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Decomposing exchange rate volatility around the Pacific Rim☆5
Journal of Asian Economics 10 (1999) 525–535
Decomposing exchange rate volatility around the Pacific Rim夽 M. H. Dungeya,* a
Department of Economics and Finance, La Trobe University, Bundoora, Vic. 3083, Australia
Received 1 December 1998; received in revised form 1 October 1999; accepted December 1999
Abstract Volatility in exchange rates is decomposed into components associated with domestic and international concerns for six Pacific Rim currencies. A latent factor model is used to model bilateral exchange rate changes as the weighted sum of three factors; two factors are uniquely associated with each of the currencies involved in the exchange rates and the other represents world shocks common to all exchange rates. The results show that international factors are more important in determining exchange rate volatility for the smaller nations of Australia, Singapore, and New Zealand, than for the larger nations of Japan and Canada. © 1999 Elsevier Science Inc. All rights reserved. JEL classifications:F31; G15; C33 Keywords: Exchange rates; Volatility; GMM
1. Introduction This paper decomposes bilateral exchange rate volatility for a selection of Pacific Rim currencies into components associated with domestic and international concerns. Governments and monetary authorities often express concern in the face of increases in exchange rate volatility and a desire to reduce it, using means such as foreign exchange intervention
夽This paper is a much revised version of a paper presented at the December 1998 ACAES Conference in Bangkok. The conference paper is in press (see Dungey and Martin, forthcoming). * Corresponding author. Tel.: ⫹61-3-9479-1514; fax: ⫹61-3-9479-1654. E-mail address: [email protected] (M. Dungey). 1049-0078/99/$ – see front matter © 1999 Elsevier Science Inc. All rights reserved. PII: S 1 0 4 9 - 0 0 7 8 ( 0 0 ) 0 0 0 3 0 - 0
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or Tobin taxes for example. The effective reduction of volatility relies on understanding its source; if exchange rate volatility for a particular currency is primarily sourced internationally there may be very little national authorities can do to alter the situation, while retaining a flexible exchange rate regime. However, if the volatility is primarily domestic in origin, then the particular source of the disturbances may bear closer examination. There is now a well-developed literature on exchange rate volatility, and an accepted measure of unconditional volatility as either the variance or standard deviation of movements in exchange rate changes. However, there has as yet been no consensus on the sources of exchange rate volatility, either by individual country or across panels. Volatility in bilateral exchange rates between six currencies is examined in this paper. The focus here is on the different experiences of Pacific Rim countries with flexible exchange rate regimes. The currencies examined are the U.S. dollar (USD), Canadian dollar (CAD), Japanese yen (JPY), Singaporean dollar (SGD), Australian dollar (AUD) and New Zealand dollar (NZD). A latent factor model of exchange rate movements in the tradition of Mahieu and Schotman (1994) and Diebold and Nerlove (1989) is used to decompose exchange rate volatility into three components, two due to each of the currencies involved in the exchange rate, and a common world factor which effects all exchange rates. The focus on international and domestic factors is similar to that taken by Engle, Ito, and Lin (1990). Estimation is accomplished through Generalized Method of Moments (GMM) using a panel of exchange rate data. The results demonstrate that the reason for the lack of consensus in the literature as to the causes of volatility lies with the differing responses of individual exchange rates to common and idiosyncratic information. Hence, studies concerned with explaining exchange rate movements with panels of observed information (such as Rose, 1994) are unlikely to be successful. The results derived in this paper are in accordance with Enders and Hurn (1994) who concluded that international events are highly influential in explaining exchange rate movements for smaller Pacific Rim nations. For instance, volatility in the Canadian dollar exchange rate is found to be largely due to Canadian factors, while volatility in the NZ dollar is primarily sourced from overseas. The paper proceeds as follows. Section 2 outlines the latent factor model and Section 3 presents the estimation technique. The data is outlined in Section 4 and results follow in Section 5. Section 6 concludes.
2. A factor model of exchange rate changes Consider a simple factor model of exchange rates, such as Eq. (1).
冘f b M
s io ⫽
ij ij
(1)
j⫽1
where sio is the change in the log of a bilateral spot exchange rate expressed as currency i against a numeraire currency 0, fij are the factors which influence sio, and bij is the response coefficient for the exchange rate to each factor. There are M factors involved in determining the changes in the exchange rate, each of which is assumed uncorrelated. If the factors were
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not uncorrelated then the model could be reparameterised with a new set of uncorrelated factors. Hence, the factors are defined through their lack of correlation rather than being given ‘names’. This type of model has previously been applied to exchange rate volatility using observed factors, for example Bui and Pippenger (1990). Rather than describing the exchange rate change as Eq. (1) consider a model where the individual exchange rate change can be explained by three independent latent factors. s io ⫽  i f w ⫹ ␣ i f i ⫹ ␣ 0 f 0
(2)
In Eq. (2) the factors are: fw the world factor; fi a factor uniquely associated with currency i, and f0 a factor uniquely associated with currency 0. The world factor, fw affects all bilateral exchange rate changes, but the response to that factor, i, differs between exchange rates (for example, an oil price shock will affect yen denominated exchange rates quite differently to British pound denominated exchange rates). The ‘domestic’ factor, f0, has the same impact (␣0) upon all exchange rate changes denominated in the ‘0’ currency due to arbitrage. To see this consider a system of three spot exchange rates SUSA (USD/AUD)1, SJA (JPY/AUD) and SUSJ (USD/JPY). As before sio, designates the change in the log of the spot exchange rate Sio. Suppose that the coefficient on f0 in Eq. (2) (fA in the example) is not the same for all exchange rates. s USA ⫽  1 f w ⫹ ␣ 1 f US ⫹ ␣ 0 f A
(3)
s JA ⫽  2 f w ⫹ ␣ 2 f J ⫹ ␣ 3 f A
(4)
s USJ ⫽  3 f w ⫹ ␣ 4 f US ⫹ ␣ 5 f J
(5)
Arbitrage in foreign exchange markets implies Sij ⫽ Sik/Sjk.. There is a potential error here due to Jensen’s inequality, however it is unlikely to be a significant problem in high frequency data. Hence s USJ ⫽ s USA ⫺ s JA
(6)
 3 f w ⫹ ␣ 4 f US ⫹ ␣ 5 f J ⫽  1 f w ⫹ ␣ 1 f US ⫹ ␣ 0 f A ⫺  2 f w ⫺ ␣ 2 f J ⫺ ␣ 3 f A
(7)
and
For this equation to hold for arbitrary factor values, the coefficients on each of the individual factors on both sides of Eq. (7) must be equal. Hence, the following conditions must hold.
