does domestic cooperation lead to business-cycle convergence and financial linkages?

The Quarterly Review of Economics and Finance46 (2006) 369–396

Does domestic cooperation lead to business-cycleconvergence and financial linkages?

Viviana Fernandez ∗Center for Applied Economics (CEA), Department of Industrial Engineering at the University of Chile,

Avenida Republica 701, Santiago, Chile

Received 6 February 2006; received in revised form 6 February 2006; accepted 6 February 2006Available online 5 May 2006

Abstract

We test for convergence – a la Massmann and Mitchell [Massmann, M., & Mitchell, J. (2004). Recon-sidering the evidence: Are Euro area business cycles converging? Journal of Business Cycle Measurementand Analysis, 1(3), 275–307] – among the industrial sectors of some APEC members—Japan, South Korea,Malaysia, Mexico, the U.S. and Canada for January 1971–March 2004; and, Australia, Japan and SouthKorea for 1957:01–2003:04. We conclude that business-cycle convergence is far from complete. We alsoreject convergence in the stock and exchange rate markets. A less stringent definition of co-movement, dueto Vahid and Engle [Vahid, F., & Engle, R. (1993). Common trends and common cycles. Journal of AppliedEconometrics, 8(4), 341–360], provides evidence of common cycles in the industrial sectors of Australia,Japan and South Korea, and in the stock and exchange rate markets of developed and growth-competitiveeconomies belonging to APEC.© 2006 Board of Trustees of the University of Illinois. All rights reserved.

JEL classification: B41; E32

Keywords: Business-cycles convergence; Wavelets; Common features

1. Introduction

Business-cycles convergence has received considerable attention in recent years, particularlydue to economic and monetary union in Europe (EMU). According to Mundell (1961)’s optimalcurrency area (OCA) theory, two countries or regions will benefit from monetary union if theyshare similar business cycles, trade intensively and rely on efficient adjustment mechanisms

∗ Tel.: +56 2 978 4047; fax: +56 2 689 7895.E-mail address: [email protected].

1062-9769/$ – see front matter © 2006 Board of Trustees of the University of Illinois. All rights reserved.doi:10.1016/j.qref.2006.02.003

mailto:[email protected]

dx.doi.org/10.1016/j.qref.2006.02.003

370 V. Fernandez / The Quarterly Review of Economics and Finance 46 (2006) 369–396

(e.g., labor mobility, price flexibility of production factors, government transfers) to smoothasymmetric shocks. Consequently, considerable effort has been made to quantify the synchronicityof business cycles among current members of the EMU, and future members of the EuropeanUnion (EU).

Some recent studies in business-cycles convergence dealing with the EU and other regions areArtis and Zang (1997, 1999), Selover (1999), Torres and Vela (2003), Fidrmuc and Korhonen(2004), Lim and McAleer (2004), Massmann and Mitchell (2004), Babetskii (2005) and Bezmenand Selover (2005).

Artis and Zang (1997) analyze the relationship between the Exchange Rate Mechanism (ERM)of the European Monetary System (EMS) and international business cycles.1 Using U.S. andGerman cycles as benchmarks, they conclude that business cycles of ERM countries becamemore synchronized with the German cycle, and less synchronized with the U.S. cycle in the ERMperiod (starting 1979:04). Artis and Zang (1999) extend their previous study to consider a largernumber of countries and a longer time-period. They conclude that a high degree of business-cyclessynchronization is associated with low volatility in exchange rates.2

More recent studies find mixed evidence about business-cycles convergence of Euro-zonecountries. In particular, Massmann and Mitchell (2004) confirm Canova (1998)’s finding thatthe properties of business cycles depend on how they are gauged. However, they conclude thatinference about convergence is to a great extent independent of business-cycles quantification.They use seven different trend-cycle decomposition methods and Harding and Pagan (2001)’sturning-point rule to show that over 1960–2001 the Euro zone has alternated many times betweenperiods of convergence and divergence.

Other studies have focused on business-cycle correlation of the Euro zone and Central andEastern European countries (CEECs). Fidrmuc and Korhonen (2004) survey about 30 publicationswith nearly 350 point estimates of business-cycle correlation between the CEECs and the Eurozone. They conclude that several CEECs (e.g., Hungary, Poland and Slovenia) already exhibithigh correlation with the Euro-zone business cycles, and that correlation coefficients are quitesensitive to estimation methodologies.

More recently, Babetskii (2005) analyzes trade intensity and synchronization of shocks between10 CEEC countries (Cyprus, the Czech Republic, Hungary, Poland, among others) and theEuropean Union, and these 10 countries and Germany. Based on Blanchard and Quah (1989)’sbi-variate structural VAR methodology, he concludes that trade integration leads to higher sym-metry of demand shocks, but that the effect on supply shocks is ambiguous. Furthermore, he findsthat a decrease in exchange rate volatility has a positive effect on demand shocks convergence butno significant impact on supply shocks.

Selover (1999) investigates the international transmission of business cycles among the Asso-ciation of Southeast Asian Nations (ASEAN) five-countries (Indonesia, Malaysia, the Philippines,Singapore and Thailand), and between the five-ASEAN nations and their major trading partners,the United States, Australia, Japan and the European Union. Based on vector autoregression anal-ysis, he finds weak evidence of transmission of business cycles among the ASEAN economies,and between the ASEAN economies and their major trading partners. Selover argues that theexplanation for such weak evidence can be found in commodity price fluctuations, wars andmajor political disturbances, which have interfered with the natural course of business cycles.

1 The European Monetary System was organized in 1979 to stabilize foreign exchange and inflation rates among membereconomies. At the beginning of 1999, the same European Union members adopted the Euro as a single currency.

2 The degree of synchronicity is measured as the cross-correlation of business cycles at displacement zero.

V. Fernandez / The Quarterly Review of Economics and Finance 46 (2006) 369–396 371

In a more recent study, Lim and McAleer (2004) apply different tests of convergence to deter-mine if there is a convergence club for ASEAN-5, as well as ASEAN-5 and the United States. Theyconclude that unit root and cointegration techniques do not support income convergence betweenpairs of ASEAN-5 countries. Moreover, Lim and McAleer find no evidence of technologicalcatching up by ASEAN-5 to the United States, apart from Singapore.

Torres and Vela (2003) in turn study the consequences of regional economic integration betweenMexico and the United States over the 10 years following the enactment of the North AmericanFree Trade Agreement (NAFTA). They conclude that, as the manufacturing sectors of the twonations have become more integrated, their business cycles have become more synchronized.And, as a result, the volatility of the Mexican trade balance has declined.

A comprehensive study on business-cycle synchronization and transmission patterns can befound in Bezmen and Selover (2005), who focus on the major Latin American countries and theirlinkages with the United States and Europe. Their findings show that there is moderate evidenceof a unique Latin American business cycle and of business cycle transmission among the LatinAmerican economies. Indeed, most transmission linkages come from outside Latin America. TheEuropean business cycle has a slightly stronger influence upon most Latin American economiesthan the influence of the U.S. business cycle. Moreover, the most influential Latin Americaneconomy in terms of business-cycle transmission is Brazil.

Recent studies that deal with Asia-Pacific Economic Cooperation (APEC) member economies,which are the focus of our article, are Tang (2003), Michelis and Neaime (2004) and Worthingtonand Higgs (2004). Tang (2003) examines whether the APEC integration promoted economicgrowth among the member countries during 1989–2000, and he analyzes whether the developedand developing member countries would derive different growth-enhancing effect from the inte-gration. He concludes that the developed countries with better infrastructures would derive highergrowth effect from the integration than the developing countries. In addition, Tang finds that theopen trade facilitated by the APEC integration has contributed to higher growth in the developedrather than developing countries.

