Wages, the Terms of Trade, and the Exchange Rate Regime

Purvis, Douglas D. Article Wages, the Terms of Trade, and the Exchange Rate Regime Zeitschrift für Wirtschaftsund Sozialwissenschaften (ZWS) - Vierteljahresschrift der Gesellschaft für Wirtschaftsund Sozialwissenschaften, Verein für Socialpolitik Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Purvis, Douglas D. (1979) : Wages, the Terms of Trade, and the Exchange Rate Regime, Zeitschrift für Wirtschaftsund Sozialwissenschaften (ZWS) - Vierteljahresschrift der Gesellschaft für Wirtschaftsund Sozialwissenschaften, Verein für Socialpolitik, ISSN 0342-1783, Duncker & Humblot, Berlin, Vol. 99, Iss. 1-2, pp. 9-39, https://doi.org/10.3790/schm.99.1-2.9 This Version is available at: https://hdl.handle.net/10419/291421 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Wages, the Terms of Trade, and the Exchange Rate Regime By Douglas D. Purvis* The issue of relative country size is obviously one of much practical significance. But the choice of relative country size as the central theme of this conference is also timely in terms of the development of the current literature on macroeconomic theory in an open economy. Certainly the dominant theme in the current literature is the monetary approach to balance of payments and exchange rate analysis. One of the most attractive features of the monetary approach in its early stages was its general equilibrium nature, and one of its earliest and most important "victories" was the laying-to-rest of the partial equilibrium elasticities approach. But in emphasizing the monetary nature of balance of payments and exchange rate phenomena, recent writings in the field have paid increasingly less attention to general equilibrium interactions, and have worked with highly aggregated models which abstract from the type of real phenomena which the earlier traditions had emphasized. The question of relative country size is one which necessitates that attention be refocussed on structural aspects of the economy. The purpose of this paper is to explore the implications of imposing some "real, structural characteristics" on a model which is otherwise very monetary in spirit. One of the key insights of the monetary approach is that it made explicit the distinction between the exchange rate, being the relative price of national monies, and the terms of trade, being the relative price of traded goods. This distinction was often blurred in older Keynesian models in which output prices were treated as constant in terms of the domestic currency so that a change in the exchange rate was also a change in the relative price of national outputs. Monetary models, in contrast, have tended to emphasize models with full employment and fixed terms of trade, although neither assumption is essential to the * Yale University. This paper has evolved from my presentation at Queen's Summer Workshop in Monetary Economics, July 1976, and I am indebted to participants there for helpful discussion and to Robert Ford for collaboration at that early stage. (See Ford [1976].) I would also like to thank Ronald Findlay and Carlos Rodriguez for useful comments on an earlier version of this paper. Remaining opinions and errors are my own responsibility. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 10 Douglas D. Purvis approach. Such models suggest that the principal effect of a devaluation is to raise the domestic price level with the ensuing fall in the value of domestic assets eliciting a reduction in absorption and a trade account surplus. This surplus appears independent of elasticity conditions and is inherently temporary, lasting only until the loss in financial wealth is recovered. No role need be given to relative price or output effects.1 The approach is consistent with the existence of a multiplicity of assets, and the term "monetary approach" is in many ways a misnomer for "portfolio balance" approach. The approach taken in this paper is one suggested by the question of relative country size viewed in a monetary framework. We abandon the "small, open economy" tradition by explicitly disaggregating traded goods into imports and exports and treating their relative price as variable, thus re-emphasizing the distinction between the exchange rate and the terms of trade by displaying each explicitly and assigning the appropriate role to each.2 In addition, further structure will be given to the model by explicitly considering the behavior of aggregate supply and the nominal wage rate. This approach is, I believe, in the spirit of, and largely complementary to, the monetary approach. But it is also a reaction to recent trends in that approach which stress small, "reducedform" models depicting the exchange rate or the balance of payments as being determined by monetary forces alone rather than as the consequence of simultaneous interaction between monetary and real phenomena. Throughout, the framework of analysis is one of monetary equilibrium; given the values of the exogenous variables and the predetermined level of financial wealth, the model can be solved for the values of the endogenous variables at a moment in time. That solution also yields the rate of change of some of the predetermined variables so that a dynamic path for the model is also implied; stability requires that the dynamic path converge to a stationary long-run solution.3 1 It is common for goods to be disaggregated into traded and non-traded goods, the relative price of which plays a central role in short-run adjustment of the system. For an analysis of such a model that is very complimentary to the analysis of this paper, see Genberg and Kierzkowski (1975). 