Mr. Porter, economist in the Financial Studies Division of the Research Department, is a graduate of the University of Adelaide (Australia) and Stanford University (California). He formerly taught at Simon Fraser University (British Columbia, Canada) and visited the University of Essex (England) on a Canada Council Research Grant in 1969–70.
The author is deeply grateful for the comments and suggestions of staff colleagues and R. I. McKinnon and E. S. Shaw of Stanford University, and to Douglas Fisher and J. Michael Parkin for their remarks and criticisms at a seminar at the University of Essex in 1970. He wishes to emphasize that responsibility for the present text is his alone.
See, for example, John Maynard Keynes, A Tract on Monetary Reform (London, 1923), pp. 115–39. A review of the recent literature may be found in Lawrence H. Officer and Thomas D. Willett, “The Covered-Arbitrage Schedule: A Critical Survey of Recent Developments,” Journal of Money, Credit and Banking, Vol. II (1970), pp. 247–57.
See J. R. Hicks, Value and Capital (Oxford University Press, Second Edition, 1946), pp. 141–52; David Meiselman, The Term Structure of Interest Rates (Englewood Cliffs, N. J., 1962).
We may write (2) as follows:
which is equivalent to (5) above.
If a = 0, then we obtain Case 1 as a special example of Case 2.
The data referred to were obtained from the sources listed below. These same data were used in the econometric work discussed below.
a. Interest rates. We examined the yields on Canadian and U.S. Treasury bills and bonds. (The U. S. Treasury Bulletin monthly yield curves and treasury bill quotations provided the basic U. S. data. Canadian data are from the Bank of Canada, Statistical Summary.) Quarterly, end-of-month, quotations were obtained for a range of maturities in both countries, and these yields were then plotted, one graph being drawn for each time period. A continuous curve was then drawn and used to obtain theoretical yields of securities of identical maturity for both countries. In some instances the theoretical yields obtained were sensitive to the manner in which the curve was drawn; however, the errors are likely to have been small in relation to the interest rate differentials. The three-month data are not completely satisfactory, since the Canadian Treasury bill market is less highly developed than the bond market.
b. Exchange rates. The absence of published daily exchange rate quotations led us to use the average monthly quotations from the Bank of Canada, Supplement to the Statistical Summary. However, the daily quotations from the internal records of private banks were also used. (Herbert G. Grubel, Forward Exchange, Speculation, and the International Flow of Capital, Appendix A, pp. 167–82, Stanford University Press, 1966.) Grubel’s data commence in 1955; in the results using exchange rate data over the period 1953–60, the monthly average data were used for 1953–54 and the Grubel data for 1955–60. Estimating the same regressions using only the monthly average data does not significantly change any of the results. This is so because changes in the monthly average of daily quotations are close approximations to the changes in the end-of-month quotations over the same periods.
Actual, or anticipated, taxation of foreign assets and liabilities can cause yields to diverge between countries for reasons that may have little to do with exchange rate expectations. This particular complication is unlikely to have been important for Canada in the period of flexible rates (see Gerald K. Helleiner, “Connections Between United States’ and Canadian Capital Markets, 1952–1960,” Yale Economic Essays, Vol. 2, Fall 1962, pp. 351–400), although it may have been important since December 1960, the date on which the Canadian Government introduced a 15 per cent withholding tax on interest paid on foreign holdings of provincial and government bonds.
Harry Markowitz, Techniques of Portfolio Selection (New York, 1959).
J. Tobin, “Liquidity Preference as Behavior Towards Risk,” The Review of Economic Studies, Vol. XXV (February 1958), pp. 65–86.
The analysis requires that country X borrow from country W, and the results would have to be modified if it is assumed that X is a creditor country.
