In a currency area, when a country faces a positive shock inflation goes up, real interest rate decreases and competitiveness deteriorates. We show that the stability of equilibrium depends on the rationality of expectations and budget balance of the public sector.Publicad

Alonso, Alberto

Corchón, Luis C.

Guzmán, Vanesa

Economics Letters

English

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Instability and Trade in Currency Areas

Universidad Carlos III de Madrid e-Archivo

Instability and trade in currency areas☆Alberto Alonso a,1, Luis C. Corchón b,⁎, Vanesa Guzmán c,2a Department of Applied Economics III, Universidad Complutense de Madrid, Campus de Somosaguas, 28223 Madrid, Spainb Department of Economics, Universidad Carlos III de Madrid, 126 Madrid Road, Getafe, 28903 Madrid, Spainc Department of Economics, Universidad San Pablo CEU, 23 Julián Romea Road, 28003 Madrid, SpainReceived 15 October 2004; accepted 23 June 2006Available online 13 November 2006AbstractIn a currency area, when a country faces a positive shock inflation goes up, real interest rate decreases andcompetitiveness deteriorates. We show that the stability of equilibrium depends on the rationality of expectationsand budget balance of the public sector.© 2006 Elsevier B.V. All rights reserved.Keywords: Currency areas; Trade; Real interest rate; Common monetary policy; National fiscal policiesJEL classification: F15; E631. IntroductionIn a currency area, compensating the effect of an idiosyncratic shock on a member country byadjusting the exchange rate is no longer an option. The literature recognizes several factors that maytake the role of exchange rate: factor mobility (Mundell, 1961), price/wage flexibility (Friedman, 1953;Kawai, 1987), fiscal federalism (Kenen, 1969) and trade among member countries (McKinnon, 1963).☆ This paper was presented at the Economic Theory Seminar in Malaga. We acknowledge comments from the audience andOlivier Blanchard and financial support from CAYCIT, BEC 2002 02194. We are solely responsible for any error ormisunderstanding.⁎ Corresponding author. Tel.: +34 91 6249617; fax: +34 91 6249329.E mail addresses: alberto@ccee.ucm.es (A. Alonso), lcorchon@eco.uc3m.es (L.C. Corchón), vanguz@telefonica.net(V. Guzmán).1 Tel.: +34 91 3942580; fax: +34 91 3942582.2 Tel.: +34 922 150591.1The latter effect arises either from income or inflation rate differentials.3 In this note we concentrate onthe second effect. The conjecture is that such an effect stabilizes the economies in the currency areabecause if a country experiences, say, a positive shock, its inflation goes up, decreasing the compe-titiveness of this country and neutralizing the initial effect (Alesina et al., 2001, 18 19). We call thisthe competitive effect.However, when the rate of inflation goes up, the real interest rate decreases. This effect goes in theopposite direction to the competitive effect because it stimulates the economy of the country that hasexperienced the positive shock. We call this the real interest effect (this effect is the basis of the so-called“Walters critique” to the EMS).In this note we provide a simple model to study the working of both effects that bears some resemblanceto a model of Tobin (1975) for a closed economy. We assume two countries and that all relevant functionsare linear. We also assume that the only difference between countries is the size of potential output. Publicexpenditure is, either constant or tuned in order to offset inflation. The central bank only cares aboutmaintaining a constant average inflation. We show that if the central bank attains its target, the nominalinterest rate is constant (Lemma 1).We identify a