A systematic framework for analyzing the dynamic effects of permanent and transitory shocks

Abstract

This paper proposes a systematic framework for analyzing the dynamic effects of permanent and transitory shocks on a system of n economic variables. We consider a two-step orthogonolization on the residuals of a VECM with r cointegrating vectors. The first step separates the permanent from the transitory shocks, and the second step isolates n− r mutually uncorrelated permanent shocks and r transitory shocks. The decomposition is computationally straightforward and entails only a minor modification to the Choleski decomposition commonly used in the literature. We then show how impulse response functions can be constructed to trace out the propagating mechanism of shocks distinguished by their degree of persistence. In an empirical example, the dynamic responses to the identified permanent shocks have properties similar to shocks to productivity, the real interest rate, and money growth, even though no economic theory was used to achieve the identification. We highlight two numerical issues that could affect any identification of permanent and transitory shocks.