Online Program

Differences-in-Differences with Multi-State Outcomes (306623)

Bill Blot, Vanderbilt University Medical Center 
*John Graves, Vanderbilt University 
Laura Anne Hatfield, Harvard Medical School 
Nancy L. Keating, Harvard Medical School 
Michael McWilliam, Harvard Medical School 

Keywords: Differences-in-differences, Medicaid, health status

Difference-in-differences analyses typically rely on a regression model to estimate the parameter of interest, expressed as an interaction between an indicator for the post-treatment period and an indicator for treatment. This interaction coefficient represents the differential change from pre- to post-treatment in the treatment group relative to the comparison group. To interpret this parameter as the causal impact of the treatment requires assuming the untreated potential outcomes of the treated and comparison groups would have evolved similarly in the absence of treatment. This assumption is scale-dependent, so the functional form of the regression model is a crucial choice. We discuss the special challenges of diff-in-diff inference for ordinal outcomes. In our application (health effects of Medicaid expansion in a cohort study), the outcome of interest is self-rated health, expressed as an ordinal variable. An additional challenge is how to handle the risk of mortality. We consider both linear probability models and multinomial regression, and discuss how to interpret the resulting parameter estimates.