Monetary Policy in a Monetary Union Bernardino Adão Banco de Portugal
Nuno Alves Banco de Portugal
Jose B. Brito Banco de Portugal Isabel Correia∗ Banco de Portugal, Universidade Católica Portuguesa and CEPR January 17, 2006
Abstract The idea that a common monetary policy in a monetary union imposes costs when compared with independent policies at the country level is largely widespread in the literature. This result leads directly to a greater emphasis on national fiscal policies. We show in this paper that a common monetary policy has more power to asymmetrically affect countries than is usually stated in the literature. Aggregate shocks in a union where countries are identical but specialized in different goods have asymmetric effects across countries. JEL: E31; E41; E58; E62
∗ Correspondence Bernardino Adão -
[email protected], José B. Brito
[email protected], Isabel Correia -
[email protected]. The views expressed in this paper are the authors and not necessarily those of Banco de Portugal. We thank participants in seminars at the Banco de Portugal, the ECB, Society for Economic Dynamics Annual Meeting in Budapest and 20th Annual Congress of the European Economic Association in Amsterdam.
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1
Introduction
How does the transmission mechanism of monetary policy depend on the usual characterization that separates a monetary union from a country: the low mobility of factors and the absence of substantial government transfers across economies in the union? How different can the transmission mechanism of the common monetary policy be across identical countries? In this paper we analyze these positive policy questions in a commonly used economic environment. It is well known that the systematic use of discretionary monetary policy produces bad outcomes. However, if monetary policy reacts to shocks it may improve economic performance, namely in the presence of nominal rigidities. To understand how this reaction of policy to fundamentals should be designed it is important to understand the transmission of monetary policy as well as the transmission of the other fundamental shocks in the economy. It is the joined effects of shocks plus policy reactions that determine the final outcomes. This paper studies the transmission mechanism of aggregate shocks: technology shocks and monetary policy shocks, when the countries are identical and when they differ in dimension, government expenditures size and price rigidity. Our model economy is a standard dynamic monetary general equilibrium model. This model economy consists of two countries with a common monetary policy, a common market for goods and a common market for bonds. Labor markets are segmented across the two countries. We consider two environments: one where firms do not have any price setting restrictions and another where firms have restrictions of the Calvo type in the setting of prices. Fiscal policy is decentralized at the national level and there are no transfers across countries. The two countries share identical preferences and both have technologies which are linear in labor. The monetary instrument is the nominal interest rate, which is the most usual assumption in the recent literature. There are two main characteristics in the chosen environment that lead to results that differ from those prevalent in the literature. The first main difference of our model economy is that money has a role in transactions and therefore holding money has a cost. The monetary aggregate that helps in transactions is dominated in rate of return by the other assets. We follow Christiano, Eichenbaum and Evans (1997) and introduce the advantage of holding money, the liquid asset, at the firms. Firms are obliged to pay wages with money, that they borrow from financial intermediaries. The central bank injects reserves at these financial intermediaries. This structure implies that, even in a completely flexible world, monetary policy is not neutral since different interest rates affect the real economy like a tax. The second difference is that we do not have state contingent asset markets across countries, nor an equivalent scheme of transfers across countries that would result in the same equilibria. The hypothesis that there are contingent markets is standard in the literature (Duarte and Obstfeld, 2004, albeit in a different context is an exception). However, we show that results change substantially when this hypothesis is dropped. In general, a common monetary policy has not only aggregate effects but is also able to affect differently two 2
identical countries. Both deviations from the literature (e.g. Benigno (2001)) convey more importance to the monetary policy: the first one because monetary policy, through the nominal interest rate, has effects even in the flexible price economy; the second because monetary policy - by impacting on the terms of trade and on relative allocations - has additional power in relation to the usual convention where common monetary policy cannot affect identical countries differently. In this sense, this paper represents a step forward in trying to understand the transmission mechanism of policy and of fundamental shocks in an economy with flexible prices and in an economy with a Calvo price-setting hypothesis. The paper proceeds as follows. In Section 2 we consider a few very stylized closed real economy models to illustrate the role of incomplete markets in understanding the idiosyncratic effects of aggregate shocks. In Section 3 we describe the basic two-country monetary union. We use this section to understand the transmission mechanism of shocks, monetary shocks and technology shocks, in two alternative environments with identical countries: The first is an environment with flexible prices, where our main results can be exploited analytically, and some intuition on the connection with incomplete markets can be developed; the second is an environment with price-setting frictions. We also try to exploit the difference in the transmission of aggregate shocks when countries differ in some dimension like strength of frictions, size and government expenditures. Section 4 contains concluding remarks.
2
Aggregate shocks, idiosyncratic effects and complete markets
The idea that optimal currency areas should be associated with factor mobility and a system of government transfers comes from the fact that the existence of idiosyncratic shocks, or common shocks when there are different frictions among countries, would create a cost to a common monetary policy. This cost would be minimized with the mobility of factors and the possibility of risk sharing through government transfers. We want to illustrate in this section how the failure of the conditions for optimal currency areas leads in general to idiosyncratic effects of common shocks in the area. The main result on the monetary transmission mechanism of this paper is indeed an endorsement of this finding: since monetary policy is by definition common in the area, monetary shocks will have in general different effects in identical countries. In this section it is illustrated the connection between idiosyncratic effects of a common shock and the existence of complete markets. The absence of the conditions for optimal currency areas, low labor mobility and no government transfers, creates an incompleteness of markets even for common shocks. In particular, a shock that hits a country as distinctive effects in its regions if the country does not possess perfect labor mobility or complete markets. We consider a business cycle model with just one country. There are two
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regions or areas in this country, H and F , with populations n and 1 − n respectively. In the notation employed below the variables without an asterisk refer to region H and those with an asterisk refer to region F. In each region there is a representative household that is infinitely lived. The households of region H and F start with the same initial wealth W0 = W∗0 and have identical preferences. The representative consumer of region HPmaximizes the expected ∞ discounted value of all future flows of utility, U0 = E0 t=0 β t u (Ct , Nt ) , where E0 denotes the mathematical expectation conditional on information available in period t = 0, with β < 1, where Ct is composite consumption and Nt is hours of labor. The instantaneous utility function is a GHH function, i.e. u (Ct , Nt ) = ³ ´1−σ (Nt )1+χ 1 , σ > 0, χ > 0. There are two different goods, good h 1−σ Ct − 1+χ and good f . The two goods are not perfect substitutes, the elasticity of substitution between the two goods is ξ and the composite consumption of the h i ξ ξ−1 ξ−1 ξ−1 representative household in region H is, Ct = κh (Ch,t ) ξ + κf (Cf,t ) ξ , where κh and κf reflect the preferences of the household towards good h and f . Each good is produced according to a production function linear in the amount of labor used, Yi,t = At Ni,t , for i = h, f, where Yi,t is the quantity of good i and Ni,t is the quantity of labor used in the production of good i. The parameter At represents a technological shock common to both productions. Firms behave as perfect competitors. Government consumption is exogenous. The government consumes identical F amounts of the two goods, GH t = Gt . Taxes are lump sum and public debt is zero. This implies that in each period taxes are equal to government expenditures. Good f is the numeraire. The relative price of good h is pt .
