Difference-in-differences for categorical outcomes

To discuss and develop difference-in-difference estimators for categorical outcomes and apply them to estimate the effect of the Affordable Care Act's Medicaid expansion on insurance coverage.

Secondary analysis of Survey on Income and Program Participation (SIPP) data on health insurance coverage types before (January 2013) and after (December 2015) Medicaid expansion in 39 US states (19 expansion and 20 non-expansion).

We develop difference-in-difference methods for repeated measures (panel data) of categorical outcomes. We discuss scale-dependence of DID assumptions for marginal and transition effect estimates and specify a new target estimand: the difference between outcome category transitions under treatment versus no treatment. We establish causal assumptions about transitions that are sufficient to identify this and a marginal target estimand. We contrast the marginal estimands identified by the transition approach versus an additive assumption only about marginal evolution. We apply both the marginal and transition approaches to estimate the effects of Medicaid expansion on health insurance coverage types (employer-sponsored; other private, non-group; public; and uninsured).

We analyzed 16,027 individual survey responses from people aged 18-62 years in the 2014 SIPP panel.

We show that the two identifying assumptions are equivalent (on the scale of the marginals) if either the baseline marginal distributions are identical or the marginals are constant in both groups. Applying our transitions approach to the SIPP data, we estimate a differential increase in transitions from uninsured to public coverage and differential decreases in transitions from uninsured to private, non-group coverage and in remaining uninsured.

By comparing the assumption that marginals are evolving in parallel to an assumption about transitions across outcome values, we illustrate the scale-dependence of difference-in-differences. Our application shows that studying transitions can illuminate nuances obscured by changes in the marginals.