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On Buying Cheap and Selling Dear: Professor Powrie's ParadoxAuthor(s): H. C. EastmanSource: The Canadian Journal of Economics and Political Science / Revue canadienned'Economique et de Science politique, Vol. 30, No. 3 (Aug., 1964), pp. 431-435Published by: Wiley on behalf of Canadian Economics AssociationStable URL: http://www.jstor.org/stable/139709 .

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Notes and Memoranda 431

3. I concluded that fiscal policy in a small country has no effect upon employment when the exchange rate is flexible. This conclusion remains true when interactions with the rest of the world are brought into account, but it becomes, of course, progressively less true as the size of the country, relative to the rest of the world, increases. An interesting conclusion is that fiscal policy in a small country has no effect upon income at home, but it has an ordinary multiplier effect on income in the rest of the world; conversely, fiscal policy in a large country has a large effect upon employment at home but a negligible influence upon employment in the rest of the world. The ratio of the multipliers, in fact, conforms closely to the ratio of the incomes, unless considerable disparities exist between income and interest elasticities of demand for money in the two countries.

4. I concluded originally that under flexible exchange rates monetary policy in a small country would have a "classical" effect upon income in the sense that income increases in proportion to the open market operation. A corollary of this is that it also has a considerable influence in the opposite direction on foreign income. But as the size of the country is made (hypothetically) large relative to the rest of the world, the high degree of effectiveness of monetary policy is diminished, and so is its opposite impact on the rest of the world.

A final comment seems worth making. During Canada's experience with flexible exchange rates the Canadian business cycle paralleled the US business cycle so closely that the traditional theory of insulation is, at best, inadequate. My analysis suggests a new international mechanism of cyclical transmission based on capital flows and interest rate changes. As the US economy, say, contracts, and Canadian exports fall, US interest rates also fall, the interest differential in favour of Canada rises, capital moves to Canada and the depreciation of the Canadian dollar is forestalled, leaving a trade balance multiplier effect sufficient to cause income contraction in Canada. This cyclical mechanism might have been (but was not) ruptured by a prompt reaction of the Canadian monetary authorities in the direction of ease in the case of US contraction, and in the direction of restraint in the case of U.S. inflation.

ON BUYING CHEAP AND SELLING DEAR: PROFESSOR POWRIE'S PARADOX

H. C. EASTMAN University of Toronto

PROFESSOR Powrie's article on international short-term capital movements' is untypically obscure in its theoretical treatment of capital movements that reduce the range within which the exchange rate fluctuates or, what is the same thing, that reduce short-term fluctuations about a central trend some- times called the normal rate. The unease begins where the reader is told that

1"Short-term Capital Movement and the Flexible Canadian Exchange Rate, 1953- 1961, this JOURNAL, XXX, no. 1, Feb., 1964, 76-94.

Vol. XXX, no. 3, Aug., 1964



432 Canadian Journal of Economics and Political Science

"short-term capital movements related to (Pn - Nn) would still usually be the most efficient stabilizers . . . ," but that "short-term capital movements related to (Pn - Pn_L ) can also be powerful stabilizers, even when they bear no statistical relation to (Pn- Nn )" (p. 85, italics mine). In other words we are invited to contemplate the paradox of capital movements that reduce the amplitude of fluctuations in the rate of exchange without net resistance to departures of the rate from its long-term trend.

Capital movements, guided by whatever considerations, reduce the amplitude of fluctuations only in so far as they cause selling at high and buying at low rates of exchange, for how else would peak prices be reduced and the lowest ones raised? The author is unable to resolve the paradox, hence the hedging and the struggle with unreal distinctions in the definition of stabilization.