2 The traded/non-traded goods disaggregation suggests that "openness" is an important characteristic of an economy; the striking constancy of the share of services in various countries' economies suggests that this may not be as distinctive a feature as is commonly thought. "Smallness" seems a more operative concept. 3 This approach follows the pioneering work of Blinder and Solow (1973). Turnovsky (1976) and Kouri (1976) extend the analysis to the open economy under fixed and flexible exchange rates, respectively. On the former, see also Purvis (1976). In Kouri's model, financial wealth is endogenous at a moment of time since it depends on the exchange rate. In terms of the momentary equilibrium, I will treat expectations as predetermined. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 Wages, the Terms of Trade, and the Exchange Rate Regime 11 However, for a variety of reasons to be discussed below, we will be primarily concerned with the momentary equilibrium. In the next section the basic model is developed in the context of fixed exchange rates; the analysis is extended to flexible exchange rates in Section II. Finally, in Section III, some concluding comments are offered on long-run equilibrium and other aspects of the issue of relative size. It is useful to note at the outset that the model obeys the homogeneity postulate and is characterized by long-run neutrality in the sense that a proportionate change in all nominal magnitudes leaves the real equilibrium unaltered. In particular, the exchange rate is neutral in the sense that if the model is stable, a change in the exchange rate would, with flexible wages and prices, lead to a proportionate change in the equilibrium values of all prices and nominal assets, and no change in real variables. Of course, such neutrality does not necessarily obtain in the short run; an exchange rate change can affect the terms of trade in the short-run as a result of ensuing wealth, wage-cum-output, and substitution effects, a possibility that doesn't arise, except in the absence of perfect arbitrage, in monetary models which rely on the small country assumption rather than the homogeneity postulate to distinguish the terms of trade from the exchange rate. I. Relative Size and Momentary Equilibrium: Fixed Exchange Rates This section develops, and examines, the short-run comparative static properties of a simple two-good model which captures the features of relative country size discussed above. The export good is produced and consumed domestically and bears the domestic currency price P. The import good Ls produced abroad and is available for import at the exogenous foreign currency price Q*. The exchange rate, c, is defined to be the domestic currency price of one unit of foreign exchange (when the currency depreciates, the exchange rate goes up) so by the assumption of perfect goods arbitrage, the domestic currency price of imports is Q = eQ*. Domestic production, Y, is governed by a neoclassical production function Y (Nf K) which depends on employment, N, and the capital stock, K. Assuming the capital stock to be fixed and competitive firms maximizing short run profits, we can specify an aggregate supply function (1) YS = S(P,Q;oc) , $!><), S2< 0 where a is a shift parameter. There are four special cases of equation (1) that are of interest: OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 12 Douglas D. Purvis (i) Keynesian I (Si = Y> 0, = 0). This obtains when the nominal wage rate, W, is rigid and there is excess supply of labor. Actual employment is determined by the demand for labor which is inversely related to the real wage in terms of the home good, W/P. (ia) Keynesian II (Si = oo, S2 = 0). This is the extreme Keynesian case of perfectly elastic output, and is common in the textbooks and the literature of the 1960's. As has been shown by Barro and Grossman (1971) it can be motivated by a quantity-constrained fixedprice equilibrium. (ii) Classical I (Y^1 > Si = — S2 > 0). In this case the nominal wage adjusts to clear the labor market; labor demand is as in (i) above but the supply of labor depends upon the real wage defined in terms of a price index involving both import and domestic goods prices. An increase in P causes some increase in output as the real wage falls; however the changes are not as large as in case (i) since in this model the nominal wage rises to partially offset the increase in P. A equiproportionate change in P and Q causes an equiproportionate change in W and no output change. By normalizing so that initial P and Q equal 1, we get Si = — S2.4 (iia) Classical II (Si = S2 = 0). This is a special case of (ii) above where the real wage demanded by workers is independent of the price of imports and might, in some circumstances, be thought of as characterizing exchange rate illusion in the labor market.5 In the fixed exchange rate case, Q is exogenous so the general cases (1) and (ii) give rise to an upward rising aggregate supply curve; the special cases (ia) and (iia) correspond to horizontal and vertical supply curves, respectively. We shall concentrate in what follows on the general cases (i) and (ii). The foreign demand for exports of the home good is given by (2) Xd = X (n; §) , Xx < 0 where n is the relative price of exports in terms of imports (P/Q), i. e., the terms of trade, and f$ is a shift parameter. Again, the extreme cases 4 Output in this case depends on relative prices, Y = G (P/Q), and dY = (G'/Q) dP - (G' P/Q2) dQ . Setting P = Q = 1 yields St = — S2 = G'. Throughout we set P = Q = n = e = Q* = 1. This normalization means that derivatives will represent percentage changes. Salop (1974) uses a similar model of aggregate supply in her analysis of devaluation. 