the monetary model of exchange rates: evidence from the canadian float of the 1950s

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Journal of Macroeconomics, Spring 1997, Vol. 19, No. 2, pp. 349–362 349 Copyright 1997 by Louisiana State University Press 0164-0704/97/$1.50 TAUFIQ CHOUDHRY PHILLIP LAWLER University of Wales Swansea United Kingdom The Monetary Model of Exchange Rates: Evidence from the Canadian Float of the 1950s * This paper applies the Johansen cointegration technique to examine the validity of the monetary model of exchange rate determination as an explanation of the Canadian dollar–United States dollar relationship over the period of the Canadian float 1950–62. A single cointegrating vector is identified whose coefficients conform in broad terms to the restrictions implied by the mon- etary model, thus lending support to the interpretation of the model as describing a long-run equilibrium relationship. This support is reinforced by the results derived from the associated error-correction model, which identify a clear short-run tendency for the exchange rate to revert to the equilibrium value defined by the estimated long-run model. 1. Introduction Despite widespread agreement that exchange rates are determined within asset markets, persuasive empirical models within the asset approach have proved notoriously difficult to construct. Although achieving some early successes (Hodrick 1978 and Dornbusch 1979), the most widely tested var- iant of the asset approach, the monetary model of exchange rate determi- nation, fails to provide a convincing explanation of exchange rate movements post-1978 (Dornbusch 1980 and Hayes and Stone 1981). Particularly dam- aging is Meese and Rogoff’s (1983) finding that, in terms of out-of-sample forecasting performance, the monetary model proves inferior to a random walk. 1 In what follows we reassess the validity of the monetary model as an explanation of exchange rate determination. The key feature of our study is its focus on the Canadian-United States dollar exchange rate during the *We thank two anonymous referees for several helpful comments and suggestions. The re- maining errors and omissions are our responsibility alone. 1 An excellent survey of empirical studies of the monetary model is provided in MacDonald and Taylor (1992).

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Journal of Macroeconomics, Spring 1997, Vol. 19, No. 2, pp. 349–362 349Copyright � 1997 by Louisiana State University Press0164-0704/97/$1.50

TAUFIQ CHOUDHRYPHILLIP LAWLER

University of Wales

Swansea

United Kingdom

The Monetary Model of ExchangeRates: Evidence from the CanadianFloat of the 1950s*

This paper applies the Johansen cointegration technique to examine the validity of the monetarymodel of exchange rate determination as an explanation of the Canadian dollar–United Statesdollar relationship over the period of the Canadian float 1950–62. A single cointegrating vectoris identified whose coefficients conform in broad terms to the restrictions implied by the mon-etary model, thus lending support to the interpretation of the model as describing a long-runequilibrium relationship. This support is reinforced by the results derived from the associatederror-correction model, which identify a clear short-run tendency for the exchange rate to revertto the equilibrium value defined by the estimated long-run model.

1. Introduction

Despite widespread agreement that exchange rates are determinedwithin asset markets, persuasive empirical models within the asset approachhave proved notoriously difficult to construct. Although achieving some earlysuccesses (Hodrick 1978 and Dornbusch 1979), the most widely tested var-iant of the asset approach, the monetary model of exchange rate determi-nation, fails to provide a convincing explanation of exchange rate movementspost-1978 (Dornbusch 1980 and Hayes and Stone 1981). Particularly dam-aging is Meese and Rogoff’s (1983) finding that, in terms of out-of-sampleforecasting performance, the monetary model proves inferior to a randomwalk.1

In what follows we reassess the validity of the monetary model as anexplanation of exchange rate determination. The key feature of our study isits focus on the Canadian-United States dollar exchange rate during the

*We thank two anonymous referees for several helpful comments and suggestions. The re-maining errors and omissions are our responsibility alone.

1An excellent survey of empirical studies of the monetary model is provided in MacDonaldand Taylor (1992).

