Robust Inference in Models Identified via Heteroskedasticity

Identification via heteroskedasticity exploits variance changes between regimes to identify parameters in simultaneous equations. Weak identification occurs when shock variances change very little or multiple variances change close to proportionally, making standard inference unreliable. I propose an $F$-test for weak identification in a common simple version of the model. More generally, I establish conditions for validity of nonconservative robust inference on subsets of the parameters, which can be used to test for weak identification. I study monetary policy shocks identified using heteroskedasticity in high-frequency data. I detect weak identification, invalidating standard inference, in daily data, while intraday data provide strong identification.