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Working Paper Series Fiscal Policy and Regional Inflation in a Currency Union WP 03-11 Margarida Duarte Federal Reserve Bank of Richmond Alexander L. Wolman Federal Reserve Bank of Richmond This paper can be downloaded without charge from: http://www.richmondfed.org/publications/ Fiscal Policy and Regional In‡ation in a Currency Union¤ Margarida Duartey Alexander L. Wolmanz Federal Reserve Bank of Richmond Working Paper No. 03-11 August 2003 JEL Nos. F33, F02, E62 Keywords: currency union, …scal policy, in‡ation di¤erentials Abstract This paper investigates the ability of a region participating in a currency union to a¤ect its in‡ation di¤erential with respect to the union through …scal policy. We study the interaction between regional …scal policy and in‡ation di¤erentials in a ‡exible price, two-region model with both traded and nontraded goods. For symmetric regions, changes in one region’s tax rule that decrease the volatility of its in‡ation di¤erential also decrease the volatility of its output. The decrease in the volatility of the in‡ation di¤erential is brought about by an increase in the volatility of tax rates. The e¤ect of the tax rule on output volatility – but not in‡ation volatility – depends on country size. For a small country lower volatility of in‡ation di¤erentials is associated with higher volatility of output. This relationship results from the fact that small countries are more open, and hence there is a greater role for traded goods productivity shocks. ¤ We would like to thank Michael Dotsey, Tommaso Monacelli, Fabio Natalucci, Cedric Tille, and partici pants in the 2002 SED meeting in New York, the International Forum on Monetary Policy at the European Central Bank, the Federal Reserve System Committee on International Economics, the 2003 Midwest Macro conference, and the 2003 Econometric Society meeting for comments on this and an earlier version, and Elise Couper for research assistance. This paper does not necessarily represent the views of the Federal Reserve System or the Federal Reserve Bank of Richmond. y Federal Reserve Bank of Richmond, margarida.duarte@rich.frb.org. z Federal Reserve Bank of Richmond, alexander.wolman@rich.frb.org. 1. Introduction Regions participating in a currency union delegate monetary policy – the principal tool for controlling their in‡ation rate – to a central authority. However, a currency union typically does not involve homogeneous, perfectly integrated regions, and in‡ation rates therefore vary across regions. The currency union comprising the United States is homogeneous and integrated enough that no attention is paid to in‡ation di¤erentials across regions; state-level consumer price index data is not even collected. The European Monetary Union is another matter. Domestic in‡ation rates continue to play an important role in discussions of individual countries’ economic conditions. And at the EU level, Ireland was reprimanded by the European Union’s …nance ministers in 2001 for pursuing easy …scal policy in the face of a high in‡ation rate. More recently, Pedro Solbes, the European Commissioner for Economic and Monetary A¤airs, stated that for Ireland today, “the in‡ation question, as in Spain, has to be tackled on the national level.”1 Should a region in a currency union wish to exert in‡uence over its own in‡a tion rate – or its in‡ation di¤erential relative to the rest of the union – it must turn to …scal policy. When …scal policy is its only available instrument, several questions arise. Can the regional …scal authority a¤ect its in‡ation di¤erential? If so, what types of policies are e¤ective, and what consequences do they have for real economic activity? This paper investigates the ability of a region participating in a currency union to a¤ect its in‡ation di¤erential with respect to the union through …scal policy. We study the interaction between regional …scal policy and in‡ation di¤erentials in a ‡exible-price, two-region model with both traded and nontraded goods. In our framework, price (and in‡ation) di¤erentials arise from both movements in the relative price of nontraded goods across countries and deviations from the law of one price for traded goods. There is an exogenous stream of government expenditures, and the regional …scal authority has access to a labor income tax, seigniorage revenue, and debt to …nance these expenditures. The model is driven by shocks to government expenditures and to productivity. Because regional …scal authorities can issue debt, they have some ‡exibility as to the pattern of distortionary taxes. We assume that the tax rate is determined by a rule that responds to the level and change in the stock of outstanding government debt.2 We study the implications of modi…cations to the benchmark 1 Irish 2 This Times, January 31, 2003, page 51. type of rule has been commonly used in large, quantitative models (see Johnson, 2001). tax rule that are aimed at in‡uencing the region’s in‡ation di¤erential. The tax rate is distortionary, so changes in its cyclical behavior alter the behavior of real variables, including the price of the home consumption basket relative to the for eign consumption basket. Thus, regional …scal authorities do have the ability to a¤ect the regional in‡ation di¤erential. Speci…cally, by lowering (raising) the distortionary tax rate in response to positive (negative) in‡ation di¤erentials, a regional …scal authority can decrease the absolute value of its in‡ation di¤erential in response to the shocks driving the model. We …nd that for symmetric regions, changes in one region’s tax rule that decrease the volatility of its in‡ation di¤erential also decrease the volatility of its output. The decrease in the volatility of the in‡ation di¤erential is brought about by an increase in the volatility of tax rates. We also consider the behavior of the smaller of two regions in an asymmetric currency union. For small countries, the relationship between the tax rule and volatility of in‡ation di¤erentials is similar to the symmetric case. Likewise, small countries experience essentially the same relationship between the tax rule and tax rate volatility. However, the e¤ect of the tax rule on output volatility depends on country size. For a small country lower volatility of in‡ation di¤erentials is associated with higher volatility of output. This relationship results from the fact that small countries are more open, and hence there is a greater role for traded goods productivity shocks. Early research on currency unions, dating back to Mundell (1961), concerns the optimal composition of a currency area. In modern dynamic equilibrium models, it has been di¢cult to …nd conditions under which it is optimal for a region to delegate its monetary policy (see, for example, Monacelli, 2001). Given the existence of a currency union, Benigno (2002) studies optimal monetary policy and Bergin (2001) shows how non-constant demand elasticities can generate in‡ation di¤erentials through deviations from the law of one price. We use a general equilibrium model to study how regional …scal policy a¤ects regional in‡ation di¤erentials.3 4 Beetsma and Jensen (2002) also study regional …scal policy in a general equilibrium model of a currency union. They describe 3 An empirical literature documents regional variation in in‡ation within currency unions. Cecchetti, Mark, and Sonora (2002), Parsley and Wei (1996), and Rogers (2001) study price level convergence, and Canova and Pappa (2003) study the e¤ects of …scal shocks on price dispersion. 