Shift-share instruments and dynamic adjustments: the case of immigration

A prominent class of instruments combines local shares with aggregate shifts. We demonstrate that estimates using these “shift-share” instruments are inherently vulnerable to bias from dynamic adjustments to past shocks. To illustrate, we show that estimates of the partial equilibrium impact of immigration on wages employing a frequently-used shift-share instrument are unlikely to identify a causal effect. We propose a dynamic variant of the shift-share estimator that yields consistent and substantially more negative estimates than those using the conventional instrument. Our results are a cautionary tale for a large body of empirical work relying on shift-share instruments for causal inference. JEL No. C36, J15, J21, J61