canadian foreign exchange policies: intervention, control, cointegration

Canadian Foreign Exchange Poficies: Intervention, Control, Cointegration

By

G. Geoffrey Beoth and Mustafa Chowdlmry

C o n t e n t s : I. Introduction. - lI. The Control Model. - Ill. Cointegration and Control. - IV. Conclusion. - Appendix.

I. latrmlucttm

T he current international monetary r e , me, which has evolved subsequent to the general repudiation of the Bretton Woods agreement, is best described as a floating rate system in which

central banks occasionally, but irregularly, attempt to intervene in the foreign exchange market in an effort to alter exchange rates. Interven- tion in this "managed" system may be implemented by central banks changing (i) their official reserve positions, (ii) domestic interest rates relative to foreign ones, and (iii) exchange rate market expectations largely through the first two implementation channels. The rationale often given for intervention is that it is able to help calm disorderly markets and correct existing trade imbalances.

That intervention is believed to be effective and important by central banks, finance ministers and secretaries, and others is evinced by international agreements and public announcements. For example, in late September 1985, the G5 countries (France, Japan, West Ger- many, the United Kingdom, and the United States) in the Plaza Accord agreed to intervene to promote the continuing depredation of the U.S. dollar, particularly with respect to the Japanese yen and the West German mark. In early 1987, the G7 countries (G5 plus Canada and Italy) formulated the Louvre Agreement, from which it could be inferred that reference zones for the West German mark/U.S, dollar and Japanese yen/U.S, dollar exchange rates were established. Even more recently The Wall Street Journal (January 23, 1989, p. 13) re-

Remark: An earlier version of this study was partially supported by the Institutional Research Program (CFY 1987-88) of the Canadian Embassy. The authors thank the Embassy for their support and also thank Vedat Akgiray, Elizabeth B. Booth, Clive W. J. Granger, and Tae-Hwy Lee for their helpful comments. Responsibility for the contents of the paper, of course, remains with us.

22 Weltwirtschaftlichcs Archiv

ported that "[c]entral banks of at least 10 major industrial nations flooded the foreign exchange market with dollars last week, pushing the U.S. currency down. . . " and that analysts thought that the central banks achieved their intended result of depreciating the U.S. dollar.

The long standing policy of the Bank of Canada to intervene in order to maintain orderly markets and in doing so to not maintain a particular exchange rate level is well documented [Department of Finance and Treasury Board of Canada, 1971, 1982; Murray et al., 1990]. As a reflection that the United States is by far the largest of its trading partners, Canada is particularly concerned with the U.S./Ca- nadian dollar exchange rate. Governor of the Bank of Canada, Bouey [1982], maintains that the Bank of Canada reacts strongly to changing interest rates in the United States because of their effect on the exchange rate between the two countries. Governor Crow [1988], citing the 1984 Annual Report of the Bank of Canada, indicates that to manage this exchange rate in the prior year or so, the central bank took steps to protect the existing exchange rate by increasing domestic interest rates. However, Gregory [1987] provides evidence that the Canadian response to U.S. interest fluctuations is not necessary to stabilize the exchange rate.

A number of studies have investigated whether Canadian intervention has been successful during the 1952-60 floating rate regime and the current floating regime, which began in 1971. Although different methods are used, virtually all investigations reach the same conclusion. For instance, Eastman and Stykolt [1956], Wonnacott [1965], and Pippinger and Phillips [1973] report that during the float in the 1950s, intervention did have an impact. Similarly, Haas and Alexan- der [1979], Longworth [1980], and Danker ct al. [1985] report intervention successes by the Bank of Canada in the 1970s, as does Murray ct al. [1990] in the 1980s. These latter studies yield two interesting observations. First, the results of Haas and Alexander [1979] and Danker et al. [1985] imply that sterilized intervention is effective. Second, that the Canadian authorities employ a policy of "'leaning against the wind" is supported by Longworth [1980] and Murray et al. [1990].

The purpose of this study is to re-examine the impact of intervention by the Bank of Canada on the Canadian/U.S. dollar exchange rate during the early and mid-1980s. The paper contributes to the literature in two primary ways. First, it focuses on a time period in which Canada aggressively intervened to mitigate the dramatic depreciation of the Canadian dollar and its subsequent recovery. Except for

Booth/Chowdhury: Canadian Foreign Exchange Policies 23

the beginning and end of this period, the United States maintained a virtual "hands-off" poficy with respect to intervention. Second, a stochastic control theoretic model is used as a framework for describing the Bank of Canada's intervention policies. Not only is a control model a particularly appropriate way to conceptualize the relationship between central bank intervention and exchange rates, but also the use of optimal control can be tested using multiple cointegration, a relatively new econometric technique. The results of this study support the notion that the Bank of Canada follows a policy of nonsterilized intervention and implements it using an optimal control rule.