Taufiq Choudhry and Phillip Lawler

350

Canadian float of 1950–1962. Despite its significance as a precursor to theperiod of generalized floating post-1973, this episode remains little exploredby the empirical exchange rate literature.2 Our approach employs the Jo-hansen multivariate cointegration technique (Johansen 1988) to model thelong-term relationship determining the exchange rate. This methodology isaccepted as preferable to the Engle-Granger (1987) two-step procedure,which has also been used to model exchange rate behavior (Boothe andGlassman 1987 and McNown and Wallace 1989).3 Having examined thelong-run exchange rate determination process, we then construct and esti-mate an error correction model to describe short-run dynamics.

In preview of our results, we are able to show that a stationary long-run relationship exists between the Canadian-United States dollar exchangerate and the relevant variables of the monetary model during the statedperiod. Moreover, the error correction model indicates the presence of asignificant short-run interaction between the exchange rate and othervariables.

The format of the paper is as follows. Section 2 provides a discussionof the monetary model and the theoretical background to our approach.Section 3 presents the empirical methodology and results. Finally, Section4 concludes.

2. Theoretical Background

Underlying the most basic variant of the monetary approach are twokey relationships. First, a stable demand for money function with the pricelevel, income, and the interest rate as its arguments. Second, purchasingpower parity, which is assumed to be continuously maintained via completeand instantaneous price flexibility. The reduced-form expression for the ex-change rate to which the approach gives rise is

e � (m � m*) � � (y � y*) � � (r � r*) , (1)41 2

where e is the spot exchange rate (units of domestic currency per unit offoreign currency), m is the exogenously given domestic money stock, y do-

2One notable exception to this is provided by Girton and Roper (1977), which develops amodel to simultaneously explain exchange rate movements and official intervention for Canadaover the period 1952–1974.

3MacDonald and Taylor (1994) and McNown and Wallace (1994) also apply the Johansenprocedure in their investigation of the monetary model of the exchange rate.

4Underlying (1) is the simplifying assumption of identical domestic and foreign income andinterest elasticities of the demand for money, �1 and �2, respectively.

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mestic real income and r the domestic short-term nominal interest rate.5

The foreign counterparts to these domestic variables are indicated by anasterisk. The view of exchange rate determination encapsulated in Equation(1) is usually referred to as the flexible price monetary approach. This ter-minology reflects both the emphasis placed by the approach on relativemoney supplies as a determinant of exchange rates and the key assumptionwhich underpins the model, that is, perfect price flexibility.

Frankel’s (1979) real interest rate differential model, while acceptingthe central role of relative money supplies in exchange rate determination,dispenses with the assumption of instantaneous price adjustment. The flex-ible price monetary model is then seen as determining the long-run equilib-rium exchange rate, but in the short-run sticky prices lead to departuresfrom purchasing power parity6 and hence to deviations of the current spotrate from its equilibrium value.

The crucial insight provided by Frankel’s model is that actual exchangerate movements may be decomposed into changes in the long-run equilib-rium exchange rate and disequilibrium adjustment of the current spot ratetowards this long-run value. Nonetheless, the source and form of the dise-quilibrium dynamics which underlie his approach are somewhat specific andrestrictive. More generally, we might expect lags in the demand for money,possibly money market disequilibrium, and gradual output adjustment all tocontribute towards deviations of the exchange rate from its long-run valueand provide sources of adjustment dynamics additional to that associatedwith sticky prices. Taking on board this fact leads logically to the recognitionof cointegration, error-correction methodology as the appropriate techniquefor exchange rate modeling. Implementation of this methodology allows thelong-run relationship determining the exchange rate to be estimated inde-pendently of the short-run adjustment dynamics. The latter may then beanalyzed using an error-correction model.

Following Frankel’s arguments Equation (1) is now interpreted as arelationship describing long-run equilibrium.7 Using the fact that, givenlong-run purchasing power parity and uncovered interest parity, the long-run value of the short-term interest differential is equal to the expected long-

5All variables (other than r) are expressed as logarithms.6It is widely recognized that substantial deviations from PPP can occur in the short run. The

crucial question then is whether these deviations are corrected over the longer term. This isprecisely the issue addressed by cointegration studies of the relationship between exchangerates and national price levels. Choudhry, McNown, and Wallace (1991) use cointegration teststo examine the Canada-United States PPP relationship during the Canadian float of the 1950s.They find evidence which is broadly favorable to PPP interpreted as a long-run relationshipover the period.

