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Rational expectations, market shocks, and the exchange rate
KENT P. KIMBROUGH Duke Unioersity
Rational Expectations, Market Shocks, and the Exchange Rate* The world economy has been subjected to numerous real shocks in recent years. In addition, purchasing-power parity seems to have collapsed. Critics of the monetary approach to the exchange rate have been quick to draw attention to these facts. This paper extends the basic framework of the monetary approach so that it provides a useful tool for explaining the impact of real shocks on the exchange rate and so that it is compatible with the existence of significant deviations from purchasing-power parity. The real shocks that are discussed include changes in commercial policy, the terms of trade, and productivity. It is demonstrated that real shocks influence the exchange rate through two distinct channels-a real-income channel and a deviations from purchasing-power-parity channel.
The world economy has been assailed by a multitude of real shocks in the past decade-the relative price of oil has risen dramatically, supply disruptions have been commonplace, some countries have renounced free trade and have begun to pursue more protectionist commercial policies while others have begun to move in the opposite direction, and patterns of productivity change have varied greatly across countries. In addition, purchasing power parity seems to have collapsed.’ The purpose of this paper is to modify the basic framework of the monetary approach to the exchange rate in order to examine the exchange-rate effects of various real shocks. In as much as deviations from purchasing power parity are a real phenomenon associated with relative price movements, this will also allow for a systematic analysis of the effects of deviations from purchasing power parity on the exchange rate. It is shown that, in general, there are two conceptually distinct channels through which real shocks influence the exchange rate. First, real shocks alter real income, and hence the demand for money, thereby affecting the
*I would like to thank for their helpful comments I would also like to thank ‘See Frenkel (1981) for during the 1970s.
Grant Gardner, George Tauchen, and Dudley Wallace which clarified several technical aspects of this paper. an anonymous referee for useful remarks. an analysis of the collapse of purchasing power parity
journal of Macroeconomics, Summer 1985, Vol. 7, No. 3, pp. 297-312 Copyright 0 1986 by Wayne State University Press.
297
Kent P. Kimbrough equilibrium exchange rate. Secondly, real shocks that alter relative prices will be associated with changes in deviations from purchasing power parity, and, in order to offset the incipient impact of these changes on the domestic price level and thus maintain money market equilibrium, the exchange rate will adjust. The paper is organized as follows: Section 1 presents a simple version of the monetary approach to the exchange rate. Section 2 extends this simple model to allow for the aforementioned extensions. Section 3 examines the determination of the equilibrium exchange rate under rational expectations. Section 4 discusses the effects of various real shocks on the exchange rate. The fifth, and final, section of the paper discusses the implications of the analysis and outlines some possible extensions.
1. The Monetary Approach The monetary approach to the exchange rate begins with a recognition of the fact that the exchange rate is the relative price of two monies. This implies that the equilibrium exchange rate is obtained when the outstanding stocks of the two monies are willingly held. The equilibrium exchange rate must, therefore, be consistent with the money market equilibrium condition M/P = L (Y, i) ,
(1)
where M is the domestic money supply, P is the domestic price level, L(e) is the demand for real cash balances by domestic residents which is assumed, for simplicity, to depend on domestic real income, Y, and the domestic nominal interest rate, i. If purchasing power parity holds, then
P = sp* ,
(2)
where2 P* is the foreign price level, and S is the spot (or current) exchange rate defined as the domestic currency price of foreign exchange. Combining (1) and (2) yields
S = M/P*L(Y, i) . Equation (3) is the by now familiar for the equilibrium exchange rate.3
monetary
(3) approach expression
*Throughout the paper an asterisk denotes a foreign variable. %ee, for example, Dornbusch (1978) and Frenkel and Clements
(1981).
Rational Expectations,
Market
Shocks, Exchange Rate
This paper extends this simple monetary approach model of exchange-rate determination in two directions. First, the assumption that purchasing power parity holds will be replaced by the weaker assumption that markets for internationally traded goods are effectively arbitraged. This will allow for a discussion of the role of deviations from purchasing power parity in the exchange-rate determination process.4 Second, the determination of domestic real income will be examined at a slightly more disaggregated level than is usual in monetary-approach models of exchange-rate behavior. This increased disaggregation will allow for a fairly rich analysis of the exchange-rate effects of real shocks. It should be pointed out that these extensions of the monetary approach to the exchange rate are not intended to alter its basic message-that the equilibrium exchange rate is determined when the outstanding stocks of money are willingly held-but to enrich the analysis by showing that the monetary approach is, in principle, compatible with the existence of substantial and persistent deviations from purchasing power parity and that it provides a useful framework for discussing the effects of a much wider array of market shocks than is perhaps currently believed.
2. The Framework It is assumed that the home country is a small open economy which produces and consumes two traded goods: exportables, X, and importables, 1. Full employment is assumed to prevail, and individual’s expectations are assumed to be formed rationally under conditions of full current information. Asset portfolios consist of domestic money and bonds. Being small, the home country takes world prices and interest rates as given (but not fixed as they are subject to random variation due to stochastic shocks to world supply and demand conditions). Relative Prices, Deviations from Purchasing Power Parity, and the Price Level Let the domestic and foreign price levels at time t, be given by
Vhis modification of the strong purchasing power parity assumption is not new. The same formulation can be found in Dornbusch (1976) and Clements and Frenkel (1980).
299
Kent P. Kimbrough where Pkt (k = X, I) is the domestic currency price of good k, and 0~~is the share of good k in domestic expenditure. Foreign variables are defined similarly. It is also assumed that arbitrage in the markets for goods X and I guarantees that
(1 + At) Pm = StPft ; and
PI, = (1 + GvI*t ;
(5)
where A, is the home country’s export tax rate and rt its tariff rate.’ Combining (4) and (5) it can be shown that
P, = S,P,*D;’ ,
(6)
D, = (1 + X,)“x(l + TJ-“‘(PI”;/P~J+“I .
