Lagged Explanatory Variables and the Estimation of Causal Effect

Lagged explanatory variables are commonly used in political science in response to endogeneity concerns in observational data. There exist surprisingly few formal analyses or theoretical results, however, that establish whether lagged explanatory variables are effective in surmounting endogeneity concerns and, if so, under what conditions. We show that lagging explanatory variables as a response to endogeneity moves the channel through which endogeneity biases parameter estimates, supplementing a selection on observables assumption with an equally untestable no dynamics among unobservables assumption. We build our argument intuitively using directed acyclic graphs and then provide analytical results on the bias of lag identification in a simple linear regression framework. We then use Monte Carlo simulations to show how, even under favorable conditions, lag identification leads to incorrect inferences. We conclude by specifying the conditions under which lagged explanatory variables are appropriate responses to endogeneity concerns.