7With m, y, and r and their foreign counterparts all relating to long-run values.

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run inflation differential P � P*,8 the expression for the long-runequilibrium exchange rate can be written as

e � (m � m*) � � (y � y*) � � (P � P*) . (2)1 2

In fact, the expected long-run inflation differential, P � P*, is often proxied(Frankel 1979 and Dornbusch 1980) by the differential in long-run interestrates, and this practice is followed here. Although the substitution is usuallyjustified on grounds of empirical expedience, it can be given a rigorous theo-retical rationalization by appeal to rational term structure arguments. Finally,recognizing that the assumed equality of the domestic and foreign demandfor money parameters which underlies Equations (1) and (2), as well as theunit coefficients on the money supply terms, should be tested rather thansimply imposed, we have, introducing a stochastic error-term into therelationship,

e � c m � c m* � c y � c y* � c r � c r* � e . (3)91 2 3 4 5 L 6 L t

The relationship represented by Equation (3) forms the basis of our analysisof long-term equilibrium exchange rate determination using cointegrationtechniques. If the monetary model provides a valid view of the exchangerate determination process in the long run, then c1, c4 and c5 should eachbe positive, with c2, c3 and c6 all negative. Since the model is estimated inunrestricted form (Equation 3), we are able to test whether the coefficientson the money supply terms conform to the values implied by the monetaryapproach, and also whether the restrictions of identical income and interestelasticities are valid, i.e., we have the following testable hypotheses:

H1: c � 1.1

H2: c � �1.2

H3: c � �c .1 2

H4: c � �c .3 4

H5: c � �c .5 6

8Uncovered interest parity implies the interest differential is equal to the expected rate ofdepreciation of the domestic currency. But with PPP holding in the long run the expected long-run rate of depreciation is equal to the expected differential between the domestic and foreigninflation rates.

9An L subscript is used to distinguish a long-term interest rate from the unsubscripted short-term interest rate.

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353

We discuss the formulation and estimation of our short-run error correctionmodel in Section 3.

3. Empirical Methodology and Results

(i) The Data and the Unit Root TestsCanada took the decision to float its currency in October 1950 in re-

sponse to unremitting speculative pressures which had developed during thecourse of the year in anticipation of a revaluation of the Canadian dollar.The float had lasted just over eleven and a half years when, following adisconcerting slide in the value of the Canadian dollar, it was repegged at0.925 United States dollar. During the episode only limited intervention wasundertaken by the Exchange Fund Account, and was designed to smoothshort-run exchange rate movements rather than to counteract more funda-mental pressures.10

The data used in our study relates to the period beginning October1950 and ending May 1962, the last month of the float. All data are monthlyand seasonally unadjusted, and are obtained from International FinancialStatistics, Statistics Canada, Federal Reserve Bulletin and the Federal Re-serve Bank of St. Louis. The money stock variable used for both countriesis M1, the long-term interest rate is represented by the long-term govern-ment bonds rate, and industrial production is used as a proxy for income.The exchange rate is expressed as Canadian dollars per United States dollar.Except for the interest rates, all data are applied in logarithmic form.

Since cointegration tests require a certain stochastic structure of thetime series involved, the first step in the estimation procedure is to deter-mine if the variables are stationary or nonstationary in levels. For our pur-poses all variables should be nonstationary in levels, i.e., they should containa unit root (I(1) processes). The “augmented Dickey-Fuller test” (ADF)(Said and Dickey 1984) is applied to check for the presence of a unit root(s)in individual series.11 Since numerous articles and books contain detailedanalyses of the ADF test, it is not provided here in order to save space.Based on the evidence provided by the Akaike Information Criterion, themaximum number of lags used in the ADF is twelve. Insignificant lags (stan-dard F-test) were dropped from the regressions only if their elimination didnot produce serial correlation. Tests are conducted to check for two roots

10See Wonnacott (1972) for an excellent analysis of Canadian exchange rate policy over theperiod 1950–71.

