We study Structural Vector Autoregressions in which a structural shock of interest (e.g., an oil supply shock) is identified using an external instrument. The external instrument is taken to be correlated with the target shock (e.g., the instrument is relevant) and to be uncorrelated with other macroeconomic shocks of the model (e.g., the instrument is exogenous). The potential weak correlation between the external instrument and the target structural shock compromises the large-sample validity of standard inference. We suggest a confidence set for the coefficients of the Structural Impulse-Response function and we show that its asymptotic confidence level is not affected by the instrument strength. The implementation of our confidence set requires no more work than solving a single-variable quadratic equation. In an empirical application studying the dynamic effects of a structural oil supply shock in the global crude oil market, we use the external instrument approach to report impulse-response functions, forecast-error variance decompositions and to estimate the oil supply shock. Contrary to previous studies, our inference results suggest there is not enough evidence to argue that a structural oil supply shock has only a small and transitory effect on the real price of oil.
Joint work with James H. Stock and Mark W. Watson
Keywords: Structural Vector Autoregressions, Narrative Approach, Instrumental Variables, Weak identification