Inflation Dynamics and International Linkages: A Model of the United States, the Euro Area, and Japan

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 745 July 2002 INFLATION DYNAMICS AND INTERNATIONAL LINKAGES: A MODEL OF THE UNITED STATES, THE EURO AREA AND JAPAN Gunter Coenen and Volker Wieland International Finance Discussion Papers Numbers 744-751 were presented on July 5-6, 2002 at the first conference organized by the International Research Forum on Monetary Policy established by the European Central Bank, the Federal Reserve Board, the Center for German and European Studies at Georgetown University, and the Center for Financial Studies at Goethe University. NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp. The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or any other person associated with the Federal Reserve System.

Inflation Dynamics and International Linkages: ∗ ,† A Model of the United States, the Euro Area and Japan Gu¨nter Coenen European Central Bank Volker Wieland Goethe University of Frankfurt and European Central Bank First Version: January 2002 This Version: July 2002 Abstract In this paper we estimate a small macroeconometric model of the United States, the euro areaandJapanwithrationalexpectationsandnominalrigiditiesduetostaggeredcontracts. Comparing three popular contracting specifications we find that euro area and Japanese inflationdynamicsarebestexplainedbyTaylor-stylecontracts,whileBuiter-Jewitt/Fuhrer- Moore contracts perform somewhat better in fitting U.S. inflation dynamics. We are unable to fit Calvo-style contracts to inflation dynamics in any of the three economies without allowing either for ad-hoc persistence in unobservables or a significant backward-looking element. ThecompletedmodelmatchesinflationandoutputdynamicsintheUnitedStates, the euro area and Japan quite well. We then use it to evaluate the role of the exchange rate for monetary policy. Preliminary results, which are similar across the three economies, indicate little gain from a direct policy response to the exchange rate. JEL Classification System: E31, E52, E58, E61 Keywords: macroeconomic modelling, nominal rigidities, inflation persistence, international linkages, monetary policy rules ∗ Correspondence: Coenen: Directorate General Research, European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany, tel.: +49 69 1344-7887, e-mail: gunter.coenen@ecb.int; Wieland: Professur fu¨r Geldtheorie und -politik, Johann-Wolfgang-Goethe Universit¨at, Mertonstrasse 17, D-60325 Frankfurt am Main, Germany, tel.: +49 69 798-25288, e-mail: wieland@wiwi.uni-frankfurt.de, homepage: http://www.volkerwieland.com. † The opinions expressed are those of the authors and do not necessarily reflect views of the European Central Bank. Volker Wieland served as a consultant at the European Central Bank while preparing this paper. We are grateful for helpful comments from Ben McCallum, Ilian Mihov and participants at the InternationalResearchForumonMonetaryPolicyinFrankfurtandtheSocietyforComputationalEconomics conferenceinAixenProvence. WearealsogratefulforresearchassistancebyAnna-MariaAgrestifromthe European Central Bank. Any remaining errors are of course the sole responsibility of the authors.

Non-Technical Summary In this paper we estimate a small three-country model with nominal rigidities and rational expectations to fit inflation and output dynamics in the three major world economies, the UnitedStates,theeuroareaandJapan. Wethenusethismodeltostudytheperformanceof alternativemonetarypolicystrategiesfocusingontheroleoftheexchangerateformonetary policy. We begin our empirical analysis by investigating whether inflation dynamics in the United States, the euro area and Japan are consistent with staggered nominal contracts and rational expectations. We consider the three specifications of nominal rigidity that have been most popular in the recent empirical literature, the staggered nominal contracts models of Calvo (1983) and Taylor (1980, 1993a) with random-duration and fixed-duration contractsrespectively,aswellastherelativereal-wagecontractingmodelproposedbyBuiter and Jewitt (1981) and estimated by Fuhrer and Moore (1995a,b). Our findings can be summarized as follows: we are unable to estimate the inflation equation based on Calvo’s specification except if we allow for ad-hoc persistence in supply shocks or some degree of adaptive expectations. Taylor’s specification, which explicitly depends on lagged prices and output gaps, performs better. We are able to estimate statistically signifcant and economically meaningful parameters for all three countries consistent with rational expecations and amaximumcontractlengthofoneyear. However, incaseofU.S.dataTaylor’sspecification doesnotpassatestofoveridentifyingrestrictions. FuhrerandMoore’sspecificationobtains the best fit to U.S. data, but is dominated by Taylor’s specification for Japanese and euro area data. Concerning output dynamics we specify an open-economy aggregate demand equation that relates output to the ex-ante real interest rate and the real exchange rate as well as some additional lags of the output gap. Given estimates of the aggregate demand equation and the historical policy rule for the United States, the euro area and Japan we proceed to investigate the importance of international linkages and spillovers for the model’s empirical 2

fit as well as optimal policy design. The empirical fit of the model is quite good and the historical structural shocks implied by the multi-country model are essentially white noise. However, international linkages only seem to play a minor role. Comparing the three-country open-economy version to a version with three closed economies we find that in both cases model-generated output and inflation autocorrelations and cross-correlations are quite close to those implied by the data. International spillovers of domestic shocks turn out to be rather small when exchange rates are flexible and short-term interest rates are set according to policy rules that focus on stabilizing domestic variables. Finally, we investigate the role of the exchange rate in the design of monetary policy rules. We compute optimized simple interest rate rules in the open-economy model and also in a variation of this model that allows for a direct effect of the real exchange rate on inflation. We find that it is largely sufficient to respond to output, inflation and lagged interest rates. Little seems to be gained from an explicit response of nominal interest rates to the exchange rate. 3

1 Introduction In this paper we estimate a small three-country model with nominal rigidities and rational expectations to fit inflation and output dynamics in the three major world economies, the United States, the euro area and Japan. We then use this model to study the performance of alternative monetary policy strategies focusing on the role of the exchange rate for monetary policy. Our approach to building a macroeconometric model to be used for policy analysis is oriented on the following three principles. First, the model should fit the data under rational expectations. Thus, we avoid the assumption that policymakers can persistently fool market participants. Secondly, the model should explain the predictable dynamics of key macroeconomic variables such as output and inflation. Thus, we avoid ad-hoc specification of persistence in unobserved error processes. Thirdly, in specifying the final model equations we try to incorporate elements of models derived under optimising behavior of representative agents but we give priority to the preceding two principles. We begin our empirical analysis by investigating whether inflation dynamics in the United States, the euro area and Japan are consistent with staggered nominal contracts and rational expectations. We consider the three specifications of nominal rigidity that 1 have been most popular in the recent empirical literature , the staggered nominal contracts models of Calvo (1983) and Taylor (1980, 1993a) with random-duration and fixed-duration contractsrespectively,aswellastherelativereal-wagecontractingmodelproposedbyBuiter and Jewitt (1981) and estimated by Fuhrer and Moore (1995a,b). Each contracting specification implies a different structural inflation equation that we try to fit to the data taking reduced-formoutputdynamicsasgivenandassumingrationalexpectationsregardingfuture output and inflation. In case of Calvo- and Taylor-style contracts these inflation equations havebeenshowntobeconsistentwithoptimisingbehaviorofrepresentativehouseholdsand 2 monopolistically competitive firms. The inflation equation resulting from Fuhrer-Moore- 1See for example the recent papers by Coenen and Wieland (2000), Gal´ı and Gertler (1999), Neiss and Nelson (2001), Roberts (1997), Sbordone (2002) or Rudd and Whelan (2002). 2Concerning Calvo-style contracts see for example Rotemberg and Woodford (1997), Clarida, Gal´ı and Gertler (1999) and Sbordone (2002). Concerning Taylor-style contracts see for example Chari, Kehoe and 1

