We present a model of a currency area in which labor markets of country members are isolated but there is trade among these countries. When a country experiences a negative (resp. positive) shock, inflation goes down (up). This causes two effects. On the one hand the real interest rate of this country increases (decreases). On the other hand the goods produced in this country become more (less) competitive. We show that the stability of the system depends on several factors, including a large competitive effect, how inflation expectations are formed and fiscal policy. In general, stability requires a trade-off between the rationality of expectations and budget balance

Alonso, Alberto

Corchón, Luis C.

Guzmán, Vanesa

English

Name not available

Instability and trade in currency areas

Universidad Carlos III de Madrid e-Archivo

  Working Paper 04-30  Economics Series  10 June 2004   Departamento de Economía Universidad Carlos III de Madrid Calle Madrid, 126 28903 Getafe (Spain) Fax (34) 91 624 98 75    INSTABILITY AND TRADE IN CURRENCY AREAS1    Alberto Alonso 1, Luis C. Corchón 2  and Vanesa Guzmán 3    Abstract  We present a model of a currency area in which labor markets of country members are isolated but there is trade among these countries. When a country experiences a negative (resp. positive) shock, inflation goes down (up). This causes two effects. On the one hand the real interest rate of this country increases (decreases). On the other hand the goods produced in this country become more (less) competitive. We show that the stability of the system depends on several factors, including a large competitive effect, how inflation expectations are formed and fiscal policy. In general, stability requires a trade-off between the rationality of expectations and budget balance.      1.Departament of Economía Aplicada III. Universidad Complutense de Madrid 2.Departament of Economics . Universidad Carlos III de Madrid 3.Departament of Economic San Pablo- CEU      .                                                           1 This paper was presented in the Economic Theory Seminar in Malaga. We acknowledge comments from the audience and financial support from CAYCIT, BEC 2002-02194.      INSTABILITY AND TRADE IN CURRENCY AREAS1  Alberto Alonso Department of Economía Aplicada III Universidad Complutense  Luis C. Corchón Department of Economics Universidad Carlos III  Vanesa Guzmán Department of Economics Universidad San Pablo-CEU   ABSTRACT: We present a model of a currency area in which labor markets of country members are isolated but there is trade among these countries. When a country experiences a negative (resp. positive) shock, inflation goes down (up). This causes two effects. On the one hand the real interest rate of this country increases (decreases). On the other hand the goods produced in this country become more (less) competitive. We show that the stability of the system depends on several factors, including a large competitive effect, how inflation expectations are formed and fiscal policy. In general, stability requires a trade-off between the rationality of expectations and budget balance.                                                  1 This paper was presented in the Economic Theory Seminar in Malaga. We acknowledge comments from the audience and financial support from CAYCIT, BEC 2002-02194.   2 1: INTRODUCTION  In a currency area, compensating the effect of an idiosyncratic shock on a member country by adjusting its exchange rate is no longer an option. The literature recognizes several factors that may take the role of exchange rate: factor mobility (Mundell [1961]), price/wage flexibility (Friedman [1953], Kawai [1987]), fiscal federalism (Kennen [1969]) and trade among member countries (McKinnon [1963]). The latter effect arises either from income or inflation rate differentials2. In this note we concentrate on the second effect. The conjecture is that such effect stabilizes the economies in the currency area because if a country experiences, say, a positive shock, its inflation rate goes up, decreasing the competitiveness of this country and neutralizing the initial effect (Alesina et al. [2001] pp. 18-19). We call this the competitive effect. However, when the rate of inflation goes up, the real interest rate decreases. This effect goes in opposite direction to the competitive effect because it stimulates the economy of the country that has experienced a positive shock. We call this the real interest effect.  In this note we provide a simple model to study the working of both effects. We assume two countries and that all relevant functions are linear. An interpretation of the latter assumption is that we study the economy in a neighbourhood of the (unique) stationary equilibrium. We also assume that the only difference between countries is the size of potential output. Public expenditure is, either constant or tuned in order to offset inflation.  