11According to DeJong et al. (1992) the augmented Dickey-Fuller test is the most useful inpractice among all the unit root tests.

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TABLE 1. Augmented Dickey-Fuller Tests Results

Variables Null: One Unit Root Null: Two Unit Roots

Ex �1.60/(0) �8.32a/(0)CM1 �2.96/(6) �3.04b/(9)UM1 �2.21/(0) �12.66a/(0)CY �2.93/(0) �10.11a/(0)UY �3.10/(9) �6.93a/(0)CL �1.34/(0) �8.56a/(0)UL �2.17/(3) �4.18a/(3)

NOTE: a & b imply rejection of the null at 1% and 5% level respectively.Significant number of lags in the parentheses.EX � Exchange rate, CM1 � Canadian M1, UM1 � United States M1, CY � Canadian

income, UY � United States income, CL � Canadian long-term interest rate, UL � UnitedStates long-term interest rate.

first, and if rejected, then one root is tested for. The single unit root test isconducted with both a constant and trend, while the two root test onlyincludes a constant. In this manner, the alternative hypothesis in the oneroot test is trend stationary with a nonzero constant, while the alternativehypothesis in the two root test is stationary after first difference with a non-zero constant. The ADF tests are applied with monthly seasonal dummiesin order to eliminate seasonality. The seasonal dummies enter the relation-ship exogenously. Table 1 presents the results from the ADF tests. All vari-ables are able to reject the two root null hypothesis but are unable to rejectthe single root hypothesis. Thus the results show that all variables are sta-tionary after first differencing but are nonstationary in levels, i.e., all variablesare I(1) processes.12 Fuller (1976) provides the critical values required inthe ADF test.

(ii) Cointegration Test Methodology and ResultsCointegration tests in this paper are conducted by means of the

method developed by Johansen (1988), and Johansen and Juselius (1990).13

The Johansen method applies the maximum likelihood procedure to deter-mine the presence of cointegration vectors in nonstationary time series. Jo-hansen and Juselius provide two different tests, the trace test and the max-imum eigenvalue test, to determine the number of cointegrating vectors. If

12In all cases the trend in the ADF test for a single unit root was insignificant.13The Johansen procedure provides more robust results compared to other cointegration

methods when there are more than two variables (Gonzalo 1994).

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a nonzero vector(s) is indicated by these tests, a stationary long-run rela-tionship(s) is indicated.14 According to Dickey et al. (1991), cointegratingvectors are obtained from the reduced form of a system where all of thevariables are assumed to be jointly endogenous. Thus, cointegrating vectorscannot be interpreted as representing structural equations. However, coin-tegrating vectors may be due to constraints that an economic structure im-poses on the long-run relationship among the jointly endogenous variables.According to Dickey et al. (1991, 65) the larger the number of significantvectors the more robust is the result. More than one nonzero vector impliesthat the economic system is found to be stationary in more than one direc-tion. Osterwald-Lenum (1992) provides the appropriate critical values re-quired for these cointegration tests. The significant cointegrating vector(s)is given economic meaning using normalization on the log of the exchangerate. The normalized vectors comprise the implied long-run elasticities ob-tained from these normalized equations.

As stated earlier, the unrestricted model (Equation [3]) is tested for astationary long-run relationship. Table 2 presents the results from the coin-tegration tests. Based on the AIC, the number of lags applied in the test arefour.15 Only the trace test indicates one significant cointegrating vector atthe 5% level.16 This result implies the existence of a stationary long-runrelationship of the form of Equation (3).17 The existence of such a relation-ship lends support to the monetary approach as an explanation of equilibriumexchange rate behavior over the relevant period. The normalized equationis reported in Table 2, which shows all coefficients, other than that relating

14A more detailed analysis of the Johansen method is provided in Dickey et al. (1991) andDickey and Rossana (1994).

15The Johansen test results are sensitive to the lag length in the VAR (Gonzalo 1994, 220).According to Gonzalo, the cost of overparameterizing by including more lags is small in termsof efficiency lost but this is not true in the case of underparameterization.

