The Spot-forward Exchange Rate Relation And International .
THE SPOT-FORWARD EXCHANGE RATE RELATION ANDINTERNATIONAL MARKET CONDITIONSMatt McPherson, Gonzaga UniversityJohn Vilasuso, West Virginia UniversityABSTRACTThis paper examines whether the relation betweenspot and forward exchange rates is stable, and if not,the implications for international market conditions.We document structural breaks for the U.S. and U.K.currencies vis-a-vis the Canadian dollar. We considertwo applications in an effort to determine theconsequences of this structural change in internationalasset and goods markets. First, we find that thedynamic structure linking stock return volatility acrosscountries is affected by change in the spot-forwardrelation, and second the elasticity of Canadian importdemand with respect to spot exchange rates has alsobeen affected by this change.INTRODUCTIONSince the collapse of the Bretton Woods system offixed parities in the early 1970s, the forward exchangerate has assumed a primary role in hedging againstfluctuations in future spot exchange rates. Theeffectiveness of hedging currency risk, however,depends in part on the relation between spot andforward exchange rates. If, for example, the forwardrate is used to predict future spot exchange rates, theninstability in the spot-forward exchange rate relationproduces larger forecast errors. Tong (1996) and Briysand Solnick (1992) show that in the context of adynamic hedging model, larger forecast errors reducethe benefits of hedging currency risk. 1 Consequently,1The effects of instability in the spot-forwardexchange rate relation can also be interpreted in termsof a risk premium. In the absence of news, for example,larger forecast errors are associated with a higher riskpremium (see, e.g. Fama 1984). This is confirmed inempirical studies by Wolff (1987) and Nijman, Palm,and Wolff (1993) who report that approximately halfof the forecast error is due to variation in the riskpremium.structural change in the spot-forward exchange raterelation may affect trade in international asset andgoods markets. The objectives of this paper are thustwofold. First, we empirically examine whether thelong-run relation between spot and forward exchangerates is stable over the post-Bretton Woods era,2 andsecond we explore the implications for internationalmarket conditions should the spot-forward relationexhibit structural change.Stability of the spot-forward exchange raterelation is examined using the test developed byHansen (1992) based on the fully modified estimatorof Phillips and Hansen (1990). This methodology isparticularly appealing in exchange rate studies for anumber of reasons. First, we focus on the long-run orcointegrating relation between spot and forwardexchange rates. Because numerous studies support theclaim that these series are cointegrated, the regressoris necessarily endogenous.3 The fully modifiedestimator - in contrast to ordinary least squares corrects for endogeneity bias.4 Second, there is noneed to specify a priori the timing of structuralchange. Instead, the testing methodology evaluates the(alternative) hypothesis of a break of unknown timing.2Surprisingly little work has examined whether the spotforward exchange rate relation is stable. One exception isa recent paper by Sakoulis and Zivot (1999). Sakoulisand Zivot focus on the forward premium and documentmultiple structural breaks. A key difference between thiswork and our paper is that we empirically estimate thelong-run relation between spot and forward exchangerates, rather than restricting it to be a (1 - 1)cointegrating vector.3See, for example, Hakkio and Rush (1989), Liu andMaddala (1992), Naka and Whitney (1995), and Norrbinand Reffett (1996).4Norrbin and Reffett (1996) also recognize the effects ofinvalid exogeneity assumptions on cointegrationanalysis.282005 Proceedings of the Midwest Business Economics Associationʹ′
