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Canada’s Foreign Exchange Market: A Quarterly Model

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1960
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CANADA adopted a fluctuating exchange rate system in September 1950.1 Since then, the foreign exchange value of the Canadian dollar has been determined by the interplay of market forces, except for some official intervention in the exchange market reported as intended to prevent excessive short-term fluctuations. Since 1952, this official intervention has been exercised on only a moderate scale, and official sales or purchases of exchange by the Canadian Exchange Fund Account have not been the dominating influence in determining exchange rate fluctuations from one quarter to another. The combined current and long-term capital account has shown substantial quarterly net balances. These balances have varied between plus $200 million and minus $200 million, and have exceeded $100 million, or about 10 per cent of Canada’s quarterly export receipts, in nearly half of the quarters. In view of these relatively large swings in the current and long-term capital account and of the moderate extent of official intervention in the exchange market, the stability of the Canadian dollar during the last eight years is remarkable. Since 1952, the exchange rate has remained within the range of US$1.00 to US$1.06, and the change from one quarter to another has never exceeded 2 per cent. It will be argued below that this high degree of stability was chiefly the result of the responsiveness of equilibrating short-term capital movements to changes in the exchange rate.

The theory of the determination of the foreign exchange rate, which has been developed and refined during the last three or four decades, is largely a theory of long-run equilibrium. The discussion has centered on the problem of the stability of the foreign exchange market in the absence of capital movements.2 Lack of national income and balance of payments data for periods shorter than one year has prevented any empirical study of the short-run balance of payments adjustment process under flexible exchange rates even in the few historical cases where a fluctuating exchange system was in operation for a longer time period and under reasonably normal conditions.3 Canada’s foreign exchange experience during the 1950’s and the availability of quarterly data on Canada’s national accounts and balance of payments afford an opportunity to add to our knowledge of the process by which the level of a fluctuating exchange rate is determined in the short run, and of the role played by a fluctuating exchange system in the economic policy of a dependent economy.

I. A Model of Canada’s Foreign Exchange Market

The model of Canada’s foreign exchange market which is here examined takes its starting point from the proposition that the foreign exchange rate during a particular quarter is determined by the demand for and the supply of foreign exchange. The transactions which give rise to such demand and supply may be divided into four classes: (1) exports and imports of goods and services, (2) long-term capital movements, (3) purchases or sales of gold or foreign exchange by the central bank, or by some other designated official agency, in the course of intervention in the exchange market, and (4) short-term capital movements.

In longer-run models, the combined current and long-term capital account is assumed to balance at the equilibrium exchange rate. Since long-term capital movements are believed to be independent of the foreign exchange rate, the problem of the stability of the foreign exchange market in the long run has to do only with the price elasticities and marginal propensities of imports and exports.

In short-run analysis, however, the responsiveness of short-term capital movements to exchange rate changes must also be taken into account. In fact, if the exchange rate remains close to the current figure, the exchange rate elasticities of demand for imports and exports are likely over short periods to be quite low. Thus, in the absence of substantial official intervention in the exchange market, the achievement of reasonable exchange rate stability depends on a high exchange rate elasticity of short-term capital movements.

The paucity of information on short-term capital transactions makes it impractical to use separate data on gross capital imports and gross capital exports. The approach chosen in constructing the model was dictated by the fact that the most reliable data available on short-term capital movements are the net balances recorded in the quarterly balance of payments estimates.

The model specifies equations designed to explain the magnitudes of Canada’s exports and imports of goods and services and of the net long-term capital inflow into Canada. But the key to the model is the relation between the exchange rate and the net balance of short-term capital movements. The remainder of this section is, therefore, devoted to an examination of this relation.

Since the balance of payments in the accounting sense always balances, the short-term capital balance is equal to the negative value of the sum of the current account balance, the long-term capital balance, and the net change in official reserves. This identity is a part of the model, but the short-term capital balance also measures the extent to which speculative positions in foreign exchange are taken. By “speculative position” is meant a holding or a claim which gives rise to an uncovered foreign exchange risk. The term thus includes both active and passive speculation. Active speculation is the assumption of positions in foreign exchange for the purpose of making an exchange profit. The failure to cover in the forward market a foreign exchange position ancillary to some other transaction constitutes passive speculation.4

