Adaptive Centering with Random Effects: An Alternative to the Fixed Effects Model for Time-Varying Treatments

Of widespread interest in social science are observational studies in which entities (persons, schools, states, countries, etc.) are exposed to varied treatment conditions over time. As in all observational studies, the non-randomized assignment of treatments poses challenges to valid causal inference. An attractive feature of panel studies with time-varying treatments, however, is that the design makes it possible to remove the influence of unobserved time-invariant confounders in assessing the impact of treatments. The removal of such confounding is typically achieved by including fixed effects of the repeatedly measured entities. In some cases, these entities are clustered in larger units, and the time-invariant influences of these larger units can be removed by adding additional dimensions of fixed effects; also, entity-invariant temporal influences can be removed through time fixed effects. In this paper, I introduce an alternative procedure: adaptive centering of treatment variables with random effects. I show that this alternative procedure can replicate the fixed effects analysis of time-varying treatments in any dimension of clustering and offers several comparative advantages: the incorporation into standard errors of multiple sources of uncertainty; the modeling of heterogeneity of treatment effects; estimation of treatment effects at multiple levels and their interaction; improved estimates of unit-specific effects; and computational simplicity. The paper shows how adaptive centering can efficiently estimate effects in an L-level model using one or more dimensions of clustering. 3