The Beveridge-Nelson Decomposition and Impulse-Response Analysis in the Presence of Markov-Switching: Has the Persistence of Real GDP Changed Since the Mid 1980 s?

The Beveridge-Nelson Decomposition and Impulse-Response Analysis in the Presence of Markov-Switching: Has the Persistence of Real GDP Changed Since the Mid 1980 s?

We show that, for a class of univariate and multivariate Markov-switching models, exact calculation of the Beveridge-Nelson (BN) trend/cycle components is possible. The key to exact BN trend/cycle decomposition is to recognize that the latent ¯rst-order Markov-switching process in the model has an AR(1) representation, and that the model can be cast into a state-space form. Given the state-space representation, we also show that impulse-response analyzes can be done with respect to an asymmetric discrete shock as well as to a symmetric continuous shock. The methodologies developed are applied to Kim, Morley, Piger s (2005) univariate Markov-switching model of real GDP with a post-recession `bounce-back e？？ect and Cochrane s (1994) vector error correction model of real GDP and real consumption extended to incorporate Markov switching. Based on the parameter estimates, the calculated BN trend/cycle components, and the impulse-response analyzes for each of these empirical models, we raise the possibility that the persistence of real GDP might have increased since the mid-1980 s in the U.S.