Ebook Business Cycle Dynamics With Duration Dependence And Leading Indicators
The question of whether business cycle phases are duration dependent has been of interest for many decades. One widely held view is that the older an expansion is, the more likely it is to end. There was much discussion along these lines in the US in the late 1990s as that expansion approached – and eventually passed the longest previous US expansion ever recorded (since the 1850s). On the other hand, many economists have questioned whether there is any strong underlying rationale for this belief or whether it is simply the business cycle analogue of the view that ’nothing lasts forever’.
Whilst it is obvious that no business cycle phase has ever lasted forever and is never likely to – the issue surrounding duration dependence is whether there exists statistical evidence that the probability of a phase change systematically increases with the length of the current phase. Furthermore, even if current phase duration does seem to be a determinant of the probability of phase termination, there may well be some underlying economic processes taking place systematically over time which increase the likelihood of the phase ending. Thus, if other factors are indeed important in determining phase shifts, then apparent duration dependence may simply reflect the influence of other more fundamental variables. In the same way therefore that a trend variable may or may not remain statistically significant after incorporating other explanatory variables, the same may well be true of duration once other explanatory variables are incorporated into the analysis. We believe this to be an important question and we therefore seek to address the issue here.
In our empirical analysis we use the business cycle phase chronology for the US determined by the National Bureau of Economic Research (NBER) dating panel. As we discuss below, this chronology represents a set of reference dates which is agreed upon by a group of recognized experts at the NBER, is widely used, and has been used to examine duration dependence in the business cycle using a range of different methodologies. However the business cycle is essentially a conceptual construct – and at that an ultimately unobservable construct. The best that can be done is to carefully conceptually define it and then use a range of datasets to triangulate on the most appropriate dates of the phase changes. There may well be alternative methodologies and resulting chronologies for the US to that of the NBER. However, we argue that the NBER methodology has the longest pedigree and the NBER chronology is the most widely accepted, cited and used set of phase change dates for the US business cycle. Given this, we elect to study duration dependence explicitly using the NBER chronology.
Our approach can be contrasted with the duration-dependent regime switching extensions of Hamilton (1989) which explicitly assume that the latent regime state is unobservable and must be inferred. In fact every Markov-switching model of US GDP we are aware of benchmarks the regime probabilities against the NBER chronology. Hamilton-type models are most useful in situations where there is no clear a priori knowledge of the phase change dates. However, for the case of the US business cycle, to ignore the existence of such dates as the NBER chronology is to ignore very important relevant information.
Earlier research that uses the NBER chronology to explore duration dependence (i.e., Sichel (1991), Zuehlke (2003) and Diebold and Rudebusch (1990) discussed below) use either non-parametric methods or a hazard function which uses only the length of each phase. However, we model the state of the business cycle as a first-order Markov process and allow the transition probabilities to vary as a function of both leading indicators and phase durations. In particular, we directly model the probability of staying in a phase or changing phases as a multinomial Logit (and Probit) process. We believe this modeling specification represents a more complete framework and will not only bring into further relief the strength of duration dependence in the US business cycle evident in the data, but will also provide for richer interpretations of the resulting estimated model.
We also believe our approach to the issue of duration dependence nicely complements the Markov-regime switching approach of Durland and McCurdy (1994). Their approach an extension of Hamilton’s (1989) - models an observed cyclical variable (GDP in their case) whose distribution is influenced by unobserved latent states. The estimated conditional density of the observable cyclical variable allows the econometrician to infer something about both the unobserved state of the variable under study as well as its apparent duration dependence. In contrast to this, we investigate duration dependence directly by relying on the phase changes, and hence business cycle durations, implied by the NBER-determined business cycle chronology.
Our approach is clearly only available when one has access to such a well respected business cycle chronology, and without it, one would apply the more computationally intensive approach of Durland and McCurdy (1994). Which approach yields better inference about business cycle duration depends ultimately on one’s stance on whether the NBER chronology or the set of latent states implicit in US GDP is a better proxy for the US business cycle chronology. Interestingly, we find that the standard errors from our approach are tighter than the standard errors reported in approaches that do not use the NBER dates. This suggests that using the NBER chronology allows us to learn much about business cycle phase dynamics.
Of course, we do not take the position that the NBER dating committee is infallible nor that the dates are sacrosanct. Nonetheless, we believe a chronology determined by a committee of respected experts employing a consistent methodology and using a variety of macroeconomic indictors is likely to be superior to the noisy signal about the state of the business cycle inferred from a single cyclical variable such as GDP. We have also verified in a simulation exercise that the main conclusions about the importance of duration dependence in modelling phase changes is robust to minor variations in the chronology as determined by the dating committee. And so, given the widespread use of the NBER chronology, it seems sensible to us to directly use it to construct tests of US business cycle duration dependence?
In the next section we discuss earlier related literature. We then present the modelling framework and how it relates to the Hamilton approach – of which it may be regarded as a special case variant. The estimation results follow, with concluding remarks presented in Section 5.
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