International Policy Coordination and Simple Monetary Policy Rules

Berger, Wolfram Article International Policy Coordination and Simple Monetary Policy Rules Swiss Journal of Economics and Statistics Provided in Cooperation with: Swiss Society of Economics and Statistics, Zurich Suggested Citation: Berger, Wolfram (2010) : International Policy Coordination and Simple Monetary Policy Rules, Swiss Journal of Economics and Statistics, ISSN 2235-6282, Springer, Heidelberg, Vol. 146, Iss. 2, pp. 451-479, https://doi.org/10.1007/BF03399323 This Version is available at: https://hdl.handle.net/10419/185957 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Phone +33 320 54 58 92, fax +33 320 57 48 55, email w.berger(at)ieseg.fr, and Technical University of Cottbus, Konrad-Wachsmann-Allee 1, 03046 Cottbus, Germany. International Policy Coordination and Simple Monetary Policy Rules Wolfram Bergera JEL classification: F41, F42, E52, E58 Keywords: policy coordination, policy rule, consumer price targeting, producer price targeting, monetary targeting 1. Introduction What is the optimal design of monetary policy in open economies? This is a long-standing issue in monetary economics. From the most recent debate it is far from clear that monetary policy in open economies should have any international dimension at all. Several writers including Clarida, Gali and Gertler (2002), Gali and Monacelli (2005) and Obstfeld and Rogoff (2002) make a strong case in favor of an inward-looking monetary policy. They argue that producer prices should be chosen as a target for welfare maximizing monetary policy. The baseline of these studies is that international integration in goods and financial markets decreases the need to take account of macroeconomic developments abroad when deciding about the optimal monetary policy stance. According to these authors there is in effect no difference in the policy problem faced by policymakers in closed and open economies. However, authors such as Corsetti and Pesenti (2005), Devereux, Lane and Xu (2004), Kollmann (2002), Smets and Wouters (2002) and Sutherland (2005, 2006), point out that this result only holds in relatively simple models. More complex models imply that targeting producer prices is generally not optimal. Hence, the debate in the literature on optimal monetary policy in times of highly integrated goods and financial markets is far from settled. The optimal choice of the monetary policy target, the weight assigned to external factors in monetary policy decisions and the question, which simple, i.e. non-optimal, 452 Wolfram Berger targeting rule can best support the efficient resource allocation belong to the issues that are controversially discussed. Employing a stochastic general equilibrium framework of the New Keynesian type, this paper addresses these questions by accounting for an important change in the nature of international cross-country linkages brought about by globalization. The production sequence of final consumption goods increasingly stretches across many countries and is associated with vertical trade. In the light of these changes, the interdependence of countries is increasingly based on trade along vertical production chains. That is, cross-border trade involves both intermediate and final goods (see Hummels, Ishii and Yi, 2001 and Yi, 2003). The aim of this paper is to investigate how these structural changes impact the monetary policy design. We therefore differentiate between final consumption goods and the intermediate goods needed to produce them. A fraction of final goods producers has to set the nominal prices of consumer goods in advance of the realization of shocks, while prices of intermediate goods are taken to be perfectly flexible. We further suppose that the degree of pass-through for consumption goods prices may be less than complete, and as in Sutherland (2005), both productivity and cost-push shocks are considered. We are not only interested in the optimal monetary policy in this model but also investigate a range of simple targeting rules as guidelines to assess policy options and prepare policy decisions. Obstfeld (2001) and Devereux and Engel (2007) also consider two-stage production processes but, contrary to our model, trade only occurs on one level in their models. Huang and Liu (2004) investigate the impactof monetary shocks in a model with a multistage production chain. Shi and Xu (2007) also present a model with more than one production stage and stage-specific productivity shocks and examine the optimal monetary policy in this framework. They also deal with the value of exchange rate flexibility under full and zero pass-through. Our approach differs from these previous studies. We are not only interested in the welfare-maximizing monetary policy but also in the welfare effects of simple policy rules in the presence of different types of shocks – productivity and costpush – and varying degrees of pass-through and cross-country interdependence in production. The goal is to present an encompassing model that enables us to examine whether and how a range of different factors influences the effects and, therefore, the design of monetary policy in open economies. In this model, and in contrast to other related papers such as those cited above, world aggregate welfare is maximized when monetary policy responds to both types of shocks irrespective of whether they originate at home or abroad. Further, which simple targeting rule performs best in welfare terms in our model hinges International Policy Coordination and Simple Monetary Policy Rules 453 1 Another major difference between Sutherland’s and this paper is that in our model not only productivity but also cost-push shocks give rise to changes in the socially optimal resource allocation and thus call for a monetary policy reaction. 