working papers
working papers
Abstract: I develop a framework linking pretrend tests, data-driven preperiod selection, and estimation in difference-in-differences without additional identifying assumptions. Under baseline identification, an additional preperiod identifies the same effect exactly when its pretrend restriction holds. Rejection over an extended window need not invalidate a shorter-window design. In extended two-way fixed effects, compatible covariance construction equates pretrend Wald and GMM J statistics, enabling moment selection from event-study output. Under stated conditions, Wald-BIC consistently selects valid restrictions; complementary focused MD addresses local bias and variance while consistently estimating the baseline-identified effect. Doubly robust and nonlinear DiD applications extend the framework beyond linear regression.
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STATA package : (GitHub repository)
Abstract: It is well-known that nonlinear generalized method of moments (GMM) estimators often encounter computational challenges 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 demonstrates improved computational performance while maintaining first-order asymptotic efficiency, which is particularly beneficial in cases involving a large number of moment conditions. The enhancement arises from (i) the better-behaved curvature of the GMM objective function (e.g. strict local convexity) for estimating the underlying parameter, and (ii) the availability of a closed-form solution for the final estimate. 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 method has been applied to Ahn, Lee, and Schmidt's (2013) panel data model with multiple time-varying individual effects. This paper provides a STATA command.
PDF file: Download (version: Jan 30, 2025)
STATA ado file: Download
(Studies in Nonlinear Dynamics and Econometrics, 2024) DOI
(Economics Letters, 2020, Volume 192, Article 109184) DOI