5 Exchange illusion could also suggest that W responds differently to a change in e than to a change in Q*, a subtlety I ignore in what follows. Note that our cases (i) and (ii) are extremes, and one could imagine intermediate cases where wages respond partially to changes in Q. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 Wages, the Terms of Trade, and the Exchange Rate Regime 13 common in the literature can be treated as special cases where Xi = 0 (exogenous exports) and Xi = — oo (small-open economy). An additional source of demand for domestically produced goods arise from government which I assume not to purchase any imports. I treat government expenditure in real terms, g, as a parameter and assume that the nominal government deficit, G, is financed by domestic credit creation: (3) G = Pg — T = C where T is nominal taxes, C is the domestic credit component of the money supply, and a " •" indicates a time derivate. (In the remainder of this and the next section I assume nominal taxes to be zero.) Total domestic expenditure in terms of home goods is given by (4) E = E (Y, A/P, 1 In) t 0 < E1 < 1 , E2 > 0 , Es> 0 where A is nominal wealth in terms of the domestic currency, as defined below. The third term represents the Laursen-Metzler argument that an improvement in the terms of trade increases real income and hence reduces the ratio of expenditures to income (1950, p. 286). Equation T (4) implicitly defines a savings function, A = Y —— — E, which responds positively to income and the terms of trade, and negatively to real wealth, with partial derivatives reflecting the income constraint. Expenditure is allocated between home goods and imports according to (5) E = D (E, n) + — m (E, n) . Now define M (E, ri) to be the home goods equivalent of expenditure on imports; i. e., M(E,ri) = — m (E, n) so Mi = — mi and M2 = — (rri2 — ^ JZ Jt Jt m), and further, from (5), M2 = — D2. If the expenditure-held-conn stant demand for home goods is well behaved with respect to n (i. e., if D-2 < 0), then the demand for imports must be elastic and so the home good equivalent for the demand for imports must be well-behaved (M2 > 0).6 Thus we can write (5') E = D (E, Jt) -f M (E, n) , 1 > Dx = 1 - Mx > 0 , D2 = - M2 < 0 . « The import elasticity Em = — (3 ml3 (1 In)) (1 ln)lm = m^/M. From the definition of M, this equals 1 + (P/M) M2 which is greater than one since M2 is positive. If m (.) were not elastic, D would not be monotonic in n. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 14 Douglas D. Purvis Wealth is comprised of domestic money, L, plus the domestic currency equivalent of foreign assets, F = eF*. In order to avoid the complications associated with interest earnings on assets and the complexities of the interest rate consequences of exchange rate expectations, and in order to emphasize the role of the exchange rate as the relative price of national monies, I assume that F* is non-interest bearing foreign currency.7 Therefore (6) A = C + R + eF* where R is the stock of foreign exchange reserves held by the central bank, evaluated at cost: exchange rate changes generate direct wealth effects only to the extent that the public holds foreign currency; capital gains or losses incurred by the central bank on its foreign exchange holdings are not assumed to be monetized.8 Equilibrium in the market for domestically produced goods is given by (7) (7) Y S = E + g + (Xd-M) = D + g + Xd . Equivalently we can define the amount of home goods available for export as (8) Xs = Ys — (D + g) and rewrite the equilibrium (7) in terms of the equality between export supply and demand (7') XS = Xd . Under fixed exchange rates A is predetermined and Q is exogenous (eQ*). We could solve equations (1), (2), (4), (5'), (7') and (8) for P, Y, Xd, Xs, E and M. Momentary equilibrium in the model — given Q = eQ*, 9, r* and A — is illustrated in Figure 1. The export supply locus in the right hand quadrant starts at the value of P at which domestic demand for domestic output, D + g, equals supply, Ys.9 (The export supply 7 Dornbusch (1967 a, b) has developed models which make the interest rate endogenous in the short run due to exchange rate expectations. Kouri has a model similar to ours, but, by assuming Q* is always constant, he fails to make clear the different role played by e and Q* that I emphasize below. 8 Porter (1975) emphasizes that portfolio shifts in the anticipation of exchange rate changes shift the wealth effects of a depreciation from the private sector to the central bank, thus nullifying much of the force of the devaluation. 