2 It would also have been possible to model the simple policy rules in the form of instrument (Taylor-type) rules in this paper. See, e.g., McCallum and Nelson (2005) and Svensson (2005) for a discussion on the merits of targeting and instrument rules. critically on two factors, the degree of the cross-country vertical integration in production and the relative importance of productivity and cost-push shocks. Generally, following a policy rule that allows for some degree of price flexibility such as monetary targeting generates better welfare results than strictly targeting a well-defined price index in the presence of comparatively strong cost-push shocks. However, if productivity shocks predominate, a well-defined price index like the producer or the consumer price should be chosen as the monetary policy objective. If price targeting rules turn out to be best, the degree of vertical integration is decisive for which price index fares best as monetary policy objective. Producer price index targeting only generates better welfare results than CPI targeting if vertical integration between countries is either rather low or rather high. Stabilizing foreign goods prices, too, as is done under CPI targeting does not yield any additional benefit then. In these cases, the consumption goods production nearly entirely relies on either domestic or foreign inputs so that the marginal production costs of home and foreign consumption goods (and thus their prices) are almost completely determined in either country. A policy that is only concerned with the stabilization of domestically produced goods prices – where, from a global point of view, it does not matter whether home goods prices are stabilized by home or foreign monetary adjustments – therefore comes closest to the optimal policy rule for this parameter combination. Our analysis of simple targeting rules therefore lends support to the conclusion derived in other papers (see above) that the producer price index is the optimal choice of a monetary policy target in an open economy only under very special conditions. These results extend previous work in the literature on monetary policy rules. In a related paper, Sutherland (2005) also finds that the welfare performance of a range of simple targeting rules depends on the relative volatility of costpush and productivity shocks. However, as opposed to the model presented in this paper, Sutherland does not aim at examining the effect of increasing crosscountry interdependence on the choice of simple monetary rules.1 A large part of the literature investigates simple monetary policy rules by using Taylor type rules (see, e.g. Feve, Matheron and Poilly, 2007 who estimate Taylor rules for the eurozone and Bullard and Singh, 2008 as recent examples).2 Leith 454 Wolfram Berger 3 To keep the model tractable and to be able to derive results analytically, we stick to a static model. and Wren-Lewis (2009) investigate whether consumer price inflation might be a better target than producer price inflation in a two-country model. They also argue in favor of the producer price index as the monetary policy objective based, however, on a different reasoning than the literature cited above. They conclude that the adoption of inflation targets based on consumer prices could be a cause of concern since that may result in indeterminacy, such that there will not be a unique perfect foresight equilibrium path. This can be avoided by choosing the producer price index. Other papers demonstrate the merits of an interest rate peg in a standard New Keynesian model of a closed economy (Hoermann and Schabert, 2009) or argue in favor of forecast-based rules (Batini, Harrison and Millard, 2003 in a model that is calibrated using data for the UK). The closed economy context and the inclusion of inflation forecast rules, i.e. rules that prescribe an reaction to deviations of expected inflation from target, distinguish the latter two papers significantly from ours. The remainder is structured as follows. The model is developed in the next section. In section 3, the welfare criterion is derived and the determination of consumption and output is discussed. In section 4, the optimal monetary policy rule and welfare under the optimal policy rule are derived. Section 5 compares the welfare results of four simple targeting rules with the help of a simple numerical example. Section 6 concludes. 