Michelis and Neaime (2004) analyze income convergence in the Asia-Pacific region and itssubsets of East Asia and ASEAN over 1960–1999. For the period 1960–1989, they find evidenceof conditional beta-convergence3 in a group of 17 APEC countries and in 10 East-Asia countries.No evidence of income convergence is found for the ASEAN group of countries. For the period1990–1999, Michelis and Neaime find weak evidence of conditional beta convergence in a groupof 16 APEC countries, and much weaker evidence of income convergence in East Asia. Theyattribute this finding to the damaging effects of the financial crisis in the second half of the 1990s.In addition, their empirical evidence shows that openness to international trade is statistically themost important variable for sustaining economic growth in the Asia-Pacific region.

Worthington and Higgs (2004) examine the short- and long-run price linkages among the APECequity markets over 1995–2000. Their results indicate that there is a stationary long-run relation-ship and significant short-run causal linkages among the APEC equity markets. Australasian,Northern Asian and South American markets are relatively more influenced by domestic marketconditions; North American markets relatively more by regional factors; and Southern Asianmarkets more strongly influenced by markets outside either their own or geographically closedomestic markets.

3 There exists conditional beta convergence when the partial correlation between the growth in income over time andits initial level is negative.


Our study focuses on business-cycle convergence and financial markets co-movement amongAPEC countries. Our methodology is based on Massmann and Mitchell (2004)’s, but with a twist.Specifically, we present a new trend-cycle decomposition method based on wavelet analysis.Wavelets have increasingly gained popularity in recent years in the fields of economics andfinance, where they have been applied to various subjects, ranging from the permanent incomehypothesis to portfolio theory. The advantage of wavelets over other statistical methods is thatthey allow for decomposing a time series into orthogonal smooth and detailed components, whereeach component is localized in time. In the context of business-cycle decomposition, waveletsrepresent a non-parametric procedure to clearly distinguish between trend and cycle, by giving toeach one a different time dimension. In particular, the trend of a time series will be associated withits long-term behavior (i.e., smooth or low frequency parts), whereas its cycle will be associatedwith its medium-term behavior (i.e., detailed or high frequency parts).

Overall, our estimation results show that convergence has not yet been reached. Indeed, we findsome degree of asynchronicity among the business cycles of the different economies analyzed. Inaddition, we investigate whether economic cooperation has led to a higher degree of co-movementof stock and exchange rate markets cycles. We find more synchronization among the former thanthe latter. In other words, economic cooperation does not guarantee that domestic currencies willbe more aligned against the U.S. dollar.

In order to complement our analysis, we resort to Vahid and Engle (1993)’s methodology totest for the presence of serial correlation common features (i.e., cycles) in the data series (A recentapplication of this technique can be found in Harvey & Mills, 2005.). We find some evidence ofcommon cycles in industrial production of Australia, Japan and South Korea, and in the stockindices and exchange rates of developed and growth-competitive economies. In other words,even though our findings do not support the notion of convergence, we find evidence in favorof common features in some particular data sets. Overall, our conclusions seem to go more inline with Tang (2003)’s than with Michelis and Neaime (2004)’s and Worthington and Higgs(2004)’s.

This article is organized as follows. Section 2 gives a brief background on wavelet analysis,and discusses three approaches to decompose a time series into its trend and cycle components.The concept of convergence, a la Massmann and Mitchell, and Vahid and Engle’s methodologyto test for common cycles are also presented. Section 3 describes the data used in the empiricalsections. Section 4 presents and discusses our estimation results on business-cycles convergencefor our sampled APEC countries. Section 5 focuses on the effect of economic cooperation onstock and exchange rate markets linkages. Section 6 presents our empirical findings of commoncycles in the data sets under analysis. Finally, Section 7 concludes.

2. Statistical tools

2.1. A brief description of wavelets

Wavelets, a refinement of Fourier analysis, which dates back to the late 1980’s, offer a pow-erful methodology for processing signals, images and other types of data. Recent applicationsof wavelet methods in economics and finance have dealt with the permanent income hypothesis,the estimation of systematic risk of an asset (beta), and the interaction between emerging anddeveloped stock markets, among other themes (e.g., Connor & Rossiter, 2005; Fernandez, 2005;Gencay, Whitcher, & Selcuk, 2001, 2002, 2003, 2005; Hong & Kao, 2004; Lin & Stevenson,2001; Ramsey, 1999, 2002; Ramsey & Lampart, 1998; Whitcher, 2004).


In particular, a wavelet allows for decomposing a signal into fine and coarse resolution compo-nents (see, for instance, Bruce & Gao, 1996; Percival & Walden, 2000). Wavelets can be classifiedinto father and mother wavelets. Father wavelets (φ) represent the smooth and low-frequency partsof a signal, whereas mother wavelets (ψ) characterize its detailed and high-frequency parts. Themost widely used wavelets are the orthogonal ones (i.e., haar, daublets, symmelets and coiflets).In particular, the orthogonal wavelet series approximation to a continuous signal f(t) is given by

f (t) ≈∑k

sJ,kφJ,k(t) +∑k

dJ,kψJ,k(t) +∑k

dJ−1,kψJ−1,k(t) + · · · +∑k

d1,kψ1,k(t) (1)

where J is the number of multi-resolution components or scales and k ranges from 1 to the numberof coefficients in the corresponding component. The coefficients sJ,k, dJ,k, . . ., d1,k are the wavelettransform coefficients, whereas the functions φj,k(t) and ψj,k(t) are the approximating waveletfunctions.

Applications of wavelet analysis usually utilize a discrete wavelet transform (DWT). The DWTcalculates the coefficients of the approximation in (1) for a discrete signal of final extent, f1, f2,. . ., fn. That is, it maps the vector f = (f1, f2, . . ., fn)′ to a vector � of n wavelet coefficients thatcontains sJ,k and dj,k, j = 1, 2, . . ., J. The sJ,k’s are called the smooth coefficients and the dj,k’s arecalled the detail coefficients. Intuitively, the smooth coefficients represent the underlying smoothbehavior of the data at the coarse scale 2J, whereas the detail coefficients provide the coarse scaledeviations from it.

When the length of the data n is divisible by 2J, there are n/2 coefficients d1,k at the finest scale21 = 2. At the next finest scale, there are n/22 coefficients d2,k. Similarly, at the coarsest scale, there

are n/2J coefficients each for dJ,k and sJ,k. Altogether, there are n(∑J

i=1(1/2i) + (1/2J ))

= n

coefficients. The number of coefficients at a given scale is related to the width of the waveletfunction. For instance, at the finest scale, it takes n/2 terms for the functions ψ1,k(t) to cover theinterval 1 ≤ t ≤ n.

Expression (1) can be rewritten as

f (t) ≈ SJ (t) +DJ (t) +DJ−1(t) + · · · +D1(t), (2)

where SJ (t) =∑ksJ,kφJ,k(t) and DJ (t) =∑kdj,kψJ,k(t) are denominated the smooth and detailsignals, respectively.

The terms in expression (2) represent a multi-resolution decomposition (MRD) of the signalinto the orthogonal signal components SJ(t), DJ(t), DJ−1(t), . . ., D1(t) at different scales. Forinstance, when analyzing monthly data, wavelet scales are such that scale 1 is associated with 2–4month dynamics, scale 2 with 4–8 month dynamics, scale 3 with 8–16 month dynamics, scale 4with 16–32 month dynamics and so on.

In order to illustrate these ideas, Fig. 1(a) depicts a MRD decomposition of the Japaneseproduction index for six decomposition levels. The time series labeled as “sum” represents theraw production index, whereas D1 through S6 are the orthogonal components into which the rawdata is decomposed. For instance, the D1 crystal captures high-frequency or noisy components ofthe series associated with short-term dynamics. As the scale J increases, we are able to capturethe lower-frequency parts of the series. In particular, the trend component is mostly captured bythe S6 crystal. Therefore, in order to construct an estimate of the business-cycle, we discard thelow scale (high frequency) noise contained in D1 and D2 and exclude the low frequency base-linedrift captured by S6.