The algebraic model provided by Professor Powrie shows, once again, that fluctuations in the rate of exchange are reduced by inflows of capital that are related to rises in the rate between the previous period and the present and by outflows caused by falls in the rate, because such action provides addi- tional supply or demand for foreign exchange at what would otherwise be the peaks and troughs in the fluctuations of the rate. To what, then, can be attributed his failure to find statistical evidence of stabilizing capital movements related to the difference between the normal rate and the rate as it would have been in the absence of capital movements, when their existence was revealed by a significant relation to (P -Pn-P1)? The error resides in not remembering that the rate used in the calculations is Pn, the observed rate whose fluctuations are in fact reduced, not the rate that would have existed in the absence of capital movements. The movements of the observed rate are not in phase with those that would have existed in the unstabilized rate in the cases in which the short-term capital movements are related to changes in the observed rate between the past and the present period, namely to (Pn Pn-P )

The assumption that capital movements resist changes in the rate means that capital flows are inward during the rising phase of the fluctuation in the observed rate, are absent at the peak, and outward in the downswing in the observed rate. It follows that inflows and outflows balance each other on either side of the peak of the observed rate (and similarly for the trough) so that no net capital movement related to the difference between the observed rate and the normal rate takes place. The correlation between such capital movements and (Pn-Nn) is necessarily zero. But if the price used in the calculation is not the observed rate, but the rate that would have existed in the absence of stabilizing capital movements, net sales of foreign exchange are seen to take place when the rate would otherwise have been high and purchases when it would otherwise have been low.

Curve A in Figure 1 traces the time-path of the rate of exchange as it would be in the absence of short-term capital movements. Curve B traces the time-path of the rate when inflows and outflows of short-term capital are made according to the difference between the rate that would have existed in the absence of capital movement and the normal rate. The capital movements




Price of Foreign Exchange

A ~~~~~~~~~~~h

Nor al; Rate X k

Time

Short-Term Capital Movement

7A..._-__E

Time

FIGURE 1

are shown by curve D. Curve A and curve B are in phase so that the capital movements bear the same relationship in time to the fluctuations in the rate that would have existed in the absence of capital movements as they do to the observed rate so long as the observed rate is not perfectly stable. Underlying the diagram is the assumption that a given capital movement always brings about the same difference between the observed rate and the rate as it would have been had no capital movement taken place. Curve C traces the time-path of the rate when inflows and outflows of capital are related to the difference in the observed rate between the present and the previous period. The capital movements are shown by curve E.

Three main points can be made on the basis of the diagram. First, the relationship of curves C and E show that no net capital movements occur when C is high or low in relation to the normal rate. This is a reflection of the assumption that capital flows in as the observed rate rises and flows out when it falls. The absence of a net capital movement is what Professor Powrie measured. Second, the relationship of curves A and E show that net capital movements are positively related to the difference between the rate as it would have existed in the absence of short-term capital movements (and whose fluctuations are reduced) and the normal rate. Some capital flows in an



434 Canadian Journal of Economics and Political Science

unstabilizing direction, but most flows in when the rate would otherwise have been high and flows out when it would have been low. Of the inward capital movement shown by the area f g h i j k between curves A and C, only f g k depresses the observed rate away from the normal level. This is less than the area f h k, which is one-half the capital movement.2 Third, the type of stabilization resulting from capital movements related to the difference between the rate that would exist in the absence of capital movements and the normal rate is more efficient than when they are related to changes in the observed rate. Efficiency is here measured by the smallness of the capital flow that achieves a given reduction in the amplitude of fluctuations in the rate. The degree of stability in curves B and C is identical, the only difference between the two curves being in phase, but the area under curve E is larger than under curve D and these areas show the capital movements required to achieve that stability. The area under curve E relative to that under curve D is expressed by [(Ao + Bo)/ (Ao - Bo) ii provided Ao p? Bo, where Ao is the maximum deviation of curve A from the normal rate, and Bo is the maximum deviation of curve B (and curve C) from the normal rate.3

The conclusion is not that "on the Eastman-Stykolt definition of stabilizing there were no stabilizing short-term capital movements in the Canadian foreign exchange market between 1954 and 1961" (p. 85), but that the correlation of capital movements and (Pn - N.) is logically incapable of revealing their existence in cases in which the time shape of the exchange fluctuations is altered by short-term capital movements.

