A few years ago, Taka Masaki, Tom Pepinsky, and I published an article in the Journal of Politics titled “Lagged Explanatory Variables and the Estimation of Causal Effects,” where we looked at the phenomenon (then relatively widespread in political science, less so in economics) of lagging an explanatory variable in an effort to exogenize it–that is, the phenomenon whereby one replaces x_{it} by x_{it-1}.
That article was well-received, and it has since also become well-cited, but one of the things we did not touch upon was the phenomenon (seemingly relatively more widespread in economics, less so in political science) of lagging an explanatory variable to use it as an instrumental for itself–that is, the phenomenon whereby one instruments x_{it} with x_{it-1}.
In work concurrently written with our 2017 Journal of Politics article, Reed (2015) had also looked at the use of lags as controls, but he concluded by suggesting the use of lagged variables as instrumental variables (IVs) instead of as controls.
In a new working paper with my PhD student Yu Wang titled “Lagged Variables as Instruments,” we build on the work in Reed (2015) and on the structure of my earlier work to look at the use of lagged variables as IVs. Whereas Reed only consider simultaneity as a source of bias, however, we generalize to look at any unobserved confounder.
Here is the abstract of this new paper:
Lagged explanatory variable remain commonly used as instrumental variables (IVs) to address endogeneity concerns in empirical studies with observational data. Few theoretical studies, however, address whether lagged IVs mitigate endogeneity. We develop a theoretical setup in which dynamics among the endogenous explanatory variable and the unobserved confounders cannot be ruled out and look at the consequences of lagged IVs for bias and the root mean square error (RMSE). We then use Monte Carlo simulations to illustrate our analytical findings. We show that when lagged explanatory variables have no direct causal effect on the dependent variable or on the unobserved confounders, the lagged IV method mitigates the endogeneity problem by reducing both bias and the root mean squared errors given specific parameter values relative to the naïve OLS case. If either or both of the causal relationships above are present, however lagged IVs increase both bias and the RMSE relative to OLS, and they virtually blow up the likelihood of a Type I error to one.