9 D + g can be derived either by solving (7) for equilibrium income and substituting that value into D, or by using Y = D + g + X<* to define Y as a function of P, and substituting in D. The two would intersect at equilibrium OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 Wages, the Terms of Trade, and the Exchange Rate Hegime 15 P P D*g 0 home goods 0 exports i o Fig. 1 : Equilibrium with Fixed Exchange Rates curve is flatter than Ys since it combines the slope of Ys and D.) The intersection of Xs with the export demand curve determines P; tracing back to the left-hand quadrant we can determine Y and D. At the equilibrium price, the level of exports equals horizontal distance VW in the left-hand quadrant, and the dashed line g + D + Xd intersects Ys to yield an equivalent characterization of the equilibrium. Note that this goods market equilibrium is found without reference to asset equilibrium; only the predetermined stock of financial wealth was used. This suggests immediately that monetary policy can have no effect in the short run; credit expansion will, under fixed exchange rates give rise to instantaneous offsetting portfolio switches. Asset equilibrium considerations are, however, important in determining the various external accounts and hence in determining the motion of the system. This is spelled out in the appendix. Of particular interest is the trade account surplus, given by (9) Z = X-M = Y-QE + g) In the assumed absence of debt servicing requirements, Z is equivalent to the current account. Thus the trade account surplus also gives the net rate of accumulation of foreign assets, eF + R, which in turn equals the excess of domestic saving over domestic credit creation. P; the second would be less price elastic since the reduced form for Y would be negatively related to P. = (A — G) / P . OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 16 Douglas D. Purvis P g.DrX \ 0 home goods Fig. 2: The Trade Account Under Fixed Exchange Rates The behavior of the trade account is illustrated in Figure 2, which can be used to relate our analysis to the three traditional approaches. Holding income constant, we plot the total demand for home goods, D + g + Xd, and the total home good equivalent of domestic demand, g + E, as functions of the price level. The horizontal distance^ defines the trade balance as a function of the price level, plotted as Z (P; Yo). The slope of D + g + Xd is given by Xi + D2 - Di (E2 A + E3) which is unambiguously negative. The slope of g 4E is given by — (E2 A + E3), also negative. In order for the Zp to be negative, as drawn, we require that the Augmented Elasticity Condition (AEC) given by (10) be met. (10) AEC: X1 + D2 + (1-D1)E2A + E3)=X1-M2 + M1(E2A + Es)<0 . This is similar to the Marshall-Lerner condition with the domestic import elasticity measured as the substitution effect plus the wealth and Laursen-Metzler effects on expenditure. An increase in income causes both curves to shift right, and the trade account for given price level unambiguously deteriorates (i. e., Zy < 0 as illustrated by Z(P; Yi) where Yi > Y0) since g + D + Xd shifts by only a fraction D\ of the shift in g + E (given by E% dY). These two results illustrate the elasticity and absorption approaches respectively. The third approach, given by the monetary theory of the balance of payments, contends that the overall balance of payments will equal the OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 Wages, the Terms of Trade, and the Exchange Rate Regime 23 As has been well-recognized, the opportunity to engage in such stockswitches depends not only on "perfect international financial markets," but also on the commitment of the central bank to provide or absorb domestic currency in order to maintain the exchange rate. Not surprisingly then, the recursive nature of the momentary equilibrium disappears under a flexible exchange rate regime wherein the central bank no longer has such a commitment. Under flexible exchange rates, the money supply is exogenously determined by the monetary authority, and momentary equilibrium must be consistent with it as well as with equilibrium in the goods market. Hence with c, and therefore Q, now endogenously determined, the single equation analysis of Section I cannot be used here. To illustrate this, consider the analysis of devaluation conducted in the preceding section. Given an exogenous change in e we were able to deduce the equilibrium changes in P and Y from the goods market equilibrium and the value of total wealth A. We could have then proceded to analyze the ensuing change in money as a result of portfolio rearrangement. It is easily shown using the system developed below that if a change in money were introduced exogenously into the flexible exchange rate system, then the same exchange rate change would fall out endogenously. But in reversing the experiment, a simultaneous system would have to be used to calculate the exchange rate change. However, current monetary writings (Dorribusch [1976 a, b], Kouri [1976]) have suggested that the exchange rate is essentially determined by portfolio equilibrium alone, and that flow decisions determine the capital account (and presumably the rate of change of the exchange rate). The approach taken in this section is to emphasize that the determination of c, P, Y, E, F* and e is a simultaneous one. Accordingly, the balance of payments equations of the appendix are modified to note that the only source of change in the money supply arises from the government deficit and that foreign assets can only be accumulated by net commodity sales. Since the government is neither buying nor selling foreign exchange there is no foreign source of additional money. That is, the balance of payments must be zero, which is equivalent to the requirement that the public be willing to hold the existing stock of money,14'15 and the capital account deficit must equal the current ac14 Equivalently, we could specify that the public be willing to hold the existing stock of foreign assets! The force of the statement is simply that discrete asset swaps are ruled out so the monetary equilibrium must now be consistent with the existing distribution of assets. This, of course, presumes that foreigners hold no domestic currency; this means in terms of more common models, as Ron McKinnon pointed out to me, that it is impossible to change one's forward cover position. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 24 Douglas D. Purvis count surplus. The goods market equilibrium (7) must be solved simultaneously with the portfolio balance condition given by (14) (14) L = l(Y; 6) A , Zy>0 where A is financial wealth as defined in (6) above, L is the domestic money supply (C + R)16 and S is a vector of other variables which may affect portfolio balance. (For example, Kouri stresses the role of exchange rate expectations.) Note that from (14) and (6) we can deduce the demand for foreign assets, F* = f (Y ; G) A ; / (.) = 1 - I (.) ; fY=-lY so that only one asset equilibrium condition need be considered. Substituting for Y in (14) and differentiating yields (15) Aly St dP + (Aly S2 -1IF*) de= - Aly S2 dQ* + (1 - I) dR Combining (14) with goods market equilibrium (11) yields a system of two equations in the unknowns P and e. Equilibrium is depicted in Figures 5 and 6. Goods market equilibrium under flexible exchange rates as given by (11) is depicted by XX; as can be readily seen it has a slope X!2 which is positive but less than one. In the same figures three possible loci of asset equilibrium as given by (14) are depicted by MM, which has a slope - (Aly S2 + IF*)/Aly Si ^ 0. (Unless otherwise specified, we shall assume F* > 0.) Under the reasonable dynamic postulate that the exchange rate rises if there is excess supply of domestic money and the price level rises if there is excess demand for goods, the stability condition is that MM cut XX from above; i. e., that the basic determinant of the system, A = X Aly Si + 2 (Aly S2 + IF*) be positive. However, A is a priori of indeterminate sign which indicates a potential instability in the flexible exchange rate system; this instability turns out to be related to earlier analyses of the foreign exchange market which concentrated solely on flow equilibrium, and is worth exploring in some detail. 15 This is in contradistinction to Kouri's contention (pp. 285 - 287) that stock and not flow equilibrium must be used to close the model. This difference arises in part due to differences in the models as discussed above. But there is a broader issue. I would contend that stock and flow equilibrium are both involved since in monetary equilibrium one is content with existing stocks only if they are changing at the desired rate. One could argue that in the models under discussion, as opposed to a model with transactions costs as alluded to by Kouri (p. 287) and analyzed in detail an Purvis (1975, appendix) the flow demand for money is not determinate; but this does not render the balance of payments indeterminate under fixed exchange rates nor does it make the fact that under flexible rates the flow supply is zero, of no consequence. 16 C is strictly an accounting relation between the government and the central bank; open market operations must involve R and F* only. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 Wages, the Terms of Trade, and the Exchange Rate Regime 25 P Fig. 5: Momentary Equilibrium (MM negatively sloped) Fig. 6: Momentary Equilibrium (MM positively sloped) (a) unstable (b) stable It is clear that a sufficient condition for stability is that MM be negatively sloped. A depreciation in general has two effects on the excess demand for money: a positive wealth effect and a negative income effect. If MM is positively sloped the income effect dominates and hence a depreciation in the face of an excess supply of money is destabilizing; only if the XX is steeper than MM, i. e., only if the money market responds relatively more strongly to changes in P so that changes in P in response to goods market conditions will also equilibrate the money market, will the process be damped. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 26 Douglas D. Purvis It is interesting to examine the influence of the various parameters of the model on the potential for instability. Consider first the influence of exchange rate changes on wages as manifested in the value of S2. It is easily seen that in the Keynesian sticky wage case with S2 = 0, MM is negatively sloped, and the system is necessarily stable. In the other extreme case with S2 = 0 = Si (case (ii a) of exchange rate illusion), income would be fixed so that only one value of the exchange rate would be consistent with (14); MM would be vertical, the wealth effect would dominate, and the system would be stable. Further, it can be shown that as S2 increases in absolute value the slope of MM increases faster than the slope of XX thus increasing the changes of instability. [If MM is positively sloped (S2 = — Si), F* > 0 ensures that the