Uncertain Short‐Run Restrictions and Statistically Identified Structural Vector Autoregressions

ABSTRACT This study proposes a combination of a statistical identification approach with potentially invalid short‐run zero restrictions. The estimator shrinks towards imposed restrictions and stops shrinkage when the data provide evidence against a restriction. We demonstrate that incorporating valid restrictions through the shrinkage approach enhances the efficiency of the statistically identified estimator, and the impact of invalid restrictions vanishes as the sample size increases. Applying the estimator to an oil market model indicates that incorporating stock market data into the analysis is crucial, as it enables the identification of information shocks, which are shown to be important drivers of the oil price.