exchange rate volatility and the united states exports: evidence from canada and japan

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J. Japanese Int. Economies 19 (2005) 51–71

www.elsevier.com/locate/jjie

Exchange rate volatility and the United Statesexports: evidence from Canada and Japan

Taufiq Choudhry

School of Management, University of Bradford, Emm Lane, Bradford BD9 4JL, UK

Received 14 March 2003; revised 14 November 2003

Available online 14 January 2004

Choudhry, Taufiq—Exchange rate volatility and the United States exports: evidence from Caand Japan

This paper investigates the influence of exchange rate volatility on the real exports of theStates to Canada and Japan during the current flexible exchange rate period (1974–199Johansen multivariate cointegration method and the constrained error correction (general-to-smethod are applied to study the relationship between real exports and its determinants (inexchange rate volatility). Conditional variance from the GARCH(1,1) model is applied as excrate volatility. Both nominal and real exchange rates are employed in the empirical study. Rindicate a significant effect of the exchange rate volatility on real exports. These exchangvolatility effects are mostly negative.J. Japanese Int. Economies 19 (1) (2005) 51–71. School oManagement, University of Bradford, Emm Lane, Bradford BD9 4JL, UK. 2003 Elsevier Inc. All rights reserved.

JEL classification: F1; F10

Keywords: Real exports; Volatility; GARCH; Conditional variance; Cointegration; Error correction

1. Introduction

One of the major concerns since the introduction of the flexible exchange rate hawhether the increase in exchange rate variability (uncertainty) has affected the interntrade flow. Higher exchange rate volatility leads to higher cost for risk-averse tradeto less foreign trade(Arize et al., 2000). In other words, greater exchange risk increathe riskiness of trade profits, leading risk-averse traders to reduce trade. Thus, a the

E-mail address: [email protected].

0889-1583/$ – see front matter 2003 Elsevier Inc. All rights reserved.doi:10.1016/j.jjie.2003.11.002

http://www.elsevier.com/locate/jjie

52 T. Choudhry / J. Japanese Int. Economies 19 (2005) 51–71

w andndaskus000)

e flow.ilitys. Fortmente rate is

by a

angeurrent

ect of

e raterate

ted by3)

rial

as andct on

firms.)tically

quires

hangepaperpaperodels

red tod thanrche rate

helpednks.

d

framework seems to indicate a negative relationship between international trade floexchange rate variability.1 Some studies such asCoes (1981), Cushman (1983), Akhtar aSpence Hilton (1984), Thursby and Thursby (1987), Kenen and Rodrik (1986), M(1986), De Grauwe (1988), Chowdhury (1993), Arize (1995, 1998) and Arize et al. (2do provide evidence that exchange rate variability does reduce international tradAccording toArize (1998), knowledge of the degree to which exchange rate volataffects trade is important for the design of both exchange rate and trade policieexample, if exchange rate volatility leads to a reduction in exports, trade adjusprogrammes that emphasized export expansion could be unsuccessful if exchangvolatile. In addition, the intended effect of a trade liberalization policy may be doomedvariable exchange rate and could precipitate a balance-of-payment crisis(Arize, 1998 andArize et al., 2000). The purpose of this paper is to investigate the effects of the exchrate variability (volatility) on United States exports to Canada and Japan during the cflexible exchange rate period.

Some previous studies have also reported indicating no or very little significant effthe exchange rate variability on international trade.Bailey et al. (1987)claim that earlierstudies conducted during the 1970s fail to find a significant effect of the exchangvariability on international trade simply due to the lack of enough flexible exchangeperiod data.2 Bailey et al. (1986, 1987)fail to find any significant effect of the exchange ravariability on the trade flow of seven OECD countries. A similar result is also provideGotur (1985), Aschheim et al. (1987), Koray and Lastrapes (1989), and Gagnon (199. Anempirical investigation by theIMF (1984)covering exports from the seven large industcountries produces only two cases where the effect is significant and negative.Asseery andPeel (1991), Franke (1991), Giovannini (1988), Sercu and Vanhulle (1992) and DellZillberfarb (1993)have shown that exchange rate variability imposes a positive effeinternational trade. These studies consider international trade as an option held byLike any other option, the value of trade may rise with volatility.De Grauwe (1988shows the relationship between exchange rate volatility and trade flows is analyindeterminate. As indicated byArize (1995) and Arize et al. (2000), conflicting resultsimply the effect of exchange rate variability on international trade is uncertain and remore empirical and theoretical research.

As stated above, this paper empirically investigates the relationship between excrate variability (volatility) and the United States export to Canada and Japan. In thisthe exchange rate variability is measured using the univariate GARCH model. Thealso applies the multivariate cointegration method and constrained error correction mto study the stated relationship. Furthermore, monthly data is applied as compathe popular quarterly data or annual data, and a relatively longer period is coveremost other papers.3 McKenzie (1999)emphasized a few key points in future reseain this field. First, the need for care in specifying the technique by which exchang

1 According toKlaassen (2002), this perception that greater exchange rate risk reduces trade hasmotivate monetary unification in Europe and is also related to currency market intervention by central ba

2 SeeBailey et al. (1986, 1987)for citations of these earlier studies.3 Koray and Lastrapes (1989)also use monthly data in their paper, andChowdhury (1993), Arize (1995) an

Arize et al. (2000)apply the Johansen multivariate method of cointegration.

T. Choudhry / J. Japanese Int. Economies 19 (2005) 51–71 53

andd timeoblems

partlyprofits

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ationsvelyns toded by

r thethesences ist of thees than

arkets)

omycosts

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volatility is measured, with increased attention to the application of the GARCHrelated models. Second, application of data disaggregated by sector, market anperiod. Third, the need to apply proper methods necessary to correct prospective prof serial correlation and nonstationarity in time series data.