The remainder of this paper is divided into three sections. In the first section, the control model is developed. In doing so, it is necessary to define the model's variables and their order of integration. The second section is devoted to illustrating the relationship between control theory and cointegration. The study's major results are also presented in this section. Conclusions are offered in the third section, with mathematical detail following in the Appendix.

H. The Control Model

A control model contains three types of variables: dependent, target, and control. The dependent variable is the variable that is to be influenced, and the target variable is the desired value of the dependent variable. Control variables are those variables that can be at least partially affected. The idea is for control variables to be mani- pulated in such a way that over time the difference between the dependent and target variables is very small, preferably zero.

1. V a r i a b l e s a n d D a t a

As a first step in constructing a control model for foreign exchange intervention, dependent, control, and target variables that are eco- nomically appropriate and statistically stationary are selected. Using the economic criterion, the dependent variable is defined to be the Canadian/U.S. dollar exchange rate {e} measured in units of the number of Canadian dollars needed to buy one U.S. dollar, hereafter usually referred to as the "exchange rate."

Given the various pronouncements of the Canadian government officials, appropriate control variables are Canadian interest rates (i'~ and Canadian reserves of U.S. dollars {R}. These reserves are by far the largest component (sometimes as large as 50 percent) of the total.

24 Wcltwirtschaftlichcs Archiv

The contribution of other currencies to total reserves is negligible. U.S. dollar reserves are also unarguably the most volatile by a large margin, and holdings of gold and SDR's and the IMF position exhibit the lowest volatility. It is worthwhile to mention that other control variables, such as foreign currency debt, may also be employed.

Since the Bank of Canada's target exchange rate {e*} is not ob- servable, it is necessary to proxy it using one or more instrumental variables. In the same spirit that the control variables are chosen, U.S. interest rates {i ~'} are used as the instrumental variable, although other candidates, such as domestic economic conditions and terms of trade, are possible. Short-term fluctuations cause rapid movement of capital across the border. A positive (negative) shock in the capital account is negatively (positively) reflected in the current account. If intervention policy is primarily used to break the link between capital movements and the current account, U.S. interest rates are a suitable instrument for the target exchange rate. In any case, the precise func- tional relationship between the target exchange rate and the instrumental variable is partially determined by specific intervention policies.

The period of analysis runs from the beginning of January 1980 to the end of December 1986. All interest rate and reserve data are Wednesday observations, which results in 364 data points. Weekly data are used because daily data often contain a great deal of noise and monthly data may mask intervention activities. The exchange rate quotes are collected from The Wall Street Journal (various issues) and represent interbank quotations. The interest rate series are provided by the Federal Reserve Bank of New York. The specific proxy series used are the 3-month Canadian finance paper rate and the 90-119- day U.S. commercial paper rate. Canadian reserve data are supplied by the Canadian Ministry of Finance. These data reflect net positions and, according to Houle [1988], changes in this position is fairly indi- cative of Canadian intervention activity, even though some noninter- vention transactions are included, such as earnings on reserves and selected government receipts and disbursements. Houle's contention requires that a net increase (decrease) in official reserves be brought about by a preponderance of U.S. dollar purchases (sales) by the Bank of Canada.

In all cases, nominal values of these variables are used. It may be argued that the Bank of Canada has both nominal and real exchange rate targets. However, the focus is on nominal values, since targets are usually stated in nominal terms, and neither private nor public data


are available on a weekly basis for policy makers to gauge real effects. All four variables are expressed in logarithms, with interest rates first being expressed in "one plus the decimal rate" format.

To examine the issue of stationarity, the unit root test constructed by Dickey and Fuller [1979], augmented with nuisance variables as suggested by Said and Dickey [1984], is applied to each of the four transformed variables, with the null hypothesis being that a unit root exists. The results are reported in Table 1. The null hypothesis cannot be rejected for the exchange rate and the two interest rates but it can be rejected for reserves. That the exchange rate and interest rates are I (1) variables is not surprising because they are generated in specula- tive markets. However, there is no a priori reason for reserves to be a stationary (i.e., an I (0)) variable. One reason for the observed stationarity may be that the Bank of Canada tries to maintain, on average, a certain level of U.S. dollar reserves to facilitate international transactions and uses other control variables, such as the is- suance of foreign currency debt, to help achieve its intervention goals. This tendency to maintain a long-run level of reserves would show up as mean reverting tendency in reserves. In view of the integration results, the exchange rate and both interest rates enter the control model as first differences, while reserves as the policy variable enter in their level form.

