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CESifo-Delphi Conferences on Global Economic Imbalances: Prospects and Remedies CESifo Conference Centre, Munich 11 - 12 November 2005 International Transmission Effects of Monetary Policy Shocks: Can Asymmetric Price Setting Explain the Stylized Facts? Caroline Schmidt CESifo Poschingerstr. 5, 81679 Munich, Germany Phone: +49 (89) 9224-1410 - Fax: +49 (89) 9224-1409 [email protected] http://www.cesifo-group.org International Transmission Eects of Monetary Policy Shocks: Can Asymmetric Price Setting Explain the Stylized Facts? Caroline Schmidt> † August 2005 Abstract How does an unexpected domestic monetary expansion aect the foreign economy? Does it induce an increase or a decline in foreign production? In the traditional two-country Mundell-Fleming model, monetary policy reveals «beggar-thy-neighbor» eects. Yet, empirical evidence from VARs indicates that U.S. monetary policy has positive international transmission eects on both foreign (non-U.S. G-7) output and aggregate demand. In this paper, I show that a two-country dynamic general equilibrium model with sticky prices can account for these «stylized facts» if we introduce international asymmetries in the price-setting behavior of firms insofar as home (U.S.) firms set Mailing address: Konjunkturforschungsstelle der ETH Zürich, Weinbergstasse 35, CH8092 Zürich, Switzerland, Phone: ++41-44-632-6899, Fax: ++41-44-632-1218, E-mail: [email protected]. † I am grateful for comments and suggestions from Mick Devereux at an early stage of this work. Financial support from the Swiss National Science Foundation is gratefully acknowledged. The paper also benefited substantially from two anonymous referee reports. Remaining errors are my own. 1 export prices in their own currency only (producer-currency pricing), whereas producers in the rest of the world price their exports to the U.S. in the local currency of the export market (local-currency pricing). Keywords: Asymmetric price setting, Local-currency pricing, New Open Economy Macroeconomics, International transmission eects of monetary policy, VARs JEL Classification: F41; E52 2 1 Introduction In this paper, I show that allowing for international asymmetries in the price-setting behavior of firms can help to understand the international transmission eects of monetary policy shocks. How does a domestic monetary expansion aect the foreign economy? Does it induce an increase or a decline in foreign production? And is it ‘beggar-thy-neighbour’ or does it raise foreign welfare? In the traditional MundellFleming Model, a monetary expansion at home causes a decline in foreign output. This result is due to the expenditure-switching eect induced by the depreciation of the home country’s currency. However, empirical evidence obtained from vector autoregressions assessing the eects of U.S. monetary policy contradicts this implication. Instead, U.S. monetary policy is rather found to have positive spill-over eects on foreign (non-U.S. G-7) output as well as on foreign aggregate demand. It will be shown in this paper that these stylized facts can be replicated in a generalized SDGE-model with sticky prices if we introduce international asymmetries in the price-setting behavior of firms. With the publication of the Redux model in 1995, Obstfeld and Rogo launched what is now called the “New Open Economy Macroeconomics” (NOEM), a branch of research which aims at developing a new workhorse model for open economy macroeconomics.1 Since 1995 a growing number of extensions to the Redux model have been developed, also concerning pricing decisions of firms. In one extension of this literature, Betts and Devereux (2001, 2000, 1996) show that the price-setting behavior of firms (local-currency pricing compared to producer-currency pricing) crucially determines the direction of the international transmission eects in response to a monetary shock. In Betts and Devereux (2001) the positive transmission eect on foreign output is reproduced for the assumption of complete local-currency pricing in 1 For an excellent survey of the research in this area see Lane (2001a), but also Sarno (2001), Fendel (2002a) and for a more recent contribution Lane and Ganelli (2003). 3 both countries. Yet, this eect is not transmitted to foreign demand, which remains unaected, in contrast to the implications of the empirical evidence. The contribution of this paper is to show that introducing asymmetries in the price-setting behavior of firms across countries in a generalized standard NOEMmodel helps to overcome this shortcoming. Empirical evidence established by Clark and Faruqee (1997) and others, suggests that the degree of exchange-rate passthrough to import prices is noticeably lower in the U.S. compared to other G-7 countries and that most of U.S. trade is invoiced in U.S. dollars. For illustrational purpose, I investigate in this paper the limiting assumption of complete producercurrency pricing in the home country, which represents the U.S., and complete localcurrency pricing in the foreign country representing the rest of the world which is assumed to consist of the non-U.S. G-7 countries. In this setting, I find that a monetary expansion in the U.S. raises production as well as aggregate demand in the foreign country. These results indicate that the suggested asymmetric price-setting behavior provides an explanation to the empirical evidence. The structure of the paper is as follows. The next section assesses some empirical evidence on the international transmission eects of monetary policy, focusing on the results obtained from vector autoregressions. In this context, not only evidence on the international transmission eects of monetary policy on output, but also on consumption and investment is presented.2 It will be shown that for the flexible exchange rate period, starting 1974, U.S. monetary policy has had positive spill-over eects on foreign output for a number of countries as well as for a weighted average of the nonU.S. G-7 countries. This positive international transmission eect is also present for foreign aggregate consumption and investment. In section 3, a generalized NOEMmodel is derived. It also includes a plausibilisation of the asymmetric price-setting behavior. Using a first-order approximation around the symmetric steady-state, a 2 The way consumption is aected might be crucial for the resulting welfare implications. 