style contracts, however, has been criticized for lacking such a foundation in optimizing 3 behavior. Our empirical findings can be summarized as follows: we are unable to estimate the inflation equation based on Calvo’s specification except if we allow for ad-hoc persistence in supply shocks or some degree of adaptive expectations. Taylor’s specification, which explicitly depends on lagged prices and output gaps, performs better. We are able to estimate statistically signifcant and economically meaningful parameters for all three countries consistent with rational expecations and a maximum contract length of one year. However, incaseofU.S.dataTaylor’sspecificationdoesnotpassatestofoveridentifyingrestrictions. Fuhrer and Moore’s specification obtains the best fit to U.S. data, but is dominated by Tay- 4 lor’s specification for Japanese and euro area data. Thus, for the final inflation equations of our multi-country model we pick Taylor’s specification for Japan and the euro area, and Fuhrer and Moore’s specification for the United States. Concerning output dynamics, we are not aware of a possible specification that would satisfy all three modelling principles. Although there is an active and rapidly growing literature on closed and open-economy models, which are consistent with optimizing behavior of representative households and firms, these models do not yet seem able to match hump-shaped output dynamics without introducing persistence in unobservables. Instead we specify an open-economy aggregate demand equation that relates output to the ex-ante real interest rate and the real exchange rate as well as some additional lags of the output 5 gap. While these lags do not yet have micro-foundations, we prefer to incorporate such predictable output dynamics explicitly in the output equation rather than assuming per- McGrattan (2000) and King and Wolman (1999). 3Christiano,EichenbaumandEvans(2001)providesuchafoundationforaspecificationofpriceandwage contractswithpartialindexation,whichimpliesaninflationequationthatisquitesimilartoFuhrer-Moore’s relative real wage contracting model. 4These findings confirm earlier results in Coenen and Wieland (2000) for the euro area and Fuhrer and Moore (1995) for the United States, although with our sample the Taylor specification performs better on U.S. data than in Fuhrer and Moore’s earlier investigation. Recent work by Guerrieri (2002) even suggests that with a longer sample Taylor-style contracts are not rejected for U.S. data. 5WiththisapproachwefollowTaylor(1993a). Theresultingestimatedmodelalsohasmanysimilarities to the calibrated model considered by Svensson (2000). 2

sistence in unobservable shock processes. Clearly, these lags will have implications for the design of monetary policy rules in either case. Given estimates of the aggregate demand equation and the historical policy rule for the United States, the euro area and Japan we proceed to investigate the importance of international linkages and spillovers for the model’s empirical fit as well as optimal policy design. The empirical fit of the model is quite good and the historical structural shocks implied by the multi-country model are essentially white noise. However, international linkagesonlyseemtoplayaminorrole. Comparingthethree-countryopen-economyversion to a version with three closed economies we find that in both cases model-generated output and inflation autocorrelations and cross-correlations are quite close to those implied by the data. International spillovers of domestic shocks turn out to be rather small when exchange rates are flexible and short-term interest rates are set according to policy rules that focus on stabilizing domestic variables. Finally, we investigate the role of the exchange rate in the design of monetary policy rules. We compute optimized simple interest rate rules in the open-economy model and also in a variation of this model that allows for a direct effect of the real exchange rate on inflation. We find that it is largely sufficient to respond to output, inflation and lagged interest rates. Little seems to be gained from an explicit response of nominal interest rates to the exchange rate. Finally, we also investigate the extent of possible gains from international monetary coordination. The paper proceeds as follows. Section 2 presents the supply side of the model, that is, the alternative staggered contracts specifications, and reports the empirical findings for the United States, the euro area and Japan. In section 3, we discuss the determination of aggregate demand, the role of monetary policy and international linkages. We also report estimation results regarding aggregate demand equations and forward-looking policy rules. Section 4 reviews the empirical fit of the complete multi-country model, while section 5 investigates the extent of international spillovers. In section 6 we analyze the role of the exchange rate for monetary policy rules, while section 7 concludes. 3

2 The supply side: inflation dynamics and staggered contracts 2.1 Calvo-style contracts Calvo-style random-duration contracts have been the workhorse of the recent theoretical literature on monetary policy in models with nominal rigidities and optimizing representative households and firms. Typically, intermediate goods firms that are monopolistically competitive are assumed to set prices on a staggered basis. The duration of a given firm’s price x t is random but the probability that a firm keeps its price fixed in a given period (or gets to change its price) is constant. As shown by Rotemberg and Woodford (1997) and others a log-linearized version of the optimal price setting rule for x t together with the definition of the aggregate price index p t implies a log-linear relationship between inflation (π t = p t −p t−1), expected inflation and marginal cost. Assuming output is proportional to marginal cost this relationship implies the so-called ‘New Keynesian’ Phillips curve, π t = κEt[π t+1]+γq t , (1) where q t = y t −y∗ denotes the gap between current output y t and the ‘natural’ output level y∗ that would occur with completely flexible prices. κ refers to the discount factor. t Recent empirical studies with U.S. and euro area data have typically rejected equation (1) and have shown that some degree of ad-hoc serial correlation in supply shocks or share ω of price setters with backward-looking ‘rules-of-thumb’ behavior is necessary to fit the 6 data. Thus, wewillalsoconsidertwoempiricalextensionsoftheinflationequationimplied by Calvo-style contracts. First an extension with purely rational expectations but serially correlated supply shocks: π t = κEt[π t+1]+γq t+u t (2) u t = ρu t−1+σ (cid:1)π (cid:7) π , 6Some authors have argued that the New-Keynesian Phillips curve fits the data if one uses unit labor cost, which is a more direct measure of marginal cost than the output gap, in the equation (cf. Gal´ı and Gertler (2000) and Sbordone (2002). However even in those cases allowing for ad-hoc persistence in the error process or an backward-looking element seems to be necessary to fit the data. 4

where ρ measures the degree of serial correlation in the supply shock u t. The innovation (cid:7) π tothissupplyshockisassumedtobeseriallyuncorrelatedwithzeromeanandunitvariance and scaled by the parameter σ (cid:1)π . Secondly, a hybrid version with weighted forward-looking and backward-looking expectations, π t = (1−ω)Et[π t+1]+ωπ t−1+γq t+σ (cid:1)π (cid:7) π , (3) where ω refers to the share of backward-looking price-setters. 2.2 Taylor-style contracts In contrast to Calvo’s model, Taylor-style contracts are of fixed duration. The original motivation for this type of nominal rigidity was the existence of long-term nominal wage contracts. Understood as a source of nominal wage rigidity, Taylor-style fixed duration contracts imply that the aggregate wage level can be expressed as a weighted average of current and previously negotiated contract wages x t−i (i = 0,1,...,η(x)), which are still in effect. FuhrerandMoore(1995a)andothershavetreatedtheaggregatepriceandaggregate wage indices interchangeably, which is consistent with a fixed markup. In this case the aggregate price level p t can be related directly to contract wages: η(cid:1)(x) p t = f i x t−i . (4) i=0 The weights f i (i = 1,...,η(x)) on contract wages from different periods are assumed to 7 benon-negative,non-increasingandtime-invariantandneedtosumtoone. Theparameter η(x) corresponds to the maximum contract length. Workers negotiate long-term contracts and compare the contract wage to past contracts that are still in effect and future contracts that willbenegotiated overthe lifeofthiscontract. The contractwagex t inTaylor’smodel is determined as follows:   η(cid:1)(x) η(cid:1)(x) x t = Et  f i p t+i+γ f i q t+i  +σ (cid:1)x (cid:7) x,t , (5) i=0 i=0 7As discussed in Taylor (1993a) this assumption is consistent with the existence of wage contracts of different length in constant proportions. 5

where q t = y t −y t ∗ again denotes the output gap. Thus, the contract wage x t is negotiated with reference to the price level that is expected to prevail over the life of the contract as well as the expected deviation of output from its potential over this period. Since the price indices p t+i reflect contemporaneous and preceding contract wages, (5) implies that wage setters look at an average of nominal contract wages negotiated in the recent past and expected to be negotiated in the near future when setting the current contract wage. The sensitivity of contract wages to excess demand is measured by γ. The contract wage shock (cid:7) x,t, which is assumed to be serially uncorrelated with zero mean and unit variance, is scaled by the parameter σ (cid:1)x . More recently, Chari, Kehoe and McGrattan (2000) have derived further microfoundations for an equation such as (5). However, in their model x t stands for contract prices rather than contract wages. They build a representative agent model with monopolistically competitive firms and impose a Taylor-contract-style constraint that firms set prices for a fixed number of periods and do so in a staggered fashion. In particular, each period, 1/η firms are assumed to choose new prices that are then fixed for η periods. 8 A log-linear approximation of a stripped-down version of their equilibrium implies a contract price equation that coincides with Taylor’s contract wage equation (5). Thus, they are able to express the parameter γ as a function of deeper technology and preference parameters. For empirical purposes it will be more convenient to rewrite equations (4) and (5) in terms of the quarterly inflation rate π t and the real contract wage x t −p t. Thus, inflation ratescanbeusedinestimation. Thecontractwages,whichareunobservable,canbeinferred 9 from past output and inflation data given an assumption regarding initial conditions. In comparison to the inflation equation (1) that results under Calvo-style contracts, it is important to note that the inflation equation resulting from Taylor-style contracts will depend explicitly on lagged inflation and on lagged output gaps if the maximum contract length exceeds two quarters. 8Thus,inthismodelthenominalrigidityoccursinintermediategoodsmarkets,whilethereislaborand capital markets clearing. 9For a more detailed discussion see Coenen and Wieland (2000). 6

