  This paper studies the testability of identifying restrictions commonly
employed to assign a causal interpretation to two stage least squares (TSLS)
estimators based on Bartik instruments. For homogeneous effects models applied
to short panels, our analysis yields testable implications previously noted in
the literature for the two major available identification strategies. We
propose overidentification tests for these restrictions that remain valid in
high dimensional regimes and are robust to heteroskedasticity and clustering.
We further show that homogeneous effect models in short panels, and their
corresponding overidentification tests, are of central importance by
establishing that: (i) In heterogenous effects models, interpreting TSLS as a
positively weighted average of treatment effects can impose implausible
assumptions on the distribution of the data; and (ii) Alternative identifying
strategies relying on long panels can prove uninformative in short panel
applications. We highlight the empirical relevance of our results by examining
the viability of Bartik instruments for identifying the effect of rising
Chinese import competition on US local labor markets.