2. The Model 2.1 Basic Assumptions The world economy consists of two equally sized countries inhabited by a continuum of households of the yeoman-farmer type.3 Households over the [0,1] interval live in the home country, while households in the (1,2] interval are residents of the foreign country. Analogously, goods over the [0,1] interval are produced in the home country while goods in the (1,2] interval are produced in the foreign country. In the following sections, the equations for the representative home household are presented while the equations for the representative foreign household are omitted most of the time. Generally, mirror images hold for the foreign country. Throughout the paper, an asterisk indicates a foreign variable. International Policy Coordination and Simple Monetary Policy Rules 455 4 This framework can be thought of as a static version of Calvo (1983)’s staggered price setting. 5 The production technology is linear in work effort (see below). Following, e.g., Sutherland (2005) we suppose that consumption goods are produced by two type of agents. The first type of agents, called “fixed-price agents”, is required to set prices before shocks occur and monetary policy is set. The second type, called “flex-price agents”, operates in markets where prices are set after the realization of shocks and the setting of monetary policy. In both countries, the share of fixed-price agents in the population is given by v, so that 1 − v is the share of flex-price agents. v can therefore be interpreted as a measure of the degree of price stickiness.4 Markets for intermediate goods, however, are characterized by full price flexibility. That is, all intermediate goods producers are flex-price producers. In the following, the subscript “1” (“2”) will indicate variables related to fixed-price (flex-price) agents. 2.2 Preferences and Prices The utility of the representative home household is given by log log ( ) 0 M UE C Kyz P χχ ⎡⎤ =+−,>. ⎢⎥ ⎢⎥ ⎣⎦ (1) C denotes a consumption index defined below; M denotes the domestic end-ofperiod money stock, P is the consumer price index (also defined below) and y(z) is the output of intermediate good z. E is the rational expectation operator and K denotes a stochastic shock to the labor supply (productivity shock). The third term on the right hand side expresses the disutility of work effort in terms of output.5 Both home and foreign shocks are symmetrically distributed over a finite interval with [log ] [log ] 0EKEK ∗ == and 2 [log ] [log ] . K VAR K VAR K σ ∗ == The consumption indices are defined as: 11 1 1 22 2 2 2( ) ( ) 2( ) ( ) HF FH CCCC CC ∗∗∗ =,=. (2) Combined with the assumption of zero initial non-monetary wealth, the structure of the preferences implies that financial markets are redundant (see Cole and Obstfeld (1991) and Corsetti and Pesenti (2005)). Home and foreign 456 Wolfram Berger consumers share their consumption risks perfectly without financial markets. The ratio of marginal utilities in consumption is equal to the ratio of aggregate prices, (C / C ∗)−1 = P / (SP ∗ ), where P and P ∗ denote the home and the foreign countries’ CPI and S is the exchange rate expressed as the price of foreign currency in home currency. CH and CF are indices of home and foreign differentiated consumption goods with 11 12 12 ()() ()() vv vv HHH FFF CCC CCCμμ −− ,, ,, =,= (3) with μ = v−v(1 − v)−(1−v). The bundles of fixed-price and flex-price consumption goods are defined as CES aggregates over individual consumption goods with the elasticity of substitution φ for all bundles. CH,i(z) and CF,i(z∗) denote a home household’s consumption of a particular brand produced by type i. z denotes a home variety, z ∈ [0,1], while z∗ ∈ (1,2] denotes a foreign variety. The price indices corresponding to the consumption goods indices are derived in the usual way. The CPI and the producer price indices are given by 11 22 HF PP P= (4) 11 12 12 vv vv HHHFFF PPPPPP −− ,, ,, =,=. (5) The price indices of fixed-price and flex-price goods are 11 11 1 11 1 1 11 11 ,2 2 0 12 11 11 2 2 11 11 () () , 1 11 () () 1 v HH H H V v FF F F v PPzdzP Pzdz vv PPzdzP Pzdz vv φφ φ φ φφ φφ −− − − −− ,, , ⎡⎤ ⎡⎤ +⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ∗− ∗ ∗− ∗ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ,, , , ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥+ ⎣⎦ ⎣⎦ ⎡⎤⎡ ⎤ ⎢⎥⎢ ⎥ =,= ⎢⎥⎢ ⎥ − ⎢⎥⎢ ⎥ ⎣⎦⎣ ⎦ =,= . − ∫∫ ∫∫ (6) PH,i(z) and PF,i(z∗) are individual goods prices denominated in home currency. 2.3 Production We differentiate between final consumption goods and the intermediate goods needed to produce them. In both countries, producers in the final consumption goods sector and in the intermediate goods sector enjoy a degree of monopoly International Policy Coordination and Simple Monetary Policy Rules 457 6 The production technology can be explicitly written as y(z ) = K −1h with h denoting the work effort of the representative household. Shocks K > 0 are therefore negative productivity shocks reducing the quantity of goods produced with a given labor input. power. Final commodities are produced by bundling a continuum of differentiated intermediate goods. Both countries operate the same technology: 1 () 12 Hi H F Yz yy i αα κ− ,=,=,, (7) with κ = α−α(1 − α)−(1−α). yH and yF denote bundles of home and foreign intermediate goods, which are defined as CES aggregates over individual intermediate goods with an elasticity of substitution of ω. The parameter α is understood as a measure of the degree of vertical