2.3 Fuhrer-Moore style contracts The distinction between Taylor-style nominal wage contracts and Fuhrer-Moore’s relative real wage contracts concerns the definition of the wage indices that form the basis of the intertemporal comparison underlying the determination of the current nominal contract wage. Thus, Fuhrer and Moore’s specification should not be understood as a real wage rigidity, but rather as an alternative nominal rigidity. Workers negotiating their nominal wage are assumed to compare the implied real wage with the realwages on overlapping contracts in the recent past and near future. As aresult, the expected real wage under contracts signed in the current period is set with reference to the average real contract wage index expected to prevail over the current and the next three quarters:   η(cid:1)(x) η(cid:1)(x) x t −p t = Et  f i v t+i+γ f i q t+i  +σ (cid:1)x (cid:7) x,t , (6) i=0 i=0 (cid:6) wherev t = η i= (x 0 ) f i(x t−i −p t−i)referstotheaverageofrealcontractwagesthatareeffective at time t. Fuhrer and Moore (1995a) prefer this specification to Taylor-style contracts because it gives more weight to past inflation and consequently provides a better fit to the observed degree of inflation persistence in the United States. It has been criticised, however, for lacking explicit microfoundations that are available for the inflation equations resulting from Calvo- or Taylor-style contracts. 2.4 Estimation We estimate the three different staggered contracts models in two stages. In the first stage, we fit unconstrained VAR models to output and inflation in the three economies. In the secondstageweusetheunconstrainedVARsasauxiliarymodelsinestimatingthestructural parameters of the staggered contracts specifications by indirect inference methods. These estimates are obtained assuming that market participants form rational expectations of future output and inflation. The estimation methodology is described in more detail in the 7

appendix. The data that we use in the first stage to estimate the unconstrained VARs comprises real GDP and the GDP deflator for the United States and Japan and area-wide averages of 10 those same variables for the euro area. In constructing output gaps we need a measure of potentialoutput. FortheUnitedStatesandJapanwehaveinvestigatedvariousalternatives suchaslog-lineartrendswithandwithoutbreaks, aswellasestimatesthatcanberecovered from output gap estimates of the OECD and the Congressional Budget Office. The results we will focus on in the following are based on the OECD’s estimate, however our findings are quite robust to the alternatives we have considered. For the euro area we stick to the 11 log-linear trends used in our earlier paper (cf. Coenen and Wieland (2000)). A chart of 12 the data used for estimation is shown in Figure A in the appendix. The estimation results with U.S., euro area and Japanese data are summarized in Table 1. We were unable to obtain statistically significant and economically meaningful estimates of the inflation equation (1) implied by Calvo-style contracts for any of the three economies. This is perhaps not so surprising given the recently documented failure of this specificationtofitU.S.inflationdynamics(atleastintheversionwhichimposesproportionality of marginal cost and output). Thus, the first three rows refer to our estimates for the extended versions of Calvo’s specification (that is, equation (2) and equation (3), respectively), which incorporate either some share of backward-looking price-setters (0 < ω < 1) or positive serial correlation in supply shocks (ρ > 0). We were not able to obtain meaningful and significant estimates for a version with purely rational expectations and serial correlation in supply shocks with U.S. data. Instead we report estimates of a hybrid version with a 50% share of price setters with adaptive 10Theeuroareadata,whichareaveragesofmembercountrydatausingfixedGDPweightsatPPPrates, have been obtained from the ECB area-wide model database (see Fagan et al. (2001)). 11ThereasonbeingthatavailableOECDoutputgapestimatesdonotallowtheconstructionofpotential output series that would be appropriate for our quarterly euro area data. 12Fortheeuroareathechartshowsthede-trendedinflationseries. Historicaleuroareainflationcontains a downward trend due to the gradual policy-driven convergence of inflation rates in Italy and France to German levels during the EMS. For further discussion we refer the reader to Coenen and Wieland (2000) and the sensitivity analysis in this paper. 8

Table 1: Estimated Contracting Specifications Calvo κ ω ρ γ σ (cid:1) p-value(d) United States(a,b) - 0.4797 - 0.0041 0.0017 0.0068[2] (0.0103) (0.0011) 0.0001 Euro Area(a,c) 0.99 - 0.6322 0.0206 0.0012 0.2601[2] (0.0568) (0.0067) (0.0001) Japan(a,b) 0.99 - 0.8863 0.0071 0.0007 < 10−5[2] (0.0536) (0.0114) (0.0003) Taylor f 0 f 1 f 2 f 3 γ σ (cid:1)x p-value(d) United States(a,b) 0.2535 0.2535 0.2534 0.2396 0.0095 0.0054 < 10−15[3] (0.0164) (0.0171) (0.0056) 0.0003 Euro Area(a,c) 0.2846 0.2828 0.2443 0.1883 0.0158 0.0042 0.2658[2] (0.0129) (0.0111) (0.0131) (0.0059) (0.0003) Japan(a,b) 0.3301 0.2393 0.2393 0.1912 0.0185 0.0068 0.0162[3] (0.0303) (0.0062) (0.0057) (0.0006) Fuhrer-Moore f 0 f 1 f 2 f 3 γ σ (cid:1)x p-value(d) United States(a,b) 0.6788 0.2103 0.0676 0.0432 0.0014 0.0004 0.8749[2] (0.0458) (0.0220) (0.0207) (0.0008) (0.0001) Euro Area(a,c) 0.7664 0.1712 0.0546 0.0078 0.0014 0.0002 0.1644[2] (0.0136) (0.0121) (0.0063) (0.0003) (0.0000) Japan(a,b) 0.8986 0.0828 0.0149 0.0037 0.0001 0.0001 0.0027[2] (0.0428) (0.0338) (0.0086) (0.0001) (0.0001) Notes: (a) Simulation-basedindirectestimatesusingaVAR(3)modelofquarterlyinflationandtheoutput gap as auxiliary model. Estimated standard errors in parentheses. (b) Output gap measure constructed using OECD data. (c) Inflation in deviation from linear trend and and output in deviation from loglinear trend. (d) Probability value associated with the test of overidentifying restrictions. Number of overidentifying restrictions in brackets. expectations as shown in the first two rows of Table 1. With euro area and Japanese data we succeeded in estimating inflation equations with purely rational expectations as long as we allow for a significant degree of serial correlation in supply shocks and restrict the 9

discount rate κ to 0.99. The ad-hoc persistence parameter ρ is estimated to be 0.63 and 0.89respectively. 13 Finally, wenotethatonlytheeuroareaestimatesoftheextendedCalvo specification pass a test of overidentifying restrictions (see last column). 14 Estimation results for Taylor-style contracts as well as Fuhrer and Moore’s preferred relative-real-wage contracts are reported in the remaining rows of Table 1. The inflation process under those specifications is defined by equations (4), (5) and (6). The first 3 columns contain estimates of three of the contract weights (f 0 ,f 1 ,f 2). The fourth weight, f 3, is determined by the constraint that the weights sum to one. The fifth column contains the estimate of the contract slope parameter γ, while the sixth column reports the estimate of the scaling factor of contract wage shocks. Starting with the results for Taylor contracts we note that the estimated sensitivity parameter γ has the appropriate signs and are statistically significant for all three economies (at the 5% level for the euro area and Japan and the 10% level for the United States). Unfortunately, the test of overidentifying restrictions rejects this specification for U.S. data 15 andalsoforJapanesedata. WithregardtoFuhrer-Moorecontractsweobtainstatistically significant and economically meaningful estimates for the United States and the euro area. As indicated by the p-value for the test of overidentifying restrictions Fuhrer-Moore contracts perform better in terms of matching U.S. inflation dynamics, but worse in terms of euro area inflation dynamics than Taylor contracts. Furthermore, the Fuhrer-Moore specification is rejected more strongly in the case of Japan. Our findings broadly confirm earlier 16 investigations by Fuhrer and Moore (1995) concerning the United States and Coenen and Wieland (2000) concerning the euro area, albeit with different methodology, different data sample and more flexibility in the estimation of the contract weights f i. Sensitivity studies. Wehaveexperimentedsomewhatwiththechoiceofpotentialoutput 13We also obtain estimates of the hybrid version with adaptive expectations, which are not reported in the table (ω equals 0.38 for the euro area and 0.48 for Japan). 14For a more detailed discussion of variations of relative real wage contracts see Coenen and Wieland (2000). 15With regard to Japan, however, we have been able to estimate a version of Taylor contracts for an alternative output gap measure that passes this test. These sensitivity studies are discussed further below. 16Although in our case Taylor’s specification does not fail as miserably. 10