4 one percent permanent increase in home money supply is investigated. The resulting impulse response functions obtained for the three alternative assumptions on price-setting behavior (complete producer-currency pricing, complete local-currency pricing and asymmetric price-setting behavior) are presented and discussed in section 4. It will be shown that only for the assumption of asymmetric price setting, the empirical findings can be replicated. Finally, the corresponding implications on welfare are presented before section 5 concludes. 2 Empirical evidence Empirical evidence on international transmission eects of monetary policy has been provided by a number of authors, albeit mainly for the U.S. Estimating a two-country VAR, Betts and Devereux (2001) determine the eects of U.S. monetary policy on foreign output. The foreign country (or the ‘rest of the world’) is proxied by a GDPweighted average of the non-U.S. G-7 countries. For the two expansionary monetary shocks considered, Betts and Devereux find that foreign output rises significantly. A positive international transmission eect of U.S. monetary policy on both U.K. and German output is also found by Faust and Rogers (2003), and Miniane and Rogers (2003) provide evidence for a positive international transmission eect of U.S. monetary policy on output even for a large set of countries. Although there is considerable evidence on the transmission eects on foreign output, less evidence has been provided for the eects on foreign aggregate demand. However, if we are interested in the eects on the foreign economy in terms of welfare, the way foreign consumption is aected is crucial. Holman and Neumann (2002) provide evidence for positive spill-over eects of an expansionary U.S. monetary policy shock on Canadian consumption and investment besides output. A more extensive investigation of the international transmission eects of U.S. monetary policy which likewise includes the eects on foreign demand is undertaken by Kim (2001). As 5 in Betts and Devereux (2001), he constructs a weighted average of non-U.S. G-7 countries to proxy for the rest of the world. Besides an - albeit smaller - positive transmission eect on foreign output, Kim also finds an increase in foreign aggregate demand in response to an expansionary U.S. monetary policy shock. However, Kim does not distinguish between consumption and investment. To provide more in depth evidence for the eects on foreign consumption and investment in a two-country-setting, I estimate a two-country VAR similar to the approaches of Betts and Devereux (2001) and Kim (2001) to determine the eects of a U.S. monetary policy shock on a weighted average of non-U.S. G-7 countries’ economic aggregates. As Kim (2001) and Holman and Neumann (2002), I use quarterly data from 1974:1 to 2001:4.3 I consider two alternative monetary policy instruments, the federal funds rate (FFR) and the ratio of non-borrowed reserves to total reserves (NBR/TR). The variables included in the benchmark model are U.S. GDP, U.S. consumer prices (CPI), non-U.S. G-7 GDP, FFR, (NBR/TR), a foreign short term interest rate (IR non-U.S. G-7) and the real exchange rate (REER) for the shock to the federal funds rate. For the shock to the non-borrowed reserves to total reserves ratio, the variable included comprise U.S. GDP, U.S. CPI, non-U.S. G-7 GDP, (NBR/TR), the interest rate dierential between the U.S. and the non-U.S. G-7 and the REER . The real exchange rate is defined such that an increase in REER corresponds to a depreciation of the U.S. dollar. As in Kim (2001), I add the variables of interest one by one as the last element to the system and then re-estimate the VAR for each variable. The system is estimated in levels, where all variables except the interest rates enter the system in logs, and four lags are included. For the identification I use the Choleski decomposition.4 3 The non-U.S. G-7 data are taken from the IMF-IFS CD-Rom, U.S. data stem from the Bureau of Economic Analysis or the Federal Reserve Economic Data. All data are seasonally adjusted except for the interest rates and the exchange rates. 4 For a more detailed description of the analysis and the results, the reader is referred to Schmidt (2004). 6 Figure 1: Impulse responses to a negative one std. dev. innovation in the U.S. federal funds rate 1 CPI US GDP US 1 0.5 0 −0.5 0 5 10 15 FFR US GDP non−US G7 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 −0.5 0 5 10 15 −1 20 0.5 IR non−US G7 1 0.5 NBR/TR 0 0.5 0.5 0 −0.5 0 −0.5 20 1 −0.5 0.5 0 5 10 15 20 0 5 10 15 20 0 −0.5 REER US vs. non−US G7 10 5 0 −5 For both shocks considered, I find significant spill-over eects not only for foreign output, but also for non-U.S. G-7 consumption and investment. In the following, only the resulting impulse responses to a negative one standard deviation innovation of the U.S. federal funds rate are presented, which are displayed in Figure 1.5 The dotted and dashed lines represent one and two standard errors respectively.6 In response to a surprise decrease in the U.S. federal funds rate, both the domestic and the foreign economy experience an increase in output, where the rise in foreign output is more delayed. Also, the U.S. real exchange rate depreciates significantly. Figure 2 displays the eects on foreign consumption and investment. As outlined 5 To facilitate the comparison with the monetary shock in the model, I focus on an expansionary monetary shock. 6 The standard errors are obtained from 1000 Monte Carlo draws following Doan (1992) and Uhlig (2001). 