Causal Overlap Effects: A Cumulative Fixed Effect Approach

Abstract

Social scientists often ask about the effect of increasing one's duration of exposure to a social context on one's outcomes, i.e. the overlap effect. Past studies adopted a unidimensional treatment effect framework to estimate the effect of overlap, imposing important restrictions. In this paper, we propose a new causal framework of multidimensional treatments where the overlap effects include both the duration and the content of overlap, under which, for instance, the grandparent overlap effect is defined as the union of all causal effects of a grandparent's observed and unobserved characteristics (i.e., the content) on the grandchild across their shared life course (i.e., the duration). The multidimensional framework allows for a more flexible and context rich approach to effect heterogeneity, where unobserved contextual characteristics play two roles as unobserved confounders and as integral components of overlap effects -- overlap effects in this framework are not easily estimated with conventional fixed effects estimation. Hence, we develop a new cumulative fixed effects (CFE) approach that can estimate a range of interesting heterogeneous causal overlap effects from three-wave individual panel data. We show that the CFE approach is unbiased even in highly non-linear simulations, and we discuss assumptions and extensions.