measure for Japan and the United States. With regard to Japan we found that Taylor-style contracts cannot be rejected when a log-linear trend with break is used. However, we prefer to stick with the parameter estimates obtained based on OECD potential output data. Our findings for the United States are confirmed when using a log-linear trend or CBO estimates of potential output. For the euro area, we stick with the assumptions of a linear trend in inflation and a log-linear trend in output. We have subjected these assumptions to 17 a barrage of sensitivity tests in Coenen and Wieland (2000). A further difference to our earlier work and that of Fuhrer and Moore is that we relax the constraint on the contract weights. This constraint implied that the weights were determined by a single parameter s such that f i = .25+(1.5−i)s, s ∈ (0,1/6]. Estimates for the United States, the euro area and Japan with this constraint are reported in Table A in the appendix. Our broad conclusions are unaffected. Following the three modelling principles discussed in the introduction we choose Taylorcontracts for the supply-side of our model in the euro area and Japan. To match U.S. inflation dynamics we have to compromise on one of the principles, i.e. either pick Taylor’s specification which induces insufficent inflation persistence or Fuhrer and Moore’s specification which is not quite consistent with optimizing behavior. In this paper, we proceed with Fuhrer-Moore’s contracts for the supply side of the U.S. economy. 3 The demand side: output dynamics, monetary policy and international linkages 3.1 Model equations On the demand side of our model, we need to specify the determination of the output gap, the transmission of monetary policy and international linkages. As discussed in the introduction we take a semi-structural approach, which embodies rational expecations regarding 17Wealsoreferthereadertothisearlierpaperwithregardtoourreasonsforthecontroversialassumption of a linear trend in inflation. This trend in euro area inflation is due to the gradual convergence process undergone by Italy, France and other high-inflation countries. Thus it may be best understood as resulting fromagradualchangeintheinflationtargetofthosecountries,whichshouldnotbeattributedtostructural wage or price rigidities or other sources of shocks. 11

future interest rates, inflation and exchange rate changes, in the spirit of macroeconometric models such as Taylor (1993a) or the Federal Reserve’s FRB/US model, but does not explicitly incorporate all the restrictions that would be implied by optimizing behavior of a representative agent. Equation (7) in Table 2 relates the output gap q t to several lags of itself, the lagged ex-antelong-termrealinterestrater t−1 andthetrade-weightedrealexchangeratee t w . The demand shock (cid:7) d,t in equation (7) is assumed to be serially uncorrelated with mean zero and unit variance and is scaled with the parameter σ (cid:1) . A possible rationale for including d lagsof output istoaccount for habit persistenceinconsumption as well asadjustment costs and accelerator effects in investment. We use the lagged instead of the contemporaneous value of the real interest rate to allow for a transmission lag of monetary policy. The tradeweighted real exchange rate enters the aggregate demand equation because it influences net 18 exports. Next we turn to the financial sector and relate the long-term real interest rate to the short-term nominal interest rate, which is the principal instrument of monetary policy. Three equations determine the various interest rates. The short-term nominal interest rate i t is set according to the interest rate rule defined by equation (8) in Table 3. According to this rule policymakers change the nominal interest rate in response to inflation deviations from the policymaker’s target π∗ and output deviations from potential. This specification accommodates both forecast-based rules (with forecast horizons θ > 0) and outcome-based rules(θ = 0). Theinflationmeasureπ(4) istheannualaverageinflationrateandtheinterest t rate is annualized. Furthermore, the real equilibrium rate r∗ provides a reference point for the policy rule. Note also that this rule simplifies to the one proposed by Taylor (1993a) if θ = 0 and ρ = 0. As to the term structure that is defined in (9), we rely on the accumulated forecasts of the short rate over η(l) quarters which, under the expectations hypothesis, will coincide 18Fornowweomitadirectchannelthroughwhichforeignoutputaffectsdomesticoutput,butweplanto explore this channel in future work. 12

Table 2: Aggregate Demand, Interest Rates and Exchange Rates Aggregate Demand q t =δ(L)q t−1+φ(r t−1 −r∗)+ψew t +σ (cid:1) d (cid:7) d,t , (7) (cid:6) where δ(L)= η j= (q 1 ) δ j Lj−1 Monetary Policy Rule i t =ρ(L)i t−1+(1−ρ(1))(r∗+Et[π t ( + 4) θ ]) +αEt[π t ( + 4) θ −π∗]+βq t+σ (cid:1)p (cid:7) p,t , (8) (cid:6) where ρ(L)= η j= (i 1 ) ρ j Lj−1 and π t (4) =p t −p t−4 (cid:7) (cid:8) (cid:6) Term Structure l t =Et η( 1 l) η j= (l 1 )i t+j−1 (9) (cid:7) (cid:8) Real Interest Rate r t =l t − 4Et η( 1 l) (p t+η(l) −p t) (10) Trade-Weighted Real ew t ,(i) =w (i,j) e( t i,j) +w (i,k) e t (i,k) (11) Exchange Rate (cid:7) (cid:8) (cid:9) (cid:7) (cid:8)(cid:10) Open Interest Parity e( t i,j) =Et e( t+ i,j 1 ) + i( t j)− 4Et p( t+ j) 1 −p( t j) (cid:9) (cid:7) (cid:8)(cid:10) − i( t i)− 4Et p( t+ i) 1 −p( t i) (12) Notes: q: outputgap;r: long-termrealinterestrate;r∗: equilibriumrealinterestrate;ew: trade-weighted real exchange rate; (cid:2) d: aggregate demand shock; i: short-term nominal interest rate; π∗: inflation target; π(4): year-on-yearinflation;(cid:2) p: monetarypolicyshock;l: long-termnominalinterestrate;e: bilateralreal exchange rate. with the long rate forecast for this horizon. The term premium is assumed to be constant and equal to zero. We then obtain the long-term ex-ante real interest rate (defined in (10)) by subtracting inflation expectations over the following η(l) quarters. The trade-weighted real exchange rate is defined by equation (11). The superscripts (i,j,k) are intended to refer to the economies within the model without being explicit about the respective economy concerned. Thus, e(i,j) represents the bilateral real exchange rate between countries i and j, e(i,k) the bilateral real exchange rate between countries i and k, and consequently equation (11) defines the trade-weighted real exchange rate for country i. The bilateral trade-weights are denoted by (w (i,j) ,w (i,k) ,...). Finally, equation (12)constitutestheopeninterestrateparityconditionwithrespecttothebilateralexchange 13

rate between countries i and j in real terms. It implies that the difference between today’s real exchange rate and the expectation of next quarter’s real exchange rate is set equal to the expected real interest rate differential between countries i and j. In the deterministic steady state of this model the output gap is zero and the long-term real interest rate equals its equilibrium value r∗ . The equilibrium value of the real exchange rate is normalized to zero. Since the overlapping contracts specifications of the wage-price block do not impose any restriction on the steady-state inflation rate, it is determined by monetary policy alone and equals the target rate π∗ in the policy rule. 3.2 Estimation In estimating the demand side of our model we take an equation-by-equation approach that is simpler than the indirect inference approach used for the supply side. The reason is that the indirect inference approach would require including two more variables in the unconstrained VAR, the interest rate and the exchange rate. This proved rather difficult in our earlier work on the euro area. We now proceed in parallel for the United States, the euro area and Japan and estimate the parameters of the aggregate demand equation (6) by means of the Generalized Method of Moments (GMM). To do so, we first construct the expost real long-term rate by replacing expected future with realized values in equations (8) and (9). Then we estimate the parameters by GMM using lagged values of output, inflation 19 20 and interest rates and real exchange rates as instruments. The estimation results for the aggregate demand equation using U.S., euro area and Japanese data are reported in Table 3. The estimates obtained with U.S. data indicate a hump-shaped output pattern with a positivecoefficientonthefirstlagofoutputthatisgreaterthanoneandnegativecoefficients 19NotealsothatinestimationweusetheCPI-basedrealeffectiveexchangeratesratherthanthebilateral real effective rates calculated on the basis of the constructed weights. In solving the model we will stick to the endogeneously determined bilateral rates. 20Notethesampleperiodsareasfollows: U.S.(80:Q1-98:Q4),euroarea(80:Q1-98:Q4)andJapan(80:Q1- 97:Q1). The differences in length are due to differences in data availability, initial lags, and leads used in constructinglong-termrates. AstothetermstructureequationweusedahorizonoftwoyearsfortheU.S. and the euro area but three years for Japan. In all three equations we used the HP-detrended real effective exchange rate in estimation. 14

