Laura Hatfield, Associate Professor of Health Care Policy (Biostatistics) at Harvard Medical School, will present: “Model What You Can and Assume the Rest”: Selecting Models for Robustness in Quasi-Experimental Analysis.
Abstract: In settings where we observe outcomes before and after treatment in both a treated group and an untreated comparison group, the treated group’s average effect (ATT) is a common causal quantity of interest. Popular designs for identifying and estimating the ATT include difference-in-differences, comparative interrupted time series (CITS), and synthetic controls. Each of these uses slightly different causal assumptions to identify the target causal estimand.
We propose a novel identification assumption that unifies the causal identification assumptions of these different designs. We assume equality, in expectation, between the prediction error in the post-treatment period of (1) the treated group’s untreated potential outcomes and (2) the control group’s untreated potential outcomes. We refer to this assumption as “equal expected prediction errors”. We show that DID, CITS, and related designs are special cases. The differences arise because they use different models to predict average untreated potential outcomes. In this paper, rather than try to choose a “correct” model, we anticipate a sensitivity analysis to violations of our causal assumption and select the model that maximizes robustness to violations. To demonstrate our ideas, we apply them to study the effects of concealed carry laws on crime and gun-related violence. (This is joint work with Thomas Leavitt.)
All are Welcome.