2. Exchange rate variability and the effect on international trade

Exchange rate variability is a source of concern because currency valuesdetermine the price paid or received for output and, consequently, this affects theand welfare of producers and consumers(Akhtar and Spence Hilton, 1984). In otherwords, exchange rate variability can affect the volume of goods traded internatioby making prices and profits indeterminate or uncertain. If the forward exchange mcannot be used (such as in emerging markets) to create a perfect hedge against erisk, economic agents will prefer domestic products over imported ones if it is unclthe time a purchase order is placed what the exchange rate level will actually bepayment is due.

For some developed countries currencies forward markets can be used to redhedge exchange rate risk but it has been proven that forward markets fail to comeliminate exchange rate risk(Akhtar and Spence Hilton, 1984 and Arize et al., 2000). Evenif hedging in the forward markets (and futures markets) were possible, there are limit(Arize et al., 2000). The size of the contracts is generally large, the maturity is relatishort, and it is difficult to plan the magnitude and timing of all international transactiotake advantage of the forward market. Failure to provide perfect hedge is compounthe empirical fact that forward rates are a poor predictor of the future spot rates.4 Moreoverany cost of forward hedging will reduce the international trade: importers who pay foforward hedge will face higher prices for the foreign goods and exporters who incurhedging costs will pass along the cost as higher prices. The end result in both instaa reduction of trade. Furthermore, exchange rate is a major determinant of the cosforeign products; prices of traded goods are more affected by exchange rate changprices for local substitutes. A risk averse importer or buyer would prefer domestic mto reduce the likelihood of future variations in outlays(Akhtar and Spence Hilton, 1984.The same holds for sales markets and exporters.

Sercu and Uppal (2003)based on a model of a stochastic general-equilibrium econwith international commodity markets that are partially segmented due to shippingshow it is possible to have a negative or a positive effect of the exchange rate voon international trade. If the source of increase in exchange rate volatility is dueincrease in the volatility of the endowment processes, then trade will raise with a rexchange rate volatility. But, if the increase in the exchange rate volatility is due an incin the degree of segmentation of commodity markets, then trade will fall with a riexchange rate volatility. This conclusion applies to trade between developed countrdeveloping countries.

4 SeeChoudhry (1999)for citations of papers that claim the forward exchange rate is a poor predictorfuture spot exchange rate.


orda and

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This paper employs a model similar to the one used inChowdhury (1993), Arize(1995, 1998) and Arize et al. (2000). The following relationship is tested to check fthe effects of exchange rate variability on the United States real exports to CanaJapan:

(1)ln(Xt ) = δ1 ln(Yt ) + δ2 ln(Pt ) + δ3 ln(Vt ) + εt ,

where ln(Xt ) is the log of real United States exports to Canada or Japan,Yt is the log ofreal income (industrial production) of Canada or Japan,Pt is a measure of relative expoprices of the United States to Canada or Japan,Vt is the exchange rate variability in loandε is the error term.Equation (1)can be derived as a long-run solution of behavioudemand and supply functions for exports(Gotur, 1985). Based on the standard theothe real income of the importing country should have a positive effect on the export(Bailey et al., 1986, 1987). Thus the coefficient on real income (δ1) should be positiveThe relative price is the ratio of the export prices of the United States to those of Cor Japan. Changes in the price ratio represents changes in the term of trade, rethe impacts of changes in nominal exchange rates, differing rates of inflation acountries and changes in relative prices in each country between its non-tradedand its exports(Bailey et al., 1986, 1987). According toArize (1995) and Arize et al(2000), the coefficient of the price ratio (δ2) should be negative. As indicated byBaileyet al. and Arize (1995), the influence of the exchange rate variability (Vt ) on exports isuncertain. Investigation of the size and direction of the impact imposed by the excrate variability (Vt ) on the export is the main theme of this study. The long-run relationrepresented byEq. (1)is investigated by means of the Johansen multivariate cointegrtests and the constrained error correction model is applied to check for causality bethe variables.

According toAkhtar and Spence Hilton (1984), the variance or standard deviationsthe exchange rate is the most commonly used definition of the exchange rate variBailey et al. (1986, 1987)apply two different definitions of exchange rate variabilThe polynomial distributed lag of the absolute value of the period-to-period chanthe exchange rate and the logarithms of the moving standard deviations of the exrate.Kenen and Rodrik (1986), Koray and Lastrapes (1989), Chowdhury (1993) andet al. (2000)apply a moving sample standard deviation. According toJansen (1989),this unconditional measure of volatility lacks a parametric model for the time varvariance of a time series. Therefore, according toArize (1995), the exchange rate volatilitmay be modelled by the Autoregressive Conditional Heteroscedastic (ARCH) moEngle (1982).5 In this paper, conditional variance of the first difference of the log ofexchange rate is applied as volatility (variability). The conditional variance is estimatmeans of the Generalized Autoregressive Conditional Heteroscedastic (GARCH) moBollerslev (1986). Kroner and Lastrapes (1993), Caporate and Doroodian (1994) an(1999)also apply the GARCH model to estimate the volatility of exchange rate.