To illustrate the point, let us assume that the net balance of Canada’s current and long-term capital account and the change in official reserves leaves a deficit to be settled by a corresponding short-term capital inflow into Canada. The settlement may be partly in cash and partly in commercial credit. To the extent that the exchange risk on Canadian dollars, or on claims to Canadian dollars, acquired by nonresidents is not covered in the forward market, these positions are speculative in the broad meaning of the term employed here. To the extent that the exchange risk is covered in the forward market, the supply of forward Canadian dollars will exceed that portion of the demand for forward Canadian dollars which has its origin in commercial transactions. The attempt to find forward cover for these net positions would be frustrated and the spot and forward rates would continue to depreciate indefinitely were it not for the fact that at some lower exchange rate speculators will be willing to take uncovered positions in spot or forward Canadian dollars.5 Equivalent results are obtained if the Canadian deficit is assumed to be settled in part through a reduction in foreign exchange balances, say U.S. dollars, held by Canadian residents. Thus, a given Canadian deficit of X Canadian dollars will always tend to lead to a depreciation of the Canadian dollar, both spot and forward, sufficient to induce active and passive speculators to hold exactly X Canadian dollars more than before. Covered interest arbitrage and covered commercial credit do not supply foreign exchange to the market as a whole. The function of covered interest arbitrage is to transfer foreign exchange between the spot and forward markets whenever speculators prefer to operate in one of the markets while there is imbalance in the other.

If the speculators’ demand for, and supply of, foreign exchange were perfectly exchange-rate elastic, the rate would never change. On the other hand, if nobody were willing to speculate, the rate fluctuations would have to be large enough to make the current account balance equal to the long-term capital balance plus changes in official reserves during every quarter, every month, and every week. For Canada, neither of these two extremes has been true. In order to evaluate the degree of responsiveness of speculative short-term capital movements to changes in the exchange rate, we must specify and test a speculative excess demand function for Canadian dollars.

The profit which an active speculator hopes to make, or the loss which a passive speculator hopes to avoid, depends on the difference between the current exchange rate and the rate expected to rule at some future date, as well as on any other cost or return arising from the holding of foreign exchange for a specified period. Speculators’ exchange rate expectations are not directly observable. But for our purpose it is sufficient to note that exchange fluctuations will tend to induce stabilizing speculation, provided the elasticity of exchange rate expectations is less than unity. For in this case, depreciation lowers the value of the exchange rate relative to the expected future rate and thus opens a margin of anticipated profit on short-term investments in the depreciated currency. Similarly, by raising the exchange value of a currency relative to the expected future rate, appreciation leads to the anticipation of an exchange profit on investments in foreign currencies. Other things being equal, the size of these profit margins depends on the magnitude of the underlying exchange rate variations. With plausible assumptions about behavior under conditions of uncertainty, we may expect the sums which individual speculators will be willing to commit in the foreign exchange market during a particular quarter to vary with the expected profit rate and thus with the size of the current change in the exchange rate. Furthermore, since individual speculators are likely to hold different views about the future exchange rate, a large variation in the rate will move a larger number of them from one side of the market, through a range of indecision, to the other side of the market, than would a small rate change. The data do not reveal the expected rates of profit on short-term investments in foreign exchange assets. But for about one half of the quarters observed, the change in the average quarterly exchange rate from the preceding quarter was between 1 and 2 per cent. Consequently, exchange profits of at least 4 to 8 per cent per annum, plus or minus the short-term interest differential, could be realized quite frequently. Such potential profit margins appear large enough to produce the necessary incentives on which the mechanism described in this paragraph must rely.

From the argument presented in this section it follows that the fundamental variable on which the speculative excess demand for Canadian dollars depends is not the level of the exchange rate, but the current rate of change of the exchange rate. Since statistical tests must be based on data referring to finite time periods, the current rate of change must be approximated by the difference between two consecutive exchange rate levels. The hypothesis to be tested is, therefore, that the speculative excess demand for Canadian dollars during a particular quarter is inversely related to the change in the average quarterly exchange rate from the preceding quarter to the quarter in question.

The speculative demand function for Canadian dollars contains two other variables. In the first place, allowance must be made for the cost of holding Canadian dollars. This cost is represented by the difference between the Canadian short-term interest rate and the relevant short-term interest rate abroad. It can thus be positive or negative. In view of the predominance of the United States in Canadian external financial relations, the U.S. Treasury bill rate has been used to compute the Canadian-foreign interest differential. Secondly, a variable has been included whose purpose is to indicate changes in exchange rate expectations by the magnitude and the direction of the deviation of the Canadian forward exchange rate from its interest parity. (A detailed derivation of the speculative demand function is given in Appendix II).