4 Bergin (2000) and Sims (1999) consider implications of the …scal theory of the price level for a monetary union. We focus on monetary and …scal policy regimes in which there is a unique equilibrium. Nonetheless, the particular form of a region’s …scal policy rule a¤ects the equilibrium behavior of in‡ation. 2 the optimal coordinated monetary and …scal policies whereas we treat policy as exogenous. In addition, the models di¤er in their assumptions about the instru ments of …scal policy and the role of government spending. Beetsma and Jensen allow for lump-sum taxes and assume that government spending yields utility to consumers. We assume that the government must rely on a labor income tax and debt to fund spending that is a pure resource drain. Furthermore, in Beetsma and Jensen consumer price levels are identical across countries and in‡ation is measured by the change in the producer price index. The paper proceeds as follows. In section 2 we present the model. Section 3 describes the model’s calibration. Section 4 is devoted to developing a basic understanding of the model; we describe the channels which lead in‡ation to vary across countries, and discuss the dynamic responses to productivity and government spending shocks. Section 5 contains our results for symmetric regions on the implications of using …scal policy to a¤ect the in‡ation di¤erential, and section 6 is devoted to the small country case. Section 7 concludes. 2. Model The currency union is composed of two regions, denoted home and foreign, that share the same currency. A central monetary authority issues the currency and conducts monetary policy. Each region has a …scal authority, which is responsible for …scal policy in the region. The two regions share the same structure but may di¤er in size. Each region is specialized in the production of a continuum of varieties of a tradable and nontradable good. Monopolistically competitive …rms produce these goods using labor, which is immobile across regions. Prices are ‡exible. The regions are populated by a continuum of households of measure N (home) and N ¤ (foreign). Households in each region supply labor to domestic …rms and consume all varieties of both home and foreign tradable goods, as well as all varieties of the region’s nontradable good. We assume that, in order to consume a traded good, agents need to combine it with nontraded goods.5 That is, a consumer must purchase ´ additional units of the local nontraded good in order to obtain utility from a traded good. Hence nontraded goods are used both for 5 This assumption re‡ects the need to combine di¤erentiated traded goods with distribution services (intensive in local nontraded goods) before households can consume the former. This corresponds to the setup in Corsetti and Dedola (2002), except that for the purpose of our paper, and without any loss of generality we do not need to model the distribution sector separately. 3 consumption and distribution purposes. Households also demand real balances, which are an argument in their utility function. We assume that asset markets are complete. Thus, in every state of the world the ratio of marginal utilities of per capita consumption across regions is equated to the ratio of consumption price levels across regions.6 We describe only the home region’s economy. An analogous description applies to the foreign region. The subscript f (or h) denotes a good’s country of origin, whereas the superscript ¤ denotes a foreign region variable; for example, PT¤;h is the price of a traded good produced in the home country and consumed in the foreign country. 2.1. Households Households derive utility from consuming a composite good (ct ), leisure time t (1 ¡ lt ), and from holding real money balances ( M ). Households maximize the Pt expected discounted value of the utility ‡ow, "1 µ ¶# X M U0 = E0 ¯ tu ct ; 1 ¡ lt; t (2.1) P t t=0 where E0 denotes the mathematical expectation conditional on information available in period t = 0, ¯ 2 (0; 1) is the discount rate, and u is the momentary utility function, assumed to be concave and twice continuously di¤erentiable. 2.1.1. The Composition of Consumption The composite consumption good is an aggregate of traded and nontraded goods (cT;t and cN;t ) as follows: » · ¸ »¡1 »¡1 »¡1 » » ct = · T cT;t + · N cN;t : (2.2) The elasticity of substitution between the traded and nontraded good is », and ·T and ·N determine the agent’s bias towards the traded good. Consumption of traded goods is a similar aggregate of home- and foreign- produced traded goods (cT;h;t and cT;f ;t ): ° · ¸ °¡1 °¡1 °¡1 ° ° cT;t = ·T;h cT;h;t + ·T ;f cT;f ;t ; (2.3) 6 See, for example, Chari, Kehoe, and McGrattan (2002). 4 where ° > 0 denotes the elasticity of substitution between the home and foreign composite traded goods, and the weights ·T;h and · T;f determine the agent’s bias for the domestic traded good. Each country produces a continuum of varieties of the traded good, indexed by i 2 [0; 1] ; and a continuum of varieties of the nontraded good, indexed by j 2 [0; 1]. The local nontraded good and the local and imported traded goods in (2.2) and (2.3) are aggregates of these continua of varieties: cN;t = µZ 1 cN;t (j) µ¡1 µ dj 0 cT;h;t = µZ 1 cT ;h;t (i) µ¡1 µ µ ¶ µ¡1 and cT ;f;t = µZ 1 cT ;f;t (i) 0 µ¡1 µ µ ¶ µ ¡1 ; (2.5) µ ¶ µ¡1 ; (2.6) di 0 di (2.4) ; where µ > 1 is the elasticity of substitution between any two varieties of the same good, and the price elasticity of demand for a given variety. 2.1.2. Demands and Price Indices The numeraire we will work with is the common currency: Let Pt denote the price of the composite consumption good and PT;t and PN;t denote the prices of the composite traded and nontraded goods, respectively. And let PT;h;t (i), PT;f ;t (i), and PN;t (i) denote the prices set by the producers of the home and foreign traded goods and of the local nontraded good of type i, respectively. Since ´ units of the nontraded composite good need to be purchased for every unit consumed of traded good i, the cost to the household to consume one unit of traded good i is e¤ectively PT;h;t (i) + ´PN;t for the home good and PT;f ;t (i) + ´PN;t for the foreign good.7 Given the consumer’s demand for the composite consumption good, the de mand for each lower level good can be determined by solving a cost minimization problem. Substituting these demands back into the appropriate consumption ag gregator then yields the corresponding price index. 7 More formally, consumers should be viewed as having Leontief preferences over any individ ual traded good and ´ times the composite nontraded good. 5 Composite Goods The price index for the composite consumption good, Pt , is ³ ´1=(1¡») Pt = ·»T (PT;t )1¡» + ·»N (PN;t )1¡» ; where the price indices for the traded and nontraded goods aggregates are given by ¡ ¢1=(1¡°) ° PT;t = · °T;h (PT ;h;t )1¡° + · T;f (PT ;f;t )1¡° and µZ PN;t = 1 PN;t (i) 1¡µ dj 0 1 ¶ 1¡µ : In addition, the price indices PT ;h;t and PfT;t for the local and imported composite traded goods are given by PT;h;t = µZ 1 (PT;h;t (i) + ´PN;t ) 1¡µ di 0 and PT;f ;t = µZ 1 (PT;f;t (i) + ´PN;t ) 1¡µ di 0 1 ¶ 1¡µ 1 ¶ 1¡µ : These price indices re‡ect the requirement that ´ units of the nontraded composite good be purchased for every unit consumed of traded good i. The demand functions for each variety of each good are given by µ ¶ PN;t (i) ¡µ cN;t (i) = cN;t; (2.7) PN;t à !