Treatment Effects with Multiple Outcomes
This paper proposes strategies for defining, identifying, and estimating features of treatment-effect distributions in contexts where multiple outcomes are of interest. After describing existing empirical approaches used in such settings, the paper develops a notion of treatment preference that is shown to be a feature of standard treatment-effect analysis in the single-outcome case. Focusing largely on binary outcomes, treatment-preference probability treatment effects (PTEs) are defined and are seen to correspond to familiar average treatment effects in the single-outcome case. The paper suggests seven possible characterizations of treatment preference appropriate to multiple-outcome contexts. Under standard assumptions about unconfoundedness of treatment assignment, the PTEs are shown to be point identified for three of the seven characterizations and set identified for the other four. Probability bounds are derived and empirical approaches to estimating the bounds—or the PTEs themselves in the point-identified cases—are suggested. These empirical approaches are straightforward, involving in most instances little more than estimation of binary-outcome probability models of what are commonly known as composite outcomes. The results are illustrated with simulated data and in analyses of two microdata samples. Finally, the main results are extended to situations where the component outcomes are ordered or categorical.
I am grateful to Domenico Depalo, Paddy Gillespie, Hyunseung Kang, Chuck Manski, and participants in presentations at Queen's University Belfast, the University of Bergamo, the University of Chicago, and the University of Wisconsin-Madison for helpful comments, suggestions, and guidance on the literature. Partial support was provided by the Robert Wood Johnson Foundation (Evidence for Action Grant 73336), and by the UW-Madison Center for Demography and Ecology (NICHD grant P2CHD047873). The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research.