Real Exchange Rate Fluctuations in a Small Open Economy Under Fixed and Flexible Exchange Rates

Klein, Martin Article Real Exchange Rate Fluctuations in a Small Open Economy Under Fixed and Flexible Exchange Rates Zeitschrift für Wirtschaftsund Sozialwissenschaften (ZWS) - Vierteljahresschrift der Gesellschaft für Wirtschaftsund Sozialwissenschaften, Verein für Socialpolitik Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Klein, Martin (1987) : Real Exchange Rate Fluctuations in a Small Open Economy Under Fixed and Flexible Exchange Rates, Zeitschrift für Wirtschaftsund Sozialwissenschaften (ZWS) - Vierteljahresschrift der Gesellschaft für Wirtschaftsund Sozialwissenschaften, Verein für Socialpolitik, ISSN 0342-1783, Duncker & Humblot, Berlin, Vol. 107, Iss. 1, pp. 51-66, https://doi.org/10.3790/schm.107.1.51 This Version is available at: https://hdl.handle.net/10419/291655 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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Sozialwissenschaften (ZWS) 107 (1987), S. 51 - 66 Duncker & Humblot, Berlin 41 Real Exchange Rate Fluctuations in a Small Open Economy Under Fixed and Flexible Exchange Rates By Martin Klein* This paper examines the implications of a standard macroeconomic model of a small open economy for real exchange rate fluctuations in different nominal exchange rate regimes. The two central questions are the following. First, does macroeconomic theory offer an explanation for the observed high level of real exchange rate fluctuations in the flexible exchange rate period? Second, are these fluctuations destabilizing with respect to domestic output or are they rather the symptom of the proper functioning of the real exchange rate as an automatic stabilizer? 1. Introduction This paper examines the problem of real exchange rate fluctuations in a macroeconomic model of a small open economy. The two central questions are the following. First, does macroeconomic theory offer an explanation for the observed high level of real exchange rate fluctuations in the flexible exchange rate period? Second, are these fluctuations destabilizing with respect to domestic output, or are they rather the symptom of the proper functioning of the real exchange rate as an automatic stabilizer? Our point of departure is the following "stylized fact". Exchange rate fluctuations - real as well as nominal - have increased dramatically since the end of the Bretton-Woods system and the transition to'flexible exchange rates. There are two competing explanations for this phenomenon. The first one states that the increase in exchange rate fluctuations took place because of the transition to flexible exchange rates, the second one states that it reflects an increase in exogenous disturbances in the world economy and in discrepancies between major economies. Loosely speaking, according to * Exchange rates have been rather volatile in recent years. However, as someone has observed, economists' opinions about exchange rates have been even more volatile. This is especially true for myself during the work on the present paper. People who have more or less sucessfully intervened in order to dampen the volatility of my opinions are: Manfred J. M. Neumann, Jiirgen von Hagen and Eckhard Wurzel at the University of Bonn, Hans Genberg and the other participants at the Konstanz Seminar for Monetary Theory and Policy, 1984. ZWS 107 (1987) 1 4* OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.107.1.51 | Generated on 2023-04-04 12:09:56 52 Martin Klein first explanation the exchange rate regime is the cause of the disease, according to second one it is rather the cure. A priori, both explanations are equally as likely and since this is an empirical issue the decision between them must ultimately be settled empirically. Nevertheless, there are also theoretical issues involved and this is what we are dealing with in this paper. We will examine the theoretical background of the first one of the two alternative explanations. If the dramatic increase in real exchange rate fluctuations is actually due to the transition to flexible rates then our standard macroeconomic models should give us clearcut implications in this respect, and if these implications fail to come forth the case for the first explanation will be considerably weakened. This leads us back to our two central questions, namely, do our macroeconomic models actually offer an explanation for high real exchange rate fluctuations, and