Fig. 1. Japanese industrial production index. (a) Multi-resolution decomposition. (b) Trend and business-cycle decom-position.


Although it is outside the scope of this study to analyze the superiority of wavelets to otheravailable trend-cycle decomposition methods, we believe wavelets represent a promising approachbecause they do not impose any parameterization on the trend and cyclical components of thedata.

2.2. Trend-cycle decomposition methods

We utilize three trend-cycle decomposition methods: linear de-trending, a univariateunobserved-component structural model and wavelet analysis. As mentioned earlier, the latterrepresents a new methodology for obtaining the business cycle of a time series, which has notbeen previously utilized in the literature.

Linear de-trending is the easiest method to implement. This consists of running a linear regres-sion of a time series (yt), such as a production index, against a constant term and a deterministictime trend (t). The estimated cyclical component is given by yt − βt, where β is the coefficienton t. This method has been a standard tool for separating trends from cycles in the past. However,many macroeconomic series contain unit roots, which are not removed by this method (see, forinstance, Baxter & King’s, 1999, discussion). Therefore, linear de-trending will not be a suit-able tool for trend-cycle decomposition in many cases, and therefore its output should be takencautiously.

Unlike the linear de-trending method, the basic univariate unobserved-component structuralmodel, which is estimated by the Kalman filter approach, allows for the presence of a stochastictrend in the data:

yt = µt + κt + ξt (3)

where µt is the unobserved trend component, κt the unobserved cyclical component and ξt is theunobserved irregular component. The non-stationary trend componentµt takes the form of a locallinear trend:

µt+1 = µt + βt + ηt

βt+1 = βt + εt(4)

where ηt ∼ N (0, σ2η) and εt ∼ N (0, σ2

ε ) are both white-noise processes, µ1 ∼ N (0, ω) and β1 ∼ N(0, ω), with ω large.

The stochastic cycle component, which is given by yt −µt = κt + ξt, can be expressed in terms ofsine and cosine functions (see Zivot & Wang, 2003, chapter 14, for details). If σ2

ε = 0, µt followsa random-walk process with drift β1 (This is the assumption we make in our computations.).When σ2

η = σ2ε = 0, µt follows a deterministic trend, and both the unobserved-component and

de-trending methods yield the same trend-cycle decomposition.In the case of the wavelet filter, when using monthly data the business cycle is reconstructed

from the crystals at scales 3–6 (i.e., 8–128 month dynamics). For quarterly data, we define thecycle as the time series reconstructed from scales 2 to 4 (i.e., 4–32 quarters dynamics). Sucha choice was made in order to remove the noise associated with the short-term dynamics fromthe data, and to exclude the long-term trend associated with the highest scale. Eliminating theslow-moving components of the series ensures to get rid of the presence of a unit root.4

4 For the series we deal with in Sections 4 and 5, we checked that we had successfully removed the unit roots from thecyclical component by using the wavelet filter.


On the other hand, given that the orthogonal wavelet decomposition tends to do poorly at thefirst and last data points, we select a relatively small number of scales. Indeed, as J increases, thenumber of coefficients at the upper scales (equal to n/2J) gets smaller due to a fixed number ofobservations. And, therefore, the quality (i.e., degree of detail) of the reconstructed series declines.

Fig. 1(b) illustrates the use of the three decomposition methods for the Japanese industrialproduction index. The left-hand side panel depicts the trend component whereas the right-handside panel depicts the cyclical component of the index, according to each of the three business-cycle filters. First of all, according to the Kalman and wavelet filters, we see that the trend of thedata is not exactly linear. Second, there is a close correspondence between these two filters—exceptfor the first and last data points, where the wavelet reconstruction of the trend is poorer.

When it comes to the cyclical component, the linear de-trending method yields a very jaggedestimate as it puts a heavier weight on the high-frequency components of the data. By contrast, thewavelet filter yields the smoothest cycle estimate as it removes more of the noise associated withshort-term dynamics. Again, for intermediate data points over the sample period, the Kalman andwavelet filters resemble one another to a great extent.

It is worth noticing that the estimate of the cyclical component of a time series is not invariantto the choice of the wavelet filter. For instance, among the daublet functions, the haar yields avery jagged estimate, which resembles that of the linear de-trending method. Therefore, we optfor an orthogonal wavelet function (daublet-8) that removes most of the irregular components,but which does not yield an excessively smooth cyclical component.5

In addition to the above three trend-cycle decomposition methods, and following Massmannand Mitchell (2004), we apply Harding and Pagan (2001)’s methodology to identify businesscycles in terms of turning points in the data. This can be used as a benchmark for evaluating theability of the different de-trending methods to match the turning points.

Harding and Pagan’s procedure stipulates that phases last at least two quarters, and completecycles last at least five quarters. In other words, for monthly data, a peak in the growth rate willbe observed at time t* if

ixt∗ > 0

ixt∗+i < 0

}i = 1, . . . , 6 (5)

where xt is the growth rate of the {xt} process (e.g., industrial production index) and ixt∗ =xt∗ − xt∗−i, ixt∗+i = xt∗+i − xt∗ , i = 1, . . ., 6.

2.3. Business-cycle convergence

In order to test for the presence of business-cycle convergence, we resort to the methodologydeveloped by Massmann and Mitchell, op. cit., which consists of the following steps. For a sampleof n countries and the corresponding growth rates in their cyclical components, there are n(n − 1)/2pair-wise correlation coefficients of such cyclical components. For each time t, the j-th correlationcoefficient (ρjt) is estimated by using an h-month window, j = 1, . . ., n(n – 1)/2. Next, for each t, the

5 As discussed by Percival and Walden (2000), Section 4.11, the filter width is a key element to take into consideration. Inparticular, wavelet filters of the very shortest widths (i.e., daublet 4, haar) can introduce artifacts into the resulting analysis,such as unrealistic blocks and sharks’ fins. By contrast, wavelet filters with a large width can provide a more accuratecharacterization of a time series. However, their use may be subject to the following problems: (i) more coefficients areinfluenced by boundary conditions, (ii) phase shifts in the DWT coefficients and (iii) an increase in computational load.


sample mean of the n(n – 1)/2 estimated correlation coefficients (mt), its corresponding varianceand the variance of the estimated correlation coefficients (v2

t ) are computed:

mt = 1

N

N∑j=1

ρjt var(mt) = 1

N2

N∑j=1

var(ρjt) + 2N−1∑i=1

N∑j=i+1

cov(ρit , ρjt) (6)

v2t = 1

N − 1

N∑j=1

(ρjt −mt)2 (7)

where N ≡ n(n – 1)/2.Two necessary conditions are required for convergence (Massmann and Mitchell, page 287): mt

and v2t should tend to one and zero, respectively, along the sample period. The second condition is

imposed in order to ensure that the probability distribution function of the correlation coefficientsdoes not spread out.

In addition to convergence, we focus on co-movement and asynchronicity in business cycles.Co-movement is tested as follows: under the null hypothesis of absence of co-movement ρ =1N

∑Nj=1ρj = 0, whereas under the alternative hypothesis, ρ > 0. In order to implement this test,

we construct a t-statistic for mt as mt/var(mt)1/2, where mt and var(mt) are given by expression(6). Under the null hypothesis, this t-statistic is asymptotically distributed as N(0,1).

Asynchronicity in turn is measured by means of the Spearmanıs rank correlation between con-temporaneous and lagged values of the growth rate of the cyclical components of the n countries.Specifically, the Spearman’s rank correlation is a non-parametric method to measure correlationbetween two random variables X and Y, and which is defined as

ρs = 1 − 6

( ∑d2i

M(M2 − 1)

)(8)

where di is the difference in the ranks assigned to the corresponding values of the two series X andY, where M is the number of (X,Y) pairs in the sample. Like the Pearson correlation coefficient,the rank correlation takes on values between −1 and 1.

