Symmetry versus Asymmetry in a Fixed Exchange Rate System

Lane, Timothy D.; Gros, Daniel Article Symmetry versus Asymmetry in a Fixed Exchange Rate System Kredit und Kapital Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Lane, Timothy D.; Gros, Daniel (1994) : Symmetry versus Asymmetry in a Fixed Exchange Rate System, Kredit und Kapital, ISSN 0023-4591, Duncker & Humblot, Berlin, Vol. 27, Iss. 1, pp. 43-66, https://doi.org/10.3790/ccm.27.1.43 This Version is available at: https://hdl.handle.net/10419/293270 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Introduction There are widely recognized benefits of maintaining stable exchange rates area among a group of countries with high mobility of goods, services, and factors of production (Mundell 1961). The agreement reached at the Maastricht summit in December 1991 to establish European Monetary Union (EMU), however, came only as the outcome of prolonged negotiation among the member countries, and the agreement left some countries the right to opt out of certain aspects of the arrangements. In interpreting the differences in countries' preferences of exchange rate regime that these negotiations imply, it is important to compare EMU with the relevant alternatives - not only with floating rates, the alternative generally considered in the literature on optimal currency areas, but also the Exchange Rate Mechanism (ERM) of the European Monetary System (EMS) that precedes it.2 The EMS, like EMU, is intended to create a "zone of monetary stability" in Europe. An important difference is that it implies an asymmetry among its members - with Germany controlling its money supply, while the other countries use their monetary policies to stabilize their exchange rates with Germany (e.g. Giavazzi and Giovannini, 1989). The focus in the literature has been mainly on whether this asymmetric system could help enable other central banks to stabilize inflation by borrowing credibility from the Bundesbank (e.g. Giavazzi and Pagano, 1986, Giavazzi and Giovannini, 1987, Melitz, 1988, Lane and Rojas- 1 International Monetary Fund and Centre for European Policy Studies, respectively. The views expressed are the those of the authors, and do not necessarily represent those of either institution. The authors thank Robert Flood, Martin Klein, Jeroen Kremers, Axel Weber, and seminar participants at the IMF and the Kostanz Seminar for helpful comments; any remaining errors are the authors' sole responsibility. 2 Surveys of the EMS can be found in Gros and Thygesen, 1988, or in Ungerer et al., 1986. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 44 Timothy D. Lane and Daniel Gros Suarez, 1992). The present paper has a different emphasis: to examine the implications of symmetric and asymmetric systems for different countries, in the terms that are typically emphasized in the literature on optimal currency areas - viz - the stability of real income.3 In addressing this issue, it is important to note that "it takes two to tango": even if, for instance, an asymmetric currency area is in the interest of the group of countries as a whole, its maintenance requires that both "center" and "peripheral" countries take actions consistent with this asymmetry. This is also true of a symmetric currency area. Consider, for example, a simplified setting, in which two countries (which, for ease of exposition, will be referred to as Germany and France) each have to choose whether to incorporate exchange rate feedback in their determination of the money supply. This is implicitly a very simple game theoretic setting, in which the monetary arrangement that emerges is a Nash equilibrium that emerges from a combination of choices made by the two countries. Table 1 Germany Exchange Rate Feedback No Feedback France Exchange Rate Feedback BCA GDA No Feedback GFA FF Thus, if both countries incorporate exchange rate feedback, the result is bilaterally maintained currency area (BCA), which in many respects is similar to EMU.4 If France stabilize the exchange rate but Germany does not, adhering instead to money supply targets, the result is a Greater 3 Other literature (e.g. Marston, 1985) has focused on whether a small country can stabilize its real income more effectively by joining a currency union. See also Melitz, 1985, Roubini, 1989, and various contributions in Bhandari, 1985. 4 In this paper, we are treating the BCA as a limiting case of regimes in which both central banks intervene to some extent, that is «* —• oo, rather than evaluated at the limit itself. At the limit - perhaps typified by European Monetary Union (EMU) - a bilateral arrangement would also require agreement on the target exchange rate and on the overall stance of monetary policy, either through direct agreement or through the formation of a European central bank; this would be incompatible with non-cooperative equilibrium. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 Symmetry versus Asymmetry in a Fixed Exchange Rate System 45 Deutschmark Area (GDA); a Greater Franc Area (GFA) is the mirror image. If neither country intervenes, a Free Float (FF) results. Strategic interaction among sovereign countries can be modeled most simply as a Nash equilibrium.5 In this example, asymmetry may emerge as a Nash equilibrium, even though it is neither country's favorite regime. For instance, the emergence of a GDA from the independent choices of sovereign nations requires that Germany prefer a GDA to BCA, but requires that France prefer a GDA to a FF. These are the only relevant alternatives, provided that France cannot compel Germany to incorporate exchange rate feedback into its monetary policy and Germany cannot prevent France from taking the exchange rate into account. It is not necessary, in order for the asymmetric arrangement to persist, for either partner to prefer GDA to either of the other two options that are not available to it: Germany need not prefer GDA to GFA or FF, and France need not prefer GDA to BCA and GFA. In order to see whether the interests of different members of the EMS might diverge on the desirability of moving to a symmetric system, it is necessary to analyze and compare how various shocks are transmitted to prices and output in each country under the three different regimes. In this paper, we shall do this, using a simple variant of the Mundell-Flem- ing model with rational expectations to make each country's preferences over policy regimes more concrete. The model assumes perfect capital mobility as now seems appropriate given the elimination of capital controls by all ERM members as of end 1992. The rest of the paper proceeds as follows. Section II contains a brief presentation of the model, a derivation of output and the exchange rate, and some discussion of how the effects of monetary policies interact within the model. In Section III, we use the model to derive the implications of alternative, symmetric or asymmetric, exchange rate arrangements for the variability of prices and incomes in each country. In Section IV, we compare the transmission of shocks under these alternative regimes, and use this comparison to specify under what circumstances an asymmetrical arrangement like the EMS would emerge from the voluntary choices of its sovereign members. In Section V, the possibility of interest rate feedback in a currency union is considered. Section VI concludes the paper. 5 Nash equilibrium is attractive in this context because it does not assume any strategic asymmetry but permits asymmetric behavior to emerge as an equilibrium. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 46 Timothy D. Lane and Daniel Gros II. The model The model is a modified two-country version of the standard ad hoc rational expectations model (e.g., Barro, 1976). The model is simplified by assuming stochastic purchasing-power parity. There are also random shocks to aggregate supply and to money demand in each country, as well as to worldwide demand. Rational expectations are assumed.6 For expositional convenience, we shall again refer to one country as "Germany" and the other "France". The equations are as follows: (1) 2h = 7(Pt - Et-xpt) + w\ (2) y*t = 7*(p*t - Et-ip*t) + w*t (3) pf = pj + st + uf (4) mt - pt = yt - 6it + vt (5) m\ - p*t = y*t - 6*i*t + v*t (6) it = i*t + Etst +1 - st (7) yt + y; = -Tp"1 {U + EtPt + i - Pt) + oiUpt + udt - p/ip Here yuyt* are the logs of real national income in Germany and France, respectively, expressed as deviations from their trend levels; Pt.Pt* are the logs of the two countries' price levels; st is the log of the nominal exchange rate, that is the price of francs in terms of deutsche marks; mt and mt* are the logs of the money supplies in the two countries; it and it* are the nominal interest rates in the two countries; 6, 6*, 7, 7*, p and V are parameters, a is a parameter reflecting France's weight in world expenditure. The supply shocks wts and wts*, money demand shocks vt and vt*, purchasing power parity (PPP) shock utp and world demand shock utd are all assumed to be independently distributed with zero mean and variances crs2, as*2, av2, av*2, crp2, and ad2, respectively.7 6 This model is very similar to the three-country framework presented in Lane 1990, and the two-country model in Lane 1989. ? Stockman (1988) has provided some empirical evidence on the relative magnitudes of various sources of disturbances in Europe. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 Symmetry versus Asymmetry in a Fixed Exchange Rate System 47 Equations (1) and (2) are expectational aggregate supply equations. Equations (3) and (4) are semilog money demand equations with unitary income elasticity. Equation (5) is a stochastic PPP relationship, while equation (6) requires uncovered interest parity. The absence of any shock to this relationship reflects the liberalization of capital movements Project 1992, which should remove any significant barriers to interest arbitrage. Equation (7) is a world demand equation, indicating that world demand depends on real interest rates; the reason that the PPP shock ut p appears in this equation is that it is associated with a temporary divergence between real interest rates in the two countries. We shall be assuming for simplicity (as in Barro (1976)) that the authorities wish to stabilize real income8 around its natural or full information level - thus also minimizing the variance of unanticipated price movements.9 We shall assume that the authorities can observe exchange rates, but cannot immediately observe the current levels of income and prices. The authorities may choose to deviate from their money supply targets in response to movements of the exchange rate, as these incorporate information about this period's shocks; the resulting monetary feedback rules can be represented as follows: (8) mt = mT t - K,(st - sj) (9) m* = mT t* + K* (st - sf ) Various simple rules can be represented as special cases, depending on the policy parameters in equation (8) and (9): with flexible exchange rates, K, = K* = 0, while fixed exchange rates imply that K and/or K* —> oo, depending on which central bank maintains the peg. Bilateral foreign exchange market intervention implies that K, K* ^ 0. Incorporating these feedback rules, income in Germany is: (10) yt - Ws t = (7/A) {tth W\ + 7TUws t* + TT13 up t + IR^VT + + TT16U* } where 8 The authorities' concern about the expected rate of inflation is reflected in the target money supply, mt T and mt T*, respectively. 9 The assumption that the full-information level of income is optimal rules out the time-consistency problem which is central to the "credibility" view of the EMS, e.g., Giavazzi and Pagano (1986), Giavazzi and Giovannini (1987). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 48 Timothy D. Lane and Daniel Gros A = - {(1 + 7) (1 4- 7*) (1 + 6){1 + 6*) - 77* 66* + (1 + 7K + (1 + 7*) k + (1 + 7 + 7*)(<$*K + Sk*) + W> - 1) • [(1 + 7)7*+ + 1* SS* + 7* (6*k + <$/C*)]} n 11 = (1 + 7*) (1 + Ip6 + 6*) + ip{6*K + 6K,*) + 1P66* + K* + (il> - 1)7*6* 7T12 = (1 + ip6*)K + Ip6( 1 + <5* + /c*) 7T13 = -[(<* + 7*)ip(66* + 6*K, + 6k*) + aip( 1 + 7*)<$ + (1 +7*)«] TT14 = (i + 7*) (1 + <n + + (</> -1) 7* ^15 = *> ~ ll>l*6 7T16 = + + 6 K* + (1 + 7*) <$] A similar expression may be derived for income in France, mutatis mutandis. As is clear from equation (10), income in each country is affected by shocks occurring in both countries, as well as by PPP and global demand shocks. The impact of the various shocks is influenced by the exchange market intervention policies pursued by both countries' authorities, as reflected by the parameters k and k* . We can also find a solution for the exchange rate: (11) St = (1/A) {7T3UWSt + 7T32WSt* + 7XZ2UPt + 7r34 Vt + 7T35 V* + 7T36 U* } where 7T31 = (1 + 7*) (1 4- %!)6) 4- Ip 1*6* + (1 - ^)6* 7T32 = "[(I + 7) (1 + + </>7<$ + (1 " 1>)S] 7T33 = aip{ 1 + 7)<$* + (1 - aip){l + 7*) <5 + ^7(1 + 7*) <5 + ^7* (1 4- 1)6* + aip{ 1 + 7) (1 + 7*) 7T34 = (1 4- ipl)6* + (1 4- 7*) 4- V7*<5* ^35 = - [(1 + 1p-y)6 + (1 + 7) + 7T36 = </>[(! + 7)^ - (1 + 7*) Thus, the exchange rate also depends on all the shocks that impinge on the two countries, and the effect on these shocks is conditioned by the OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 Symmetry versus Asymmetry in a Fixed Exchange Rate System 49 policies pursued in the two countries (as these appear in the determinant of the system, A). Supply and demand shocks in the two countries have parallel and opposite effects on the exchange rate. World demand shocks affect the exchange rate only to the extent that the two countries differ in their structure. The exchange rate is also affected by PPP shocks. This model provides a setting in which the two countries' choices among alternative policy rules, and the ways in which these choices interact, can be examined. We proceed with this analysis in the following section. III. Some Simple Policy Rules In this section, we shall consider some alternative simple rules for monetary policy, and examine these rules' implications for the transmission of shocks within and between the two economies. We find that, depending on the variances of different kinds of shocks, the regimes have different implication for the variance of national income in the two countries. We shall compare four simple alternative regimes, as discussed in