a b s t r a c t
We show that, for a class of univariate and multivariate Markov-switching models, exact calculation
of the BeveridgeNelson (BN) trend/cycle components is possible. The key to exact BN trend/cycle
decomposition is to recognize that the latent first-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 show that impulse-response function analysis can be processed with respect to either
an asymmetric discrete shock or to a symmetric continuous shock. The method presented is applied
to Kim, Morley, Piger's [Kim, C.-J., Morley, J., Piger, J., 2005. Nonlinearity and the permanent effects of
recessions. Journal of Applied Econometrics 20, 291309] univariate Markov-switching model of real
GDP with a post-recession `bounce-back' effect and Cochrane's [Cochrane, J.H., 1994. Permanent and
transitory components of GNP and stock prices. Quarterly Journal of Economics 109, 241263] vector
error correction model of real GDP and real consumption extended to incorporate Markov-switching.
The parameter estimates, the BN trend/cycle components, and the impulse-response function analysis
for each of these empirical models suggest that the persistence of US real GDP has increased since the
mid-1980's.