do they imply that these fluctuations are destabilizing? We will try to answer them by means of a standard macroeconomic model of a small open economy. The number of publications about the macroeconomic properties of different exchange rate regimes is now legion. Our reference section offers only a small selection. For instance, Fischer (1976), Flood (1979), Tumovsky (1983), and Eaton/Tumovsky (1984) have done studies which are related to the present one. Our analysis differs from theirs not so much in spirit but rather in that we concentrate on real exchange rate fluctuations. In their models this is ruled out since the exchange rate is tied to purchasing power parity. We establish the following results. First, flexible exchange rates do not per se imply high volatility of real exchange rates. Rather, this depends on the flexibility of domestic output prices. Only if the price level within each period is predetermined (sticky) the fixed exchange rate system leads to smaller real exchange rate fluctuations. Second, with flexible output prices the relative degree of real exchange rate fluctuations in both regimes depends crucially on the origin of the exogenous disturbances. If output demand and money demand shocks predominate the flexible rate regime leads to greater real exchange rate stability. Finally, even if - with sticky prices - the flexible rate regime leads to higher real exchange rate fluctuations this does not necessarily imply higher output fluctuations. Rather, depending on the origin of the exogenous disturbances real exchange rate fluctuations may be stabilizing. In the remainder of the paper we proceed as follows. In the following section we concentrate exclusively on the first of our two questions. We model an economy in which output prices are flexible and output supply is exogenously given. The second question is then examined in section three. There the situation is reversed, prices are inflexible and output is endogenous. Finally, the last section contains the conclusions. ZWS 107 (1987) 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.107.1.51 | Generated on 2023-04-04 12:09:56 Real Exchange Rate Fluctuations in a Small Open Economy 53 2. Flexible output prices a) The model The model of this section consists of the following equations: (1) yt = y + ut (2) yd t = y + ai (mt - pt) + a2qt + wt (3) yt = ydt (4) mt = md t = pt - bxit + b2yt + vt (5) it = r* + Etst +1 - st where yt (yd) supply (demand) of domestic output y normal output ™>t(™>dt) domestic money supply (demand) Pt domestic price level qt = st - pt real exchange rate st spot exchange rate it domestic nominal interest rate r* foreign nominal (equal to real) interest rate Etxt + i conditional expectation of xt +1, given all the relevant information available at t uu vt, wt white noise random disturbances (mutually independent) al> a2> i>2 > 0 Output supply fluctuates stochastically around an exogenously given long-run growth path which is designated by y ("normal output"). All trends and cycles have been removed so that y is a constant. Output demand depends positively on real balances and on the real exchange rate. The omission of the real interest rate as an argument in domestic output demand does not restrict the generality of the model. In fact, given our assumptions about the stochastic structure of the model the real interest rate and the real exchange rate are perfectly correlated so that one of the two is redundant. This can be demonstrated as follows. Suppose we had included the expected real interest rate in eq. (2) as follows: yt = y + ai (mt ~ Pt) + a2qt - a3 (it - Etpt + i - pt) + wt ZWS 107 (1987) 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.107.1.51 | Generated on 2023-04-04 12:09:56 54 Martin Klein Using the condition of uncovered interest parity and the definition of the real exchange rate, this can be manipulated to yield Vt = Y + CL\ (mt - pt) + a2qt - a3 (r* + Etpt+1 - qt) + wt In the following we will see that in both exchange rate regimes we have Et <?t +1 = 0 so that this equation reduces to yt = y + a1 (ra, - pt) + (a2 + a3) qt - <z3r* + wt. This is essentially equivalent to the output demand equation used in the paper. Eq. (4) describes equilibrium in the money market. Money supply is exogenous in the flexible exchange rate regime and endogenous with the fixed rate. Real money demand depends positively on domestic output and negatively on the domestic interest rate. We assume perfect