Comment on A Comparison of Two Business Cycle Dating Methods

Harding and Pagan note that their stripped-down Markov-switching model (3)-(5) is an example of a standard state-space model, albeit with non-Gaussian innovations. This is indeed true of a broad class of Markov-switching models, as noted by Hamilton (1994, Section 4.1). Hence one could always use the Kalman filter in Markov-switching models to find the linear projection of the unobserved regime on past observables. The optimal nonlinear inference developed in my 1989 paper takes the form of a probability between zero and one, while the linear projection from the Kalman filter may fall outside these bounds, but in some cases the two inference rules may be very similar. In Harding and Pagan's empirical example, the linear projection gives a good approximation to the optimal nonlinear filter inference (Figure 1), but is rather less convincing in representing the smoothed inference (Figure 2). Harding and Pagan note that their linear representation of the latter involves some additional approximations as well. Harding and Pagan then use the steady-state Kalman filter and approximate smoother equations to characterize the Markov-switching algorithm for dating cycles. The former, for example, amounts to a rule that if a geometric average of current and past quarterly GNP growth rates falls below-0.15%, then one would say the U.S. was in a