7 Figure 2: Impulse Responses of non-U.S. G-7 Consumption and Investment in response to a negative 1 standard deviation Innovation in the U.S. federal funds rate 1.5 1.5 1 1 0.5 0.5 0 0 −0.5 0 5 10 15 −0.5 0 20 non-U.S. G-7 Consumption 5 10 15 non-U.S. G-7 Investment before, the resulting impulse response functions are obtained by adding the corresponding variables separately as the last element to the benchmark VAR, which is then re-estimated for each individually included variable. As can be seen from Figure 2, both non-U.S. G-7 consumption and investment increase significantly in response to an expansionary U.S. monetary policy shock.7 The maximum eect of a negative one standard deviation innovation of the U.S. FFR on non-U.S. G-7 consumption amounts to an increase of about 0.25% and is almost similar to the magnitude of the rise in non-U.S. G-7 GDP. The peak eect on non-U.S. G-7 investment of 0.7% is about 3 times the size of the increase in GDP. According to these results, an expansionary U.S. monetary impulse not only induces an increase in foreign output, but is also transmitted to foreign consumption and investment. These eects are found to be robust to dierent weightings for the construction of the non-U.S. G-7 variables as well as for dierent identifications of the monetary policy shock, although the magnitude of the eects can be aected.8 The empirical results seem to question some of the implications of traditional 7 U.S. consumption and investment increase as well. Robustness checks comprised the inclusion of a commodity price index to reduce the prizepuzzle eect, which induces a more pronounced eect on foreign investment, whereas the eect on foreign consumption is less important. Ordering the shock first and hence allowing all variables to respond to the shock immediately has almost no eect on the impulse response functions. 8 8 20 monetary open-economy models. They especially cast doubt on the importance of the ‘expenditure-switching’ eect, which drives the transmission to foreign output in most monetary open-economy models such as the Mundell-Fleming and the Dornbusch model, but is also inherent in the Redux model by Obstfeld and Rogo. An effect in the opposite direction on foreign output might occur in response to a monetary induced worldwide decline in the interest rates, causing overall demand to increase. If the latter eect is large enough it will compensate for the expenditure-switching eect and foreign output increases. Kollmann (2001a), who also studies international transmission eects of monetary policy shocks in a NOEM model, obtains a positive transmission on both foreign output and aggregate demand by making use of this second eect. However, his results seem to rely on the extremely low calibration values for interest and consumption elasticities of money demand. Yet, recent estimations of money demand elasticities conducted by Chari, Kehoe and McGrattan (2002) seem to indicate that these are much higher than the values used by Kollmann. As is shown below, employing the values of Chari, Kehoe and McGrattan, the positive spill-over eect on foreign output is not reproduced. A dierent approach to reproduce empirical findings with a theoretical model is followed by Betts and Devereux (2001). Introducing complete local-currency pricing in a two-country SDGE-model with sticky prices, they can replicate the positive transmission eect on foreign output. However, the positive eect is not transmitted to foreign demand. In the following sections, I show that if we introduce international dierences in the price-setting behavior of firms, a dynamic general equilibrium model with sticky prices can account for the positive international transmission eects of monetary policy on both foreign output and aggregate demand, independent of the calibration values for money demand elasticities. 9 3 The Model In the following, a two-country dynamic general equilibrium model with nominal price rigidities in the tradition of the Redux model by Obstfeld and Rogo (1995a), henceforth OR, is derived.9 There are two countries, home and foreign, each inhabited by a continuum of agents normalized to 1. The home country represents the U.S., while the foreign country represents the rest of the world which is assumed to consist of the non-U.S. G-7 countries. Agents consume consumption goods, supply labor and accumulate capital which they rent out to firms. A continuum of individual monopolistic firms resides in the home and the foreign country, which are respectively indexed by } k 5 [0> 1] and } i 5 [0> 1]. Each firm produces a single dierentiated good, whereas labor and capital are assumed to be homogenous and can be substituted across firms without any cost. To distinguish foreign from home agents, the foreign variables will be identified with an asterisk. 3.1 Consumers Preferences of the representative agent residing in the home country have the following explicit form. " # µ ¶13 " 13 X F " P v v + + ln (1 Kv ) X = Hw v3w 1 1 S v v=w Direct utility is derived from consumption of a basket of dierentiated goods Fw , from real money balances Pw Sw , and from leisure (1 Kw ). The parameter denotes the representative home agent’s subjective discount factor. The intertemporal elasticity of substitution is given by 1 , while is crucial for money demand elasticities. 9 Since the main features of the model are standard, the derivation is kept rather brief. 10 The home agent faces the following intertemporal budget constraint. i k + hw Ew+1 + Sw w = (1 + lw ) Ewk + (1 + lWw ) hw Ewi + w Sw Fw + Sw Yw + Pw + Ew+1 +Zw Kw + uwN Sw Nw + Pw31 (1) Nominal expenditures on consumption Sw Fw , investment Sw Yw , money balances i k and hw Ew+1 and the payment of Pw , two internationally traded riskless bonds Ew+1 nominal lump-sum taxes amounting to Sw w may not exceed the sum of nominal returns from last period’s bonds in terms of the home currency, i.e. (1 + lw ) Ewk and (1 + lWw ) hw Ewi , nominal profits w from the shares of home firms, nominal wage income Zw Kw , nominal rental payments received on the capital stock uwN Sw Nw , plus last period’s money balances Pw31 . I assume that all agents within one country hold equal shares of all firms residing in this country, and home (foreign) firms profits are distributed equally among all home (foreign) agents. The explicit form of the law of motion for capital is Nw+1 ! {Nw+1 Nw }2 = (1 ) Nw + Yw = 2 Nw (2) Capital depreciates at the constant rate and increases with investment Yw but at a decreasing rate because of non-linear capital adjustment costs, which are governed by !. The agent maximizes her expected lifetime utility X with respect to Fw > Pw , Kw , i k and Ew+1 subject to her intertemporal budget constraint and to the law Nw+1 , Ew+1 of motion for the capital stock. The resulting first order conditions of the domestic 11 representative agent are 5 Fw3 6 ¶ µ 9 : Sw 9 3 : = Hw 9(1 + lw+1 ) Fw+1 : 7 8 Sw+1 {z } | (3) (1+uw+1 ) " ## 1 " Pw 1 = "Fw Hw Sw 1 1+l1w+1 (4) 1 Zw = Fw3 (1 Kw ) Sw (5) µ ¶ ·µ ¶ ¸ 2 2 Nw+1 Nw+1 