international capital mobility so that uncovered interest parity holds (Eq. (5)). Finally, we assume that all the exogenous random disturbances are independent white noise processes with zero means and constant variances. This implies that their conditional expectations are zero as well. Formally we can write: Et -1 ut = Et _1 vt = Et -1 wt = 0 The model is homogeneous of degree zero in mu pt, sf, Etst + i. A permanent rise of the money supply by, say, 5 % thus results in a permanent rise of the price level and the spot exchange rate by the same percentage, leaving the real exchange rate unchanged. However, the same is not true for temporary changes in the money supply. Even if the price level and the spot exchange rate were to rise by the same amount, the expectation of the future spot rate would have to remain constant since the change in the money supply is confined to the current period, by definition of being temporary. From the condition of uncovered interest parity this would lower the domestic interest rate, raising the demand for real balances. This in turn would lower the price level and increase output demand through a real balance effect. Given that the supply of output is exogenous, restoration of equilibrium in the output market would require a drop of the real exchange rate. Thus we have shown that a temporary change of the money supply will not leave the real exchange rate unchanged. In other words, although prices are perfectly flexible, short-run changes in the money supply are nonneutral. In the following we will examine the implications of the model for real exchange rate fluctuations in different exchange rate regimes, namely with a flexible and with a fixed exchange rate. As it is well known a fixed exchange rate is not feasible in the long run if monetary growth rates in the domestic and foreign country differ. Thus, in order to make the comparison ZWS 107 (1987) 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.107.1.51 | Generated on 2023-04-04 12:09:56 Real Exchange Rate Fluctuations in a Small Open Economy 55 of both exchange rate regimes consistent in the model, we assume a situation where a fixed rate is feasible, i. e. we assume that there are not long-run discrepancies in the domestic and foreign monetary growth rates. The domestic country (being the small country) has adopted the growth rate of the foreign money supply.1 The two exchange rate regimes then only differ in their short-run money supply rules, that is, in both regimes the trend path of money supply is identical, but with the flexible rate the money supply stays exactly on this path whereas with the fixed rate there are temporary deviations. In addition to this, we assume that the announced monetary target is perfectly credible so that targets and conditional expectations with respect to mt coincide. This will formally be stated as follows. The preannounced path for the money supply in both regimes is (6) Et-1mt + j = 0, j = 0,1,2,... With the flexible rate the monetary target is maintained exactly. That is, we have (7) Et-lmt + j = mt + ] = 0 , j = 0,1,2,... With the fixed rate the monetary target can only be maintained on average across a large number of periods. Within each single period there will be deviations from target due to foreign exchange intervention. Thus, the realizations of the money stock will in general be different from their preannounced values. For the first period we can write: (8) Et-imt ^ mt The difference Et _ i mt - mt is deviation from the money supply target. It is contingent on the realizations of the exogenous disturbances b) The solution for fixed and flexible exchange rates Now we turn to the solution of the model. With the flexible rate the endogenous variables are the real exchange rate and the price level. Eqs. (1) through (5) can be arranged to yield the following two equations for output and asset market equilibrium, respectively.2 (9) a2qt ~ Q-iPt = ut-wt 1 Fischer (1983) has shown that abandoning the independence of the domestic money supply (with a fixed exchange rate) results in a welfare loss. We do not treat this aspect of the choice between fixed and flexible rates in this paper. 