Lagged Explanatory Variables and the Estimation of Causal Effects

Abstract

Across the social sciences, lagged explanatory variables are a common strategy to confront challenges to causal identification using observational data. We show that “lag identification” — the use of lagged explanatory variables to solve endogeneity problems — is an illusion: lagging independent variables merely moves the channel through which endogeneity biases causal estimates, replacing a “selection on observables” assumption with an equally untestable “no dynamics among unobservables” assumption. We build our argument intuitively using directed acyclic graphs, then provide analytical results on the bias resulting from lag identification in a simple linear regression framework. We then present simulation results that characterize how, even under favorable conditions, lag identification leads to incorrect inferences. These findings have important implications for current practice among applied researchers in political science, economics, and related disciplines. We conclude by specifying the conditions under which lagged explanatory variables are appropriate for identifying causal effects.

Keywords: Causal Identification, Treatment Effects, Lagged Variables

JEL Classification: C13, C15, C21