integration in goods production. A high value of α means that cross-country vertical integration in production is quite low while a low value of α indicates a quite pronounced cross-country interdependence in production. The demand for home intermediates stems from home and foreign countries’ consumption goods producers. The aggregate equilibrium conditions for home and foreign intermediate goods read 11 11 (1 ) , (1 ) HH HH H F II FF FF H F II pp yy y Y Y ppS ppS yyy Y Y pp αα αα −− ∗∗ ∗ −− ∗∗ ∗∗ ∗ ∗ ⎡⎤ ⎡ ⎤ ⎢⎥ ⎢ ⎥ =+= + − ⎢⎥ ⎢ ⎥ ⎣⎦ ⎣ ⎦ ⎡⎤ ⎡ ⎤ ⎢⎥ ⎢ ⎥ =+= − + . ⎢⎥ ⎢ ⎥ ⎣⎦ ⎣ ⎦ (8) pH and p∗ F are the price indices of the home and foreign intermediate goods bundles. pI and p∗ I denote the intermediate goods price indices in home and foreign currency which are given by (1 ) ()( ) IHF ppSp αα∗− = and (1 ) ()( ) . IFH pppS αα∗∗ − = The law of one price holds for individual intermediate goods. Purchasing power parity in terms of intermediate goods bundles, however, does not hold owing to the home bias in the production of final goods. It is further assumed that each household produces a differentiated intermediate good. The production of an intermediate good requires labor input only. The domestic and foreign production technologies are identical and are linear in hours of work. One unit of labor input yields one differentiated intermediate good.6 458 Wolfram Berger 2.4 Consumption and Money Demand Households decide optimally about their (intratemporal) consumption allocation and their money holdings. Home household’s demands for home fixed-price and flex-price goods, CH,1(z) and CH,2(z), and for foreign fixed-price and flex-price goods, CF,1(z∗) and CF,2(z∗), are given by 11 11 111 1 11 22 222 2 1 11 1 () 11 () , 2 () 11 () (1 ) , 12 () 1 () HH H HHH HH HH H HHH HH F FF F Pz P P Cz C C v C vP P P Pz P P Cz C C v C vP P P Pz Cz C vP φ φ φ −−− ,, ,,, , −−− ,, ,,, , − ∗ , ∗ ,, , ⎡⎤ ⎡⎤ ⎡⎤ ⎢⎥ ⎢⎥ =,= ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎣⎦ ⎢⎥ ⎣⎦ ⎣⎦ ⎡⎤ ⎡⎤ ⎡⎤ ⎢⎥ ⎢⎥ =,=− ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ −⎣⎦ ⎢⎥ ⎣⎦ ⎣⎦ ⎡⎤ ⎢⎥ =, ⎢⎥ ⎢⎥ ⎣⎦ 11 1 1 11 22 222 2 1, 2 () 11 () (1 ) 12 FF F F FF F FFF FF PP Cv C PP Pz P P Cz C C v C vP P P φ −− , , −− ∗− ,, ∗ ,,, , ⎡⎤ ⎡⎤ ⎢⎥ =⎢⎥ ⎢⎥ ⎢⎥ ⎣⎦ ⎣⎦ ⎡⎤ ⎡⎤ ⎡⎤ ⎢⎥ ⎢⎥ =,=−. ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ −⎣⎦ ⎢⎥ ⎣⎦ ⎣⎦ (9) Foreign demands can be described by similar equations. The representative home household of type i = 1,2 faces a budget constraint that is given by: 0(1 )[ () () () ()] (1 ) ( ) ( ) f Hi Hi Hi Hi int HHHFF MM PzC z SPzC z p z y z PC PT p y p y τ τ ∗∗ ,, ,, −=+ + ++ − − − − . (10) M0 and M are money holdings at the beginning and at the end of the period. T denotes real lump-sum taxes in terms of the consumption index and τint and τf are (the usual) production subsidies for final (f) and intermediate goods (int) producers. Households’ optimal money demand is derived by maximizing their utility function subject to their budget constraint. The first order condition for the optimal money demand implies that money market equilibrium is given if M = χPC. The money supply is set by the central bank by following a monetary rule that may depend on all shocks. International Policy Coordination and Simple Monetary Policy Rules 465 is set by following a monetary rule that may depend on the shocks K, K ∗, ϕ and ϕ ∗. The home policy rule is given by 0. KK MMKK ϕϕ δ δδ δϕϕ ∗ ∗ ∗∗ = Expressed in log deviation form, we have ˆˆˆˆˆ KK MK K ϕϕ δδ δϕδϕ ∗∗ ∗∗ =+ ++. (20) The reaction parameters , K δ, K δ∗ϕ δand ϕ δ∗are chosen before shocks occur and prices are set. 4.2 Optimal Monetary Policy and Welfare Optimal rules are chosen by optimally setting the feedback parameters , K δ , K δ∗ϕ δ and ϕ δ∗ for the home economy and their counterparts , K δ∗, K δ∗ ∗ ϕ δ∗ and ϕ δ∗ ∗ for the foreign economy. If monetary policy is internationally coordinated, the single world central bank specifies the home and foreign policy rules by choosing the following set of feedback parameters: 22 22 22 22 2(2 1) [1 ( 2)] 2(2 1) [1 ( 2)] 2 (1 )(1 )(1 4 (1 )) [1 ( 2)] 2 (1 )(1 )(1 4 (1 )) [1 ( 2)] C C C C C KK C K K C C uv b u vuu uv b u vuu v vuu v vuu ϕϕ ϕ ϕ δδ δδ ηη αα δδ ηη αα δδ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ −− ==− +− +− ==+− +−− − ==− +− −−− − == . +− (21) The superscript “C” indicates the cooperative case. The feedback parameters for the coordinated solution show that the optimal monetary policy for complete price flexibility (v = 0) is undefined. In this case output and work effort are exogenously determined and completely independent of monetary policy (see equation (21)). Hence, aggregate welfare (16) cannot be affected by monetary policy. If, however, price flexibility is less than perfect, monetary policy is able to influence the resource allocation (see the discussion above). Equations (21) show that both policymakers (generally) react to both home and foreign productivity and home and foreign cost-push shocks. A shock that lowers productivity in the intermediate goods sector ˆ (0 )K> leads to an increase in the marginal production costs of consumption goods and causes the socially 466 Wolfram Berger 14 As discussed above, global welfare depends only on the variance of the disutility of work effort (see