Somewhat similar objections can be raised against the two points made in the long footnote on page 88. The author speculates on the assumption Stykolt and I may have made about the nature of private short-term capital movements when we discussed offlcial exchange stabilization policy in 1956.4 In fact we made none, restricting ourselves to examining the effect of official intervention on exchange fluctuation, whatever their cause. What influenced private capital movements or, indeed, whether there were any, still seems to me irrelevant to this problem unless one assumes interdependence between private and official short-term capital movements. In other words, curve B' in Figure 2 of the footnote is identical to curve B in the footnote's Figure 1

2This is prove in Harry C. Eastman and Stean Stykolt, "Exchange Stabilization Once Again," id., XXIV, no. 2, May, 1958, 28.

Let A A( sin x

Then C B- sn(x -a), since the maximum value of C is BO and if ics curs where te curve for C intrsects the curve for A, then

0 = ( r/2) - in -1 (BI/A0) D =A -B (AO- BO) sin x D sin x E = A -C A sin x -B(o sin (x-O) =E sn + ( )x Sustituting for in the euation for E, and combining the two sine functions into

one gives Eo =\/ (A02 - B12) and ) -sin -1(B IAo). The ratio of the areas under the half cycles of two sine curves of the same period is

the ratio o eir amplitudes. Therefore the ratio of the area under a half cycle of E to that uer a half cycle o D is

EI/D0, V V(AO2 -132)/(AO -B) V(AO + BO))/(AO - BO)1 I am inde for t solution of this problem to my versatile clleague, Pro:fesor W. E. Grasbam.

4HIarry C. Eastman and Stefan Stykolt, "ExhaT ge Staabilization in Canu l1a, 19 04A, thS JoU NAL, XXII, no. 23 May 195




for the purpose of official intervention, since they both show the rate fluctuations that would take place without intervention the purpose of which is to reduce them. It follows therefore that the relation of C' to B' in the footnote's Figure 2 should be identical to that of C to B in Figure 1 of the footnote. How- ever, as it is drawn, C' begins to fall before crossing B'. This implies that, part of the time, the official stabilization fund is selling while the observed rate is falling. But this behaviour is contrary to the assumption of Powrie now, and ourselves then, that official transactions respond to (Pn - P.,). This behaviour is consistent only with an assumption that the fund sells when the rate is high rather than only when it is rising. As has already been shown, selling at high prices and buying at low ones is more efficient stabilizing activity than countering all changes in the rate, and that is why the peak of C' relative to B' in Figure 2 is lower than that of C relative to B in Figure 1 and also why the turning point is less displaced in time by official intervention.

These comments in no way detract from the value of Professor Powrie's statistical analysis which significantly increases our knowledge of the nature of short-term capital movements in the period he examines. Indeed, our knowledge about these movements derived from their relation to (Pn -Pn_l), reduces the importance of measuring their relation to the difference between the rate as it would have existed had they not taken place and the normal rate, because we know a priori from the first relationship that they are stabilizing.

JOHNSON'S NORTHERN TOUR: A TRAVELLER'S GUIDE PAST THE MARSHES*

H. G. JOHNSON

University of Chicago

IT is gratifying to think that 8434 per cent of the pages of The Canadian Quandary are so acceptable to Dr. Marsh as to call for no comment from him, and perhaps churlish to take issue with his remarks on the short section he singles out for criticism. But I feel obliged to do so, since Marsh has either misunderstood or misinterpreted important aspects of my argument. In this comment I shall not take up his criticisms point by point-I trust the readers to read in the book what I wrote in it, not what Marsh reads into it-but will instead indicate briefly how and why I think he has gone wrong.

The section on Monetary Policy consists of two chapters, both growing out of research conducted in 1962 for the Royal Commission on Banking and Finance. One is a summary of a lengthy econometric study of lags in the effect of monetary policy in Canada by Dr. J. W. L. Winder and myself, now available from the Commission;' the other is an essay on alternative orienta- tions towards the role of monetary policy in a modern economy, which includes

OA reply to Donald B. Marsh, "Johnson's Tour of the Northern Dominion," this JOURNAL,

XXX, no. 2, May, 1964, 258-65, a review of my The Canadian Quandary (Toronto: McGraw-Hill of Canada, 1964).

IHarry G. Johnson and J. W. L. Winder, Lags in the Efects of Monetary Policy in Canada (Ottawa, 1964).

Vol. XXX, no. 3, Aug., 1964