(7)
where
As can be seen from (6), D, is a measure of deviations from purchasing power parity. The definition of D, given by (7) indicates that deviations from purchasing power parity are a real phenomenon. In the present framework these deviations depend on commercial policy variables (A, and TJ, world-demand patterns as reflected by the expenditure shares ox, cq, and a?, and the terms of trade.6 Before proceeding it will be useful to take the natural logarithm of (6) to obtain pt = 5, + pt* - 4,
(6’)
where, as is the convention throughout the paper, lower case letters represent the natural logarithms of their upper case counterparts (e.g., s, = In St). ‘In principle the “wedges” in (5a) and (5b) could be viewed as representing quantitative restrictions on trade. However, this would significantly complicate the analysis as maintenance of fixed quantitative restrictions would automatically make the wedges random variables dependent on domestic supply and demand conditions and stochastic world prices. ‘The most significant modifkation would be to extend the model to include nontraded goods thus introducing terms reflecting the relative price of nontraded goods into (7). This would allow for a discussion of the issues raised by Balassa (1964). but would complicate the analysis by introducing endogenous relative prices into the model. 300
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Specification of Real Zncome As noted earlier, it is assumed that the home country produces two goods, X and I, and that all resources are fully employed. The outputs of these two goods at any time t are Qxt and QZband are given by Qxt = Qxeuxt ;
Qzt = QzeUit;
where Qx and Q1 represent “normal,” or output’ and ux, and uzt are random variables distributed, zero means, and variances ai porary changes in productivity due to work political unrest, etc.’ The home country’s nominal income
(8)
“permanent,” levels of (independent, normally and u:) reflecting temstoppages, bad weather, at time t is
PxtQx,+ PztQz, + fit ; where R, is the government’s net revenue from Real income, Y, is simply nominal income divided Therefore, using the preceding expression and the domestic price level given in (4, it follows
its taxes on trade.g by the price level. the expression for that
y = Qxt + (Pz,IPxJQzt+ W ’xt t PztlPx,j”l .
(9)
In order to simplify the analysis further, it is also assumed that the home country’s terms of trade at time t are Pfi/P& = (PT/Px*)e”*+‘t ;
(10)
where (P,*/P;F)eP’is the logarithm of the normal, or permanent, terms of trade facing the home country and E, is a random variable (nor‘If the factors of production are allocated to each section prior to the time the random variables uxt and u,, are revealed to producers, ox and 0, will depend on expected relative prices as the economy moves along a concave production possibilities frontier. ‘Given the specifications of the random variables uxr and u,~, the expected outputs of goods X and I are ox exp (1/22x) and or exp (l/24). However, if the distributions of uxt and ua are stable over time the terms exp(l/Wx) and exp(l/w) will be constants which can be suppressed for purposes of the following discussion. ‘An explicit expression for R, is given in the appendix.
301
Kent P. Kimbrough mally distributed, zero mean, and variance a:) reflecting the stochastic elements of world demand and supply conditions.” Using (5) along with (8)-(10) it is shown in the appendix that in the neighborhood of free trade the logarithm of real income at time t can be approximated by
where tlk (k = 1, 2) is the share of good k in real income. Expression (12) reflects the fact that real income depends on the output of goods X and I and the terms of trade. An increase in the output of good k by 1% will increase real income by ok%, while a deterioration in the terms of trade by 1% will reduce real income by (aI - el)%. Asset Market Equilibrium The final necessary ingredients for a discussion of the exchange-rate-determination process are the asset market equilibrium conditions. Money market equilibrium requires that the (stochastic) supply of domestic money, M,, equal the demand for money by domestic residents, Mt. The money demand function is assumed to be of the Cagan type, and thus the money market equilibrium condition (in logarithmic form) is
m, = ;p,+ 4th - rli, ;
(12)
where + is the income elasticity of the demand for money, and -r-l is the interest-rate semielasticity of the demand for money. In addition, it is assumed that domestic and foreign bonds are perfect substitutes on an uncovered basis so that the domestic nominal interest rate is linked to the foreign nominal interest rate by l1 i, = if + (EJ~+~ - s,) ;
(13)
where E,s,+, is the spot exchange rate asset holders expect to prevail at time t + 1 on the basis of the information available to them at time t. “‘The same qualifications that were mentioned in footnote eight apply here also. “As shown by Frenkel and Ftazin (1980) this condition will be equivalent to covered interest parity if asset holders are risk neutral and prices are nonstochastic. Since the latter condition is not met in the present setup the two conditions will not be equivalent. 302
Rational Expectations, Market Shocks, Exchange Rate 3. Expectations and the Equilibrium Exchange Rate In this section the elements of the preceding discussion are brought together, and it is shown that the equilibrium exchange rate at time t depends on current and expected future values of the domestic money supply, the world price level, the world interest rate, outputs of goods X and I, the commercial policy variables A and 7, and the terms of trade. Substituting the uncovered interest arbitrage condition, (13), and the expression for the domestic price level, (6’), into the money market equilibrium condition, (12), and solving for s, yields
st = &
(mt - Pt* + dt - $9, +
Tip) + -!1+rl
E,s,+, .
(14)
The equilibrium spot exchange rate at time t is, therefore, a weighted average of current conditions and expected future conditions as summarized by E,s,+~. By repeatedly updating (14), taking expectations of the resulting expression, and substituting back into (14) it can be shown that the equilibrium exchange rate at time t is given by
Et(mt+j - p&j + 4,
- +yt+j + +;F+j) .
(15)
Except for the term reflecting the effects of deviations from purchasing power parity on the exchange, this expression is similar to others already found in the literature [see Bilson (1978) and Mussa (1976a)]. However, it highlights the two main channels through which real shocks may influence the exchange rate. First, the E,y,+j terms capture the exchange-rate effects of real shocks as they manifest themselves through changes in actual or expected real income. This is the “real income channel.” Second, in as much as (7) shows that deviations from purchasing power parity are a real phenomenon, real shocks also influence the exchange rate via their impact on these deviations as captured by the E,d,, terms in (18). This is the “deviations from PPP channel.” To complete the analysis of this section, and set the stage for the discussion of the exchange rate effects of various market shocks that is presented in the next section, it is useful to derive one last expression for the spot exchange rate. This is done by taking the 303
Kent P. Kimbrough logarithm
of (7), and using (lo), to obtain” d, = c&
Substituting
- cxfrt + (CYT- a&p*
+ E,) .
(16)
(16) and (11) into (15) yields
Eh+,
- P,*+J+ %+kj
- 4 [%(Q* + u,,t+J + flz(Qz + uz,t+.iN + %ht+j - fJz7t+j +
[bt - az)+ 4+z - ezN* + Et+J *
(17)
Expression (17) shows that the equilibrium exchange rate at time t depends on current and expected future values of all of the exogenous random variables of the model, which of course implies that the equilibrium exchange rate is determined as a part of the general equilibrium of the economy.
