Relaxing the Exclusion Restriction in Shift-Share Instrumental Variable Estimation

Many economic studies use shift-share instruments to estimate causal effects. Often, all shares need to fulfill an exclusion restriction, making the identifying assumption strict. This paper proposes to use methods that relax the exclusion restriction by selecting invalid shares. I apply the methods in simulations and two empirical examples: the effect of immigration on wages and of Chinese import exposure on employment. I find that weak instruments and strong violations of the exclusion restriction do not worsen the performance of the estimators. In both applications, the coefficients change considerably but this is reconcilable with the arguments made in the literature