Table 3: Estimated Aggregate Demand Equations: United States, Euro Area and Japan δ 1 δ 2 δ 3 φ ψ σ (cid:1) p-value(e) d United States(a,b) 1.2184 -0.1381 -0.2116 -0.0867 0.0188 0.0071 0.9685[19] (0.0320) (0.0672) (0.0532) (0.0193) (0.0061) Euro Area(a,c,d) 1.0521 0.0779 -0.1558 -0.0787 0.0188 0.0054 0.9665[19] (0.0381) (0.0417) (0.0342) (0.0335) (0.0047) Japan(a,b) 0.9071 -0.0781 0.0122 0.0068 0.9990[21] (0.0124) (0.0272) (0.0053) Notes: (a) GMMestimatesusingaconstant,laggedvalues(uptoorderthree)oftheoutputgap,thequartelyinflationrate,theshort-termnominalinterestrateandtherealeffectiveexchangerateasinstruments. In addition, current and lagged values (up to order two) of the foreign inflation and short-term nominal interest rates have been included in the instrument set. The weighting matrix is estimated by means of the Newey-West (1987) estimator with the lag truncation parameter set equal to the maturity implied by thedefinitionofthelong-termnominalinterestrateminusone. Estimatedstandarderrorsinparentheses. (b) Output gap measure constructed using OECD data. (c) Output measured in deviation from log-linear trend. (d) For the euro area, the German long-term real interest rate has been used in the estimation. Similarly,Germaninflationandshort-termnominalinterestrateshavebeenusedasinstruments. (e)Probabilityvalueassociatedwiththetestofoveridentifyingrestrictions. Numberofoveridentifyingrestrictions in brackets. on the following lags. We also find a negative effect of the long-term real interest rate on aggregatedemand, whichishighlystatisticallysignificant, andapositiveeffectofthetradeweighted real exchange rate. The positive sign on the exchange rate coefficient is consistent with a stimulative effect of a real depreciation on net exports since the bilateral exchange rates are defined in terms of domestic over foreign currencies. As to the euro area, we also find hump-shaped output dynamics, a negative effect of the real interest rate and a positive effect of the real exchange rate. Note however, that we used the German constructed long-term real interest rate in estimation lacking a convincing measure of area-wide real interest rates prior to European Monetary Union. Similarly, we obtain statistically significant estimates of the exchange and interest rate sensitivities with the proper signs for aggregate demand in Japan. However, for Japan the output pattern does not imply a hump-shaped response. 15

Finally the p-values for the test of overidentifying restrictions that are reported in the last column of Table 3 indicate that we cannot reject these specifications for any of the three economies. In principle, the above aggregate demand equations together with the staggered contracts specifications estimated in the preceding section would be sufficient to evaluate the properties of alternative interest rate rules for monetary policy. However, if we want to know how well the complete model fits the data and if we want to identify the historical structural shocks that would be consistent with the complete multi-country model under rational expectations we also need to characterize historical monetary policy. To this end we fit the type of policy reaction function defined by equation (8) in Table 2 to historical short-term nominal interest rates. Estimates are reported in Table 4. In line with other authors we find that a forecast-based version, which implies that short-term nominal interest rates are changed in response to variations of one-year ahead forecasts of inflation and the current output gap performs well in fitting historical interest rates. We allow for partial adjustment by introducing up to two lags of the short-term nominal interest rate in the reaction function. The reaction function for the U.S. interest rate implies a sizeable long-run policy reaction to the forecast of the inflation rate that is substantially greater than one and thereby ensures stability of the model. The response to the output gap turns out to be a good bit smaller. Since GDP-weighted averages of European interest rates prior to EMU seem unlikely to be appropriate as a measure of the euro-area-wide historical monetary policy stance, we resort to estimating a reaction function for the German interest rate that we have already used in estimating euro area aggregate demand as discussed above. The German estimates, which are reported in the second row of Table 4, also indicate a stabilizing 21 inflationresponsebutnooutputresponse. Finally,forJapanwealsoestimateasignificant 21Work by Clarida, Gal´ı and Gertler (1998) suggests that German interest rate policy since 1979 is summarizedquitewellbysuchaforecast-basedinterestraterule. Claridaetal. (1998)alsoarguethatGerman monetarypolicyhadastronginfluenceoninterestratepolicyintheU.K.,FranceandItalythroughoutthis period and may have led to higher interest rates in those countries than warranted by domestic conditions at the time of the EMS crisis as suggested in Wieland (1996). 16

Table 4: Estimated Monetary Policy Rules: United States, Germany and Japan ρ 1 ρ 2 α β σ (cid:1)p p-value(d) United States(a,b) 0.7745 0.2851 0.0840 0.0110 0.8474[9] (0.0620) (0.1081) (0.0428) Germany(a,b,c) 1.1169 -0.3480 0.2039 0.0054 0.7155[12] (0.0739) (0.0594) (0.0383) Japan(a,b) 1.2672 -0.4160 0.1239 0.0048 0.4057[9] (0.1385) (0.1069) (0.0396) Notes: (a) GMM estimates using a constant, lagged values (up to order three) of the output gap, the quartely inflation rate, the short-term nominal interest rate and the real effective exchange rate as instruments. The weighting matrix is estimated by means of the Newey-West (1987) estimator with the lag truncation parameter set equal to four. Estimated standard errors in parentheses. (b) Output gap measureconstructedusingOECDdata. (c) ForGermany,laggedvalues(uptoorderthree)ofgovernment consumption relative to potential output have been included in the instrument set. (d) Probability value associatedwiththetestofoveridentifyingrestrictions. Numberofoveridentifyingrestrictionsinbrackets. 22 stabilizing response to inflation but not to the output gap. 4 The empirical fit of the multi-country model Having estimated demand and supply-side equations of our model separately a natural question is how well the complete model fits the data. To assess the overall fit of the structural multi-country model we start by computing the implied historical series of structural shocks. The relevant sample period is 1980:Q1 to 1998:Q4. These structural shocks differ from the single-equation residuals, because expectations of future variables are computed to be consistent with the complete model. Interest rates are set according to the estimated forecast-based policy rules. Long-term rates satisfy the term-structure and Fisher relationships. Nominal exchange rates are flexible, but satisfy the open interest rate parity condition. Our investigation of historical structural shocks indicates that the implied 22Thesampleperiodsforthethreeregressionsareasfollows: U.S.(79:Q4-99:Q4),Germany(79:Q2-98:Q4) and, Japan (79:Q2-95:Q2). The choice of starting dates for the U.S. and the euro area was motivated by earlier work of Clarida et al., while the end date for Japan was chosen so as to exclude the zero-nominalinterest rate period. 17

Figure 1: Correlation Pattern of Historical Structural Shocks lagged εus lagged εus lagged εeu lagged εeu lagged εja lagged εja d x d x d x 0.5 εus 0.0 d −0.5 0.5 εus 0.0 x −0.5 0.5 εeu 0.0 d −0.5 0.5 εeu 0.0 x −0.5 0.5 εja 0.0 d −0.5 0.5 εja 0.0 x −0.5 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 Quarters Quarters Quarters Quarters Quarters Quarters Notes: Solid bars: Correlation functions implied by the complete multi-country model. Dotted lines: Asymptotic 95%-confidence bands. demand and supply shocks are sufficiently close to white noise. The correlogram of these shocks is shown in Figure 1. Overall, the correlograms of the historical shocks do not reveal significant serial cor- 23 relation. This finding provides some support that our model fits the historical sample reasonably well. As a further test of the fit of our model we compute the implied autocorrelation func- 23The only exception is a significant 4-th order correlation for euro area contract wage shocks. 18

