Composite Causal Effects for Time-Varying Treatments and Time-Varying Outcomes

We develop an approach to conceptualizing causal effects in longitudinal settings with time-varying treatments and time-varying outcomes. The classic potential outcome approach to causal inference generally involves two time periods: units of analysis are exposed to one of two possible values of the causal variable, treatment or control, at a given point in time, and values for an outcome are assessed some time subsequent to exposure. In this paper, we develop a potential outcome approach for longitudinal situations in which both exposure to treatment and the effects of treatment are time-varying. In this longitudinal setting, the research interest centers on not two potential outcomes, but a matrix of potential outcomes, requiring a complicated conceptualization of many potential counterfactuals. Motivated by several sociological applications, we develop a simplification scheme – a composite causal effect estimand – with a forward looking sequential expectation that allows identification and estimation of effects with a number of possible solutions. Our approach is illustrated via an analysis of the effects of disability on subsequent employment status using panel data from the Wisconsin Longitudinal Study.