¡µ PT;h;t (i) + ´PN;t cT;h;t (i) = cT;h;t : (2.8) T Ph;t and cT;f;t (i) = à PT;f ;t (i) + ´PN;t T Pf;t !¡µ cT;f;t : (2.9) Naturally, the demands for traded goods depend on the cost to the household of consuming one unit of the good and therefore re‡ect the price of nontraded goods. The terms cN;t , cT;h;t , cT ;f;t denote the demand for the relevant composite good and are derived analogously. For example, cN;t = k»N (PN;t =Pt )¡» ct : 6 2.1.3. The Budget Constraint The representative consumer in the home region holds currency, Mt , issued by the central monetary authority and trades a complete set of state contingent nominal bonds with the consumer in the foreign region. We denote the price at date t when the state of the world is s t of a bond paying one unit of currency at date t + 1 if the state of the world is s t+1 by Q (st+1 js t) and we denote the number of these bonds purchased by the home agent at date t by D (s t+1 ). The home consumer also holds riskless nominal bonds issued by the home and foreign …scal authorities, Bh;t and Bf ;t , both paying (1 + Rt ) currency units in period t + 1.8 The agent’s intertemporal budget constraint, expressed in currency units, is X Pt ct + Mt + Bh;t + Bf ;t + Q (st+1 jst ) D (st+1 ) (2.10) s t+1 · (1 ¡ ¿ t ) Ptwt lt + Mt¡1 + D (st ) + ¦t + (1 + Rt¡1 ) (Bh;t¡1 + Bf ;t¡1 ) ; where ¦t represents pro…ts of domestic …rms (assumed to be owned by the do mestic consumer) and (1 ¡ ¿ t ) Pt wt lt represents nominal labor earnings after tax. The consumer chooses sequences for consumption, ct , labor, lt , state contingent bonds, D (s t+1), government bonds, Bh;t and Bf;t , and money holdings, Mt , in order to maximize the expected discounted utility (2:1) subject to the budget constraint (2:10). 2.2. The Regional Fiscal Authority The …scal authority in the home region issues nominal debt, Bt , taxes labor income at rate ¿ t , and receives seigniorage revenues from the central monetary authority, Zt . These revenues are spent on public consumption, g t, and interest payments on the debt. Public consumption does not yield utility to households in our model. The region’s government budget constraint is given by Bt + N ¿ t Pt wt lt + Z t = (1 + Rt¡1 ) Bt¡1 + Pt g t : (2.11) The government has the same preferences as the consumer for the di¤erent varieties of the local nontraded good and both traded goods. Therefore, given 8 Because home and foreign agents can both freely buy and sell home and foreign government bonds, arbitrage ensures that there is a common nominal interest rate. Our assumption of complete asset markets independently guarantees that the nominal interest rate is common across countries. 7 a level of total government consumption gt , government demands for individ ual goods are given by expressions analogous to the individual consumption de mands (2:7), (2:8), and (2:9) ; for example, gN;t (i) = (PN;t (i) =PN;t )¡µ gN;t = (PN;t (i) =PN;t )¡µ kN» (PN;t=Pt )¡» gt . We are interested in studying the roles of both regional …scal policy shocks and systematic …scal policy in a¤ecting in‡ation di¤erentials across regions. Fiscal policy shocks can be associated with either taxation or spending, and likewise systematic …scal policy can be associated with either taxation or spending. We follow much of the literature in assuming that the ratio of government spending to output follows an exogenous stochastic process, whereas the labor income tax rate is determined by a feedback rule that incorporates a response to the stock of debt.9 This response insures that the government will be able to pay the interest on its debts. The share of total public consumption in output, g=y, is given by µ ¶ µ ¶ g g = cg + ½g + "g;t ; (2.12) y t y t¡1 ¯ ¯ where ¯½g ¯ < 1 and "g;t » N (0; ¾ g ). The tax rate ¿ t on labor income is determined by a feedback rule that targets the debt/GDP ratio b according to ¡ ¢ ¡ ¢ ¿ t = ¿ t¡1 + ®b;¿ b t ¡ b + ®¢b;¿ (b t ¡ bt¡1 ) + ®p;¿ ¼ t ¡ ¼ Ut : (2.13) Note that we have allowed for a response of the tax rate to the in‡ation di¤erential (¼Ut denotes union-wide in‡ation, to be de…ned below). This response is how we model …scal policy as attempting to a¤ect in‡ation di¤erentials. 2.3. Firms There are two sectors of production in each region, the traded, T , and nontraded, N , sector. The production function for each …rm i in each sector is given by zt lt (i), where lt (i) represents labor input and zt is a sector- and country-speci…c productivity shock. We denote the real marginal cost by à t = wt =zt . Note that marginal cost is “country-sector speci…c;” two …rms in the same country in the same sector have the same level of productivity and hence (since they face the same wage) the same marginal cost. Firms are monopolistically competitive and prices are ‡exible. 9 Johnson (2001) criticizes the arbitrariness of the approach taken by much of the literature (and by us). See Mitchell, Sault, and Wallis (2000) for a study of di¤erent rules used in the literature. 8 2.3.1. The Tradable Goods Sector Firm i chooses PT;h;t (i) and PT¤;h;t (i), the prices to charge in each market for its good. We assume that home and foreign markets are segmented; thus, the law of one price need not hold for traded goods. As it will become clear below, due to the need to use ´ units of the local nontraded good in order to derive utility from traded goods, …rms producing these goods may …nd it optimal to price discriminate across the two markets, setting PT ;h;t (i) 6= PT¤;h;t (i). The pro…t maximization problems for the producer of traded good i are µ ¶µ ¶¡µ PT ;h;t (i) PT;h;t (i) + ´PN;t max ¡ ÃT ;t yT ;h;t (2.14) PT ;h;t (i) Pt PT;h;t and max ¤ PT;h;t(i) µ PT¤;h;t (i) ¡ à T;t Pt ¶Ã ¤ PT¤;h;t (i) + ´PN;t PT¤;h;t !¡µ y¤T;h;t ; where yT;h;t = N cT ;h;t + g T;h;t denotes home demand in period t for the composite home traded good and y¤T;h;t = N ¤c¤T;h;t + gT¤ ;h;t denotes foreign demand. These problems imply that the price of a domestically produced traded good in the home and foreign markets is, respectively µ ¶ PT;h;t (i) µ ´ PN;t = 1+ à T;t (2.15) Pt µ¡1 µÃ T;t Pt and µ ¶ PT¤;h;t (i) µ ´ PN¤ ;t = 1+ ÃT;t : Pt µ¡1 µÃT ;t Pt (2.16) That is, prices are a markup over the standard measure of marginal cost, where the markup is increasing in the relative price of nontraded goods. Increases in the relative price of nontraded goods raise the market power of a traded goods producer, by decreasing the traded goods producer’s share of the traded goods consumer price. As shown in Corsetti and Dedola (2002), with ´ > 0, the elasticity of demand for home traded goods is not necessarily the same across countries and it will di¤er if the relative price of nontraded goods di¤ers across countries. The monopolistic …rm takes this fact into account when choosing its prices and may …nd it optimal to charge di¤erent prices across markets. 