Many studies exploit geographic variation in the concentration of immigrants to identify their impact on labor market or other outcomes. National inflows of immigrants are interacted with their past geographic distribution to create an instrument, in the hopes of breaking the endogeneity between local conditions and the location choice of immigrants. We present evidence that estimates based on this shift-share instrument are subject to bias from a conflation of short- and long-run responses, which stems from the interplay of two factors. First, local shocks may trigger adjustment processes that gradually offset their initial impact. Second, the spatial distribution of immigrant arrivals can be highly stable over time. In the U.S., their distribution has in recent decades been almost perfectly serially correlated, with the same cities repeatedly receiving large inflows. Estimates based on the conventional shiftshare instrument are therefore unlikely to identify a causal effect. However, we propose a “double instrumentation” solution to the problem that – by isolating spatial variation that stems from changes in the country-of-origin composition on the national level – produces estimates that are likely to be less biased. Our results are a cautionary tale for a large body of empirical work, not just on immigration, that rely on shift-share instruments for causal identification.