the introduction: a free float (FF), a greater deutschmark area (GDA), a greater franc area (GFA), and a bilaterally maintained currency area (BCA).10 In our analysis, we shall proceed as follows. First, we shall discuss the four alternative regimes, concentrating on a special case in which the interest elasticity of money demand is 6 = 6* = 0, the interest elasticity of aggregate demand is ip = 1, the slope of the aggregate supply curve is the same in both countries 7 = 7*, and both countries have the same weight in aggregate demand, a = 1/2. We also consider a somewhat more general case: we present the equations for this more general case in the Appendix I, and use a table to summarize the effects of various types of shock in this case. This enables us to consider how the relative magnitude of different types of shocks affects each country's preference for each monetary regime. 1. Free Float (FF) We assume that under a FF each country adheres to a constant growth rate monetary rule, while maintaining a flexible exchange rate vis-à-vis !0 We deal with intermediate cases, with o < k < 00 and o < k, <00 in another paper, Gros and Lane (1992). 4 Kredit und Kapital 1/1994 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 50 Timothy D. Lane and Daniel Gros the rest of the world. In this case, since each central bank fixes its money supply irrespective of observations of the exchange rate, K = K* = 0. This implies that (in the simplified special case) German income is A similar expression can be derived for French income. As we see, if the interest elasticity of money demand in both countries is zero, flexible exchange rates and money supply rules insulate each country's income from shocks occurring in the other country, as well as from shocks to the PPP relationship. Income in each country is affected only by supply and demand shocks occurring in that country. The reason that flexible exchange rates insulate each country's income from external shocks in this case is that the exchange rate absorbs all the effect of the PPP shock, as well as the difference between French and German shocks: As we see, all the shocks except the worldwide demand shock affect the exchange rate, with the effects of shocks in Germany being the opposite of those of shocks in France. The insulation provided by exchange rate flexibility is not complete if the interest elasticity of money demand is not zero. The reason for this is that the exchange rate, in turn, is linked with interest rates via the interest arbitrage condition (6). This implies that any shock affecting the exchange rate must affect interest rates, and therefore, if money demand is interest sensitive, will also affect prices and incomes. For example, a positive transitory supply shock in France temporarily raises the value of the franc; since a temporary appreciation is associated with the expectation of a subsequent depreciation, this leads interest rates to increase in France and decrease in Germany, thereby affecting demand for money and the price level in opposite directions in the two countries. In the more general case, domestic, foreign and PPP shocks all influence both countries' price levels and national incomes, although domestic shocks still have a greater impact on domestic income than foreign shocks under this regime. The results for this more general case are presented in the Appendix I. (12) yt -wst = - [7/(l + 7)] (u>; + ut) (13) st = [1/(1 + 7)] {™st - w? + 7«f + vt - v\} OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 Symmetry versus Asymmetry in a Fixed Exchange Rate System 57 freedom, i.e. the overall monetary policy stance for the currency area, 772 + TTi* = mT + mT* is independent of the exchange rate and is not used for stabilization purposes; this is a simple result of rules (8) and (9) for the limiting case in which k* —> oo. This is not a necessary consequence of a common currency area. The possibility that some degree of stabilization policy could be preserved within a common currency area - as long as the national central banks continue to exist - can be explored by considering the possibility of interest rate feedback in montary policy. It is conceptually a straightforward matter to add interest rate feedback in the general case of monetary policy (as in Gros and Lane (1989), although the results become somewhat unwieldy when generalized to include interest rate as well as exchange rate feedback. The monetarypolicy feedback rule is modified to (17) mt = mT - K(st - st T) + A (it - it T) for Germany, and (18) mt* = mT* - k* (st - st T) + A* (it* - it T*) for France. In the limiting case in which exchange rates are fixed, a single interest rate must prevail throughout the currency area, and from the point of view of stabilizing community income