At this juncture, it is important to recognize that, with respect to intervention by changing Canadian reserves, the analysis is unilateral in that it considers only Canada and not the United States. Unfortu-

Table I - Estimate of Augmented Dickey-Fuller Statistic (test that there is a uni

Variable

Exchange rate {e} U.S. dollar reserves {R} Canadian interest rate { i ' } U.S. interest rate { i '}

root)

t-statistic

-0 .903 - 3.237 * - 1.565 -2 .083

Note: (*) indicates significance at the 5-percent level. Letting x denote a particular variable, the t-statistics are derived from the following augmented Dickey- Fuller regression: Ax~ -- b o + b 1 x,_ l + ~ = l bi+ l Ax,_ 1 + u,, with n ffi 5 denoting the number of nuisance variables used to account for possible autocorrelation in Ax. The tabular entries are the t-statistics for b~. Fuller [1976] provides a critical value at the 5-percent level of signif~J~ce of ~2.88 for 250-500 observations.

26 Weltwirtschaftliches Archiv

nately, U.S. weekly or daily intervention data are not available to the general public. In this particular case, however, nonavailability of these data may not be too serious. This contention rests on the obser- vation that when the U.S. intervened during the study period it ap- pears to have been focused on the West German mark and Japanese yen and not the Canadian dollar. It is also supported by noting that in many ways the U.S. economy dominates the Canadian economy because of its sheer size. As partial recognition of this phenomenon, Freedman [1982] suggests that the U.S. exchange rate should be incor- porated in the formulation of Canada's monetary policy.

2. M o d e l S t r u c t u r e a n d H y p o t h e s e s

In determining its intervention activities, it is posited that at the end of week t the Bank of Canada sets the desired change in the exchange rate that is to occur by the end of week t + 1. To attempt to meet the desired level and to maintain an orderly market, the Bank also sets the control variables at the end of week t. Success in attaining these goals is assumed to be determined by a quadratic loss function.

More formally, let the loss function L be specified as:

L = E {(Ae+ + 1 - Ae*) 2 + o~ (Ae, + 1 - Ae+)2}, (1)

where E (.) is the mathematical expectations operator and A is the first difference operator. The first term on the right penalizes the Bank for deviations of the actual change (the dependent variable) from the desired change (the target variable), where the desired change is formulated with consideration given solely to market fundamentals. The subscripts for the two exchange rate changes are different because the desired change for t + 1 is set by the Bank in period t. The second term penalizes the Bank for large fluctuations in actual exchange rates, which reflects the desire of the Bank of Canada to promote an orderly exchange rate market. The two penalties are tied together by a weight- ing factor ~o. If co > 1 (< 1), the second policy goal is more (less) important to Bank policy makers than the first.

The control variables are related to the succeeding period's exchange rate by a function called the plant equation. In particular,

Ae,+t = ~AJ~ ~ + /~(R , -~ , ) + e,+l, (2)

where ~+ represents the conditional mean reserves and t~ + t is an error term. The coefficient ~, has a nonpositive sign. An increase (decrease) in Canadian interest rates, given U.S. interest rates, results in an inflow


(outflow) of capital from the United States. This causes an appreciation (depreciation) in the value of Canadian dollars./~ has a positive sign because an increase (decrease) in U.S. dollar reserves over (under) its conditional mean by the Bank of Canada results in a depreciation (appreciation) of the exchange rate. As mentioned earlier, there may be some other exogenous variables affecting the amount of change in the following week, but they are removed from the plant equation for simplicity.

The optimal values of the control variables are obtained by mini- mizing the loss function (1). The dependent variable, Aet+ 1, is replaced by the right-hand side of the plant equation. From the first-order condition, the following equation obtains:

(1 + ~ ) ~ A ~ + (1 + oJ) /~(Rt- Rt) - Ae* - o~Aet = 0 . (3)

If this first-order condition does not hold, (i.e., the right-hand side is nonzero), optimal control does not exist.

