APPENDIX Dating of Business Cycles and Korean Export Cycles Using the Bry and Boschan (BBQ) Algorithm
In constructing the BBQ algorithm to determine the turning points (peaks and troughs) in quarterly industrial production and Korean export data, the original Bry and Boschan (1971) business cycle-dating algorithm has been adapted as follows.
Artis, M., Z. Kontolemis, and D. Osborne, 1997, “Business Cycles for G7 and European Countries,” Journal of Business 70, pp. 249–79.
Brain, C.W., S.S. Shapiro, and 1983, “A Regression Test for Exponentiality: Censored and Complete Samples,” Technometrics 25, pp. 69–76.
Bry, G., and C. Boschan, 1971, Cyclical Analysis of Time Series: Selected Procedures and Computer Programs (New York: National Bureau of Economic Research).
Burns, A.F., and W.C. Mitchell, 1946, Measuring Business Cycles, NBER Studies in Business Cycles No.2 (New York: National Bureau of Economic Research).
Cashin, P., C. J. McDermott, A. Scott, 2002, “Booms and Slumps in World Commodity Prices,” forthcoming, Journal of Development Economics.
Cashin, P., and S. Ouliaris, 2001, “Key Features of Australian Business Cycles,” IMF Working Paper 01/171 (Washington, D.C.: International Monetary Fund).
Diebold, F.X., and G.D. Rudebusch, 1990, “A Nonparametric Investigation of Duration Dependence in the American Business Cycle,” Journal of Political Economy 98, pp. 596–616.
Harding, D., and A. Pagan, 2002, “Dissecting the Cycle: A Methodological Investigation,” forthcoming, Journal of Monetary Economics.
Harding, D., and A. Pagan, 2001, “Extracting, Analyzing and Using Cyclical Information,” mimeo, Melbourne Institute of Applied Economic and Social Research, University of Melbourne.
Hodrick, R.J., and E.C. Prescott, 1980, “Post-War U.S. Business Cycles: An Empirical Investigation,” Discussion Paper No. 451, (Pennsylvania: Carnegie-Mellon University).
Hoffmaister, A., and J.E. Roldos, 2001, “The Sources of Macroeconomic Fluctuations in Developing Countries: Brazil and Korea,” Journal of Macroeconomics 23, pp. 213–39.
Kim, K., and Y.Y. Choi, 1997, “Business Cycles in Korea: Is There Any Stylized Feature?,” Journal of Economic Studies 24, pp. 275–93.
King, R.G., and C.I. Plosser, 1994, “Real Business Cycles and the Test of the Adelmans,” Journal of Monetary Economics 33, pp. 405–438.
Kydland, F., and E.C. Prescott, 1990, “Business Cycles: Real Facts and a Monetary Myth,” Quarterly Review, Federal Reserve Bank of Minneapolis, pp. 3–18.
Pagan, A., 1999, “Bulls and Bears: A Tale of Two States,” The Walbow-Bowley Lecture. North American Meeting of the Econometric Society, Montreal, June 1998.
Watson, M.W., 1994, “Business-Cycle Durations and Postwar Stabilization of the U.S. Economy,” American Economic Review 84, pp. 24–46.
This paper was prepared by Paul Cashin (RES) and Hong Liang (APD).
As an alternative measure of economic activity, we also examined classical cycles in real GDP for Korea, Japan and the United States. However, Korea’s long period of expansion since the early 1960s yielded only one peak and one trough in real GDP (in the late 1990s), obviating our ability to analyze Korean cycles in GDP. Previous analyses have found that turning points in industrial production are closely related to the NBER’s business cycle turning points for the United States (see Artis et al. (1997)).
The seasonally adjusted industrial production indices (for Korea, Japan and the United States) are taken from line 66 of IFS (1995=100). The annualized nominal data on Korean exports (in millions of U.S. dollars) to: the world (country code 001 of DTS); the United States (country code 111 of DTS); the European Union (country code 998 of DTS); and Japan (country code 158 of DTS) have been deflated by the GDP deflator (base 1996) of the United States (taken from the OECD’s Analytical Database) to form the respective series for real exports. All real export series were then seasonally adjusted using the ratio-to-moving average method of EViews.
Harding and Pagan (2001) argue that nonparametric approaches to ascertaining turning points in the business cycle (such as the Bry-Boschan algorithm) compare favorably with that of parametric approaches (such as the Markov switching model), due to the former’s greater transparency, simplicity and robustness to variations in the sample selected.
The Appendix sets out the BBQ (Bry-Boschan quarterly) algorithm used to date turning points in the classical cycle.
The results for the duration of expansions, contractions and completed business cycles (for Japan and the U.S.) in Table I.2 are close to those obtained by Artis et al. (1997) using monthly industrial production data and an adaptation of the Bry-Boschan cycle-dating algorithm.
A negative (positive) Brain-Shapiro statistic is associated with positive (negative) duration dependence (Diebold and Rudebusch, 1990).
The series xi is exactly pro-cyclical (counter-cyclical) with xj if Cij = 1 (Cij = 0). The index of concordance was introduced by Harding and Pagan (2002), and has previously been applied to analyze co-movement in industrial country business cycles by McDermott and Scott (2000).
Faced with a realized concordance index of, for example, 0.7, it is natural to assume that this is large relative to zero. However, even for two unrelated series the expected value of the concordance index may be 0.5 or higher. For example, consider the case of two fair coins being tossed. The probability that both coins are in the same phase—that is, both heads or both tails—is 0.5.
Concordance is also a useful concept of co-movement because it represents a way to summarize information on the clustering of turning points—that is, whether expansions (contractions) in different series turn into contractions (expansions) at the same time.
To illustrate, McDermott and Scott (2000) consider an example with two independent random walks of 100 observations each, with variances chosen so as to generate series that look like “typical” economic time series. A jump point is added halfway through both series. As expected, the concordance statistic measures 0.5. However, the correlation of the first-differenced series is large and significant, even though the two series are otherwise random. This result reflects the fact that correlation, as scaled covariance, mixes the concepts of duration and amplitude into one measure. The correlation statistic is therefore not easily interpreted—a high number may be the result of significant co-movement through time, or, as here, the result of a single large event that is common to the two series.