Parallel Worlds: Fixed Effects,
and Panel Data
The first thing to realize about parallel universes... is that
they are not parallel.
Douglas Adams, Mostly Harmless
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
instrumental variables, 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.
One of the oldest questions in labor economics is the connection between union membership and wages. Do workers whose wages are set by collective bargaining earn more because of this, or would they earn more anyway, perhaps