The essentials of the model may be summarized as follows: Canadian imports and exports of goods and services are functions of the exchange rate and of other variables. The long-term capital balance does not depend on the exchange rate. When the sum of the current account balance, the long-term capital balance, and the change in official reserves shows a deficit for a particular quarter, the Canadian dollar will tend to depreciate during that quarter. The depreciation must be sufficient to induce an increase in Canadian dollar holdings abroad or a reduction of private foreign exchange holdings in Canada, or both, equal to the deficit remaining at the lower exchange rate. When there is a Canadian surplus, the rate will tend to apppreciate sufficiently to induce an increase in foreign exchange holdings in Canada or a reduction of Canadian dollar holdings abroad, or both, equal to the surplus remaining at the higher exchange rate. The depreciation or appreciation of the Canadian dollar from the preceding quarter is, therefore, expected to depend on the size of the deficit or surplus. This relation is modified by the varying size of the differential between Canadian and foreign short-term interest rates and by the value of a variable indicating the state of exchange rate expectations.

II. Statistical Results

The model described in the preceding section could be tested by subjecting each equation individually to least-squares multiple regression analysis. However, application of the least-squares technique to a system of simultaneous equations will generally result in biased estimates of the coefficients. To avoid this bias, the coefficients have been computed by the “limited-information” version of the general maximum-likelihood method developed by the Cowles Commission for Research in Economics.6 Least-squares estimates have also been computed for comparison purposes. The model consists of 7 stochastic equations and 6 identities. Apart from the 13 jointly dependent variables, it contains 16 predetermined variables. All relations are taken to be linear in the original variables. The computations were carried out for the 24-quarter period 1952–57.7

Details concerning the structure of the model and the estimates are given in Appendix I. While certain additional features are present, the model corresponds basically to the simple theory of the short-run balance of payments adjustment process outlined in Section I. Equation 9 defines Canada’s surplus or deficit on current and long-term capital account plus the change in official reserves.8 The equilibrium exchange rate9 is determined by the equality of this balance with the speculative net demand for (or, if negative, the net supply of) Canadian dollars (equation 8). Equation 1, therefore, determines the change in the exchange rate from the preceding quarter which is necessary to bring about the equality of equation 8.

Turning first to the speculative excess demand function, we note that the signs of the coefficients are as expected on the basis of the underlying hypothesis. Other things equal, a reduction of the exchange rate by 1 cent will stimulate a speculative demand for Canadian dollars of $24 million during the quarter in which the depreciation occurs. In the least-squares estimate, the amount is somewhat larger. While the indicator of exchange rate expectations, e, has been taken as a predetermined variable, it shows in fact a slight negative correlation with the change in the exchange rate, Δr. The variable e, which induces an additional demand for Canadian dollars when it indicates that the Canadian dollar is expected to appreciate, and vice versa, thus takes some of the credit which rightfully belongs to the variable Δr. The best informal guess that it has been possible to make is that a depreciation or appreciation of the Canadian dollar by 1 cent has been sufficient to settle a deficit or surplus of $50–100 million during a particular quarter. The short-term interest differential between Canada and the United States appreciably affects the size of the exchange rate change necessary to settle a given deficit or surplus. A short-term interest differential of 1 per cent per annum (0.25 per cent per quarter) in favor of Canada attracts some $30 million of speculative funds per quarter into Canada, and thus tends to raise the Canadian exchange rate by perhaps as much as 12 to 1 cent.

For the import sector, the model assumes an infinitely elastic supply of imports at the exogenously determined import price level measured in terms of U.S. dollars. Equation 2 represents the demand for imports. The large investment component of Canada’s imports indicated the inclusion of domestic investment in the import demand function. The marginal propensity to import out of disposable income is 0.2, while the marginal propensity to import out of investment expenditure is 0.6. The price coefficient, deflated by Canada’s domestic price level, implies a price elasticity, at the mean values of imports and price, of about minus unity in the limited-information estimate and of minus one-half in the least-squares estimate.

The outcome in the export sector is less successful. While equation 3 implies an elasticity of demand of somewhat less than unity for exports with respect to foreign industrial production, several attempts to modify the specification of the equation resulted in the price coefficient having the wrong sign. The price coefficient in the export supply equation 4 is positive, as expected, in the limited-information estimate, but not in the least-squares estimate. The attempt to show the export volume and the export price index to be determined by equations 3 and 4 must be judged to have failed.