Under the null hypothesis that the population rank correlation is zero and for M > 10, thesignificance of ρs can be contrasted using a t-test (see Mason, Lind, & Marchal, 1999, chapter15):

t = ρs√M − 2√

1 − ρ2s

∼ t(M − 2) (9)

2.4. Common features

In order to introduce the concept of common features utilized in Section 6, let us consider twotime series y1t and y2t generated by the following unobserved component model

y1t = λ t + ε1t

y2t = t + ε2t

where has a particular feature, while ε1t and ε2t do not. The linear combination

y1t − λy2t = ε1t − λε2t


does not have the feature, so represents a common feature. Engle and Kozicki (1993) define afeature, which is present in each of a set of time series, to be common if, and only if, there exists alinear combination of the series that does not have the feature. Examples of common features aretrends, seasonal patterns and serial correlation. Of particular interest to us is the concept of serialcorrelation common features introduced by Vahid and Engle (1993). A common serial correlationfeature among the first differences of a set of cointegrated I(1) variables implies that their cycles –the remainders after removing their common trends from their levels – are common. Specifically,if yt represents an n-vector of I(1) variables, the elements of its first difference yt have a serialcorrelation feature if there exists a linear combination of them that is not correlated with the past(i.e., that behaves like white noise).

Specifically, let us consider a pth-order VAR representation of an n-vector of time series (see,for instance, Vahid and Engle, op. cit, and Harvey & Mills, 2005):

yt = � +p∑i=1

�iyt−i + �t = � + �(L)yt−1 + �t t = 1, . . . ,T (10)

where yt = (y1t, y2t, . . ., ynt)′, � is a vector of intercepts, �i are matrices of lag coefficients and Lrepresents the lag operator. Provided that |In − �(L)L| = 0 has roots on or outside the unit circle(i.e., units roots are allowed), Eq. (10) admits the vector correction model (VECM) representation:

yt = � + �yt−1 +p−1∑i=1

�iyt−i + �t = � + �yt−1 + �(L)yt−1 + �t (11)

where

�i = −p∑

j=i+1

�j and � =p∑j=1

�j − In = �(1) − In.

If � has rank r < n, then there are r cointegrating relationships and n − r random walks. The� matrix can be written as � = ��′ where � and � are both n × r matrices of rank r, and et = �′yt

represents an r-vector of I(0) equilibrium errors. Consequently, Eq. (11) can be rewritten as

yt = � + �et−1 + �(L)yt−1 + �t (12)

Given that yt is I(0), it admits a MA(∞) representation

yt = C(L)(� + �t) = C(1)� + C(1)�t +C∗(L)�t (13)

where C(L) = (In − �(L)L)−1 = C(1) +C∗(L), = 1 − L.

From (13), we obtain that

yt = C(1)�t + C(1)t∑

j=0

�t−j + C∗(L)�t

If there are r cointegrating vectors, C(1) has rank n − r and it can written as C(1) = ��′, where� and � both n × (n − r) matrices of rank n − r. Therefore, by letting

�t = �′⎛⎝�t +

t∑j=0

�t−j

⎞⎠ = �′� + �t−1 + �′�t ct = C∗(L)�t


we obtain the common-trends representation of yt:

yt = ��t + ct�t = �t−1 + �′�t

(14)

in which yt is expressed as a linear combination of n − r random walks (i.e., the common trends�t) plus a stationary component, ct, which represent the cyclical component of yt. Common cyclesin the data will arise if C*(L) is of reduced rank. In other words, if there are linear combinationof the elements of yt that do not contain these cyclical components. Mathematically, this impliesthat there are s linearly independent vectors (i.e., cofeature vectors), contained in the n × s matrix such that ′ct = ′C∗(L)�t = 0. Under this assumption, we obtain a common trend-commoncycle representation of yt:

yt = ��t + �ct (15)

where � is a n × (n − s) of rank (n − s) so that the cycle ct is a linear combination of an (n − s)-element cycle ct . The number of cofeature vectors or common cycles, s, belonging to can be atmost n − r. When s = n − r, there is a unique trend-cycle decomposition yt = yτt + yct .

The s cofeatures vectors and the r cointegrating vectors can be incorporated into the VECMrepresentation, giving rise to the pseudo-structural model

(Is ∗′

s(n−s)0(n−s)s In−s

)yt =

(0s(n(p−1)+r)

�∗1 . . .�

∗p−1�∗

)⎛⎜⎜⎜⎜⎝yt−1

...

yt−p+1

et−1

⎞⎟⎟⎟⎟⎠+ � + �t (16)

where �∗1 contains the last n – s rows of �1, etc. Model (16) has s(n − s) parameters in the first

s equations and (n – s)(n(p − 1) + r) parameters in the remaining n – s equations. The unrestrictedVECM (12) has n(n(p − 1) + r) parameters, so that the number of constraints imposed by (16)is {n(n(p – 1) + r) – s(n – s) – (n – s)(n(p − 1) + r)}= s2 + ns(p − 1) + rs – ns (see Vahid and Engle,op cit, for further details). The validity of the constraints can be tested by a likelihood ratio test,which is asymptotically distributed as Chi-square with degrees of freedom equal to the numberof constraints, s2 + ns(p − 1) + rs − ns.

3. The data

In Section 4, we focus on business cycle convergence in a sample of Asia-Pacific EconomicCooperation (APEC) countries. APEC is a forum established in 1989 for facilitating economicgrowth, cooperation, trade and investment in the Asia-Pacific region. Unlike the World TradeOrganization, or other multi-lateral trade bodies, APEC has no treaty obligations required of itsparticipants.6 Specifically, our sample consists of six countries, for which we have complete infor-mation on industrial production for January 1971–March 2004: Japan, South Korea, Malaysia,

6 APEC has 21 members, which account for more than a third of the world’s population, approximately 60% of worldGDP, and about 47% of world trade. APEC’s member economies are Australia, Brunei Darussalam, Canada, Chile,People’s Republic of China, Hong Kong, Indonesia, Japan, Republic of Korea, Malaysia, Mexico, New Zealand, PapuaNew Guinea, Peru, The Republic of the Philippines, The Russian Federation, Singapore, Chinese Taipei, Thailand, UnitedStates of America and Vietnam (source: http://www.apec.org).

http://www.apec.org/


Mexico, the U.S. and Canada. All countries in our sample joined APEC in November 1989, exceptfor Mexico, which became a member economy in November 1993. Information on industrial pro-duction was obtained from the International Monetary Fund’s IFS data base.

In Section 5, we analyze the degree of financial markets co-movement among APEC members.In doing so, we resort to data from Morgan Stanley Capital International (MSCI), and test whethereconomic cooperation has had any impact on co-movement of exchange rates and stock marketsamong member economies. We extend the sample of Section 4 to consider the following 12 coun-tries: the U.S., Canada, Australia, Hong Kong, Singapore, Japan, New Zealand, Chile, Mexico,Taiwan, Indonesia and South Korea. All countries joined APEC in 1989, except for Taiwan andHong Kong, which became member economies in 1991, and Mexico and Chile, which joinedAPEC in 1993 and 1994, respectively.

Monthly data for stock indices, in local currency and U.S. dollars, for the U.S., Canada,Australia, Hong Kong, Singapore and Japan are available from January 1970 onwards; for NewZealand, from January 1982 onwards, and for Chile, Mexico, Taiwan, Indonesia and South Korea,from January 1988 onwards. The monthly percent variation of each exchange rate is constructedas the difference between the monthly percent changes of the corresponding country stock indexin local currency and U.S. dollars.

The analysis on common features of Section 6 is carried out with the same data sets abovedescribed.

4. Testing for business-cycle convergence

4.1. Core sampled APEC countries

We first test for the existence of unit-roots in the industrial production indices of the sampledcountries: Japan, South Korea, Malaysia, Mexico, the U.S. and Canada. Our computations showthat levels are characterized by a stochastic trend, whereas first differences are integrated of order0. The log transformation modifies the magnitude of the augmented Dickey-Fuller (ADF) testnoticeably in some cases, but the conclusions with respect to the existence of unit roots are overallunchanged. The exception is Malaysia, for which we would reject the existence of a unit root atthe 5% level when considering the natural logarithm of the industrial production index. Whenlooking at the first differences and their logs, the magnitudes of the ADF are fairly similar, andwe strongly reject the existence of unit roots. This implies that growth rates – our focus of interest– are integrated of order 0.