3 ⫺ 1 ⫹ 2 ⫽ 0
(8)
␣4 ⫺ ␣1 ⫽ 0
(9)
␣5 ⫹ ␣2 ⫽ 0
(10)
␣0 ⫺ ␣3 ⫽ 0
(11)
Hence, from Eq. (11), the coefficient ␣3 in Eq. (4) can be replaced by ␣0. Thus a common factor, with the same coefficient, is introduced into exchange rates against a common
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numeraire, here Eq. (3) and Eq. (4). Using just those two equations the coefficients for the cross-rate, Eq. (5) can be recovered using Eq. (8) to Eq. (10) with no restrictions on 1, 2, ␣1, ␣2 or ␣0. This manner of reducing the number of parameters to be estimated relieves the covariance restrictions imposed in Mahieu and Schotman (1994) when estimating a similar model. Identification of the system Eq. (3) and Eq. (4) requires 1⫽2; that is the response coefficient to world shocks cannot be the same for these two exchange rates. In practice 1 needs to be well distanced from 2 otherwise the system will be nearly unidentified. Arbitrage therefore justifies a specification like Eq. (2). It is possible to separate the domestic from foreign shocks because of the structure of Eq. (3) and Eq. (4). Only a domestic shock (f0) causes both Eq. (3) and Eq. (4) to change by the same amount. The other country factor (fi, i ⫽ 0) captures movements unique to the individual exchange rate. The world shock will capture common factor movements, but with differing response coefficients. A simple model of exchange rate changes such as Eq. (2) can then be used to decompose exchange rate volatility. The unconditional variance of Eq. (2) gives an expression for exchange rate volatility in terms of the weighted variances in each of the component unobserved factors. Consider a system of n bilateral exchange rates expressed against a common numeraire currency. There are n ⫹ 1 currencies involved in the exchange rate system. For ease of exposition each currency is uniquely associated with one issuing country—so there are also n⫹1 countries involved in the system. A system of equations of the form of (2) can be written as:
冤 冥冤 s 10
s 20 ..
s n0
⫽
1 ␣0 ␣1
0
..
0
2 ␣0
0
␣2 . .
0
..
..
..
..
..
..
n ␣0
0
0
..
␣n
冥冤
fw f0 f1 f2 .. fn
冥
or s ⫽ Bf,
(12)
where s is an n ⫻ 1 vector of stacked exchange rates, f is an (n ⫹ 2) ⫻1 vector of latent factors and B is an n ⫻ M matrix of coefficients attached to the factors. Then, var共s兲 ⫽ Bvar共 f 兲 B⬘
(13)
The variance-covariance matrix var(s) will have n(n ⫹ 1)/2 unique elements; hence using these moment conditions we can identify at most n(n ⫹ 1)/2 parameters from this system of equations. There are n parameters relating to the world factor (the i, which must be sufficiently different for the system to be identified), and n ⫹ 1 relating to idiosyncratic factors (the ␣i). Using the moment conditions produced by applying Eq. (13), and letting var(f) ⫽ In⫹2, produces the necessary identification condition that nⱖ 4; at least four bilateral exchange rates are necessary to estimate this system. Var(f)⫽In⫹2 is assumed as var(f) is unobserved. To the extent that this assumption is violated the parameter estimates will absorb the true variance of the unobserved factors. That
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is, an estimate of ␣i will in fact be an estimate of ␣i公var(fi). In this case comparing the absolute values of the coefficients is not very informative. However, the decomposition of the unconditional variance of Eq. (2) is unaffected by this assumption as follows:
␣ 02 ⫽ contribution of the numeraire currency to volatility in the exchange rate var s i0 ␣ 2i ⫽ contribution of currency i factor to volatility in the exchange rate var s i0  2i ⫽ contribution of the world factor to volatility in the exchange rate var s i0 The true value of var(fi) does not impinge on these results. Using this model, factor contributions to exchange rate volatility will be estimated for a panel of Pacific Rim exchange rates in Section 5.
3. Estimation method The problem to hand is well suited to estimation by Generalized Method of Moments (GMM) techniques. The unobserved nature of the factors means there is insufficient information to identify parameters in a simple regression analysis. However, the parameters can be estimated using the variance-covariance matrix of the data. A consistent estimate of the
冘 T
model parameters, ˆ , is obtained by satisfying t⫽1 mt 共ˆ 兲 ⫽ 0, where mt() represents the moment conditions at time t. However, there are generally more moments in mt() than elements in , that is the moment conditions will generally consist of p equations in k ( )⬘m ( ), unknowns. When p ⫽ k an estimator of is that value of which minimizes m where m ( ) is defined as a vector containing sample estimates of the moment conditions. When p ⬎ k there is an excess of moment conditions available to determine the parameter values. One solution would be to discard p-k of the moment conditions and estimate from the remainder. This solution would remain consistent, but would not be efficient because it ignores information (the discarded moment conditions). A preferred way of proceeding is to choose the ˆ which most closely satisfies all moment conditions. Hansen (1982) suggests the use of k linear combinations of the moment conditions, using m t ( ) ⫽ ant() where the t() are the original p ⬎ k moment conditions, and an forms linear combinations of these conditions. Now the optimal parameter estimator ˆ is obtained ()⬘a⬘nan (), or more generally ()⬘W (), where () is defined as the by minimizing vector of sample moment conditions. Hansen shows that the optimal structure for the ⫽ 冋 var冉 冘 共 兲冊册
⫺1
T
weighting matrix W is a⬘n an
t⫽1
t
. To take into account the effect of the
linear combination an when p ⬎ k, ˆ is the solution to the first order condition for the objective function:
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冉 冊
⭸ 共 ˆ 兲 ⬘ 共 ˆ 兲 ⫽ 0 a⬘na n ⭸
(14)
and substituting the optimal value for an⬘an
冉 冊 冋 冉 冘 冊册 ⭸ 共 ˆ 兲 ⬘ var ⭸
T
⫺1
t共 兲
共 ˆ 兲 ⫽ 0
(15)
t⫽1
The variance of ˆ is obtained as:
冋冉 冊冋 冉 冘 冊册 冉 冊册
1 var共 ˆ 兲 ⫽ 2 T
共 ˆ 兲 ⬘ ⭸ var ⭸
T
t⫽1
⫺1
t共 ˆ 兲
共 ˆ 兲 ⭸ ⭸
⫺1
(16)
So the most efficient estimates of ˆ are found using the prescribed W; this weights the more variable moments more heavily in the estimation process. In practice, we do not have the true variance matrix, and instead rely on a consistent estimate. The initial consistent estimate of var(兺t ()) can be obtained with W ⫽ I. In order to account for possible autocorrelation in t the Newey and West (1987) estimator is used. In the application of this paper the efficient estimates showed some instability in recursive estimation, perhaps due to the non-existence of higher order moments. In this situation the consistent estimates obtained by using W ⫽ I are preferred to the efficient estimates.
