Abstract: I propose an alternative two-step generalized method of moment (GMM) estimator when an exactly-identified underlying parameter is available. The resulting estimator does not have the higher-order asymptotic bias arising from the choice of a preliminary weighting matrix.
"Difference-in-differences Estimator of Quantile Treatment Effect on the Treated"
(with Jefferey M. Wooldridge)
Abstract: We propose a difference-in-differences (DID) estimator of the quantile treatment effect on the treated (QTT). The new distributional DID assumption has two distinctive features. Firstly, it is necessary and sufficient for the the usual DID assumption (with covariates) to hold for any strictly increasing transformation of the outcome variable. Secondly, it is partially testable through a shape restriction. We formalize that the new condition requires net changes of untreated outcome density to be common. It would be misleading to view this condition as a mandate to partition the population into two subgroups with specific characteristics. We establish uniform consistency and weak convergence of the proposed estimator of QTT and related functions. The estimators and 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.
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"Linearized GMM Estimator"
Abstract: Given a standard moment condition, I show that there exists an underlying exactly-identified parameter. Exploiting the underlying parameter, an alternative GMM estimator based on a linearized moment function is proposed. The linearized moment function is linear in the original parameter. The asymptotic properties of the linearized GMM estimator are investigated. In particular, the higher-order asymptotic bias is derived.
"Short Panel Data Quantile Regression Model with Flexible Correlated Effects: A Partially Linear Model Robust to Misspecification"
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.
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"Asymptotic Efficiency of Joint Estimator relative to Two-stage Estimator under Misspecified Likelihoods"
Abstract: The two-stage estimator is often more tractable when there are nuisance parameters that can be separately estimated and plugged into an objective function. The joint estimator tends to bear the higher computational cost since it estimates all parameters in one stage by optimizing the sum of objective functions used in the two stages. It is well-known that joint estimator is asymptotically more efficient than two-stage estimator if the objective function is the true log-likelihood. When the objective function is not the true log-likelihood, I show that the relative asymptotic efficiency of joint estimator still holds under a finite number of moment conditions that are testable. The implications of the main result on models based on quasi-limited information likelihoods are discussed.