Republic of Korea: Selected Issues

This Selected Issues paper focuses on some of the key stylized facts of Korean business and export cycles over 1960–2001, and calculates a chronology for the classical cycle in these series by applying a variant of the Bry and Boschan (1971) cycle-doling algorithm. It highlights that the Korean classical business cycle and exports cycles are extremely asymmetric, as they exhibit long-lived expansions and much shorter-lived contractions. The results also indicate that the probability of ending a contraction or expansion phase in Korean industrial production and Korean real exports is independent of their duration.

Abstract

This Selected Issues paper focuses on some of the key stylized facts of Korean business and export cycles over 1960–2001, and calculates a chronology for the classical cycle in these series by applying a variant of the Bry and Boschan (1971) cycle-doling algorithm. It highlights that the Korean classical business cycle and exports cycles are extremely asymmetric, as they exhibit long-lived expansions and much shorter-lived contractions. The results also indicate that the probability of ending a contraction or expansion phase in Korean industrial production and Korean real exports is independent of their duration.

I. Features of Korean Business and Export Cycles1

In this study we identify and describe some of the key stylized facts of Korean business and export cycles over the period 1960–2001, and calculate a chronology for the classical cycle in these series by applying a variant of the Bry and Boschan (1971) cycle-dating algorithm. We find that (1) the Korean classical business cycle and exports cycles are extremely asymmetric, as they exhibit long-lived expansions and much shorter-lived contractions; (2) the probability of ending a contraction or expansion phase in Korean industrial production and Korean real exports is independent of their duration; (3) there is some support for the view that Korean business cycles are synchronized with U.S. and Japanese business cycles (particularly in the 1990s), but much stronger evidence that Korean exports co-move with fluctuations in economic activity in the U.S. and Japan.

A. Introduction

1. This paper attempts to identify and describe key features of Korean business and export cycles during the period 1960–2001. It will focus on the following questions: What are the key stylized facts of Korean economic cycles? Do expansions and contractions in the level of Korean economic activity have similar features? In particular, are there asymmetries in the duration and amplitude of expansions and contractions? Is there any support for the notion that expansions and contractions in Korean economic activity have a fixed duration? Since previous studies on Korean business cycles emphasize on the role of external demand, the paper will also examine the relationship between Korean business cycles and its exports cycles. In particular, is the Korean business cycle synchronized with fluctuations in the business cycles of its major trading partners, and is the Korean business cycle synchronized with cycles in its real exports?

2. The study of business cycles has a long history in economics. Since the seminal work of Burns and Mitchell (1946) and their colleagues at the National Bureau of Economic Research (NBER), work on cyclical instability has traditionally been concerned with analyzing the attributes of expansions and contractions in the level of economic activity or output (the classical cycle). In examining classical business cycles, contractions (expansions) are described as periods of absolute decline (increase) in a series. An alternative concept to the NBER definition of business cycle fluctuations, spurred by the contribution of Lucas (1977), is that of the growth cycles—fluctuations of economic activity around a long-run trend. As such, growth cycle peaks and troughs are determined on the basis of detrended series.

3. Existing studies of Korean business cycles focus on growth cycle analyses, using different methods of detrending. Kim and Choi (1997) identify three business cycles in the period 1970–91, using data detrended by the HP filter. They find that external factors, such as the U.S. output and oil prices, play a significant role in shaping business cycles in Korea. Using a structural VAR approach, Hoffmaister and Roidos (2001), however, find that external shocks explain only a small fraction of the variance of output in Korea. This paper, by contrast, focuses on the concept of level contractions to analyze Korean business cycles for two reasons. First, classical cycles in the level of economic activity often occur at the same time as key macroeconomic shocks (such as asset price collapses and commodity price spikes), and movements in the absolute level of economic activity are typically of greater interest to policymakers than fluctuations in activity relative to its trend. Second, the dating of turning points in classical cycles avoids the need to implement a detrending method (as is required in deriving growth cycles), which are known to often yield distorted estimates of the growth cycle (Canova 1998).

4. The paper is organized as follows. Section B describes the data set. In Section C, using a variant of the Bry and Boschan (1971) cycle-dating algorithm, we provide a chronology for classical cycles in industrial production and real exports in Korea.2 We then compare and contrast key features of the resultant phases of these cycles. This section also contains a nonparametric analysis of the presence of synchronization between cycles in Korean real exports and Korean industrial production. Section D concludes.