5 Arize (1995)also applies two other definition of exchange rate volatility. The standard moving avvariance of the first difference of exchange rate and the linear moment model. In the linear moment movariance of a variable is specified as a linear function of the regressors used in an auxiliary regression thatthe mean of the variable of interest.


hangethe

the realpaper

imation.olatilityes dollarchange

bility)log of

imatedmodel

n thedasticity

rmorderby the

gedceering

One of the main debates in this field is the use of the nominal or the real excrate. As stated byBailey et al. (1986, 1987), persuasive arguments can be made forapplication of both exchange rates.Akhtar and Spence Hilton (1984)provide a detailedanalysis of the advantages and disadvantages of the application of the nominal andexchange rates in the study of exchange rate volatility on international trade. Thisemploys both the nominal exchange rate and the real exchange rate in the model estTwo different sets of exchange rates for both Canada and Japan are applied. First, vof the nominal exchange rate and then real exchange rates between the United Statand the Canadian dollar or the Japanese yen are employed. In this manner, which exrate volatility has the larger influence on real exports may be studied.

3. Exchange rate volatility. Univariate GARCH(p,q) model

In previous studies several different measures of exchange rate volatility (variahave been applied. As stated above, conditional variance of the first difference of thethe exchange rate is applied as volatility in this paper. The conditional variance is estby means of the Generalized Autoregressive Conditional Heteroscedastic (GARCH)of Bollerslev (1986).

In the GARCH model, the conditional variance of a time series depends uposquared residuals of the process and has the advantage of incorporating heterosceinto the estimation procedure of the conditional variance(Bollerslev, 1986). Accordingto Bollerslev et al. (1992)the GARCH(p, q) model can be viewed as a reduced foof a more complicated dynamic structure for the time varying conditional secondmoments. First difference of the (nominal or real) exchange rate can be presentedGARCH(p, q) model as follows:

(2)yt = µ + εt ,

(3)εt/Ωt−1 ∼ N(0, ht ),

(4)ht = ω +q∑

j=1

βjht−j +p∑

j=1

αjε2t−j ,

whereyt is equal to log(et /et−1), et is the exchange rate (nominal or real),µ is the meanyt conditional on past information (Ωt−1) and the following inequality restrictionsω > 0,βj > 0 andαj > 0 are imposed to ensure that the conditional variance (ht ) is positive. Thesize and significance ofαj indicates the magnitude of the effect imposed by the lagerror term (εt−j ) on the conditional variance (ht ). In other words, the size and significanof theαj indicates the presence of the ARCH process in the residuals (volatility clustin the data). The estimatedht (conditional variance) from the GARCH(p, q) model isapplied in the estimation ofEq. (1).


.

finite

nce.ofce) is

nada tosts the

idualsof serial

withoodn

f

Table 1Test results from the GARCH(1,1) models

US/Canada nominal exchange rateyt = 0.0041∗∗∗ + εt ht = 0.000017 + 0.1074∗ε2

t−1 + 0.7873∗∗∗ht−1(5.627) (1.440) (1.846) (7.437)

L = 1189.20, α1 + β1 = 0.895, LB(6) SSR= 1.60, LB(6) SR= 2.45

US/Canada real exchange rateyt = 0.000086+ εt ht = 0.0000047+ 0.1181∗∗∗ε2

t−1 + 0.8590∗∗∗ht−1(1.420) (1.434) (3.082) (21.160)

L = 1134.7, α1 + β1 = 0.977, LB(6) SSR= 1.56, LB(6) SR= 2.23

US/Japan nominal exchange rateyt = −0.00289∗ + εt ht = 0.000098 + 0.1195∗∗ε2

t−1 + 0.7720∗∗∗ht−1(−1.652) (1.493) (2.410) (6.816)

L = 910.31, α1 + β1 = 0.892, LB(6) SSR= 1.91, LB(6) SR= 8.40

US/Japan real exchange rateyt = 0.00062+ εt ht = 0.000017∗ + 0.0778∗∗∗ε2

t−1 + 0.8656∗∗∗ht−1(0.591) (1.839) (2.191) (18.030)

L = 1057.97, α1 + β1 = 0.933, LB(6) SSR= 2.72, LB(6) SR= 6.63

Notes: t -statistics in the parentheses. L= log likelihood function value, LB= Ljung–Boxstatistics at six lags, SSR= standardized squared residuals, SR= standardized residuals.

* Significant at the 10% level.** Idem., 5%.

*** Idem., 1%.

Table 1shows the results from the GARCH(1,1) models for all four exchange rates.6 Inall cases the ARCH coefficient (α1) is found to be significant implying volatility clusteringAccording toEngle and Bollerslev (1986), if α1 + β1 = 1 in a GARCH(1,1) model, thisimplies two things: persistence of a forecast of the conditional variance over allhorizons and an infinite variance for the unconditional distribution ofεt . In other words,whenα1 + β1 = 1, current shock persists indefinitely in conditioning the future variaSuch a model is known as the Integrated-GARCH, or IGARCH, model. As the sumα1andβ1 approaches unity, the persistence of shocks to volatility (conditional variangreater and the decay rate of the shock is slower.7 The half-life of the shock ranges from31 months in the case of the real exchange rate between the United States and Ca7 months for the United States and Japanese nominal exchange rate. In all four teLjung–Box statistics fails to indicate any serial correlation in the standardized resand the standardized squared residuals at the 5 percent level using 6 lags. Absence

6 In a GARCH(p, q) model different combinations ofp andq may be applied but, as indicated byBollerslevet al. (1992, p. 10), p = q = 1 is sufficient for most financial and economic series.Bollerslev (1988)providesa method of selecting the length ofp andq in a GARCH model. Tests in this paper were also conducteddifferent combinations ofp andq with p = q = 2 being the maximum lag length. Results based on log-likelihfunction and likelihood ratio tests indicate that the best combination isp = q = 1. These results are available orequest.