The central bank only cares about maintaining a constant average inflation. We show that if the central bank attains its target, the nominal interest rate is constant (Lemma 1).                                                   2 The early literature focussed on price levels, not on inflation rates.   3 We identify a range of parameters for which equilibrium is stable (Proposition 1). It turns out that without an activist fiscal policy, these values are not very reasonable. In particular, expectations in equilibrium cannot be rational. This is due to the fact that the competitive effect does not work if agents anticipate correctly inflation because in this case supply becomes totally inelastic. Moreover, it might be that a country is gaining share in international markets even if its inflation is rising if this inflation is lower than the inflation of its partners. In other words, a country receiving a positive shock has a rising inflation, but not necessarily a relatively high inflation.3  The rest of the paper goes as follows. Section 2 describes the model and analyzes the dynamic trajectories. Section 3 gathers our conclusions.    2: THE MODEL  Time is continuous. All variables are assumed to be twice continuously differentiable with respect to time. A dot above a variable represents its derivative with respect to time. Two dots indicate a second derivative. There are two countries denoted by j = 1, 2. Let Yjn be the potential income of country j. Let λ and 1- λ be the relative size of the potential income of countries 1 and 2, i.e.  (1 - λ ) Yn1 = λ Yn2 [1]  Countries are assumed to be identical except for the scale factor λ.                                                  3 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 not persist, producing a cycle. See our comments at the end of Section 2.   4 The income of j, denoted by Yj, is the sum of consumption, investment, public expenditure, denoted by Gj and net exports denoted by Sj. Investment is an affine function of the real interest rate, denoted by rj. Consumption is affine on income net of taxes. Taxes are affine on income. Thus,  Yj =  Fj – Bj rj + Cj Sj + Dj Gj,      Fj, Bj , Cj , Dj, > 0.  [2]  This is the usual IS curve. Taking units, D1 = D2 = 1. Since countries are identical except for the scale factor, C1 = C2 = C, say, and the relative impact of the interest rate on output equals the relative size of this country, i.e. (1 - λ) B1 = λ B2. If i is the nominal interest rate and πej is the expected rate of inflation of country j, rj ≡ i - πej. Expectations are formed according to  πej = a πj – b πj   a > 0. [3]  Thus, if the inflation rate is constant and a = 1 we have perfect foresight. From [3] we get πje = a πj – b πj.         The supply side is modelled by a Phillips curve with expectations, i.e.       (Yj – Yjn)                     πj = β  + πej . Letβj ≡ β/Yjn . Then,                                                                Yjn        πj = βj(Y1 – Yjn) + πej [4]  Notice thatβj(Yjn -Y1) =  πej - πj = (a – 1) πj – b  πj . Therefore if a ≈ 1, b < 0 is absurd because it implies that when real output is above potential output, the inflation rate is decreasing. Thus, from now on we assume b > 0.   5 Net exports are assumed to be   P2 S1 = Q Ln ()α , Q > 0, α > 0. P1  where Pj is the price in j. Clearly, S1 = - S2. When prices are identical in both countries, S1 = 0. Setting K ≡ Q α, we obtain   S1= K (π2 - π1) [5]  National fiscal authorities implement fiscal policies to stabilize their respective economies in such a way that the variation in public expenditure is linear on the rate of change of inflation.4   Gj = - δj πj,         δj ≥ 0,          (1 - λ) δ1 = λ δ2.                                       [6]     Finally, we assume that the central bank stabilizes weighted average inflation, denoted byπ and defined asπ ≡ λ π1 + (1 - λ) π2.     Lemma:  If average inflation is constant, the nominal interest rate is constant.  Proof: Plugging [2] and [4] in the definition ofπ,  π = λ{β1[F1 – B1(i - π1e) + CS1 + G1 – Yn1] + π1e} +    + (1 - λ){β2[F2 – B2(i - π2e)- CS1 + G2  – Yn2] + π2e}                                                     4 For simplicity, we disregard boundary problems associated with the non-negativity of public expenditure.   6 Differentiating with respect to time and rearranging.  πe1[λ(β1B1+1)]+πe2[(1-λ)(β2B2+1)]+CS1[λβ1-(1-λ)β2]λβ1G1+(1-λ)β2G2 i =    λβ1B1+ (1 - λ)β2B2  Using [3], [5] and [6]  π1aλ[β1(B1 - δ1) -β2(B2 - δ2)] - π1bλ(β1B1 -β2B2)+K[(π - π1)/(1-λ)]C[λβ1-(1-λ)β2] i = -  λβ1B1 + (1 - λ)β2B2  Thus, under our assumptions,  i = 0.   