slope is less than one.] Proposition III. Increased wage responsiveness to exchange rate changes increases the chances that the flexible rate system will be unstable. Given this last proposition and observing that the flexible-wage, full-employment model is commonly used in monetary models of the exchange rate, it is curious that instability does not arise in such models. The answer lies in the role played by a second parameter of our model, relative country size. In the small open economy case generally used by monetarists, XX takes on a slope of one which guarantees that it will be steeper than MM so long as F* is positive. Proposition IV. The small open economy assumption is sufficient to assure that an economy with net foreign asset holdings will be stable under flexible exchange rates. Note that in this case, relative prices can be thought of as determined by XX and the price level (exchange rate) by MM, and the simultaneous model (12) and (15) can be replaced by a recursive solution relating the exchange rate to the money supply. This is the interpretation I give to Kouri's model. As the elasticities (Xi + D2) fall in absolute value, the slope of XX decreases, increasing the potential for instability. The stability condition A > 0 can be interpreted as an Augmented-Marshall-Lerner-Condition which defines, for the other parameters of the system, a critical value for the sum — (Xi + D2) to exceed in order to ensure stability. A third parameter affecting stability is the net foreign asset position, F*. Consider, for example, a Financially Large Country which has enough influence in international financial transactions that its international borrowings are denominated in terms of the home currency. Britain as the financial center for the Sterling Area was an example OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 Wages, the Terms of Trade, and the Exchange Hate Regime 27 of such a country, just as the United States and Switzerland may be current examples. In terms of our model, F* would be exchange-indexed so that an exchange rate change has no wealth effects. In case (i) with S2 = 0, the financially large country will have a flat MM curve. Asset equilibrium is consistent with only one level of income and hence only one price level; the system is stable. In case (ii) with S2 = — Su relative prices are now fixed since again only one level of output is consistent with asset equilibrium, and MM has a slope of one. Proposition V. A financially large country will be unstable under flexible exchange rates if wages respond to the exchange rate (F* positive is sufficient for stability in Case i; necessary in Case ii.) (If the country is a net borrower so that F* is negative, instability is also ensured since MM takes on a slope greater than one.) Even the SOE assumption is of no avail now since that would fix output at a level not necessarily consistent with existing asset proportions, thus frustrating portfolio balance motives and possibly generating a speculative rush. The system is overdetermined since we now have two independent conditions on the relative price structure. Finally it is useful to think of combinations of these parameters in order to emphasize the general equilibrium nature of the exchange rate. For example, the usual Keynesian problem of low elasticity — (Xi -f D2) could be offset by low response of wages to the exchange rate (thus increasing the price elasticity of output) or a high F* (c affecting expenditure in the latter case via wealth rather than substitution effects.) Using Figures 5 and 6 we can now briefly examine the impact on momentary equilibrium of fiscal policy, dg, or a purchase of foreign exchange assets by the central bank, dR = — edF*. The comparative static results are summarized in Table 2, where throughout we assume F*> 0. Consider first an increase in government purchase of home goods. In the general case where relative size matters, this creates, at existing prices, an excess demand for goods and causes the XX curve to shift vertically. Assuming stability, the exchange rate falls (i. e., the currency appreciates), domestic prices rise if MM is negatively sloped, and fall if MM is positively sloped. Proposition VI. With flexible wages and variable terms of trade, expansionary fiscal policy under flexible exchange rates will cause domestic prices to fall if the income effect on the demand for money exceeds the wealth effect. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 28 Douglas D. Purvis Table 2 Comparative Statics under Flexible Exchange Rates Exogenous Changes Case Induced Change Exogenous Changes Case Domestic Prices dPa) Domestic Output dYa) Exchange Hate dea) Fiscal Policyb) dg = 1 i IF* -j- > 0 (0) SidP>0 (0) Aly Si ^ * 1 <0 (0) Fiscal Policyb) dg = 1 ia 0 (NA) IF* ^ XAly + lF* j >0 (0) Fiscal Policyb) dg = 1 di IF* - Aly / v ^§0(0) depends on slope of MM Sx (dP - de) > 0(0) — Aly Si ^ J—1 < dP (0) Fiscal Policyb) dg = 1 iia i>0 (0) 0 (0) 0 Monetary Policyc) = HP - = 1 i A>0[AIyS1 + IF*) SxdP> 0 (0) V > dP (dP) A Monetary Policyc) = HP - = 1 ia 0 ¿M>0 (0> (1 - Et Di) ^ My I >0(0) Monetary Policyc) = HP - = 1 ii l>° S1 (dP - de) <0 (0) y >dP (dP) A Monetary Policyc) = HP - = 1 iia 2 IF* > ° ( IF* ) 0 0 a) Second (bracketed) entry gives results for small country assumption. b) dZ/dg < 0 by AEC. c) dZ/dR uncertain in case (i) — all but wealth effect or imports lead to