9 The market clearing condition for home traded good i is given by N cT ;h;t (i) + N ¤ c¤T;h;t (i) + g T;h;t (i) + g ¤T h;t (i) = zT ;t lT ;t (i) ´ yT;t (i) ; (2.17) and, similarly, the market clearing condition for foreign traded good i is ¤ N cT ;f;t (i) + N ¤ c¤T;f ;t (i) + gT ;f ;t (i) + gT¤ ;f;t (i) = zT¤ ;t lT¤ ;t (i) ´ yT;t (i) : (2.18) Note that individual household demands are expressed in per capita terms whereas government demands and …rm-level labor inputs are not. 2.3.2. The Nontraded Goods Sector The pro…t maximization problem for a producer of nontraded good i is max PN;t(i) µ PN;t (i) ¡ ÃN;t Pt ¶µ PN;t (i) PN;t ¶¡µ yN;t ; where yN;t denotes total demand for the composite nontraded good. This term has two components since nontraded goods are demanded by households and gov ernment for both consumption and distribution purposes. This problem implies the usual pricing condition PN;t (i) µ = à : Pt µ ¡ 1 N;t (2.19) The market clearing condition for nontraded goods is di¤erent from the one for traded goods, as it re‡ects the quantity of nontraded goods demanded for “distribution” purposes as well as the quantity demanded for consumption. The market clearing condition for home nontraded good i is then given by µ ¶ cT ;h;t (i) + cT;f ;t (i) (N cN;t (i) + gN;t (i)) 1 + ´ = zN;t lN;t (i) ´ yN;t (i) : cN;t It is important to note that the variable cN;t (i) does not include the nontraded goods purchased for their role in distribution; these goods are accounted for by the term in ´. 10 2.4. The Central Monetary Authority The central monetary authority issues non-interest bearing money and allocates seigniorage revenue to the regions. Let the superscript U denote a union-wide variable; for example total nominal money balances in the union are MtU = Mt + Mt¤ . In period t, the monetary authority earns revenue from printing money equal to U U Mt ¡ Mt¡1 and it distributes this revenue among the regional …scal authorities.10 Recalling that Z denotes seigniorage, we have U MtU ¡ Mt¡1 ´ ZtU = Zt + Z t¤ : (2.20) We have to specify the rule for allocating seigniorage. We will assume that seigniorage is allocated according to each country’s share of nominal consump tion in the stationary steady-state, sc , so that Z t = sc ZtU : (2.21) The monetary authority is assumed to follow an interest rate rule similar to the rules studied by Taylor (1993) and Clarida, Gali, and Gertler (1998). In particular, the nominal interest rate Rt is set as a function of the lagged nominal rate, next period’s expected in‡ation rate in the union, and union-wide real output, £ ¡ ¢ ¡ ¢¤ ¹ + ½R Rt¡1 +(1 ¡ ½R ) ®¼ Et ¼Ut+1 ¡ ¼U + ®y ln yU =yU ; (2.22) Rt = (1 ¡ ½R ) R t where a bar over a variable denotes its target value. In order to implement this rule, the central monetary authority needs a measure both for the price level and real output in the whole currency union, PtU and yUt , respectively. We de…ne the “union-wide” price level, PtU , as a weighted average of each region’s price level, where the weight is determined by the region’s share of nominal consumption. That is, PtU = sc;t Pt + (1 ¡ sc;t ) Pt¤ : 10 In the description central monetary authority we abstract, without loss of generality, from the monetary authority’s balance sheet and from each government’s borrowing from the mon etary authority. To solve the model, we need to specify how the revenue from money creation is allocated across regions. We do this by choosing a rule for the allocation of the change in the monetary base. This choice eliminates the need to keep track of the central bank’s balance sheet. If we were, instead, to specify the allocation rule in terms of the central bank’s interest revenues, we would need to keep track of its balance sheet. 11 In order to de…ne “union-wide” real output, we …rst de…ne union nominal output as the sum of each region’s nominal output, yUt n = ytn + yt¤n . Union real output is obtained by de‡ating union nominal output by the union price level, Un yUt = yPt U . t 2.5. Equilibrium and Model Solution We focus on the symmetric equilibrium of the model in which all …rms in the same sector choose the same price. An equilibrium for this economy is de…ned as a collection of allocations for home and foreign consumers, allocations and prices for home and foreign …rms, composite good prices, real wages, and bond prices that satisfy the e¢ciency conditions for households and …rms (…rst-order conditions for the maximization problems stated above) and market clearing conditions, given the policy rules assumed for the monetary and …scal authorities.11 The remaining market clearing conditions needed to solve the model are for the labor markets in the two countries: T N lt = lh;t (i) + ltN (i) : (2.23) As before, individual household labor supply in period t, lt , is expressed in per capita terms, whereas …rm-level labor inputs lTt (i) and lN t (i) are not. We approx imate the equilibrium linearly around its steady-state. 3. Calibration In this section we report the parameter values used in solving the model. Our benchmark calibration assumes that the regions in the currency union are symmet ric and share the same structure and parameter values. The model is calibrated using German data, unless otherwise noted, and we assume that a time period in the model corresponds to one quarter. 3.1. Preferences and Production We follow Chari, Kehoe, and McGrattan (2002) closely in the preference speci… cation. The momentary utility function is given by à µ ¶ µ ¶± ! 1¡¾ ± M 1 M (1 ¡ l)1¡º U c; l; = ac± + (1 ¡ a) +à : P 1¡¾ P 1¡º 11 In the interest of space we do not present the e¢ciency conditions. 12 We set the curvature parameter, ¾, equal to two. The parameters à and º are set to 17:4 and 1:5, respectively, so that the fraction of working time in steady-state is 0:25 and the elasticity of labor supply, with marginal utility of consumption held constant, is 2. The parameters a and ± are obtained from estimating the money demand equation implied by the …rst-order condition for bond holdings. Using the utility function de…ned above, this equation can be written as log Mt 1 a 1 R ¡1 = log + log ct + log t : Pt ±¡1 1¡a ±¡1 Rt To estimate ± and a we used German quarterly data from 1995:01 to 2000:01 for M1, CPI, real private consumption and the three-month Libor rate. We set 1 ±¡1 equal to our estimate of the interest elasticity, ¡0:45, and obtain ± = ¡1:22. The value for the weight coe¢cient a was set to 0:91 and it was derived from the estimate for the intercept, ¡1:026. The discount factor, ¯ , is set to 0:99, implying a 4% annual real rate in the stationary economy. For the consumption index cT we need to assign values to °, the elasticity of substitution between domestic and imported traded goods, and to ·T h and ·T f , the weights on consumption of home and foreign traded goods. Collard and Dellas (2002) estimate ° for France and Germany using data from 1975:1 to 1990:4. Their estimate for France is 1:35 while their point estimate for Germany is substantially higher (2:33) but also very uncertain. In the benchmark calibration we set ° equal to 1:5, which is also the standard value used in models calibrated for US data. The weight ·T h is set equal to 0:63 so that the import share in steady state is 25% of GDP and we use the normalization ·°T h + · T° f = 1 to obtain ·T f . The consumption index for c depends on », the elasticity of substitution between traded and nontraded goods, and on · T and · N , the weights on consump tion of traded and nontraded goods. We use Mendoza’s (1995) estimate of the elasticity of substitution between traded and nontraded goods for industrialized countries and set » equal to 0:74.12 To set the weight ·T we refer to Stockman and Tesar (1995) who report that nontraded goods account for about half of output in OECD countries. We set ·T = 0:86 to match this ratio and use the normalization ·»T + ·»N = 1 to obtain ·N . Finally, we need to choose the values for the distribution parameter ´ and for µ, the elasticity of substitution across varieties of goods. Based on Burstein, Neves, 12 This estimate is bigger than the one found by Stockman and Tesar (1995), who use data from both developing and industrialized countries. 