range of parameters for which equilibrium is stable (Proposition 1). It turns out thatwithout an activist fiscal policy, these values are not very reasonable. In particular, expectations inequilibrium cannot be rational. This is due to the fact that the competitive effect does not work if agentsanticipate correctly inflation because in this case supply becomes totally inelastic. Moreover, a countryreceiving a positive shock has a rising inflation, but not necessarily a relatively high inflation.42. The modelTime is continuous. All variables are twice continuously differentiable with respect to time. A dot abovea variable represents its derivative with respect to time. Two dots indicate a second derivative.There are two countries denoted by j 1,2. Let Ynj be the potential income of country j. Let λ and 1 λbe the relative size of the potential income of countries 1 and 2, i.e.ð1 kÞYn1 kYn2 ð1ÞCountries are identical except for the scale factor λ. The income of j, Y j, is the sum of consumption,investment, public expenditure, G j, and net exports, S j. Investment is linear on the real interest rate, r j.Consumption is linear on income net of taxes. Taxes are linear on income. ThusY j Fj Bjrj þ CjS j þ DjG j ð2Þwhere Fj,Bj,Cj,DjN0. This is the usual IS curve. Taking units, D1 D2 1. Since countries are identicalexcept for the scale factor, C1 C2 C, and the relative impact of the interest rate on output equals the3 The early literature focussed on price levels, not on inflation rates.4 If inflation is rising in a country, eventually, it will catch up to the inflation in the other country. However, at this point,potential output is different from real output (except in exceptional cases). Therefore the equality between inflation rates will notpersist, producing a cycle. See our comments at the end of Section 2.2relative size of this country, (1 λ)B1 λB2. If i is the nominal interest rate and Πej the expected rate ofinflation of country j, i r j+Πej. Expectations are formed according toP je aPj bP• jð3Þwhere aN0. Thus, if inflation rate is constant and a 1 we have perfect foresight. From Eq. (3) we getPe• jaP• jbP•• j.The supply side is modelled by a Phillips curve with expectations, i.e.Pj b¯jðY j Y jnÞ þP je ð4Þwhere b¯jub=Yjn.Notice that β j (Ynj Y j) Πej Π j (a 1)Πj bΠy j. Therefore if a≈1, bb0 is absurd because itimplies that when actual output is larger than potential output, inflation rate is decreasing. Thus, from nowon we assume bN0.Net exports are assumed to beS•1QLnP2P1 awhere QN0, αN0 and P j is the price in j. Clearly, S1 S2. When prices are identical in both countries,S1 0. Setting K Qα we obtainS•1KðP2 P1Þ ð5ÞThe fiscal authority of each country implements a fiscal policy to stabilize the national economy suchthat the variation in public expenditure is linear on the rate of change of inflation.5G•jdj P• jð6Þwhere δj≥0 and (1 λ)δ1 λδ2.Finally, we assume that the central bank stabilizes weighted average inflation, Π, defined asΠ λΠ1 +(1 λ)Π2.Lemma. If average inflation is constant, the nominal interest rate is constant.Proof. Plugging Eqs. (2) and (4) in the definition of Π:P¯ kfb¯1½F1 B1ði P1eÞ þ CS1 þ G1 Yn1  þP1egþ ð1 kÞfb¯2½F2 B2ði P2eÞ CS1 þ G2 Yn2  þP2egDifferentiating with respect to time and rearranging:i• Pe•1½kðb¯1B1 þ 1Þ þPe•2½ð1 kÞðb¯2B2 þ 1Þ þ CS•1½kb¯1 ð1 kÞb¯2 þ kb¯1G•1þð1 kÞb¯2G•2kb¯1B1 þ ð1 kÞb¯2B25 For simplicity, we disregard boundary problems associated with the non-negativity of public expenditure.3Using Eqs. (3), (5) and (6)i• P•1ak½b¯1ðB1 d1Þ b¯2ðB2 d2Þ P••1bkðb¯1B1 b¯2B2Þ þ K½P¯ P1=1 kC½kb¯1 ð1 kÞb¯2kb¯1B1 þ ð1 kÞb¯2B2Thus, under our assumptions, iy 0. □From now on we assume that the central bank achieves its objective. Plugging Eqs. (2) and (3) in Eq.