equation (16)). optimal level of work effort in the home country to fall.14 Flex-price consumption goods producers react by raising prices while fixed-price producers are unable to do so by definition. A monetary contraction is therefore required to stabilize marginal costs and thus the mark-up. However, whether this monetary contraction occurs in the home or in the foreign country depends on the degree of vertical integration given by α. The policymaker, whose country uses relatively more of the home input goods to produce final consumption goods, is best suited to reduce work effort in the home country by reducing the demand for its consumption goods. The other country reacts exactly inversely and thus adds to the effect on the global resource allocation by intensifying the resulting exchange rate changes. Hence, monetary policy adjustments in both countries work in the same direction. Neither the home nor the foreign policymaker react in the special case that α = ½. In this case, a productivity shock anywhere in the world cannot be smoothed by redirecting global consumption demand and thus work effort. Since both countries rely on home and foreign inputs in equal shares, shifting consumption from home to foreign goods or vice versa has no affect on work effort. Sutherland (2005) points out that cost-push shocks do not give rise to any change in the socially optimal level of work effort. A welfare-maximizing monetary policy thus does not provide for a response to this type of shocks. In our model, however, cost-push shocks in one country also lead (generally) to a monetary policy reaction in both countries. As long as there is a minimum degree of price flexibility, responding to cost-push shocks is optimal for the policymakers unless α = ½. The existence of a home bias (α ≠ ½) gives the home and, if there is a certain but less than complete degree of pass-through (0 < η < 1), the foreign policymakers an incentive to react. Flex-price producers in the consumption goods sector react to a positive cost-push shock (ϕ > 0) by raising prices. The resulting contraction in demand for flex-price consumption goods translates into a fall in demand for intermediate goods at home and abroad and thus affects work effort in both countries. To reduce work effort of fix-price producers a monetary contraction is required that gives rise to a fall in consumption demand. The foreign policymaker reacts exactly inversely. A shock ϕ > 0 causes a foreign monetary expansion that reinforces the appreciation of the domestic currency and thus helps to redirect international demand away from home toward foreign consumption International Policy Coordination and Simple Monetary Policy Rules 467 15 As pointed out above, fixed-price output is insulated against cost-push shocks (cost-push shocks do not affect the socially optimal level of work effort) so that a monetary response for v = 1 is not required. goods. For similar reasons as spelled out above, the home and the foreign policymaker do not respond to cost-push shocks if α = ½. Whether the foreign policymaker adjusts the foreign money supply in response to a home cost-push shock depends critically on the degree of pass-through η. While the strength of the home monetary policy response increases in η, the foreign policymaker reacts less aggressively if η increases. The higher η is, the more the adjustment burden is shifted to the home policymaker. If the pass-through is complete, the foreign money supply is not adjusted anymore if cost-push shocks occur in the neighbor country. Then, the substitution and the income effect of monetary changes abroad exactly cancel each other out. Similarly, if there is no pass-through (η = 0), the foreign policymaker does not react to home cost-push shocks because international demand cannot be shifted away from home towards foreign goods and vice versa through exchange rate changes. If consumption goods prices are completely sticky (v = 1), there is no response to cost-push shocks when policies are coordinated, either. The reason is that in this case output of consumption goods is not affected by cost-push shocks and therefore work effort expended in the production of intermediates is not altered.15 Similarly, for α = ½ there is no reason for a monetary policy adjustment. If there is no home bias in the production of intermediate goods, the effects of a change in final goods demand are equally split between the home and the foreign country. Hence, the policymakers need not intervene to reach the welfare-maximizing allocation of work effort between both countries. Generally and in contrast to the work of Sutherland (2005), however, not reacting to cost-push shocks is not optimal. 5. Simple Rules and Welfare 5.1 Simple Targeting Rules The optimal monetary policy rules have a relatively simple form in this model. Optimal rules, however, might become highly complicated and hardly feasible to compute in more complex models and thus impossible to implement in practice. This section is therefore devoted to the analysis of simple, i.e. non-optimal, policy rules. Simple rules are not understood as a specification that the policymaker 468 Wolfram Berger 16 Interpreted in this sense, a simple rule gives the central bank a fallback option for difficult times. 