Equation 5 shows the net long-term capital inflow10 into Canada as depending on the level of undeflated fixed business investment, net borrowing of Canadian provincial governments, and the excess of the Canadian over the U.S. long-term interest rate. The equation shows the substantial extent of foreign financing of private investment and particularly of provincial, and presumably also of municipal, borrowing. Also of interest is the large apparent influence of the long-term interest differential. With a given U.S. interest rate, a rise of one percentage point in the Canadian long-term rate would tend to attract an additional $90 million of long-term capital per quarter.11

The relation between disposable income and gross national product (6), and the consumption function (7), as well as a number of necessary identities, are self-explanatory. Consumption and disposable income were considered jointly dependent variables and thus equations 6 and 7 are obtained, as it were, as by-products of the model.

III. Conclusions

While it is clear that the model would have to be considerably improved and refined before quantitative economic policy could be based on it, a number of tentative conclusions may be drawn from it even now.

Stabilizing exchange speculation appears to have been much more instrumental in keeping the fluctuations of the Canadian dollar within relatively narrow limits than either official intervention in the exchange market or the price effect of exchange variations on imports and exports. A depreciation of the Canadian dollar by 1 cent was found to induce a short-term capital inflow into Canada of about $24 million during a quarter. For reasons mentioned earlier, the true value might be expected to be even higher. On the other hand, official intervention in the market usually involved only small dollar amounts relative to the size of the balances to be settled. The price elasticity of real import demand was found to be around unity, so that the Canadian dollar value of imports would be unaffected by a change in the exchange rate. On the export demand side, the results are inconclusive, the price coefficient having the wrong sign; but it is unlikely that the true short-run elasticity of demand for exports is very large. It seems, therefore, that short-term capital has been the principal stabilizer of the Canadian exchange rate.

The model contains an interesting implication concerning the difference between the export multiplier and the investment multiplier in Canada. From the estimated marginal propensities to consume and to import and from the relation between disposable income and gross national product, the export multiplier12 would appear to be approximately 2. But in the case of an autonomous increase in investment, the effective multiplier is considerably smaller, since, according to the import demand function, less than one half of the rise in investment constitutes an increase in demand for Canadian output. The investment multiplier is therefore approximately unity or perhaps slightly less. When investment, exports, and government expenditures on goods and services increase or decrease at the same time, the multiplier will be between 1 and 2, and it will be closer to the lower limit the larger is the share of investment in the increment of autonomous expenditure.

While the import demand function explains why, in Canada, an investment boom leads to a particularly large increase in imports, the long-term capital equation confirms the view that the effect of an investment boom on the Canadian exchange market is ordinarily mitigated by substantial foreign financing of domestic investment. The model indicates that, including the multiplier effect, imports will tend to rise by almost three fourths of an increase in domestic investment.13 But one third of this increase in imports would be financed by an increase in long-term borrowing; when the likelihood of an increase in the long-term interest rate during an investment boom is taken into account, the proportion of investment-induced imports which will be financed by long-term capital is even larger, unless the long-term interest rate in the United States is also increasing at the time.

A joint consideration of the estimated effects of the short-term and the long-term interest differential on Canada’s foreign exchange market points to the paramount importance of Canadian monetary policy in the determination of the exchange rate and also to the relatively small scope for Canadian monetary action independent of monetary policy in the United States. During a boom period in Canada, high interest rates and tight money are necessary to maintain the exchange value of the Canadian dollar. A Canadian boom accompanied by an easy money policy would undoubtedly have a very unsettling effect on the Canadian exchange market. In long-run perspective, the relatively small deviations of the Canadian exchange rate from parity with the U.S. dollar must be explained by reference to the close coordination of Canadian financial policies with the policies pursued abroad, chiefly in the United States.

The model presented in this paper confirms the view that in an otherwise stable economic environment unrestricted capital movements need not be feared as a source of instability. In fact, a workable fluctuating exchange system with a minimum of official intervention must rely on stabilizing capital movements and could not exist without them. The Canadian experience of the 1950’s shows that, as long as the trust in continued domestic monetary stability induces stabilizing exchange rate expectations, substantial swings in the balance of payments can be settled by private short-term capital movements, with reasonably small exchange fluctuations.14 It must be recognized, however, that the degree of over-all monetary stability which has characterized Canada’s domestic and external financial relations, and which is a necessary ingredient of a workable fluctuating exchange system, would have been present during the 1950’s in very few other countries. Unqualified generalization from the success of Canada’s exchange market experiment would, therefore, seem unwarranted.

APPENDICES

I. The Structure of the Model

The model consists of 13 equations. Equations 8 through 13 are identities. For the stochastic equations, 1 through 7, the limited-information maximum-likelihood estimates (L.I.) are given first, the least-squares estimates (L.S.) are given second. The standard errors of the parameter estimates are put in parentheses below the coefficients. The value for d is the Durbin-Watson test statistic for serial correlation (in the case of 24 observations, serial correlation should not be suspected— on the 95 per cent level of confidence—if d exceeds 1.33,1.43, and 1.54, respectively, in equations containing 1, 2, and 3 predetermined variables), In the least-squares estimates, R2 is the square of the multiple correlation coefficient.

