Is there a duration dependence in Taiwan's business cycles?

Abstract

This paper intends to investigate the duration dependent feature of Taiwan's business cycles. The constant Markov switching model is revised to take account of the duration dependent feature. The most innovative findings herein are that there is no duration dependence for contraction for the circa pre-1990 periods and no duration dependence for expansion for the circa post-1990 periods. However, there is duration dependence for economic expansion for the circa pre-1990 and duration dependence for contraction for circa post-1990 periods, respectively. In addition, the recessionary dates identified by the duration dependent Markov switching model are identical to the officially defined recessionary chronologies.

Keywords:

• Duration dependence
• business cycle
• Markov switching model
• Gibbs sampling

Acknowledgments

We would like to thank the associate editor and two anonymous referees for helpful comments and suggestions. Financial support from National Science Council (NSC 91-2415-H-029-001) is grateful. The usual disclaimer applies.

Notes

¹Another possible shortcoming of Hamilton's model is that it is univariate. The model cannot capture another important feature of business cycle, i.e. ‘co-movement’. See Kim & Yoo (1995), Chauvet (1998), and Kim & Nelson (1998) for extensions.

²Durland & McCurdy (1994) adopt the quasi MLE method, while Kim & Nelson (1998) and Pelagatti (2001) employ the Bayesian MCMC method to find the unknown parameter estimates. See Kim & Nelson (1999) for a thorough review on the specification and estimation of the Markov switching model.

³According to time series plot of the growth rate of real GDP, the variation or variance of Taiwan's economic growth rates decline substantially explicitly around 1987 or 1988 by eye. For the purpose of ease of exposition, in the text, we still regard 1962 to 1987 as circa pre-1990 period, and take 1988 to 2001 as the circa post-1990 period.

⁴The prior inputs for the DDMS model are included in the first two columns of Table 4.

⁵We still cannot deny the fact that very few observations will exert a problem in estimation work, and may produce unreliable results.

⁶The parameter estimates for other sample periods are available from the author upon request.

⁷We also estimate alternative models such as by restricting all lags to be zero. However, the estimation results are similar but the associated model-dating recessionary dates are less consistent with the CEPD-defined chronologies.

⁸The most innovative aspect of the Markov switching model is the ability to objectively date an economy's states by the so-called filtered and smoothed probabilities. The filtered probabilities (collected in a (T × 1) vector denoted ξ _{t| t} (d), i.e. ξ _{t| t} (d) = p(S _t  = j| y ^t , D _t−1 = d), j = 1, …, T, where y ^t is the information set) denote the conditional probability that the analyst's inference about the value of S _t is based on information obtained through date t. It is also possible to calculate smoothed probabilities, ξ _{t| T} (d) = p(S _t  = j| y ^T , D _t−1), j = 1, …, T, which are based on the full sample.

⁹A recession is expected if the predicted probability exceeds 0.5 following the 0.5 rule.

¹⁰We only show the BF results and kernel density plots of β₂ and β₄ for 1962–1987 and 1988–2001 because the conclusions are unchanged for other periods.

¹¹The calculation of BF for expansion, for example in 1962–1987, is as follows. The value of the conditional density of β₂ at 0 can be read from the graph (it is circa 1.2), we used as prior N(0, 5) that in 0 is 0.178 and the ratio is 6.74, that is in favor of the hypothesis β₂ = 0.