Comment on A Comparison of Two Business Cycle Dating Methods. James D. Hamilton

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1 Comment on A Comparison of Two Business Cycle Dating Methods James D. Hamilton 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

2 recession that quarter, where the geometric decay factor is given by Harding and Pagan compare this with a stripped-down Bry and Boschan (1971) rule, which would declare a recession had started if both y y t 1 and y y 2 were negative. Harding and t t t Pagan find the latter rule more appealing on grounds of transparency, robustness, simplicity, and replicability. Although the two approaches to dating business cycles may appear very comparable when expressed in these terms, there is an important philosophical distinction between them. The Harding-Pagan criterion is simply a rule that one applies, irrespective of the data or one s purpose. If one were so inclined, one could use this rule to find business cycles in records of rainfall in Mongolia or the counts of spots on a shuffled deck of cards. By contrast, the statistical model underlying the Markov-switching dates holds that there is a real event (an economic recession) that either occurred or didn t. The event, though unobserved directly by the econometrician, has tangible consequences for the observed growth rates, and the econometrician s job is to form an optimal inference about whether a recession occurred based on the observed data, or indeed whether the data-generating process is characterized by such events at all. 1 Equation (8) implies a 1 b c 1 b ^ z ~ t t = + yt ~ y = w y where t i t i is a geometric average of current and past growth rates with weights i= 0 i w = b ( 1 b) summing to unity. Hence zˆ < (1/ 2) if and only if i ~ < c 1 [ a + (1 b) / 2] = y t t t

3 If a recession were nothing more than a numerical relation between yt and y t 2, then there would be nothing for the NBER dating committee to meet about and discuss as grown-ups. Either yt is smaller than y t 2 or it isn t, and that s that. For that matter, the added details of the algorithm to which Bry and Boschan devoted a good deal of thought, such as ensuring that the inferred expansions and contractions were of minimum duration, would seem a pointless frivolity if this were simply a rule we made up. I would suggest that, instead, the whole body of literature on dating business cycles is implicitly accepting the fundamental view that an economic recession is a real event about which we are trying to draw an inference. The difference between the Harding-Pagan approach and the Markov-switching approach is that the latter formulates a specific statistical model of the object of interest and derives the optimal inference about it, whereas the former leaves vague and intuitive exactly what this algorithm is intended to measure. Once one acknowledges that business cycles are a feature that a given data set may or may not exhibit, it seems natural that the criteria for dating them would depend on the particular properties of the data. We should want to use a different rule for a country with a very high average growth rate compared to a country with a low average growth rate, or for a country with much poorer quality of national income data compared to one with superior data. The fact that parameters such as 0.43 and above are estimated features of the data strikes me as an appealing quality of the Markov-switching approach. The robustness of the Harding-Pagan approach, which insists on using the same rule regardless of the data, could well be regarded as a liability rather than an asset. The rule works well on postwar U.S. data, but that is a feature of the data, not the rule.

4 Despite these differences with the authors, I find myself agreeing with their fundamental conclusion. I, too, feel that the algorithm for dating business cycles proposed in my 1989 paper is not the best one to use, though my reasons are rather different from those of Harding and Pagan. My main concern is that superior methods have been developed since Specifically, the 1989 paper just used univariate GNP data. A key concern for students of the business cycle has always been with comovements of different variables-- a recession is something that shows up in a number of different series at the same time. Thinking of a recession as an unobserved process that affects a vector of Markov-switching economic time series has produced a number of useful insights about business cycles; see for example Chauvet (1994), Kim and Nelson (1999), Chauvet, Juhn, and Potter (2002), and Kim and Murray (2002), and the references therein. By contrast, the Harding and Pagan approach does not generalize at all naturally to consideration of vectors. I also agree, and here without qualifications, with Harding and Pagan s interest in transparency. I think it is a mistake to let any model become a complicated black box, whose method of inference is too arcane or mysterious to be questioned. On this score, their process of stripping down the Markov-switching framework and then finding a linear approximation to its inference is very helpful in understanding what the procedure does, and a welcome contribution to the literature.

5 References Bry, G., and Boschan, C Cyclical Analysis of Time Series: Selected Procedures and Computer Programs (National Bureau of Economic Research, New York). Chauvet, Marcelle An econometric characterization of business cycle dynamics with factor structure and regime switches. International Economic Review 39, Chauvet, Marcelle, Juhn, Chinhui, and Potter, Simon Markov-switching in disaggregate unemployment rates. Empirical Economics, forthcoming. Hamilton, James D A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, Hamilton, James D State space models, in: Engle, Robert F., and McFadden, Daniel L., eds., Handbook of Econometrics, Vol. 4 (North-Holland, Amsterdam) Kim, Chang-Jin, and Murray, Christian J Permanent and transitory components of recessions. Empirical Economics, forthcoming. Kim, Chang-Jin, and Nelson, Charles R State-Space Models with Regime Switching, MIT Press, Cambridge, MA.