There are two types of intervention strategies. The first, sterilized intervention occurs when the change in reserves is offset by a change in the money supply, thereby negating any impact that reserves may have on interest rates. The second, nonsterilized intervention results when reserves are not offset. If intervention is sterilized, a dynamic relationship between e t, e* and z~ ~ does not exist. To illustrate, dividing (3) by the difference operator A results in:

oJet+e*-(l+o~)~,~a=~(l+o~) f~ (Rt_i-~t_l) . (4) l = 0

Since (R,-R,) is an I(0) variable, its cumulative sum is I(l). The right-hand side of (4), therefore, has infinite variance. The same out- come holds when the optimal control rule is not used, regardless of whether intervention is sterilized or not. This is because the right-hand side of (4) contains the cumulative sum of the nonzero right-hand side term of (3), thereby rendering it nonstationary. In both situations, a dynamic equilibrium relationship is not present because the variables drift apart from each other in such a way that the expected time elapsed before they meet again is infinite. Thus, if sterilization policy is pursued, shocks to the level of reserves at any point of time have persistent effects on the exchange rate. This may be somewhat similar to the persistent effect of current account shocks on exchange rates as demonstrated by Dornbusch [1987].

28 Weltwirtschaftl iches Archiv

m . Cointegratioa and Control

The cointegration theory is a natural extension to the literature on error-correction mechanism introduced by Sargan [1964] and later popularized by Davidson et al. [1978]. Granger [1981] introduced the concept of cointegration, and the link between cointegration and error-correction mechanism was established by the Granger Represen- tation Theorem in Engle and Granger [1987]. Applications of cointegration theory have since been numerous, especially in the foreign currency literature, e.g., Meese and Rogoff [1988], Enders [1988], Cor- bae and Ouliaris [1988], Gubitz [1988], Baillie and Bollerslev [1989]. With the exception of Baillie and Bollerslev, these applications have been restricted to bivariate cointegration.

That error-correction mechanisms provide a testable framework for optimal control was first pointed out in Nickell [1985]. Subse- quently, Granger [1988] established the relationship between causality, cointegration and control. Granger and Lee [1989; 1990] showed that optimal proportional control implies multivariate cointegration, and optimal proportional and summation control imply multicointegration, which is a stricter cointegration concept.

The test of cointegration involving more than two variables is handled differently than that of bivariate cointegration, which is ex- plained in detail by Engle and Granger [1987]. Although there can be only one equilibrium relationship between any two variables, a set of more than two variables can have more than one equilibrium relation. For example, in a three-variable environment, one, two or no equilibrium relationships may exist. If there are no cointegrating relations, the three variables are not cointegrated. A multivariate cointegration test similar to the one suggested in Johansen [1988] and used by Baillie and Bollerslev [1989] is employed in this paper. The test is based on canonical correlation, and its details are presented in the Appendix.

Whether there are at most r cointegrating vectors is tested using Johansen's [1988] J-statistic. The estimates of this J-statistic for different values of r are given in Table 2. The value of the statistic for testing against the null hypothesis of no cointegration is 66.64, which far exceeds the 95-percent critical value. Similarly, the null hypothesis that there is at most one cointegrating vector is also rejected. However, the null hypothesis of at most two cointegrating vectors cannot be rejected. Thus it may be concluded that there are two cointegrating vectors relating et, i~ ~ and ~ . These results indicate that the implica- tions of equation (4) can be rejected. In other words, there is no

Booth/Chowdhury: Canadian Foreign Exchange Poficies

Table 2 - Estimate of the J-Statistic (test that there are at most r cointegrating vectors)

29

�9 J 9.5-percent critical value

0 66.64 23.9 1 21.37 12.0 2 3.45 4.2

Note: Critical values are obtained from Johansen [1988].

persistent gap created among the dependent, control and an instrument of the target variable, suggesting that the Bank of Canada is intervening in foreign exchange markets using nonsterilized optimal proportional control.

IV. Conclusion

Nonsterilized intervention by the Bank of Canada to influence the U.S.-Canadian dollar exchange rate using an optimal control rule is supported. This is because intervention using optimal control with nonsterilization implies a dynamic equilibrium relationship among the exchange rate, its target value and the Canadian interest rate. The existence of this equilibrium is established using a multivariate cointegration test based on canonical correlation methods.

Whether the approach used in this paper to arrive at the above conclusions can be applied to other central banks and other exchange rates is not yet determined. This is because the approach requires assumptions that may not be met in other instances. For example, domestic official reserves may not be stationary, two country rather than single country intervention policies may be the norm, and instru- ments other than the foreign interest rate to proxy the desired exchange rate may be more appropriate. How to incorporate these possibilities into a meaningful test is left for future research. However, the method employed for this study provides a useful starting point.

