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. Causal Effects for Time-Varying Treatments and Outcomes 3