4. The data This study uses weekly movements in the log of the bilateral exchange rates constructed from a panel of six currencies: the U.S. dollar (USD), the Canadian dollar (CAD), the Japanese yen (JPY), the Singaporean dollar (SGD), the Australian dollar (AUD) and the New Zealand dollar (NZD) over the period 1990 –1998.2 The changes have been centered so that the mean of each series is zero. The weekly interlude has been chosen because it captures the short-term fluctuations that are of interest, but is not subject to day of the week effects which are found in daily data (Taylor, 1986). The choice of currencies was determined by the availability of floating exchange rate regimes in the region. All currencies except the Singaporean dollar have been floating since at least the mid-1980s (New Zealand floated in March 1985). The Singaporean dollar has been classified as a managed float since 1990 (IMF, Exchange Rate Arrangements, various issues). However, it was felt that the assumption of arbitrage could be reasonably assumed given the relatively well-developed Singaporean foreign exchange market3 (BIS, 1999).
5. Results The factor model of Eq. (12) was applied to the panel of Pacific Rim currencies using each currency as the numeraire currency in turn. The volatility decompositions are presented in
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Table 1. Variance contributions with different numeraire currencies curency fw 1. USD as numeraire JPY 16.7 CAD 0.0 AUD 47.3 NZD 31.5 SGD 17.7 2. JPY as numeraire USD 16.7 CAD 3.6 AUD 45.9 NZD 34.9 SGD 6.5 3. CAD as numeraire USD 0.0 JPY 3.6 AUD 7.3 NZD 2.4 SGD 0.7
contribution of factors (%) f0 fi 5.0 1.4 8.2 18.6 32.9
78.3 98.6 44.4 49.9 49.5
78.2 17.6 40.3 55.6 85.2
5.1 78.8 13.8 9.6 8.2
98.6 78.8 86.1 93.9 97.2
1.4 17.6 6.6 6.3 2.1
currency fw
contribution of factors (%) f0 fi
4. AUD as numeraire USD 47.3 JPY 45.9 CAD 7.3 NZD 12.8 SGD 58.7 5. NZD as numeraire USD 31.5 JPY 34.9 CAD 2.4 AUD 12.8 SGD 49.7 6. SGD as numeraire USD 17.7 JPY 6.5 CAD 0.7 AUD 58.7 NZD 49.7
44.4 13.8 6.6 58.1 32.2
8.3 40.3 86.1 29.2 9.1
49.9 9.6 3.6 29.2 32.2
18.6 55.6 93.9 58.1 18.1
49.5 8.2 2.1 9.1 18.1
32.8 85.2 97.3 32.2 32.2
Table 1. The information is also shown in Figs. 1 to 6. As shown in Section 2, arbitrage implies that the decomposition be identical for any pair of currencies regardless of which currency is used as the numeraire, and this is clearly evident from the results.4 The volatility decompositions are informative about the different nature of the currencies under consideration. When considering exchange rates against the U.S. dollar, the world’s most traded currency (BIS, 1999), the currencies examined seem to fall into two distinct groups. The larger economies, by GDP, of Canada and Japan display a substantial component of exchange rate volatility sourced from factors associated uniquely with their own currencies; the impact of world and U.S. factors is relatively small. However, for the three smaller countries (as measured by GDP), Australia, New Zealand and Singapore, the impact of total international factors accounts for more than 50 percent of the decomposition of volatility in each case. Considering each of these smaller countries in turn, in the Australian case, despite the fact
Fig. 1. Cumulative contributions of factors—USD numeraire
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Fig. 2. Cumulative contributions of factors—AUD numeraire
that the contribution of international factors to AUD/USD volatility is greater than 50 percent, the Australian factor makes a sizeable impact on total volatility at around 44 percent. The Australian factor also makes a substantial contribution to explaining volatility in exchange rates against the smaller countries of New Zealand and Singapore (of 58 percent and 32 percent respectively) but is relatively unimportant against the yen and the Canadian dollar. Similarly, the New Zealand dollar factor makes a sizeable contribution to New Zealand dollar exchange rate volatility against the U.S. dollar, Australian dollar and Singaporean dollar (49, 29 and 32 percent respectively) but is unimportant for the yen and Canadian dollar exchange rates. The Singaporean factor makes relatively little contribution to the decomposition of exchange rate volatility including the Singaporean dollar for all currencies with the exception of the U.S. dollar as noted above. In the opposite vein, the Canadian dollar exchange rate volatilities are without exception explained predominantly by the Canadian factor. The largest contribution by overseas factors comes in the yen-Canadian dollar exchange rate, where 20 percent of total volatility is accounted for by the Japanese and world factors. The decomposition of the yen exchange rates indicates that the yen factor has a dominating role to play in determining exchange rate volatility for the yen exchange rate against the U.S. dollar, and the Singaporean dollar (78 and 85 percent respectively) and an important role for the rates against the Australian dollar and New Zealand dollar (40 and 56 percent respectively). Only the Canadian dollar-yen exchange rates has no substantial influence from the yen factor. The world factor seems to be important as an explanator of yen exchange rate volatility only for the Australian and New Zealand dollar rates. These results lead to the conclusion that the larger Pacific Rim countries of the U.S., Japan and Canada have different experiences to the smaller countries of New Zealand, Australia
Fig. 3. Cumulative contributions of factors—JPY numeraire
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Fig. 4. Cumulative contributions of factors—NZD numeraire