17 All rules are only considered in their strict form, i.e. policymakers are assumed to ignore other objectives. 18 Sutherland (2005) shows that asymmetric regimes are welfare inferior to symmetric ones in a model where both economies are mirror images of each other as in our model. 19 This definition is similar to the definition of a specific targeting rule introduced by Svensson (2002). Svensson, however, reserves the term target for variables that enter the policymaker’s objective (loss) function. should follow mechanically. Instead, we interpret them as a guideline to assess policy options and prepare policy decisions. This implies that large departures from what these rules suggest need to be explained carefully.16 Hence, simple rules are considered as a means to think about the best monetary policy stance. This section is therefore devoted to the welfare analysis of simple targeting rules. The key question now is: which simple policy rule best supports the world coordinated policy? Welfare associated with the targeting rules is evaluated at the global level, i.e. based on the global welfare criterion (16). Our aim is to evaluate the performance of price targeting rules such as producer and consumer price targeting that do not allow for fluctuations in a well-defined price index and of rules that allow for some degree of price flexibility and thus provide the policymaker with the opportunity to stabilize real aggregates as well.17 As an example for the latter type of policy rules we investigate monetary targeting (which implies the stabilization of nominal consumption through the money market equilibrium condition). We concentrate on symmetric policy regimes, i.e. we assume that the policymakers in both countries follow the same rule.18 We stick to a very basic formulation of policy rules to illustrate our points as discussed in the Introduction. For a discussion and evaluation of more complex non-optimal policy rules like forecast-based rules, the reader is referred to the literature reviewed above. In our model, a targeting rule is taken to mean a rule that eliminates all fluctuations in the targeted variable. Hence, a rule that targets variable X is modeled as a rule for the money supply that leads to ˆ0X= ex post. This is in line with McCallum and Nelson (1999), who define a targeting rule as a commitment to set the policy instrument rate so that a pre-defined target for the target variables is realized.19 In this paper, the simple targeting rules are expressed as statecontingent rules for the money supplies at home and abroad. The specification of the policy rules for the home economy is summarized in Table (1) (see the Appendix for details). Generally, mirror images hold for the foreign economy. International Policy Coordination and Simple Monetary Policy Rules 469 Table 1: Simple Targeting Rules Target Monetary Rule Producer Price Index ˆˆˆ ˆ (1 ) PPI MKKααϕ ∗ =− − − − Consumer Price Index 1 2 ˆˆˆ ˆˆ [] CPI MKKϕϕ ∗∗ =− + + + Money Supply ˆ0 MS M= In contrast to producer price index and money supply targeting and in accordance with the optimal policy rule the policymaker generally responds to all types of shocks irrespective of their origin under a policy of consumer price index targeting. None of these rules, however, is able to implement the welfare-maximizing resource allocation for the whole range of parameter combinations. Which one comes closest to the optimal rule as measured by its welfare implications depends on the degree of the cross-country interdependence in production, measured by α, and the relative importance of productivity and cost-push shocks. When evaluating the welfare implications of alternative targeting rules one has to keep in mind that the criterion for global welfare, given in equation (16), only depends on second moments. Non-stochastic terms therefore need not be considered in the formulations of the money supply rules and when calculating welfare. Since fixed-price agents enter a period with preset prices, optimal prices given in equations (11) and (12) are non-stochastic and therefore play no role in the welfare analysis. To allow for a meaningful discussion of price targeting rules, the monetary rules and welfare in this section are derived for v < 1. The welfare levels under each targeting rule are given in Table (2). Table 2: Targeting Rules and Welfare Target Welfare Producer Price ()() 22 , 2 22 1 1 2 2 22 2 22 1 2 ( (1) (1(21)) 1(21)) (1 ) (1 ) (1 ) (1 )(1 (2 1) ) G PPI K Wvbv vb v vu v bvv ϕ σ ηα ηα ηα σ ⎡⎤ =− + − −− + − − − ⎢⎥ ⎣⎦ ⎡⎤ −++−−+−+− ⎢⎥ ⎣⎦  Consumer Price ,22222 11 22 (2 ) (1 ) (1 ) (2 1) GCPI K Wvvvbvb ϕ σσ ⎡⎤ =− − + − − − − ⎢⎥ ⎣⎦  Money Supply () ,2 2 2 1 2 2(1) (1)(1(2)) GMS K Wvbb bvv ϕ σσ=− − + − − − −  470 Wolfram Berger 20 This result is in line with Sutherland (2005). 