7 The half-life of a shock to volatility is given by 1− [log 2/ log(α1 + β1)]. Half-life measures the period otime (number of months) over which a shock to volatility reduces to half its original size.


(a) Log of volatility—US/Canada real exchange rate.

(b) Log of volatility—US/Canada nominal exchange rate.

Fig. 1.


(c) Log of volatility—US/Japan nominal exchange rate.

(d) Log of volatility—US/Japan real exchange rate.

Fig. 1. Continued.


mpass

r bothuctionminalapaneseand theada andserveande–Bera

roots)in the

ton-

iablese

strmed

e andc

moryry and

d PJAP

s Bureaul Reserve

correlation in the standardized squared residuals implies the lack of need to encoa higher order ARCH process(Giannopoulos, 1995). Figure 1 presents the volatility(conditional variance) for all four exchange rates.

4. The data and the unit root tests

The data applied are monthly ranging from January 1974 to December 1998. FoCanada and Japan real income is presented by the monthly real industrial prodindex. The price indices are the export price indices for all three countries. The noexchange rate applied is defined as Canadian dollar per United States dollar and Jyen per United States dollar. Real exchange rate is created using these price indicesnominal exchange rates between the United States dollar and the currencies of CanJapan.8 The data are obtained from DATASTREAM and the website of the Federal ReBank of St. Louis.9 Table 2presents the basic statistics of all variables in log levelsfirst difference. Most series are skewed and have excess kurtosis. Based on Jarqustatistics almost all series are found to be non-normal.

As required by cointegration tests, first the stochastic structure (presence of unitof each series is determined. There are several different types of unit root testsliterature. This paper applies the KPSS test,Kwiatkowski et al. (1992). The KPSS tesstatistics (ηt ), which test the null of trend stationarity against the alternative of nstationarity, are calculated as

(5)ηt (q) = T −2T∑

t=1

s2t /σ 2(q),

wheres2t is the partial sum process of the residuals from the regression of the var

(time series) on an intercept and a time trend,σ 2(q) is a consistent estimate of therror variance from the same regression,q is the lag truncation parameter, andT isthe number of observations. The long-run variance is calculated following theNeweyand West (1987)procedure, which utilises Barlett windows adjustment using the firq

sample autocovariances. A test for the null of the level stationarity can be perfoby utilizing the error term from the regression of the variable on an intercept aloncalculating the test statistics as above.Kwiatkowski et al. (1992)show that the asymptotivalidity of this test holds even for small samples. Moreover,Lee and Schmidt (1996)showthat KPSS tests are also consistent against the stationary fractional alternative.Lee andAmsler (1997)show that KPSS tests are able to consistently distinguish short mefrom stationary long memory, and these processes from nonstationary long-memo

8 The real exchange rate is defined as log of (C$/US$)∗ (PUS/PCAN) for Canada and (Yen/US$)∗ (PUS/PJAP)for Japan, where PUS is the export price index of the US, PCAN is the export price index of Canada, anis the export price index of Japan.

9 These data are collected and provided by the Federal Reserve Board of Governors, the United Stateof the Census and the United States Bureau of Economic Analysis. The website address of the Federaof St. Louis database ishttp://research.stlouisfed.org/fred2/.

http://research.stlouisfed.org/fred2/


tics

ionaryed by

e testn thistigatesble toeriessingle

KPSS

Table 2Basic statistics of the variables

Variables Mean Variance Skewness Kurtosis JB statis

CanadaLevels

Real income 4.200*** 0.011 −0.250*** −0.802*** 11.172a

Price ratio −0.170*** 0.006 0.806*** −0.098 32.604a

Real exports 3.367*** 0.191 0.424*** −1.109*** 24.363a

Nominal rate vol. −9.164*** 0.037 1.635*** 3.143*** 257.189a

Real rate vol. −8.686*** 0.386 0.290*** −0.834*** 12.903a

First differenceReal income 0.0002 0.0003 0.149 1.800*** 41.447a

Price ratio −0.001 0.0002 0.025 0.904*** 10.221a

Real exports 0.004 0.0128 −0.250 0.179 3.519Nominal rate vol. −0.0001 0.0467 0.783*** 2.971*** 140.506a

Real rate vol. −0.0003 0.0254 2.256*** 6.846*** 837.462a

JapanLevels

Real income −0.751*** 0.332 −0.193*** −1.399*** 26.324a

Price ratio 0.582*** 0.126 −0.353** −0.956*** 17.653a

Real exports 2.682** 0.174 0.068 −1.388*** 24.268a

Nominal real vol. −7.120*** 0.099 0.573*** 0.226 17.031a

Real rate vol. −8.138*** 0.122 0.360** −0.776*** 14.015a

First differenceReal income 0.005** 0.001 0.314** 0.333 6.286b

Price ratio 0.004 0.0003 0.220 0.498 5.500Real exports 0.003 0.012 0.952*** 8.721*** 992.631a

Nominal real vol. 0.0022 0.026 2.536*** 9.629*** 1475.58a

Real rate vol. −0.001 0.0123 2.680*** 9.424*** 1464.39a

Note: JB statistics= Jarque–Bera statistics.a Rejection of the null at the 1% level.b Idem., 5%.

** Significant at the 10% level.*** Idem., 1%.

unit root. However, they are not able to consistently distinguish between nonstatlong memory and unit root. The critical values required in the KPSS tests are providKwiatkowski et al. (1992).