This is a more reasonable description of post-Brettonfor future research.Woods exchange rate data as it would be difficult toTHE SPOT-FORWARD EXCHANGEjustify a particular break date a priori. And third,RATE RELATIONbecause we focus on the cointegrating relationbetween the spot and forward rate, inference may beThis section is divided into two parts. In the first part,complicated due to serial correlation orwe present a brief description of the structural breakheteroskedasticity which is commonly detected intest developed by Hansen (1992), and in the secondexchange rate data (see, e.g. Bollerslev 1990; Fongpart, we apply this technique to Canadian exchangeand Ouliaris 1995). The fully modified testingrate data for the post-Bretton Woods period.methodology eliminates concern as it includes arobust estimator of the covariance matrix.A. Structural Stability TestWe document a structural break in the longHansen’s (1992) structural stability test is based on therun relation between spot and forward exchange ratesfully modified (FM) estimator developed by Phillipsfor both the U.S. and U.K. currencies vis-a-vis theand Hansen (1990). The FM parameter estimates areCanadian dollar. And perhaps more important, weobtained in two steps. In the first step, ordinary leastfind that these structural breaks have importantsquares (OLS) is used to obtain an initial estimate ofimplications for international asset and goods marketthe parameter vector, and in the second step, aconditions. The first application we explore concernssemiparametric adjustment is made to correct forthe correlation between international stock marketparameter bias induced by endogeneity of thevolatility. Bodart and Reding (1999) study the impactregressors. The importance of the semiparametricof the exchange rate regime - and the accompanyingadjustment is alluded to by Banerjee et. al. (1986) whodegree of exchange rate volatility - on the correlationpresent Monte Carlo evidence that OLS parameterbetween time-varying stock market volatilities. Here,bias can be large in finite samples.we adopt their methodology and ask whether returnvolatility is also effected by the nature of the spotLet st and f t be the spot and forward exchangeforward exchange rate relation. Empirical results findrate, respectively. Also, suppose that each series is I(1)that this is indeed the case, suggesting that volatilitywhich is almost unanimously reported in recentlinkages between international stock markets dependexchange rate studies. A cointegrating relation isin part on the spot-forward exchange rate relation.The second application we consider iscaptured by st A xt u t(1)bilateral trade flows. Because the effectiveness ofwhere xtʹ′ (1 f t ) for t 1,.,Tandhedging currency risk depends in part on the relationA [ a0 a1 ] . Let Δ f t vt such that vt is a meanbetween spot and forward exchange rates, a structuralzero covariance stationary series. Following thebreak is expected to affect the sensitivity of imports tonotation presented by Hansen (1992), definecurrency values. We follow the empirical specificationpresented by Deyak, Sawyer, and Sprinkle (1993), butandthematricesz tʹ′ ( u t vt )augment the import demand model to allow for theinfluence of a structural break in the spot-forwardexchange rate relation. Empirical results show that astructural break does affect the elasticity of Canadianimport demand with respect to exchange rates.The remainder of the paper is organized asfollows. In the next section we present a brief outlineof Hansen’s (1992) structural break test and reportresults for the country pairs Canada-U.S. and CanadaU.K. In Section 3, we explore two applications in aneffort to determine whether a break in the spotforward exchange rate relation affects internationalreturn volatility correlations and import demand. Thefinal section concludes and discusses possible avenues292005 Proceedings of the Midwest Business Economics Association
lim 1 T Tlim 1 T tΩ E( z j z t ʹ′ ) and Λ E( z j ztʹ′ ).T T t 1 j 1T T t 1 j 1Partitioned with conformity with z t , letΩuu ΩuvΛuu ΛuvΩ [] and Λ [].Ωvu ΩvvΛvu Λvv(2)(3)Finally, define-1Ωu.v Ωuu - Ωuv Ωvv Ωvu and -1(4)Λvu Λvu - Λvv Ωvv Ωvu . The term Ωu.v is the long-run variance of u t conditional on vt , and Λvu measures the extent of parameter biasdue to endogeneity of f t .In the first step, we use OLS to obtain parameter estimates of the cointegrating vector  and the residualszˆtʹ′ ( uˆt Δ f t ) . In the second step, estimates of the matrices shown in (3) are obtained. This is accomplished byestimating a VAR for pre-whitened values of zˆt ʹ′ , and estimates of Ω̂ and Λ̂ are obtained by recoloring. TheFM estimator of the cointegrating vector is 1T Tˆ ' x x' Aˆ t st xt' (0Λvu t t t 1 t 1 -1where st st - Ω̂uv Ωvv vt . The FM residuals are then u t st - Aˆ xt .)