and Singapore when it comes to explaining the sources of exchange rate volatility. This conclusion is consistent with the evidence of Enders and Hurn (1994) who examined the behavior of real exchange rate changes for Pacific Rim and industrialized countries, and concluded that the movements of the smaller Pacific Rim countries were influenced by those of a panel of nations including Japan and the U.S. Further, they found evidence for relationships between the smaller Pacific Rim countries, but little in support of similar relationships between the larger nations examined. The results in this paper show that for U.S.-based exchange rates the partner currency factor has a substantial role to play in explaining volatility. For the Japanese based rates the Japanese and world factors comprise the majority of the sources of volatility, with the exception of Canada. Canadian exchange rate volatility seems to be almost totally reliant on Canadian factors. In the case of each of the smaller Pacific Rim nations the contributions of the combined world and other currency factors dominate the decomposition of exchange rate volatility when the partner currency is a major currency. Between Pacific Rim countries the decomposition is less clear-cut— each currency has a role to play in explaining exchange rate volatility.
6. Conclusions A latent factor model was used to model bilateral exchange rate changes as the weighted sum of three factors, where two of the factors are uniquely associated with each of the currencies involved in the exchange rates and the other represents world shocks common to all exchange rates. A decomposition of the unconditional variance of this model gives the
Fig. 5. Cumulative contributions of factors—CAD numeraire
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Fig. 6. Cumulative contributions of factors—SGD numeraire
contribution of each of the domestic and international factors to total exchange rate volatility in that exchange rate. This method was applied to a panel of Pacific Rim currencies, comprising the U.S., Canadian, Singaporean, Australian and New Zealand dollars and the Japanese yen using weekly exchange rate data from 1990 to 1998. The results show substantial differences between the exchange rate volatility decompositions for the larger Pacific Rim countries of the U.S., Japan and Canada, from the smaller countries of Australia, Singapore and New Zealand. For the smaller countries the combined overseas factors dominate exchange rate volatility assessed against the larger countries. Volatility decompositions for exchange rates between the smaller countries show a more diverse pattern. Canadian dollar denominated exchange rate volatility is dominated by the Canadian factor, as is yen denominated volatility dominated by the yen factor in general. For the U.S. dollar denominated exchange rates, which make up the majority of world foreign exchange turnover (BIS, 1999), the combination of world and U.S. factors dominate the volatility decomposition against the smaller Pacific Rim nations, but the smaller country factors are nevertheless a substantial influence in each case. These results indicate the difficulties that arise in attempting to apply panel data techniques to identify common macroeconomic fundamentals in a diverse set of exchange rates. The extent to which individual exchange rates respond to domestic and international factors varies widely in any given group of exchange rates. Individual country differences are demonstrably important in understanding bilateral exchange rate volatility. The result that different countries’ exchange rate volatilities are differently influenced by international and domestic factors implies that there is no clear blueprint for understanding or reducing exchange rate volatility across the board. Large countries such as Japan and Canada may be able to use appropriately aimed domestic policies to reduce volatility given the substantial domestic factor contributions to volatility for those countries. However, for some countries the source of exchange rate volatility is primarily international and hence largely outside their policy control. This is the experience of Australia, Singapore and New Zealand in the 1990s.
Notes 1. I have cited exchange rates according to quotation convention. USD/AUD should be read as the number of Australian dollars per U.S. dollar and not vice versa.
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2. The data were sourced from the Reserve Bank of Australia and are 4:00pm Wednesday observations. In the case where Wednesday was not a trading day, Thursday observations were taken, and in the case of no Thursday trading, Tuesday observations were used. 3. BIS (1999) reported that total turnover in the world foreign exchange markets involved 87 percent U.S. dollars, 21 percent Japanese yen, 4 percent Canadian dollars, 3 percent Australian dollars and insignificant amounts of New Zealand and Singaporean dollars: this is of a total of 200 percent as both sides of a transaction are included. Turnover in specific locations however, differed slightly from this. In 1998, 18 percent of transactions occurred in the U.S. market, 8 percent in the Japanese market, 7 percent in Singapore, 2 percent in each of Canada and Australia and an insignificant amount in the New Zealand market. 4. This result is sensitive to the number of overidentifying conditions in the system. For example, in a seven or more currency system the variance decompositions vary slightly—see Dungey (1997). In this five variable system the differences are very slight, in the order of 10⫺2.