4. Market Shocks and the Exchange Rate In this section the exchange-rate effects of real shocks such as changes in the output of goods X and I, changes in commercial policy, and changes in the terms of trade are examined.13 The Impact of Unanticipated, Permanent Shocks Suppose that between periods t - 1 and t one of the underlying determinants of the exchange rate, call it z, were to change unexpectedly by A”zt = zt - Et-l~t. If asset holders perceive this change to be permanent then E,z,+~ - Et-l~t+j = A”zt for all j and, denoting this common value by A%, expression (17) implies that the unexpected change in the exchange rate, A”s, = s, - EtMIst, will be
‘2Recall that the initial equilibrium is one of free trade implying ln(1 t AJ = h, and ln(l + TJ = T*. Vhe model can also be used to study the exchange rate effects of monetary shocks. However, such a discussion is not presented here. For discussions of the exchange rate effects of monetary shocks in rational expectations models similar to the one presented here see Barro (1978), Bilson (1978), and Mussa (1976a).
304
Rational Expectations,
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Shocks, Exchange Rate
where pz is the coefficient of z in (17). This implies the following results for the exchange rate effects of various unanticipated and permanent real shocks: AU& -
=
-c/d&
k=X,Z;
Acik AU& -= Ah
ax;
A’%, x = -aI;
084
WW
Expressions (lSa)-(l&) highlight several important points concerning the effects of real shocks on the equilibrium exchange rate. First, (18a) shows that an unanticipated, permanent increase in the output of either good will increase the demand for money and thereby lead to an appreciation of the domestic currency relative to its previously anticipated value. It should be noted that output increases, in light of the small country assumption, do not alter relative prices and hence have no effect on deviations from purchasing power parity. They thus influence the equilibrium exchange rate only through the real income channel.14 The model presented here is therefore consistent with the well-known result that, all else being equal, growth will be accompanied by an appreciation of a country’s currency when exchange rates are flexible, or a balance-of-payments surplus when exchange rates are fixed. Second, (18b) implies that trade restrictions will have different effects on the exchange rate depending on whether they are directed at imports or exports. The imposition of a tariff will raise the domestic price level if the exchange rate remains at its previously expected value, E,-ls,. However, this will result in an excess demand for domestic money, and therefore, the domestic currency must appreciate in order to maintain equilibrium. In contrast, the imposition of an export tax tends to lower the domestic price level ‘“If the small country assumption were relaxed, or if nontraded goods were introduced into the model, output increases would also influence the exchange rate via the deviations from PPP channel. In this case it is possible for growth to be accompanied by a depreciation of the growing country’s currency. See, for example, Kimbrough (1982).
Kent P. Kimbrough and hence the domestic currency must depreciate to maintain equilibrium. Both types of commercial policies work only through the deviations from PPP channel since the initial equilibrium is one of free trade which implies that levying a small tariff or export tax has no effect on real income. This implies that Lerner’s symmetry theorem does not generalize to the monetary effects of tariffs and export taxes. This result has been previously noted by Mussa (1976b). Finally, (18~) shows that a deterioration in a country’s terms of trade may lead to an appreciation or a depreciation of its currency. This is a consequence of the fact that terms of trade changes influence the exchange rate through both the real income channel and the deviations from PPP channel simultaneously. It is, however, interesting to note that the underlying source of existing trade patterns plays an important role in determining the net effect of a terms of trade deterioration on the exchange rate. If trade is due solely to differences in production patterns across countries (I@ = a,), as suggested by the Hecksher-Ohlin theorem, the real-income channel is the only avenue through which terms of trade changes influence the exchange rate, and the domestic currency unambiguously depreciates in response to a deterioration of the terms of trade. However, if trade is due solely to differences in consumption patterns across countries (o$ < OLJ, the impact of terms of trade changes on the exchange rate coming through the deviations from PPP channel run counter to those working through the real-income channel, and the exchange rate may appreciate or depreciate. Therefore, it may be concluded that the more important international differences in production patterns are in explaining existing trade patterns, and the greater the income elasticity of the demand for money, the more likely it is that the real income channel will dominate, and a deterioration in a country’s terms of trade will tend to be associated with a depreciation of its currency.
The impact of Other Types of Shocks Up to this point, it has been assumed that the various market shocks are unanticipated and that once they have occurred they are perceived to be permanent. This assumption can be relaxed, and the exchange-rate effects of other types of market shocks considered. In particular, it is important to distinguish between anticipated and unanticipated shocks on the one hand and transitory and permanent shocks on the other. These distinctions are summarized in Table I for the exchange rate effects of a one percent export 306
Rational Expectations,
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Shocks, Exchange Rate
TABLE 1. Effects of a 0 ne -P ercent Export change Rate s,
Tax on the Spot Ex-
Permanent
Transitory
Unanticipated Anticipated (h periods in advance)
tax.l5 The general principles are easily extended to deal with the other market shocks considered earlier in this section. The distinction between anticipated and unanticipated shocks can be seen by looking down either column of Table I. For example, consider the effects of permanently imposing a one-percent export tax. If the export tax is anticipated h periods before it is actually imposed, as might be the case if the government announces its commercial policies in advance, the news is “discounted” and today’s spot exchange rate depreciates by less than it would if the export tax were unanticipated. The reason that the mere anticipation of an export tax affects today’s exchange rate is that the announcement of the export tax causes asset holders to anticipate higher rates of depreciation in future periods as the actual imposition of the export tax draws near. This reduces the demand for money thus leading to an immediate depreciation of the domestic currency. It should be noted that the further in advance of its imposition the export tax is anticipated (i.e., the larger h), the smaller its impact on today’s exchange rate. The distinction between transitory and permanent disturbances is highlighted by the rows of Table I. For example, suppose the imposition of a one-percent export tax is unanticipated. If asset holders perceive that the export tax will be rescinded next period, the domestic currency will depreciate by less than ox percent, The reason for this is that the future removal of the export tax leads asset holders to anticipate an appreciation between periods t and t + 1, thus dampening the decline in the demand for money brought about by the current export tax. Generally speaking, both anticipated and transitory shocks have qualitatively similar, but smaller effects on the spot exchange rate “The
entries in Table I can be derived from Equation
(17).
307
Kent P. Kimbrough than their unanticipated and permanent counterparts. stances, the fundamental reason for this is that they ferent information to asset holders concerning future thus have different implications for the expected rate tion of the domestic currency.