2.1
Mobile labor
We first consider the case when labor is perfectly mobile across regions. Firms optimality conditions are given by wt = pt At , wt∗ = At , where wt and wt∗ are the wages paid in the production of good h and f , respectively.Since labor markets are not segmented wages must be equal, wt = wt∗ , and thus pt is equal to one. This implies that for any level of productivity, prices, wages and taxes are identical among households, and therefore they make identical decisions. Common technological shocks have no idiosyncratic effects. This is stated in the lemma below for comparison purposes. Lemma 1 If labor is mobile then common technological shocks have no idiosyncratic effects.
2.2
Immobile labor
Now we assume that labor is immobile across regions but goods are not. Good h is produced using labor of household H, Yh,t = At Nt , and good f is produced using labor of household F , Yf,t = At Nt∗ .
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There are state contingent assets inside each region. Let us denote by Qt,t+s+1 and Q∗t,t+s+1 the value at t of one unit of good f at t + s + 1 in a particular state, in region H and F , respectively. Household H is subject to the intertemporal set of budget constraints Et
∞ X s=0
Qt,t+s+1 [pt (Ch,t+s + Gt ) + Cf,t+s − wt+s Nt+s ] ≤ Wt , t ≥ 0,
and household F is subject to the intertemporal set of budget constraints Et
∞ X s=0
£ ¤ ∗ ∗ ∗ ∗ Q∗t,t+s+1 pt Ch,t+s + Cf,t+s + G∗t − wt+s Nt+s ≤ W∗t , t ≥ 0,
the Gt and G∗t represent taxes paid in region H and F (since the government budget is always balanced) and Wt and W∗t represent the assets in region H and F accumulated until t. 2.2.1
With contingent asset markets across regions
In general when labor markets are segmented the relative price is not unity and wages are not equalized across regions, wt∗ = At , wt = pt At . However, if there contingent asset markets across regions, wages will be equalized across regions. This result is stated in lemma 2 Lemma 2 If there are state contingent asset markets across regions then common technological shocks have no idiosyncratic effects. Proof: One easy way to verify this lemma is to use the guess and verify method. We guess that the equilibrium must be such that Nt = Nt∗ , and pt = 1 for all t in all future states. We show that when that happens there is an equilibrium where consumptions, labor amounts and wages are identical across states of nature. Since these type of economies have a unique equilibrium, the allocation and price proposed if an equilibrium it will be the only one. The period zero intertemporal budget constraints for household H and F are given by E0
∞ X t=0
Q0,t [pt Ch,t + Cf,t − pt At Nt + pt Gt ] ≤ W0 ,
and E0
∞ X t=0
£ ¤ ∗ ∗ Q∗0,t pt Ch,t + Cf,t − At Nt∗ + Gt ≤ W∗0 , where W0 = W∗0 .
If state contingent asset markets exist across regions we have Q0,t = Q∗0,t , for every t and all states. If Nt = Nt∗ , and pt = 1 for all t in all future states then the period zero intertemporal budget constraints for household H and F would 5
be identical. Since for the same level of labor and pt = 1, households value consumption sequences equally and face identical prices all households choose identical consumptions in all states. That is uCh (t) = uCh∗ (t) and uCf (t) = uCf∗ (t). Since by assumption Nt = Nt∗ always then wt =
−uN (t) −uN ∗ (t) = = wt∗ , for all t and all states uCf (t) uCf∗ (t)
As wages are equal in all states, the price pt is always one as we assumed. The price does not react to the common shock and is identical to the case where labor markets are not segmented. ¥ 2.2.2
Without state contingent asset markets across regions
Next, we consider the case where labor markets are segmented and there are only state contingent asset markets in each region so that in general, Qt,t+s+1 6= Q∗t,t+s+1 for all t and s. We show that the complete markets solution is obtained only when government expenditures are zero. If that is not the case then when there is a common shock the supply of good h will be different from the demand of good h for an invariant relative price of good h. The implication is that a common shock changes the relative price of good h and the relative incomes of the two regions. In other words, a common shock has idiosyncratic effects in the countries. In the following we determine the total demand for good h. The net incomes of the representative agents of each region are It = At pt Nt − pt Gt and It∗ = At Nt∗ − Gt The relative demand of the representative households of region H and F are µ µ ¶ξ ¶ξ ∗ Cf,t κf κf Cf,t = pt and ∗ = pt (1) Ch,t κh Ch,t κh and the private demand for good h, ∗ nCh,t + (1 − n)Ch,t = Ψ(pt ) [nIt + (1 − n)It∗ ] ∙ ³ ´ξ ¸ κf where Ψ(pt ) = 1/ pt + κh pt . The clearing condition in the market for
good h is given by
nNt At = Ψ(pt ) [nIt + (1 − n)It∗ ] + nGt
(2)
Below we show that when Gt and G∗t are zero the price level does not change in order for the market clearing condition (2) to hold when there is a common technology shock. However, as soon as Gt or G∗t become positive the price level must change in order for the market clearing condition (2) to hold when there is a common technology shock. 6
Lemma 3 When Gt = 0 a common technological shock does not change the equilibrium price pt . Proof : To prove this lemma we again use the guess and verify method. In the following the hat in the top of a variable means the proportional change in the variable. Assume that pt is invariant, pbt = 0, after a technological bt , i.e. wages change shock. Since wt∗ = At , and wt = pt At , then w bt∗ = w bt = A b b∗ = C b∗ from (1). b proportionally to labor productivity. Also Cf,t = Ch,t and C f,t h,t Since the labor supply of the household of region H must satisfy h i 1 ξ−1 ξ−1 ξ−1 −1 κh (Ch,t ) ξ κh (Ch,t ) ξ + κf (Cf,t ) ξ pt = , χ wt (Nt ) and the labor supply of the household of region F must satisfy 1 ∙ ³ ¸ ξ−1 ´ ξ−1 ³ ´ ξ−1 ³ ´− 1ξ ξ ξ ∗ ∗ ∗ κh Ch,t + κf Cf,t κh Ch,t pt = ∗ χ ∗ wt (Nt ) bt = 0 and w bt∗ = 0. Thus, N bt = N bt∗ = Aet . When Gt = 0, then w bt − χN bt∗ − χN χ the market clearing condition (2) implies ³ ´ ³ ´ bt bt∗ bt + N bt + N nIt A (1 − n)It∗ A bt = bt + A + . N nIt + (1 − n)It∗ nIt + (1 − n)It∗
Thus, the same pt is still an equilibrium price. Since in this economy the equilibrium is unique it is the only one.¥ Finally, we show that as soon as there are government expenditures and there are no state contingent asset markets across regions then the relative price in the economy will react to a common technology shock. Lemma 4 If Gt = G∗t 6= 0 then pt reacts to the common technology shock. Proof: Suppose to get a contradiction that pt does not react to the shock. If the price is unchanged, from (2) we obtain that the change in the demand for the good is n ³ ´ ³ ´o bt + (1 − n)At Nt∗ A bt∗ bt + N bt + N Ψ(pt ) nAt pt Nt A . (3) Ψ(pt ) [nIt + (1 − n)It∗ ] + npt Gt
Since this´ expression in general is different from the change in the supply ³ bt + N bt , we have obtained a contradiction ¥ A ∙ ³ ´ξ ¸ κ κ However, if κhf = 1, then Ψ(pt ) = 1/ pt + κhf pt = 1/2 when pt = 1. If
additionally Gt = G∗t and n = 0.5 then (3) can be rewritten as n ³ n ³ ´o ´o bt + N bt∗ bt + N bt∗ Ψ(pt ) [It∗ + It ] A + Ψ(pt ) [Gt + G∗t ] A Ψ(pt ) [It + It∗ ] + Gt 7
,
³ ´ bt + N bt . Thus, pt = 1 is an which is equal to the change in the supply A equilibrium in all states. We have proved that in general a common shock changes the relative price of the goods and the relative income of the regions if preferences are GHH, labor markets are segmented and there is no trade of state contingent assets across regions (or no government transfers across regions that replicate the complete asset market allocation). Thus, a common shock has asymmetric effects. This result is robust to changes in preferences, we used GHH preferences for simplicity.