References BIS. (1999). Central Bank Survey of Foreign Exchange and Derivatives Market Activity, 1998. Basle. Bui, N., & Pippenger, J. (1990). Commodity prices, exchange rates and their relative volatility. Journal of International Money and Finance 9, 3–20. Diebold, F. X., & Nerlove, M. (1989). The dynamics of exchange rate volatility: A multivariate latent-factor ARCH model. Journal of Applied Econometrics 4, 1–22. Dungey, M. H. (1997). A Multilateral Approach to Decomposing Volatility in Bilateral Exchange Rates. Australian National University Working Paper in Economics and Econometrics No. 320. Dungey, M. H., & Martin, V. L. Contagion in the East Asian currency crisis. In J. Behrman, J. Dutta, S. Husted, & S. Pitayanon (Eds.), Restructuring the Economies of Asia for the New Millennium. Amsterdam: Elsevier Science. Enders, W., & Hurn, S. (1994). Theory and tests of generalized purchasing-power parity: common trends and real exchange rates in the Pacific Rim. Review of International Economics 2, 179 –190. Engle, R. F., Ito, T., & Lin, W. (1990). Meteor showers or heat waves? Heteroskedastic intra-daily volatility in the foreign exchange market. Econometrica 58, 525–542. Hamilton J. D. (1994). Time Series Analysis.Princeton, NJ: Princeton University Press. Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica 50, 1029 –1054. Mahieu, R., & Schotman, P. (1994). Neglected common factors in exchange rate volatility. Journal of Empirical Finance 1, 279 –311. Newey, W., & West, A. (1987). A simple positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708. Rose, A. K. (1994). After the deluge: do fixed exchange rates allow inter-temporal volatility trade-offs? CEPR Discussion Paper No. 1240. Taylor, S. (1986). Modelling Financial Time Series. Chichester, UK: John Wiley & Sons.
Decomposing exchange rate volatility around the Pacific Rim夽 M. H. Dungeya,* a
Department of Economics and Finance, La Trobe University, Bundoora, Vic. 3083, Australia
Received 1 December 1998; received in revised form 1 October 1999; accepted December 1999
Abstract Volatility in exchange rates is decomposed into components associated with domestic and international concerns for six Pacific Rim currencies. A latent factor model is used to model bilateral exchange rate changes as the weighted sum of three factors; two factors are uniquely associated with each of the currencies involved in the exchange rates and the other represents world shocks common to all exchange rates. The results show that international factors are more important in determining exchange rate volatility for the smaller nations of Australia, Singapore, and New Zealand, than for the larger nations of Japan and Canada. © 1999 Elsevier Science Inc. All rights reserved. JEL classifications:F31; G15; C33 Keywords: Exchange rates; Volatility; GMM
1. Introduction This paper decomposes bilateral exchange rate volatility for a selection of Pacific Rim currencies into components associated with domestic and international concerns. Governments and monetary authorities often express concern in the face of increases in exchange rate volatility and a desire to reduce it, using means such as foreign exchange intervention
夽This paper is a much revised version of a paper presented at the December 1998 ACAES Conference in Bangkok. The conference paper is in press (see Dungey and Martin, forthcoming). * Corresponding author. Tel.: ⫹61-3-9479-1514; fax: ⫹61-3-9479-1654. E-mail address: [email protected] (M. Dungey). 1049-0078/99/$ – see front matter © 1999 Elsevier Science Inc. All rights reserved. PII: S 1 0 4 9 - 0 0 7 8 ( 0 0 ) 0 0 0 3 0 - 0
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M.H. Dungey / Journal of Asian Economics 10 (1999) 525–535
or Tobin taxes for example. The effective reduction of volatility relies on understanding its source; if exchange rate volatility for a particular currency is primarily sourced internationally there may be very little national authorities can do to alter the situation, while retaining a flexible exchange rate regime. However, if the volatility is primarily domestic in origin, then the particular source of the disturbances may bear closer examination. There is now a well-developed literature on exchange rate volatility, and an accepted measure of unconditional volatility as either the variance or standard deviation of movements in exchange rate changes. However, there has as yet been no consensus on the sources of exchange rate volatility, either by individual country or across panels. Volatility in bilateral exchange rates between six currencies is examined in this paper. The focus here is on the different experiences of Pacific Rim countries with flexible exchange rate regimes. The currencies examined are the U.S. dollar (USD), Canadian dollar (CAD), Japanese yen (JPY), Singaporean dollar (SGD), Australian dollar (AUD) and New Zealand dollar (NZD). A latent factor model of exchange rate movements in the tradition of Mahieu and Schotman (1994) and Diebold and Nerlove (1989) is used to decompose exchange rate volatility into three components, two due to each of the currencies involved in the exchange rate, and a common world factor which effects all exchange rates. The focus on international and domestic factors is similar to that taken by Engle, Ito, and Lin (1990). Estimation is accomplished through Generalized Method of Moments (GMM) using a panel of exchange rate data. The results demonstrate that the reason for the lack of consensus in the literature as to the causes of volatility lies with the differing responses of individual exchange rates to common and idiosyncratic information. Hence, studies concerned with explaining exchange rate movements with panels of observed information (such as Rose, 1994) are unlikely to be successful. The results derived in this paper are in accordance with Enders and Hurn (1994) who concluded that international events are highly influential in explaining exchange rate movements for smaller Pacific Rim nations. For instance, volatility in the Canadian dollar exchange rate is found to be largely due to Canadian factors, while volatility in the NZ dollar is primarily sourced from overseas. The paper proceeds as follows. Section 2 outlines the latent factor model and Section 3 presents the estimation technique. The data is outlined in Section 4 and results follow in Section 5. Section 6 concludes.
