Identification of Average Treatment Effects in Nonparametric Panel Models
Susan Athey, Guido Imbens
TL;DR
This paper develops a fully nonparametric factor framework for causal analysis in panel data, focusing on identifying average treatment effects when unobserved unit and time components drive outcomes. It proves that the conditional mean $\mu(\alpha_i,\beta_t)=E[Y_{it}|\alpha_i,\beta_t]$ is identifiable and consistently estimable even without observing the latent factors, by constructing sets of units that match on the latent mean function via covariances. The ATT is identified under Latent Factor Unconfoundedness and an overlap condition, with a feasible estimator for $\mu_{it}$ and a causal estimator for $\tau$ built from these conditional means. Beyond treatment effects, the paper extends to nonparametric decompositions of outcome differences across groups, illustrating broad applicability to problems like gender wage gap analysis. The results generalize linear factor and TWFE models and provide a principled route to identification and inference in rich nonparametric panel settings.
Abstract
This paper studies identification of average treatment effects in a panel data setting. It introduces a novel nonparametric factor model and proves identification of average treatment effects. The identification proof is based on the introduction of a consistent estimator. Underlying the proof is a result that there is a consistent estimator for the expected outcome in the absence of the treatment for each unit and time period; this result can be applied more broadly, for example in problems of decompositions of group-level differences in outcomes, such as the much-studied gender wage gap.