Max Share Identification of Multiple Shocks: An Application to Uncertainty and Financial Conditions

Abstract

We generalize the Max Share approach to allow for simultaneous identification of a multiplicity of shocks in a Structural Vector Autoregression. Our machinery therefore overcomes the well-known drawbacks that individually identified shocks (i) tend to be correlated to each other or (ii) can be separated under orthogonalizations with weak economic ground. We show that identification corresponds to solving a nontrivial optimization problem. We provide conditions for non-emptiness of solutions and point-identification, and Bayesian algorithms for estimation and inference. We use the approach to study the effects of uncertainty and financial shocks, allowing for the possibility that the former responds contemporaneously to other shocks, distinguishing macroeconomic from financial uncertainty and credit supply shocks. Using U.S. data we find that financial uncertainty mimics a demand shock, while the interpretation of macro uncertainty is more mixed. Furthermore, variation in uncertainty partially represents the endogenous response of uncertainty to other shocks.