5.2 Numerical Example The welfare results are further illustrated with the help of a numerical example. The parameter setting chosen for the numerical simulation is taken from the literature. The share of fixed price agents is assumed to be v = 0.75 so that a certain degree of price flexibility is retained. For the parameter measuring the degree of pass-through in the home and foreign country we assume η = η∗ = 0.46, which corresponds to empirical evidence for the short run average pass-through elasticities across OECD countries (see, e.g., Campa and Goldberg, 2005 and Choudhri and Hakura, 2001). We examine three different cases. In the first case, both productivity and costpush shocks are equally important. Formally, 22 1. Kϕ σσ== In the second case, we suppose that productivity shocks are much more important than cost-push shocks. Formally, this case can be captured by assuming that σK 2 = 1 and σϕ 2 = ⅓. In the third case, the assumption concerning the relative importance of shocks is reversed, i.e. we now suppose that σK 2 = ⅓ and σϕ 2 = 1. Figures (1)–(3) summarize the welfare results for varying degrees of the home bias parameter α. Figure (1) clearly shows that a policy such as monetary targeting that allows for some price flexibility is welfare superior to strictly targeting a price index if both types of shocks are highly volatile.20 Demand for intermediate goods can be smoothed most effectively by stabilizing a combination of real aggregates and prices as in the case of monetary targeting. Thus, the needed flexibility in prices in the presence of substantial cost push shock volatility is allowed for. A key point of this paper, as pointed out above, is that work effort in the home country generally depends on all types of shocks in a highly interdependent world irrespective of the country they hit. A policy of CPI targeting is therefore generally superior in welfare terms to targeting the producer price index. In line with the optimal monetary policy, monetary policy under CPI targeting responds to all shocks (see Table 1). Producer and consumer price index targeting only generate almost equal welfare results if α is around ½. In this case, both strategies imply similar responses to productivity shocks at home and abroad (see Table 1). The different responses to foreign cost-push shocks under producer and consumer price index targeting then are only of the second order. Since an equal share of consumption spending is allocated to home and foreign goods, increases in final goods prices have an identical impact on work effort in the home and foreign country if there is no home bias in production. Hence, producer price index targeting which implies a quite strong monetary policy reaction to the domestic International Policy Coordination and Simple Monetary Policy Rules 471 21 See the literature cited in the Introduction. cost-push shock generates identical welfare results as CPI targeting that calls for a (weaker) monetary policy reaction to both ϕ and ϕ∗. In a large number of studies, however, producer price index targeting has been found to be a monetary policy strategy that is able to implement the welfare-maximizing resource allocation.21 These studies argue that targeting producer prices may bring about the welfare-maximizing resource allocation because the distortions created by price stickiness are neutralized. However, the results displayed in Figure (1) clearly indicate that stabilizing the prices of domestically produced consumption goods is not sufficient to stabilize work effort. If productivity and cost-push shocks are equally volatile, a policy of targeting the producer price index generally generates the largest welfare loss of all rules considered. In this model, the analysis of the optimal policy rule above clearly demonstrates that the welfare-maximizing resource allocation can only be implemented if the policymakers also respond to cost-push shocks abroad, i.e. to shocks that only affect foreign goods prices (as long as η ≠ 0, η ≠ 1 and v < 1 as discussed above). Only for a very special parameter combination, producer price index targeting is able to implement the welfare-maximizing (flex-price) resource allocation even if all producers are unable to readjust prices after the monetary policy decisions have been made (v = 1). This is the case if no cost-push shocks occur (their variance is assumed to be equal to zero) and exchange rate changes fully pass through Figure 1. Welfare Performance of Simple Targeting Rules for σϕ 2 = σK 2 = 1 MS CPI PPI –0.8 –0.6 –0.4 –0.2 0 Welfare 0.2 0.4 0.6 0.8 1.0 alpha 472 Wolfram Berger 22 More precisely, no producer has an incentive to change prices even if he could. into prices. For this parameter combination, producer price index targeting perfectly stabilizes producers’ mark-up irrespective of α and thus removes the incentive for price changes.22 Thus, the standard case as laid out by, e.g., Clarida, Gali and Gertler (2002) is replicated. We now turn to the case where productivity shocks are the major source of concern. Even if monetary policy is predominantly concerned with productivity shocks, producer price targeting as recommended by other studies (see, e.g., Sutherland, 2005) does not generally constitute the best simple rule. We show that this result needs to be qualified if the increasing vertical integration of countries is explicitly taken into consideration. Then, the answer to the question which price targeting rule is best in welfare terms depends on how interdependent countries are, as measured by α. CPI targeting is less strict than producer price index targeting since it allows for some flexibility in producer prices. This