# Relaxing the Exclusion Restriction in Shift-Share Instrumental Variable Estimation

## TL;DR

This paper introduces methods to relax the strict exclusion restriction in shift-share instrumental variable estimation, allowing for invalid shares and improving causal inference in economic studies.

## Contribution

It proposes novel techniques to relax the exclusion restriction in shift-share IV estimation and demonstrates their application in empirical examples.

## Key findings

- The estimated effect of immigration on wages becomes lower and sometimes negative.
- Results on Chinese import exposure and employment are mostly robust to the new methods.
- The new methods reconcile some previous discrepancies in causal estimates.

## Abstract

Many economic studies use shift-share instruments to estimate causal effects. Often, all shares need to fulfil 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 two empirical examples: the effect of immigration on wages and of Chinese import exposure on employment. In the first application, the coefficient becomes lower and often changes sign, but this is reconcilable with arguments made in the literature. In the second application, the findings are mostly robust to the use of the new methods.