Thread by @jmwooldridge

Have we yet figured out when we should include a lagged dependent variable in either time series or panel data models when the goal is to infer causality? (For forecasting the issue is clear.) Recent work on macroeconomics on causal effects is a positive sign.

#metricstotheface

And the answer cannot be, "Include y(t-1) if it is statistically significant." Being clear about potential outcomes and the nature of the causal effects we hope to estimate are crucial. I need to catch up on this literature and I need to think more.

In panel data settings, if our main goal is to distinguish state dependence from heterogeneity, clearly y(t-1) gets included. But what if our interest is in a policy variable? Should we hold fixed y(t-1) and the heterogeneity when measuring the policy effect?

For a one-period causal effect, we often include the pre-treatment outcome to account for confounded assignment. But doing that over numerous time periods, it isn't clear what that recovers.

Ideally, putting in y(t-1) is always equivalent to an infinite distributed lag in the policy variables. Unfortunately, this requires strong assumptions -- as I discuss in Ch 18 of my intro econometrics book.

I start sweating every time someone asks, "Should I include y(t-1) in my panel data model?"