Once we have identified the cyclical component of each index, we compute pair-wise cor-relation coefficients of monthly growth, using an h-period rolling window. We next utilize themethodology outlined in Section 2.3 to determine the existence of convergence. The trend-cycledecomposition methods considered are those depicted in Fig. 1: linear de-trending, wavelets andthe Kalman filter (i.e., unobserved-component model). In addition, we apply Harding and Pagan(2001)’s turning-points methodology to identify business cycles. Harding and Pagan’s rule appliedto the growth rate of an index yields a binary time series, where the value of one indicates a stateof expansion, and zero, otherwise. At the following step, we compute the mean correlation coef-ficient and its variance, according to expression (6), for the binary time series obtained for thedifferent countries.

Trend-cycle decomposition by wavelets and the Kalman filter is carried out with the S-PlusFinMetrics 1.0 and Wavelets 2.0 modules. Estimation of mt and var(mt) in turn is done with thegeneralized method of moments (GMM) routine of TSP/GiveWin 4.5. Given that we actually


Table 1Method-of-moments estimates of mt and v2

t for core APEC countries in the sample

Linear de-trending Wavelets Kalman filter Harding–Pagan

mt v2t mt v2

t mt v2t mt v2

t

Mean 0.031 0.029 0.086 0.149 0.041 0.033 0.009 0.032Q1 0.010 0.021 0.008 0.071 0.015 0.023 −0.019 0.018Q2 0.036 0.028 0.066 0.121 0.039 0.032 0.012 0.031Q3 0.057 0.034 0.146 0.182 0.066 0.041 0.055 0.044Observations 345 345 345 345 345 345 345 345

Notes: (1) The data are monthly and cover October 1975–March 2004. (2) Q1, Q2 and Q3 stand for first, second and thirdquartile, respectively. (3) Core APEC countries in the sample are Japan, South Korea, Malaysia, Mexico, the U.S. andCanada.

utilize a number of moment conditions equal to the number of parameters to be estimated (i.e.,pair-wise correlation coefficients), GMM boils down to the method of moments.

Table 1 gives account of our estimation results, for a 3.5-year rolling window. The meancorrelation coefficient averaged only 0.031 and 0.041 along the sample period, according to thelinear de-trending and Kalman filter methods, respectively. The wavelet method overall yields agreater estimate of mt, but also a greater variance of the correlation coefficients. This result isnot surprising given the discussion of the previous section. Indeed, given that the wavelet filterpreserves more of the low-frequency components of the series, the correlation between cyclicalcomponents and its corresponding variance will be larger as most of the power of the productionindices is located at lower frequencies.

Evidence in favor of convergence would imply the existence of an inverse relation between mt

and v2t . According to Fig. 2 such a pattern is observed only for the wavelet trend-cycle decompo-

sition and, to some degree, for the Kalman filter approach. The evolution of our four estimates ofmt, including Harding–Pagan’s, is depicted in Fig. 3. Over the Asian crisis, the mean correlationbecame smaller and even negative, according to the Harding–Pagan’s procedure. Indeed, indus-trial production in Japan, Malaysia and South Korea was more severely hurt by the economiccrisis than in Canada, Mexico and the U.S. Towards the end of 1999, the four methods yieldthat the mean correlation becomes again positive, and generally greater than for the rest of thesample period. In other words, in the past few years, industrial production growth in the AsiaPacific countries has tended to exhibit a greater degree of co-movement. It is worth noticing thatthe trend-cycle decomposition method that has the highest correlation with Harding and Pagan’sturning point analysis is the wavelet-based one (0.13), whereas the one with the lowest correlationis the linear de-trending method (0.05).

Given that we observe a tendency for greater co-movement in the most recent past, we nextinvestigate whether joining APEC has contributed to it. We repeat our estimation by splittingthe sample into two sub-periods: 1971–1989 and 1990–March 2004. Except for Mexico, whichjoined APEC in November 1993, all the other countries in our sample joined APEC in November1989. Fig. 4 depicts the t-statistic for mt, along with 90% confidence bands, for the two sub-periods. According to the linear de-trending and Kalman filter methods, we conclude that themean correlation was overall statistically insignificant from zero for 1971–1989.7 In other words,on average, there is no evidence of co-movement in the business cycles of the sampled countries.

7 The wavelet estimate is not computed due to the small number of observations in each sub-period.


Fig. 2. Relation between mt and v2t for the core sampled APEC countries. (a) Linear de-trending method. (b) Wavelet

method. (c) Kalman filter. Note: The countries considered are Japan, South Korea, Malaysia, Mexico, the U.S. and Canada.


Fig. 3. Mean estimates of the core sampled APEC countries relative to Harding–Pagan’s turning points. Note: Thecountries considered are Japan, South Korea, Malaysia, Mexico, the U.S. and Canada.

Fig. 4. t-Statistic for mt of core sampled APEC countries. (a) Prior to 1990. (b) From 1990 onwards. Notes: (1) Thehorizontal dashed lines represent 90% confidence bands. (2) The countries considered are Japan, South Korea, Malaysia,Mexico, the U.S. and Canada.


Fig. 5. t-Statistic for mt for the Australian, Japanese and South Korean industrial sectors.

By contrast, for the second sub-period, mt becomes positive and statistically significant from theend of 2000 onwards, approximately.

4.1.1. Testing for convergence among Australia, Japan and South KoreaMonthly data of Australian industrial production is not available from the IFS data base after

December 1977. Therefore, in order to study the degree of convergence between Australia andsome large Asian economies, we resorted to quarterly data, which is available for Japan and SouthKorea for 1957:3–2003:3.

Fig. 5 depicts our estimation results. In this case, the three different trend-cycle decompo-sition methods yield more homogeneous estimates, at least for some quarters over the sample.The mean correlation exhibits an erratic pattern, which is characterized for some periods of rela-tively large co-movement (late 1980’s according to the three methods; 1995–1996 and 2000–2003according to the Kalman filter method). As a result, the statistical significance of the mean cor-relation coefficient sharply fluctuates over the sample period. Indeed, the mean correlation wasstatistically insignificant between the late 1970’s and mid-1980’s. From 1989 onwards, whensignificant, the t-statistic is negative, indicating that, on average, business cycles are inverselycorrelated.

4.1.2. Asynchronicity of business cyclesWe next compute the correlation between contemporaneous and lagged growth rates in indus-

trial production of our sampled countries along the business cycle by means of the Spearman’srank correlation. In doing so, we take a rolling window of 7 years for the linear de-trending,wavelet and Kalman filter methods (e.g., M = 84 for the core sampled APEC countries), and arolling window of 14 years for the Harding–Pagan procedure. The lag between observations is 2years. As we see from Table 2, when taking observations apart in time, the probability distributionof the mean correlation coefficient yielded by the three trend-cycle decomposition methods andby Harding–Pagan procedure tends to exhibit less dispersion than when computing the mean cor-relation coefficient using contemporaneous observations (Table 1). For instance, if we calculatethe interquartile range (=Q3 − Q1) of mt in Tables 1 and 2, we observe that, except for the linearde-trending method, all the other three business-cycles identification procedures have a smaller


Table 2Descriptive statistics of Spearman’s rank correlation


(a) Core sampled APEC countriesMean 0.321 0.298 0.300 0.306Q1 0.294 0.240 0.287 0.296Q2 0.312 0.323 0.300 0.305Q3 0.344 0.346 0.311 0.316Observations 216 216 216 216

(b) Australia, Japan and South KoreaMean 0.370 0.432 0.381 0.257Q1 0.293 0.383 0.320 0.204Q2 0.370 0.429 0.380 0.255Q3 0.438 0.462 0.491 0.304Observations 124 124 124 124

Notes: (1) In Panels (a)–(c), we use a rolling window of 7 years for the linear de-trending, wavelet and Kalman filtermethods, and a rolling window of 14 years for the Harding–Pagan procedure. The lag between observations is 2 years.The effective sample periods for Panels (a) and (b) are, respectively, April 1986–March 2004 and 1973:1–2003:4. (2) Q1,Q2 and Q3 stand for first, second and third quartile, respectively.

interquartile range. In addition, the Spearman’s rank correlation coefficients are much larger,averaging around 0.3.