13 and Rebelo (2000), we set ´ equal to 0:9 so that distribution services represent 45% of the retail price of traded goods in steady state. The elasticity of substitution between di¤erent varieties of a given good, µ, is related to the markup chosen when …rms adjust their prices. The markup for …rms in the nontraded sector is simply µ= (µ ¡ 1). We set µ = 10, which is a representative value in the literature. It implies a markup of 1:11, which is consistent with the empirical work of Basu and Fernald (1997) and Basu and Kimball (1997). For the same elasticity of substitution among varieties of traded goods, the steady state markup for …rms in the traded goods sector is larger due to the presence of distribution costs. In steady state, the markup for …rms in the traded sector is 1:22, about 10% higher than in the nontraded goods sector because of the added market power generated by the distribution costs. 3.2. Monetary and Fiscal Policy Rules The parameters of the nominal interest rate rule are taken from the estimates in Clarida, Gali, and Gertler (1998, Table I) for the Bundesbank. We set ½r = 0:91, ®p;r = 1:31, and ®y;r = 0:25=4, where this last term is converted for quarterly data. The target values for R, ¼ U , and y U are their steady-state values. We assume that in steady-state prices grow at 2% per year (or 0:5% per quarter). The parameters for the tax rule are taken from Mitchell, Sault, and Wallis (2000). We convert their values for quarterly data and set ®b;¿ = 0:04=16 and ®¢b;¿ = 0:3=4. 3.3. Exogenous processes The technology shocks£are assumed to ¤follow an AR (1) process z t+1 = Az zt + " zt , where zt is the vector ztT ; ztN ; zt¤T ; zt¤N and Az is a 4 £ 4 matrix. The vector "zt represents the innovation to z. Stockman and Tesar (1995) provide estimates for a joint productivity process such as this one, but that process is annual, and the home and foreign countries are interpreted as symmetric and together comprising the entire industrialized world. Our model is quarterly, and the home and foreign countries are loosely interpreted as Germany and France, which likely experience higher correlation of productivity shocks. We adjust the Stockman and Tesar 14 process to account for these two di¤erences, and end up with 2 3 0.199 0.249 -0.010 0.094 6 0.176 0.593 0.036 0.044 7 7 Az = 6 4 -0.010 0.094 0.199 0.249 5 0.036 0.044 0.176 0.593 and 2 3 2 ²Tt ;h 1 0 N;h 7 6 6 ² t 7 60 1 "zt = 6 4 ²Tt ;f 5 + 4 1 0 0 1 ²tN;f 3 7 7 5 · ²Tt ;c ²tN;c ¸ ; with each ² independently distributed across both time and sectors and ¾ 2²T;i = ¾2 0:02422 , ¾ 2²N;i = 0:01232 , and ¾²2c = 0:3636, for i = h; f.13 ²i Shocks to government expenditures in each country are assumed to follow the same independent AR (1) process gt+1 = c+Ag gt +"gt , where gt represents the share of government expenditures in GDP. We estimated this process using quarterly data for Germany from 1991:2 to 2001:3. The estimate for Ag is 0:57 and the estimate for ¾ 2"g is 0:000166. 4. The Mechanisms Behind Regional Price Di¤erentials The model contains three distinct mechanisms that can generate price (and in ‡ation) di¤erentials across regions. Each mechanism works through the presence of local nontraded goods. First, households consume both traded and nontraded goods, implying that the consumption price indices in the two countries correspond to distinct baskets of goods. Even if the law of one price holds for all traded va rieties, the consumption price indices di¤er in the two countries in response to 13 We arrived at this representation for productivity in two steps. First, we computed a quarterly productivity process that came close to replicating the Stockman-Tesar process when it was time-aggregated. Next, we imposed the common shock structure of Collard and Dellas, who estimate a joint AR(1) process for aggregate productivity for Germany and France. We assumed that the variance ratio of common to idiosyncratic shocks was as they report for Germany. We chose the levels of idiosyncatic shock variances so that, (i) when combined with our Az matrix, the ratio of own variances of traded and non-traded productivity was that implied by the original Stockman and Tesar process, and (ii), the standard deviation of hp-…ltered output relative to its mean was 1.1%, which is what we estimated for Germany. We intend to estimate this process directly in future work. 15 movements in the relative price of nontraded goods across countries. Second, due to the need to use local nontraded goods for the consumption of traded goods, the consumer price of traded varieties depends on the price of the local nontraded composite good. Third, movements in the relative price of nontraded goods across countries will lead traded goods’ producers to price discriminate across markets (equations (2.15) and (2.16)). For these reasons, the consumer price of traded goods (and thus the consumption price indices) di¤ers in the two countries in response to movements in the relative price of nontraded goods across countries.14 Any exogenous shock which a¤ects the relative price of nontraded goods across regions generates an equilibrium price di¤erential across regions through the mech anisms just described. We now look at the equilibrium price di¤erential associated with permanent shocks to government spending and home nontraded productiv ity. In these experiments we assume that countries are equal-sized and monetary policy is given by a constant money growth rate.15 We consider di¤erent alterna tives for the options available to the …scal authority to balance its budget each period. Government Expenditure Shock Fiscal policy in each region is summa rized by an exogenous process for government expenditures as a share of output and by a feedback rule for the labor income tax. Here we illustrate the e¤ects of permanent shocks to government spending on price di¤erentials for di¤erent as sumptions on the tools available to the government to …nance its budget. Recall that in our setup government spending is a pure resource drain on the economy. Figure 1 displays the response of selected variables to a one percentage point permanent increase in the share of government spending in output, when govern ment spending is …nanced by lump-sum taxes. The shock generates an increase in government spending of about 5.8%, increasing demand for both home and foreign traded goods as well as for the local nontraded goods (partly to be used for the distribution of traded goods). Domestic real output increases by less than 1% and the transmission of the shock to foreign output is even smaller.16 The shock has 14 In the presence of nontraded goods, distribution costs are not necessary for generating relative price changes across countries. However, they do generate deviations from the law of one price, which have been documented to contribute importantly to the observed movements in relative prices across countries. 15 The analysis of relative price levels across countries does not require the use of a monetary model. In a real two-country model of relative national price levels Duarte (2003) …nds results analogous to those presented in this section. 