2. A factor model of exchange rate changes Consider a simple factor model of exchange rates, such as Eq. (1).
冘f b M
s io ⫽
ij ij
(1)
j⫽1
where sio is the change in the log of a bilateral spot exchange rate expressed as currency i against a numeraire currency 0, fij are the factors which influence sio, and bij is the response coefficient for the exchange rate to each factor. There are M factors involved in determining the changes in the exchange rate, each of which is assumed uncorrelated. If the factors were
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not uncorrelated then the model could be reparameterised with a new set of uncorrelated factors. Hence, the factors are defined through their lack of correlation rather than being given ‘names’. This type of model has previously been applied to exchange rate volatility using observed factors, for example Bui and Pippenger (1990). Rather than describing the exchange rate change as Eq. (1) consider a model where the individual exchange rate change can be explained by three independent latent factors. s io ⫽  i f w ⫹ ␣ i f i ⫹ ␣ 0 f 0
(2)
In Eq. (2) the factors are: fw the world factor; fi a factor uniquely associated with currency i, and f0 a factor uniquely associated with currency 0. The world factor, fw affects all bilateral exchange rate changes, but the response to that factor, i, differs between exchange rates (for example, an oil price shock will affect yen denominated exchange rates quite differently to British pound denominated exchange rates). The ‘domestic’ factor, f0, has the same impact (␣0) upon all exchange rate changes denominated in the ‘0’ currency due to arbitrage. To see this consider a system of three spot exchange rates SUSA (USD/AUD)1, SJA (JPY/AUD) and SUSJ (USD/JPY). As before sio, designates the change in the log of the spot exchange rate Sio. Suppose that the coefficient on f0 in Eq. (2) (fA in the example) is not the same for all exchange rates. s USA ⫽  1 f w ⫹ ␣ 1 f US ⫹ ␣ 0 f A
(3)
s JA ⫽  2 f w ⫹ ␣ 2 f J ⫹ ␣ 3 f A
(4)
s USJ ⫽  3 f w ⫹ ␣ 4 f US ⫹ ␣ 5 f J
(5)
Arbitrage in foreign exchange markets implies Sij ⫽ Sik/Sjk.. There is a potential error here due to Jensen’s inequality, however it is unlikely to be a significant problem in high frequency data. Hence s USJ ⫽ s USA ⫺ s JA
(6)
 3 f w ⫹ ␣ 4 f US ⫹ ␣ 5 f J ⫽  1 f w ⫹ ␣ 1 f US ⫹ ␣ 0 f A ⫺  2 f w ⫺ ␣ 2 f J ⫺ ␣ 3 f A
(7)
and
For this equation to hold for arbitrary factor values, the coefficients on each of the individual factors on both sides of Eq. (7) must be equal. Hence, the following conditions must hold.
3 ⫺ 1 ⫹ 2 ⫽ 0
(8)
␣4 ⫺ ␣1 ⫽ 0
(9)
␣5 ⫹ ␣2 ⫽ 0
(10)
␣0 ⫺ ␣3 ⫽ 0
(11)
Hence, from Eq. (11), the coefficient ␣3 in Eq. (4) can be replaced by ␣0. Thus a common factor, with the same coefficient, is introduced into exchange rates against a common
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numeraire, here Eq. (3) and Eq. (4). Using just those two equations the coefficients for the cross-rate, Eq. (5) can be recovered using Eq. (8) to Eq. (10) with no restrictions on 1, 2, ␣1, ␣2 or ␣0. This manner of reducing the number of parameters to be estimated relieves the covariance restrictions imposed in Mahieu and Schotman (1994) when estimating a similar model. Identification of the system Eq. (3) and Eq. (4) requires 1⫽2; that is the response coefficient to world shocks cannot be the same for these two exchange rates. In practice 1 needs to be well distanced from 2 otherwise the system will be nearly unidentified. Arbitrage therefore justifies a specification like Eq. (2). It is possible to separate the domestic from foreign shocks because of the structure of Eq. (3) and Eq. (4). Only a domestic shock (f0) causes both Eq. (3) and Eq. (4) to change by the same amount. The other country factor (fi, i ⫽ 0) captures movements unique to the individual exchange rate. The world shock will capture common factor movements, but with differing response coefficients. A simple model of exchange rate changes such as Eq. (2) can then be used to decompose exchange rate volatility. The unconditional variance of Eq. (2) gives an expression for exchange rate volatility in terms of the weighted variances in each of the component unobserved factors. Consider a system of n bilateral exchange rates expressed against a common numeraire currency. There are n ⫹ 1 currencies involved in the exchange rate system. For ease of exposition each currency is uniquely associated with one issuing country—so there are also n⫹1 countries involved in the system. A system of equations of the form of (2) can be written as:
冤 冥冤 s 10
s 20 ..
s n0
⫽
1 ␣0 ␣1
0
..
0
2 ␣0
0
␣2 . .
0
..
..
..
..
..
..
n ␣0
0
0
..
␣n
冥冤
fw f0 f1 f2 .. fn
冥
or s ⫽ Bf,
(12)
where s is an n ⫻ 1 vector of stacked exchange rates, f is an (n ⫹ 2) ⫻1 vector of latent factors and B is an n ⫻ M matrix of coefficients attached to the factors. Then, var共s兲 ⫽ Bvar共 f 兲 B⬘
(13)
The variance-covariance matrix var(s) will have n(n ⫹ 1)/2 unique elements; hence using these moment conditions we can identify at most n(n ⫹ 1)/2 parameters from this system of equations. There are n parameters relating to the world factor (the i, which must be sufficiently different for the system to be identified), and n ⫹ 1 relating to idiosyncratic factors (the ␣i). Using the moment conditions produced by applying Eq. (13), and letting var(f) ⫽ In⫹2, produces the necessary identification condition that nⱖ 4; at least four bilateral exchange rates are necessary to estimate this system. Var(f)⫽In⫹2 is assumed as var(f) is unobserved. To the extent that this assumption is violated the parameter estimates will absorb the true variance of the unobserved factors. That
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is, an estimate of ␣i will in fact be an estimate of ␣i公var(fi). In this case comparing the absolute values of the coefficients is not very informative. However, the decomposition of the unconditional variance of Eq. (2) is unaffected by this assumption as follows:
␣ 02 ⫽ contribution of the numeraire currency to volatility in the exchange rate var s i0 ␣ 2i ⫽ contribution of currency i factor to volatility in the exchange rate var s i0  2i ⫽ contribution of the world factor to volatility in the exchange rate var s i0 The true value of var(fi) does not impinge on these results. Using this model, factor contributions to exchange rate volatility will be estimated for a panel of Pacific Rim exchange rates in Section 5.
