Research

When estimating treatment effects with two-way fixed effects (2WFE) models, researchers often use matching as a pre-processing step when the parallel trends assumption is thought to hold conditionally on covariates. Specifically, in a first step, each treated unit is matched to one or more untreated units based on observed time-invariant covariates. In the second step, treatment effects are estimated with a 2WFE regression in the matched sample, reweighting the untreated units by the number of times they are matched. We formally analyze this common practice and highlight two problems. First, with variation in treatment timing, the post-matching 2WFE estimator that pools all treated cohorts has an asymptotic 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. We characterize the joint asymptotic distribution of the vector of cohort means over time and their matched counterparts, and use our results to provide consistent, asymptotically normal estimators of treatment effects, event-study coefficients and other aggregate magnitudes, with valid standard errors that account for the matching step. We illustrate our results with simulations and with an empirical application.

Nonlinear equations of motion are central to many policy contexts, including resource management and public health, where dynamics such as fish reproduction and disease transmission are inherently nonlinear. Because policy insights in these settings fundamentally hinge on these nonlinearities, standard linear approximations are inadequate. Moreover, strategic interactions between jurisdictions compound the computational burden of estimating such models. We develop a tractable Generalized Method of Moments (GMM) framework for dynamic games that accommodates heterogeneous agents alongside fully nonlinear, interactive state dynamics. We provide sufficient conditions under which our approach is feasible and establish its consistency and asymptotic normality. Finally, we apply the framework to a multi-country fishery game in East Asia, quantifying strategic harvest responses to climate-driven shifts in ocean currents.