In both intransmit difevents, and of deprecia-
5. Implications and Extensions Recent events indicate that it is important that models of exchange-rate determination be capable of explaining the effects of real shocks, and that they be compatible with the existence of deviations from purchasing power parity. This paper has extended the monetary approach to the exchange rate and shown that it provides a useful framework for analyzing the exchange-rate effects of such events. It was shown that real shocks influence the equilibrium exchange rate through two conceptually distinct channels: the real income channel and the deviations from PPP channel. In addition, specific results were derived concerning the effects of productivity changes, commercial policy changes, and terms of trade changes on the exchange rate. Several extensions of the specific model employed to derive these results suggest themselves. First, the model could be broadened to include endogenous relative prices either by introducing nontraded goods into the model or by allowing the home country to be large. In both cases the introduction of stochastic supply and demand functions would be the key ingredient of such an extension. Second, wealth could be introduced explicitly into the money demand function, thus allowing the model to be used to examine the implications of asset accumulation for exchange-rate dynamics and, in particular, to focus on the relation between the current account and the exchange rate. Finally, some scope for shortrun monetary nonneutrality could be introduced into the model. A useful framework for such an analysis would be to integrate the current setup with that of Kimbrough (1984). This would allow for a discussion of the interaction between business cycles and exchange-rate fluctuations. Although these extensions would undoubtedly modify some of the specific results of this paper, they would leave its basic message intact-the monetary approach to the exchange rate can easily be extended to incorporate deviations from purchasing power parity and a much wider array of real shocks than is perhaps commonly believed. Received: September 1984 Final oersion received: January 1985
Rational Expectations,
Market
Shocks, Exchange Rate
Appendix This appendix demonstrates that in the neighborhood of free trade the natural logarithm of real income can be approximated by expression (11). Omitting the time subscript to simplify the notation, expression (11) becomes
or using (8) and (lo),
Showing that (A.l) can be derived from (9) will complete the proof. Again, omitting the time subscript for simplicity, (9) becomes
where
p = Qx + WPx)Q, + W ’x .
(A-3)
The nominal tariff plus export tax revenue, R, is given by
R = ~pT(cr - QJ + APx(Q, - C,) ; where Ck (k = I, X) represents domestic consumption of good k. Using (5), this expression shows that
RIP, = 41 + UPTIPWI
- QJ + A(Qx - GJ .
(A-4)
Using (A.4) in (A.3), and substituting from (5) into the resulting expression yields
p = Qx + 0 + 4(1 + W ’f/*IP;f:)Q, + $1 + A)(f’T/P$)(G - QI) + MQx - Cx) .
64.5)
Now, it is well known that for small changes f = Y - YD,
64.6) 309
Kent P. Kimbrough where yO = In Y,, Y, is the initial level of real income, and a “A” over a variable denotes its percentage change. Taking the percentage change of both sides of (A.2) and using (A.6) yields
Using (5) it follows from this that in the neighborhood of free trade y = y. + 9 - cQ(h+ 7) - crQ)c - &) .
(A-7)
Using (A.4) it can be shown that in the neighborhood of free trade 3 = e,@ + e&
- P2 + 61) + a,(h + 7) ;
(A4
where, as implied by the envelope theorem, 6, and & reflect only those output changes due to shifts in the production possibilities frontier (PPF) and not those due to movements along a given PPF as relative prices changes. Substituting (A.8) into (A.7) yields
Approximating all percentage changes by logarithmic differences, this becomes
Y= 04,+ eIq,- bI - m* + y.
- v-u:+ e,q;- 64- f4hei.
(-4.9)
Expression (A.9) implies that for (A.l) to be a valid approximation, at least up to a constant, the following must be true: y. = b +
e,q; + elq; - (0~~- e,)pz.
Taking antilogs, this means that
Since (4) implies that PO= P~O[(Pt’,))l/(P$,)]aI, this means that B must be chosen so that in the neighborhood of free trade domestic nominal income at world prices, YN = PfQx + PPQ,, is given by 310
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Shocks, Exchange Rate
YN = B(P$Qx)ex(P;rQl)e’.
(A. 10)
It can be seen that for (A. 10) to hold B = (1/8,)“r(1/0,)“1 is required.
References Balassa, B. “The Purchasing Power Parity Doctrine: A Reappraisal.” journal of Political Economy 72 (December 1964): 584-96. Barr-o, R. J. “A Stochastic Equilibrium Model of an Open Economy under Flexible Exchange Rates.” Quarterly Journal of Economics 92 (February 1978): 149_64. Bilson, J. F.O. “Rational Expectations and the Exchange Rate.” In The Economics of Exchange Rates: Selected Studies. J.A. Frenkel and H.G. Johnson, eds. Reading, MA: Addison-Wesley, 1978, 75-96. Clements, K.W., and Frenkel, J.A. “Exchange Rates, Money, and Relative Prices: The Dollar-Pound in the 1920s.” Journal of Znternational Economics 10 (May 1980): 249-62. Dornbusch, R. “The Theory of Flexible Exchange Rate Regimes and Macroeconomic Policy.” Scandinavian Journal of Economics 78 (May 1976): 255-75. -. “Monetary Policy under Exchange Rate Flexibility.” In Managed Exchange Rate Flexibility: The Recent Experience. Federal Reserve Bank of Boston Conference Series, No. 20, 90-122. Frenkel, J.A. “The Collapse of Purchasing Power Parity during the 1970s.” European Economic Review 16 (May 1981): 145-65. -, and Clements, K.W. “Exchange Rates in the 1920s: A Monetary Approach.” In Development in an Znflationary World. M.J. Flanders and A. Razin, eds. New York: Academic Press, 1981, 283-318. and Razin, A. “Stochastic Prices and Tests of Efficiency of Foreign Exchange Markets.” Economic Letters 6 (1980): 165-70. Kimbrough, K. P. “Growth, Relative Prices and Exchange Rates.” Economic Letters 10 (1982): 137-43. -. “Commercial Policy and Aggregate Employment under Rational Expectations. ” Quarterly Journal of Economics 99 (August 1984): 567-85. Mussa, M. “The Exchange Rate, the Balance of Payments and Monetary and Fiscal Policy under a Regime of Controlled Floating.” Scandinavian Journal of Economics 78 (May 1976): 22948. 311
Kent P. Kimbrough -.
“Tariffs and the Balance of Payments.” In The Monetary Approach to the Balance of Payments. J.A. Frenkel and H.G. Johnson, eds. Toronto: University of Toronto Press, 1976, 187221.
