Macroeconomic Responses to Uncertainty Shocks: The Perils of Recursive Orderings

Abstract

A common practice in empirical macroeconomics is to examine alternative recursive orderings of the variables in structural vector autogressive (VAR) models. When the implied impulse responses look similar, the estimates are considered trustworthy. When they do not, the estimates are used to bound the true response without directly addressing the identification challenge. A leading example of this practice is the literature on the effects of uncertainty shocks on economic activity. We prove by counterexample that this practice is invalid in general, whether the data generating process is a structural VAR model or a dynamic stochastic general equilibrium model.

Keywords: Cholesky decomposition; orthogonalization; simultaneity; endogeneity; uncertainty; business cycle

JEL Classification: C32, C51, E32