16 Betts and Devereux (1999) …nd identical responses of home and foreign output to government 16 a negative e¤ect on private consumption, bigger in the home country than in the foreign country, and it generates a one time permanent positive price di¤erential with respect to the foreign region of about 0:15 percentage points.17 The real wage increases in the home country while it decreases in the foreign country. Since the relative price of home traded goods to foreign traded goods increases, home and foreign households and governments substitute consumption away from home traded goods towards foreign traded goods. This substitution e¤ect leads to the relative expansion of the traded goods sector in the foreign country, while the nontraded goods sector expands relatively more in the home country. Figure 2 displays the response to the same shock when the government … nances its spending with labor income taxes instead of lump-sum taxes. The e¤ect on the price di¤erential generated by the shock is now about 0:8 percentage points, substantially higher than in the previous case. Due to the higher labor income taxes in the home country (needed to …nance the increased government spending), the (pre-tax) real wage required by home households to work more and meet the increased demand for home goods increases more than in the previous case. In equilibrium, the home household works less and consumes less. Prices of home goods now increase more relative to the price of foreign goods than before, implying that agents substitute even more towards foreign goods. In the benchmark model we allow for the government to …nance its spending with both labor income taxes and debt. Each period labor income taxes are de termined by the tax feedback rule (2.13) that depends on that period’s net change and level of public debt, as well as the previous period’s tax rate; public debt, in turn, adjusts to insure that the government’s intertemporal budget constraint holds. In response to a government spending shock, the regional …scal authority issues new debt and raises labor income taxes. The tax feedback rule introduces dynamics to the shock response, absent in the cases where the increase in govern ment spending is …nanced period-by-period by either lump-sum or labor income taxes.18 spending shocks. In our model the response of home and foreign outputs is not identical because there are nontraded goods. 17 As mentioned above, the assumption of complete asset markets implies that u =P = u¤ =P ¤ c c every period. This condition implies that the ratio of price levels moves together with the ratio of marginal utilities of consumption. Abstracting from the presence of money in the utility function, this condition implies a negative relationship between price di¤erentials and consumption di¤erentials. 18 In their analysis of the government’s …nancing decision, Baxter and King (1993) abstract from government debt, arguing that any path for debt can be replicated with transfers, for a 17 Figure 3 displays the response to the same shock in the benchmark environment with debt. In the period of the shock, the government issues new public debt and increases the labor income tax slightly as well. Therefore, the impact e¤ect of the shock resembles its e¤ect when government expenditure is …nanced with lumpsum taxes (…gure 1). In the following periods, both public debt and labor income taxes increase; as taxes increase the behavior of the model resembles that in the case where labor income taxes …nance government spending (…gure 2). After the public debt returns to its steady-state level, the response of all variables equals the impact response from …gure 2. The overshooting that occurs in intermediate periods is generated by the dynamics of the tax rule. Productivity shock to nontraded goods sector Figure 4 plots the re sponse to a 1% permanent increase in productivity in the home nontraded goods sector when the government balances its budget with lump-sum taxes. This shock generates a negative price di¤erential, with the home price level decreasing about 0:5% and the foreign price level increasing about 0:15%. With optimal risk shar ing, the fall in the home relative price is associated with a fall in the ratio of marginal utilities of consumption across countries and an increase in home rela tive consumption. In response to this shock, home producers of nontraded goods lower their prices. Due to the presence of distribution costs, the fall in nontraded goods prices also reduces the consumer price of home and foreign traded goods in the home country, but relatively less than the fall in the price of nontraded goods. Home consumption increases for all goods and real output increases in the home country; increased home demand for foreign traded goods also raises foreign real output. The foreign household, whose productivity has not changed, works more and the home household works less by substituting hours away from the relatively more productive sector. The magnitude of the response to this shock changes little when we consider the alternative options for public revenue, namely distortionary taxes and public debt. In fact, when labor income taxes are the only source of public revenue available, the response of these taxes to the shock is small, implying that the response of all variables is not a¤ected signi…cantly by the revenue sources at the government’s disposal. given sequence of distortionary taxes. We are explicitly concerned with the interaction between debt and tax rates, as parameterized in equation (2.13); debt matters because the tax rate responds to it. 18 In contrast to a shock to nontraded goods productivity, a permanent produc tivity shock to the traded goods sector in one country generates a small price di¤erential. In fact, for our benchmark calibration, a 1% increase in productivity in the home traded goods sector generates a negative home price di¤erential of 0:03 percentage points. The sign of this price di¤erential contrasts with the textbook Balassa-Samuelson e¤ect, where, in response to higher productivity in the traded goods sector, a country experiences an increase in its price level relative to the foreign country.19 In our model, the sign of the price di¤erential associated with a shock to productivity in the traded goods sector hinges on the value of the elasticity of substitution between home and foreign traded goods, °. A permanent shock to home productivity in the traded goods sector leads a producer of these goods to lower its price relative to the price of foreign traded goods. For high values of ° , or high elasticity of substitution between home and foreign goods, both home and foreign agents substitute more towards the home traded good and away from the foreign traded good in response to a given decline in the relative price of home traded goods. Therefore, the higher is °, the bigger is the response of home traded goods output relative to foreign traded goods output and the bigger is the increase in home wage relative to foreign wage to induce the home households to produce relatively more traded goods. That is, for high values of ° the real wage increases relatively more in the home country and the home price level increases relative to the foreign price level, a prediction in line with the textbook Balassa-Samuelson e¤ect. For low values of °, the real