312
Rational Expectations, Market Shocks, and the Exchange Rate* The world economy has been subjected to numerous real shocks in recent years. In addition, purchasing-power parity seems to have collapsed. Critics of the monetary approach to the exchange rate have been quick to draw attention to these facts. This paper extends the basic framework of the monetary approach so that it provides a useful tool for explaining the impact of real shocks on the exchange rate and so that it is compatible with the existence of significant deviations from purchasing-power parity. The real shocks that are discussed include changes in commercial policy, the terms of trade, and productivity. It is demonstrated that real shocks influence the exchange rate through two distinct channels-a real-income channel and a deviations from purchasing-power-parity channel.
The world economy has been assailed by a multitude of real shocks in the past decade-the relative price of oil has risen dramatically, supply disruptions have been commonplace, some countries have renounced free trade and have begun to pursue more protectionist commercial policies while others have begun to move in the opposite direction, and patterns of productivity change have varied greatly across countries. In addition, purchasing power parity seems to have collapsed.’ The purpose of this paper is to modify the basic framework of the monetary approach to the exchange rate in order to examine the exchange-rate effects of various real shocks. In as much as deviations from purchasing power parity are a real phenomenon associated with relative price movements, this will also allow for a systematic analysis of the effects of deviations from purchasing power parity on the exchange rate. It is shown that, in general, there are two conceptually distinct channels through which real shocks influence the exchange rate. First, real shocks alter real income, and hence the demand for money, thereby affecting the
*I would like to thank for their helpful comments I would also like to thank ‘See Frenkel (1981) for during the 1970s.
Grant Gardner, George Tauchen, and Dudley Wallace which clarified several technical aspects of this paper. an anonymous referee for useful remarks. an analysis of the collapse of purchasing power parity
journal of Macroeconomics, Summer 1985, Vol. 7, No. 3, pp. 297-312 Copyright 0 1986 by Wayne State University Press.
297
Kent P. Kimbrough equilibrium exchange rate. Secondly, real shocks that alter relative prices will be associated with changes in deviations from purchasing power parity, and, in order to offset the incipient impact of these changes on the domestic price level and thus maintain money market equilibrium, the exchange rate will adjust. The paper is organized as follows: Section 1 presents a simple version of the monetary approach to the exchange rate. Section 2 extends this simple model to allow for the aforementioned extensions. Section 3 examines the determination of the equilibrium exchange rate under rational expectations. Section 4 discusses the effects of various real shocks on the exchange rate. The fifth, and final, section of the paper discusses the implications of the analysis and outlines some possible extensions.
1. The Monetary Approach The monetary approach to the exchange rate begins with a recognition of the fact that the exchange rate is the relative price of two monies. This implies that the equilibrium exchange rate is obtained when the outstanding stocks of the two monies are willingly held. The equilibrium exchange rate must, therefore, be consistent with the money market equilibrium condition M/P = L (Y, i) ,
(1)
where M is the domestic money supply, P is the domestic price level, L(e) is the demand for real cash balances by domestic residents which is assumed, for simplicity, to depend on domestic real income, Y, and the domestic nominal interest rate, i. If purchasing power parity holds, then
P = sp* ,
(2)
where2 P* is the foreign price level, and S is the spot (or current) exchange rate defined as the domestic currency price of foreign exchange. Combining (1) and (2) yields
S = M/P*L(Y, i) . Equation (3) is the by now familiar for the equilibrium exchange rate.3
monetary
(3) approach expression
*Throughout the paper an asterisk denotes a foreign variable. %ee, for example, Dornbusch (1978) and Frenkel and Clements
(1981).
Rational Expectations,
Market
Shocks, Exchange Rate
This paper extends this simple monetary approach model of exchange-rate determination in two directions. First, the assumption that purchasing power parity holds will be replaced by the weaker assumption that markets for internationally traded goods are effectively arbitraged. This will allow for a discussion of the role of deviations from purchasing power parity in the exchange-rate determination process.4 Second, the determination of domestic real income will be examined at a slightly more disaggregated level than is usual in monetary-approach models of exchange-rate behavior. This increased disaggregation will allow for a fairly rich analysis of the exchange-rate effects of real shocks. It should be pointed out that these extensions of the monetary approach to the exchange rate are not intended to alter its basic message-that the equilibrium exchange rate is determined when the outstanding stocks of money are willingly held-but to enrich the analysis by showing that the monetary approach is, in principle, compatible with the existence of substantial and persistent deviations from purchasing power parity and that it provides a useful framework for discussing the effects of a much wider array of market shocks than is perhaps currently believed.
2. The Framework It is assumed that the home country is a small open economy which produces and consumes two traded goods: exportables, X, and importables, 1. Full employment is assumed to prevail, and individual’s expectations are assumed to be formed rationally under conditions of full current information. Asset portfolios consist of domestic money and bonds. Being small, the home country takes world prices and interest rates as given (but not fixed as they are subject to random variation due to stochastic shocks to world supply and demand conditions). Relative Prices, Deviations from Purchasing Power Parity, and the Price Level Let the domestic and foreign price levels at time t, be given by
Vhis modification of the strong purchasing power parity assumption is not new. The same formulation can be found in Dornbusch (1976) and Clements and Frenkel (1980).
299
Kent P. Kimbrough where Pkt (k = X, I) is the domestic currency price of good k, and 0~~is the share of good k in domestic expenditure. Foreign variables are defined similarly. It is also assumed that arbitrage in the markets for goods X and I guarantees that
(1 + At) Pm = StPft ; and
PI, = (1 + GvI*t ;
(5)
where A, is the home country’s export tax rate and rt its tariff rate.’ Combining (4) and (5) it can be shown that
P, = S,P,*D;’ ,
(6)
D, = (1 + X,)“x(l + TJ-“‘(PI”;/P~J+“I .