improvement. — dZ/dR > 0 in case (ii) by AEC. (Although the initial impact is excess demand for goods and prices rising, there is also excess supply of money in this case; e rises causing excess supply of goods and generating a cyclical adjustment whereby OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 Wages, the Terms of Trade, and the Exchange Rate Regime 29 prices eventually fall.) Income unambiguously rises; P can fall only when 1S2 = — Si; and if P falls, it falls by less than the exchange rate so dY > 0. Using AEC it can be shown that the trade account deteriorates. In the SOE case no relative price change is required to offset the induced excess demand so XX doesn't shift. Thus in this case the government expenditure has no effect on the price level, the exchange rate or the level of income; the traditional result about the ineffectiveness of fiscal policy under flexible exchange rates is reestablished. Proposition la» In a small open economy, fiscal policy is not effective in influencing income under flexible exchange rates. In this case, the impact effect on the trade account is to cause a deterioration in the exact amount of the government expenditure. These results conform to those obtained by Kouri; in addition, if we were to combine case (ii) with the SOE assumption we can view the model recursively whereby the goods market by determining relative prices also fixes income; asset equilibrium then determines the price level and hence the exchange rate. Monetary policy creates an excess supply of money and causes MM to shift vertically. In the general case, and again assuming stability, this means that both the price level and the exchange rate rise, the latter by more by virtue of the slope of XX being less than one. This means that in case (i) output rises but in case (ii) output falls. Proposition VII. With flexible wages and variable terms of trade, expansionary monetary policy under flexible exchange rates will be inflationary on prices but contractionary for output. This is because the induced exchange depreciation will cause a wage explosion which results in higher real wages, this increase in W/P being in turn dependent upon the impact on the terms of trade. In the Kouri case of responsive wages and fixed relative prices, there will be no output response, and the exchange rate and prices will have to rise to eliminate the excess demand for money. Proposition Vila. In a small open economy with flexible wages, monetary policy will not affect output but will cause an equal change in P and e, both rising more than proportionately to the monetary disturbance. If wages are responsive to the exchange rate, or if relative prices are fixed, then expansionary monetary policy will unambiguously cause a deterioration of the trade account. (In the absence of one of the two stated conditions, the impact of wealth on expenditure is uncertain; see OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 30 Douglas D. Purvis the discussion of devaluation in Section I above.) Finally, it can easily be shown that for any devaluation considered in Section I, there is an equivalent monetary policy under flexible rates; the induced depreciation in Section II will equal the exogenous devaluation of Section I, and the induced change in demand for money of Section I will equal the exogenous change in money supply of Section II. Consider now the effects of an exogenous increase in the foreign price, dQ*. These results are summarized in Table 3. At existing values of P and e, assuming unchanged demand for exports as a function of relative prices, this creates an excess demand for the home good and XX shifts vertically by a proportion rj/H of dQ*. If S2 = 0, MM will remain unaltered, and since MM is negatively sloped, it is obvious that P (and hence income) rises and e falls; both change less than proportionately to dQ*; (dP — dc) can be shown to be less than dQ* so the terms of trade deteriorate. Proposition VIII is easily proven: Proposition VIII. In an economy with rigid wages and variable terms of trade, an increase in the foreign currency price of imports leads to a less than proportionate increase in the price of the export good. Further the price increase that would obtain under fixed exchange rates exceeds that which occurs under flexible rates; in the latter case a less than proportionate appreciation of the currency occurs. If wages respond to dQ*, output would fall at initial (P, e) causing an excess supply of money and increasing the excess demand for the home good. The MM curve shifts up exactly proportionately to dQ*. It is easily shown that, just as under fixed exchange rates, flexible wages increase the responsiveness of domestic to foreign prices.17 As can be seen from Figures 7 and 8, the comparative static results depend qualitatively on the slope of MM. If the wealth effect of a change in c dominates the income effect (in terms of the money market) so MM is negatively sloped, then P rises less than proportionately to Q*; it can be shown that the change in P is less than would obtain under fixed rates so that flexible exchange rates in this case do provide some insulation from foreign inflation. But perhaps surprisingly, the adjustment involves a depreciated currency (c rises) ensuring that the terms of trade and output fall, and the fall in output is greater than that which would have occurred under fixed exchange rates! If MM is positively sloped, flexible rates do not even provide price insulation since P rises more than proportionately to Q* and hence more than fixed-rate increase. 