The t-test in (9) for the core sampled APEC countries leads us in general to reject ρs = 0 infavor of ρs > 0 during February 1978–February 2004, whereas for Australia, Japan and SouthKorea the evidence against the null hypothesis is not very strong along 1964:4–2002:2.

From the above evidence, we conclude that convergence of industrial production has not yetbeen reached among APEC countries. Instead, we find that business cycles are asynchronous.That is, either demand or supply shocks in one country transmit slowly to others.

5. Financial linkages among APEC members

5.1. Stock markets

Unit-root tests applied to the stock indices of the U.S., Canada, Australia, Hong Kong, Sin-gapore, Japan, New Zealand, Chile, Mexico, Taiwan, Indonesia and South Korea – in levels andlog-levels – lead us to conclude that we generally accept the presence of a stochastic trend ineach index (for Singapore and South Korea the evidence is not as strong), while growth rates arestationary. As in Section 4, we decompose each country stock index, expressed in local currency,into its trend and cycle by the three methods earlier discussed. We next compute all possiblecombinations of pair-wise correlation coefficients, and obtain their mean and its variance fromexpression (6), and the variance of all correlation coefficients from expression (7).

We report our results for the whole sample of countries (sample period: January1988–December 2004), and for three subgroups: developed countries (the U.S., Canada, Australia,Hong Kong, Singapore and Japan; sample period: January 1970–December 2004), emerging coun-tries (Chile, Mexico, Taiwan, Indonesia and South Korea; sample period: January 1988–December2004), and growth-competitive economies (the U.S., Taiwan, Singapore, Australia and Japan; sam-ple period: January 1988–December 2004). The latter correspond with the top-five economieslisted on the Growth Competitiveness Index (GCI) 2003, and which also belong to APEC. The


Table 3Statistics of co-movements in stock markets


mt v2t mt v2

t mt v2t mt v2

t

(a) Whole sampleMean 0.192 0.078 0.222 0.129 0.173 0.060 0.088 0.036Q1 0.159 0.068 0.198 0.110 0.078 0.055 0.077 0.032Q2 0.189 0.077 0.217 0.119 0.164 0.059 0.086 0.036Q3 0.204 0.084 0.253 0.152 0.290 0.065 0.095 0.040Observations 132 132 132 132 132 132 110 110

(b) Developed countriesMean 0.059 0.095 0.037 0.132 0.223 0.076 0.132 0.055Q1 −0.003 0.053 −0.059 0.063 0.054 0.039 0.064 0.031Q2 0.033 0.085 0.032 0.100 0.218 0.057 0.116 0.047Q3 0.121 0.112 0.122 0.171 0.332 0.071 0.177 0.070Observations 377 377 377 377 377 377 363 363

(c) Emerging countriesMean 0.044 0.068 0.055 0.173 0.124 0.044 0.070 0.037Q1 0.023 0.041 −0.031 0.104 −0.020 0.030 0.060 0.035Q2 0.050 0.063 0.066 0.159 0.104 0.040 0.069 0.037Q3 0.069 0.089 0.119 0.243 0.164 0.050 0.080 0.038Observations 161 161 161 161 161 161 109 109

(d) Growth-competitive economiesMean 0.329 0.038 0.371 0.068 0.277 0.070 0.044 0.019Q1 0.223 0.012 0.217 0.037 0.091 0.012 0.013 0.013Q2 0.314 0.033 0.405 0.049 0.208 0.051 0.039 0.016Q3 0.442 0.056 0.494 0.096 0.474 0.121 0.074 0.028Observations 161 161 161 161 161 161 110 110

Note: mt and v2t are method-of-moments estimates. The whole sample comprises the U.S., Canada, Australia, Hong

Kong, Singapore, Japan, New Zealand, Chile, Mexico, Taiwan, Indonesia and South Korea. The sample period is January1988–December 2004. In Panel (b), developed countries are the U.S., Canada, Australia, Hong Kong, Singapore and Japan.The sample period is January 1970–December 2004. In Panel (c), emerging countries are Chile, Mexico, Taiwan, Indonesiaand South Korea. The sample period is January 1988–December 2004. In Panel (d), growth-competitive economiescorrespond with the U.S., Taiwan, Singapore, Australia and Japan. The sample period is January 1988–December 2004.For the whole sample, we use a 6-year rolling window, and for the subgroups of developed and emerging countries, a3.5-year rolling window. The data source is Morgan Stanley.

GCI is contained in the Global Competitiveness Report 2003–2004, which is elaborated by theWorld Economic Forum (http://www.weforum.org).8 For the whole sample, we use a 6-yearrolling window, given that we have to compute 55 pair-wise correlation coefficients. For the threesubgroups, we use a 3.5-year rolling window.

Statistics for mt and v2t for the whole sample and for the developed and emerging economies

groups show that there is no evidence of convergence of stock markets cycles among APECmember economies, and that co-movement of such cycles is relatively low (Table 3, Panels(a)–(c)). In addition, the mean correlations for developed and emerging countries were statistically

8 The Growth Competitiveness Index is composed of three indexes: the technology index, the public institutions indexand the macroeconomic environment index. These indexes are calculated on the basis of both hard and survey data.

http://www.weforum.org/


Fig. 6. Co-movement in stock markets. (a) Whole sample. (b) Developed countries. (c) Emerging countries. (d) Growth-competitive economies. Note: In Panel (a), the whole sample comprises the U.S., Canada, Australia, Hong Kong, Singapore,Japan, New Zealand, Chile, Mexico, Taiwan, Indonesia and South Korea. The sample period is January 1988–December2004. In Panel (b), developed countries are the U.S., Canada, Australia, Hong Kong, Singapore and Japan. The sampleperiod is January 1970–December 2004. In Panel (c), emerging countries are Chile, Mexico, Taiwan, Indonesia and SouthKorea. In Panel (d), growth-competitive economies correspond with the U.S., Taiwan, Singapore, Australia and Japan.The sample period is January 1988–December 2004. For the whole sample, we use a 6-year rolling window, and for thesubgroups of developed and emerging countries, a 3.5-year rolling window. Dashed lines represent a 90% confidenceband.

insignificant between the early and mid 1990’s (linear de-trending and Kalman filter methods),and have shown an increasing trend only since 1999, approximately (under the Kalman filter forthe developed group, and under both the Kalman filter and wavelets methods for the emerginggroup). The growth-competitive economies comparatively exhibit much more synchronization oftheir stock markets cyclical components (Panel (d) of Table 3).

When considering the whole sample, the mean correlation exhibits a greater magnitude andhigher statistical significance than when looking at either developed or emerging economies inisolation (Panels (a)–(c) of Fig. 6). Under the three trend-cycle decomposition methods, both thelevel and statistical significance of the mean correlation rose from 1999 onwards. It is possible thatsynchronicity of the stock markets of APEC members has increased since economies recoveredfrom the Asian crisis. In particular, the t-ratio of the mean correlation yielded by the linearde-trending method exhibits a noticeably decrease over 1998, which is mainly explained by anincrease in its volatility. Regarding growth-competitive economies, we observe that the mean


correlation exhibits an increasing statistical significance from 1998 onwards for the three trend-cycle decomposition methods. Such a pattern is most likely due to the characteristics of thoseeconomies rather than to their condition of APEC members.