wage increases relatively more in the foreign country because agents do not substitute as much towards home traded goods, and the price level increases in the foreign country relative to the home country. We choose a value of ° – 1.5 – that is standard in the literature. Yet, in our model this implies that the conventional Balassa-Samuelson e¤ect does not hold. 5. Fiscal Policy and In‡ation Di¤erentials Because we model the government spending process as exogenous, if a regional …scal authority wishes to in‡uence the behavior of regional in‡ation relative to the rest of the monetary union, its sole means for doing so is to move the labor income tax.20 To study the feasibility and e¤ectiveness of policies aimed at stabi19 See, for example, Obstfeld and Rogo¤ (1995), page 210. assume that if a region wishes to a¤ects its in‡ation rate, it recognizes the dominance of the central bank in determining the overall level of in‡ation, and concentrates on the regional 20 We 19 lizing in‡ation relative to the union, we vary the parameter ®pt; which represents feedback from the regional in‡ation di¤erential to the tax rate.21 To summarize the e¤ects of changes in the policy rule, we simulate the model using the shock processes described above, and illustrate the relationship between the volatility of the in‡ation di¤erential and that of output, the de…cit/GDP ratio, and the tax rate. For our benchmark case of equal sized countries, the results are presented in …gure 5. Figure 5.b displays the relationship between ®pt and the endogenous volatility of the in‡ation di¤erential, as measured by its standard deviation in percentage points.22 Figure 5.b shows that a region within a currency union can reduce the volatility of its in‡ation di¤erential relative to the rest of the union by responding to the in‡ation di¤erential with a negative coe¢cient in the tax rule. In fact, by choosing a strongly negative coe¢cient on the in‡ation di¤erential, a region can essentially force its in‡ation rate to move with that of the rest of the union. Furthermore, this nominal stability does not carry with it instability in real output; …gures 5.A and 5.B together show that as the tax rule coe¢cient on the in‡ation di¤erential is reduced, both the variance of the in‡ation di¤erential and the variance of output fall. However, output volatility is an equilibrium response to given shock processes; decreases in output volatility should not be thought of as necessarily welfare-enhancing. This idea is reinforced by …gure 5.C, which shows the locus of tax rate and in‡ation di¤erential variances. Locally, introducing a negative coe¢cient on in‡ation in the tax rule reduces the variance of the tax rate, but changes in the tax rule that lead to signi…cant stabilization of the in‡ation di¤erential also lead to signi…cantly greater volatility of the distortionary tax rate. Finally, …gure 5.D illustrates the relationship between the volatility of the in‡ation di¤erential and the frequency with which an arbitrary 3% de…cit to GDP ratio is exceeded.23 The Stability and Growth Pact imposes a 3% limit on the de…cit to GDP ratio for member countries of the European Monetary Union. Even in‡ation di¤erential relative to the unionwide average. 21 In terms of units, ® pt is the level derivative of the tax rate with respect to the in‡ation di¤erential. For example, if ®pt = ¡1:0; then an in‡ation di¤erential of one percentage point would decrease the tax rate by one percentage point compared to a situation with zero in‡ation di¤erential. 22 We plot this relationship with the in‡ation volatility on the horizontal axis, instead of the tax rule parameter, because the other panels relate in‡ation volatility to other statistics involving endogenous variables. 23 The probability that the de…cit exceeds three percent of GDP is a monotonic transformation of the volatility of the de…cit to gdp ratio. 20 without a tax rule response to in‡ation, the 3% bound is violated quite frequently – almost 40% of the time – and the frequency increases slightly with policies which substantially reduce the volatility of the in‡ation di¤erential. Fundamentally, volatility in any of the endogenous variables is a result of volatility in productivity and government spending. Thus, the tax rule alters endogenous volatility by altering the response to productivity shocks and govern ment spending shocks. Recall from above that shocks to nontraded productivity and to government spending, as opposed to traded goods productivity, are pri marily responsible for the volatility of price di¤erentials.24 In response to a shock to home nontraded productivity, we saw that the home country’s output rose and its relative in‡ation rate fell. This was in response to a simple permanent shock, as opposed to a shock to the more complicated calibrated process. However, the same qualitative response occurs to a calibrated shock. When the home …scal authority responds with a negative coe¢cient on the in‡ation di¤erential, this tends to raise the home tax rate relative to the benchmark case. The higher tax rate inhibits labor supply, consumption rises less than in the benchmark case, and output actually falls. In addition, home relative to foreign consumption rises less than in the benchmark case. Complete risk sharing implies that the smaller increase in home relative consumption translates into a smaller decrease in the home relative price level. In response to non-traded goods productivity shocks then, a regional …scal policy that responds to in‡ation di¤erentials with a negative sign has the e¤ect of decreasing the variance of in‡ation di¤erentials and output. In the case of government spending, we saw above that a simple random walk shock raised home output. Relative to the foreign country, the shock lowered home consumption and raised the home price level and tax rate. The same qualitative response occurs with our calibrated shock. When the regional …scal authority puts a negative coe¢cient on the in‡ation di¤erential, it responds by decreas ing the home tax rate. This increases labor supply, amplifying the increase in output in the home country. But, the tax response also has the e¤ect of decreas ing the consumption di¤erential across countries, and with complete risk-sharing this translates into a decrease in the in‡ation di¤erential. Thus, with respect to government spending shocks, …scal policy that responds to in‡ation di¤erentials induces a negative relationship between volatility of output and that of in‡ation 24 It is worth (foot)noting, however, that this does not imply that volatility of the price dif ferential for nontraded goods accounts for the volatility of overall in‡ation di¤erentials. In fact, most of the volatility of price di¤erentials across countries in the model is attributable to volatility of the price di¤erential for traded goods. 21 di¤erentials. Because the positive relationship attributable to productivity shocks is stronger, the overall e¤ect of the …scal response to in‡ation is to a¤ect volatility of output and the in‡ation di¤erential in the same direction. Conventional wisdom – associated with a Phillips curve – would say that in order to decrease the volatility of the in‡ation di¤erential a region’s …scal author ity should respond to in‡ation di¤erentials with contractionary policy. Without a Phillips curve we …nd that in order to decrease the volatility of the in‡ation dif ferential, the regional …scal authority lowers the tax rate in response to a positive in‡ation di¤erential. 