tions of inflation and output and compare them to the empirical autocorrelation functions 24 implied by the unconstrained bivariate VARs for each country. Such an approach has also been used by Fuhrer and Moore (1995a) and by McCallum (2001), who argued that autocorrelation functions are more appropriate for confronting macroeconomic models with the data than impulse response functions because of their purely descriptive nature. The comparison of autocorrelation functions of inflation and output in the three economies is reported in Figure 2. The solid lines refer to the autocorrelation functions implied by the complete multi-country model. They are derived with interest rates set according to the estimated forecast-based policy rules, flexible nominal exchange rates and aggregate demand and contract wage shocks drawn from the covariance matrix of historical structural shocks. The first panel in each row shows the autocorrelations of inflation, the second and third panel the lagged cross-correlations of inflation and output and the fourth panel the autocorrelations of output. The thin dotted lines in each panel of Figure 2 correspond to the asymptotic 95% confidence bands associated with the autocorrelation functions of the individual bivariate unconstrained VAR(3) models used in the estimation 25 of the staggered contracts specifications. The autocorrelation functions implied by the structural multi-country model fall within the confidence bands implied by the unconstrained VARs. Thus, the structural model appears to fit inflation and output dynamics quite well, in particular in light of the fact that the estimation was carried out with limited information methods. We summarize that the model is capable to match both, inflation persistence (panels in the first column) and output persistence (panels in the fourth column) for all three economies. As to the crosscorrelations of output and inflation, we find that high output tends to lead to high inflation in subsequent quarters (second column of panels). However, the confidence bands tend to be quite wide. 24ThesearetheVARsthatservedasapproximatingprobabilitymodelsintheestimationofthecontracting parameters. 25For a detailed discussion ofthe methodology andthe derivation of the asymptotic confidence bandsfor the estimated autocorrelation functions the reader is referred to Coenen (2000). 19

Figure 2: Fitting Inflation and Output Dynamics with the Structural Model Inflation, Lagged Inflation Inflation, Lagged Output Gap Output Gap, Lagged Inflation Output Gap, Lagged Output Gap 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.5 United States 0.0 0.0 0.0 0.0 −0.5 −0.5 −0.5 −0.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.5 Euro Area 0.0 0.0 0.0 0.0 −0.5 −0.5 −0.5 −0.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 1.0 1.0 1.0 1.0 0.5 0.5 0.5 0.5 Japan 0.0 0.0 0.0 0.0 −0.5 −0.5 −0.5 −0.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Quarters Quarters Quarters Quarters Notes: Solid line: Autocorrelation functions implied by the complete multi-country model. Dash-dotted line: Autocorrelation functions implied by the single-country models. Dotted lines: Asymptotic 95%confidence bands implied by bivariate unconstrained VAR’s of inflation and output. Finally, the dot-dashed lines in Figure 2 correspond to autocorrelation functions based on three separate models of these economies without international linkages. They are based onre-estimatedaggregatedemandequationswhichdonotincludetheeffectiverealexchange 26 rate. Typicallythesecorrelationfunctionsalsoremainwithintheconfidencebandsimplied by the bivariate unconstrained VARs. This provides a first indication that accounting 26Estimatesfortheclosed-economyaggregatedemandequationsarereportedinTableBintheappendix. 20

for the exchange rate channel affecting aggregate demand is not crucial to capturing the observed degree of output and inflation persistence. Furthermore, the comparison with the autocorrelation functions implied by the multi-country model shows that the exchange rate channel introduces noticeable but relatively small changes in output and inflation persistence. 5 International linkages and spillovers We now turn to consider the magnitude of international spillover effects within our model. We maintain the assumption of flexible nominal exchange rates, which implies that nominal interestratescanbesetindependentlybythecentralbanksofthethreeeconomies. However, we want to focus on the differences in adjustment to unexpected shocks that arise from differencesinthestructureoftheeconomiesratherthanfromdifferencesinmonetarypolicy. For this reason we assume that each central bank implements Taylor’s rule: i t = r∗ +π∗ +1.5(π t (4)−π∗ )+0.5q t , (13) where π(4) again stands for annual average inflation, π∗ for the inflation target and r∗ for t the real equilibrium interest rate. We start by evaluating the consequences of an unexpected temporary demand shock of 0.5 percentage points of potential output in each of the three economies. The dynamic responses of output, inflation, short-term nominal interest rates and real effective exchange rates for the three economies are shown in Figure 3. Solid lines refer to U.S. variables, dashed lines to euro area variables and dot-dashed lines to Japanese variables. In response to the positive demand shock in the euro area shown in the middle row of Figure 3euroareaoutput risesfor2quartersandthen declinesagain. The positiveoutput gap induces a temporary increase in inflation. In response, euro area nominal interest rates rise sufficiently so as to induce higher real interest rates and counterbalance the increase in output and inflation. The existence of the exchange rate channel introduces a second counterbalancing force, because the euroappreciatesinnominal and realtermsvis-a`-visthe 21

Figure 3: Comparing Demand Shocks in the United States, the Euro Area and Japan Output Gap Annual Inflation Short−Term Nominal Interest Rate Real Effective Exchange Rate 1.0 1.0 1.0 5.0 0.5 0.5 0.5 2.5 United States 0.0 0.0 0.0 0.0 −0.5 −0.5 −0.5 −2.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 1.0 1.0 1.0 5.0 0.5 0.5 0.5 2.5 Euro Area 0.0 0.0 0.0 0.0 −0.5 −0.5 −0.5 −2.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 1.0 1.0 1.0 5.0 0.5 0.5 0.5 2.5 Japan 0.0 0.0 0.0 0.0 −0.5 −0.5 −0.5 −2.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Quarters Quarters Quarters Quarters Notes: Solid line: United States. Dashed line: Euro Area. Dot-dashed line: Japan. other currencies. The depreciation of the Yen and US$ has only a very small expansionary effect in Japan and the United States. As output returns to potential and inflation to the central bank’s target, the real exchange rates also return to their equilibrium values. The top and bottom rows of Figure 3 show the consequences of aggregate demand shocks of 0.5 percentage points in the United States and Japan. Qualitatively, the demand shockshavethesameconsequencesineacheconomy,howevertheyexhibitsomequantitative differences. For example, the inflationary impact of the demand shock is largest in the 22

Figure4: ComparingContractWageShocksintheUnitedStates, theEuroAreaandJapan Output Gap Annual Inflation Short−Term Nominal Interest Rate Real Effective Exchange Rate 1.0 1.0 1.0 5.0 0.5 0.5 0.5 2.5 United States 0.0 0.0 0.0 0.0 −0.5 −0.5 −0.5 −2.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 1.0 1.0 1.0 5.0 0.5 0.5 0.5 2.5 Euro Area 0.0 0.0 0.0 0.0 −0.5 −0.5 −0.5 −2.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 1.0 1.0 1.4 5.0 0.5 0.5 0.7 2.5 Japan 0.0 0.0 0.0 0.0 −0.5 −0.5 −0.7 −2.5 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Quarters Quarters Quarters Quarters Notes: Solid line: United States. Dashed line: Euro Area. Dot-dashed line: Japan. United States due to the Fuhrer-Moore style overlapping contracts specification, which induces more inflation persistence. Also, output in Japan does not exhibit a hump-shaped pattern as would be expected given the estimated coefficient on the lags of the output gap in the aggregate demand equation. We also compare the domestic and international consequences of a short-run supply shock, that is, a shock to the contract wage equations in our model. As shown in Figure 4 apositivecontractwageshockputsupwardpressureoninflation. Monetarypolicyresponds 23

by increasing interest rates. As a result, output declines and the exchange rate appreciates. International consequences are again minor when nominal exchange rates are flexible. The output costs of stabilizing inflation are not surprisingly largest in the United States, for which we have chosen a supply-side specification with Fuhrer-Moore contracts. 6 Monetary policy rules and the role of the exchange rate Finally we turn to assessing the stabilization performance of alternative monetary policy rules and the role of the exchange rate for monetary policy within our multi-country model. Wereportinitialresultsfromanexploratoryanalysisthatindicatessomeinterestingavenues for further work but should still be considered preliminary. Our starting point is an evaluation of simple outcome-based interest rate rules, which respond to the annual average inflation rate, the output gap and the lagged short-term nominal interest rate. An important argument in favor of such rules is that they seem to be surprisingly robust to model uncertainty (see for example the introduction to Taylor, ed., (1999) and Levin, Wieland and Williams (1999, 2001)). However, from a perspective of monetary policymaking in open economies such rules have been criticized for lacking an explicitfeedbacktotheexchangerate(cf. Ball(1999), BatiniandHaldane(1999), Svensson (2000) and Taylor (2001)). Thus, in this paper, we consider the following class of policy rules: i t = ρi t−1+(1−ρ)(r∗ +π t)+α(π t (4)−π∗ )+βq t+ξew t . (14) First, we restrict the response parameter ξ on the exchange rate to be equal to zero and choose the other three response parameters so as to minimize the policymaker’s loss function. Weassumethatthislossfunctionequalstheweightedaverageoftheunconditional variances of inflation and output gaps, L = Var[π t]+λVar[q t]. (15) FollowingtheapproachinLevinetal. (1999,2001)weminimizethelossfunctionsubject to the constraint that the volatility of the change of the nominal interest rate is no greater 24