it would be optimal to use the information it provides to determine the overall monetary stance; either country would prefer an appropriately chosen interest rate feedback policy to the monetarist monetary rule characterized in sections III and IV above. If the aggregate supply relationship is the same in both countries (7 = 7*), and if both are equal in size (a = 1/2), then the optimal feedback response for Germany is A = {27(<72 + <r2*) + (1 + 27)(a2 + a2*) + (7 + 2) (7 + 1/2) (7 + 1) a\] /{21{a] + <7S2*) + (7 + 2) (7 + 1/2 fai - 7^} - A* while France's optimal feedback parameter is A* = {27K2 + er,2,) + (1 + 27)(<t2 + a2*) + (7 + 2) (7 + 1/2) (7 + /{27(a2 + a2,) + (7 + 2) (7 + l/2)2a2 - 7*5} - A OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 58 Timothy D. Lane and Daniel Gros Inspection of equation (19) and (20) uncovers the following result: even if the variances of supply and demand shocks differ across the two countries, both countries agree on the optimal total degree of feedback to the interest rate, A + A*. This is essentially because, as the EMS converges to a common currency area, and if capital is mobile as has been assumed throughout the analysis, shocks in each country are transmitted to prices in both countries in an identical manner, even though, because of stochastic shocks to aggregate supply and PPP relationships, the countries' actual levels of output and prices may still fluctuate relative to one another. Perfect capital mobility and the convergence to unified exchange rates also imply that it does not matter in which country the money supply is altered in response to interest rate movements. Therefore, a combination of intervention policies that minimizes the variance of one country's income also minimizes that of the other country's income. All that would have to be coordinated between the two sets of authorities is how responsibility for the agreed overall degree of interest rate feedback is to be assigned to the central banks of the two countries; this is a trivial coordination problem, which has no distributional consequences. Regardless of whether interest rate feedback were chosen by the individual national central banks or by a European central bank, there would be no need to weigh different countries' interests in choosing the optimal degree of interest rate feedback to incorporate into monetary policy.15 Differences between the structure of the two economies would imply that the degree of interest rate feedback that is optimal from each country's standpoint may differ. If the interest rate were set by a European central bank, it would be natural to assume that the interest rate feedback parameter is chosen to minimize the variance of the weighted average of the national incomes of the two countries. This would, however, raise the possibility of conflict of interest between countries: both countries would prefer that overall monetary policy reacts somewhat to the interest rate, but one country may prefer a "monetarist" EMU to an activist one that takes a European point of view in determining the degree of interest rate feedback. VI. Conclusion In this paper, we have sought to present a model to explain how either symmetric or asymmetric monetary arrangements could emerge from the is A somewhat similar result has recently been presented by Begg (1990). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 Symmetry versus Asymmetry in a Fixed Exchange Rate System 59 choices of sovereign countries. In our discussion, we have stressed the fact that "it takes two to tango": to explain an asymmetrical relationship, one must explain why the leader leads, as well as explaining why the follower follows. In doing so, care must be taken to specify what alternatives can be chosen by each party. In this framework, we find that an asymmetrical system like the EMS is likely to arise from the voluntary choices of both anchor and peripheral countries if the variance of supply and portfolio shocks is relatively large in the peripheral countries. In this case, it is actually the peripheral countries that gain from an asymmetrical EMS, in the sense that they would prefer the EMS to either flexible exchange rates or a symmetrical currency area; if there are large shocks in the peripheral countries, the anchor country would prefer the EMS to a symmetric currency area, but would prefer flexible exchange rates to either of the other alternatives. Another important case in which an asymmetrical currency area may be a Nash equilibrium is the case in which world demand shocks are important, but the different countries differ in their economic structure; in the paper, the case considered is one in which there may be differences in the interest elasticity of demand for money in the two countries. It is