(5)The possibility of a structural change in the cointegrating relation is evaluated using a Wald-type test. Forexample, suppose a change occurs at time τ such that At A1 for t τ , and At A2 for t τ . If the timingof the break is known, then the null hypothesis A1 A2 is evaluated using-1-1ˆ u.v}F nt tr{ S nʹ′t V nt S nt Ωwheret vu(6)tˆ )ʹ′) , V nt M nt - M nt M -1nn M nt , and M nt x m x mʹ′ .S nt ( x m uˆ - (0 Λ ʹ′mm 1m 1Essentially, F nt is a Wald test where A1 and A2 correspond to subsample parameter estimates and the fullsample variance is used to construct the test statistic. If the timing of the break is unknown - as is usually the casein practice - then the null hypothesis is evaluated using SupF sup (t/T) Θ F nt(7)where Θ is a compact set of (0,1). In the empirical work to follow, we follow the suggestion of Andrews (1991)and set Θ [0.10, 0.90] . Critical values for SupF are tabulated by Hansen (1992). As noted by Hansen,the SupF test is appropriate for examining the existence of an abrupt change in the long-run relation betweenspot and forward exchange rates.2005 Proceedings of the Midwest Business Economics Association30
B. Empirical ResultsData were obtained from Statistics Canada andconsist of monthly spot and 90-day forward exchangerates for the U.S. and the U.K. currencies vis-a-vis theCanadian dollar. The sample begins on June 1970which corresponds to the official date beginning thefloating period. The data end in December 1999.Unit root tests (not shown) find that spot andforward exchange rates are I(1), which is consistentwith previous studies. Plots of F nt are shown inFigures 1 and 2. Estimates are based on prewhiteningzˆt using a VAR(1). Heteroskedastic andautocorrelation consistent estimates of Ω̂ and Λ̂ usea Barlett kernel where the bandwidth parameter is setaccording to the guidelines presented by Andrews(1991). The 5-percent critical value for SupF is alsoshown. Beginning with results for the U.S. dollarshown in Figure 1, the SupF test points to theexistence of a statistically significant structural breakin the spot-forward exchange rate relation at the 5percent level. A break is also evident for the U.K.currency as Figure 2 illustrates that the SupF statisticexceeds its 5-percent critical value.The magnitude of the SupF statistics alongwith p-values are collected in Table 1. P-values arecomputed using the polynomial approximationprovided by Hansen (1992). The timing of the breakis also reported which corresponds to the date atwhich F nt achieves its maximum value. In the case ofthe U.S. currency, the break in the spot-forwardexchange rate relation occurs in March 1975, whilethe break date for the U.K. currency occurs almosttwo years later: February 1977.FM parameter estimates of the intercept ( a0 ) and theslope ( a1 ) terms included in the vector A arecollected in Table 2. For comparison, OLS estimatesare also shown. Differences between the estimatedparameters is due to endogeneity bias associated withOLS estimation. That is, parameter differences can beattributed to the semiparametric adjustment shown inexpression (5) for the FM estimator that corrects forendogeneity bias. For the full sample shown in panelA, the effects of regressor endogeneity are moreapparent for the U.K. currency. For example, theintercept term is almost five times larger when FMestimation is used. In contrast, endogeneity bias isnegligible for the slope parameter as the FM and OLSestimates are almost identical.To examine the influence of the structuralbreaks, we re-estimate the spot-forward exchange raterelation for the subperiods defined by the break datesshown in Table 1. Parameter estimates are shown inpanels B and C of Table 2. For both FM and OLSestimation, there are notable differences in theparameter estimates. Results for the U.K. currency forthe two subperiods are consistent with the work ofSakoulis and Zivot (1999) on the forward premium.5For instance, the restriction that spot and forwardexchange rates are linked by a (1 - 1)ʹ′ cointegratingvector