6. Country Size and In‡ation Di¤erentials Within the European Monetary Union, many of the discussions of regional in‡a tion di¤erentials have concerned small countries, for example Ireland and Portugal. To study the role of country size, we vary the home country’s relative population, N=(N + N ¤ ): Figure 6 displays the same loci as Figure 5, this time for a country that com prises one-third of the union’s population, compared to one-half in the previous …gures. First, note that in Figure 6.B, changes in the tax feedback rule have roughly the same e¤ect on the in‡ation di¤erential for the small country as they do in the symmetric case. And, tax rate volatility has a similar relationship to in‡ation di¤erential volatility as in the symmetric case. However, for a small coun try the relationship between the variances of output and the in‡ation di¤erential is u-shaped instead of positive; decreasing the standard deviation of the in‡ation di¤erential by more than about 30% means increasing the variance of output. To understand the di¤erence between the small and symmetric cases we focus on the interaction of traded goods productivity shocks with country size. A decrease in relative population raises the country’s level of openness, as measured by its export share of GDP.25 Greater openness leads to increased importance of traded goods productivity shocks in accounting for volatility of in‡ation dif ferentials. We might then expect that when …scal policy responds to in‡ation di¤erentials, traded goods productivity shocks drive the relationship between the 25 The relationship between country size and export share follows from the risk sharing condi tion which equates per capita marginal utilities. In the case in which ¾ = a = 1, this condition equates per capita nominal expenditure across countries. Then, to the extent that per capita expenditure is equated for each traded good, smaller countries must have higher export shares. For our calibration, this simple condition does not hold but we …nd the same qualitative result. 22 volatility of in‡ation di¤erentials and the volatility of output. This is indeed the case. The dashed line in …gure 6 shows that, with only traded goods productivity shocks, there would be a negative relationship between the volatilities of the in‡a tion di¤erential and output. For symmetric countries this relationship would be positive. For other shocks there are no signi…cant di¤erences between the small country and symmetric cases. To understand why the dashed line has a negative slope for a small country we turn to the response to a traded productivity shock. For a small country, such a shock causes a positive in‡ation di¤erential, whereas for the symmetric case it generates a tiny negative in‡ation di¤erential.26 Thus, when we allow the tax rule to respond to the in‡ation di¤erential with a negative coe¢cient, for the small country this means the tax rate falls in response to a traded goods productivity shock. For the large country the tax rate instead rises slightly, and output does not rise as much as in the small country. 7. Conclusion This paper investigates the extent to which regional …scal policy can a¤ect the behavior of regional in‡ation in a general equilibrium model of a two-region cur rency union. We …nd that a regional …scal authority can decrease the absolute value of its in‡ation di¤erential in response to the shocks driving the model by lowering (raising) the distortionary tax rate in response to positive (negative) in ‡ation di¤erentials. By simulating the model with calibrated exogenous processes we …nd that the e¤ect on the volatility of output of …scal policies that lower the volatility of the in‡ation di¤erential depends critically on the relative size of the two regions. While for symmetric regions lower volatility of in‡ation di¤erentials is associated with lower volatility of output, in the case of a small region the former comes about with an increase in the volatility of output. An alternative speci…cation of the …scal policy response to in‡ation would work through government spending. There is a tradition of treating government spending as exogenous; we followed this tradition and thus it was natural for taxes to be the instrument of …scal policy. We conjecture that under the alternative speci…cation, the implications of …scal policy responding to in‡ation di¤erentials would mirror those described here.27 26 The small country thus experiences a traditional Balassa-Samuelson e¤ect. It appears that the value of ° above which there is a Balassa-Samuelson e¤ect is increasing in country size. 27 We have in mind that decreases in government spending would imply decreases in the tax 23 We assumed that prices are ‡exible. Our focus on the behavior of in‡ation di¤erentials does not require that the model contain any mechanism for monetary non-neutrality. Flexible prices simplify the model substantially while allowing us to address our question of interest. Nevertheless, it would be natural to add price stickiness to the model. Our model predicts too much variability of the in‡ation di¤erential when compared to the data. Price stickiness might be necessary for the model to match the observed variability of in‡ation di¤erentials. In addition, price stickiness would lead to meaningful time-variation in distortions. It would be interesting to study the e¤ect on these distortions of …scal policies that respond to in‡ation di¤erentials. We are pursuing these issues in ongoing work (see Duarte and Wolman [2002] for a preliminary version). This paper addressed solely positive questions raised by the use of …scal policy to a¤ect in‡ation di¤erentials in a currency union. Our emphasis on positive ques tions was motivated by the attention that has been focused recently on national in‡ation in EMU member countries. Speci…cally, there have been suggestions that countries should pursue policies aimed at a¤ecting their national in‡ation rates. 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[24] Stockman, A. and L. Tesar (1995), “Tastes and Technology in a Two-Country Model of the Business Cycle: Explaining International Comovements,” Amer ican Economic Review 85 (1), 168-185. [25] Taylor, J. (1993), “Discretion versus Policy Rules in Practice,” CarnegieRochester Conference on Public Policy 39, 195-214. 26 Figure 1. Response to a government spending shock, with lump sum taxes (home = solid foreign = dashed) all variables are measured in percent deviations from steady state Figure 2. Response to a government spending shock, with distortionary taxes (home = solid foreign = dashed) all variables are measured in percent deviations from steady state Figure 3. Response to a government spending shock; distortionary taxes respond to debt (home = solid foreign = dashed) all variables are measured in percent deviations from steady state Figure 4. Response to a nontraded productivity shock, with lump sum taxes (home = solid foreign = dashed) Figure 5. Implications of varying degrees of tax rule response to the regional inflation differential (x-axis is standard dev. of inflation differential) Figure 6. Small country, with tax rule response to inflation differential (x-axis is standard dev. of inflation differential) with traded goods productivity shocks only
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