shown that, given such a difference in structure, even if this common demand shock is the only one affecting output in the two countries, an asymmetric exchange rate arrangement may emerge from the voluntary choices of the two countries. Our analysis helps explain why the move towards a European single market has been accompanied by a reconciliation of divergent preferences toward exchange rate areas. As barriers to trade and factor movements are reduced or eliminated, departures from the law of one price might be expected to diminish. German unification, by increasing the variability of shocks in that country, also reduces the advantages - both to Germany and to other countries - of using Germany as an anchor country. Our model suggests that member countries may now have less to gain by maintaining asymmetric monetary arrangements in Europe. Appendix I In this Appendix, we consider the transmission of various shocks to the exchange rate and to income in the two countries, using a more general case than is developed in the main body of the paper. In particular, we relax the assumption, made in presenting equations (12) through (16), that 8 = 8* = 0. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 60 Timothy D. Lane and Daniel Gros In this more general case, under a free float, income in Germany is (Al) yt-w\ = (7/AFF) • {^wst + trFiV + + nlFvt + ^FF v\ + u* } where AFF = -[(1 + 7)2(1 + 6 + 6*) + (1 + 2 <y)66*} PF FF 7T 17 = — (1 + 7)(1 + 6 + 6*) + 66* (7 +86* +7)6 ttFF = <5(1 + FF = (1 + 7)(1 + FF c ^15 = -1& = -[(1 +7)« + W) Similar results hold, mutatis mutandis, for French income. Thus, in the general case, the FF regime does not insulate either country's income from shocks occurring in the other country, or from PPP or world demand shocks. A positive supply shock in either country leads both countries' incomes to rise by less than the amount of the shock. A positive money demand shock will lower income at home and raise it abroad. A PPP shock also raises income in one country and lowers it in the other, while a positive world demand shock raises both countries' incomes. All of these, as well as domestic supply and portfolio shocks, lead national income to deviate from its natural level. Domestic shocks do, however, have a greater impact on domestic income than foreign shocks under this regime. The reason that exchange rate flexibility does not insulate an economy against external shocks in this more general case, in contrast to the special case presented in the text, is the following: the exchange rate reflects various shocks, both internal and external. The reduced form for the exchange rate is: (A2) (l/AFF) • FF FF „ FF„ W\ + TT^ W\ + 7Tj3A Uf + 7rJ4A Vt + 7T „FF „ , FF + 36 where OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 Symmetry versus Asymmetry in a Fixed Exchange Rate System 61 = (1 + 7) (1 + 6) + 7S* nf2F = - (1 + 7) (1 + - 7* = 7 (1 + 7) (1 + 6 + 6*) + | (1 + 7) - 6) 7rf4F = l+7 + (l + 27)<5* = -[(1 + 7) + (1 + 27)= (1 + 7)(** " 6) As we see, all the shocks except the worldwide demand shock affect the exchange rate, with the effects of shocks in Germany being the opposite of those of shocks in France. The exchange rate, in turn, is linked with interest rates via the interest arbitrage condition (6). For example, a positive transitory supply shock in France temporarily raises the value of the franc; since a temporary appreciation is associated with the expectation of a subsequent depreciation, this leads interest rates to increase in France and decrease in Germany, thereby affecting demand for money, and therefore the price level and income in both countries. Next, let us consider a GDA, in which the Bundesbank adheres strictly to a money supply target, while the Banque de France stabilizes the franc-DM exchange rate. Here, German income is (A3) Vt ~wst = (7/AGDA) . + *iiDA«f + *SDA«f + + ir<?DA»; + *SDA«?} where AGDA = _[(1 + 7) + (1 + 27) 6] ir<*DA = l + * *gDA = « GDA ( , M c ^GDA _ , = ~ V7 + Ty 14 GDA _ n 7TGDA - -6 7T 1R = U 16 — 0 Thus, German income is insulated from French portfolio shocks, which are absorbed by the French demand for money; all other shocks have OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 62 Timothy D. Lane and Daniel Gros some effect on German income (although French supply shocks have a smaller impact than similar shocks in Germany). Supply shocks in either country lead to negative price surprises, leading income to fall short of its natural level (although, in general, by less than the amount of the shock). A positive shock to German money demand leads to a decrease in German income. A rise in world demand increases income in Germany. French supply shocks and PPP shocks are transmitted to German income via prices and interest rates. French income is