is not rejected for each subperiod. In this case,observed differences in the estimated values of theintercept term can be interpreted as structural changein the forward premium. Parameter estimates for thesubperiods are also very different for the U.S. dollar.But in the case of the U.S. dollar, both the slope andintercept change. For example, the null hypothesisthat U.S. spot and forward exchange rates are linkedby a (1 - 1)ʹ′ cointegrating vector is rejected, and therestriction that slope estimates are the same acrosssubperiods is also rejected for both estimationmethods. In addition, the estimated value of theintercept term is also statistically different acrosssubperiods.APPLICATIONSOur objective in this section is to determine whetherthe detected breaks in the spot-forward exchange raterelation have affected conditions in international assetand goods markets. Two applications are consideredin turn.A. International Stock Market CorrelationsIn a recent paper, Bodart and Reding (1999)5A key result presented by Sakoulis and Zivot (1999) isthat structural change in the forward premium mayexplain the forward premium puzzle. This anomaly refersto the common finding that the forward exchange rate isnot an unbiased predictor of future spot exchange rates(see Engel 1996 for a review of this literature). Sakoulisand Zivot show via Monte Carlo simulations that if a truestructural change is ignored, then a rejection of theforward rate unbiasedness hypothesis may be traced toparameter bias.312005 Proceedings of the Midwest Business Economics Association
show that for a sample of European countries, theexchange rate regime influences the correlationbetween asset return volatilities. In this part, we adopttheir methodology and ask whether a structural breakin the spot-forward relation has affected cross countrystock market volatility correlations. A bivariateGARCH(1,1)modelisspecified:(8)r t µ ρ r t -1 et** ***r t µ ρ r t - 1 et2ht k γ et -1 η ht -1*2* ****ht k γ ( et -1 ) η ht -1ijt*t(9)(10)(11)1/2(12)h [r ξ Bt ] [ ht h ]where r t are Canadian returns, r*t are foreign returns(either U.S. or U.K.), and ϕ t N(0, H t )where ϕ t ʹ′ ( et e*t ) and vech( H t ) ( ht hijt h*t )ʹ′ .We adopt the constant correlation specification ofBollerslev (1990) as shown in (12), but also includethe influence of structural change in the spot-forwardrelation which is captured by the parameter ξ . Anindicator variable Bt is used such that we set Bt 1before the break dates shown in Table 1, and Bt 0otherwise. Note that if ξ 0 , the model reduces tothe constant correlation, r , specification.The model is estimated using quasi-maximumlikelihood. Stock return data consist of monthly indexreturns including dividends, and were obtained fromthe Morgan Stanley database. Parameter estimates areshown in Table 3. Focusing on ξ , empirical resultssupport the claim that cross-country return volatilitycorrelations are affected by structural change in thespot-forward exchange rate relation at the 5-percentsignificance level for the U.K., and at the 10-percentlevel for the U.S.6This influence, however, is very different for thecountry pairs. Bodart and Reding (1999) suggest thattheory can explain both a positive and a negative6The bivariate GARCH(1,1) model appears toadequately fit the data. Ljung-Box tests applied to thesquared standardized residuals do not indicate thepresence of statistically significant serial correlation.estimate of ξ . During periods of high exchange ratevolatility, contagion effects are more likely due tonoise trading or herd behavior. Therefore, investorsare more apt to use international markets to discerndomestic market conditions, and a positive relationbetween asset market volatility correlation andexchange rate volatility is anticipated. On the otherhand, consider a situation where exchange ratevolatility is lower, possibly due to credibleinterventionist policies. In this situation, fundamentalsare more important which ultimately leads to greatervolatility correlation, thereby supporting an inverserelation. For the exchange rates examined here, wefind statistically significant higher exchange ratevolatility after the break dates. Specifically, squared(log differences) spot exchange rates are