Nw ! Nw+2 3 N 3 1+! Fw = Hw 1 + uw+1 + Fw+1 2 Nw 2 Nw+1 (6) (1 + lw+1 ) Hw · · 3 µ ¶¸ 3 ¸ ¡ ¢ Fw+1 Fw+1 hw+1 W = 1 + lw+1 Hw Sw+1 Sw+1 hw (7) The first optimality condition, equation (3), is the Euler equation which determines the optimal intertemporal consumption path. Equation (4) characterizes the money market equilibrium. The third optimality condition, equation (5), determines optimal labor supply, while the agent’s optimal investment decision is determined by equation (6). For the assumption of certainty equivalence used for the linear approximation of the model below, the last optimality condition, equation (7), reduces to the uncovered interest parity. The household’s consumption basket is defined as an aggregate of the consumption of home and foreign goods, which takes the explicit form of a CES-function. ¶ 31 µ ³ ´ 31 ¢ 31 1 1 ¡ i k Fw = Fw + (1 ) Fw 12 (8) Fwk and Fwi are the home agent’s consumption baskets that consist of domestically produced goods and imported foreign goods respectively.10 The coe!cient determines the degree of home bias in consumption, while the parameter denotes the elasticity of substitution between domestically produced goods Fwk and imported foreign goods Fwi . Both Fwk and Fwi consist of a weighted average of home and foreign dierentiated goods each of which is produced by an individual monopolistic firm. The composition of the commodity basket of home goods consumed by agents in the home country is defined as 31 4 31 Z ¡ ¢ 31 Fwk = C fkw } k g} k D = 0 Consumption of foreign goods is allocated analogously. The parameter denotes the elasticity of substitution between dierent goods produced within one country, but also governs the magnitude of the markup. For simplicity, I assume that investment features the same composition as consumption. Then, expenditure minimization of home and foreign agents results in the following total demand for the representative home good k |wk ¶3 Swk [Fw + Yw ] Sw ¶3 µ kW ¶3 µ kW Sw sw (k) + (1 ) [FwW + YwW ] = kW SwW Sw µ sk (k) (k) = w k Sw ¶3 µ (9) Total demand for good k consists of the demand of home and foreign agents weighted with the corresponding expdinture share and depends on relative prices and substitutabilities besides the aggregate level of expenditures for consumption and investment in both countries. The individual price of the representative home 10 A notational remark: The superscript k denotes the goods and prices of home producers, whereas i denotes goods and prices of foreign producers. As goods are traded, we also dierentiate between prices and goods that are valid for respective markets: Variables marked with an asterisk identify goods that are sold in the foreign market and prices that are charged in the foreign currency. 13 good k is skw (k). Swk denotes the price level for the basket of domestically produced goods, which is defined as 1 51 6 13 Z ¡ k ¡ k ¢¢13 k Swk = 7 g} 8 = sw } (10) 0 Correspondingly, Swi , the home price index for imported goods from the foreign country, is defined as 1 6 13 51 Z ³ ´ 13 ¡ ¢ g} i 8 Swi = 7 siw } i (11) 0 ¡ ¢ where siw } i denotes the home currency price of the foreign good variety } i . The domestic price level of all goods purchased by home agents is then a weighted average of Swk and Swi 1 · ³ ´13 ¸ 13 ¡ k ¢13 i Sw = Sw + (1 ) Sw = (12) Accordingly, skW w (k) is the foreign currency price of the representative home good k, SwkW denotes the foreign currency price level of goods imported from the home country and SwW is the absolute consumer price level in the foreign country. As Ricardian equivalence holds in this type of models, assuming a balanced budget has no consequence on the results of the following analysis. For simplicity it is assumed that all seigniorage revenue accruing to the central bank is redistributed to agents in form of a lump-sum transfer Pw Pw31 = Sw w = This reduces the home economy’s budget constraint to i k + Ew+1 hw = (1 + lw ) Ewk + (1 + lWw ) Ewi hw + w + Zw Kw + Sw uwN Nw (13) Sw Fw + Sw Yw + Ew+1 14 3.2 3.2.1 Firms Pricing Each firm will set its price so as to maximize expected profits, taking its individual demand schedule, equation (9), into account. Yet, firms are assumed to set nominal prices in advance. Following Calvo (1983), each firm faces the same constant probability (1 ) every period to change its price next period and to keep the price constant, independent of its history of price changes. By the law of large numbers, a constant fraction (1 ) of firms will actually change their prices each period, while the remaining fraction cannot adjust their prices. Following Betts and Devereux (2001, 2000, 1996) and Engel (2000), I also distinguish between two types of firms who dier in their price-setting behavior. One type, the subset (1 v) of firms, sets one price for its good, independent of the market where the good is sold. Since the price is set in the currency of the producer, this pricing behavior is referred to as producer-currency pricing (henceforth PCP). In the presence of short-run price rigidities import prices of these goods exhibit a complete exchange-rate pass-through. The second type of firm, represented by the remaining fraction v, is assumed to set two dierent prices, one for the home market and one for the foreign market. As both prices are denominated in the respective local currency of the market, this price-setting behavior is referred to as local-currency pricing (henceforth LCP).11 Contrary to the case of PCP goods, import prices of LCP goods are not aected by a change in the exchange rate in the presence of sticky prices. How the two alternative price-setting assumptions aect the international transmission of monetary policy shocks has already been analyzed by Betts and Devereux (2001). However, Betts and Devereux presume throughout their analyses an identical fraction of LCP firms in both countries, which is either set to 0 or 1. 11 Firms are assumed to possess su!cient market power, so that international price dierences for the same good cannot be arbitraged away by agents. 