From now on we assume that the central bank achieves its objective. Plugging [2] and [3] in [4],   π1 (β1B1 + 1)b = π1 [(β1B1 + 1)a – 1] + β1 (F1 – B1i + CS1 + G1 – Yn1)   Differentiating wrt time and using [5], [6] and the definition ofπ we get   (π - π1) π1 (β1B1 + 1)b = π1 [(β1B1 + 1)a - β1δ1 – 1]+ β1CK  [7] (1 - λ)  λ π2 = -    π1 [8]   (1 - λ)  Clearly, if [7] is solved, [8] is solved too. Therefore let us solve [7].    7 Proposition 1: If a < (1 + β1δ1) /(β1B1 + 1) and the competitive effect is large enough, the trajectory of the rate of inflation of country 1 is stable. Proof: [7] can be written as  π1 + d1 π1 +d2 π1t = D where      (β1B1 + 1)a – 1 - β1δ1  d1  ≡ -       (β1B1 + 1) b   β1CK  d2  ≡     (β1B1 + 1) b (1 - λ)   This is a differential equation whose particular integral is found by setting π1 = π1 = 0. [7] implies that at this point, π1 = π. To obtain the trajectory we solve the quadratic equation z2 + d1z +d2 = 0, i.e.  - d1 ± √d12 – 4d2 z =   2  The system is stable if both roots are negative. We have three cases. 1) If d12 > 4d2, the roots, say , z1 and z2, are two real numbers, z1 ≠ z2. Stability requires -d1 ± √d12 – 4d2 < 0; i.e. d2 < 0; this condition never holds because d2 is positive. Thus, the system is unstable and the inflation rate diverges from the stationary equilibrium. 2) If d12 = 4d2, both roots take the same value, z1 = z2 = - d1/2. Stability requires d1 > 0 which is equivalent to a < (1 + β1δ1)/(β1B1 + 1). 3) If d12 < 4d2, both roots are imaginary. For this case to arise, the competitive effect (i.e. CK) has to be large. In this case the system describes a   8 cyclic path. For equilibrium to be stable, i.e. for diminishing amplitude in cycle, we need d1 > 0, or, equivalently, a < (1 + β1δ1)/(β1B1 + 1).  Notice that if we have only the competitive effect (δ1 = δ2 = B1 = B2 = 0), the sufficient condition for convergence is a < 1. If a = 1 the trajectory is an orbit. Under no fiscal policy (δ1 = δ2 = 0), the condition is a < 1 /(β1B1 + 1). In both cases stability requires some myopia in the perception of the changes in the rate of inflation (if expectations are quickly revised a ≈ 1). But if fiscal authorities choose δ1 such that d21 ≤ 4d2 and a < (1 + β1δ1)/(β1B1 + 1), inflation rates converge to the stationary equilibrium. This highlights the importance of fiscal policy in order to attain convergence.   3: CONCLUSION  In this note we have studied the stability of a currency area where shocks are compensated by trade among country members. In our model a large competitive effect is necessary but not sufficient for convergence. In absence of fiscal policy, stability also requires expectations not rational at the steady state (i.e. a < 1). If this condition fails, fiscal policy becomes necessary for convergence. Needless to say, the robustness of this conclusion must be checked in more general models (more than two countries, asymmetries, non-linear functions). Other suggestions for further research are: 1: In a currency area investment in a country may depend on the differential of real interest rates, i.e. on the differential of inflation rates.    9 2: It would be interesting to know more about fiscal rules. In particular about the existence of a rule that stabilizes the economy and in which deficits and surpluses produced during the stabilization process cancel out.  3: Perhaps our model can shed some light on the divergent behavior of some countries in the EMU in recent years, particularly Germany and Spain.   REFERENCES:  ALESINA, A.; BLANCHARD, O.; GALÍ, J; GIAVAZZI, F y UHLIG, H. (2001): Defining a Macroeconomic Framework for the Euro Area, Monitoring the European Central Bank 3, London: CEPR.  FRIEDMAN, M. (1953): Essays in Positive Economics, University of Chicago Press.  KAWAI, M. (1987): “Optimum Currency Areas”, The New Palgrave: A Dictionary of Economics, Nueva York: Stockton Press.  KENEN, P.B. (1969): “The Theory of Optimum Currency Areas: An Eclectic View” en MUNDELL, R.A. y SWOBODA, A.K. (eds.): Monetary Problems of the International Economy, Chicago: University of Chicago Press, 41-60.  McKINNON, R. (1963): “Optimum Currency Areas”, American Economic Review, 53 (4), 717-725.    10 MUNDELL, R.A. (1961): “A Theory of Optimum Currency Areas”, American Economic Review, 51 (4), 657-665.  

Defining a Macroeconomic Framework for the Euro Area, Monitoring the European Central Bank 3,

Essays in Positive Economics,

Optimum Currency Areas”,

Optimum Currency Areas”, The New Palgrave: A Dictionary of Economics,

The Theory of Optimum Currency Areas: An Eclectic View”

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. © 2006 Elsevier B.V. All rights reserved

Alberto Alonso A

Luis C. Corchón B

Vanesa Guzmán C

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Instability and trade in currency areas☆

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Instability and trade in currency areas

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