(7)
where
As can be seen from (6), D, is a measure of deviations from purchasing power parity. The definition of D, given by (7) indicates that deviations from purchasing power parity are a real phenomenon. In the present framework these deviations depend on commercial policy variables (A, and TJ, world-demand patterns as reflected by the expenditure shares ox, cq, and a?, and the terms of trade.6 Before proceeding it will be useful to take the natural logarithm of (6) to obtain pt = 5, + pt* - 4,
(6’)
where, as is the convention throughout the paper, lower case letters represent the natural logarithms of their upper case counterparts (e.g., s, = In St). ‘In principle the “wedges” in (5a) and (5b) could be viewed as representing quantitative restrictions on trade. However, this would significantly complicate the analysis as maintenance of fixed quantitative restrictions would automatically make the wedges random variables dependent on domestic supply and demand conditions and stochastic world prices. ‘The most significant modifkation would be to extend the model to include nontraded goods thus introducing terms reflecting the relative price of nontraded goods into (7). This would allow for a discussion of the issues raised by Balassa (1964). but would complicate the analysis by introducing endogenous relative prices into the model. 300
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Specification of Real Zncome As noted earlier, it is assumed that the home country produces two goods, X and I, and that all resources are fully employed. The outputs of these two goods at any time t are Qxt and QZband are given by Qxt = Qxeuxt ;
Qzt = QzeUit;
where Qx and Q1 represent “normal,” or output’ and ux, and uzt are random variables distributed, zero means, and variances ai porary changes in productivity due to work political unrest, etc.’ The home country’s nominal income
(8)
“permanent,” levels of (independent, normally and u:) reflecting temstoppages, bad weather, at time t is
PxtQx,+ PztQz, + fit ; where R, is the government’s net revenue from Real income, Y, is simply nominal income divided Therefore, using the preceding expression and the domestic price level given in (4, it follows
its taxes on trade.g by the price level. the expression for that
y = Qxt + (Pz,IPxJQzt+ W ’xt t PztlPx,j”l .
(9)
In order to simplify the analysis further, it is also assumed that the home country’s terms of trade at time t are Pfi/P& = (PT/Px*)e”*+‘t ;
(10)
where (P,*/P;F)eP’is the logarithm of the normal, or permanent, terms of trade facing the home country and E, is a random variable (nor‘If the factors of production are allocated to each section prior to the time the random variables uxt and u,, are revealed to producers, ox and 0, will depend on expected relative prices as the economy moves along a concave production possibilities frontier. ‘Given the specifications of the random variables uxr and u,~, the expected outputs of goods X and I are ox exp (1/22x) and or exp (l/24). However, if the distributions of uxt and ua are stable over time the terms exp(l/Wx) and exp(l/w) will be constants which can be suppressed for purposes of the following discussion. ‘An explicit expression for R, is given in the appendix.
301
Kent P. Kimbrough mally distributed, zero mean, and variance a:) reflecting the stochastic elements of world demand and supply conditions.” Using (5) along with (8)-(10) it is shown in the appendix that in the neighborhood of free trade the logarithm of real income at time t can be approximated by
where tlk (k = 1, 2) is the share of good k in real income. Expression (12) reflects the fact that real income depends on the output of goods X and I and the terms of trade. An increase in the output of good k by 1% will increase real income by ok%, while a deterioration in the terms of trade by 1% will reduce real income by (aI - el)%. Asset Market Equilibrium The final necessary ingredients for a discussion of the exchange-rate-determination process are the asset market equilibrium conditions. Money market equilibrium requires that the (stochastic) supply of domestic money, M,, equal the demand for money by domestic residents, Mt. The money demand function is assumed to be of the Cagan type, and thus the money market equilibrium condition (in logarithmic form) is
m, = ;p,+ 4th - rli, ;
(12)
where + is the income elasticity of the demand for money, and -r-l is the interest-rate semielasticity of the demand for money. In addition, it is assumed that domestic and foreign bonds are perfect substitutes on an uncovered basis so that the domestic nominal interest rate is linked to the foreign nominal interest rate by l1 i, = if + (EJ~+~ - s,) ;
(13)
where E,s,+, is the spot exchange rate asset holders expect to prevail at time t + 1 on the basis of the information available to them at time t. “‘The same qualifications that were mentioned in footnote eight apply here also. “As shown by Frenkel and Ftazin (1980) this condition will be equivalent to covered interest parity if asset holders are risk neutral and prices are nonstochastic. Since the latter condition is not met in the present setup the two conditions will not be equivalent. 302
Rational Expectations, Market Shocks, Exchange Rate 3. Expectations and the Equilibrium Exchange Rate In this section the elements of the preceding discussion are brought together, and it is shown that the equilibrium exchange rate at time t depends on current and expected future values of the domestic money supply, the world price level, the world interest rate, outputs of goods X and I, the commercial policy variables A and 7, and the terms of trade. Substituting the uncovered interest arbitrage condition, (13), and the expression for the domestic price level, (6’), into the money market equilibrium condition, (12), and solving for s, yields
st = &
(mt - Pt* + dt - $9, +
Tip) + -!1+rl
E,s,+, .
(14)
The equilibrium spot exchange rate at time t is, therefore, a weighted average of current conditions and expected future conditions as summarized by E,s,+~. By repeatedly updating (14), taking expectations of the resulting expression, and substituting back into (14) it can be shown that the equilibrium exchange rate at time t is given by
Et(mt+j - p&j + 4,
- +yt+j + +;F+j) .
(15)
Except for the term reflecting the effects of deviations from purchasing power parity on the exchange, this expression is similar to others already found in the literature [see Bilson (1978) and Mussa (1976a)]. However, it highlights the two main channels through which real shocks may influence the exchange rate. First, the E,y,+j terms capture the exchange-rate effects of real shocks as they manifest themselves through changes in actual or expected real income. This is the “real income channel.” Second, in as much as (7) shows that deviations from purchasing power parity are a real phenomenon, real shocks also influence the exchange rate via their impact on these deviations as captured by the E,d,, terms in (18). This is the “deviations from PPP channel.” To complete the analysis of this section, and set the stage for the discussion of the exchange rate effects of various market shocks that is presented in the next section, it is useful to derive one last expression for the spot exchange rate. This is done by taking the 303
Kent P. Kimbrough logarithm
of (7), and using (lo), to obtain” d, = c&
Substituting
- cxfrt + (CYT- a&p*
+ E,) .
(16)
(16) and (11) into (15) yields
Eh+,
- P,*+J+ %+kj
- 4 [%(Q* + u,,t+J + flz(Qz + uz,t+.iN + %ht+j - fJz7t+j +
[bt - az)+ 4+z - ezN* + Et+J *
(17)
Expression (17) shows that the equilibrium exchange rate at time t depends on current and expected future values of all of the exogenous random variables of the model, which of course implies that the equilibrium exchange rate is determined as a part of the general equilibrium of the economy.