determined as follows: (A4) y\ - wf = (7/AGDA) . {*<pAu,; + + *GDAttf + „GDA,, + ,GDAw; + ,GDAttf } where rGDA 1 + 6 GDA c 7T 99 = 0 GDA 23 (1 + 7) + _GDA _ -, 24 = 1 GDA 25 = 0 GDA 26 = -6 Thus, in a GDA, French income is affected by all of the shocks except French portfolio shocks, which are absorbed by the French money supply in the course of stabilizing the exchange rate. French income falls below its full information level in case of positive supply shocks or German money demand shocks, or in the case of negative world demand shocks; it is also affected by PPP shocks. The case of a GFA, in which France maintains a money supply target while Germany stabilizes the bilateral mark-franc exchange rate, is similar. Finally, let us consider the case of a bilaterally maintained currency area, or BCA. In this regime, both central banks adjust their money supplies in order to stabilize their bilateral exchange rate, so that —> oo. Accordingly, German income is OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 Symmetry versus Asymmetry in a Fixed Exchange Rate System 63 (A5) Vt-w't = (7/ABCA) . where ABCA = _[2(I + 7) + (i + 27) (6 + 6*)} while French income is determined symmetrically. Thus, under this regime, a supply or money demand shock in France affects German income to the same degree as an equal shock in Germany. It is also noteworthy that, under this regime, a positive French money demand shock lowers German income, while under the FF regime, it raises it. The results for the more general base, as presented in this Appendix are the basis of the ranking of the impact of various shocks under alternative regimes, presented in Table 1 in Section IV of the paper. The analysis in the main body of the paper is based on non-coopera- tive (Nash) equilibrium. Another possible way of establishing exchange rate arrangements would be through bargaining between the two countries: a different equilibrium might be achieved through bargaining if one country preferred a configuration of policies B, different from the Nash equilibrium A, and could get the other country to agree to configuration B by threatening to carry out actions leading to a configuration of policies C which the other country considered even worse than B (even though the other country preferred A to B). To investigate this possibility, let us consider the example in which supply shocks in France are large. In this case, the Nash equilibrium is a GDA, since Germany prefers this to BCA while France prefers it to a FF. Germany, however, Appendix II OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 64 Timothy D. Lane and Daniel Gros is dissatisfied, preferring a FF to a GDA: could Germany achieve a FF through bargaining? In this setup, Germany could try to persuade France to refrain from foreign exchange market intervention by threatening to intervene in the foreign exchange market itself, resulting in a BGA; this, however, would not be an effective threat, since although France prefers a GDA to a BCA, it also prefers a BCA to a FF, and thus would never accept a FF to avoid the threatened move to a BCA. As for France, the GDA is its most preferred alternative, so it has no incentive to try to achieve any alternative equilibrium through bargaining. Similar arguments can be made to rule out the possibility of achieving an alternative equilibrium through bargaining given other alternative assumptions about the shocks. The non-cooperative equilibrium is therefore the relevant one for analysis in this framework. Bibliography Barro, Robert S.: Rational Expectations and the Role of Monetary Policy, Journal of Monetary Economics, Vol. 2, No. 1 (Jan. 1976), pp. 1 - 32. - Begg, David: Alternative Exchange Rate Regimes: The Role of the Exchange Rate and the Implications for Wage-Price Adjustment, (mimeo, CEPR, April 1990). - Bhandari, Jagdeep S. (ed.): Exchange Rate Management Under Uncertainty (Cambridge MA: MIT Press, 1985). - Cohen, Daniel and Wyplosz, Charles: The European Monetary Union: An Agnostic Evaluation, CEPR Discussion Paper No. 306, April 1989. - Giavazzi, Francesco and Giovannini, Alberto: Models of the EMS: Is Europe a Greater Deutschmark Area?, in: Global Macroeconomics: Policy Conflict and Cooperation (New York: St. Martin's Press, 1987), pp. 237 - 72. - Giavazzi, Francesco and Giovannini, Alberto: Limiting Exchange Rate Flexibility: The European Monetary System. Cambridge, MA and London: MIT Press, 1989. - Giavazzi, Francesco and Giovannini, Alberto: The Advantage of Tying One's Hands: EMS Discipline and Central Bank Credibility, CEPR Discussion Paper No. 135, October 1986). - Gros, Daniel and Thygesen, Niels: The EMS: Achievements, Current Issues and Directions for the Future, CEPS Paper No. 35 (Centre for European Policy Studies, 1988). - Gros, Daniel