16The trace test tends to be more powerful than the maximum eigenvalue test when theeigenvalues are evenly distributed (Kasa 1992, 102). Further, according to Cheung and Lai(1993) the trace test shows more robustness to both skewness and excess kurtosis in the residualsthan the maximum eigenvalue test.

17Given the apparent disagreement between the trace and eigenvalue tests, a referee sug-gested applying the Engle-Granger (1987) two-step method as a further test for cointegration.The results from this exercise were consistent with those of the trace test. In particular, theresiduals from the monetary model regression were found to be stationary, implying a stationaryrelationship for the relevant variables. Again on the advice of a referee, the Johansen methodwas applied with a time-trend in the VAR. The results are very similar to those obtained withthe time-trend omitted. Once again, the trace test alone indicated a significant vector which,when normalized, showed the correct signs on the variables. These results, together with thoserelating to the Engle-Granger procedure, are omitted in order to save space, but are availableon request.

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TABLE 2. Cointegration Tests Results

Vectors Trace Test Eigenvalue Test

r � 0 129.34b 40.58r � 1 88.76 33.83r � 2 54.93 28.25r � 3 26.69 11.08r � 4 15.61 7.63r � 5 7.98 4.74r � 6 3.24 3.24

Normalized EquationEx CM1 UM1 CY UY CL UL

1.00 0.076a �0.411b �0.11 0.283b 0.037b �0.06c

Restriction TestsNull Hypotheses Chi-square statistics

H1: CM1 � 1 29.67*H2: UM1 � �1 32.35*H3: CM1 � �UM1 1.733H4: CY � �UY 0.980H5: CL � �UL 1.600

NOTE: a, b, & c imply significant at the 1%, 5%, & 10% level respectively.*implies rejection of the null at the 5% level.

to Canadian income, to be significantly different from zero and all to be ofthe correct signs.18

Notwithstanding this broad evidence in favor of the monetary model,the restriction tests, based on the chi-square tests of Johansen and Juselius(1990), reject the unit coefficient restriction on the money supply termsimplied by the monetary approach (H1 and H2).19 Finally, Table 2 indicatesthat we cannot reject the null hypotheses of identical (in absolute terms)

18Significance of the coefficients was tested by means of the chi-square test.19An explanation for this result is suggested by cointegration studies of PPP. While such

studies are almost unanimous in rejecting the traditional representation of PPP, e � p � p*,even as a long-run phenomenon, a number of recent papers are rather more supportive of aweak form (MacDonald 1993), that is et � d1 pt � � lt (see Patel 1990 for a rationali-d p*2 t

zation of the non-unit coefficients on the price variables). It is readily shown that this versionimplies non-unit coefficients on the money supply terms in Equation (3).

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coefficients on the two monies, the two income levels, and the two long-term interest rates.20

(iii) Error Correction Model and ResultsCointegration also implies that the transitory components of the series

can be given a dynamic error correction representation, i.e., a constrainederror correction model can be applied that captures the short-run dynamicadjustment of cointegrated variables.21 In the present context the followingrepresentation is implied:

DX � C � A(L)DX � �u � g , (5)t t t�1 t

where

C � a vector of constant terms,A(L) � a matrix of finite order lag polynomials,

X � (e, m, m*, y, y*, P, P*) and� � a vector of coefficients,

ut�1 � et�1 � 0.076mt�1 � � 0.11yt�1 �0.411m* 0.282y*t�1 t�1

� 0.037Pt�1 � .0.06P*t�1

The second term on the right-hand side of Equation (5) represents the short-term dynamic interaction between the left-hand side variable and the othervariables of the monetary model, these dynamics arising from, for example,demand for money lags, gradual output adjustment, etc. The disequilibriumadjustment of each variable towards its long-run equilibrium value is thencaptured by the error correction term, ut�1, with the coefficient on this term

20Since we were unable to reject null hypotheses H3, H4, and H5, cointegration tests usingthe restricted model (Equation 2) were also conducted. Results again indicate one nonzerovector implying a stationary long-run relationship among the variables of the restricted model.The following normalized equation was obtained:

a a be � 0.095 (m � m*) � 0.332 (y � y*) � 0.017 (P � P*) .

