Social Science Statistics Blog

To begin, it’s a big step to draw causal inferences about race in a potential outcomes framework; the maxim "no causation without manipulation"? (due, I believe, to Paul Holland) explains why. I believe that step can be taken, but that’s another subject. Suppose we take it, i.e., we decide to apply a potential outcomes framework to an immutable characteristic. The treatment (applied to the capital defendant) is being African-American, the intermediate outcome is whether the defendant is convicted, and the final outcome is whether a convicted defendant is sentenced to die. (Note that, in an instance of fairly macabre irony, if one applies the language of censoring or truncation due to death here, "death"? is an acquittal on the capital charge.)

What causal question do we care about? If all we want to study is the relationship between race and the death penalty, then we don’t care whether a defendant avoids a death sentence via acquittal or avoids a death sentence after a conviction by being sentenced to life. If, on the other hand, what we want to study is fairness in sentencing proceedings, then we need principal stratification; we need to isolate a set of defendants who would be convicted of the capital charge if African-American and convicted of the capital charge if not African-American. Both are potentially interesting causal questions. Let’s just make sure we know which we’re asking.