Parallel Worlds: Fixed Effects, Differences-in-differences, and Panel Data
The first thing to realize about parallel universes… is that they are not parallel.
Douglas Adams, Mostly Harmless (1995)
The key to causal inference in chapter 3 is control for observed confounding factors. If important confounders are unobserved, we might try to get at causal effects using IV as discussed in Chapter 4. Good instruments are hard to find, however, so we’d like to have other tools to deal with unobserved confounders. This chapter considers a variation on the control theme: strategies that use data with a time or cohort dimension to control for unobserved-but-fixed omitted variables. These strategies punt on comparisons in levels, while requiring the counterfactual trend behavior of treatment and control groups to be the same. We also discuss the idea of controlling for lagged dependent variables, another strategy that exploits timing.