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We develop a nonparametric approach that allows one to discriminate among alternative models of entry in …rst-price auctions. Three models of entry are considered: Levin and Smith (1994), Samuelson (1985), and a new model in which the information received at the entry stage is imperfectly correlated with valuations. We derive testable restrictions that these three models impose on the quantiles of active bidders' valuations, and develop nonparametric tests of these restrictions. We implement the tests on a dataset of highway procurement auctions in Oklahoma. Depending on the project size, we …nd no support for the Samuelson model, some support for the Levin and Smith model, and somewhat more support for the new model.

This supplement contains: i) the description of the procedure for selection and evaluation of the influential empirical RD papers; ii) the proofs of Theorem 1, 3, and 4; iii) the Monte Carlo results for standard and weak-identification-robust confidence sets; and iv) the additional tables from the empirical application. Influential applied papers sample procedureWe start with thirty applied papers that were cited by Lee and Lemieux (2010). Of the thirty papers, sixteen did not report enough information to perform the F -test. Of the remaining papers, more than half had specifications which would be suspect according to the test. We reach similar conclusions when only focusing on the ten most cited paper in the list (

This paper provides bounds on the errors in coverage probabilities of maximum likelihood-based, percentile-t, parametric bootstrap conÞdence intervals for Markov time series processes. These bounds show that the parametric bootstrap for Markov time series provides higher-order improvements (over conÞdence intervals based on Þrst order asymptotics) that are comparable to those obtained by the parametric and nonparametric bootstrap for iid data and are better than those obtained by the block bootstrap for time series. Similar results are given for Wald-based conÞdence regions.The paper also shows that k-step parametric bootstrap conÞdence intervals achieve the same higher-order improvements as the standard parametric bootstrap for Markov processes. The k-step bootstrap conÞdence intervals are computationally attractive. They circumvent the need to compute a nonlinear optimization for each simulated bootstrap sample. The latter is necessary to implement the standard parametric bootstrap when the maximum likelihood estimator solves a nonlinear optimization problem.

We propose a quantile-based nonparametric approach to inference on the probability density function (PDF) of the private values in …rst-price sealedbid auctions with independent private values. Our method of inference is based on a fully nonparametric kernel-based estimator of the quantiles and PDF of observable bids. Our estimator attains the optimal rate of Guerre et al. (2000), and is also asymptotically normal with the appropriate choice of the bandwidth.JEL Classi…cation: C14, D44