3. Estimation method The problem to hand is well suited to estimation by Generalized Method of Moments (GMM) techniques. The unobserved nature of the factors means there is insufficient information to identify parameters in a simple regression analysis. However, the parameters can be estimated using the variance-covariance matrix of the data. A consistent estimate of the
冘 T
model parameters, ˆ , is obtained by satisfying t⫽1 mt 共ˆ 兲 ⫽ 0, where mt() represents the moment conditions at time t. However, there are generally more moments in mt() than elements in , that is the moment conditions will generally consist of p equations in k ( )⬘m ( ), unknowns. When p ⫽ k an estimator of is that value of which minimizes m where m ( ) is defined as a vector containing sample estimates of the moment conditions. When p ⬎ k there is an excess of moment conditions available to determine the parameter values. One solution would be to discard p-k of the moment conditions and estimate from the remainder. This solution would remain consistent, but would not be efficient because it ignores information (the discarded moment conditions). A preferred way of proceeding is to choose the ˆ which most closely satisfies all moment conditions. Hansen (1982) suggests the use of k linear combinations of the moment conditions, using m t ( ) ⫽ ant() where the t() are the original p ⬎ k moment conditions, and an forms linear combinations of these conditions. Now the optimal parameter estimator ˆ is obtained ()⬘a⬘nan (), or more generally ()⬘W (), where () is defined as the by minimizing vector of sample moment conditions. Hansen shows that the optimal structure for the ⫽ 冋 var冉 冘 共 兲冊册
⫺1
T
weighting matrix W is a⬘n an
t⫽1
t
. To take into account the effect of the
linear combination an when p ⬎ k, ˆ is the solution to the first order condition for the objective function:
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冉 冊
⭸ 共 ˆ 兲 ⬘ 共 ˆ 兲 ⫽ 0 a⬘na n ⭸
(14)
and substituting the optimal value for an⬘an
冉 冊 冋 冉 冘 冊册 ⭸ 共 ˆ 兲 ⬘ var ⭸
T
⫺1
t共 兲
共 ˆ 兲 ⫽ 0
(15)
t⫽1
The variance of ˆ is obtained as:
冋冉 冊冋 冉 冘 冊册 冉 冊册
1 var共 ˆ 兲 ⫽ 2 T
共 ˆ 兲 ⬘ ⭸ var ⭸
T
t⫽1
⫺1
t共 ˆ 兲
共 ˆ 兲 ⭸ ⭸
⫺1
(16)
So the most efficient estimates of ˆ are found using the prescribed W; this weights the more variable moments more heavily in the estimation process. In practice, we do not have the true variance matrix, and instead rely on a consistent estimate. The initial consistent estimate of var(兺t ()) can be obtained with W ⫽ I. In order to account for possible autocorrelation in t the Newey and West (1987) estimator is used. In the application of this paper the efficient estimates showed some instability in recursive estimation, perhaps due to the non-existence of higher order moments. In this situation the consistent estimates obtained by using W ⫽ I are preferred to the efficient estimates.
4. The data This study uses weekly movements in the log of the bilateral exchange rates constructed from a panel of six currencies: the U.S. dollar (USD), the Canadian dollar (CAD), the Japanese yen (JPY), the Singaporean dollar (SGD), the Australian dollar (AUD) and the New Zealand dollar (NZD) over the period 1990 –1998.2 The changes have been centered so that the mean of each series is zero. The weekly interlude has been chosen because it captures the short-term fluctuations that are of interest, but is not subject to day of the week effects which are found in daily data (Taylor, 1986). The choice of currencies was determined by the availability of floating exchange rate regimes in the region. All currencies except the Singaporean dollar have been floating since at least the mid-1980s (New Zealand floated in March 1985). The Singaporean dollar has been classified as a managed float since 1990 (IMF, Exchange Rate Arrangements, various issues). However, it was felt that the assumption of arbitrage could be reasonably assumed given the relatively well-developed Singaporean foreign exchange market3 (BIS, 1999).
5. Results The factor model of Eq. (12) was applied to the panel of Pacific Rim currencies using each currency as the numeraire currency in turn. The volatility decompositions are presented in
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Table 1. Variance contributions with different numeraire currencies curency fw 1. USD as numeraire JPY 16.7 CAD 0.0 AUD 47.3 NZD 31.5 SGD 17.7 2. JPY as numeraire USD 16.7 CAD 3.6 AUD 45.9 NZD 34.9 SGD 6.5 3. CAD as numeraire USD 0.0 JPY 3.6 AUD 7.3 NZD 2.4 SGD 0.7
contribution of factors (%) f0 fi 5.0 1.4 8.2 18.6 32.9
78.3 98.6 44.4 49.9 49.5
78.2 17.6 40.3 55.6 85.2
5.1 78.8 13.8 9.6 8.2
98.6 78.8 86.1 93.9 97.2
1.4 17.6 6.6 6.3 2.1
currency fw
contribution of factors (%) f0 fi
4. AUD as numeraire USD 47.3 JPY 45.9 CAD 7.3 NZD 12.8 SGD 58.7 5. NZD as numeraire USD 31.5 JPY 34.9 CAD 2.4 AUD 12.8 SGD 49.7 6. SGD as numeraire USD 17.7 JPY 6.5 CAD 0.7 AUD 58.7 NZD 49.7
44.4 13.8 6.6 58.1 32.2
8.3 40.3 86.1 29.2 9.1
49.9 9.6 3.6 29.2 32.2
18.6 55.6 93.9 58.1 18.1
49.5 8.2 2.1 9.1 18.1
32.8 85.2 97.3 32.2 32.2
Table 1. The information is also shown in Figs. 1 to 6. As shown in Section 2, arbitrage implies that the decomposition be identical for any pair of currencies regardless of which currency is used as the numeraire, and this is clearly evident from the results.4 The volatility decompositions are informative about the different nature of the currencies under consideration. When considering exchange rates against the U.S. dollar, the world’s most traded currency (BIS, 1999), the currencies examined seem to fall into two distinct groups. The larger economies, by GDP, of Canada and Japan display a substantial component of exchange rate volatility sourced from factors associated uniquely with their own currencies; the impact of world and U.S. factors is relatively small. However, for the three smaller countries (as measured by GDP), Australia, New Zealand and Singapore, the impact of total international factors accounts for more than 50 percent of the decomposition of volatility in each case. Considering each of these smaller countries in turn, in the Australian case, despite the fact
Fig. 1. Cumulative contributions of factors—USD numeraire
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Fig. 2. Cumulative contributions of factors—AUD numeraire