3
Transmission mechanisms in a monetary union
To understand the pure effects of every shock, policy or other, we consider them exogenous, some stochastic process, and compute the impulse response of the main aggregates and country variables. It is well known that this procedure leads to problems of multiple equilibria. As in most of the literature we consider environments where equilibria are locally determined around a deterministic flexible price steady state to compute the unique equilibrium path in that neighborhood. Therefore, we use an interest rate rule that guarantees local determinacy1 . However, we try to get an equilibrium path for the interest rate that, in case of a monetary shock, is mainly driven by the non-systematic, or exogenous, part of the rule, and in the case of a non-monetary shock leads to an interest rate equilibrium path that is not significantly different from the steady state. In this way we can approximately generate the responses driven by pure (exogenous) policy or fundamental shocks. In the two-country monetary union model presented below, the simplicity of the representative household construct is preserved by assuming that households are heterogeneous between countries but not within each country2 . The model is a standard two-country monetary union, where households face a cash-inadvance, where there is perfect capital mobility, and where labor cannot move between countries. We also assume that fiscal authorities are country specific and that there are no transfers across countries. We chose preferences that are similar to the ones considered in the previous section and that simplifies greatly the computation of equilibrium. The simplicity comes from the fact that there is ’semi-aggregation’ across households in different countries. In this specification of preferences labor has no wealth effects. As the labor market is the one that is segmented across countries, this 1 Although most of the literature only considers monetary policy that guarantees local uniqueness, it is known that the monetary instruments can be used to generate uniqueness of the equilibrium. For instance, through the use of certain monetary feed-back rules or the simultaneous use of money supply and interest rates instruments, see Adão, Correia and Teles (2003) 2 That is, markets are complete inside each country so that we can represent the country economy by a representative household, but markets are not necessarily complete across countries so that aggregation may not be possible for the whole area.
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allows the separation of the labor income determination from the consumption determination. The labor income determination will be dependent on the equilibrium terms of trade, but these are common since goods are tradable. Given that the labor income and the goods’ supply in every country are a function of the relative price of goods, the aggregate equilibrium of the union can be solved using a representative agent of the union since markets for goods and bonds exist. It is in this sense that there is ’semi-aggregation’. Two environments are considered, flexible prices and Calvo price setting. It turns out that all the main insights can be obtained in the flexible prices environment. In the Calvo price setting environment we get a richer dynamic structure as the variables exhibit persistence. Even though the calibrations taken in the Calvo price setting environment are reasonable, the impulse response functions we obtain should not be taken as realistic in the sense that our model is too simple, does not include either non-tradables or capital.
3.1
The model with flexible prices
The following subsections describe in more detail the behavior of households, firms, the monetary authority and the financial intermediaries in the model of the monetary union. We assume initially that prices are perfectly flexible and later that they are staggered. When we go from the flexible price environment to the staggered price environment the only thing that changes is the way that firms choose prices. In the staggered price environment not all firms can choose the price contemporaneously, instead they choose prices in the Calvo manner. 3.1.1
Households
The monetary union is composed by two countries. The home country is country H and the foreign country is country F . The union is populated by a continuum of households, indexed by j ∈ [0, 1]. We assume that the segment [0, n] corresponds to country H’s households and segment (n, 1] to country F ’s households. The variables without an asterisk refer to country H and those with an asterisk refer to country F . In the beginning of each period, all the money is held by the households. During each period every household makes a sequence of choices in each market. In the beginning of the period, it enters the financial market and allocates the respective money holdings between deposits with the financial intermediaries remunerated at a gross interest rate Rt - and cash balances. After leaving the financial market, the households participate in the goods and labor markets. They demand goods produced in both countries and face a cash-in-advance constraint, stating that all nominal consumption must be purchased with the sum of cash-balances with the wage bill. At the end of the period, the households receive the dividends from the firms and the dividends plus the deposits (with interest) from the financial intermediaries.
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Since markets are complete in each country we assume, without loss of generality, that there are only two representative households, one for each region. Preferences are identical. The preferences of the representative home consumer are given by ∞ X Ut = E0 β t u (Ct , Nt ) (4) t=0
where β is a discount factor, Nt is labor and Ct is an index of consumption of commodity bundles in countries H and F , defined as: θ
Ct =
(Ch,t ) (Cf,t )
1−θ
(5)
θθ (1 − θ)1−θ
The index Ch,t corresponds to home consumption of the continuum of goods produced at home and Cf,t corresponds to home consumption of the continuum of goods produced in the foreign country.3 These bundles are generally defined as σ "µ ¶ 1 Z # σ−1 σ−1 1 σ n c(i) σ di (6) Ch,t = n 0 and Cf,t =
"µ
1 1−n
¶ σ1 Z
1
c(i)
σ−1 σ
σ # σ−1
di
n
(7)
where σ > 1 is the elasticity of substitution between the goods produced in each country. In these expressions, c(i) is the consumption of good i (any good i ∈ [0, n) is only produced at home and any good i ∈ [n, 1] is only produced at the foreign country). The preferences are given by, 1 u (Ct , Nt ) = 1−φ
Ã
1+χ
(Nt ) Ct − 1+χ
!1−φ
.
