Generalizing the Max Share Identification to multiple shocks identification: an Application to Uncertainty

We generalize the Max Share Identification 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 non-trivial optimization problem on the columns transforming reduced-form shocks into structural shocks. We provide conditions for existence and uniqueness of a solution, and Bayesian algorithms for estimation and inference. We use the approach to study the effects of uncertainty shocks, allowing for the possibility that uncertainty is an endogenous variable, and distinguishing macroeconomic from financial uncertainty. Using US data we find that macroeconomic uncertainty is mostly endogenous, and that overlooking this fact can lead to distortions on the estimates of its effects. We show that the distinction between macroeconomic and financial uncertainty is empirically relevant. Finally, we study the relation between uncertainty shocks and pure financial shocks, showing that the latter can have attenuated effects if one does not take into account the endogeneity of uncertainty.