2 By appropriate choice of units we have set bir* - b2y = 0. ZWS 107 (1987) 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.107.1.51 | Generated on 2023-04-04 12:09:56 56 Martin Klein (10) bL(Etqt+ i — qt) + b1Etpt + 1- (1 + b1)pt = vt+ b2ut In order to find the rational expectations solution for these two equations we proceed as follows. In the first step we assume that the conditional expectations of the future real exchange rate and price level are zero: (11) Etqt+1 = Etpt+1 = 0 In the second step we solve the model under this assumption and then show that it is consistent. If we substitute eq. (11) in eqs. (9) and (10) we get: (12) a2qt ~ diPt = ut-wt (13) biqt + (1 + bi) pt= -vtb2ut The solution for the real exchange rate and the price level is: (14) qt = fiut ~f2vt ~fzwt (15) pt = ~ f*utf5vt+ f6wt The coefficients are: h = (1 + b, - b2)/B f2 = CLy/B fZ = (1 + bJ/B U = (bi + b2)/B h = <*2/b fe = b1/B B = aibi + a2 (1 + bi) f2 through /6 are positive, the sign of/i is indeterminate. Applying the conditional expectation operator Et _ i to both sides of eqs. (14) and (15) we get Et-1qt= fiEt-tUtf2Et-iVtf3Et-1wt = 0 Et - iPt = ~ fiEt-iUtf5Et.1vt + f3Et-1wt = 0 This follows from the assumption that all exogenous disturbances are white noise.3 Since these equations hold for any time period t our initial 3 In addition to this, the white noise-property of the real exchange rate depends on the assumption that there is no cyclical component in the supply of output. ZWS 107 (1987) 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.107.1.51 | Generated on 2023-04-04 12:09:56 Real Exchange Rate Fluctuations in a Small Open Economy 57 assumption in eq. (11) is consistent. Thus, eqs. (14) and (15) are indeed a rational expectations solution. For the solution with the fixed exchange rate we proceed in the same way. The endogenous variables are now the real exchange rate and the money supply. Since the exchange rate is held fixed we can set (16) st = 0 . This implies that the real exchange rate can only change if the price level changes: (17) qt=~Pt The model can now be arranged as follows: (18) (ai + a2) qt + aimt = ut - wt (19) qt + rnt = vt + b2ut The solution is: (20) qt = 9iutg2vt - g2wt (21) rnt = g4ut + g5vt + g%wt The coefficients are: gi = (1 - aib2)/a2 g2 = ai/a2 gz = 1/a2 94 = (*>2 (ai + a2) - 1 )/a2 05 = 1 +92 9 6 = 93 92, 9z> 9s, and g6 are positive, the sign of gi and depends on the parameters. In the following we assume that the inequality a1b2<l holds, so that we have gi > 0. Notice that again the solution implies Et-iqt = Et-iPt = 0. ZWS 107 (1987) 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.107.1.51 | Generated on 2023-04-04 12:09:56 58 Martin Klein c) Exchange rate regimes and real exchange rate fluctuations We compare the two exchange rate regimes by their implied variance of the real exchange rate. Using eqs. (14) and (20) we get the following variances. For the flexible rate: (22) var (qt) = f\ var (ut) + f\ var (vt) + fi var (wt), For the fixed rate: (23) var (qt) = g\ var (ut) + g\ var (vt) + g\ var (wt), Ceteris paribus the variance of the real exchange rate in the first regime will exceed the variance in the second if, for i = 1,2,3, the absolute value of the coefficient /* exceeds the coefficient giy and vice versa. Comparing the coefficients we get: Output supply disturbances: fi^gi Money demand disturbances: < £2 Output demand disturbances: fz<g$ Now we can state our first two results. First, neither exchange rate regime leads to unconditionally lower real exchange rate fluctuations. The reason is that thè relative size of the parameters relating to the output supply disturbances, /i and can not be determined a priori. On the other hand, for money demand and output demand disturbances the flexible exchange rate unequivocally leads to a lower variance of the real exchange rate. This yields the second result, namely, if the variance of the output supply disturbances is sufficiently small relative to the variances of the other disturbances, the model implies greater real exchange rate stability with a flexible exchange rate.4 These results can be illustrated as follows. Eqs. (1), (2), and (3) can be solved for the price level as follows: (24) pt = c1qt + mt + c2 (wt - ut), where Ci = a2/ai, c2 = l/a^ This relation is depicted as the OM-curve in Figs. 1 and 2. Eqs. (4) and (5) yield the AM-curve for asset market equilibrium: 4 We can also compare price level fluctuations in both exchange rate regimes. From the definition of the fixed rate, pt = - qu we get the following equation for the price level in the fixed rate regime, pt = - gxut + g2vt + gzwu which has to be compared to eq. (17). Only with respect to output demand shocks we get a clear result, namely 