Table 5: Optimized Simple Policy Rules without Exchange Rate Feedback. United States Euro Area Japan λ ρ α β ρ α β ρ α β 0 0.94 0.38 0.04 0.99 0.26 0.05 1.02 0.18 0.02 1/3 0.92 0.25 0.16 0.90 0.11 0.24 0.99 0.13 0.09 1 0.91 0.16 0.20 0.89 0.00 0.35 0.95 0.04 0.18 3 0.89 0.08 0.23 0.92 0.00 0.35 0.96 0.00 0.20 Notes: Foreachofthecountries(j)andforeachpreferenceparameter(λ),thistableindicatestheoptimal coefficients (ρ, α and β). than under the estimated policy rules reported in Table 4. The coefficients of simple rules optimized in this manner for four alternative values of the weight λ = (0,1/3,1,3) are reported in Table 5. As in Levin et al (1999) we find that the optimal value of the interest-rate smoothing coefficient ρ is near unity. Also, the value of the coefficent on inflation, α, (on output, β) decreases (increases) with a greater weight on output variability in the loss function. The optimized response coefficients for the three economies are surprisingly similar given that the estimated model specifications anddynamicsarequitedifferent. Somewhatsurprisinglytheinflationcoefficientαisalmost equal to zero for the euro area and Japan when we consider a weight on output equal or 27 greater unity. In a second step, we relax the restriction of no exchange rate feedback and optimize over all four response coefficients (ρ,α,β,ξ). The resulting coefficients and the percent change in the loss function relative to rules without exchange rate feedback are reported in Table 6. For each of the three economies the optimal coefficient on the exchange rate turns out to be near zero, while the associated reduction in the loss function remains negligible. 27Wehaveinvestigatedwhetherthisresultisrobusttoalternativevaluesoftheconstraintoninterestrate volatility and found that allowing for a higher degree of interest rate volatility (i.e. more aggressive policy rules) induces positive response coefficients on inflation also for higher values of the weight λ. 25

Table 6: Optimized Simple Rules with Exchange Rate Feedback United States Euro Area Japan λ ρ α β ξ L ρ α β ξ L ρ α β ξ L 0 0.94 0.36 0.04 -0.00 -0.01 1.00 0.27 0.05 0.00 -0.01 1.02 0.18 0.02 0.00 -0.00 1/3 0.92 0.24 0.15 -0.00 -0.01 0.91 0.13 0.26 0.01 -0.03 0.99 0.14 0.09 0.00 -0.01 1 0.91 0.17 0.21 0.00 -0.01 0.90 0.00 0.43 0.02 -0.29 0.96 0.05 0.20 0.00 -0.04 3 0.91 0.11 0.25 0.02 -0.10 0.93 0.00 0.50 0.04 -1.59 0.97 0.00 0.23 0.01 -0.25 Notes: Foreachofthecountries(j)andforeachpreferenceparameter(λ),thistableindicatestheoptimalcoefficients (ρ, α, β andξ)andthepercentagechangeinthepolicy-makers’ lossfunctions(L)comparedwiththelossesunder optimized policy rules which exclude the real exchange rate. Thus, the existence of the exchange rate channel in the open economy does not seem to require an economically significant direct response of policy to the exchange rate within our multi-country model. Table 7: Coefficients of Cooperatively Optimized Monetary Policy Rules United States Euro Area Japan λ ρ α β ρ α β ρ α β 0 0.95 0.38 0.04 0.99 0.25 0.05 1.01 0.17 0.02 1/3 0.92 0.25 0.15 0.89 0.10 0.24 0.98 0.12 0.08 1 0.91 0.16 0.19 0.88 0.00 0.33 0.94 0.03 0.17 3 0.89 0.08 0.22 0.91 0.00 0.33 0.94 0.00 0.20 Notes: Foreachofthecountries(j)andforeachpreferenceparameter(λ),thistableindicatestheoptimal coefficients (ρ, α and β). Another issue that has been widely debated in open-economy macroeconomics concerns the gains from international monetary policy coordination. To obtain a first quantitative assessementregardingthisquestionwederivetheoptimalpolicycoefficientsundermonetary 26

cooperation with the objective to minimize the average of the losses in the three economies. These coefficients, which are shown in Table 7, turn out to be surprisingly similar to the optimal coefficients under nationally-oriented monetary policies. Furthermore, as shown in Table 8 the percentage reduction in losses that any one country could achieve by deviating from the cooperative policy unilaterally is rather small. Thus, there seems to be little to loose but also little to gain from international monetary cooperation in the context of stabilization policy within our model. However, to settle this question satisfactorily we still need to compute the non-cooperative Nash equilibrium, for which all three policy-makers minimize national (or area-wide) losses. Table 8: Stabilisation Gains of Self-Oriented National Monetary Policies United States Euro Area Japan λ L L L L L L L L L US EA JA US EA JA US EA JA 0 -0.04 0.01 0.01 0.03 -0.02 0.01 0.10 0.02 -0.02 1/3 -0.07 0.06 0.03 0.14 -0.10 0.04 0.26 0.08 -0.08 1 -0.11 0.14 0.06 0.18 -0.18 0.06 0.30 0.19 -0.21 3 -0.19 0.34 0.14 0.23 -0.33 0.11 0.45 0.36 -0.46 Notes: For each of the countries (j) and for each preference parameter (λ), this table indicates the percentage point change in the policy-makers’ loss functions (L j) when monetary policy of a single country isconductedinaself-orientedmannercomparedwiththelossesunderthecooperativelyoptimizedpolicy rules. In our view, the stark results regarding the role of the exchange rate and international policy coordination within our multi-country model require further corroboration by means of sensitivity studies. As a first step in this direction, we re-consider the channel through which the exchange rate affects the domestic economies in our model. So far, we have only included an expenditure-switching effect on aggregate demand. A natural extension would be to include a direct effect of the exchange rate on prices in each economy. To this end we need to distinguish between prices for domestic goods and import prices which 27

may be directly affected by the exchange rate depending on the degree of exchange-rate pass-through. Rather than going back and re-estimating the supply-side of our model, we simply add this channel to the existing model by defining, for each country i, the overall price level pall,(i) as the weighted sum of the domestic price level p(i) and a direct effect of t t the bilateral nominal exchange rates en,(j) via import prices, t (cid:1) p t all,(i) = (1−χ)p( t i) +χ w (i,j)(en t ,(j) +p( t j) ), j(cid:2)=i where χ measures the share of import prices and exchange-rate pass-through is assumed to 28 be immediate and complete. Table 9: Openness and Optimized Monetary Policy Rules for the United States χ=0.05 χ=0.10 χ=0.20 λ ρ α β ξ L ρ α β ξ L ρ α β ξ L Domestic-Inflation Target 0 0.88 3.79 -0.02 -0.09 -6.69 0.86 6.50 -0.04 -0.06 -1.48 0.90 4.77 -0.02 0.06 -0.75 1/3 0.81 2.80 0.31 -0.07 -0.20 0.75 5.97 0.27 0.03 -0.01 0.82 4.63 0.09 0.08 -0.06 1 0.87 1.36 0.50 0.04 -0.05 0.70 4.17 0.69 0.03 -0.00 0.73 4.20 0.32 0.15 -0.06 3 1.01 0.67 0.66 0.05 -0.13 0.83 2.15 1.31 0.22 -0.14 0.72 2.71 0.79 0.37 -0.19 Overall-Inflation Target 0 0.85 7.86 -0.07 -0.03 -2.23 0.95 4.66 -0.04 0.07 -2.55 1.04 2.34 -0.01 0.31 -14.56 1/3 0.63 6.05 0.45 0.01 -0.00 0.83 4.31 0.14 0.09 -0.19 0.99 2.24 0.03 0.32 -2.26 1 0.67 2.99 0.84 0.03 -0.02 0.71 3.51 0.43 0.14 -0.19 0.92 2.07 0.11 0.33 -0.94 3 0.88 0.94 0.87 0.05 -0.05 0.71 1.98 0.91 0.25 -0.31 0.78 1.62 0.32 0.38 -0.48 Notes: For each of the different degrees of openness (χ), for each preference parameter (λ) and for the alternative inflation targets (π∗), this table indicates the optimal coefficients (ρ, α, β and ξ) and the percentage change in thepolicy-makers’lossfunctions(L)comparedwiththelossesunderoptimizedpolicyruleswhichexcludethereal exchange rate. 28Forrecentstudiesofexchangeratepass-throughseeCampaandGoldberg(2002)andGagnonandIhrig (2002). 28

