Current Projects

Set Estimation and Inference with Models Characterized by Conditional Moment Inequalities (pdf)

A Simple Nonparametric Estimator for the Distribution of Random Coefficients in Discrete Choice Models (with Patrick Bajari, Jeremy Fox, and Stephen Ryan) (pdf)

Hedonic Regressions with Endogenous Product Characteristics (with Patrick Bajari and Jane Cooley)

Inference for Subsets of Parameters in Partially Identified Models

We propose a confidence set for the subsets of parameters under partially identified models. Our proposed CS has less conservative asymptotic coverage than other methods based on the projection idea. The subvector inference is based on the specification testing of Guggenberger, Hahn, and Kim (2008). By restricting the values other parameters can take to a confidence set under a fixed value of the parameters of interest, we are able to obtain a less conservative confidence set. We find that our proposed CS for the subsets of parameters is asymptotically locally equivalent to the infeasible CS under the true parameter set of the other parameters are known.

Semiparametric Model Selection

Submitted Papers

Stochastic Approach to Semiparametric Information Bound of Dynamic Discrete Choice Models (with Moshe Buchinsky and Jinyong Hahn)

We develop a simulation based approach that can determine whether the semiparametric efficiency bound of a dynamic discrete choice model with fixed effects is zero or not. We illustrate the usefulness of our approach by considering a simplified version of Keane and Wolpin's (1997) model, where we show that the semiparametric information is zero.

Semiparametric Estimation of Signaling Games and Equilibrium Refinements (under revision, pdf) (Supplementary Appendix, pdf)

This paper studies an econometric modeling of a signaling game with two players where one player can have one of two types. In particular, we develop an estimation strategy that identifies the payoffs structure and the distribution of types from data of observed actions. We can achieve uniqueness of equilibrium using a refinement, which enables us to identify the parameters of interest. In this game, the type distribution (i.e., conditional probability of being a particular type) is nonparametrically specified and we propose to estimate the model using a sieve conditional MLE. We achieve the consistency and the asymptotic normality of the structural parameters estimates. 

Another Efficient Estimation of Average Treatments Effects (under revision)

This paper examines an estimation of conditional moment restrictions containing unknown functions with a known link function, where the unknown functions contain only exogenous variables. This is a special case of the moment conditions considered by Ai and Chen (2003). With smaller set of regularity conditions, the consistency and a convergence rate of the unknown functions are derived. Then, it is applied to the estimation of the propensity score. Based on the proposed semiparametric estimate of the propensity score, this paper extends the result of Hirano, Imbens, and Ridder (2003) to the case of a general index function in estimation of various average treatment effects.

Working Papers

A Structural Analysis of Wholesale Used-car Auctions: Nonparametric Estimation and Testing of Dealers' Valuations with Unknown Number of Bidders (with Joonsuk Lee) (pdf)

Wholesale used-car markets have widely utilized ascending auctions for trading dealers' inventories. To study the latent demand structure of these markets, one needs to recover the underlying valuations of dealers from the bidding data observed at the auctions. Exploiting a new, rich data set on a wholesale used-car auction, we estimate the distribution of bidders' valuations nonparametrically under the symmetric independent private values (IPV) framework and nonparametrically test the validity of the IPV assumption. We show the testability of the symmetric IPV when the number of potential bidders is unknown and even when it can vary across different auctions endogenously. This means our test can allow for endogenous participations to auctions. Then, we develop a nonparametric test of such valuation paradigm. Unlike previous work on ascending auctions, our estimation and testing methods use more information from observed losing bids by virtue of the rich structure of our data. We find that the null hypothesis of IPV is not rejected with our sample after controlling for observed auction heterogeneity and therefore our estimation result is a good approximation of the underlying distribution of dealers' valuations.

Higher Order Bias Correcting Moment Equation for M-Estimation and its Higher Order Efficiency (pdf)

This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equation in the spirit of Firth (1993). In particular, this paper compares the stochastic expansions of the analytically bias-corrected estimator and the alternative estimator and finds that the third-order stochastic expansions of these two estimators are identical. This implies that at least in terms of the third order stochastic expansion, we cannot improve on the simple one-step bias correction by using the bias correction of moment equations. Though the result in this paper is for a fixed number of parameters, our intuition may extend to the analytical bias correction of the panel data models with individual specific effects. Noting the M-estimation can nest many kinds of estimators including IV, 2SLS, MLE, GMM, and GEL, our finding is a rather strong result.

Semiparametric Bound Estimation of Discrete Games (under revision)

We consider estimation and inference of parameters in discrete games allowing for multiple equilibria, without using an equilibrium selection rule. We do a set inference while game models can contain infinite dimensional parameters. Examples can include signaling games with discrete types where the type distribution is nonparametrically specified and entry-exit games with partially linear payoffs functions. A consistent set estimator and a confidence interval of a function of parameters are provided in this paper. We note that achieving a consistent point estimation often requires an information reduction (For example, the redefinition of outcome spaces). Due to this less use of information, we may end up a point estimator with larger variance and have wider confidence interval than that of the set estimator using the full information in the model. This finding justifies the use of the set inference even though we can achieve consistent point estimation. It is also an interesting future research to compare these two alternatives: CI from the point estimation with the usage of less information vs. CI from the set estimation with the usage of the full information.

Journal Articles

Specification Testing Under Moment Inequalities (with Patrik Guggenberger and Jinyong Hahn), forthcoming, Economics Letters (pdf)

The purpose of this note is to extend Imbens and Manski's (2004) insight to a situation where the parameter of interest is multi-dimensional and can be characterized by moment inequalities. We propose a specification test to test whether such moment inequalities can hold by providing a dual characterization of the moment inequalities. For a model characterized by linear moment inequalities, we find that such a test is the asymptotic version of the multi-dimensional linear one-sided tests as discussed by, e.g., Gourieroux, Holly, and Monfort (1982). On the other hand, when the model is given by nonlinear moment inequalities, we conclude that the test will be subject to practical problems of implementation because the dual characterization takes the form of multi-dimensional nonlinear one-sided hypothesis. 

Uniform Convergence Rate of the SNP Density Estimator and Testing for Similarity of Two Unknown Densities, forthcoming, Econometrics Journal, V.10, 2007 (pdf)

This paper studies the uniform convergence rate of the truncated SNP (semi-nonparametric) density estimator. The SNP density estimator developed by Gallant and his co-workers has been popularly used but its convergence rate has not been studied much except Fenton and Gallant (1996) and Coppejans and Gallant (2002). Using the uniform convergence rate result we obtain in this paper, we propose a test statistic testing the equivalence of two unknown densities where two densities are estimated using the SNP estimation and supports of two densities are possibly unbounded.

Sample Selection Model with a Common Dummy Endogenous Regressor in Simultaneous Equations: A Simple Two-Step Estimation, Economics Letters, 91-2, 2006 (pdf)

This note studies a sample selection model where a common dummy endogenous regressor appears both in the selection equation and in the censored equation. We interpret this model as an endogenous switching model and develop a simple two step estimation. This is an attractive alternative to methods considered in the literature such as Discrete Factor Approximation, ML or Method of Simulated Likelihood using GHK simulators.

Other Working Papers

Are Married Women Secondary Workers? The Evolution of Married Women's Labor Supply in the U.S. from 1983 to 2000 (with José Carlos Rodríguez-Pueblita), CBO Working paper series, 2005-11

Comparison of Finite Sample Properties of Various Test Statistics with IV (with Juergen Meinecke) (pdf)