B. Data

5. The quarterly data, for the period 1960:4 to 2001:2, are taken from International Monetary Fund’s International Financial Statistics (IFS) and Direction of Trade Statistics (DTS). All data are in logarithmic form.3

C. Dating Business Cycles Using Bry-Boschan Methods

6. The duration of phases of business cycles can be determined with the assistance of the Bry-Boschan (1971) algorithm, traditionally used to date turning points in classical cycles. The rules embodied in the Bry-Boschan algorithm have evolved from the NBER’s dating of cycles in U.S. economic activity. It attempts to filter out false turning points from noisy data, and as the algorithm is basically a pattern-recognition procedure, the philosophy underlying it is relevant to any time series.4 This approach does not rule out sequences of activity declines during an expansion, or activity rises during a contraction, but there are constraints on the extent to which these sequences of activity reversals can occur and yet be considered part of any given expansion or contraction.

7. The first step in the algorithm determines the location of potential peaks and troughs. This is done by the application of a turning point rule, which finds points that are higher or lower than an arbitrary window of surrounding points. The rule defines a local peak in series yr as occurring at time t whenever {yr > yr±k}, k = 1,…, K, while a local trough occurs at time t whenever {yr, >yr±k}, k = 1…, k. The second step enforces the condition that peaks and troughs must alternate. The third step measures the duration between these points, and a set of censoring rules is then adopted which restrict the minimum length of any phase as well as those of complete cycles. There are further rules designed to avoid spurious cycle dating at the ends of series. When the peaks and troughs in each of the time series have been dated, key features of these cycles can be measured.

Chronology of Business Cycles and Korean Export Cycles

8. The NBER rules for data at monthly frequency generally set K=5, with complete cycles at least 15 months long and all phases at least six months long. In applying these rules to the logarithm of Korean quarterly industrial production data, we follow Harding and Pagan (2002) and set K=2. This ensures that yt is a local maximum relative to the two quarters on either side of yt. In determining the minimum time the Korean industrial production series can spend in any phase or cycle, we follow the rule used by Bums and Mitchell (1946) and Harding and Pagan (2002), which requires cycles to be at least five quarters in duration, and phases (industrial production expansions and contractions) must last at least two quarters.5 Contractions are then described as periods of absolute decline in the Korean industrial production series, not as a period of below-trend growth in the series (see Watson (1994)).

Classical cycle peaks (troughs) are points when Korean industrial production moves from a positive rate of growth to a negative rate of growth (negative rate of growth to a positive rate of growth).

9. The BBQ algorithm is also used to derive peaks and troughs in U.S. and Japanese industrial production, and in Korean exports to the world, Europe, the U.S. and Japan. The results of the application of the BBQ algorithm can be seen for these series in Figures I.1 to I.7. Clearly, not all the movements in the respective series are identified as peaks and troughs. The cycles are demarcated by peaks and troughs, with periods from peaks to troughs being contractions (shaded areas), and periods from troughs to peaks being expansions (unshaded areas). For example, Figure I.1 and Table I.1 present the BBQ-algorithm peak and trough dates for Korean industrial production. Briefly, the results indicate that:

Table I.1.

Business Cycle Dates and Durations of Booms and Slumps in Korean Industrial Production and Real World Exports, 1960:4–2001:2

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Notes: For each of two phases (expansion and contraction), three sets of results are presented. These are: the turning points of each phase; the average duration (in quarters) of each phase; and the average duration of each cycle (trough-to-trough or peak-to-peak movement).
Figure I.1.
Figure I.1.

Industrial Production, Korea

Log scale

Citation: IMF Staff Country Reports 2002, 020; 10.5089/9781451822069.002.A001

Figure I.2.
Figure I.2.

Industrial Production, Japan

Log scale

Citation: IMF Staff Country Reports 2002, 020; 10.5089/9781451822069.002.A001

Figure I.3.
Figure I.3.

Industrial Production, the United States

Log scale

Citation: IMF Staff Country Reports 2002, 020; 10.5089/9781451822069.002.A001

Figure I.4.
Figure I.4.

Real Korean Exports to the World

(1995 USS in million, log scale)

Citation: IMF Staff Country Reports 2002, 020; 10.5089/9781451822069.002.A001

Figure I.5.
Figure I.5.