(1) The speculative net demand for Canacdian dollars

S = speculative net demand for (if negative, net supply of) Canadian dollars = value of short-term capital movements (million dollars).

(jointly dependent variable)

Δr = change in the exchange rate from preceding quarter; r = U.S. dollars per Can$1.00, quarterly average of daily noon rates.

(jointly dependent variable)

e = indicator of exchange rate expectations = 90-day forward premium on Canadian dollar adjusted for the U.S.-Canadian short-term interest differential (per cent per quarter).

(predetermined variable)

h = U.S. minus Canadian three-month Treasury bill rate (per cent per quarter).

(predetermined variable)

(2) Canadian demand for imports

M = real imports of goods and services (million dollars).

(jointly dependent variable)

Y’d = real disposable income less change in farm inventories (million dollars).

(jointly dependent variable)

Pm = import price index (1949 = 1).

(predetermined variable)

r = exchange rate —U. S. dollars per Can$1.00, quarterly average of daily noon rates.

(jointly dependent variable)

P0 = domestic price index of consumer and investment goods (1949= 1).

(predetermined variable)

I’= real gross domestic investment less change in farm inventories (million dollars).

(predetermined variable)

Note:–The supply of imports is assumed to be infinitely elastic at the price Pm, which consequently becomes a predetermined variable.

(3) Foreign demand for Canadian exports

Xa = real exports of goods and services (seasonally adjusted, million dollars).

(jointly dependent variable)

Px = Canadian export price index (1949 = 1).

(jointly dependent variable)

Ps = export price index of countries competing with Canada in world markets (1949 =1).

(predetermined variable)

Yaf = index of industrial production of principal customers of Canada, weighted by 1953 share in Canadian exports (1949 = 100).

(predetermined variable)

r = as above.

(4) Supply of Canadian Exports

X = real exports of goods and services (not seasonally adjusted, million dollars).

(jointly dependent variable)

Y = Canadian real GNP (million dollars); this variable represents Canada’s capacity to produce exports.

(jointly dependent variable)

Px, Pc = as above.

(5) Net long-term capital imports into Canada

L = net long-term capital imports into Canada (million dollars).

(jointly dependent variable)

IP = Canadian domestic investment in nonresidential construction, machinery, and equipment (undeflated, million dollars).

(predetermined variable)

D = net new issues of provincial bonds and debentures (million dollars).

(predetermined variable)

i = excess of Canadian over U.S. long-term interest rate (comparable bonds, per cent per annum).

(predetermined variable)

Note:-Equation 5 contains only predetermined variables on the right-hand side and consequently no separate limited-information estimate is given.

(6) Relation between disposable income and GNP

Yd = real disposable income (million dollars).

(jointly dependent variable)

Y = as above.

(7) Consumption function

C = real consumption expenditure (million dollars).

(jointly dependent variable)

Y’d = as above.

Identities

A = change in official reserves (million dollars).

(predetermined variable)

Fa = balance of migrants’ funds and inheritances (which are omitted from X and M; million dollars).

(predetermined variable)

B = Canada’s balance of payments “surplus” or “deficit” in Canadian dollars (million dollars).

(jointly dependent variable)

X, Px, M, Pm, L = as above.

Qs = seasonal adjustment factor.

(predetermined variable)

X, Xa = as above.

γ–1 = exchange rate during the preceding quarter.

(predetermined variable)

Δγ, γ = as above.

Ha = change in farm inventories (in real terms, million dollars).

(predetermined variable)

G = real government expenditure on goods and services (million dollars).

(predetermined variable)

Y, C, I’, X, M = as above.

Y’d, Yd, Ha = as above.

The coefficients of the price variables in equation 3 (L.I.) and (L.S.) and in equation 4 (L.S.) have the unexpected sign. The other coefficients have the theoretically expected sign.

II. The Speculative Demand for Foreign Exchange

An investor who has U.S. dollars at his disposal and wishes to retain his funds in that currency, except for short periods, must compare the expected yield on an investment in Canadian dollars with the yield on alternative assets. If he buys a sum of s Canadian dollars, he will pay γs U.S. dollars, γ being the price of one Canadian dollar in terms of U.S. dollars. Ignoring the cost of making the transaction and assuming that the funds will be invested in Canada for one period—say 90 days—at an interest rate of ic per quarter, the investor expects to receive in U.S. dollars the amount s(1 + ic)γ’, where γ’ is the exchange rate that he expects to rule 90 days hence. The yield is given by15

The yield w’ must be compared with the rate if that can be earned on a suitable alternative short-term investment elsewhere, e.g., U.S. Treasury bills.

