Complementarity and Identification

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 ofsupermodularitycan 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 throughsupermodular instrumental variablesto 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.

IT skills, occupation specificity and job separations

“…In contrast, and according to hypothesis 2, we expect no positive coefficient on β 6 for expert IT skills, as expert IT skills are ordinary additive (non-complementary) skills. It should be noted here that, while positive interaction effects can serve as supportive evidence of complementarities, they cannot serve as a definitive test (Tate Twinam, 2017).…”

Recent Developments in Partial Identification

“…Okumura & Usui (2014) use the assumption that the response functions are concave. Twinam (2017) uses the assumption that the response functions (involving multiple treatments) are supermodular. Kim et al (2018) use the assumption that the response functions satisfy smoothness conditions.…”

Teaching and incentives: Substitutes or complements?

“…Crucially, are supply and demand interventions substitutes or complements? Understanding complementarities between interventions is key for cost-effectiveness analyses, and thus decision-making on optimal combinations of policies (Twinam, 2017). If two interventions are complements, the gains from implementing both exceed the sum of the gains of implementing each one singly.…”