Real Korean Exports to Europe

(1995 USS in million, log scale)

Citation: IMF Staff Country Reports 2002, 020; 10.5089/9781451822069.002.A001

Figure I.6.
Figure I.6.

Real Korean Exports to the United States

(1995 USS in million, log scale)

Citation: IMF Staff Country Reports 2002, 020; 10.5089/9781451822069.002.A001

Figure I.7.
Figure I.7.

Real Korean Exports to Japan

(1995 USS in million, log scale)

Citation: IMF Staff Country Reports 2002, 020; 10.5089/9781451822069.002.A001

  • The first trough in Korean industrial production is dated as 1961:3, the second trough is dated as 1980:2, while the first peak is dated as 1979:1—this makes the period 1961:3 to 1979:1 the first expansion phase for Korean industrial production, and the period 1979:1 to 1980:2 the first contraction phase for Korean industrial production.

  • Compared with expansions, it is clear that contractions (absolute declines) in Korean industrial production are relatively rare, and short-lived, events.

  • In addition, the duration of expansions and contractions in Korean industrial production appears to shorten in the 1990s, following the long-lived expansion of the 1960s and 1970s.

10. Having determined the turning points in the cycles in each series using the BBQ algorithm, several descriptive statistics are presented, summarizing important features of the cyclical properties of each series (Table I.2). The statistics are: the number of completed cycles (dated as the maximum of the number of completed peak-to-peak or trough-to-trough cycles, column 1); the percentage of the sample period during which the series is in a contraction phase (which indicates whether rises and falls are symmetric in duration, column 2); the maximum amplitude (percent change) of contractions in each series, and the dates during which this contraction occurred (which indicates the severity of contractions, columns 3–5); and the maximum amplitude (percent change) of expansions in each series, and the dates during which this expansion occurred (which indicates the severity of expansions, columns 6–8).

Table I.2.

Descriptive Statistics of Business Cycle and Export Cycles, 1960:4–2001:2

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Source: Authors’ calculations.Notes: The series analyzed are: Japanese industrial production (JAPIP); Korean industrial production (KORIP); United States industrial production (USAIP); Korean real exports to Europe (KEURX); Korean real exports to the world (KWORX); Korean real exports to United States (KUSAX); and Korean real exports to Japan (KJAPX). Cycles denotes the number of completed cycles (the maximum of the number of peak-to-peak or trough-to-trough cycles completed). Time denotes the percentage of total time spent in a slump (contraction) phase of the cycle. Max PT is the maximum amplitude of all contractions (peak-to-trough (PT) movements), and the dates of this maximum. Max TP is the maximum amplitude of all expansions (trough-to-peak (TP) movements), and the dates of this maximum. BS (PT) and BS (TP) denote the value of the Brain-Shapiro (1983) statistic for duration dependence in contractions and expansions, respectively. The null hypothesis of the Brain-Shapiro statistic is that the probability of terminating a phase (expansion or contraction) is independent of the length of time a series has been in that phase. An asterisk denotes that the null hypothesis is rejected (using a 5 (10) percent critical value for a two-tailed test)—any result greater than the (absolute) critical value of 1.96 (1.65) indicates duration dependence in the series

11. For Korean industrial production, there were only three completed cycles over the sample period, in contrast with seven completed cycles for Japanese industrial production. For Korean industrial production, only about 10 percent of the sample is spent in a contractionary phase, compared with Korean exports to Japan, which spent over 30 percent of the sample in a contractionary phase. As might be expected, the period during which the greatest contraction in Japanese and U.S. industrial production occurred was at the time of the first oil shock (between 1974:1 and 1975:3), while for Korean industrial production the greatest contraction (a fall of 13 percent) occurred at the time of the Asian economic crisis (between 1997:4 and 1998:2).

12. In addition to information on the attributes of the cycles, the salient features of movements in each series between these turning points are also reported (Table I.3). For each of the series, the table splits the data into two phases—contractions and expansions. For each phase, results are presented for: the average duration (in quarters) of the phase; the average amplitude of the aggregate phase movement (in percent change); and the average quarterly amplitude (amplitude divided by the duration).

Table I.3.

Descriptive Statistics of Contractions and Expansions in Korean, Japanese and United States Industrial Production and Korean Real Exports, 1960:4–2001:2

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Notes: For each of two phases (expansions and contractions), and for each of exports and industrial production (IP) series, three results are presented. First, the average duration (in quarters) of each phase. Second, the average amplitude of the aggregate phase movement in each of the series (in percent change). Third, the average amplitude per quarter (amplitude divided by the duration).

