Response to Gamino

Aaron Gamino (2023) comments on our paper analyzing marriage of young adults and dependent coverage health insurance mandates in the Journal of Human Resources (Barkowski and McLaughlin 2022), arguing that we used “potentially mis-specified difference-in-difference-in-differences models” that “omit relevant interaction terms” (Gamino 2023, 17). In particular, he argues our model is biased by the exclusion of age-by-year interaction terms. When he includes these terms in our model, he obtains coefficient estimates that are close to zero for some model variations. In this reply, we argue that Gamino’s inclusion of age-by-year interaction terms in our model is inappropriate and introduces bias, and that his analysis generally supports the findings in our paper. To summarize our arguments, there are at least four important flaws un-derlying Gamino’s critique.³ First, he ignores our discussion (Barkowski and McLaughlin 2022, 641–643, 648 Figure 1) of how there is no true control group that is not affected by the treatment in our data, and how this changes our analysis from a standard difference-in-difference (DD) or triple-difference (DDD) research design. His introduction of age-by-year fixed effects to our model, consis-tent with treating our research design as a DDD, introduces bias to one of the main coefficient estimators (and hence, the entire model). Second, rather than removing bias, Gamino’s additional fixed effects absorb the remaining identifying variation in the model. Evidence for this comes from his analysis of our marriage entry variable. Our model explains much less of the variation in marriage entry than our standard outcome, marriage state. When he adds age-by-year fixed effects to the marriage entry model, estimates are either little changed or become larger in magnitude. Third, Gamino performs a placebo policy analysis to estimate bias due to omitted age-by-year fixed effects. The bias he finds suggests our estimates may understate the magnitude of the effects. This is inconsistent with the true effects being close to zero, as he argues, and represents additional evidence that his added fixed effects merely absorb important variation. Fourth, Gamino provides minimal justification for why he thinks our model is inappropriate. Gamino (2023, 18) implies we use a DDD model in a corresponding analysis in a related paper. This claim is incorrect, as the analogous model in the related paper (Barkowski, McLaughlin, and Ray 2020) is a DD model, not a DDD model. Lastly, while Gamino argues our analysis of marriage with a DD-style model is inappropriate, in his own work studying dependent coverage under the same state-level mandates (Gamino 2018), he uses a DD model when he considers marriage, and also does not include all possible multi-way-interaction terms in his analyses of other outcomes. Clearly, Gamino agrees that the type of model used in an analysis should be based on the context, and that DD-style models are appropriate in the current one, even if it does not include all possible multi-way-interaction fixed effects. In the rest of this reply, we provide more in-depth discussion of the above points. However, we also urge readers to consult our original paper, where we provide an extensive discussion on the rationale behind our model and its identi-fication. Clearly, every model has weaknesses and limitations, and as ours does not include age-by-year interaction terms, it could be affected by unobserved age-year trends—a point that was acknowledged in our paper (Barkowski and McLaughlin 2022, 684, 684 n.29). But our model was not “misspecified” or lacking the “proper” controls (Gamino 2023, 16, 18). Rather, as Gamino should have been aware, it was chosen for specific reasons that were fully discussed.