Complementarity and Identification

TL;DR

This paper explores how assumptions about complementarity, such as supermodularity, can improve the identification of treatment effects in nonparametric bounds analysis, especially with multidimensional treatments and heterogeneity.

Contribution

It extends partial identification methods by incorporating shape restrictions and cross-dimensional assumptions like supermodularity to enhance bounds on treatment effects.

Findings

Supermodularity strengthens bounds on average treatment effects.

Combining supermodularity with independence improves bounds on treatment effect distributions.

Application demonstrates improved identification in urban zoning impact study.

Abstract

This paper examines the identification power of assumptions that formalize the notion of complementarity in the context of a nonparametric bounds analysis of treatment response. I extend the literature on partial identification via shape restrictions by exploiting cross-dimensional restrictions on treatment response when treatments are multidimensional; the assumption of supermodularity can strengthen bounds on average treatment effects in studies of policy complementarity. This restriction can be combined with a statistical independence assumption to derive improved bounds on treatment effect distributions, aiding in the evaluation of complex randomized controlled trials. Complementarities arising from treatment effect heterogeneity can be incorporated through supermodular instrumental variables to strengthen identification in studies with one or multiple treatments. An application examining the long-run impact of zoning on the evolution of urban spatial structure illustrates the value of the proposed identification methods.