Research Papers
“Estimation and Inference with Many Moment Inequalities” (Job Market Paper)
In this paper, I consider estimation of the identified set and inference on a partially identified parameter when the number of moment inequalities is large relative to sample size. Many applications in the recent literature on set estimation have this feature - examples discussed in this paper include set-identified instrumental variables models, inference under conditional moment inequalities, and dynamic games. I analyze weak (set) identification from a large number of moment inequalities and show that GMM-type test statistics will often be poorly centered in this setting. This paper establishes consistency of the set estimator based on a Wald-type criterion, and gives conditions for uniformly valid inference under many weak moment asymptotics for both plug-in and subsampling procedures. I show asymptotic normality of the QLR statistic under many moment asymptotics, and demonstrate that subsampling procedures remain valid only under much slower growth rates for the number of moments than those permissible for plug-in methods. Furthermore, I compare the performance of a test based on an Anderson-Rubin (AR) type statistic which has been widely recommended in the literature, to a modified Lagrange Multiplier (LM) test proposed in this paper. In simulations with weak moment inequalities, inference using the LM statistic appears to have greater power against local alternatives than the AR-type test in most settings.
“Inference on Sets in Finance” (joint with Victor Chernozhukov and Emre Kocatulum)
In this paper we introduce various set inference problems as they appear in finance and propose practical and powerful inferential tools. Our tools will be applicable to any problem where the set of interest solves a system of smooth estimable inequalities, though we will particularly focus on the following two problems: the admissible mean-variance sets of stochastic discount factors and the admissible mean-variance sets of asset portfolios. We propose to make inference on such sets using weighted likelihood-ratio and Wald type statistics, building upon and substantially enriching the available methods for inference on sets.
“Properties of the CUE Estimator and a Modification with Moments” (joint with J. Hausman, R. Lewis, and W. Newey), accepted subject to revision at Journal of Econometrics
In this paper, we analyze properties of the Continuous Updating Estimator (CUE) proposed by Hansen Heaton and Yaron (1996), which has been suggested as a solution to the finite sample bias problems of the two-step GMM estimator. We show that the estimator should be expected to perform poorly in finite samples under weak identification, in particular the estimator is not guaranteed to have finite moments of any order. We propose the Regularized CUE (RCUE) as a solution to this problem in the linear case. The RCUE solves a modification of the first-order conditions for the CUE estimator and is shown to be asymptotically equivalent to CUE under many weak moment asymptotics as in Newey and Windmeijer (2008). RCUE will have moments up to the degree of overidentification. Our theoretical findings are confirmed by extensive Monte Carlo studies.