15 Asymmetric Price Setting The contribution of this paper is to consider dierent shares of LCP in both countries, which I refer to as asymmetric price setting. Empirical evidence provided by the ECU Institute (1995) indicates that about 92% of U.S. exports and 80% of U.S. imports are invoiced in U.S. dollars, implying a huge asymmetry in the price-setting behavior between U.S. firms exporting from and foreign firms exporting to the U.S. Further empirical evidence supporting the thesis of international dierences in LCP between the U.S. and other G-7 countries is also provided by Clark and Faruqee (1997). They compare the variance of import prices to the variance of the nominal exchange rate for the G-7 countries and find that while the relative volatility is basically zero for the U.S., it is much higher for the remaining G-7 countries.12 Similar results are provided by Knetter (1989) in a comparison of the U.S. and Germany. The results of Gagnon and Knetter (1995), who assess bilateral automobile export prices from exporters in the U.S., Germany and Japan, suggest that exports to the U.S. and Canada are invoiced in the importer’s currency, while exports to the other countries (Japan, U.K., France, Germany, Australia, Switzerland and Sweden) seem to be invoiced in the exporter’s currency. This asymmetry is also discussed in OR (2000) and Devereux, Engel and Tille (2003), but has not yet been incorporated into a theoretical model of international transmission eects of monetary policy. Yet, a recent contribution by Bacchetta and van Wincoop (2005) addresses the issue of the optimal choice of currency invoicing of exports in a static framework. In their model, this choice depends on the competition firms face in the foreign market. Bacchetta and van Wincoop find that a higher market share in the foreign market provides an incentive for firms to set prices in their own currency and vice versa, which provides a theoretical argument in favour of the asymmetric pricing behavior. In this paper, the asymmetry is implemented in form of the limiting assumption of complete PCP in the U.S. and complete LCP in the rest of the world. In the 12 The estimates of relative volatility range from 0.25 for the U.K. to 0.94 for Italy. 16 dynamic analysis presented in section 4, the transmission eects for the asymmetric price-setting assumption will be compared to the outcome for complete PCP and complete LCP in both countries. Profit maximization of the representative home PCP firm In the presence of price rigidities à la Calvo, firms set prices so as to maximize their expected discounted future profits, which are given by Hw "" X ()l \w>w+l l=0 à Sewk>S FS (k) PFw+l Sw+l Sw+l with \w>w+l = µ Fw+l Fw ¶3 ! # k>S FS |w>w+l (k) =13 k>S FS |w>w+l (k) denotes the expected total demand of the representative home PCP firm at time w + l provided that the price set at time w is still eective. The optimal price of the representative home PCP firm at time w, Sewk>S FS (k), is then derived as a markup over a weighted average of expected future nominal marginal costs. Sewk>S FS (k) = 1 Hw hP " l k>S FS l=0 () \w>w+l Gw>w+l PFw+l hP i " l k>S FS Hw () \ G w>w+l w>w+l l=0 i (14) k>S FS denotes total expected future real sales revenues of the PCP firm, given Gw>w+l that the optimal price chosen at time w is still eective. Since all PCP firms in the home country face the same constraints, each firm that can adjust its price in period w will choose the same price Sewk>S FS (k). The home country price index for home PCP goods S k>S FS is then a weighted average of last period’s price index and the optimal 13 A notational remark: The superscript S FS identifies goods produced and prices charged by PCP firms, the superscript OFS marks the respective variables for LCP firms. 17 price at time w Swk>S FS 1 · ³ ³ ´13 ¸ 13 ´13 k>S FS k>S FS = Sw31 + (1 ) Sew (k) = (15) Profit maximization of the representative LCP firm The representative LCP firm faces essentially the same optimization problem as the PCP firm, but maximizes profits arising from the home and the foreign market, choosing two dierent prices. Expected profits then are Hw "" X à ! k>OFS e S (k) PF w+l k>OFS w |w>w+l ()l \w>w+l (k) S S w+l w+l l=0 à ! # k>OFS>W e (k) h PF S w+l w+l k>OFS>W w |w>w+l + ()l \w>w+l (k) Sw+l Sw+l where \w>w+l is defined as above. Sewk>OFS>W (k) denotes the optimal export price of the representative home LCP firm set in the foreign currency, which is converted to the k>OFS k>OFS>W home currency via the exchange rate hw+l . The quantities |w>w+l and |w>w+l denote home and foreign agents’ demand for the representative home LCP good at w + l given the prices Sewk>OFS (k) and Sewk>OFS>W (k) set at time w. In the log-linearized version of the model, the optimal domestic market price of the home LCP firm is identical to the PCP firm price. Therefore, the home price index for domestically produced goods, defined in equation (10) above, can simply be written as Swk = Swk>S FS = (16) The optimal export price Sewk>OFS>W (k) of the representative home LCP firm is derived as Sewk>OFS>W (k) = 1 Hw hP " l kW>OFS PFw+l l=0 () \w>w+l Gw>w+l hw+l hP i " l kW>OFS Hw () \ G w>w+l w>w+l l=0 18 i (17) kW>OFS Correspondingly, Gw>w+l is defined as expected future real sales revenues of the LCP firm - albeit only in the export market. As the LCP price for the foreign market is set in the foreign currency, the optimal newly set price also depends on the expected future path of the nominal exchange rate, as the LCP firm needs to consider the increase in markup due to a devaluation of the home currency. The price index for domestic goods produced by LCP firms evolves analogously Swk>OFS>W 1 · ³ ³ ´13 ¸ 13 ´13 k>OFS>W k>OFS>W e = Sw31 + (1 ) Sw (k) = (18) As prices in the foreign market dier between PCP and LCP firms, the price index of imported goods is a weighted average of the average prices of foreign LCP and PCP goods Swi>OFS and Swi>S FS>W targeted at the home market. The respective weights are determined by the share vi of foreign LCP firms. Therefore, the home price index of imported foreign goods, defined in equation (11) above, simplifies to Swi 1 · ³ ´13 ¡ ´13 ¸ 13 ¢³ i>OFS i>S FS>W i i = v Sw + 1v = hw Sw (19) For analogous reasons, the foreign price index of goods imported from the home country is defined as 5 SwkW 3.2.2 ³ ´13 ¡ ¢ k>OFS>W k 7 = v Sw + 1 vk à Swk>S FS hw 1 !13 6 13 8 = Production Firms at home and abroad produce under constant-returns-to-scale, employing the following Cobb-Douglas production function, displayed for the example of the representative home firm k |w (k) = Dw Nw (k) Kw (k)13 = 19 Dw represents the common level of technology in the home country, while Nw (k) and Kw (k) denote the individual capital and labor inputs of the representative home firm k. Cost minimization implies that firms will demand factor inputs to satisfy Zw = PFw (1 ) |wk (k) |k = PFw (1 ) w Kw (k) Kw (20) and Sw uwN = PFw |wk (k) |k = PFw w Nw (k) Nw (21) where PFw denotes the nominal marginal costs of production. Since all firms in one country have to pay the same wage and face the same rental rate for capital, marginal costs are the same across all firms residing in one country. 