative risk aversion utility functions and the parameter is then partially identified in a set under a "monotonicity" condition. The recovery of

the partially identified risk aversion parameter is concluded in a confidence set (CS). The CS is constructed by inverting a test dealing with many inequality restrictions of quantiles. In the spirit of Andrews and Shi (2013), we implement quantile selection to address possible slackness. Asymptotic results show desired properties of size and power against fixed (and some local) alternatives. Confidence sets perform fairly well in finite samples and the comparison of results highlights the necessity of quantile selection. The inference is illustrated by using US Forest Service timber auction data and detects considerable risk aversion.

Exogenous entry is a convenient assumption to make for identification and inference in auction models. The second chapter examines this assumption and develops a test against endogenous entry in first-price auctions with risk aversion. The approach also takes auction observed heterogeneity into account. The desirable property of asymptotic size and consistency of the test is proven, and Monte Carlo simulations approve the test at finite samples. The application to US Forest Service timber auctions brings in interesting implication: entry is exogenous with lower entry level but is endogenous with higher entry level. The result also suggests a relatively stronger risk aversion attitude than what is obtained in the literature.

The third chapter shows nonparametric identification and estimation of private value distribution and density functions in first-price auctions with endogenous entry. In the model, symmetric bidders face a nontrivial entry cost and a binding reserve price. We identify latent structures by solving a two stage game, and estimate density

functions (point-wisely) by using and comparing two different methods. Monte Carlo experiments show good performance of our estimators.

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