Table 3presents the KPSS test results for unit roots at levels and first difference. Thfor the levels is applied with a trend and the first difference test is without a trend. Imanner the levels test checks for trend stationarity and the first difference test investhe stationarity around a level. Results show that all first difference series are unareject the null of stationarity but the level series do reject the null. In other words, all sare stationary after first difference but are nonstationary in levels. They all contain aunit root.10

10 The augmented Dickey–Fuller (ADF) test of unit root was also applied and it backs up the result of thetest. The ADF test results are available on request.


theseethod

dratingratingctor.as the

,er as

atrixtsg

ralls are

ris

Table 3KPSS (unit root) test results

Variables Lags

0 3 6

CanadaReal income 2.837*** 0.734*** 0.433***

Price ratio 3.889*** 1.005*** 0.585***

Real exports 3.754*** 1.256*** 0.789***

Nominal rate vol. 3.638*** 1.232*** 0.775***

Real rate vol. 0.686*** 0.194** 0.121*

JapanReal income 2.220*** 0.576*** 0.343***

Price ratio 2.585*** 0.682*** 0.415***

Real exports 1.217*** 0.416*** 0.263***

Nominal rate vol. 1.093*** 0.385*** 0.243***

Real rate vol. 0.794*** 0.221*** 0.136*


*** Idem., 1%.

5. Cointegration tests and results

Two or more nonstationary time series are cointegrated if a linear combination ofis stationary. Cointegration tests in this paper are conducted by means of the mdeveloped byJohansen (1988) and Johansen and Juselius (1990).11 The Johansen methoapplies the maximum likelihood procedure to determine the presence of cointegvectors in nonstationary time series. This method detects the number of cointegvectors and allows for tests of hypotheses regarding elements of the cointegrating ve12

The Johansen maximum likelihood approach sets up the nonstationary time seriesvector autoregressive (VAR):

(6)Xt = C +K∑

i=1

ΓiXt−i + ΠXt−1 + λDt + ηt , η ∼ niid(0, Y ),

whereXt is a vector of nonstationary (in levels) variables, implies first differenceC is the constant term andDt is stationary series. Such stationary variables often entdummy variables, including seasonal dummies. The information on the coefficient mbetween the levels of the seriesΠ is decomposed asΠ = αβ ′ where the relevant elemenof theα matrix are the adjustment coefficients and theβ matrix contains the cointegratin

11 This procedure provides more robust results when there are more than two variables(Gonzalo, 1994)andwhen the number of observations is greater than 100(Hargreaves, 1994). The Johansen procedure reveals ovethe least size distortion(Haug, 1996)and is still more robust than the other methods even when the errornon-normal(Gonzalo, 1994).

12 More detailed analysis of the Johansen procedure is provided inDickey and Rossana (1994) and Har(1995).


tics ofe test.etweenl

lectar

sion ofies

lier, forecond

ge rateinte-imume realtio be-ppliedsults

rmal.we yen)tor islong-nd itson is

hasests to

excesss

p of 2)is

d. These

rotems are

ificanttest may

vectors. The constant term is included in order to capture the trending characteristhe time series involved.13 The Johansen method provides two different tests, the tracand the maximum eigenvalue test to determine the number of cointegrating vector(s)14 If anonzero vector(s) is indicated by these tests, a stationary long-run relationship(s) bthe relevant variables is implied.Osterwald-Lenum (1992)provides the appropriate criticavalues required for these cointegration tests.

A likelihood ratio test and the Akaike Information Criterion (AIC) are used to sethe number of lags required in the cointegration test.15 Since there seems to be a linetrend in all the nonstationary series, cointegration tests are conducted with the inclua deterministic trend.16 Seasonality is eliminated by including monthly seasonal dummexogenously in all regressions.

Table 4presents the cointegration results for Canada and Japan. As stated earboth countries four relationships are tested for possible cointegration. The first and stests are conducted with the nominal exchange rate volatility and the real exchanvolatility respectively. Both tests of Canada (panel A) show only one significant cograting vector at 5% or above level. This is true of both the trace test and the maxeigenvalue test. Thus results indicate a long-run equilibrium relationship between thexport from the United States to Canada, real Canadian income, the export price ratween the two countries and exchange rate volatility. In both cases four lags are ain the VAR and the diagnostic tests fail to show any significant serial correlation. Reindicate the presence of non-normal residuals but, as indicated byGonzalo (1994), theperformance of the Johansen method is still robust even when the errors are non-no

The Japanese results are shown inTable 4, panel B. Both cointegration tests shotwo significant vectors using the nominal exchange rate (between the dollar and thvolatility.17 Number of lags applied is six. In the second test only one non-zero vecindicated.18 Eight lags are applied in the VAR in the second test. Results indicate arun equilibrium relationship between real export from the United States to Japan adeterminants (including the exchange rate volatility). No significant serial correlatiindicated but the residuals are non-normal again in both tests.

13 As indicated byHarris (1995) and Johansen (1992), the choice of deterministic component in the modelvital consequences for the asymptotic distribution of the rank test statistics. It is vital in cointegration tdetermine the rank and the specification of the deterministic component of the model.

14 According toCheung and Lai (1993), the trace test shows more robustness to both skewness andkurtosis in the residuals than the maximum eigenvalue test. Further, according toKasa (1992), the trace test tendto be more powerful than the maximum eigenvalue test when the eigenvalues are evenly distributed.

15 Starting with a maximum length of 12 lags, lags were eliminated if they were insignificant (as a grouat the 10% level. According toGonzalo (1994, p. 220), the cost of overparametrizing by including more lagssmall in terms of efficiency but this is not true if it is underparametrized.

16 We checked to determine the components, and results indicated the presence of a deterministic trenresults are available on request.