higherfollowing the break in the spot-forward exchange raterelation (not shown). Results then summarized inTable 3 are consistent with the ‘fundamentals’explanation for the U.S. market, but results for theU.K. are supportive of the ‘contagion’ explanation. Inany event, empirical evidence summarized in Table 3illustrates that the relation between spot and forwardexchange rates in part shapes volatility patternsobserved in international stock markets.7B. Import DemandIn this part we estimate Canadian import demandboth before and after the break date in the spotforward exchange rate relation. Because the change inthe spot-forward exchange rate relation influences theeffectiveness of hedging, we focus on whether thesensitivity of import demand to spot exchange rateshas changed. The empirical model is due to Deyak,Sawyer, and Sprinkle (1993)7As noted by Bodart and Reding (1999), it ispossible that a volatility effect - correlations betweenmarkets is higher due to higher stock market volatility - isdriving the main results reported in Table 3. To checkthis, we estimated univariate GARCH(1,1) models foreach index return series both before and after the breakdates reported in Table 1. We find no evidence that returnvolatility is higher since the break date at conventionalsignificance levels.2005 Proceedings of the Midwest Business Economics Association32
ln mt b0 b1 ln y t b 2 ln p t b3 ln p*t12 b4 ln s t δ i Di vt(13)2where mt is real Canadian imports, y t is realdomestic income measured by theCanadianindustrial production index, pt is the domestic price*measured by the Canadian wholesale price index, p tis the foreign price measured by the foreign wholesaleprice index, st is the spot exchange rate (measured asunits of foreign currency per Canadian dollar), Di is aset of monthly seasonal dummies, and vt is a meanzero disturbance term.8 Import and exchange rate datawas obtained from Statistics Canada. Remaining datawas obtained from the IFS database.The Canadian import demand equation forthe U.S. is augmented to include the influence of tradeagreements and major changes in tax policy. Weinclude the indicator variable NAFTA to capture theeffects of the North Amercan Free Trade Agreementin 1996. The trade agreement variable takes on a valueof one after the agreement is in place and zero before.We also include the variable GST to pick up theinfluence of the Goods and Service Tax (GST). TheGST variable is equal to one after the GST was put inplace, and zero before. Our reasoning for includingthis variable is that Canadian imports include travelspending which has been shown to be influenced bythe introduction of the GST, and in the case of theU.S., Canadian travel spending has at times accountedfor almost 10 percent of Canadian merchandiseimports (Vilasuso and Menz 1998). In contrast,Canadian travel spending in the U.K. is negligible, andas a result, the GST indicator variable is not includedin the estimated import demand equation.Parameter estimates are collected in Table 4.98Consistent with the work of Deyak, Sawyer, andSprinkle (1993), we find that the variables included in(13) are I(1) and evidence of a cointegrating relation (notshown). Thus, we also estimate the model in level form.9Consistent with the work of Senhadji and Montenegro(1999) on trade flows, there is little difference betweenOLS and FM parameter estimates for the import demandmodel. As a result, we report OLS estimates so as tofacilitate comparison with existing studies. See Deyak,Sawyer, and Sprinkle (1993) for a review of thisempirical literature.The import elasticity with respect to spot exchangerates is very different across subperiods. For eachestimated import demand equation, the volume ofCanadian imports appears largely unaffected by spotexchange rates before the break in the spot-forwardexchange rate relation, as parameter estimates are notsignificantly different from zero. But following thebreak dates, import demand is significantly related tospot exchange rates. These finding are consistent withthe notion that the effectiveness of hedging currencyrisk in the forward market is reduced, making importdemand more sensitive to spot exchange rates.10CONCLUSIONUsing the structural break test developed by Hansen(1992), we