17 Flexible wages and flexible exchange rates are not perfect substitutes in the adjustment process, as can be seen by comparing the second and fifth rows of Table 3. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 Wages, the Terms of Trade, and the Exchange Hate Regime 31 Table 3 Comparative Static Effect of Foreign Inflation Changes Induced by dQ* = 1 Domestic Prices DPa) Exchange Rate dea) Domestic Output dYa) 1. Rigid Wages (i) (S2 = 0)b); Variable Terms of Trade a) Fixed Exchange Rates V 0<f <1 (5 ;u) (2) 7Ì SlY>0 (2) b) Flexible Exchange Rates0) .0<si«<1 (7,7) ^ — yd -1<w + s<0 (7) SiV >0 2 + òk > (3) 2. Rigid Wages (i) (S2 = 0); Constant Terms of Trade (Small Open Economy, Xx = - oo) a) Fixed Exchange Rates 1 (2,1) (2) S1>0 (1) b) Flexible Exchange RatesO 0<lÌi (6, U) -1<i + s<0 (6) (4) 3. Flexible Wages (ii) (S2 = - S^b); Variable Terms of Trade a) Fixed Exchange Rates V 0<Y<1 (4,3) 0 (2) MiH<o (6) b) Flexible Exchange Rates«*) V + à' A ^ n ^ ^ 1 AlyS^Z-v) n ^ „ (rj — 2) IF ^ b) Flexible Exchange Rates«*) (1,U) A 0< (1) Sl A <0 (7) 4. Flexible Wages (ii) (S2 = - St); Constant Terms of Trade (SOE) Independent of Exchange Rate Regime 1 (2,1) 0 (2) 0 (5) a) Bracketed number gives ranking by column, according to algebraic change. Column one has two rankings, for 8 > 1 and 8 < 1, respectively. U means unranked as between 4, 5, and 6. b) Moving from Case (i) to (ii) 2 falls while y and X rise; their ranking, however, remains unchanged. c) 8 = Aly S^IF* > 0. MM is positively sloped if 8 > 1. d) 8' = 8/(1 - 8) g 0 as 8 > 1. if 8' > 0, dP > 1. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 32 Douglas D. Purvis Fig. 7: Foreign Inflation Partially Insulated by Flexible Rate Fig. 8: Foreign Inflation Exaggerated by Flexible Rate Proposition IX. In an economy with flexible wages and variable terms of trade, flexible exchange rates, at best, provide partial price insulation from foreign inflation, and they exacerbate the negative output effects that foreign inflation portends for such an economy. Instead of attempting an intuitive explanation of this result at this stage, it is worth examining the small open economy case whereby the terms OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53 Wages, the Terms of Trade, and the Exchange Rate Regime 39 Genberg, H. and H. Kierzkowski (1975), Short-Run, Long-Run and Dynamics of Adjustment Under Flexible Exchange Rates, unpublished MS, Graduate Institute of International Studies, Geneva. Kierzkowski, H. (1975), An Integration of Balance of Payments Theories, unpublished manuscript, Bank of Canada, Ottawa. Kouri, P. (1976), The Exchange Rate and the Balance of Payments in the Short Run and the Long Run: A Monetary Approach, Scandinavian Journal of Economics 78, 280 - 304. Laursen, S. and L. Metzler (1950), Flexible Exchange Rates and the Theory of Employment, The Review of Economics and Statistics, November, 32, 4, pp. 281 - 299. McKinnon, R. (1969), Portfolio Balance and International Payments Adjustment, and "Comment" by R. Jones, in: Mundell and Swoboda (editors), Monetary Problems of the International Economy (University of Chicago Press). — (1975), The Limited Role of Fiscal Policy in an Open Economy, unpublished MS, Stanford University. — and W. Oates (1966), The Implications of International Economic Integration for Monetary, Fiscal, and Exchange Rate Policy, Princeton Studies in International Finance No. 16. Mundell, R. (1968), International Economics (McMillan). Mussa, M. (1976), The Exchange Rate, the Balance of Payments, and Monetary and Fiscal Policy under a Regime of Controlled Floating, Scandinavian Journal of Economics 78, 229 - 248. Niehans, J. (1975), Some Doubts about the Efficacy of Monetary Policy under Flexible Exchange Rates, Journal of International Economics 5, 275 - 281. Parkin, M. (1976), Macroeconomic Models of the Open Economy: A Survey, presented to McMaster University Conference on Inflation in the Open Economy, Hamilton, March 1976. Porter, M. C. (1975), Anticipation and Policy Mix in Open Economies, in: Papers in Monetary Economics, proceedings of a Conference held in Sydney, July 1975, Reserve Bank of Australia. Purvis, D. (1975), Portfolio and Consumption Decisions: Towards a Model of the Transmission Process, in: Papers in Monetary Economics, proceedings of a Conference held in Sydney, July 1975, Reserve Bank of Australia. — (1976), On Long Run Equilibrium in the Small Open Economy, unpublished MS, Cowles Foundation, Yale University. Rodriguez, C. (1976), Short and Long Run Effects of Monetary and Fiscal Policy under Flexible Exchange Rates and Perfect Capital Mobility, unpublished MS, Columbia University. Salop, J. (1974), Devaluation and the Balance of Trade under Flexible Wages, pp. 129 - 152, in: G. Horwich and P. A. Samuelson (editors), Trade, Stability and Macroeconomics. Essays in Honor of Lloyd A. Metzler, Academic Press, New York. Turnovsky, S. (1976), The Dynamics of Fiscal Policy in an Open Economy, Journal of International Economics 6, 115 - 142. Whitman, M. von Neumann (1970), Policies for External and Internal Balance, Princeton Special Papers in International Economics No. 9. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.99.1-2.9 | Generated on 2023-04-04 11:56:53