17 According toDickey et al. (1991) and Johansen and Juselius (1990), the larger the number of non-zevectors, the more stable is the system. More than one significant vector implies that the economic sysstationary in more than one direction.

18 Tests involving the real exchange rate (between the dollar and the yen) volatility indicate one signvector by mean of the trace test but not using the maximum eigenvalue test. As stated earlier, the tracebe more robust than the maximum eigenvalue test.


ues

ns ofeach

. Thee).ationscases.xportscating

testsoses

cks upde and

Table 4Cointegration results of Canada and Japan

Vectors Max eigenvalue test Trace test Eigenval

A. CanadaNominal exchange rate volatilityLags= 4, trace correlation= 0.192, autocorrelation LM(4),χ2(16) = 7.33, normalityχ2(8) = 285.34a

r = 0 68.86*** 88.24*** 0.2094r 1 15.40 19.38 0.0512r 2 3.62 3.98 0.0123r 3 0.35 0.35 0.0012

Real exchange rate volatilityLags= 4, trace correlation= 0.116, autocorrelation LM(4),χ2(16) = 6.793, normalityχ2(8) = 222.18a

r = 0 31.80** 44.08*** 0.1028r 1 7.95 12.28 0.0268r 2 4.04 4.33 0.0137r 3 0.29 0.29 0.0010

B. JapanNominal exchange rate volatilityLags= 6, trace correlation= 0.247, autocorrelation LM(4),χ2(16) = 18.360, normalityχ2(8) = 390.33a

r = 0 28.00** 60.00*** 0.0917r 1 22.72** 32.00** 0.0751r 2 6.03 9.27 0.0205r 3 3.25 3.25 0.0111

Real exchange rate volatilityLags= 8, trace correlation= 0.273, autocorrelation LM(4),χ2(16) = 20.98, normalityχ2(8) = 281.65a

r = 0 21.18 49.91** 0.0707r 1 15.53 28.73 0.0523r 2 10.23 13.20 0.0348r 3 2.97 2.97 0.0120

a Implies rejection of the null at the 5% level.** Significant at the 5% level.

*** Idem., 1%.

6. The normalized equations and long-run elasticities

The estimated cointegrating vectors are given economic meaning by meanormalizing on the real exports. The normalized equations are obtained by dividingcointegrating vector by the negative of the cointegrating vector on real exportssignificance of the variables is tested by means of the likelihood ratio test (chi-squar

Table 5panel A presents the normalized equations for Canada and panel B the equfor Japan. The sign and size of the coefficients are not consistently the same in allOnly the real income consistently imposes an expected positive effect on the real ein all tests. In the case of Canada the income coefficients are relatively large india prominent effect of income on the United States exports. In both the Canadianthe real income is significantly different from zero. The exchange rate volatility impa significant inverse effect on exports in both the Canadian tests. This result baresults from previous studies that also indicate an inverse relationship between tra


largen. The

ive inlatility

s realn. Also,f theThus,xports.st, thesometility.

givenel canbles.more

upon

Table 5Normalized equations and long-run elasticities

A. CanadaNominal exchange rate volatility

X∗∗∗ = 6.259Y ∗∗∗ + 5.549P ∗∗∗ − 16.95V ∗∗∗(12.45) (13.19) (7.57) (63.69)

Real exchange rate volatilityX∗∗∗ = 3.201Y ∗∗∗ − 1.015P ∗∗∗ − 0.312V ∗∗∗(23.51) (19.95) (4.53) (15.63)

B. JapanNominal exchange rate volatility

X∗∗∗ = 0.743Y ∗∗∗ − 0.110P ∗∗∗ + 0.156V ∗∗∗(17.37) (7.97) (13.74) (12.17)

Real exchange rate volatilityX∗∗∗ = 0.309Y + 0.645P − 0.121V ∗∗∗(9.84) (1.15) (2.01) (5.51)

Notes: Data in parentheses in the normalized equations areχ2 statistics (likelihood ratio test).X = log of real exports,Y = log of real income,P = log of price ratio, andV = log ofexchange rate volatility.*** Significant at the 1% level.

exchange rate uncertainty. In absolute value the size of the coefficient is relativelyin the nominal exchange rate equation and small in the real exchange rate equatioprice ratio is also significant in both tests. The coefficient on the price ratio is positthe nominal exchange rate volatility test and negative in the real exchange rate votest.

The Japanese normalized equations are also shown inTable 5. Only in the first test,using the nominal exchange rate (between the dollar and the yen) volatility, doeJapanese income impose a significant effect on the United States exports to Japain the first test (nominal) exchange rate volatility impose a direct effect. The size ovolatility coefficient is less than unity (in absolute value) in both Japanese tests.Japan provides some evidence of a direct effect of exchange rate volatility on real eOnly in the first test does the price ratio impose an inverse effect. In the second teprice ratio is insignificant along with real income. Results from Canada and Japan toextent echo previous research findings of a negative effect of the exchange rate vola

7. Causality between real export and its determinants

Cointegration also implies that the transitory components of the series can bea dynamic error correction representation, i.e. a constrained error correction modbe applied that captures the short-run dynamic adjustment of cointegration varia19

The constrained error correction model allows for a causal linkage between two or

19 SeeEngle and Granger (1987)for a detailed discussion of the error correction modelling strategy basedthe information provided by cointegrated variables.


two. The

,

urcest-ntionallibriumturedalng-runong-

nottricallynatory

todns ofinating

themodell left

s with

hange

ing the

riable,s, thevalue

ht-hand

nstance,ecision

variables stemming from a common trend or equilibrium relationship. As long asor more variables are cointegrated, causality must exist in at least one directionmethodology applied in this paper follows theHendry’s (1987)“general-to-specific”paradigm. In the present context the following representation is implied:

(7)Xt = C + A(L)Xt + θ1ECt−1 + εt ,

whereC is a vector of constant terms,A(L) is a matrix of finite order of lag polynomialsX = log(X,Y,Pr ,V ), θ1 is a vector of coefficients,ECt−1 = ln(X)t−1 − δ1 lnYt−1 −δ2 lnPr,t−1 − δ3 lnVt−1 with the estimatesδ1, δ2 andδ3.