is sufficient to render CPI targeting welfare-superior to producer price index targeting in the presence of weak costpush shocks for a wide range of values for α. Producer price index targeting only generates the best welfare results if the home bias in production is relatively pronounced, i.e. the cross-country interdependence in production is either rather weak or rather strong. This is another central result of this paper. Intuitively, Figure 2. Welfare Performance of Simple Targeting Rules σK 2 = 1 and σϕ 2 = ⅓ MS CPI PPI –0.8 –0.6 –0.4 –0.2 0 Welfare 0.2 0.4 0.6 0.8 1.0 alpha International Policy Coordination and Simple Monetary Policy Rules 473 stabilizing foreign goods prices (as is done under consumer price index targeting), too, does not yield an additional benefit in terms of work effort stabilization in the home economy if α is relatively high. For similar reasons, focusing on the stabilization of domestically produced goods is better than the stabilization of domestically consumed goods if α is relatively low. From a global point of view, it does not matter whether monetary adjustments by the home or the foreign policymaker offset the impact of home or foreign shocks on work effort. If the cross-country interdependence in production is quite pronounced, home work effort is mainly stabilized by the foreign policymaker’s monetary policy measures to stabilize foreign producer prices while the home policymaker’s adjustments lead to a stabilization of work effort in the foreign country. Monetary targeting which allows for some price flexibility in exchange for the stability of a real aggregate (consumption) is clearly inferior in welfare terms to both producer and consumer price index targeting if cost-push shocks are by far less important than productivity shocks. However, allowing prices to fluctuate to some extent is clearly the best targeting rule if cost-push shocks predominate (see Figure (3)). This is also stressed by Sutherland (2005). As discussed there, policies that allow for price movements like monetary targeting are superior to price targeting rules in the presence of cost-push shocks. Cost-push shocks directly destabilize consumption goods prices and thus affect work effort. Monetary policy strategies that allow for a combination of price level and real aggregates stabilization such as monetary targeting are therefore superior in welfare Figure 3. Welfare Performance of Simple Targeting Rules σK 2 = ⅓ and σϕ 2 = 1 –0.8 –0.6 –0.4 –0.2 0 Welfare 0.2 0.4 0.6 0.8 1.0 alpha MS CPI PPI 474 Wolfram Berger terms to rules that exclusively focus on stabilizing price indices such as producer or consumer price index targeting. Strictly targeting the producer price index is the least favorable targeting rule for this parameter combination. CPI targeting which, as pointed out above, leaves some room for variability in producer prices performs slightly better in welfare terms. 6. Conclusions A vertical chain of production and trade along this chain have been found to be a characteristic feature of globalized markets. Starting from this stylized fact, this paper examines how a multistage production process that involves more than one country affects the choice of a monetary policy target. While prices of intermediate goods are assumed to be perfectly flexible, a fraction of consumption goods prices has to be set in advance. It is assumed that there is full passthrough of exchange rate changes into intermediate goods prices, but a less than perfect pass-through into the prices of final consumption goods. We are concerned first with the optimal monetary policy if policies are coordinated, i.e. with the policy rules that maximize global welfare. In a second step we investigate which simple, i.e. non-optimal, targeting rule best supports the welfare maximizing policy. Our key results can be summarized as follows. Pursuing an inward-looking policy, as suggested in recent work, is clearly not optimal in this set-up. Generally, the welfare-maximizing monetary policy implies a response to both productivity and cost-push shocks irrespective of their origin. A comparison of the welfare effects of a range of simple targeting rules shows no unambiguous result. The degree of cross-country production interconnectedness and the relative importance of cost-push and productivity shocks are keys for the welfare ranking. While the relative importance of productivity and costpush shocks is decisive for the question whether the policymaker should follow a price targeting rule or not, the degree of vertical integration determines which simple price targeting rule performs best. Producer price and consumer price targeting are welfare-inferior to a rule like monetary targeting that allows for some degree of price flexibility in the presence of comparatively strong cost-push shocks. If, however, productivity shocks are predominant, strictly targeting price indices such as the producer price index or the CPI is welfare superior to targeting other monetary policy objectives. In this case, producer price index targeting as recommended in large parts of the literature only generates better welfare results than CPI targeting if vertical integration between countries is either rather low or rather high.