Research

Identification in difference-in-differences (DiD) settings is often justified under a conditional parallel trends assumption, under which units with similar observed covariates are expected to have followed similar outcome trends in the absence of treatment. In such settings, researchers often combine matching with two-way fixed effects (2WFE) methods. Specifically, in a first step, each treated unit is matched to one or more never-treated units based on observed pre-treatment covariates. In the second step, treatment effects are estimated with a 2WFE regression in the matched sample, reweighting the never-treated units by the number of times they are matched. We formally analyze this common practice and highlight three problems. First, with variation in treatment timing, the post-matching 2WFE estimator that pools all treated cohorts has an asymptotic “pooling” bias, even when the treatment effect is constant across units and over time. Second, failing to account for the variability introduced by the matching procedure yields invalid standard error estimators, which can be biased upwards or downwards depending on the data generating process. Third, imperfect matches generate a matching bias that can be first-order for inference, but the required bias correction to address it is commonly omitted when using post-matching 2WFE estimators in empirical work. Thus, conventional t-statistics and confidence intervals based on the uncorrected estimator may be invalid. We provide consistent, asymptotically normal bias-corrected matched DiD estimators of treatment effects, event-study coefficients and other aggregate magnitudes, with consistent standard errors that account for the matching step. We illustrate our results with simulations and with two empirical applications.

Many policy contexts, from fisheries management to epidemic control, are governed by nonlinear reproduction dynamics and by strategic interaction among multiple decision makers. This combination has historically made structural estimation computationally forbidding. We develop a tractable Generalized Method of Moments (GMM) framework for dynamic resource games with heterogeneous agents and fully nonlinear, interactive state dynamics. We provide sufficient conditions under which the Markov-perfect Nash equilibrium admits analytical optimality conditions, and establish consistency and asymptotic normality of the resulting GMM estimator. Applying the framework to the Japanese anchovy fishery shared by China, Japan, and Korea, we recover each country's implicit ecological valuation and simulate the equilibrium effect of climate-driven shifts in fish migration patterns. We further show that linearizing the equations of motion, the standard route to tractability, substantially understates these ecological values.