Within a constrained error correction model, causality may arise from two so(Granger, 1988). The second term on the right-hand side ofEq. (7) represents the shorterm dynamic interaction between real exports and its determinants, and the convetests of causality may be based on the significance of these terms. The disequiadjustment of each variable towards its long-run equilibrium value is then capby the error correction term,ut−1, with the coefficient of this term in each individuequation depending on the speed of adjustment of the variable towards its loequilibrium value; the coefficient (θ1) represents the speed of adjustment towards the lrun equilibrium.20 If this coefficient is insignificant then the dependent variable doesadjust to correct departures from equilibrium. In these models a variable is economeexogenous only if the lagged changes in the dependent variables provide explapower.

Initially, zero to eight lags of the first difference of each variable inEq. (7), a constanterm (C) and one lagged error correction term (EC) generated from the Johansen methare applied.21 Then, as required by the general-to-specific method, the dimensiothe parameter space were reduced to final parsimonious specifications by eliminsignificant coefficients or imposing statistically insignificant coefficients. Undergeneral-to-specific approach, diagnostic tests of the statistical adequacy of thecomes first, with an examination of inferences for the theory drawn from the modeuntil after a statistically adequate model has been found(Brooks, 2002).22

Tables 6–9present the error correction results. In order to save space, only resultthe real export (first difference) as the dependent variable is provided.23 Tables 6 and 7present the Canadian results with the nominal exchange rate volatility and real excrate volatility respectively. In both tests, the one lagged error term (ECt−1) is significantand has the proper negative sign. Significance of the error term implies that overlook

20 With the cointegrating vector normalized on real exports, in which real exports is the dependent vathe associated element ofθ1 represents the speed of adjustment directly. In the remaining equationcorresponding elements ofθ1 represent the ratio of speed of adjustment of the relevant variables to theof its associated coefficient in the cointegration relationship.

21 In case of the dependent variable (change in the real export) one to eight lags are applied in the rigside of the equation.

22 The general-to-specific method may not be practical for small or moderate sample sizes. In such ithe large number of explanatory variables will imply a small number of degrees of freedom. Also, the dabout which variables to drop may have profound implications for the final specification of the model(Brooks,2002).

23 The remaining results are available on request.


Table 6Error correction test results. Canada: nominal exchange rate volatility

Lags Constant EC1 CX CY CPR EXV

0 0.2675 – 1.0067∗∗∗ −0.9220∗∗ 0.0500∗(0.949) (3.139) (−2.349) (1.745)

1 −0.0019∗ −0.4543∗∗∗ 0.6801∗∗ −0.8871∗∗ –(−1.9045) (−7.781) (2.090) (−2.245)

2 −0.5770∗∗∗ 0.9163∗∗ – –(−9.230) (2.885)

3 −0.4703∗∗∗ – – –(−7.630)

4 −0.5943∗∗∗ – – –(−9.719)

5 −0.1731∗∗∗ – – –(−2.772)

6 −0.1218∗∗ – – –(−2.119)

7 – – – –8 – – – –

Diagnostics:R2 = 0.399; Durbin–Watson, DW= 1.99; Jarque–Bera, JB= 2.196; serial correlation test LM=χ2(6) = 4.615; ARCH—autoregressive conditional heteroscedasticity of the residuals: ARCHχ2(1) = 0.939,ARCH χ2(3) = 6.993; Reset test—Ramsey’s specification error statistics F(1, 286)= 1.26; Chow test—structural stability test F(8, 284)= 1.92.∗,∗∗,∗∗∗ Significant at the 10%, 5% and 1% level, respectively.

Table 7Error correction test results. Canada: real exchange rate volatility

Lags Constant EC1 CX CY CPR EXV

0 −0.6500 – – – –(−1.421)

1 −0.0512∗∗ −0.3691∗∗∗ 0.8836∗∗∗ – –(−2.451) (−5.794) (2.732)

2 −0.5342∗∗∗ – – –(−8.044)

3 −0.4290∗∗∗ – – –(−6.714)

4 −0.5553∗∗∗ – – –(−8.985)

5 −0.1339∗∗ – – –(−2.128)

6 −0.0998∗ – – –(−1.712)

7 – – – –8 – – – –

Diagnostics:R2 = 0.367, DW= 1.97, JB= 2.320, LMχ2(6) = 5.17, ARCHχ2(1) = 0.191, ARCHχ2(3) =0.772, Reset test F(1, 286)= 1.34, Chow test F(8, 284)= 1.089.∗,∗∗,∗∗∗ Significant at the 10%, 5% and 1% level, respectively.


