working papers

"Linearized GMM Estimator"  

(A draft coming soon)

     Abstract: It is well-known that nonlinear generalized method of moments (GMM) estimators often encounter computational issues when the moment conditions are over-identifying and nonlinear. To enhance computational properties, I propose a novel GMM estimator based on linearized moment conditions approximated around an underlying exactly-identified (or over-identified) parameter estimate. This estimator exhibits improved computational properties while maintaining first-order asymptotic efficiency. The enhancement arises from (i) the ensured strict local convexity and the known optimal value of the GMM objective function for estimating the underlying exactly-identified parameter, and (ii) the availability of a closed-form solution for the final estimate. In a simplified version of the estimator, the closed-form solution alone replaces the second stage of the two-step GMM estimator. For any given standard moment condition, I prove the existence of such an underlying parameter, and introduce a straightforward algorithm for its identification. The added dimensions in the underlying exactly-identified parameter can be estimated one element at a time, separately. The proposed method has been applied to Ahn, Lee, and Schmidt's (2013) panel data model with multiple time-varying individual effects.

"Difference-in-differences Estimator of Quantile Treatment Effect on the Treated" 

(with Jeffrey M. Wooldridge; revised and resubmitted to Journal of Business and Economic Statistics) 

     Abstract: We propose a new difference-in-differences (DID) estimator of the quantile treatment effect on the treated (QTT). The model assumes a common time effect on the cumulative distribution functions of untreated potential outcomes, allowing for covariates. To properly guide its empirical plausibility, we demonstrate that the assumption is valid if and only if the net change in the untreated outcome densities is common across treated and control groups. Unlike the Changes-in-Changes model proposed by Athey and Imbens (2006), our model is compatible with the usual DID assumption for means, and it provides a computationally simple and straightforward way to control for covariates. We establish uniform consistency and weak convergence of the proposed estimator of QTT and the related functions. The estimators and the simultaneous confidence bands remain valid even for discrete outcome variables. As an empirical application, the distributional impact of the earned income tax credit on birth weight is investigated. We provide a STATA command.

  PDF file:  (download)

        STATA ado file: (coming soon)

"Short Panel Data Quantile Regression Model with Flexible Correlated Effects: A Partially Linear Model Robust to Misspecification"

(Major revisions requested, Econometric Reviews)

     Abstract: I propose an alternative linear model for short panel data quantile regression. The model assumes a nonparametric correlated effect (CE) that is τ-quantile-specific and time-invariant. The resulting partially linear model is robust to misspecification, and it is characterized as a best linear approximation to the truth under a generalized correlated random effect assumption. At the cost of modeling the individual heterogeneity, the new model is free of incidental parameters, and it does not restrict within-group dependence of idiosyncratic errors at all. The modeled heterogeneity is still well-aligned with the fixed effect approach in the linear mean regression model. For estimation, sieve-approximated CE is regularized by non-convex penalization which enjoys the oracle property against ultra-high dimensionality. Unpenalized sieve estimation is also available. As an empirical application, the proposed method is applied to estimate the distributional effect of smoking on birth weights.

     PDF file: (download)

     STATA ado file: (download)

Publication

"Asymptotic Efficiency of Joint Estimator relative to Two-stage Estimator under Misspecified Likelihoods"

(Conditionally Accepted, Studies in Nonlinear Dynamics and Econometrics)

  PDF file: (download)

"An Alternative Two-step Generalized Method of Moments Estimation based on a Reduced Form Model"

(Economics Letters, Volume 192, 2020, Article 109184) DOI