5.2. Exchange rates

As mentioned earlier, we calculate the percent variation in exchange rates from MSCI stockindices in local currency and U.S. dollars. We next create an exchange-rate index for each country,whose first observation is set at 100. The evolution of the index is traced back from the percentvariation in the exchange rate previously obtained. For all countries, we find that growth rates areintegrated of order 0.

Table 4Statistics of co-movement in exchange rate markets


mt v2t mt v2

t mt v2t mt v2

t

(a) Whole sampleMean 0.007 0.069 0.038 0.168 0.007 0.068 0.055 0.040Q1 −0.015 0.060 −0.047 0.146 −0.016 0.059 0.048 0.038Q2 −0.005 0.073 0.033 0.165 −0.004 0.071 0.054 0.039Q3 0.038 0.077 0.059 0.193 0.038 0.075 0.061 0.042Observations 131 131 131 131 131 131 109 109

(b) Developed countriesMean 0.100 0.118 0.057 0.213 0.100 0.118 0.059 0.141Q1 0.028 0.086 0.013 0.158 0.028 0.086 0.015 0.067Q2 0.090 0.104 0.057 0.193 0.090 0.104 0.050 0.135Q3 0.152 0.131 0.112 0.236 0.155 0.131 0.104 0.214Observations 376 376 376 376 376 376 321 321

(c) Emerging countriesMean 0.054 0.043 0.047 0.280 0.025 0.056 0.051 0.024Q1 −0.011 0.033 −0.043 0.191 −0.025 0.039 0.037 0.020Q2 0.054 0.044 0.057 0.277 0.011 0.062 0.050 0.023Q3 0.139 0.052 0.090 0.336 0.062 0.067 0.071 0.029Observations 160 160 160 160 160 160 105 105

(d) Growth-competitive economiesMean 0.018 0.158 0.075 0.255 0.019 0.157 0.129 0.023Q1 −0.042 0.096 −0.098 0.097 −0.043 0.099 0.099 0.009Q2 0.001 0.162 −0.020 0.191 0.003 0.157 0.118 0.015Q3 0.071 0.206 0.221 0.456 0.072 0.205 0.185 0.033Observations 160 160 160 160 160 160 105 105

Note: mt and v2t are method-of-moments estimates. An exchange-rate index is constructed for each country from the

percent variations in local currency and U.S. dollars of its corresponding stock index (data source: Morgan Stanley).In Panel (a), the whole sample comprises Canada, Australia, Singapore, Japan, New Zealand, Chile, Mexico, Taiwan,Indonesia and South Korea. The sample period is January 1988–December 2004. In Panel (b), developed countries areCanada, Australia, Hong Kong, Singapore and Japan. The sample period is January 1970–December 2004. In Panel (c),emerging countries are Chile, Mexico, Taiwan, Indonesia and South Korea. The sample period is January 1988–December2004. In Panel (d), growth-competitive economies correspond with Taiwan, Singapore, Australia and Japan. The sampleperiod is January 1988–December 2004. For the whole sample, we use a 6-year rolling window, and for the subgroups ofdeveloped and emerging countries, a 3.5-year rolling window.


Fig. 7. Co-movement in exchange rate markets. (a) Whole sample. (b) Developed countries. (c) Emerging countries. (d)Growth-competitive economies. Note: An exchange-rate index is constructed for each country from the percent variationsin local currency and U.S. dollars of its corresponding stock index (data source: Morgan Stanley). In Panel (a), thewhole sample comprises Canada, Australia, Singapore, Japan, New Zealand, Chile, Mexico, Taiwan, Indonesia and SouthKorea. The sample period is January 1988–December 2004. In Panel (b), developed countries are Canada, Australia,Hong Kong, Singapore and Japan. The sample period is January 1970–December 2004. In Panel (c), emerging countriesare Chile, Mexico, Taiwan, Indonesia and South Korea. The sample period is January 1988–December 2004. In Panel (d),growth-competitive economies correspond with Taiwan, Singapore, Australia and Japan. The sample period is January1988–December 2004. For the whole sample, we use a 6-year rolling window, and for the subgroups of developed andemerging countries, a 3.5-year rolling window. Dashed lines represent a 90% confidence band.

Similarly to the previous section, we decompose each country index into its trend and cycle.Given that the exchange-rate indices are referred to the U.S. dollar, we exclude the United Statesfrom the sample. Table 4 and Fig. 7 present our results. In general, we find low synchronicity ofexchange rate market cycles across countries.9 As Panel (a) of Fig. 7 shows, the mean correlationfor the whole sample of countries is statistically insignificant, for both the linear de-trending andKalman filter methods, from approximately 1998 onwards. For the group of developed countries,the magnitude of the mean correlation is slightly higher than for the whole sample (Panel (b) ofTable 4), but its statistical significance is in general low (Fig. 7(b)), particularly in recent years.

Finally, the least degree of synchronicity is exhibited by the group of emerging countries.Indeed, the mean correlation is statistically insignificant almost for the whole sample, and for thethree trend-cycle decomposition methods. The exception, towards the end of the sample, is thenegative and statistically significant mean correlation identified by the linear de-trending method.

9 Hong Kong’s exchange rate against the U.S. dollar has been fixed since the mid 1980’s, approximately.


This negative correlation would imply that while some exchange rates depreciated against theU.S. dollar, others appreciated. The group of growth-competitive economies (excluding the U.S.)in turn exhibits a positive and statistical significant mean correlation from October 2002 onwards,but only under the wavelet-based trend-cycle decomposition method.

In sum, we do not find evidence that countries’ joining APEC has contributed to convergenceof their stock and exchanges rates markets cycles. Furthermore, the evidence does not supportthe existence of strong co-movement either. In particular, exchange rates appear to behave quiteindependently, particularly among emerging countries. This is not surprising because exchangerates are usually subject to Central Banks’ interventions. For instance, from August 1984 toSeptember 1999, the exchange rate policy in Chile consisted of a floating band, whose center wasa reference exchange rate. The value of the reference exchange rate was recalculated according tothe fluctuations in the parities of a currency reference basket—comprised by the U.S. dollar, theJapanese yen and the Deutsche mark. Currently, Chile has a dirty float. Other examples of countriesthat have experienced substantial intervention in their exchange rate markets are Indonesia andSingapore.

6. A further look into economic and financial linkages: common features

After having rejected the existence of convergence as defined by Massmann and Mitchell(2004), we utilize an alternative methodology to gauge the degree of co-movement of industrialproduction, stock indices and exchange rates of APEC members. Specifically, we test for thepresence of common cycles in the data series by resorting to the statistical machinery outlined inSection 2.4. All computations were carried out by using the full information maximum likelihoodinformation (FIML) procedure canned in TSP/GiveWin 4.5. Cointegration was tested using bothJohansen and Engle-Granger methodologies. The countries and sample periods are the sameconsidered earlier.

Panel (a) of Table 5 reports our results for industrial production. Our findings show evidenceof the existence of a common cycle for the core APEC countries at the 5% but not at the 10%significance level. Furthermore, a Ljung-Box applied to the residuals of the estimated equationrejects the null hypothesis of white noise, for lags 3 and 20 at the 10% significance level. Forthe Asian economies of Japan, South Korea and Malaysia, the existence of a common cycle isrejected at any significance level. By contrast, we find strong evidence of a common cycle forAustralia, Japan and South Korea. Indeed, the coefficient on Japan industrial growth productionis both positive and statistically significant: a 1% increase in Japan industrial production leadsto a 0.49% increase in Australia industrial production. By contrast, South Korea and Australiaindustrial production growth rates are inversely associated. We obtain a 1.6% growth rate perquarter for Australia industrial production over the business cycle, when both Japan and SouthKorea growth rates are zero.

