Estimating Long-Term Treatment Effects in Dynamic Panel Data Models

We study the estimation of long-term treatment effects in short panels—where the horizon of interest exceeds the sample length—without parametric functional-form assumptions. Parametric dynamic panel models typically bundle three substantively distinct restrictions: unconfoundedness, surrogacy, and time invariance. Building on graphical causal models, we propose a framework that encodes these three assumptions separately without relying on functional form. We then use this framework to provide sufficient conditions for non-parametric identification. With these conditions in hand, we show that parametric models often impose additional assumptions that can lead to spurious identification of long-term effects through implicit extrapolation. In contrast, our graphical approach provides a transparent language to state, defend, and critique assumptions and their consequences explicitly.