Sharpening blunt instruments: Exploiting non-linearities to enhance identification

Without the ability to directly manipulate treatment assignment, scholars often turn to quasi-experimental identification strategies. Perhaps the most popular yet contentious approach has been to find a plausibly exogenous instrumental variable to estimate the treatment effect through two-stage least squares or two-stage residual inclusion. A common issue with this strategy is that potential instruments are often found to be weak, invalid, or both, in which case the identification strategy is inappropriate and the results potentially misleading. This note proposes an identification strategy with which non-linearities in the first stage can be exploited to (1) increase the strength of first-stage relationships (2) render otherwise invalid instruments valid, and (3) identify more than one treatment effect with the same source of exogenous variation. The approach is illustrated through simulations and is applied to the study of determinants of economic growth. R code is provided in the Appendix to facilitate its use in applied studies. Our proposed approach expands the domain of applicability for instrumental variables by loosening rather than imposing assumptions.