13. The results reveal an interesting stylized fact of classical business and export cycles: they are asymmetric, with contractions being much shorter in duration than expansions.

  • This duration asymmetry is most stark in the case of Korean industrial production, where average expansions last about 12 times as long as average contractions. Korea stands out as having extremely long expansions and rather short contractions, with the average business cycle in Korea lasting about 40 quarters, which is about twice as long as business cycles in Japan and the United States.

  • For all series, there is also an asymmetry in the relative amplitude of expansions and contractions—the average rise in the series during expansions is much greater than the average fall in the series during contractions. Contractions typically reduce Korean industrial production by about 8 percent, while expansions typically increase industrial production by about 62 percent. In addition, Korean exports to the United States rise on average by about three times the magnitude that they decline during contractions (about 36 percent versus 12 percent).

  • Strikingly, in spite of the strong asymmetry present in phase durations and amplitudes, the speed (per quarter amplitude) of rises in each series during expansions and the speed of falls in each series during contractions is much more symmetric. For example, real Korean world exports typically decline (rise) in a contraction (an expansion) by about 1.9 percent (2.5 percent) per quarter.6

Do Business Cycles and Korean Export Cycles Have a Fixed Duration?

14. Using more formal nonparametric tests, the nature of the expansionary and contractionary phases in Korean real exports and industrial production are examined. Specifically, the Brain-Shapiro (1983) test of duration dependence is used to investigate whether there is any tendency for expansions and contractions in these economic series to maintain a fixed duration. If true, this would imply duration dependence—the longer any expansion or contraction continues, the more likely it is to switch to the other phase.

15. Accordingly, following Diebold and Rudebusch (1990), the Brain-Shapiro statistic for duration dependence is calculated to test whether the probability of ending an expansion or contraction is dependent on how long the series has been in that expansion or contraction. The null hypothesis of the Brain-Shapiro statistic is that the probability of exiting a phase is independent of the length of time a series has been in that phase. The two possible alternatives are that either: (i) the longer an expansion or contraction persists, the greater the likelihood that the expansion or contraction will terminate (positive duration dependence); or (ii) the longer an expansion or contraction persists, the greater the likelihood that the expansion or contraction will be self-perpetuating, and hence the lower the likelihood that the expansion or contraction will terminate (negative duration dependence). The distribution of the Brain-Shapiro statistic is asymptotically N (0,1), which it quickly approaches normal even in small samples.7 The results of the Brain-Shapiro test, reported in Table I.1, indicate that:

  • For all three countries, the probability of an expansion or contraction in industrial production ending was found to be independent of its duration. Similarly, the termination probability of a contraction (expansion) in Korean real exports did not change the longer the contraction (expansion) lasted.

  • While not statistically significant, the negative duration dependence in contraction phases of Korean exports to the United States (given the positive Brain-Shapiro statistic) provides some weak evidence that the longer such export contractions continued, the lower was the probability of switching to an expansionary phase. Similarly, the negative duration dependence in expansion phases of Korean exports to Japan (given the positive Brain-Shapiro statistic) provides some weak evidence that the longer such export expansions continued, the lower was the probability of switching to a contractionary phase.

Is There Synchronization Between Business Cycles and Korean Export Cycles?

16. The previous sub-section examined the salient features of the cyclical behavior of Korean real exports and Korean, Japanese and U.S. industrial production. This subsection complements this by analyzing other changes in the strength of the link between these series. In particular, the presence or absence of synchronization between cycles in two series is investigated. In doing so, the Burns and Mitchell (1946) approach is followed in describing synchronized cycles as those where there is a clustering of turning points in the two series. For example, two cycles would be described as perfectly synchronized if their peaks and troughs occur at the same points in time. To further examine the synchronous nature of the relationship between the series, two measures of comovement are used: the correlation between industrial production and Korean real exports, and a measure of the concordance between industrial production and Korean real exports.