(4), for j 1P•1ðb¯1B1 þ 1Þb P1½ðb¯1B1 þ 1Þa 1 þ b¯1ðF1 B1iþ CS1 þ G1 Yn1 ÞDifferentiating with respect to time using Eqs. (5), (6) and the definition of Π,P••1ðb¯1B1 þ 1Þb P•1½ðb¯1B1 þ 1Þa b¯1d1 1 þ b¯1CKðP¯ P1Þ1 kð7ÞP••2 k1 kP••1 ð8ÞIf Eq. (7) is solved, Eq. (8) is solved too. Therefore let us solve Eq. (7).Proposition 1. If ab1+β 1δ1/β 1B1+1 and the competitive effect is large enough, the trajectory of therate of inflation in country 1 is stable.Proof. Eq. (7) can be written as P••1 þd1P•1þd2P1 d2P¯; whered1u ðb¯1B1 þ 1Þa 1 b¯1d1=ðb¯1B1 þ 1Þbandd2ub¯1CK=ðb¯1B1 þ 1Þbð1 kÞThis is a differential equation whose particular integral is found by settingP••1P•10. Eq. (7) impliesthat at this point, Π1 Π. To obtain the trajectory we solve the quadratic equation z2 +d1z+d2 0, i.e.z d1Fd21 4d22rThe system is stable if both roots are negative. We have three cases.1) If d12N4d2 the roots (z1, z2) are real numbers z1≠ z2. Stability requires d2b0. This condition neverholds because d2 is positive. Thus, the system is unstable and the inflation rate diverges from thestationary equilibrium.2) If d12 4d2, both roots take the same value, z1 z2 d1 /2. Stability requires d1N0; i:e:;ab1þ b¯1d1=b¯1B1 þ 1.3) If d12b4d2, both roots are imaginary. For this case to arise, the competitive effect (i.e. CK) has to belarge. In this circumstance the system describes a cyclic path. For equilibrium to be stable, i.e. fordiminishing amplitude in cycle, we need d1N0, i.e., ab1þ b¯1d1=b¯1B1 þ 1. □4order to attain convergence. Notice that the definition of average inflation implies that under instabilitytwo countries evolve in opposite directions: inflation increases in one country and decreases in the other.3. ConclusionIn this note we have studied the effect of trade among country members on the stability of a currencyarea. In our model a large competitive effect is necessary but not sufficient for convergence. In absence offiscal policy, stability also requires expectations not rational at the steady state (ab1). If this condition fails,fiscal policy becomes necessary for convergence. Perhaps our model can shed light on the performance ofsome economies of EMU in recent years, particularly Germany, France and Spain. Needless to say, therobustness of our conclusions must be checked in more general models.ReferencesAlesina, A., Blanchard, O., Galí, J., Giavazzi, F., Uhlig, H., 2001. Defining a macroeconomic framework for the Euro area.Monitoring the European Central Bank 3.Friedman, M., 1953. Essays in Positive Economics. University of Chicago Press, Chicago.Kawai,M., 1987. Optimum currency areas. TheNew Palgrave: ADictionary of Economics. Stockton Press, NuevaYork, pp. 740–742.Kenen, P.B., 1969. The theory of optimum currency areas: an eclectic view. In: Mundell, R.A., Swoboda, A.K. (Eds.), MonetaryProblems of the International Economy. University of Chicago Press, Chicago, pp. 41–60.McKinnon, R., 1963. Optimum currency areas. American Economic Review 53 (4), 717–725.Mundell, R.A., 1961. A theory of optimum currency areas. American Economic Review 51 (4), 657–665.Tobin, J., 1975. Keynesian models of recession and depression. American Economic Review 65 (2), 195–202.5

A theory of optimum currency areas.

Essays in Positive Economics.

Keynesian models of recession and depression.

Optimum currency areas.

Optimum currency areas. TheNew Palgrave: ADictionary of Economics.

The theory of optimum currency areas: an eclectic view.

http://e-archivo.uc3m.es/bitstream/handle/10016/3800/CORCHON_EL_2007_94_1_CL-ps.pdf?sequence=1

Instability and Trade in Currency Areas

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