4. Market Shocks and the Exchange Rate In this section the exchange-rate effects of real shocks such as changes in the output of goods X and I, changes in commercial policy, and changes in the terms of trade are examined.13 The Impact of Unanticipated, Permanent Shocks Suppose that between periods t - 1 and t one of the underlying determinants of the exchange rate, call it z, were to change unexpectedly by A”zt = zt - Et-l~t. If asset holders perceive this change to be permanent then E,z,+~ - Et-l~t+j = A”zt for all j and, denoting this common value by A%, expression (17) implies that the unexpected change in the exchange rate, A”s, = s, - EtMIst, will be
‘2Recall that the initial equilibrium is one of free trade implying ln(1 t AJ = h, and ln(l + TJ = T*. Vhe model can also be used to study the exchange rate effects of monetary shocks. However, such a discussion is not presented here. For discussions of the exchange rate effects of monetary shocks in rational expectations models similar to the one presented here see Barro (1978), Bilson (1978), and Mussa (1976a).
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Rational Expectations,
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Shocks, Exchange Rate
where pz is the coefficient of z in (17). This implies the following results for the exchange rate effects of various unanticipated and permanent real shocks: AU& -
=
-c/d&
k=X,Z;
Acik AU& -= Ah
ax;
A’%, x = -aI;
084
WW
Expressions (lSa)-(l&) highlight several important points concerning the effects of real shocks on the equilibrium exchange rate. First, (18a) shows that an unanticipated, permanent increase in the output of either good will increase the demand for money and thereby lead to an appreciation of the domestic currency relative to its previously anticipated value. It should be noted that output increases, in light of the small country assumption, do not alter relative prices and hence have no effect on deviations from purchasing power parity. They thus influence the equilibrium exchange rate only through the real income channel.14 The model presented here is therefore consistent with the well-known result that, all else being equal, growth will be accompanied by an appreciation of a country’s currency when exchange rates are flexible, or a balance-of-payments surplus when exchange rates are fixed. Second, (18b) implies that trade restrictions will have different effects on the exchange rate depending on whether they are directed at imports or exports. The imposition of a tariff will raise the domestic price level if the exchange rate remains at its previously expected value, E,-ls,. However, this will result in an excess demand for domestic money, and therefore, the domestic currency must appreciate in order to maintain equilibrium. In contrast, the imposition of an export tax tends to lower the domestic price level ‘“If the small country assumption were relaxed, or if nontraded goods were introduced into the model, output increases would also influence the exchange rate via the deviations from PPP channel. In this case it is possible for growth to be accompanied by a depreciation of the growing country’s currency. See, for example, Kimbrough (1982).
Kent P. Kimbrough and hence the domestic currency must depreciate to maintain equilibrium. Both types of commercial policies work only through the deviations from PPP channel since the initial equilibrium is one of free trade which implies that levying a small tariff or export tax has no effect on real income. This implies that Lerner’s symmetry theorem does not generalize to the monetary effects of tariffs and export taxes. This result has been previously noted by Mussa (1976b). Finally, (18~) shows that a deterioration in a country’s terms of trade may lead to an appreciation or a depreciation of its currency. This is a consequence of the fact that terms of trade changes influence the exchange rate through both the real income channel and the deviations from PPP channel simultaneously. It is, however, interesting to note that the underlying source of existing trade patterns plays an important role in determining the net effect of a terms of trade deterioration on the exchange rate. If trade is due solely to differences in production patterns across countries (I@ = a,), as suggested by the Hecksher-Ohlin theorem, the real-income channel is the only avenue through which terms of trade changes influence the exchange rate, and the domestic currency unambiguously depreciates in response to a deterioration of the terms of trade. However, if trade is due solely to differences in consumption patterns across countries (o$ < OLJ, the impact of terms of trade changes on the exchange rate coming through the deviations from PPP channel run counter to those working through the real-income channel, and the exchange rate may appreciate or depreciate. Therefore, it may be concluded that the more important international differences in production patterns are in explaining existing trade patterns, and the greater the income elasticity of the demand for money, the more likely it is that the real income channel will dominate, and a deterioration in a country’s terms of trade will tend to be associated with a depreciation of its currency.
The impact of Other Types of Shocks Up to this point, it has been assumed that the various market shocks are unanticipated and that once they have occurred they are perceived to be permanent. This assumption can be relaxed, and the exchange-rate effects of other types of market shocks considered. In particular, it is important to distinguish between anticipated and unanticipated shocks on the one hand and transitory and permanent shocks on the other. These distinctions are summarized in Table I for the exchange rate effects of a one percent export 306
Rational Expectations,
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TABLE 1. Effects of a 0 ne -P ercent Export change Rate s,
Tax on the Spot Ex-
Permanent
Transitory
Unanticipated Anticipated (h periods in advance)
tax.l5 The general principles are easily extended to deal with the other market shocks considered earlier in this section. The distinction between anticipated and unanticipated shocks can be seen by looking down either column of Table I. For example, consider the effects of permanently imposing a one-percent export tax. If the export tax is anticipated h periods before it is actually imposed, as might be the case if the government announces its commercial policies in advance, the news is “discounted” and today’s spot exchange rate depreciates by less than it would if the export tax were unanticipated. The reason that the mere anticipation of an export tax affects today’s exchange rate is that the announcement of the export tax causes asset holders to anticipate higher rates of depreciation in future periods as the actual imposition of the export tax draws near. This reduces the demand for money thus leading to an immediate depreciation of the domestic currency. It should be noted that the further in advance of its imposition the export tax is anticipated (i.e., the larger h), the smaller its impact on today’s exchange rate. The distinction between transitory and permanent disturbances is highlighted by the rows of Table I. For example, suppose the imposition of a one-percent export tax is unanticipated. If asset holders perceive that the export tax will be rescinded next period, the domestic currency will depreciate by less than ox percent, The reason for this is that the future removal of the export tax leads asset holders to anticipate an appreciation between periods t and t + 1, thus dampening the decline in the demand for money brought about by the current export tax. Generally speaking, both anticipated and transitory shocks have qualitatively similar, but smaller effects on the spot exchange rate “The
entries in Table I can be derived from Equation
(17).
307
Kent P. Kimbrough than their unanticipated and permanent counterparts. stances, the fundamental reason for this is that they ferent information to asset holders concerning future thus have different implications for the expected rate tion of the domestic currency.