cationrlong

placef thechange

g-runall inrt run.xporttivelyhangendges inat realfficientbothability,

latilityy testctorsminal

cointegration relationship between the variables would have introduced misspecifiin the underlying dynamic structure(Arize et al., 2000). The significance of the erroterm implies causality from all four independent variables to the real exports in therun. In Table 6, the size of the coefficient on the lagged error term (−0.0019) indicatesthat 0.19% of the adjustment of real exports towards the long-run equilibrium takesper month; this is a relatively slow rate of adjustment. According to the dynamics oequations, changes in real export, changes in the real income, relative prices and exrate volatility have significant short-run effects on real exports, in addition to the loneffects. The short-run effect of the nominal exchange rate volatility is positive but smsize (0.05). The real income imposes a larger effect than the price ratios in the shoIn Table 7, using the real exchange rate volatility the speed of adjustment of real etowards the long run equilibrium is 5.12% per month. This adjustment rate is relafaster than the one using the nominal exchange rate volatility. Using the real excrate volatility (Table 7), no significant short-run effect is found for the price ratio athe exchange rate volatility. There is evidence of short-run effect imposed by chanexchange rate volatility and real income. Results from both tests also indicate thexport of the United States to Canada is not econometrically exogenous. The coeof correlation (R2) in both tests ranges between 0.35 and 0.40. In addition, intests diagnostic statistics for serial correlation, abnormal residuals, structure instheteroscedasticity and linearity assumption are satisfactory.

Tables 8 and 9present the Japanese results using nominal exchange rate voand real exchange rate volatility respectively. In the nominal exchange rate volatilit(Table 8), two error corrections terms are applied as two significant cointegrating vewere found. The speed of adjustment is relatively high, 4.0% per month using no

Table 8Error correction test results. Japan: nominal exchange rate volatility

Lags Constant EC1 EC2 JX JY JPR EXV

0 0.8512*** – – – – – –(4.472)

1 −0.0403* −0.2125*** −0.4368*** – – −0.0822**

(−1.680) (−5.502) (−7.476) (−2.506)2 −0.3852*** – – –

(−6.594)3 −0.1900*** – −0.7532** –

(−3.500) (−2.450)4 – – – –5 – – – –6 – – – –7 – – – –8 – – – –

Diagnostics:R2 = 0.366, DW= 2.02, JB= 1.38, LMχ2(6) = 8.44, ARCHχ2(1) = 1.93, ARCHχ2(3) = 3.33,Reset test F(1, 286)= 0.0008, Chow test F(8, 284)= 1.40.


*** Idem., 1%.


short-usingesshort-

latility,latilitytricallys all

s beenationaltility)changeof thece isateonshipio andange

Table 9Error correction test results. Japan: real exchange rate volatility

Lags Constant EC1 JX JY JPR EXV

0 0.3082*** – – – –(4.854)

1 −0.1937** −0.4872*** – – –(−4.732) (−8.138)

2 −0.4056*** – – –(−6.880)

3 −0.2200*** – – 0.1103**

(−4.024) (2.189)4 – 0.3587* −1.1345*** –

(1.652) (−2.727)5 – – – –6 – – – –7 – – – –8 – – – –

Diagnostics:R2 = 0.355, DW= 2.00, JB= 1.29, LM χ2(6) = 9.07, ARCHχ2(1) = 0.864, ARCHχ2(3) =1.460, Reset test F(1, 286)= 0.70, Chow test F(8, 284)= 0.644.


*** Idem., 1%.

exchange rate volatility and 19.4% per month using real exchange rate volatility. Therun dynamics indicate a lack of short-run effect of real income on real export whennominal exchange rate volatility in the test (Table 8). The exchange rate volatility imposa significant negative short-run effect. Thus, exchange rate volatility imposes both arun and a long-run negative effect on real export. Using the real exchange rate voall variables impose effects on real export in the short run. The exchange rate voimposes a positive effect. The United States real export to Japan is also not economeexogenous. Once again theR2 is between 0.35 and 0.40. Also, once again in both testdiagnostic statistics are satisfactory.

8. Conclusion and implications

One of the major concerns since the introduction of the flexible exchange rate hawhether the increase in exchange rate variability (uncertainty) has affected the interntrade flow. This paper investigates the effects of the exchange rate variability (volaon the United States exports to Canada and Japan during the current flexible exrate period (1974–1998). In this paper, conditional variance of the first differencelog of the exchange rate is applied as volatility (variability). The conditional varianestimated from a univariate GARCH(1,1) model. The paper then applies the multivaricointegration method and constrained error correction models to study the relatibetween real exports and its determinants that is real income, export price ratexchange rate volatility. For both Canada and Japan, volatility of two different exch


l rateloyed.n realhangehipsimplyflowseans ofalso

is truetility

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anciallland,

. J. 12,

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LDCs.

he Big

retical

–327.cedastic

rates are applied in empirical tests. Both the volatility of the nominal and the reabetween the United States dollar and the currencies of Canada and Japan are emp

Results obtained indicate a stationary long-run equilibrium relationship betweeexports and its determinants for both Canada and Japan using all the two excrates volatility. Normalized equations indicate that in the majority of the relationsexchange rate volatility imposes a negative effect on real exports. This result maythat exchange rate variability measured by volatility dampens international tradefrom the United States to Canada and Japan. Further analysis is conducted by mHendry’s (1987)general-to-specific error correction (causality) tests. Error correctionsshow that causality does exist from the exchange rate volatility to real exports. Thisusing both the nominal and the real exchange rate volatility. Also causality from volato real export is also found in the short-run. Evidence of causality from all the determto real exports is found in the majority of the tests.

The results presented suggest that exchange rate volatility considerations are imfor modelling United States export behaviour to Canada and Japan. If policy makersthe stability of the nominal and real exchange rate between the United States dolCanada/Japan currencies, policy actions aimed at stabilizing these export markets ato generate uncertain results. Results presented in this paper advocate further resthis field using data from other countries.

Acknowledgments

I thank an anonymous referee for several useful comments and suggestionremaining errors and omissions are my responsibility alone.

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