Concepts of Synchronization: Correlation and Concordance

17. Concordance is measured by a non-parametric statistic that describes the proportion of time two series (xi and xj) are in the same phase, awarding one when both series are expanding or contracting together, and awarding a zero otherwise. Following Harding and Pagan (2002), let Sj, i, be a binary random variable taking the value unity when a series xi (say, industrial production) is in an expansion state, and zero when it is in a contraction state; and let Sj, i be a binary random variable taking the value unity when a series xj (say, real exports) is in an expansion state, and zero when it is in a contraction state. The index of concordance is then

Cij=T1{t=1T(St,iSj,l)+t=1T(1Sl,t)(1Sj,t)},(I.1)

where: Sj, i and Sj, i are as defined above, and T is the sample size. To interpret Cij, a value of 0.66 for the statistic indicates that 66 percent of the time, xj and xj are in the same phase (that is, both expanding or contracting together). As it is a proportion, the values of Cij are clearly bounded between zero and one.8,9

18. A disadvantage of Cij is that it does not provide a means of determining if the extent of co-movement (or synchronization) between cycles in the two series is statistically significant. To do so, a concordance test statistic is needed. If the expected value of Cij is evaluated under the assumption of mean independence, then, following Harding and Pagan (2002), the t-statistics examining the null hypothesis of no concordance between the two series can be computed from the regression coefficient estimate attached to Si, t in the regression of Sj, t against a constant term and Si, t. In addition, given that the errors from such a regression are unlikely to be i. i.d., due to the strong likelihood of serial correlation or heteroscedasticity in Si, t, the t-ratio for the regression coefficient will need to be made robust to higher-order serial correlation and heteroscedasticity.

19. In measuring concordance, the focus is on whether two series move together in any given period. That is, the interest is in periodicity—the proportion of time two series spend together in expansions or contractions—and not in the amplitude of movements in a given phase (expansion or contraction).10 Correlation, on the other hand, is based on covariance, which picks up amplitude (shifts in the level of series) as well as periodicity. It is possible for a large, one-time shift in the level of two series (for example, those induced by the oil shock of 1974) to induce significant correlation in otherwise unrelated series. In contrast, such a shock will only be important under the concordance test to the extent that the co-movement lasts for a lengthy period of time.11

Synchronization Results

20. Table I.4 presents the correlation statistics for the first differences of the industrial production and Korean real exports series. For the full sample period, significant correlations (at the 5 percent level) are found for all but three of the 21 combinations. In particular, there is a strong positive association between all four destinations for Korean exports and Korean industrial production (Table I.4). For the decade of the 1990s, there is much weaker evidence of pairwise association, with only nine of the 21 combinations being statistically significant at the 5 percent level. While Korean exports remain positively correlated with Japanese industrial production in the 1990s, there is weak evidence of an association of Korean exports to Japan with Korean industrial production (Table I.5).

Table I.4.

Correlation Statistics, First Differences, 1961:1–2001:2

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Table I.5.

Correlation Statistics, First Differences, 1990:1–2001:2

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Source: Authors’ calculations.Notes: The series analyzed are: Japanese industrial production (JAPIP); Korean industrial production (KORIP); United States industrial production (USAIP); Korean real exports to Europe (KEURX); Korean real exports to the world (KWORX); Korean real exports to United States (KUSAX); and Korean real exports to Japan (KJAPX). All series are in first differences. The critical values for significant correlations are calculated as 1.96/7½ (for 5 percent) and 1.65/7½ (for 10 percent), where T is the number of observations. Accordingly, for Table I.4 with 7=162, individual cross-correlations exceeding 0.154 (0.130) will be significant at the 5 (10) percent level. For Table I.5 with T=46, individual cross-correlations exceeding 0.289 (0.243) will be significant at the 5 (10) percent level. The bolded (italicized) cell indicates significance at the 5 (10) percent level

21. We contrast the correlation findings with our analysis of pairwise synchronization using the concordance statistic, for the full sample period (1960:4 to 2001:2). The index of concordance reveals that:

  • While industrial production in the United States and Japan moved in the same direction almost 80 percent of the time, the null hypothesis of no concordance between these two series could not be rejected (Table I.6).

  • Japanese industrial production and Korean exports to Japan were strongly synchronized, as were U.S. industrial production and Korean exports to the United States, with both pairs of series moving in the same direction about 74 percent of the time.

  • In addition, the null hypothesis of no concordance between Korean world exports and U.S. industrial production is rejected, as is the null of no concordance between Korean world exports and Japanese industrial production.

  • Finally, as with the correlation analysis, cycles in the various destinations for Korean exports were highly synchronized with one another.

Table I.6.

Concordance Statistics, 1960:4–2001:2

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22. A similar pattern emerges when examining the concordance results for the decade of the 1990s (Table I.7):

Table I.7.