By standard procedures it can be shown that the overall price index in each country is given by θ 1−θ (8) P = (Ph ) (Pf ) 1 ´R h³ i 1−σ £¡ ¢ R n ¤ 1 1 1 with Ph = n1 0 p(i)1−σ di 1−σ and Pf = p(i)1−σ di , where 1−n n p(i) is the price of good i. Households maximize utility (4) subject to a cash in advance constraint and an asset evolution equation. The cash-in-advance constraint states that households can only consume the sum of their wage bill with their holdings of cash. It is given by Ph,t Ch,t + Pf,t Cf,t = (Wt Nt + Mt − Lt )
(9)
3 With respect to the previous section in this section we simplify preferences. We consider that they are Cobb-Douglas instead.
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where Wt is the nominal wage at home, Nt is aggregate labor of the home household, Mt is the beginning-of-period stock of money held by the home household and Lt is the deposit with the monetary union’s financial intermediaries held by the home household. The representative foreign household has a similar cash-in-advance constraint, ∗ ∗ Ph,t Ch,t + Pf,t Cf,t = (Wt∗ Nt∗ + Mt∗ − L∗t ) .
The asset evolution equation for the home household is given by Mt+1 = [Wt Nt + Mt − Lt − Ph,t Ch,t − Pf,t Cf,t ] + Rt Lt + Rt Xt + Dt − Tt(10) where Dt are the dividends from firms in the home country, which are distributed to the respective owners - country home households, Rt is the gross interest rate, the amount Rt Xt corresponds to the profits of the financial intermediaries distributed to the home household, which arise due to the monetary injection Xt , and Tt are the lump-sum taxes in the home country. The first-order conditions of the households can be summarized in the following equations: ¶−σ µ 1 pt (i) ct (i) = Ch,t , for i ∈ [0, n), and (11) n Ph,t ¶−σ µ 1 pt (i) ∗ ∗ ct (i) = Ch,t , for i ∈ [0, n) (12) n Ph,t ct (i) = c∗t (i) =
1 1−n 1 1−n
µ µ
pt (i) Pf,t pt (i) Pf,t
¶−σ ¶−σ
Cf,t , for i ∈ [n, 1], and
(13)
∗ Cf,t , for i ∈ [n, 1]
(14)
∗ Ph,t θ Cf,t θ Cf,t = = ∗ 1 − θ Ch,t Pf,t 1 − θ Ch,t
³
Pi,t
(16)
1−θ Ch,t
³
UCi,t Pi,t ∗ UCi,t
(Nt )χ Wt ´1−θ = Ph,t θ Cf,t
(15)
(Nt∗ )χ
∗ 1−θ Ch,t ∗ θ Cf,t
Wt∗ Pf,t
¶ UCi,t+1 , and Pi,t+1 µ ∗ ¶ UCi,t+1 = βRt Et , for i = h, f Pi,t+1 = βRt Et
µ
´θ =
11
(17)
(18) (19)
Conditions (11) - (14) are the demands for the individual goods. Conditions (15) state that the relative consumptions of the goods in each country is inversely proportional to the relative price of the goods. Conditions (16) and (17) state that the intratemporal marginal rate of substitution between leisure and consumption is equal to the real wage in each country. Conditions (18) and (19) are the intertemporal conditions, equating the marginal utility of a unit of money deposited with the financial intermediaries at time t to the marginal utility of the expected return from that deposit at time t + 1. 3.1.2
Firms
Firms in each country have access to the following labor-only production technology yt (i) = Ait nt (i) , with i ∈ [0, 1] (20) where yt (i) is the production of good i, nt (i) is labor employed by the firm producing good i, and Ait is a technology shock hitting the firm. We will be assuming that all home firms are hit by the same shock At and all the foreign firms are hit by a common shock A∗t . In each country, labor markets are competitive. However, there is no labor mobility between countries. Each country’s representative firm i thus hires domestic labor only. Firms in each economy hire labor at a certain wage rate, Wt at home and Wt∗ in the foreign country. In order to pay in advance the wage bill to the households, firms have to borrow that amount from the financial intermediaries at Rt . The problem is completely symmetric between all households and firms in each country so that in equilibrium nt (i) = Nt for i ∈ [0, n) and nt (i) = Nt∗ for i ∈ [n, 1]. Firms choose the price to maximize their profits. The first-order condition of this problem implies that firms at home set their prices according to Ph,t = pt (i) =
σ Rt Wt for i ∈ [0, n), σ − 1 At
(21)
σ over marginal costs. Note also that i.e., prices are a constant mark-up v ≡ σ−1 the interest rate affects the firms’ marginal costs due to the assumption that firms finance their wage bill by borrowing from the financial intermediaries. The price-setting behavior of the firms in the foreign country is completely symmetric. σ Rt Wt∗ Pf,t = pt (i) = for i ∈ [n, 1]. (22) σ − 1 A∗t
3.1.3
Monetary authority
The monetary authority does two things: sets Rt , and injects reserves to the system through a lump-sum transfer Xt to the financial intermediaries. The S cash-flow in the economy implies that MtS = Mt−1 + Xt , where MtS is the total money supply in period t.
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3.1.4
Financial intermediaries
The financial intermediaries gather the supply and demand for loans. The supply of loans corresponds to the sum of the monetary injection Xt with the deposits from all the households. The demand for loans comes from the firms and equals the wage bill. These financial intermediaries make profits due to the lump sum transfer plus the net interest rate return paid by firms which are distributed to households as dividends. The way these profits are distributed across agents in the two countries is related to the way gains from seigniorage are distributed across countries. We will suppose that these are identically distributed to maintain the symmetry between the two countries. This is however an additional channel, that we do not explore, through which monetary policy can have different effects in structurally identical countries. 3.1.5
Fiscal Authority
The fiscal authority of each country makes government expenditures, Gt and G∗t , and taxes lump sum, Tt and Tt∗ . The per capita government expenditures of the home country, Gt , include only expenditures on the goods produced in the home country and in the proportions consumed by the households. The government expenditures aggregator is: σ "µ ¶ 1 Z # σ−1 σ−1 1 σ n G= g(i) σ di , i ∈ [0, n) n 0
and 1 gt (i) = n
µ
pt (i) Ph,t
¶−σ
Gh,t , i ∈ [0, n)
where g(i) are the home government expenditures on good i (∈ [0, n)). An analogous assumption is made for the government expenditures of the foreign country. 3.1.6
Clearing conditions
In equilibrium, all markets clear. The loan market clearing condition is: nWt Nt + (1 − n)Wt∗ Nt∗ = nLt + (1 − n)L∗t + Xt .