document a statistically significant changein the spot-forward exchange rate relation for the U.S.and U.K. currencies vis-a-vis the Canadian dollar.One implication of the structural break is that theeffectiveness of hedging currency risk is affected,which has important implications for conditions ininternational asset and goods markets.In this paper we explore two applications toillustrate this point. The first application concerns thecorrelation between return volatility acrossinternational stock markets. We find that the dynamicstructure linking international stock market volatility isaffected by change in the spot-forward exchange raterelation. The second application investigates Canadianimport demand. Because the effectiveness of hedgingis affected by structural change in the spot-forwardexchange rate relation, it is reasonable to conjecturethat the import elasticity with respect to spotexchange rates has also changed. Empirical evidencedoes indeed support this claim.The results of this paper can be extended in a numberof ways. For example, recent studies suggest thatworking with disaggregated trade data may yieldimportant insights. McKenzie (1999), in a survey ofthe literature, reports that restricting import demandelasticities across commodities is often rejected. At10Parameter estimates for the remaining determinants arein line with those reported by Deyak, Sawyer, andSprinkle (1993). Also consistent with their work, we findthat consumers respond differently to changes indomestic prices and foreign prices, therefore rejectinghomogeneity in prices.332005 Proceedings of the Midwest Business Economics Association
the very least, the sensitivity of import demand toexchange rates is likely to differ between durable andnondurable goods (see, e.g. Lee 1999). Anotherextension involves delving more deeply into assetmarket conditions to determine how ‘fundamentals’and ‘contagion’ effects are translated acrossinternational stock markets. We leave these topics forfuture work.REFERENCESBollerslev, T., 1990. Modeling the coherence in shortrun nominal exchange rates: A multivariategeneralized ARCH model. Review of Economicsand Statistics 72, 498-505.Bollerslev, T., Wooldridge, J. M., 1992. Quasimaximum likelihood estimation and inference indynamic models with time varying covariances.Econometric Reviews 11, 143-172Briys, E., Solnick, B., 1992. Optimal currency hedgeratios and interest rate risk. Journal ofInternational Money and Finance 11, 431-445.Deyak, T.A., Sawyer, W.C., Sprinkle, R.L., 1993. Theadjustment of Canadian import demand tochanges in income, prices, and exchange rates.Canadian Journal of Economics 26, 890-900.Engel, C., 1996. The forward discount anomaly andthe risk premium: A survey of recent evidence.Journal of Empirical Finance 3, 123-191.Fama, E.F., 1984. Forward and spot exchange rates.Journal of Monetary Economics 14, 319-338.Fong, W.M., Ouliaris, S., 1995. Spectral tests of themartingale hypothesis for exchange rates. Journalof Applied Econometrics 10, 255-271.Phillips, P.C.B., Hansen, B.E., 1990. Statisticalinference in instrumental variables regressionwith I(1) processes. Review of Economic Studies57, 99-125.Sakoulis, G., Zivot, E., 1999. Time-variation andstructural change in the forward discount:Implications for the forward rate unbiasednesshypothesis. University of Washington WorkingPaper.Senhadji, A.S., Montenegro, C.E., 1999. Time seriesanalysis of export demand equations: A crosscountry analysis. IMF Staff Papers 46, 259-273.Tong, W.H.S., 1996. An examination of dynamichedging. Journal of International Money andFinance 15, 19-35.Vilasuso, J., Menz, F., 1998. Domestic price,(expected) foreign price, and travel spending byCanadians in the United States. Canadian Journalof Economics 31, 1139-1153.Wolff, C.C.P., 1987. Forward foreign exchange rates,expected spot rates, and premia: A signalextraction approach. Journal of Finance 42, 395406.Andrews, D.W.K., 1991. Heteroskedasticity andautocorrelation consistent covariance matrixestimation. Econometrica 59, 817-858.Banerjee, A., Dolado, J. J., Hendry, D. F., Smith, G.W., 1986. Exploring equilibrium relationships ineconometrics through static models: SomeMonte Carlo evidence. Oxford Bulletin ofEconomics and