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Wiley InterScience | |||
  EconometricaVolume 72 Issue 5, Pages 1445 - 1480 Published Online: 19 Jul 2004 © 2009 The Econometric Society
Abstract | References | Full Text: PDF (Size: 315K) | Related Articles | Citation Tracking  Likelihood Estimation and Inference in a Class of Nonregular Econometric Models The previous 2000 and 2001 versions of this paper were circulated under the title "Likelihood Inference with Density Jumps." We would like to thank Joe Altonji, Stephen Donald, Christian Hansen, Jerry Hausman, Ivan Fernandez, Hide Ichimura, Jim Heckman, Shakeeb Khan, Yuichi Kitamura, Sokbae Lee, Oliver Linton, Rosa Matzkin, Whitney Newey, George Neumann, Harry Paarsch, Frank Schorfheide, Robin Sickles, Richard Spady, and Max Stinchcombe as well as participants at the December 2000 EC2 meeting, March 2001 CEME conference, Duke, LSE, MIT, Northwestern, Penn State, Princeton, Rice, University of Texas at Austin, and University of Pennsylvania for valuable suggestions. We thank three referees and the co-editor for useful input on the paper. We are especially grateful to Takeshi Amemiya for his support and advice. We gratefully acknowledge the support provided by the NSF Research Grants SES-0241810 (Chernozhukov) and SES-0335113 (Hong). Copyright The Econometric Society 2004 KEYWORDS Point process • extreme value theory • Bayes • frequentist validity of posterior • computational complexity • epi-convergence • insufficiency of maximum likelihood ABSTRACTWe study inference in structural models with a jump in the conditional density, where location and size of the jump are described by regression curves. Two prominent examples are auction models, where the bid density jumps from zero to a positive value at the lowest cost, and equilibrium job-search models, where the wage density jumps from one positive level to another at the reservation wage. General inference in such models remained a long-standing, unresolved problem, primarily due to nonregularities and computational difficulties caused by discontinuous likelihood functions. This paper develops likelihood-based estimation and inference methods for these models, focusing on optimal (Bayes) and maximum likelihood procedures. We derive convergence rates and distribution theory, and develop Bayes and Wald inference. We show that Bayes estimators and confidence intervals are attractive both theoretically and computationally, and that Bayes confidence intervals, based on posterior quantiles, provide a valid large sample inference method. Manuscript received December, 2001; final revision received November, 2003. | 
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