and Lane, Timothy D.: Monetary Policy Interaction Within and Without an Exchange Rate Arrangement; Open Economies Review Vol. 3, No. 1 (1992) pp. 61 - 82. - Lane, Timothy D.: National Sovereignty and International Monetary Order, Journal of International Economics Vol. 29 (November 1990), pp. 351 - 368. - Lane, Timothy D.: Foreign Exchange Market Intervention in Interdependent Economies: A Case for Capricious Policy?, Journal of Macroeconomics Vol. 11, No. 4 (Fall 1989), pp. 513 - 531. - Lane, Timothy D. and Rojas-Suarez, Liliana: Credibility, Capital Controls, and the EMS, Journal of International Economics Vol. 32 (1992) pp. 321 - 337. - Marston, Richard C.: Exchange Rate Unions as an Alternative to Flexible Rates. 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(Chicago and London: University of Chicago Press, 1984), pp. 407 - 442. - Melitz, Jacques: The Welfare Case for the European Monetary System, Journal of Internatio- OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 Symmetry versus Asymmetry in a Fixed Exchange Rate System 65 nal Money and Finance, Vol. 4, No. 4 (December 1985), pp. 485 - 506. - Melitz, Jacques: Monetary Discipline, Germany and the European Monetary System, Kredit und Kapital Vol. 21, No. 4 (December 1988), pp. 481 - 512. - Mundell, Robert A.: A Theory of Optimum Currency Areas, American Economic Review 51 (1961), pp. 310 - 320. - Rogoff, Kenneth: Can International Monetary Policy Coordination be Counterproductive?, Journal of International Economics, Vol. 18, No. 3 - 4 (May 1985), pp. 199 - 217. - Rogoff, Kenneth: Reputational Constraints on Monetary Policy, in: Bubbles and Other Essays, edited by Brunner, Karl and Meitzer, Allan H., Carnegie-Rochester Conference Series on Public Policy 26 (Spring 1987), pp. 141 - 81. - Roubini, Nouriel: Leadership and Cooperation in the European Monetary System: A Simulation Approach, NBER Working Paper No. 3044, Cambridge MA, July 1989. - Stockman, Alan C.: Sectoral and National Aggregate Disturbances to Industrial Output in Seven European Countries, Journal of Monetary Economics, Vol. 21, No. 2 (March/May 1988), pp. 387 - 409. - Ungerer, Horst, Evans, Owen, Mayer, Thomas and Young, Philip: The European Monetary System: Recent Developments (Washington: International Monetary Fund), Occasional Paper No. 48 (December 1986). - Weber, Axel A.: Asymmetries and Adjustment Problems: Some Empirical Evidence, unpublished paper, University of Siegen, May 1990(a). Zusammenfassung Symmetry vs. Asymmetry in einem festen Wechselkurssystem Mit dem Übergang vom Europäischen Währungssystem (EWS) zur Europäischen Währungsunion (EWU) wird ein asymmetrisches System (das EWS) durch ein symmetrisches (die EWU) ersetzt. Im Rahmen eines analytischen Zweiländermodells untersucht der vorliegende Beitrag daher die Auswirkungen von Schocks auf die beteiligten Länder in symmetrischen und asymmetrischen Währungssystemen. Diese Analyse zeigt, daß der Wegfall der noch bestehenden Handelshemmnisse durch das Binnenmarktprogramm, sowie der durch die Wiedervereinigung ausgelöste Schock, den Übergang zu einem symmetrischen System (also der EWU) attraktiver macht. Summary Symmetry versus Asymmetry in a Fixed Exchange Rate System Moving from the European Monetary System (EMS) to a European Monetary Union (EMU) implies a move from an asymmetric to a symmetric currency system. This paper uses a simple two-country model to compare the impact of various shocks on each country's economy under alternative monetary arrangements, providing a basis for comparing symmetric and asymmetric systems and permitting an interpretation of the member countries' divergent interests and the resulting Nash equilibrium. The analysis implies that the removal of trade barriers through the European Single Market plan and the additional shocks associated with German unification may partly explain the recent move toward a symmetrical system. 5 Kredit und Kapital 1/1994 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42 66 Timothy D. Lane and Daniel Gros Résumé Symétrie vs asymétrie dans un système de taux de change fixes Avec le passage du Système Monétaire Eurpoéen (SME) à l'Union Monétaire Européenne (UME). Un système asymétrique (le SME) est remplacé par un système symétrique (l'UME). Dans le cadre d'un modele analytique de deux pays, cet article examine les conséquences de chocs sur les pays membres dans des systèmes monétaires symétriques et asymétriques. Cette analyse montre que la suppression des barrières commerciales encore existantes par le programme du marché intérieur, de même que le choc provoqué par la réunification rendent plus attirant le passage vers un système symétrique (donc l'UME). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.27.1.43 | Generated on 2023-01-16 13:04:42