Statistics 48, 253-277.Bodart, V., Reding, P., 1999. Exchange rate regime,volatility and international correlations on bondand stock markets. Journal of InternationalMoney and Finance 18, 133-151.Hakkio, C.S., Rush, M., 1989. Market efficiency andcointegration: An application to the Sterling andDeutschemark exchange markets. Journal ofInternational Money and Finance 8, 75-88.Hansen, B.E., 1992. Tests for parameter instability inregressions with I(1) processes. Journal ofBusiness & Economic Statistics 10, 321-335.Lee, J., 1999. The effect of exchange rate volatility ontrade in durables. Review of InternationalEconomics 7, 189-201.Liu, P.C., Maddala, G.S., 1992. Rationality of surveydata and tests for market efficiency in the foreignexchange markets. Journal of InternationalMoney and Finance 11, 366-381.McKenzie, M.D., 1999. The impact of exchange ratevolatility on international trade flows. Journal ofEconomic Surveys 13, 71-106.Naka, A., Whitney, G., 1995. The unbiased forwardrate hypothesis re-examined. Journal ofInternational Money and Finance 14, 857-867.Nijman, T.E., Palm, F.C., Wolff, C.C.P., 1993. Premiain forward foreign exchange as unobservedcomponents: A note. Journal of Business &Economic Statistics 11, 361-365.Norrbin, S.C., Reffett, K.L., 1996. Exogeneity andforward rate unbiasedness. Journal ofInternational Money and Finance 15, 267-274.2005 Proceedings of the Midwest Business Economics Association34
Table 1. Structural break test resultsCurrency vis-a-vis theCanadian DollarSupFBreak DateU.S. Dollar14.46(0.02)March 1975British Pound12.61February 1977(0.05)Notes: P-values of the SupF test are shown in parentheses. The break date coincides withthe timing of SupF.2005 Proceedings of the Midwest Business Economics Association35
Table 2. Parameter estimatesInterceptSlopeSample PeriodFMOLSFMOLSA. June 1970 - Dec. 1999U.S. British .S. British )0.115(0.01)0.089(0.01)0.977(0.01)0.982(0.01)B. June 1970 - Break DateC. Break Date - Dec. 1999U.S. DollarBritish otes: Estimation methods are fully modified (FM) and ordinary least squares (OLS) estimation.The subsamples are defined by the break dates shown in Table 1. Robust standard errors areshown in parentheses.Table 3. Bivariate GARCH(1,1) parameter estimates2005 Proceedings of the Midwest Business Economics Association36
ParameterU.S. DollarBritish 0.222*(0.04)(0.09)Notes: GARCH(1,1) parameter estimates are based on (quasi) maximum likelihood estimation.Bollerslev and Wooldridge (1992) standard errors are shown in parentheses. A ‘*’ indicatesstatistical significance at the 5-percent level.ξ2005 Proceedings of the Midwest Business Economics Association37
Table 4. Import demand parameter estimatesImports from U.S.Imports from U.K.Variable1970-19751975-1999 1970-1977 1977-1999Constant-0.281(0.54)-0.490(0.31)ln ln pt1.898(1.00)0.266(0.19)0.574(0.31)0.775*(0.30)ln 26)ln .57)Notes: Parameter estimates are obtained from OLS estimation. Standard errors areshown in parentheses. A ‘*’ indicates significance at the 5-percent level.2005 Proceedings of the Midwest Business Economics Association38
1614125-percent critical value1086420Sep-72Sep-78Sep-84Sep-90Sep-96FIGURE 1. F nt statistics for Canada/U.S. exchange rates.2005 Proceedings of the Midwest Business Economics Association39
1412105-percent citical value86420Sep-72Sep-78Sep-84Sep-90Sep-96FIGURE 2. F nt statistics for Canada/U.K. exchange rates.2005 Proceedings of the Midwest Business Economics Association40
exchange rate data (see, e.g. Bollerslev 1990; Fong and Ouliaris 1995). The fully modified testing methodology eliminates concern as it includes a robust estimator of the covariance matrix. We document a structural break in the long-run relation between spot and forward exchange rates for both the U.S. and U.K. currencies vis-a-vis the .
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Keywords: Exchange Rate Regimes Estimation, Exchange Rate Regimes Classification, Exchange Rate Regimes, Exchange Rate Policies, and Exchange Market Pressure. 1. Introduction In order to make a sound recommendation for a country exchange rate policy, it is valuable to evaluate how well its exchange rate policies have operated in the past.
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