It is sometimes convenient to consider the net yield w over and above the yield on an alternative domestic investment:

  • w = γ’ – γ – h (approximately),16 where h = if – ic.

Similarly, the net return wc on s Canadian dollars to be invested for one quarter in the United States is approximately17

  • wc = γ − γ’ + h = −w.

Since wc = − w, the subscript may be omitted and we may say that w is the net return expected on a purchase of Canadian dollars, with the understanding that if w is negative it represents the return expected on a sale of Canadian dollars, the respective transactions to be reversed after 90 days.

If all potential investors expected a particular value of γ’ with certainty, they would buy or sell Canadian dollars to the limit of their resources, including any short-term credit available to them at rates of if or ic. The only exception would be where w equals zero or is so close to this value that the other costs of the transactions, which have been ignored in our derivation of w, would not be covered. But future exchange rates are not expected with certainty, nor do all potential investors agree on the most probable value of the future rate.

A speculator’s expectations concerning the level of the exchange rate at some future date can be described by a probability distribution whose mean shifts up or down as his appraisal of the future price of the Canadian dollar becomes more or less optimistic, and whose standard deviation becomes larger or smaller as his uncertainty about the future increases or decreases. The speculator will rarely wish to put all his eggs in one basket. But, at a given level of uncertainty, the larger the difference between the present exchange rate, γ, and the mathematical expectation of the future rate, γ’, the greater will be the incentive to engage in speculative foreign exchange transactions. Thus, if Canada has a deficit at the initial exchange rate, γt–1, it is the function of the decline in the price of the Canadian dollar, Δγt (i.e., γtγt–1), which will be negative in the present example, to lower the actual rate relative to the expected rate by an amount sufficient to induce the necessary purchases of Canadian dollars. The larger the absolute value of Δγt becomes, the larger is the number of speculators who will enter the market as buyers of Canadian dollars, and the larger the volume of funds which the typical speculator will commit in this way. The proviso must be added, however, that the elasticity of exchange rate expectations be less than unity. For with an elasticity of expectations in excess of unity, any change in the rate by 1 per cent would change the expected rate by more than 1 per cent in the same direction and, consequently, the current rate could not rise or fall relative to the expected rate.

To set out these relations, let S, the net speculative demand for Canadian dollars, depend on w; then

The elasticity of exchange rate expectations is

Since γ/γ’ will ordinarily be close to unity, the value of the slope (’/) will not differ significantly from the elasticity E. A change in the current rate, Δγ, will change the expected rate, γ’, by Δγ(’/). If we first assume that, apart from the effect of the current rate change, the rate expected to rule in the next period (t + 1) is equal to the actual rate of the last period (t – 1), then the speculative demand for Canadian dollars in period t is18

The quantity (’/) is not known in advance. Assuming the elasticity of expectations to be constant, we rewrite equation 15 in more general form as

where the estimated coefficient associated with Δrt will tend to equal [(dr’/dr)-1] times the estimated coefficient of (−ht).

So far, no allowance has been made for the effect of what might be called autonomous changes in expectations in the determination of the speculative demand for Canadian dollars. Let the extent of such a shift in exchange rate expectations in period t be measured by changes in a variable et and let this variable be inserted in equation 16. Thus

The variable et is an indicator of the prevailing exchange rate expectations in the foreign exchange market.

The indicator et is based on the relation between the spot exchange rate, γt, the (one-period) forward exchange rate, γft, and the net holding cost, ht, the last being approximated by the international short-term interest differential. The indicator of exchange rate expectations, et, is defined as

If buyers and sellers in the foreign exchange market are merely uncertain about the future exchange rate, but expect it on balance to remain at the present level, the difference between the spot rate and the forward rate (expressed as a rate per annum) will tend to equal the international short-term interest differential. If, however, according to the prevailing expectations, the price of the Canadian dollar will rise, its forward! price will tend to be higher than its spot price plus the excess (positive or negative) of the foreign over the domestic short-term interest rate. On the other hand, if, according to the prevailing expectations, the price of the Canadian currency will fall, its forward price, after adjustment for the interest differential, will tend to be lower than its spot price.