(23)
The clearing of the goods markets implies that aggregate private and public consumption of the two types of goods in both countries equals the respective output: ∗ n (Ch,t + Gt ) + (1 − n)Ch,t = At nNt (24) ¡ ∗ ¢ (25) nCf,t + (1 − n) Cf,t + G∗t = A∗t (1 − n)Nt∗ .
where Nt , Nt∗ represents already the equilibrium amount of labor respectively in the home country and foreign country.
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3.1.7
Equilibrium
A competitive equilibrium is a sequence for each country of policy variables, quantities and prices such that the private agents (firms and households) solve their problems given the sequences of policy variables and prices, the budget constraints of the governments are satisfied and markets clear. From the conditions described above we obtain the equilibrium n equilibrium o ∗ Cf,t Cf,t P Wt∗ variables Ch,t , C ∗ , Nt , Nt∗ , PWh,tt , Pf,t as a function of the relative price Ph,t f,t h,t and of the interest rate Rt , ∗ Cf,t 1 − θ Ph,t Cf,t = ∗ = . Ch,t Ch,t θ Pf,t " µ ¶1−θ #1/χ At Ph,t Nt = vRt Pf,t
Nt∗
"
µ
A∗t = vRt
Pf,t Ph,t
(26)
(27)
¶θ #1/χ
(28)
Wt At = Ph,t vRt
(29)
A∗ Wt∗ = t . Pf,t vRt
(30)
Conditions (26) show that the relative consumption of good f depends negatively on the relative price of good f and positively on the relative preference for good f , given by the ratio 1−θ θ . By (27) and (28) we know that the labor supply depends negatively on the interest rate and positively on the technology level and the relative price of the good whose production that labor is used. Toµ ³ ´1−θ ¶1/χ 1+χ Ph,t 1 χ tal production in the home country is n (At ) and total vRt Pf,t µ ¶ ³ ´θ 1/χ 1+χ Pf,t 1 . Total production in the foreign country is (1 − n) (A∗t ) χ vRt Ph,t
production in the home country is a positive function of the relative price of the home good and total production of the foreign good is a negative function of the relative price of the home good. Conditions (29) (30) say that wages measured in terms of the national goods are a positive function of the technology and a negative function of the interest rate. Using these six conditions and the clearing of the goods markets conditions P we get the condition for the relative price Ph,t , f,t
n 1−n
(At )
1+χ χ
(A∗t )
µ
1+χ χ
1 vRt
µ
³
1 vRt
Ph,t Pf,t
³
´1−θ ¶1/χ
Pf,t Ph,t
´θ ¶1/χ
14
− Gt
−
G∗t
=
θ Pf,t . 1 − θ Ph,t
(31)
Notice that the numerator in the left hand side of (31) in equilibrium is the supply of the home good directed to private consumption and the denominator is the supply of the foreign good directed to private consumption. The right hand side is the ratio of the private demand for the home good over the private demand for the foreign good. This ratio is a negative function of the relative price of the home good and a positive function of the preference parameter for the home good. In equilibrium the relative supply of the home good must equal the relative demand of the home good. It is obvious from condition (31) that the equilibrium relative price is equal to one when Gt = G∗t , At = A∗t and n = θ. However, that is not the case if n 6= θ. Since θ is a preference parameter and n refers to the dimension of the home country in general these two parameters are not equal. It follows that the terms of trade between two identical countries, with the same level of government expenditures and the same technology level, will be different from unity. For example, if the two countries have the same dimension, i.e. n = 0.5, but the home good is associated with a larger preference parameter, i.e. θ > 0.5 then for a unitary relative price the left hand side of (31), i.e. the relative supply of the home good, will be one but the right hand side, i.e. the relative demand of the home good, will be larger than one. Thus, the equilibrium relative price for the home good should be larger than one. The quantity produced of good h will be larger than the quantity produced of good f since total production of good h is a positive function of its relative price and total production of good f is a negative function of the relative price of the good h. For this reason the ratio of the private demand for the home good over the private demand for the θ Pf,t foreign good 1−θ Ph,t will be larger than one. From conditions (27) and (28) we know the level of labor will be in general different among countries. The ratio of the labor incomes is Wt Nt = Wt∗ Nt∗
µ
At Ph,t A∗t Pf,t
¶ χ+1 χ
,
(32) P
A∗
6= Att . According which is in general different from one since in general Ph,t f,t to (26) the relative consumptions will be identical among countries but since in general labor incomes are different among countries, consumptions will be different among countries too. In the following we show how the remaining equilibrium variables are pinned down. From the cash-in-advance constraint for each household we get the monetary union cash in advance constraint ¡ ¢ ¡ ¢ ∗ ∗ S Ph,t nCh,t + (1 − n) Ch,t + Xt + Pf,t nCf,t + (1 − n) Cf,t = Mt−1 S where Mt−1 = nMt + (1 − n) Mt∗ . This constraint can be rewritten as
n (At Nt − Gt ) +
M S + Xt Pf,t (1 − n) (A∗t Nt∗ − G∗t ) = t−1 . Ph,t Ph,t
15
(33)
S Since the initial value, M−1 , is historical and X0 is by assumption set by the Pf,0 and Ph,0 we get Pf,0 . monetary authority, from (33) we get Ph,0 . Given Ph,0 Additionally we assume that the monetary authority sets the interest rate in all states and the money supply in almost all states so that the equilibrium will be unique. As we show below it is necessary that for each state at date t the monetary authority chooses the money supply at date t + 1 in all the following states but one. This guarantees using, equation (33), the determination of Ph,t+1 in all but one of the states that follow a particular state at date t, for t ≥ 0. The remaining price that remains undetermined will be determined by equation (36) that we discuss in the next paragraph. The nominal unicity of equilibrium that we obtain in this way, using as exogenous instruments of monetary policy the path of interest rates and the money supplies, is equivalent in the numerical simulations performed later, to the use of an endogenous interest rate rule that guarantees local determinacy, see Adão, Correia and Teles (2003a). Condition (18) implies µ ¶³ ³ ´1−θ ´− 1−θ φ Cf,t Cf,t (Nt )1+χ Ch,t Ch,t − 1+χ Ch,t
= Et
µ
Ph,t βRt Ph,t+1
¶− φ1 µ ³ ´1−θ Cf,t+1 − Ch,t+1 Ch,t+1
(Nt+1 )1+χ 1+χ
¶³
Cf,t+1 Ch,t+1
´− 1−θ φ (34) .
