Mastering 'Metrics: The Path from Cause to Effect

by Joshua D. Angrist

This is accomplished by introducing state effects, a set of dummies for every state in the sample, except for one, which is omitted as a reference group. A regression DD analysis of data from Alabama, Arkansas, and Tennessee, for example, includes two state effects. State effects replace the single TREATs dummy included in a two-state (or two-group) analysis.

We may prefer estimates that reflect this fact by giving more populous states more weight. The regression procedure that does this is called weighted least squares (WLS).

Treatment and control groups may differ in the absence of treatment, yet move in parallel. This pattern opens the door to DD estimation of causal effects.

Why is DD better than simple two-group comparisons? GRASSHOPPER: Comparing changes instead of levels, we eliminate fixed differences between groups that might otherwise generate omitted variables bias.

How is DD executed with multiple comparison groups and multiple years? GRASSHOPPER: I have seen the power and flexibility of regression DD, Master. In a state-year panel, for example, with time-varying state policies like the MLDA, we need only control for state and year effects.

On what does the fate of DD estimates turn? GRASSHOPPER: Parallel trends, the claim that in the absence of treatment, treatment and control group outcomes would indeed move in parallel. DD lives and dies by this. Though we can allow for state-specific linear trends when a panel is long enough, masters hope for results that are unchanged by their inclusion.