3.3 Market Clearing In equilibrium, all goods, factor and asset markets need to clear in the home and the foreign economy. In the home goods market, aggregated demand consists of demand for LCP and PCP goods ¡ ¢ \wk = vk \wk>OFS + 1 vk \wk>S FS (22) Total supply in the home country can be written as \wk = Z1 0 ¡ ¢ ¡ ¢ Dw Nw } k Kw13 } k g} k = Dw Nw Kw13 (23) since all home firms produce with the same capital-labor ratio. The foreign goods market clears analogously. The home and the foreign money market are in equilibrium if national money demand corresponds to the respective exogenous supplies of home and foreign currency provided by the corresponding national central bank. Bond markets clear in equilibrium if aggregate world assets, i.e. the joint net assets of 20 home and foreign agents, are equal to zero in all periods. 3.4 Equilibrium Equilibrium is characterized by equations (2), (3), (4), (5), (6), (12), (20), (21), (14), (15), (17), (18), (22), (23), (16), (19) and their foreign counterparts, demand equation (9) for both LCP and PCP firms in the home and the foreign economy, as well as equations (7), (13) and the bonds market equilibrium, which gives 39 equations. This is a dynamic system in the following thirty-nine variables, given by [w [w = {Fw > FwW > Kw > KwW > Yw > YwW > Nw > NwW > Zw > ZwW > uwn > uwnW > lw > lWw > PFw > PFwW > hw > Ewk > Ewi Sw > SwW > Swk > Swi > SwkW > Swi W > Sewk>S FS > Sewk>OFS>W > Sewi>S FS > Sewi>OFS > Swk>S FS > Swk>OFS > Swi>S FS > Swi>OFS > \wk > \wi > \wk>S FS > \wk>OFS > \wi>S FS > \wi>OFS } The model is solved by linearizing around the symmetric steady state, where neither country owns net foreign assets.14 The assumption of an international asymmetric degree of local-currency pricing has no consequences for the determination of the steady state, since optimal steady-state prices will be equal to the flexible price solution, which is the same for both LCP and PCP firms. I abstract from real growth due to technological progress and from growth in the monetary base. Hence, in equilibrium all nominal and real variables are constant. 3.5 Calibration The calibrated parameters are presented in table 1. For the baseline calibration, I choose the following parametrization. In line with the business cycle literature, the quarterly real interest rate is set to 1% in the steady state. The consumption elasticity of money demand ( in the model) is commonly estimated to be about 14 For the solution of the model, the MATLAB code provided by Schmitt-Grohé and Uribe (2004) is employed. 21 unity, see, e.g., Mankiw and Summer (1986), which is the value I adopt. For the interest elasticity of money demand ( in the model), the estimates vary from 0=39 in Chari et al. (2002) to 0=051 in Mankiw and Summers (1986).15 For the benchmark calibration, I choose 0=39. The main results are unaected if the value estimated by Mankiw and Summers (0=051) is employed.16 The benchmark values for money demand elasticities imply that is about 2=5. The parameter determines the markup of prices over marginal costs. Consistent with the findings of Basu and Kimball (1997), which suggest a markup of about 10% in the U.S., I assume = 10. The capital share is set to 13 . This value is in line with empirical evidence on the labor share provided by Bentolila and Saint-Paul (2003), which is found to range from 62% to 68% for the G-7 countries in the 1990s. The rate of depreciation is set to 0=021, which implies an annual depreciation rate of about 10%, corresponding to the typical estimates for U.S. data. The steady state share of labour, K 0 , is set to 0=3. For simplicity, the relative preference parameter for real balances, ", is assumed to be 1. The last two assumptions further determine , the preference parameter for leisure, to be 2=8. The price adjustment parameter is set such that the average time between price adjustment for a firm is one year. This implies = 0=75. The import share in the steady state is assumed to be 15% for both countries. While the U.S. average import share in the post Bretton Woods era amounts to about 11%, import shares in the remaining G-7 countries during this time period range from 10% in Japan to almost 30% in Canada. The value for capital adjustment costs ! is set to 8, which induces an investment response to an unanticipated increase in home money supply for the baseline calibration of about 3 times the size of the corresponding output response in the home country, and thus corresponds to the findings of the 15 Both Chari et al. and Mankiw and Summers use consumption as the relevant quantity variable for the estimation of money demand elasticities, which corresponds to the setup in the model. Chari et al. (2002) also implicitly assume a unity consumption elasticity of money demand in their regression. 16 Yet, this result does not hold for an interest rate elasticity of money demand of 0=01 together with a consumption elasticity of 0=2, the values chosen in Kollmann (2001a). 22 VAR analysis. Finally, the elasticity of substitution between home and foreign goods is set equal to 1.5 as found by Hooper and Marquez (1995, Table 4.1) for the U.S. Finally, dierent degrees of pricing to market in both the home and the foreign economy are analyzed to determine the eects of dierent price-setting behavior on the international transmission mechanism of monetary policy shocks. Table 1: Calibrated parameters 2=5 " 1 10 2=5 0=021 1=5 1 ! 8 0=85 1=01 1 2=8 0=75 3 4 Results In this section, the set of impulse responses obtained for a 1% increase in the home nominal money supply is presented for three alternative price-setting assumptions: complete PCP in both countries, complete LCP in both countries and asymmetric price-setting behavior. The plotted impulse responses are percentage deviations from respective steady-state values, except for the interest rates, the current account and net foreign assets. Solid lines show the responses of home variables, dashed lines the corresponding responses of foreign variables. The horizontal axes depict the number of quarters. 