There is a similar equation for the foreign country, ¶³ µ ³ ´1−θ ´− 1−θ φ Cf,t Cf,t (Nt∗ )1+χ ∗ − 1+χ Ch,t Ch,t Ch,t
µ ¶− φ1 µ ¶³ ³ ´1−θ ´− 1−θ ∗ Ph,t φ (Nt+1 )1+χ Cf,t+1 Cf,t+1 ∗ = Et βRt − (35) . Ch,t+1 Ch,t+1 1+χ Ch,t+1 Ph,t+1
By summing both equations and using the resource constraints we get ¶³ µ ³ ´1−θ ´− 1−θ φ Cf,t Cf,t n(Nt )1+χ +(1−n)(Nt∗ )1+χ − n (At Nt − Gt ) Ch,t 1+χ Ch,t ³ ´− φ1 ³ ´− 1−θ φ Ph,t Cf,t+1 = Et βRt Ph,t+1 · Ch,t+1 µ ³ ´1−θ Cf,t+1 · n (At+1 Nt+1 − Gt+1 ) Ch,t+1 −
1+χ
∗ n(Nt+1 )1+χ +(1−n)(Nt+1 ) 1+χ
t = 0, 1, ...
¶
,
(36)
P
h,t With the exception of Ph,t+1 , all variables in (36) are determined as a function of Rt . Given the values already obtained for Ph,0 , and for some n of the Ph,to(t ≥ 1),
equation (36) gives the remaining Ph,t (t ≥ 1). And given ∞ {Pf,t }t=0
Pf,t Ph,t , Ph,t
∞
t=0
we
can get . ∞ From the intertemporal condition (34) we obtain {Ch,t }t=1 as a function of n o∞ Pf,t Ch,0 . Given Ph,t , we get {Cf,t }∞ t=0 as a function of Ch,0 , as well. The t=0
16
intertemporal budget constraint of the representative consumer in the home country is E0
∞ X t=0
where Qt+1 =
Qt+1 (Ph,t Ch,t + Pf,t Cf,t + St + Tt − Ph,t Yt ) = WA 0
(37)
β t+1 UCh,t+1 Ph,0 UCh,0 Ph,t+1 ,
is the value at 0 of a monetary unit at some state ´ ³ ¡ ¢ t − 1 (Rt − 1) where γMtS (Rt − 1) is the in t + 1, St = Mt − γMtS QQt+1 seigniorage attributed to the home country, γ represents the share of the total seigniorage attributed to the home country, and W0 is the initial nominal wealth P of the representative household of the home country. Given E0 ∞ Q t=0 t+1 St , the value at 0 of the expected discounted sum of the flows of future seigniorage, ∞ ∞ once we rewrite {Ch,t }t=0 and {Cf,t }t=0 as functions P of Ch,0 , condition (37) determines then value of o Ch,0 as a function of E0 ∞ t=0 Qt+1 St . The foreign ∞
∗ ∗ consumptions Ch,t , Cf,t can be obtained in a similar manner or instead t=0 by using the resource constraints.
3.1.8
How do Terms of Trade Respond to Shocks?
In the environment described identical countries have different outcomes after a common shock as the shock leads to a change in the relative incomes of the countries and to different labor decisions. In fact equations (27), (28) and (32) say that labor decisions and relative incomes change with an aggregate shock if and only if the terms of trade change with the shock. Here, we investigate how the terms of trade respond to shocks. We assume that in the steady state At = A∗t = A. Using equilibrium conditions this implies ¡ A 1−θ ¢1/χ ¡ A −θ ¢1/χ P ∗ that Nss = vR p , and , Nss = vR p , where p ≡ Ph,t and f,t θ 1 ∗ ∗ (ANss − Gss ) = 1−θ p (ANss − Gss ) . The loglinearization of (31) around the steady state gives i³ ´ h ∗ 1 θ θ n 1−θ n Pbh,t − Pbf,t ANss 1−n χ + 1−n (ANss − Gss ) + ANss p 1−θ χ ³ ´³ ´ (1+χ) b 1 b n θ = Gss 1−n (38) − G∗ss p1 1−θ − R A t t χ χ n 1−n
The first expression inside of the parentesis in the right hand side has the n θ ss sign of the expression G − p1 1−θ . In this expression the first term is G∗ ss 1−n the relative demand for good h by the public sector and the second term the relative demand for good h by the private sector. The sign of this expression depends on the values of the parameters. For instance, if the two countries are identical Gss = G∗ss , and n = 0.5, but the home good is associated with a larger preference parameter, θ > 0.5 then we know from the reasoning of the previous θ subsection that p1 1−θ is larger than one. The effects of idiosyncratic shocks over the terms of trade are easy to determine. The relative price of the home country
17
good increases with an aggregate technological shock or with an expansionary monetary shock (a decline in the nominal interest rate). From equation (31) we know that without government consumption expenditures the equilibrium price level will be in general different from one but constant across common shocks (technological or monetary shocks). The introduction of government consumption, that uses exclusively the national good, is enough to alter this neutrality of the terms of trade to common shocks4 . If there was a state contingent asset across the two economies the relative labor supply could not change from the steady state level, which implies, using equations (27) and (28), that the terms of trade would not change in reaction to a common shock. Since these state contingent markets could be replicated by government transfers, it is now clear the importance of assuming that not only labor markets are segmented but also the inexistence of government transfers across countries. The introduction of government consumption with a national bias is a simple way of illustrating the point that we want to stress in this paper: that in general a common shock will alter the terms of trade. In our case that happens because the shock changes the relative importance of these government expenditures in the national economies. It is immediate to conjecture that the introduction of non-tradable goods, either for private consumption or for public consumption is an additional and stronger channel through which the same type of results would show up. Again the hypothesis used in this work would be important for the results. For example Duarte and Obstfeld (2004) discuss how non-traded goods and incomplete markets can alter the results on exchange rate regimes. To understand more seriously the importance of these channels, in particular their quantitative importance, it will be very important to introduce these non-traded goods, since they represent a very high share of consumption and production. Moreover, the type of preferences that we use, for its analytical simplicity, should also be tested. When labor has no wealth effects, consumption and external assets are non stationary variables while the others, labor, output, wages and relative price are stationary. This means that the effects of temporary shocks on the stationary variables like the terms of trade are temporary but they will have permanent effects on consumption5 . On the other hand when labor has wealth effects, temporary shocks have transitory effects on all variables. Thus, the type of preferences together with the characteristics of the shocks are very important to understand how the described effects are spread over time. 4 Unless
national government expenditures are defined as a constant share of national output whatever the state of the economy. 5 For example a permanent change on aggregate technology, which would justify the growth or trend trajectory of these countries, would lead to a sustained increase of the relative price. The same would result from a monetary policy that, in a sequence of periods, declines the nominal interest rate. When the economies have non-traded goods, common shocks will imply a sustained change in the relative price that could explain inflation differentials.