The chi-square test shows that all coefficients are significantly different from zero. The coeffi-cient on the money variable was found to be different from unity at the 1% level by means ofthe chi-square test. Details of this test and its results are not provided in order to save space,but are available on request.

21See Granger (1986) and Engle and Granger (1987) for a detailed discussion of the er-ror correction modeling strategy based upon the information provided by cointegrated vari-ables.

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in each individual equation depending on the speed of adjustment of thevariable towards its long-run equilibrium value.22

Results from the error correction model are presented in Table 3. Thelag structure in the error correction model is determined by means ofAkaike’s FPE criterion. All possible combinations of one to six lags are ex-amined and the lag structure that minimizes the FPE is chosen. If morethan one lag of the variables are applied, then Table 3 shows the sum of thecoefficients on the first line, the chi-square statistics in brackets on the sec-ond line, and the number of lags used in parentheses on the third line. Withrespect to the error correction term, the constant term, and variables withone lag, the t-statistics are presented in the parentheses on the second line.Diagnostic statistics of the equation are provided below the error correctionresults.

Significance of the lagged error correction term (ut�1) implies causalityfrom all lagged independent variables to the dependent variable. The laggederror correction term in the exchange rate equation is significant (at the 5%level) implying causality from all variables in the monetary model towardsthe exchange rate. The size of the coefficient on the error term (�0.079)shows that about 8% of the adjustment towards the long-run equilibriumtakes place per month. Except for the lagged exchange rate difference andthe constant term all other variables are insignificant in the equation. Thecoefficient on the lagged exchange rate difference is positive and significantat the 10% level. In the remaining six equations, the error correction termis significant in the case of United States M1, Canadian income, and theCanadian long-term interest rate. None of the variables are found to beeconometrically exogenous. In other words, all variables of the monetarymodel seem to be affected by each other. Coefficients on the lagged differ-enced variables are found to be less than unity, exceptions being the ex-change rate in the long-term interest rate equations of both Canada and theUnited States. All seven estimated equations pass all the diagnosticevaluations.

A further test of the adequacy of the monetary error correction modelis its forecasting performance. The exchange rate error correction equationis used to forecast the exchange rate for three, six, nine, and twelve monthsover the period June 1961 to May 1962.23 As a comparison, forecasts were

22With the cointegrating vector normalized on the exchange rate, in the equation whichmodels the exchange rate as the dependent variable, the associated element of � representsthe speed of adjustment directly. In the remaining equations, the corresponding element of �

represents the ratio of the speed of adjustment of the relevant variable to the value of itsassociated coefficient in the cointegrating relationship.

23The exchange rate error correction equation is reestimated for the period October 1950 toMay 1961 for the purpose of forecasting.

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TABLE 3. Error Correction Results

Constant ut�1 RDEx RDCM1 RDUM1 RDCY RDUY RDCL RDUL

DEx 0.066b �0.079b 0.157c �0.028 �0.053 0.018 0.048 �0.001 �0.004(2.45) (�2.46) (1.79) (�0.74) (�0.80) [0.20] (1.09) [0.02] (�0.36)R̄2 � 0.12, SE � 0.08, SC v2(12) � 15.00, Reset v2(1) � 1.27, Heteroskedasticity v2(1) � 1.37

DCM1 0.117 �0.051 �0.177 0.373a �0.722a 0.176b 0.044 0.016 �0.048b

(0.943) (�0.92) (�0.76) [7.11] (�4.48) (2.21) (0.42) (0.96) (�2.10)R̄2 � 0.23, SE � 0.02, SC v2(12) � 17.18, Reset v2(1) � 3.12, Heteroskedasticity v2(1) � 1.85

DUM1 0.370a �0.166a �0.160 0.120 0.128 �0.008 0.016 0.005 �0.024(4.94) (�4.93) [0.83] [2.01] [0.67] (�0.17) (0.25) (0.57) [1.92]R̄2 � 0.21, SE � 0.012, SC v2(12) � 15.36, Reset v2(1) � 1.70, Heteroskedasticity v2(1) � 1.78

