Testing strong exogeneity in proxy SVARs with internal synthetic proxies

Proxy SVARs often rely on a single credible proxy, leaving proxy exogeneity untestable. Narrative arguments used to justify proxy validity imply a stronger form of exogeneity. We formalize the strong exogeneity assumption and propose a corresponding test based on internal synthetic proxies. The approach uses the external proxy to locate the target-shock direction in the reduced-form innovations and synthesize the candidate shock into an additional internal synthetic proxies, which allows to test the joint exogeneity of the original and internal synthetic proxy. We derive the large-sample theory for the ISP test and show that the identification strength is governed by a direct measure of the target shock's non-Gaussianity. We study weak identification under asymptotic Gaussianity and develop an identification-robust version of the test. Monte Carlo experiments demonstrate the favorable power of the test when the proxy has a low signal-to-noise ratio. Applications to monetary policy and oil supply news shocks find no evidence against the exogeneity of the benchmark proxies.