This tendency of the forward rates to deviate from their interest parities is counteracted by covered interest arbitrage. In fact, a value of et which differs from zero by more than the cost of the arbitrage transactions affords a perfectly riskless return, either on the Canadian side of the market, when et is negative, or on the foreign side, when it is positive. Nevertheless, lack of short-term funds and other imperfections of the market prevent a complete adjustment. In Canada, values of et corresponding to returns of as much as 1 to 2 per cent per annum over and above the domestic return on short-term funds have persisted for substantial periods of time.19

Large values of e must be taken as evidence that the need to transfer foreign exchange between period t and period (t + 1) exceeded the volume of short-term funds available for covered interest arbitrage. Therefore, e reveals the attitude of speculators toward the alternative of buying or selling spot versus buying or selling for forward delivery and thus their appraisal of the future of the exchange rate.

It is true that et indicates not only autonomous changes in expectations, but also differences between the expected future rate and the current rate which emanate from the change in the current rate; et is not independent of Δγt. If expectations are inelastic and the spot rate changes, it will tend to leave the forward rate behind. One should, therefore, prefer to replace et by a variable which measures only the autonomous shifts in expectations and does not itself depend on Δγt. But such a variable is not available. Consequently, the estimating equation, 17, must be used with the understanding that part of the effect on St ascribed to shifts in expectations may really be due to the variable Δγt.

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Mr. Rhomberg, who is a graduate of the University of Vienna and of Yale University and has been a member of the faculty of the University of Connecticut, is an economist in the Finance Division.

This paper was presented at the Winter Meeting 1959 of the Econometric Society in Washington, D.C. It presents part of the research for the author’s doctoral dissertation, Fluctuating Exchange Rates in Canada: Short-Term Capital Movements and Domestic Stability (Yale University, 1959). The author wishes to express his gratitude to the M.I.T. Computation Center and the International Business Machines Corporation for the use of the Electronic Data Processing Machine 704 at the Massachusetts Institute of Technology, where the largest part of the computational work was done, and to the National Science Foundation and the Cowles Commission for Research in Economics for the use of the IBM 650 at the Yale Computation Center, where some of the preliminary computations were carried out. He also wishes to thank Mr. H. C. Lampe, Department of Agricultural Economics, University of Rhode Island, who cooperated with him in the coding of the limited-information maximum-likelihood program.

At least one exception should be explicitly mentioned; see Milton Friedman, “The Case for Flexible Exchange Rates,” Essays in Positive Economics (Chicago, 1953), which discusses the short-run balance of payments adjustment process with special emphasis on short-term capital movements.

In his study, “An Experiment with a Flexible Exchange Rate System: The Case of Peru, 1950–54,” Staff Papers, Vol. V (1956–57), pp. 449–76, S. C. Tsiang had to rely on annual data and on a period of only four years.

For a similar treatment, see S. C. Tsiang, “The Theory of Forward Exchange and Effects of Government Intervention on the Forward Exchange Market,” Staff Papers, Vol. VII (1959–60), pp. 75–106.

While the Canadian authorities operated in the forward market on a fairly large scale through 1951, their intervention since 1952 has been negligible.

See Studies in Econometric Method (Cowles Commission for Research in Economics, Monograph No. 14, edited by Wm. C. Hood and Tjalling C. Koop-mans, New York, 1953).

Computations for the 28-quarter period 1951–57 yielded on the whole less good results, presumably because of certain special circumstances which characterized the first year of operation of the fluctuating exchange system, including the continuance of exchange control until December 1951. Experiments were also made with several ways of handling the problem of seasonal variation. Neither the use of seasonally adjusted values for imports, exports, consumption, income, etc., nor the use of special seasonal dummy variables gave satisfactory results for the model as a whole. The model presented here is seasonally adjusted in two respects: First, the change in farm inventories, which shows a very marked seasonal pattern, has been subtracted from the domestic investment and disposable income variables appearing in the import demand equation and in the consumption function. Second, exports and the variable which stands for foreign income in the export demand function have been seasonally adjusted. The appropriate additions have been made in the list of predetermined variables. If the number of observations had been larger, a more satisfactory and more consistent solution of the seasonal problem might have been found. The small number of observations also accounts for the absence of lagged variables. Lagged income variables were originally included in the import demand, export demand, and consumption functions. But since their inclusion did not improve the model, they are omitted in the version presented here. Combinations of such variables as price ratios have been treated as one variable in the model reported here. Computations were made with linear approximations for the products or ratios of combined variables without the results being materially affected.

The change in reserves is taken to be a predetermined variable since its correlation with exchange rate changes on a quarterly basis was not significant.

The exchange rate variable used in the model is the quarterly average of daily noon rates.