In both intransmit difevents, and of deprecia-
5. Implications and Extensions Recent events indicate that it is important that models of exchange-rate determination be capable of explaining the effects of real shocks, and that they be compatible with the existence of deviations from purchasing power parity. This paper has extended the monetary approach to the exchange rate and shown that it provides a useful framework for analyzing the exchange-rate effects of such events. It was shown that real shocks influence the equilibrium exchange rate through two conceptually distinct channels: the real income channel and the deviations from PPP channel. In addition, specific results were derived concerning the effects of productivity changes, commercial policy changes, and terms of trade changes on the exchange rate. Several extensions of the specific model employed to derive these results suggest themselves. First, the model could be broadened to include endogenous relative prices either by introducing nontraded goods into the model or by allowing the home country to be large. In both cases the introduction of stochastic supply and demand functions would be the key ingredient of such an extension. Second, wealth could be introduced explicitly into the money demand function, thus allowing the model to be used to examine the implications of asset accumulation for exchange-rate dynamics and, in particular, to focus on the relation between the current account and the exchange rate. Finally, some scope for shortrun monetary nonneutrality could be introduced into the model. A useful framework for such an analysis would be to integrate the current setup with that of Kimbrough (1984). This would allow for a discussion of the interaction between business cycles and exchange-rate fluctuations. Although these extensions would undoubtedly modify some of the specific results of this paper, they would leave its basic message intact-the monetary approach to the exchange rate can easily be extended to incorporate deviations from purchasing power parity and a much wider array of real shocks than is perhaps commonly believed. Received: September 1984 Final oersion received: January 1985
Rational Expectations,
Market
Shocks, Exchange Rate
Appendix This appendix demonstrates that in the neighborhood of free trade the natural logarithm of real income can be approximated by expression (11). Omitting the time subscript to simplify the notation, expression (11) becomes
or using (8) and (lo),
Showing that (A.l) can be derived from (9) will complete the proof. Again, omitting the time subscript for simplicity, (9) becomes
where
p = Qx + WPx)Q, + W ’x .
(A-3)
The nominal tariff plus export tax revenue, R, is given by
R = ~pT(cr - QJ + APx(Q, - C,) ; where Ck (k = I, X) represents domestic consumption of good k. Using (5), this expression shows that
RIP, = 41 + UPTIPWI
- QJ + A(Qx - GJ .
(A-4)
Using (A.4) in (A.3), and substituting from (5) into the resulting expression yields
p = Qx + 0 + 4(1 + W ’f/*IP;f:)Q, + $1 + A)(f’T/P$)(G - QI) + MQx - Cx) .
64.5)
Now, it is well known that for small changes f = Y - YD,
64.6) 309
Kent P. Kimbrough where yO = In Y,, Y, is the initial level of real income, and a “A” over a variable denotes its percentage change. Taking the percentage change of both sides of (A.2) and using (A.6) yields
Using (5) it follows from this that in the neighborhood of free trade y = y. + 9 - cQ(h+ 7) - crQ)c - &) .
(A-7)
Using (A.4) it can be shown that in the neighborhood of free trade 3 = e,@ + e&
- P2 + 61) + a,(h + 7) ;
(A4
where, as implied by the envelope theorem, 6, and & reflect only those output changes due to shifts in the production possibilities frontier (PPF) and not those due to movements along a given PPF as relative prices changes. Substituting (A.8) into (A.7) yields
Approximating all percentage changes by logarithmic differences, this becomes
Y= 04,+ eIq,- bI - m* + y.
- v-u:+ e,q;- 64- f4hei.
(-4.9)
Expression (A.9) implies that for (A.l) to be a valid approximation, at least up to a constant, the following must be true: y. = b +
e,q; + elq; - (0~~- e,)pz.
Taking antilogs, this means that
Since (4) implies that PO= P~O[(Pt’,))l/(P$,)]aI, this means that B must be chosen so that in the neighborhood of free trade domestic nominal income at world prices, YN = PfQx + PPQ,, is given by 310
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Shocks, Exchange Rate
YN = B(P$Qx)ex(P;rQl)e’.
(A. 10)
It can be seen that for (A. 10) to hold B = (1/8,)“r(1/0,)“1 is required.
References Balassa, B. “The Purchasing Power Parity Doctrine: A Reappraisal.” journal of Political Economy 72 (December 1964): 584-96. Barr-o, R. J. “A Stochastic Equilibrium Model of an Open Economy under Flexible Exchange Rates.” Quarterly Journal of Economics 92 (February 1978): 149_64. Bilson, J. F.O. “Rational Expectations and the Exchange Rate.” In The Economics of Exchange Rates: Selected Studies. J.A. Frenkel and H.G. Johnson, eds. Reading, MA: Addison-Wesley, 1978, 75-96. Clements, K.W., and Frenkel, J.A. “Exchange Rates, Money, and Relative Prices: The Dollar-Pound in the 1920s.” Journal of Znternational Economics 10 (May 1980): 249-62. Dornbusch, R. “The Theory of Flexible Exchange Rate Regimes and Macroeconomic Policy.” Scandinavian Journal of Economics 78 (May 1976): 255-75. -. “Monetary Policy under Exchange Rate Flexibility.” In Managed Exchange Rate Flexibility: The Recent Experience. Federal Reserve Bank of Boston Conference Series, No. 20, 90-122. Frenkel, J.A. “The Collapse of Purchasing Power Parity during the 1970s.” European Economic Review 16 (May 1981): 145-65. -, and Clements, K.W. “Exchange Rates in the 1920s: A Monetary Approach.” In Development in an Znflationary World. M.J. Flanders and A. Razin, eds. New York: Academic Press, 1981, 283-318. and Razin, A. “Stochastic Prices and Tests of Efficiency of Foreign Exchange Markets.” Economic Letters 6 (1980): 165-70. Kimbrough, K. P. “Growth, Relative Prices and Exchange Rates.” Economic Letters 10 (1982): 137-43. -. “Commercial Policy and Aggregate Employment under Rational Expectations. ” Quarterly Journal of Economics 99 (August 1984): 567-85. Mussa, M. “The Exchange Rate, the Balance of Payments and Monetary and Fiscal Policy under a Regime of Controlled Floating.” Scandinavian Journal of Economics 78 (May 1976): 22948. 311
Kent P. Kimbrough -.
“Tariffs and the Balance of Payments.” In The Monetary Approach to the Balance of Payments. J.A. Frenkel and H.G. Johnson, eds. Toronto: University of Toronto Press, 1976, 187221.
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