The Canadian exchange rate was floated in October 1950. We have chosen to focus on interest rate differentials from 1953, on the grounds that until 1953 the Canadian short-term security market was extremely thin (R. M. Macintosh, “Broadening the Money Market,” Canadian Banker, Autumn 1954) and that interest rates were pegged in the United States up until the 1951 accord. Over the period 1953–60, the effect of taxation policy in the United States and Canada on the yield differences on government bonds is regarded to have been negligible (Helleiner, op. cit.). In December 1960 the Canadian Government introduced a 15 per cent withholding tax on interest paid on foreign holdings of provincial and government bonds, and in 1961 the Government began to intervene actively in the foreign exchange market, in contrast to its passive role in the previous decade. For these reasons, our end point for the series of interest rate differentials was chosen as December 1960, thus providing us with the period 1953–60, a period that was relatively free from large-scale intervention in either the securities or foreign exchange market. (For an up-to-date survey of Canadian monetary policy over the whole period, see Gordon Boreham, Eli Shapiro, Ezra Solomon, and William L. White, Money and Banking: Analysis and Policy in a Canadian Context (Canada, 1969), pp. 748–73, and Bank of Canada, Annual Reports, 1950–69. Paul Wonnacott, The Canadian Dollar, 1948–1962 (University of Toronto Press, 1965), is also a useful reference. An excellent and comprehensive econometric study of the Canadian economy may be found in Rudolf R. Rhomberg, “A Model of the Canadian Economy under Fixed and Fluctuating Exchange Rates,” The Journal of Political Economy, Vol. LXXII (February 1964), pp. 1–31. A study of speculation and exchange rate stability may be found in William Poole, “The Stability of the Canadian Flexible Exchange Rate, 1950–1962,” The Canadian Journal of Economics and Political Science, Vol. XXXIII (1967), pp. 205–17.)
The exchange rate was pegged again in May 1962. In order to avoid the particular effects of the transition to the fixed exchange rate and the uncertainty attached to the June 1962 election, we have commenced our second period on July 31, 1962 and continued it to October 1968.
The exchange rate data refer to average monthly figures. The interest rate ratios were computed using yield curves based on end-of-month data.
The following example illustrates hypothesis (A):
If λ = 0.4, the weight given to the current observed value of the exchange rate (i = 0) is 0.6; the weight for the previous period (i = 1) is 0.4 × 0.6 = 0.24 and the weights for the preceding periods are (0.4)2 × 0.6 = 0.096, when i = 2; (0.4)3 × 0.6 = 0.0384, when i = 3; and (0.6)k × 0.4 when i = k. The sum of these weights approaches 1.0 as i increases.
This expression may also be written
There have been various references to this sort of behavior. For example, Rhomberg, in a discussion of the stability of the Canadian flexible exchange rate (op. cit., p. 5), makes reference to expectations of the exchange rate moving away from “unusually high or unusually low” values.
We cannot reject the hypothesis of positive serial correlation in the error terms, and hence our t-ratios are biased upward. The presence of positive serial correlation is not surprising, since acts of policy, such as open market operations, are likely to account for part of the error terms, and these acts will inevitably be positively correlated over time.
This assumption would seem consistent with evidence contained in the study by Helleiner, op. cit.
However, it is clear that a much more complete study would be required before anything definite could be said about the adjustment process.
The recent economic history of Canada makes item (b) unlikely to be of any great importance.
This situation is analogous to recent arguments and evidence pertaining to closed economies. The argument, in the closed economy case (Milton Friedman, “The Role of Monetary Policy,” The American Economic Review, Vol. LVIII, March 1968, pp. 1–17), is that sustained monetary expansion leads, eventually, to anticipations of inflation, and these anticipations cause nominal interest rates to rise—possibly above the level ruling prior to the acts of sustained monetary expansion.
We have omitted to adjust the yield ratios for the foreign exchange risk factor. By assuming that (
Although the standard errors are biased downward owing to significant positive serial correlation.
It is clear that we could interpret this result as indicating disequilibrium in the Canadian Treasury bill market in the short run; i.e., that the high value of the Canadian Treasury bill rate causes capital inflow, which causes Kt+3 to fall. This was found to be so in the study by Rhomberg, op. cit. The presumption is, therefore, that in terms of our analysis the Canadian Treasury bill rate,
However, the significance attached to the estimates of any particular equation decreases with the number of regressions run (i.e., the wider the range of maturities and time horizons), since the probability of finding, by chance, a maturity with a yield ratio that correlates with subsequent exchange rate changes increases with the range of maturities tried.
If there were perfect covered interest arbitrage,
The test of significance is an F-test on the ratios of the two variances.
See Tobin, op. cit., and Markowitz, op. cit.
With respect to the mounting literature on portfolio models of international capital flows, interest rates, in the countries between which capital flows, are assumed to be exogenous and independent of the capital flows. This is a serious weakness that we avoid by invoking the small country assumption and solving for the interest rates consistent with stock equilibrium.
The results shown above can easily be generalized to any number of assets in the dependent country, X. If RFi, RFj are the yields on any two assets in X, then we can write down the following results from our generalized first-order conditions:
Thus, the difference between yields in X depends on the difference in the variances and correlation coefficients with yields in W. The constant multiplicative factor is a function of the spread between the risky and the riskless assets (RW – RD), the variance in W, and the expected value of X’s currency.