The multivariate test for cointegration may be defined in the following manner. Denote the 3-<limensional random vectors (et, e*,, it)'

30 W e l t w i r t s c h a f t l i c h e s A r c h i v

by Yr. Assuming that y, follows the 3-dimensional autoregressive pro- C~SS"

A(B) y, = (5)

where ~ is a 3-dimensional Gaussian random vector with zero mean and diagonal covariance matrix. A(B) is a 3-dimensional matrix polynomial lag operator that has one unit root, since e , i t and e,*, which is proxied by ~ , have unit roots.

Any such polynomial lag operator can be decomposed into two parts,

A(B) = A(1)B + (I -B)A. (B), (6)

where A -(B) is another matrix polynomial lag operator with no unit roots.

If y, is cointegrated in r < 3 different ways, then the rank of A(I) is r and A(1) can be written as a cross product of two 3 x r matrices, i.e.,

A(1) --- a0 ' , (7)

such that the columns of 0 are the cointegrating vectors, i n other words, although y, is a vector of I(1) variables, the linear combina- tions, 0'y t, are stationary.

The multivariate cointegration test is, therefore, based on the estimation of the rank of 0. The cointegrating matrix 0 and its rank are calculated in the following way:

1) Ay, and Yt-1 are regressed on lagged differences; 2) from the above regression the two (3 • 1) residual vectors, ~ and

-1, are estimated; and 3) the canonical correlations between ~ and ~-1 are estimated using

maximum likelihood methods, with the corresponding canonical variates providing an estimate of 0.

Johansen [1988] provides a likelihood-ratio test of the hypothesis that there are at most r cointegrating vectors of rank (0) < r. The statistic is:

3 J = - T 5". l o g 0 - 2 ~ ) , (A4)

i = r + l

where 2,+x, ..., 23 are the 3 - r smallest squared canonical correlations. Johansen [ibid.] also provides 95-percent critical values of J using Monte Carlo methods.


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Z u s a m m e n f a s s u n g : Kanadische Wechselkurspolitik: Intervention, Kon- trolle, Kointegration. - Die Verfasser testen unter Rfickgriffauf die Kointegrationstech- nik und den Ansatz der optimalen Kontrolle, wie sich die olTtzieUvn Interventionen der Bank of Canada auf den Devisenkurs zwischen dem kanadischen und amerikanischen Dollar ausgewirkt haben. Wenn sich die Bank des Ansatzes der optlmslen Kontrolle bedient, tun ihre Interventionen zu steuern, und keine Sterilisierungsmal3nahmen an- wendet, dann sind Wechselkurs, sein Zielwert und der kanadische Zinssatz im dynamischen Gleichgewicht miteinander verbunden. Die Existenz dieser dynamischen Gleich- gewichtsbeziehung wird mit Hilfe yon multivariaten Kointegrationsmethoden getestet und besuitigt.


R ~ s u m ~ : Les polltiques canadiennes du taux de change: intervention, contr61e, et co-integration. - Les m6thodes de contr61e optimal et de co-int6gration sont utilis~s pour tester l'effet de l'intervention officiel par la Banque de Canada sur le cours dollar canadien/dollar am~ricain. Si la Banque utilise l 'approche de contr61e optimal pour diriger ses interventions et ne prend pas de mesures de st~rillsation, fl existe une relation d'~luilibre dynamique entre le taux de change actuel, le taux de change dc~sir~ et le taux d'int~r~t canadien. En utilisant les m6thodes de co-int6gration aux variables multiples, on a affirm~ l'existence d'une relation d'&luilibre dynamique.

R e s u m e n : Las pollticas de cambio canadienses: intervenci6n, control, cointegracibn. - En este trabajo se utiliza un enfoque mixto de control 6primo y cointegracibn para llevar a cabo un test del impacto de una intervenci6n oficial por parte del Banco del Canad~ en el mercado de cambios Canad~-EE UU. Si el banco et/liTa control bpti- mo para guiar sus politicas de intervencibn y no emplea procedimlentos de esteriliza- cibn existe una relacibn de equilibrio clin~mica entre la tasa de cambio, su valor meta y la tasa de inter~ canadiense. La existencia de una relacibn de equilibrio clin~hnica es verificada empiricamente aplicando m~todos multivariantes de cointegraci6n. La hip6- tesis nula de no cointegraci6n es rechazada, con lo cual se implica la existencia de un equillbrio din~mico.

canadian foreign exchange policies: intervention, control, cointegration

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