DCY �0.287b 0.131b �0.238 0.170 �0.707a 0.038 0.363a 0.039b �0.024(�2.05) (2.07) (�0.85) (1.54) (�3.84) (0.40) (2.88) (2.04) (�0.87)

R̄2 � 0.16, SE � 0.024, SC v2(12) � 5.55, Reset v2(1) � 0.71, Heteroskedasticity v2(1) � 0.33DUY 0.113 �0.05 0.045 �0.063 0.047 �0.112c 0.325a 0.022 0.016

(1.15) (�1.14) (0.23) (�0.78) [0.08] (�1.64) [8.94] (1.59) (0.85)R̄2 � 0.14, SE � 0.017, SC v2(12) � 6.55, Reset v2(1) � 0.02, Heteroskedasticity v2(1) � 0.03

DCL 1.441b �0.645b �2.923c �0.411 0.170 �0.255 �0.488 0.100 0.107(2.11) (�2.09) [3.01] (�0.74) [0.02] (�0.55) (�0.80) [0.56] [0.35]R̄2 � 0.03, SE � 0.11, SC v2(12) � 10.00, Reset v2(1) � 0.91, Heteroskedasticity v2(1) � 0.27

DUL 0.254 �0.112 1.167 0.628c 0.100 0.339 0.728c 0.381c �0.257b

(0.55) (�0.54) [1.06] (1.68) [0.02] (1.08) (1.77) [18.94] [4.54]R̄2 � 0.26, SE � 0.077, SC v2(12) � 16.57, Reset v2(1) � 2.92, Heteroskedasticity v2(1) � 1.81

NOTES: a, b, & c imply significance at 1%, 5%, & 10% level respectively, t-statistics in parentheses ( ), Chi-square statistics in brackets [ ].SE � Standard error of the regression, SC � Serial correlation at lags 12.

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also made with two alternative models; a simple random walk and a simplerandom walk with a drift. The root-mean-square error (RMSE) statisticsfrom all three tests are then compared. In all cases the error correctionmodel outperforms both the random walk models across the range of fore-casting horizons.24

4. Conclusion

The present paper has examined the validity of the monetary approachto exchange rate determination as an explanation of the Canadian dollar–United States dollar relationship over the period 1950–1962. As noted in theintroduction, the Canadian float has received relatively little attention interms of the application of formal econometric methodology, despite itsimportance as an experiment in exchange rate flexibility during the BrettonWoods era.

The implementation of cointegration-error correction techniques al-lowed the conceptual distinction between the process of long-run equilib-rium exchange rate determination and short-run exchange rate dynamics,introduced in the context of the monetary approach by Frankel (1979), tobe implemented empirically. Our most important conclusion derives fromour cointegration tests. These indicate the existence of a long-run relation-ship between the Canadian–United States dollar exchange rate, relativemoney supplies, income levels and exchange rates, which conforms in broadterms with the monetary model. Our cointegration results are reinforced bythose of the error-correction model. These identify a clear tendency for theexchange rate to revert to its long-run equilibrium value, with 8% of theadjustment taking place each month.

Our findings mirror those of a number of recent papers, in particularMacDonald and Taylor (1994) and McNown and Wallace (1994). Thus ourown work may be viewed as part of a wider reappraisal of the validity of themonetary approach to exchange rate determination. Of course, whether thisreappraisal will result in a more general rehabilitation of the monetary modelis an issue which can be determined only by substantial further research.

24The following table presents the RMSE statistics from the three models for all forecastinghorizons.

Models Three Months Six Months Nine Months Twelve Months

Random Walk 0.010 0.027 0.037 0.040Random Walk-D 0.013 0.031 0.045 0.049Error Correction 0.007 0.015 0.015 0.013

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Received: December 1994Final version: February 1996

References

Boothe, Paul, and Denise Glassman. “Off the Mark: Lessons for ExchangeRate Modelling.” Oxford Economic Papers 39 (1987): 443–55.

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