Abstract When researchers cannot randomly assign a treatment, as is often the case in international relations, they rely on observational data and use quasi-experimental designs with instrumental variables. Despite new advances in this area, even instruments with high first–stage relevance (large F–statistics) may fail the exclusion restriction if they affect the outcome through uncontrolled channels. In applied studies, the widespread use of the same instruments to explain various outcomes “collectively” invalidates them. For instance, in studying economic growth, population size has been used as an instrument for total trade, trade openness, export diversity, foreign aid, and foreign direct investment. The existence of multiple pathways through which population affects economic growth invalidates the exclusion restriction. This paper proposes an identification strategy with which non-linearities in the first stage can be exploited to (1) render otherwise invalid instruments valid, (2) increase the strength of first-stage relationships, and (3) identify more than one treatment effect with the same source of exogenous variation. The approach is illustrated through simulations and applications to economic growth and democratization. We provide online resources with R code to facilitate its use in applied studies.
Schwarz et al. (Wed,) studied this question.