that the contribution of international factors to AUD/USD volatility is greater than 50 percent, the Australian factor makes a sizeable impact on total volatility at around 44 percent. The Australian factor also makes a substantial contribution to explaining volatility in exchange rates against the smaller countries of New Zealand and Singapore (of 58 percent and 32 percent respectively) but is relatively unimportant against the yen and the Canadian dollar. Similarly, the New Zealand dollar factor makes a sizeable contribution to New Zealand dollar exchange rate volatility against the U.S. dollar, Australian dollar and Singaporean dollar (49, 29 and 32 percent respectively) but is unimportant for the yen and Canadian dollar exchange rates. The Singaporean factor makes relatively little contribution to the decomposition of exchange rate volatility including the Singaporean dollar for all currencies with the exception of the U.S. dollar as noted above. In the opposite vein, the Canadian dollar exchange rate volatilities are without exception explained predominantly by the Canadian factor. The largest contribution by overseas factors comes in the yen-Canadian dollar exchange rate, where 20 percent of total volatility is accounted for by the Japanese and world factors. The decomposition of the yen exchange rates indicates that the yen factor has a dominating role to play in determining exchange rate volatility for the yen exchange rate against the U.S. dollar, and the Singaporean dollar (78 and 85 percent respectively) and an important role for the rates against the Australian dollar and New Zealand dollar (40 and 56 percent respectively). Only the Canadian dollar-yen exchange rates has no substantial influence from the yen factor. The world factor seems to be important as an explanator of yen exchange rate volatility only for the Australian and New Zealand dollar rates. These results lead to the conclusion that the larger Pacific Rim countries of the U.S., Japan and Canada have different experiences to the smaller countries of New Zealand, Australia
Fig. 3. Cumulative contributions of factors—JPY numeraire
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Fig. 4. Cumulative contributions of factors—NZD numeraire
and Singapore when it comes to explaining the sources of exchange rate volatility. This conclusion is consistent with the evidence of Enders and Hurn (1994) who examined the behavior of real exchange rate changes for Pacific Rim and industrialized countries, and concluded that the movements of the smaller Pacific Rim countries were influenced by those of a panel of nations including Japan and the U.S. Further, they found evidence for relationships between the smaller Pacific Rim countries, but little in support of similar relationships between the larger nations examined. The results in this paper show that for U.S.-based exchange rates the partner currency factor has a substantial role to play in explaining volatility. For the Japanese based rates the Japanese and world factors comprise the majority of the sources of volatility, with the exception of Canada. Canadian exchange rate volatility seems to be almost totally reliant on Canadian factors. In the case of each of the smaller Pacific Rim nations the contributions of the combined world and other currency factors dominate the decomposition of exchange rate volatility when the partner currency is a major currency. Between Pacific Rim countries the decomposition is less clear-cut— each currency has a role to play in explaining exchange rate volatility.
6. Conclusions A latent factor model was used to model bilateral exchange rate changes as the weighted sum of three factors, where two of the factors are uniquely associated with each of the currencies involved in the exchange rates and the other represents world shocks common to all exchange rates. A decomposition of the unconditional variance of this model gives the
Fig. 5. Cumulative contributions of factors—CAD numeraire
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Fig. 6. Cumulative contributions of factors—SGD numeraire
contribution of each of the domestic and international factors to total exchange rate volatility in that exchange rate. This method was applied to a panel of Pacific Rim currencies, comprising the U.S., Canadian, Singaporean, Australian and New Zealand dollars and the Japanese yen using weekly exchange rate data from 1990 to 1998. The results show substantial differences between the exchange rate volatility decompositions for the larger Pacific Rim countries of the U.S., Japan and Canada, from the smaller countries of Australia, Singapore and New Zealand. For the smaller countries the combined overseas factors dominate exchange rate volatility assessed against the larger countries. Volatility decompositions for exchange rates between the smaller countries show a more diverse pattern. Canadian dollar denominated exchange rate volatility is dominated by the Canadian factor, as is yen denominated volatility dominated by the yen factor in general. For the U.S. dollar denominated exchange rates, which make up the majority of world foreign exchange turnover (BIS, 1999), the combination of world and U.S. factors dominate the volatility decomposition against the smaller Pacific Rim nations, but the smaller country factors are nevertheless a substantial influence in each case. These results indicate the difficulties that arise in attempting to apply panel data techniques to identify common macroeconomic fundamentals in a diverse set of exchange rates. The extent to which individual exchange rates respond to domestic and international factors varies widely in any given group of exchange rates. Individual country differences are demonstrably important in understanding bilateral exchange rate volatility. The result that different countries’ exchange rate volatilities are differently influenced by international and domestic factors implies that there is no clear blueprint for understanding or reducing exchange rate volatility across the board. Large countries such as Japan and Canada may be able to use appropriately aimed domestic policies to reduce volatility given the substantial domestic factor contributions to volatility for those countries. However, for some countries the source of exchange rate volatility is primarily international and hence largely outside their policy control. This is the experience of Australia, Singapore and New Zealand in the 1990s.
Notes 1. I have cited exchange rates according to quotation convention. USD/AUD should be read as the number of Australian dollars per U.S. dollar and not vice versa.
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2. The data were sourced from the Reserve Bank of Australia and are 4:00pm Wednesday observations. In the case where Wednesday was not a trading day, Thursday observations were taken, and in the case of no Thursday trading, Tuesday observations were used. 3. BIS (1999) reported that total turnover in the world foreign exchange markets involved 87 percent U.S. dollars, 21 percent Japanese yen, 4 percent Canadian dollars, 3 percent Australian dollars and insignificant amounts of New Zealand and Singaporean dollars: this is of a total of 200 percent as both sides of a transaction are included. Turnover in specific locations however, differed slightly from this. In 1998, 18 percent of transactions occurred in the U.S. market, 8 percent in the Japanese market, 7 percent in Singapore, 2 percent in each of Canada and Australia and an insignificant amount in the New Zealand market. 4. This result is sensitive to the number of overidentifying conditions in the system. For example, in a seven or more currency system the variance decompositions vary slightly—see Dungey (1997). In this five variable system the differences are very slight, in the order of 10⫺2.
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