18
3.1.9
How do aggregate shocks affect individual economies?
Once understood that common shocks can affect the terms of trade, it is immediate to see that a common shock can affect differently the national economies. We just discussed that those different effects would be temporary for temporary shocks for those aggregates which are stationary like labor and output. But consumption, either aggregate or of every good, will be affected permanently. These permanent effects on consumption are ’compensated’ by permanent effects on the position of every economy in external assets holdings. The country that produces the good whose price was temporarily higher would have a consumption higher forever and a permanent balance of trade deficit that is financed by the assets accumulated during the periods when, given the higher terms of trade, the economy had a trade balance surplus with the rest of the union. The more pronounced the cumulative effect on the terms of trade, the higher will be the permanent effect on the consumption and on the net asset position of every national economy.6 In the model there are two ways through which monetary policy affects the economy. The interest rate is a wedge between the marginal rate of substitution and the marginal rate of transformation. A reduction in the interest rate decreases that wedge and increases production of both goods. The other way the monetary policy affects the economy is through its effect on the terms of trade. As we have seen through equation (31) there is a one to one relationship between the interest rate and the terms of trade. The change in the terms of trade will have a negative effect over the production in one country and a positive effect over the production of the other. When the common shock that we want to focus is a monetary shock, another cause of asymmetry that can amplify or dwarf the previous effects, is the distribution of the inflation tax. We constructed the model supposing that this distribution is equitable so that the other channels of asymmetry could be highlighted. We know however that for example in the European Monetary Union the distribution is not equitatitive nor easily related with any economic indicator. Then, again for quantitative proposes, this distinction should be incorporated into the exercise. The discussion here as well as the earlier was done in an environment where firms could choose prices contemporaneously. When there is some type of nominal rigidity, the power of monetary policy is enhanced and the type of arguments developed above can be extended. In this framework the effect on the equilibrium terms of trade continues to be a channel of transmission.
3.2
The model with Calvo Prices
In this subsection we extend the conclusions of the previous subsection to the case with sticky price frictions. To take into account the possibility of heteroge6 This is an effect similar to the one described in Alves (2003), where the distribution of liquidity across countries in the union is asymmetric. In his framework a temporary monetary shock has asymmetric permanent effects due to different financial frictions among countries.
19
neous price behavior by firms, we follow Calvo (1983) and assume that in each period only a fraction (1 − ξ p ) of firms is able to change prices optimally. We also assume that firms who do not re-optimize simply update their prices with lagged inflation. The problem of each firm is to choose the price that maximizes expected profits. The problem of a firm in the home country who is able to change the price at time t is the following: " P (j)π π ...π # ∞ t t t+1 t+i−1 X yt,t+i (j) i Pt+i M ax Et (ξ p β) Qt,t+i (39) t+i Rt+i −W Pt+i At+i yt,t+i (j) i=0 where Qt,t+i is a discount factor between periods t and t + i which is related to the marginal utility of consumption of the home households and π t is the inflation in period t. Note that yt,t+i (j) is the demand for firm j’s output (j ∈ [0, n)) at time t + i conditional on the choice of price at time t, i.e., Pt (j). Log-linearizing the first order condition of (39) with respect to Pt (j) around a zero inflation steady state, subject to demand, and aggregating the log-linearized equations for both optimizing and non-optimizing firms yields the following equation for aggregate inflation: ³ ´ bt + N bt − A bt = 0 w bt − pbh,t + R (40) ct − Pbt and pbh,t = Pbh,t − Pbt . In this framework, inflation depends where w bt = W on lagged inflation and on current and future marginal costs. The case with flexible prices can be recovered by imposing ξ p = 0 in (40). The equation for the inflation of goods produced in the foreign country is completely analogous to (40). We will now evaluate the mechanics of the model with Calvo prices after monetary, technological and government expenditure shocks, in turn. Our aim here is to illustrate the results presented in the previous section and extend them to an environment with sticky-price frictions. π bt −
3.2.1
β bt+1 1+β Et π
−
1 bt−1 1+β π
−
(1−ξp )(1−ξp β ) ξp (1+β)
Calibration
The calibration of the preferences and technology follows the literature closely, so we will not describe it in detail. In the baseline calibration, we assume that firms change prices on average every 3 quarters. The firms’ steady state markup is calibrated to be 1.2 and the inverse of the elasticity of labor supply to be 0.6. The processes for the shocks are consistent with several contributions in the literature (see, for example, Altig et al., 2004). Table (1) presents the calibration of all parameters.
20
Preferences, technology and price-setting frictions
β = 0.993 φ = 1.5
χ = 0.6 θ = 0.5
μ = 1.2 ξ p = ξ ∗p = 0.67
Size of the shocks Persistence of the shocks
εS = 0.012 ρs = 0.8
εG = 0.01 ρG = 0.5
εR = −0.012 ρR = 0
Table 1: The benchmark calibration 3.2.2
Response to monetary policy, technology and government expenditure shocks
Figure 1 presents the response of the union to a monetary policy shock in the case without price-setting frictions. The monetary shock is identified as a disturbance b εR in the following interest rate policy rule: bt−1 + 0.2 · π bt = 0.95 · R bt−1 + b εR R
(41)
The upper panels of the figure show the response of Rt and ∆Mt . The four center panels show the response of the union’s variables. The lower four panels show the relative responses of the variables (measured as the differences in the deviations from steady state in the home country relative to the foreign country). The shock is calibrated in order to imply a contemporaneous fall of 50 b.p. in the interest rate. To support this fall in the interest rate, the monetary authority has to inject reserves into the system, raising money growth by about 0.8 per cent. The impact of this shock on the monetary union’s aggregates follows the intuitions already outlined in section 3. In particular, consumption, employment, inflation and real wages in the monetary union rise after the fall in interest rates. Figure 1 presents impulse responses for three different parameterizations in flexible prices: the first has n = θ and G = G∗ > 0; the second has n > θ and G = G∗ > 0; the third has n = θ and G > G∗ > 0. The lower four panels in the figure highlight that only in the first case do the variables in both countries follow the same path. In all other cases, the common monetary policy has idiosyncratic effects in each country. The intuition for these differentials is straightforward. In the case where n > θ, a common expansionary monetary shock lowers the relative demand for goods produced in country H, which implies a smaller rise in prices, real wages and employment in that country. In the case where G > G∗ > 0, a larger fraction of the production of country H is insensitive to the monetary shock. This implies that relative prices, employment and real wages fall in that country. In Figure 2 we incorporate price frictions in the model and highlight three cases where a common monetary policy has idiosyncratic effects on the different countries. These are the case where n 6= θ, where G 6= G∗ , and where ξ p 6= ξ ∗p . We model these differences one at a time and show that each of them is able to deliver the idiosyncratic effects of monetary policy. The intuition for the model’s responses in the first two cases is analogous to the case without any 21
