Comment on “A comparison of two business cycle dating methods”

✍ Scribed by James D. Hamilton

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 65 KB
• Volume: 27
• Category: Article
• ISSN: 0165-1889
• DOI: 10.1016/s0165-1889(02)00077-5

✦ Synopsis

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 ÿlter in Markov-switching models to ÿnd 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 ÿlter 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 ÿlter inference (Fig. 1), but is rather less convincing in representing the smoothed inference (Fig. 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 ÿlter 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 recession that quarter, where the geometric decay factor is given by 0.43. 1 Harding and Pagan compare this with a stripped-down Bry and Boschan (1971) rule, which would declare a recession had started if both y t -y t-1 and y t -y t-2 were negative. Harding and Pagan ÿnd the latter rule more appealing on grounds of transparency, robustness, simplicity, and replicability.