Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

/pdf/the-theory-of-industrial-organization-19bejph0ej.pdf

The Theory of Industrial Organization

This paper proposes a general approach and a computationally convenient estimation procedure for the structural analysis of auctioni data. Considering first-price sealed-bid auction models within the independent private value paradigm, we show that the underlying distribution of bidders' private values is identified from observed bids and the number of actual bidders without any parametric assumptions. Using the theoiy of minimax, we establish the best rate of uniform convergence at which the latent density of private values can be estimated nonparametrically from available data. We then propose a two-step kernel-based estimator that converges at the optimal rate.

Optimal Nonparametric Estimation of First-price Auctions

This paper outlines recently developed techniques for estimating the primitives needed to empirically analyze equilibrium interactions and their implications in oligopolistic markets. It is divided into an introduction and three sections; a section on estimating demand functions, a section on estimating production functions, and a section on estimating "dynamic" parameters (parameters estimated through their implications on the choice of controls which determine the distribution of future profits). The introduction provides an overview of how these primitives are used in typical I.O. applications, and explains how the individual sections are structured. The topics of the three sections have all been addressed in prior literature. Consequently each section begins with a review of the problems I.O. researchers encountered in using the prior approaches. The sections then continue with a fairly detailed explanation of the recent techniques and their relationship to the problems with the prior approaches. Hopefully the detail is rich enough to enable the reader to actually program up a version of the techniques and use them to analyze data. We conclude each section with a brief discussion of some of the problems with the more recent techniques. Here the emphasis is on when those problems are likely to be particularly important, and on recent research designed to overcome them when they are.

/pdf/econometric-tools-for-analyzing-market-outcomes-3fvu82sra8.pdf

Econometric Tools for Analyzing Market Outcomes

The Theory of Incentives I: The Principal-Agent Model

In view of the non-identification of the first-price auction model with risk-averse bidders, this paper proposes some parametric identifying restrictions and a semiparametric estimator for the risk aversion parameter(s) and the latent distribution of private values. Specifically, we exploit heterogeneity across auctioned objects to establish semiparametric identification under a conditional quantile restriction of the bidders’ private value distribution and a parameterization of the bidders’ utility function. We develop a multistep semiparametric method and we show that our semiparametric estimator of the utility function parameter(s) converges at the optimal rate, which is slower than the parametric one but independent of the dimension of the exogenous variables thereby avoiding the curse of dimensionality. We then consider various extensions including a binding reserve price, affiliation among private values, and asymmetric bidders. The method is illustrated on U.S. Forest Service timber sales, and bidders’ risk neutrality is rejected.

/pdf/semiparametric-estimation-of-first-price-auctions-with-risk-2p8ciyja2j.pdf

Semiparametric Estimation of First-Price Auctions with Risk Averse Bidders*

http://directory.umm.ac.id/Data%20Elmu/jurnal/J-a/Journal%20of%20Econometrics/Vol98.Issue1.Sep2000/2121.pdf

Conditionally independent private information in OCS wildcat auctions

This paper studies the nonparametric identification of the first-price auction model with risk averse bidders within the private value paradigm. First, we show that the benchmark model is nonindentified from observed bids. We also derive the restrictions imposed by the model on observables and show that these restrictions are weak. Second, we establish the nonparametric identification of the bidders' utility function under exclusion restrictions. Our primary exclusion restriction takes the form of an exogenous bidders' participation, leading to a latent distribution of private values that is independent of the number of bidders. The key idea is to exploit the property that the bid distribution varies with the number of bidders while the private value distribution does not. We then extend these results to endogenous bidders' participation when the exclusion restriction takes the form of instruments that do not affect the bidders' private value distribution. Though derived for a benchmark model, our results extend to more general cases such as a binding reserve price, affiliated private values, and asymmetric bidders. Last, possible estimation methods are proposed.

Nonparametric Identification of Risk Aversion in First‐Price Auctions Under Exclusion Restrictions

We consider the structural estimation of the affiliated private value (APV) model in first-price sealed-bid auctions. The model allows for bidders' individual efficiencies and opportunity costs, while permitting dependence among bidders' private values through affiliation. We establish the nonparametric identification of the APV model, characterize its theoretical restrictions, and propose a computationally convenient and consistent two-step nonparametric estimation procedure for estimating the joint private value distribution from observed bids. Using simulated bid data, we provide a step-by-step guide on how to implement our procedure and show the good behavior of our estimator in small samples.

Isabelle Perrigne

Papers

Optimal Nonparametric Estimation of First-price Auctions

Semiparametric Estimation of First-Price Auctions with Risk Averse Bidders*

Conditionally independent private information in OCS wildcat auctions

Nonparametric Identification of Risk Aversion in First‐Price Auctions Under Exclusion Restrictions

Structural Estimation of the Affiliated Private Value Auction Model