Panel (b) show estimates for the stock markets of the developed, emerging and growth-competitive economies in the sample. For the developed countries, we find evidence of onecommon cycle, whose coefficients are statistically significant except for Hong Kong and the con-stant term. The estimated relationship shows that the greatest (and positive) impact on the U.S.stock market cycle comes from Canada. Indeed, an increment of 1% in the growth rate of theCanadian stock index translates into an increase of 1.2% in that of the U.S. For the emergingeconomies, we also find a common cycle. But, its statistical significance is rather weak, except forthe Chile, Mexico and South Korea. For the growth-competitive economies, we find two commoncycles.


Table 5Common cycles

(a) Industrial production

(i) Core APEC countries likelihood ratio test

Value d.f. p-Value

13.333 7 0.069

One common cycle (variables in growth rates)

Japan Constant South Korea Malaysia Mexico U.S. Canada

Coefficients 1.00 −0.013 0.878 −0.246 −0.063 −0.713 2.770t-Test in () (−4.182) (28.953) (−19.725) (−3.357) (−19.921) (50.881)

Ljung-Box test (p-value)

Lag 3 Lag 9 Lag 20

0.014 0.134 0.096

ii) Japan, South Korea, Malaysia likelihood ratio test (one common cycle)

Value d.f. p-Value

24.54 4 0.000

iii) Australia, Japan and South Korea likelihood ratio test

3.28 5 0.656


Australia Constant Japan South Korea

Coefficients 1.00 0.016 0.487 −0.490t-Test in () (6.726) (7.166) (−12.174)


Lag 3 Lag 9 Lag 20

0.418 0.263 0.401

(b) Stock markets

(i) Developed countries likelihood ratio test

Value d.f. p-Value

21.19 8 0.270


U.S. Constant Australia Japan Canada Hong Kong Singapore

Coefficients 1.00 0.31E−02 −0.157 −0.173 1.184 0.009 −0.428t-Test in () (1.102) (−5.253) (−5.916) (32.591) (0.511) (−19.155)


Table 5 (Continued )


Lag 3 Lag 9 Lag 20

0.985 0.845 0.597

(ii) Emerging countries likelihood ratio test

Value d.f. p-Value

2.91 7 0.893


Chile Constant Mexico Taiwan Indonesia South Korea

Coefficients 1.00 −0.60E−02 0.511 −0.040 0.018 −0.058t-Test in () (−1.291) (8.673) (−0.837) (0.515) (−1.954)


Lag 3 Lag 9 Lag 20

0.621 0.174 0.204

(iii) Growth-competitive countries Likelihood ratio test

Value d.f. p-Value

8.83 16 0.920

Two common cycles (variables in growth rates)

U.S. Constant Singapore Australia Japan

Coefficients 1.00 0.013 −0.239 −0.614 0.494t-Test in () (2.922) (−5.910) (−8.766) (10.944)


Lag 3 Lag 9 Lag 20

0.847 0.738 0.614

Taiwan Constant Singapore Australia Japan

Coefficients 1.00 0.58E−02 2.283 −2.538 −0.320t-Test in () (0.180) (17.901) (−11.460) (−2.246)


Lag 3 Lag 9 Lag 20

0.998 0.906 0.850

(c) Exchange rates

(i) Developed countries likelihood ratio test

Value d.f. p-Value

10.82 16 0.820


Table 5 (Continued )

Two common cycles (variables in growth rates)

Australia Constant Canada Hong Kong Singapore

Coefficients 1.00 0.41E−02 −0.228 −2.135 1.654t-Test (2.231) (−11.611) (−20.804) (20.567)


Lag 3 Lag 9 Lag 20

0.740 0.261 0.524

Japan Constant Canada Hong Kong Singapore

Coefficients 1.00 0.40E−02 −0.371 −5.370 2.848t-Test (1.102) (−15.836) (−44.383) (29.776)


Lag 3 Lag 9 Lag 20

0.925 0.067 0.093

(ii) Growth-competitive countries likelihood ratio test

Value d.f. p-Value

0.567 5 0.989


Taiwan Constant Singapore Australia Japan

Coefficients 1.00 −0.15E−02 −0.985 0.414 0.160t-Test (−1.078) (−12.701) (11.722) (4.918)


Lag 3 Lag 9 Lag 20

0.530 0.230 0.024

Notes: (1) The Ljung-Box test detects whether the error term of the common-cycle equation is white noise. (2) In Panel (a),the sample for the core APEC countries is January 1971–March 2004. For Australia, Japan and South Korea, the sampleperiod is 1957:1–2003:4. (3) In Panels (b) and (c), the sample period for the developed markets is January 1970–December2004. For emerging and growth-competitive economies, the sample period is January 1988–December 2004.

Finally, Panel (c) shows the common cycles found in the exchange rate series. Our evidencesupports the existence of a serial correlation common feature among developed and growth-competitive economies. For the former, we find statistical support for a common cycle amongthe growth rates of Australia, Canada and Singapore currencies against the U.S. dollar. Strongevidence is also found for Japan, Hong Kong and Singapore. Among growth-oriented economies,a statistical significant relationship holds for Taiwan, Singapore and Australia.

In sum, there is evidence, although not overwhelming, of the existence of common cycles inindustrial production, stock indices and exchange rates among the APEC members examined. Thestrongest relationships are found for Australia, Japan and South Korea industrial production, and


for the stock and exchange markets of developed and growth-competitive economies. The firstfinding differs from our conclusion of Section 4.1.1, where convergence among Australia, Japanand South Korea industrial production was strongly rejected. The second finding about stock andexchange markets of developed and growth-competitive economies is more in agreement withour earlier conclusions regarding the existence of some degree of co-movement in the time seriesof those countries. In other words, Massmann and Mitchell’s definition of convergence might betoo stringent to capture the existence of common features or co-movement in the data.

7. Conclusions

Our study analyzes whether convergence in the real and the financial sectors have taken placeamong different APEC member economies. Based on monthly data of the industrial sector forJanuary 1971–March 2004, we quantify the degree of business-cycle convergence among Japan,South Korea, Malaysia, Mexico, the U.S. and Canada. We also look at the case of Australia, Japanand South Korea, based on quarterly data for 1957–2003. In doing so, we utilize Massmann andMitchell (2004)’s definition of convergence and apply different techniques to identify businesscycles.

In particular, the novelty of our study is to use a wavelet-based method for such purpose.Wavelet analysis is a powerful tool for decomposing time-series data into orthogonal componentswith different frequencies. Each frequency is localized in the time domain, which makes it possibleto extract from a time-series its trend and cycle.

Our estimation results show that business-cycles convergence of Asia-Pacific countries is stillfar from complete. However, after joining APEC, the mean correlation of industrial productioncycles of member economies has tended to increase. An important factor to take into account ispersistence: the mean correlation of business cycles exhibits a smoother path when taking a widerrolling window and observations apart in time. In other words, business cycles are not necessarilysynchronized.

Based on an extended sample of countries, we do not find evidence that APEC has contributedto a higher degree of co-movement of stock and exchanges rates markets cycles of its membereconomies. In particular, exchange rates appear to behave quite independently, particularly amongemerging countries. This is not surprising because exchange rates are usually subject to CentralBanks’ interventions.

Given that convergence a la Massmann and Mitchell is always rejected for the time seriesexamined, we utilize an alternative methodology to quantify co-movement. Specifically, we resortto Vahid and Engle (1993)’s technique to test for the presence of common cycles in industrialproduction and stock and exchange rate markets. Our evidence shows that developed and growth-competitive economies are more likely to have common features. This conclusion goes in linewith the evidence found by Tang (2003) for APEC economies.

Acknowledgements

Financial support from FONDECYT Grant No. 1050486 and from an institutional grant of theHewlett Foundation to CEA is greatly acknowledged. The author would like to thank the helpfulcomments of participants at the 3rd INFINITI Conference held at Trinity College, Dublin, in June2005. Further comments and suggestions from two anonymous referees are greatly acknowledged.All remaining errors are the author’s.


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does domestic cooperation lead to business-cycle convergence and financial linkages?

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