93 >/6The relative impact of the other disturbances depends on the specific parameter constellation. ZWS 107 (1987) 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.107.1.51 | Generated on 2023-04-04 12:09:56 Real Exchange Rate Fluctuations in a Small Open Economy 65 with respect to domestic output, or are they rather the symptom of the proper functioning of the real exchange rate as an automatic stabilizer? We establish the following results. First, the transition from fixed to flexible exchange rates does not per se imply greater volatility of real exchange rates. Rather, this depends on the flexibility of domestic output prices. Second, with flexible output prices the relative degree of real exchange rate fluctuations in both regimes depends crucially on the origin of the exogenous disturbances. Third, even if - with sticky prices - the flexible rate regime leads to higher real exchange rate fluctuations this does not necessarily imply higher output fluctuations. Rather, depending on the origin of the exogenous disturbances real exchange rate fluctuations may be stabilizing. Zusammenfassung Diese Arbeit befaßt sich mit den beiden folgenden Fragen. Erstens, liefert die gängige makroökonomische Theorie eine Erklärung für das hohe Niveau der realen Wechselkursfluktuationen, das wir seit der Einführung flexibler Wechselkurse beobachten? Zweitens, üben diese Fluktuationen einen destabilisierenden Einfluß auf die Konjunktur eines Landes aus, oder sind sie vielmehr Symptom der Tatsache, daß Wechselkurse die Rolle automatischer Stabilisatoren erfüllen? Es ergeben sich folgende Resultate. Erstens, der Übergang von fixen zu flexiblen nominalen Wechselkursen impliziert nicht per se höhere Fluktuationen der realen Wechselkurse. Vielmehr hängt dies vom Grad der Flexibilität der Outputpreise ab. Zweitens, wenn das Outputpreisniveau hinreichend flexibel ist, so hängt das relative Ausmaß der realen Wechselkursfluktuationen in beiden Wechselkursregimes kritisch davon ab, in welchem Markt die exogenen Störungen, die die Ökonomie destabilisieren, ihren Ursprung haben. Drittens, auch in den Fällen, in denen flexible Wechselkurse eindeutig zu höheren Fluktuationen der realen Wechselkurse führen, ist nicht notwendig eine Destabilisierung der Konjunktur die Folge. Vielmehr hängt dies wieder vom Ursprung der exogenen Störungen ab. References Argy, V. / Porter, M. (1972), The Forward Exchange Market and the Effects of Domestic and External Disturbances Under Alternative Exchange Rate Systems. IMF Staff Papers 19, 503 - 32. Boyer, R. (1978), Optimal Foreign Exchange Intervention. Journal of Political Economy 86, 1045 - 56. Dornbusch, R. (1976), Expectations and Exchange Rate Dynamics. Journal of Political Economy 84, 1161 - 76. Eaton, J. / Turnovsky, S. J. (1984), The Forward Exchange Market, Speculation, and Exchange Market Intervention. The Quarterly Journal of Economic 1, 45 - 69. Fischer, St. (1977), Stability and Exchange Rate Systems in a Monetarist Model of the Balance of Payments, in: Aliber, R. (ed.), The Political Economy of Monetary Reform. London, 59 - 73. — (1983), Seigniorage and Fixed Exchange Rates: An Optimal Inflation Analysis, in: P. A. Armella, R. Dornbusch and M. Obstfeld (eds.), Financial Policies and the World Capital Market: The Problem of Latin American Countries. Chicago, 59 - 70. ZWS 107 (1987) 1 5 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.107.1.51 | Generated on 2023-04-04 12:09:56 66 Martin Klein Flood, R. P. (1979), Capital Mobility and the Choice of Exchange Rate System. International Economic Review 20,405-416. Frenkel, J. A. / Aizenman, J. (1983), Aspects of the Optimal Management of Exchange Rates, in: E. Ciaassen, und P. Salin (eds.), Recent Issues in the Theory of Flexible Exchange Rates. Amsterdam, 201 - 25. Genberg, Hans (1981), Effects of Central Bank Intervention in the Foreign Exchange Market. IMF Staff Papers 28, 451 - 76. Henderson, Dale W. (1982), The Role of Intervention Policy in Open Economy Financial Policy: A Macroeconomic Perspective, International Finance Discussing Papers. Washington D.C. (Board of Governors of the Federal Reserve System). Turnovsky, S. J. (1983), Exchange Market Intervention Policies in a Small Open Economy, in: J. Bhandari and B. H. Putnam (eds.), Economic Interdependence and Flexible Exchange Rates. Cambridge, Mass., 286 - 311. ZWS 107 (1987) 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.107.1.51 | Generated on 2023-04-04 12:09:56