4.1 PCP vs LCP Figure 3 displays the impulse responses for complete PCP in both countries, which is the primal assumption made by OR (1995a), as well as in the Mundell-FlemingDornbusch model. In response to the surprise increase in home money supply in period 1, home production as well as home aggregate demand increase. Although foreign consumption and investment experience a temporary — but smaller — increase 23 Figure 3: Impulse responses to a permanent increase in home money supply for the benchmark calibration and complete PCP Home & Foreign Output 1 Home & Foreign Consumption 0.4 0.3 0.5 Home & Foreign Investment 4 2 0.2 0 −0.5 0 0.1 0 10 20 0 0 Terms of Trade 10 20 −2 r, r* 0 0 0 −0.2 −0.05 −2 −0.4 −0.1 −4 −0.6 −0.15 −6 −0.8 0 10 20 −0.2 0 Nominal & Real Exch. Rate 10 20 −8 0 −3 x 10 0 P, P* 1.5 1 1 0.5 0.5 0 10 20 ib, ib* 10 20 CA & NFA in % of GDP 0.4 0.3 0.2 0 0 10 time 20 −0.5 0.1 0 10 time 20 0 0 10 time 20 as well, foreign output is basically unaected. The monetary expansion in the home country causes a decline in the home nominal and real interest rate le and u as depicted in Figure 3. This in turn induces a boom in home demand as implicit returns on consumption and investment in terms of utility and the real rental rate on capital outweigh the associated costs in terms of u. At the same time the home currency depreciates. For complete PCP, import prices exhibit a complete exchange rate pass-through. Thus, the depreciation leads to a decline in the average foreign import price, whereas the average price of home agents’ imports rises. Since the consumer price index which is used to deflate real money balances comprises respective import prices, the monetary impulse initiated in the home country is spread to the foreign economy, inducing an increase in foreign 24 consumption and investment as well. Foreign output, however, remains unchanged since the expenditure-switching due to the change in relative prices redirects the whole augmentation in world aggregate demand towards goods produced at home. This result corresponds to the findings of Betts and Devereux (2001). The impact on the foreign economy depends on the import share, which is presumed to be 15%. As can be seen from Figure (3), the home country experiences a deterioration of its terms of trade. At the same time, the home country runs a current account surplus and accumulates net foreign assets throughout the whole adjustment process. Compared to the findings in OR (1995), who also assume complete PCP, the main implications are similar. In response to the monetary expansion at home, the eect on foreign output is found to be ambiguous in the short run. For a consumption elasticity of money demand equal to 1, as assumed for the simulations presented here, the eect turns out to be negative, while the magnitude depends the monopolistic distortion and on relative country sizes. The eect on foreign consumption is not explicitly derived. Yet, OR show that as the home country runs a current account surplus in response to the shock, foreign agents’ consumption exceeds foreign production in the short run. Let us now turn to the international transmission eects for complete LCP in both countries. The corresponding impulse responses are shown in Figure 4. Again, an unanticipated increase in home money supply raises home production as well as home consumption and investment in the short run. However, when all producers set their export prices in the export currency, the increase in money supply also raises foreign production, whereas foreign aggregate demand even slightly falls. For complete LCP, there is no exchange rate pass-through to import prices. On the one hand, this inhibits the foreign consumer price level to fall and thus prevents a decline in foreign nominal and real interest rates. Therefore, foreign consumption and investment do not rise. On the other hand, with no exchange rate pass-through 25 Figure 4: Impulse response to a permanent increase in home money supply for the benchmark calibration and complete LCP Home & Foreign Output 1 Home & Foreign Consumption 0.3 0.2 0.5 Home & Foreign Investment 4 2 0.1 0 −0.5 0 0 0 10 20 −0.1 0 Terms of Trade 10 20 −2 r, r* 1 0.1 5 0 0.5 0 −3 x 10 10 20 ib, ib* 0 −0.1 0 −0.5 −5 −0.2 0 10 20 −0.3 0 Nominal & Real Exch. Rate 10 20 −10 0 P, P* 1.5 1 1 0.5 0.5 0 10 20 CA & NFA in % of GDP 0.05 0 −0.05 0 0 10 time 20 −0.5 −0.1 0 10 time 20 −0.15 0 10 time 20 to import prices, the expenditure-switching eect is repressed. Hence, the increase in home agents’ demand is directed to both home and foreign goods according to the respective expenditure shares of home agents on imports and domestic goods. Note, however, that although foreign production rises, foreign agents’ income falls. The devaluation of the home currency deteriorates the foreign country’s terms of trade. Whereas foreign import prices basically remain unaected, foreign export prices denoted in the foreign currency fall. Since the deterioration in the terms of trade more than compensates the increase in foreign production, foreign ‘real income’ falls. 26 4.2 Asymmetric Price Setting So far, the same degree of LCP was assumed in both countries. Yet, as outlined in section 3.2.1, empirical evidence indicates asymmetries in the degree of LCP between the U.S. and the other G-7 countries. For illustrational purposes, I consider a stylized scenario where all trade in goods is invoiced in the home currency, i.e. in U.S. dollars. Put dierently, I assume complete PCP in the home country and complete LCP in the foreign country. As displayed in Figure 5, the unanticipated increase in home (U.S.) money supply induces a decline in nominal and real interest rates in both countries, as for the assumption of complete PCP. On this account, foreign consumption and investment rise. At the same time foreign output increases. For complete asymmetric price-setting, a devaluation of the U.S. dollar induced by the U.S. monetary expansion reduces the foreign currency price of foreign country’s imports as in the case of complete PCP. This in