Concordance Statistics, 1990:1–2001:2

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Source: Authors’ calculations.Notes: The series analyzed are: Japanese industrial production (JAPIP); Korean industrial production (KORIP); United States industrial production (USAIP); Korean real exports to Europe (KEURX); Korean real exports to the world (KWORX); Korean real exports to United States (KUSAX); and Korean real exports to Japan (KJAPX). Concordance measures the extent to which the cycles in two series are synchronized, and is the proportion of time that the two series are concurrently in the same phase (that is, concurrently in a boom (expansion) period or concurrently in a slump (contraction) period). The i, jth cell represents concordance between the ith and jth series; the numbers along the diagonal are therefore unity. Following Harding and Pagan (2001), the t-statistics (in square brackets) were computed from the regression of Sj, t = a + bSi, t + ut, where: a is a constant term, ut is the error term, Si, t is a series taking the value unity when the tth series is in an expansionary phase and zero when the tth series is in a contractionary phase, and Sj, t is a series similarly defined for the jth series. The t-statistic tests the null hypothesis of no synchronization (that is, H0: b=0 in the above regression) between series Si, t and series Sj, t, and the t-statistics were computed using the Newey-West heteroskedastic autocorrelated consistent standard errors. The bolded (italicized) cell indicates significance at the 5 (10) percent level.
  • While Korean exports to the United States and Korean industrial production became mildly countercyclical (moving together only 41 percent of the time), cycles in Korean and Japanese industrial production and in U.S. and Korean industrial production became synchronized. In particular, during the 1990s Korean and U.S. industrial production, and Korean and Japanese industrial production, moved together 89 percent and 61 percent of the time, respectively. Such an association is indicative of greater linkages between Korean economic activity and the world economy.

  • However, there continued to be little evidence of synchronization between cycles in Japanese and U.S. industrial production, with the two series moving in the same direction only 50 percent of the time (about the same proportion as a toss of two fair coins landing on the same side).

  • Finally, there continued to be strong evidence of synchronization between cycles in Japanese industrial production and Korean exports to Japan, with both series moving in the same direction about 74 percent of the time.

D. Conclusion

23. In this study we have examined some of the key stylized facts of Korean business and export cycles over the period 1960–2001, and calculated a chronology for the classical business cycle. We have several notable findings. First, the Korean classical business cycle and export cycles are very asymmetric, as they exhibit long-lived expansions and much shorter-lived contractions, with much greater amplitude of movement in expansions than contractions. Second, the probability of ending a contraction or expansion in Korean industrial production is independent of its duration; similarly, there was little evidence that the phases of the Korean real export cycle maintained a fixed duration. Third, while there is only weak support for the view that Korean business cycles are synchronized with U.S. and Japanese business cycles (especially prior to the 1990s), our results indicate that Korean exports are synchronized with fluctuations in economic activity in the U.S. and Japan.

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.

Step 1: Make First Pass at Dating Peaks and Troughs

The algorithm picks an initial selection of peaks and troughs, where a peak is located at the highest point in the series using a window two quarters either side of that point, and vice versa for troughs.

Step 2: Enforce Alternation of Peaks and Troughs

The algorithm checks that none of the peak dates and trough dates are shared.

Step 3: Censor Dates

  • (i) The algorithm enforces the restriction that cycles (peak-to-peak and trough-to-trough) are at least five quarters long.

  • (ii) The algorithm censors the dates at the end of the series by eliminating turns within two quarters of both ends of the series, and by eliminating peaks (troughs) at both ends which are lower (higher) than values closer to the end.

  • (iii) The algorithm again checks the restriction that cycles (peak-to-peak and trough-to-trough) are at least five quarters long.

  • (iv) The algorithm eliminates phases whose duration is less than two quarters long.

Step 4: Statement of Final Turning Points

The algorithm selects the final peak and trough dates.

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1

This paper was prepared by Paul Cashin (RES) and Hong Liang (APD).

2

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)).

3

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.

4

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.

5

The Appendix sets out the BBQ (Bry-Boschan quarterly) algorithm used to date turning points in the classical cycle.

6

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.

7

A negative (positive) Brain-Shapiro statistic is associated with positive (negative) duration dependence (Diebold and Rudebusch, 1990).

8

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).

9

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.

10

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.

11

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.

Republic of Korea: Selected Issues
Author: International Monetary Fund