price frictions. As for the case with ξ p = 0.67 and ξ ∗p = 0.5 it is straightforward to observe that relative prices of the goods produced in the stickier country home country in our case - fall. This fall is related to two factors. On the one hand, a smaller fraction of firms is able to change prices in each quarter in the home country. On the other hand, and as a by-product of the first, the firms in the home country that are able to optimize prices choose to raise them by a smaller amount (relative to the firms in the foreign country). This occurs because the firms’ relative demand depends on their relative price. Since a larger fraction of firms leave prices unchanged in the home country, it is rational for the optimizing firms in that country not to change prices by much. The dampened effects in the prices of goods produced in the home country implies that the real effects on employment and real wages in that country are magnified in relative terms. In quantitative terms, the lower panels of figure 2 allow an interesting comparison between the three cases. From these panels, we can conclude that differences in the size of n relative to θ or differences in the steady state per capita level of government expenditures may have implications for the relative allocations across countries that are comparable to the differences induced by one country having Calvo price durations of 3 quarters and the other having price durations of 2 quarters. Figures 3 and 4 present the response of the aggregates to a common technology shock and to an idiosyncratic technology shock in country H, respectively. In both cases the technology shock is calibrated as an AR(1), with standard deviation 0.012 and an autoregressive parameter equal to 0.8. In order to uncover the response due specifically to the technology shock we assume that the monetary authority follows an interest rate rule that implies an almost unchanged path for the interest rate, while ensuring local determinacy of the system. The rule is the following: bt = 0.99999 · R bt−1 + 0.001 · π R bt−1
(42)
Figure 3 shows that a common technology shock yields idiosyncratic effects in the two countries of the monetary union, even with a virtually unchanged interest rate. Again, this happens in any of the three cases under study: n 6= θ, G 6= G∗ and ξ p 6= ξ ∗p . The fall in employment and consumption observed after the positive technology shock has been extensively discussed in the literature (see Galí, 1999), and is related to the large fraction of firms unable to optimally choose prices in each quarter. Money growth falls in the period of the shock, supporting the fall in inflation and consumption in the union. Taking these dynamics into account, the intuitions for the impulse responses of relative consumption, employment and real wages are analogous to the case of the monetary shock. As for relative prices, they rise in the case of ξ p = 0.67 and ξ ∗p = 0.5, since a smaller fraction of firms is able to lower prices in the home country. It is also interesting to note that the impact of technology shocks is symmetric to the effects of monetary policy shocks. This is related to the firms’ financing of the wage bill with the financial intermediaries. 22
Figure 4 describes the case of a technology shock in the home country. The shock has a relatively greater impact in the home country. This is clear from the panels describing the evolution of relative prices, relative employment and relative real wages. Moreover, the heterogeneity between the allocations in each country is larger with idiosyncratic technology shocks compared to the case with common technology shocks. Finally, it is interesting to note that the effect of this idiosyncratic shock on the union’s aggregates decreases with the weight of country H’s goods on the preferences of the union’s households (θ). In conclusion, these simulations illustrate and confirm the results presented in the previous sections for the case of a monetary union with price-setting frictions. In such an environment we also show that irrespective of the shock hitting the union, the common monetary policy delivers heterogeneous allocations across countries. This result is only overturned in very special circumstances, when all three n = θ, G = G∗ > 0 and ξ p = ξ ∗p hold.
4
Concluding Remarks
The conventional wisdom is that common shocks in a monetary union do not have idiosyncratic effects. Since in a monetary union the effects of a common monetary shock are similar to the effects of an aggregate shock, an important consequence of this conventional wisdom is that monetary policy cannot be used to respond to idiosyncratic shocks, like technological shocks of different magnitude in the different countries of the monetary union. In this paper we challenge this conventional wisdom. We show that the usual dichotomy between aggregate (or common) shocks and idiosyncratic (or asymmetric) shocks is not the best one. Heterogeneity of the effects is not perfectly correlated with the heterogeneity of the shocks that caused them. We identify the assumptions that must hold in order for a common shock in the union to have different effects in identical countries in the union. Those conditions are absence of complete markets and segmented labor markets. Under those conditions the common monetary policy can have a greater power since it has different effects in different countries. It may be possible for the central bank to achieve several objectives with its policy. We study the transmission of monetary policy of aggregate technological shocks and of idiosyncratic technological shocks. Various variables that affect the transmission mechanisms are considered. We establish how the different transmissions mechanisms depend on the following variables: dimension of the countries, size of the government expenditures and degree of price staggereness. Once understood the transmission mechanisms the following step will be to ascertain policy recommendations. Even though monetary policy can have beneficial effects, because of the inefficient scale of production with monopolistic competition, it is not possible to use this policy systematically to take advantage of these effects. However, there is still a role for stabilization policy. This policy can be used in response to technological or other shocks so that the negative welfare effects of the nominal rigidities, together with the other distortions in
23
the economy, are minimized. Here too, like in the literature of optimal fiscal and monetary policy in closed economies with nominal rigidities (see Correia, Nicolini and Teles, 2002, and Adao, Correia and Teles, 2003a,b), the use of fiscal instruments is essential for the determination of the optimal monetary policy. Therefore, to discuss optimal policy in a monetary union we need to introduce not only country specific government expenditures but also different types of taxes. There are other few important aspects that deserve more attention, than the one given to them in the paper, and that we intend to study further in future work. We would like to know if the quantitative nature of the results changes significantly when we consider explicitly non-tradable goods, for private consumption and for public consumption, physical capital and preferences where labor has wealth effects.
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[10] Dixit, A. and L. Lambertini (2003), "Symbiosis of Monetary and Fiscal Policies in a Monetary Union", Journal of International Economics 60, 235—247. [11] Duarte, M. and A. Wolman (2003), "Fiscal Policy and Regional Inflation in a Currency Union", Federal Reserve Bank of Richmond Working Paper No. 03—11. [12] Duarte, M. and M. Obstfeld, (2004), ”Monetary Policy in the Open Economy Revisited: The Case for Exchange-Rate Flexibility Restored”, mimeo. [13] Galí, J, and T. Monacelli (2004), "Optimal Fiscal policy in a Monetary Union", mimeo. [14] Mundell, R. (1961), "A Theory of Optimum Currency Areas", American Economic Review 51, 657—665. [15] Obstfeld, M. and K. Rogoff (1996), Foundations of International Macroeconomics, Cambridge: MIT Press.
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