Since there is only one jointly dependent variable in this equation, the least-squares estimate and the limited-information estimate are identical.

In view of the crudity of the equation, it should be noted that it “predicts” the net long-term capital balance during the six quarters following the period on which the model is based with an average error of only 8 per cent, and without any help from the constant term, which is negative while the long-term capital balance is positive throughout.

This relation ignores any magnification of domestic demand through an export-induced increase in domestic investment.

According to the coefficients presented in Appendix I, equations 2, 6, and 7, an increase in investment, ΔI, will lead to an increase in demand for domestic output of 0.4ΔI, while ΔY will be 0.8ΔI, and ΔYd, the change in disposable personal income, will be 0.64ΔI. Thus

ΔM=0.2ΔYd+0.6ΔI=0.73ΔI.

Similar conclusions were reached by S. C. Tsiang in “Fluctuating Exchange Rates in Countries with Relatively Stable Economies: Some European Experiences After World War I,” Staff Papers, Vol. VII (1959–60), pp. 244–73.

w=amountreturnedamountadvanced1=s(1+ic)γγs1, which reduces to the expression in the text. If the funds are expected to be repatriated after n periods, w’ is evaluated from

(1+w)n=γn(1+ic)nγ,

where γ’n is the exchange rate expected to rule after n periods. In the text, we shall continue to make the simplifying assumption that such investments are planned for one period, although they may be renewed at the end of each period.

The relation is

w=wif=γγ+γicγifγ.

In the case here being considered, the exchange rate is close to unity and the expected changes in the exchange rate are ordinarily small. Therefore, the right-hand expression yields the approximation in the text.

The yield wc to a Canadian investor in U.S. Treasury bills over and above the yield ic which he could earn on Canadian Treasury bills is

wc=amountreturnedamountadvanced1ic=sγ(1+iγ)/γs1ic=γγ+γifγicγ

which, by the reasoning in the preceding footnote, gives the approximation in the text.

Since

wt=γtγtht=(γt1+Δγtdγdγ)γtht=(γt1+Δγtdγdγ)(γt1+Δγt)ht=Δγt(dγdγ1)ht.

This formulation includes the special cases where E, the elasticity of expectations, equals zero, St = f(− Δγtht), and where E equals approximately unity, St = f(− ht).

If the short-term credit market were not imperfect, a tendency toward such a shortage of funds for arbitrage purposes, say in Canada, would raise the Canadian short-term interest rate until the return on arbitrage operations vanished. Persistence of such a return is, therefore, evidence of credit rationing on the part of the banks. In fact, Canadian banks are reported to be reluctant to extend credit for pure exchange transactions, even to the extent of requiring a cash margin or deposit to cover their risk of nonfulfillment of the contract (Sidney A. Shepherd, Foreign Exchange in Canada: An Outline, Toronto, 1953, p. 59). Negative values of e, indicating a short-term investment opportunity for owners of Canadian funds, can thus approach values at which the use of funds for interest arbitrage begins to compete with higher-yielding assets. For instance, in December 1952 and January 1953, Canadian funds converted into U.S. dollars and invested in U.S. Treasury bills would have yielded 3.7 per cent per annum, while the Canadian Treasury bill rate was 1.35 per cent; and in December 1956, this yield was 5.6 per cent, with the Canadian bill rate at 3.67 per cent at that time. On the other hand, on the U.S. side of the market, no such limitation on available arbitrage funds seems to have existed after 1951. The largest yields over and above the U.S. Treasury bill rate obtainable for arbitrageurs with U.S. funds were % per cent. This explains why from 1952 to 1957 the value of e, while sometimes larger and sometimes smaller, was almost always negative. Another factor which helps to explain this phenomenon is the Canadian trade deficit with the United States. In the course of normal operations of Canadian exporters and importers to cover exchange risks, the demand for U.S. dollars on the part of the importers will tend to exceed the exporters’ supply of forward U.S. dollars, and the forward price of the Canadian dollar will tend to be weak, i.e., the forward U.S. dollar will be at a premium. Similarly, forward sterling was almost always at a discount, because of the Canadian trade surplus with the United Kingdom, and also because of the exchange control restrictions on arbitrage operations in the sterling area.

To the extent that covered interest arbitrage does not fully close the gap measured by e, the size of this gap may be interpreted as a rough indicator of the market’s expectations concerning the future of the exchange rate. Large negative values of e imply that the Canadian dollar is expected to depreciate. Unfortunately, e is probably not a good indicator of expected appreciation, since U.S. interest arbitrage does not allow large positive values of e to develop.

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