turn leads to a decline in the foreign overall consumer price level S W as shown in Figure 5, inducing an increase in foreign real balances. The excess supply on the foreign money market allows for a decline in the foreign nominal and real interest rates, which brings forth an increase in foreign consumption and investment demand. This propagation mechanism corresponds with the one resulting for complete PCP. On the other hand, import prices of foreign goods for home agents do not change with the devaluation, as they are set in the home currency, the U.S. dollar. As there is no exchange rate pass-through to U.S. import prices, home agents have no incentive to switch from foreign to home goods, and the expenditure-switching eect is clearly extenuated.17 Thus, the increase in home demand is directed to both home and foreign goods in proportion to the expenditure shares of U.S. agents. Accordingly, foreign production, which is demand-determined in the short run, increases. Thus, for the specific assumption 17 In this setting, the home country’s terms of trade still improve initially, albeit by much less. The reason is that both home country import prices and export prices (in the home currency) are initially basically fixed, and hence there is not much room for a change in the terms of trade. 27 Figure 5: Impulse responses to a permanent increase in home money supply for the benchmark calibration and complete asymmetric price-setting behavior Home & Foreign Output 1 Home & Foreign Consumption 0.4 0.3 0.5 Home & Foreign Investment 4 2 0.2 0 −0.5 0 0.1 0 10 20 0 0 Terms of Trade 0.1 0.1 0 0.05 −0.1 0 −0.2 0 10 20 −2 0 r, r* 0.15 −0.05 10 20 −0.3 −0.005 0 10 20 −0.01 0 P, P* 1 1 0.5 0.5 0 20 0 Nominal & Real Exch. Rate 1.5 10 ib, ib* 10 20 CA & NFA in % of GDP 0.15 0.1 0.05 0 0 10 time 20 −0.5 0 0 10 time 20 −0.05 0 10 time 20 of complete asymmetric price-setting behavior, the home monetary impulse leads to both, an increase in foreign output and an increase in foreign demand. This result suggests that asymmetric price setting in the export markets might partly be responsible for the documented positive international transmission eects of U.S. monetary policy shocks to output and demand in the non-U.S. G7-countries and can thus contribute to explaining the stylized facts. 4.3 Welfare The price setting of firms is crucial for welfare results. This has already been demonstrated by a number of authors for closed form solutions. Betts and Devereux (2000) explicitly derive how the assumption of local-currency pricing aects the interna28 tional welfare implications of a monetary shock. They show that for a high degree of local-currency pricing, expansionary monetary policy has ‘beggar-thy-neighbour’ effects. Tille (2001) as well as Corsetti and Pesenti (2001) on the other hand find that for producer-currency pricing, monetary policy has ‘prosper-thy-neighbour’ eects and can even be ‘beggar-thyself’ for the country raising the nominal money supply. To provide some further insights into the welfare implications for the three alternative pricing assumptions, the corresponding percentage changes in utility of home and foreign agents were computed.18 As in OR (1995), only consumption and leisure eects are considered for utility. As the eects are derived within a firstorder approximation, the results displayed in table 2 should be viewed only as a first approximation, as the eects of uncertainty are not taken into account. Table 2: Welfare Eects PCP LCP Asymmetric Price Setting dU of home agents 0.00065 0.00670 0.00385 dU of foreign agents 0.00212 -0.00392 -0.00065 Similar to the results derived in closed form solutions, a monetary expansion has ‘prosper-thy-neighbour’ eects for the assumption of complete PCP and ‘beggar-thyneighbour’ eects for the assumption of complete LCP using the baseline calibration. This is due to the reversed eects on foreign output and consumption. As derived above, for the assumption of complete PCP foreign consumption and investment rise while foreign labor supply remains unaected in the short run. For LCP, on the contrary, foreign production (and thus labor input) rises in the short run, without any expansionary eect on foreign consumption. For the asymmetric price-setting assumption introduced in this paper, both foreign output and demand rise in response to the monetary expansion. Hence, the resulting welfare eects are in between the two extreme cases of PCP and LCP. 18 Welfare eects were derived as the discounted sum of all future utility changes compared to the steady state path of utility. 29 5 Conclusion This paper addresses the issue of international transmission eects of monetary policy. In a first step, empirical evidence for positive transmission eects of U.S. monetary policy shocks on non-U.S. G-7 output, consumption and investment was presented. In the remaining part of the paper, I showed that these stylized facts can be reproduced in a two-country dynamic general equilibrium model with sticky prices, if we introduce international asymmetries in the price-setting behavior of producers. Empirical evidence and optimality considerations of firms seem to suggest that most U.S. firms set their prices in their own currency even for goods designated for export and hence pursue a producer-currency pricing strategy. At the same time, because of the size of the U.S. market, producers in Europe and Japan seem more likely to set the prices for their exports to the U.S. in U.S. dollars and hence pursue a localcurrency pricing strategy. This asymmetric price-setting behavior of firms allows for positive spill-over eects of a U.S. monetary shock on the non-U.S. G-7 countries, as the expenditure-switching eect is eliminated in the U.S., while a decline in import prices (and hence the overall price level) in the foreign country remains present, which induces foreign consumption and investment to rise. Therefore, asymmetries in the price-setting behavior of firms across countries seem promising for a better understanding of the international transmission of business cycles induced by monetary policy. 30 References Bacchetta, Philippe & Eric Van Wincoop (2005), ‘A Theory of the Currency Denomination of International Trade’, Journal of International Economics (forthcoming) . Basu, Susanto & Miles S. 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