Table 9 reports the coefficients of optimized policy rules in the United States given alternative values for the direct effect of exchange rates on U.S. overall inflation (i.e. χ = 0.05,0.10or0.20). Weconsidertwodifferentscenarios,oneinwhichmonetarypolicytargets domestic inflation only and one where it targets overall inflation. Wage-setters are assumed to look at overall inflation. Introducing a direct effect of the exchange rate on prices clearly changes some of our earlier results. First, the optimal policy response to inflation is now rather large. Secondly, we now obtain more substantial gains from including the exchange rate in the policy rule. These gains are greatest when the policymaker targets overall inflation and the share of import prices is rather large. In our ongoing work we are investigating the robustness of these findings. 7 Conclusion Our empirical analysis of inflation and output dynamics in the United States, the euro area and Japan has provided some new results regarding the role of staggered contracts as sources of nominal rigidity and inflation persistence. First, we find it impossible to match inflation dynamics with Calvo-style random-duration contracts except if we allow for a significant share of price setters with backward-looking behavior or for ad-hoc persistence in supply shocks. For Taylor-style fixed duration contracts, however, we obtain economically meaningfulandstatisticallysignificantparameterestimatesforallthreeeconomies. Fuhrer- Moore-stylecontractsonlydominateTaylor-stylecontractsforU.S.inflationdynamics. One possible interpretation of this finding is that the United States just suffer from a higher degree of nominal rigidity than the euro area or Japan. A plausible alternative interpretation is that this difference in historical inflation persistence may be due to a difference in historical monetary policy. In particular, since U.S. monetary policy accommodated oil-price induced inflation increases in the 1970s, much more than Japanese or German monetary policymakers, thehigherdegreeofhistoricalinflationpersistencemayalsohavebeencaused by a lack of credibility to keep inflation under control in the late 1970s and early 1980s (see 29

also Erceg and Levin (2001) on this point). After completing our macro-econometric model with an admittedly more ad-hoc specification of the demand side we find that it fits inflation and output dynamics quite well. Including or excluding the real exchange rate channel on the demand side does not seem to matter much for the ability of this model to account for the observed degree of inflation and output persistence. International spillovers turn out to be rather small as long as nominal exchange rates are flexible. Our preliminary investigation of optimized simple policy rules indicates little gain from a direct policy response to the real exchange rate. Furthermore, potential gains from international monetary coordination of stabilization policies seem rather limited. Such coordination may be more important in exceptional circumstances, for example when interest rate policy in one economy is constrained by the zero bound on nominal interest 29 rates. 29See for example, Svensson (2001), McCallum (2000). 30

References Anderson, G. S. and G. R. Moore, 1985, A linear algebraic procedure for solving linear perfect foresight models, Economics Letters, 17, 247-252. Ball, L., 1999, Policy rules for open economies, in John B. Taylor (ed.), Monetary Policy Rules, NBER and Chicago Press, June 1999. Batini, N. and A. Haldane, 1999, Forward-looking rules for monetary policy, in John B. Taylor (ed.), Monetary Policy Rules, NBER and Chicago Press, June 1999. Blanchard, O. J. and C. Kahn, 1980, The solution of linear difference models under rational expectations, Econometrica, 48, 1305-1311. Buiter, W. H. and I. Jewitt, 1981, Staggered wage setting with real wage relativities: Variations on a theme of Taylor, The Manchester School, 49, 211-228, reprinted in W. H. Buiter (ed.), 1989, Macroeconomic theory and stabilization policy, Manchester: Manchester University Press. Campa, J.M. and L. Goldberg, 2002, Exchange rate pass-through into import prices: A macro or micro phenomenon ?, working paper, Federal Reserve Bank of New York, April 2002. Calvo,G.A.,1983,Staggeredpricesinautility-maximizingframework,JournalofMonetary Economics, 12,3, 383-398. Chari, V. V., P. Kehoe and E. McGrattan, 2000, Sticky price models of the business cycle: Canthecontractmultipliersolvethepersistenceproblem?,Econometrica,68,5,1151-1180. Christiano, L., Eichenbaum, M. , and M. Evans, 2001, Nominal rigidities and the dynamic effects of a shock to monetary policy, Federal Reserve Bank of Cleveland, Working Paper No. 01/07. Clarida, R., J. Gal´ı and M. Gertler, 1998, Monetary policy rules in practice: Some international evidence, European Economic Review, 42, 1033-1067. Clarida, R., J.Gal´ıandM.Gertler, 1999, Thescienceofmonetarypolicy: AnewKeynesian perspective, Journal of Economic Literature, 37, 1661-1707. Coenen, G., 2000, Asymptotic confidence bands for the estimated autocovariance and autocorrelation functions of vector autoregressive models, European Central Bank, Working Paper No. 9. Coenen, G. and V. Wieland, 2000, A small estimated euro area model with rational expectations and nominal rigidities, ECB Working Paper, No. 30. Erceg, C. and A. Levin, 2001, Imperfect credibility and inflation persistence, Finance and Economics Discussion Series, Federal Reserve Board, No. 2001-45. Fagan, G., J. Henry and R. Mestre, 2001, An area-wide model (AWM) for the EU11, ECB Working Paper No. 42. 31

Fuhrer,J.C.andG.R.Moore,1995a,Inflationpersistence,QuarterlyJournalofEconomics, 110, 127-159. Fuhrer, J. C. and G. R. Moore, 1995b, Monetary policy trade-offs and the correlation between nominal interest rates and real output, American Economic Review, 85, 219-239. Gagnon, J. and J. Ihrig, 2002, Monetary policy and exchange rate pass-through, working paper, Federal Reserve Board, March 2002. Gal´ı, J. and M. Gertler, 1999, Inflation dynamics: A structural econometric analysis, Journal of Monetary Economics, 44, 195-222. Gouri´eroux, C.andA.Monfort, 1996, Simulation-based inferencemethods, Oxford: Oxford University Press. Gouri´eroux, C., A. Monfort and E. Renault, 1993, Indirect inference, Journal of Applied Econometrics, 8, Special issue: Econometric inference using simulation techniques, S85- S118. King, R. and A. Wolman, (1999), What should the monetary authority do when prices are sticky, in: John B. Taylor, Monetary Policy Rules, NBER and Chicago Press. Levin, A., Williams, J.C., and V. Wieland, The performance of forecast-based monetary policy rules under model uncertainty, Finance and Economics Discussion Series, 2001-39, Federal Reserve Board. Levin, A., Williams, J.C., and V. Wieland, Robustness of simple monetary policy rules under model uncertainty, in John B. Taylor (ed.), Monetary Policy Rules, NBER and Chicago Press, June 1999. McCallum,B.T,2000,Theoreticalanalysisregardingazerolowerboundonnominalinterest rates, Journal of Money, Credit and Banking, 32. McCallum, B. T., 2001, Analysis of the monetary transmission mechanism: methodological Issues, in Deutsche Bundesbank (ed.), The monetary transmission process: Recent developments and lessons for Europe, Basingstoke: Palgrave. McCallum, B. T. and E. Nelson, 1999, Performance of operational policy rules in an estimated semiclassical structural model, in Taylor, 1999. Neiss, K. and E. Nelson, 2002, Inflation dynamics, marginal cost and the output gap: Evidence from three countries, working paper, Bank of England. Newey, W. K. and K. D. West, 1987, A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica, 55, 703-708. Roberts, J., 1997, Is inflation sticky?, Journal of Monetary Economics, 39, 173-196. Rotemberg, J. and M. Woodford, 1997, An optimization-based econometric framework for theevaluationofmonetarypolicy, NBERMacroeconomicsAnnual, Cambridge: MITPress. Rotemberg,J.andMWoodford,1999,Interest-raterulesinanestimatedstickypricemodel, 32

in Taylor, 1999. Rudd, J. and K. Whelan, 2002, Should monetary policy target labor’s share of income?, working paper, Federal Reserve Board. Rudebusch, G. and L. E. O. Svensson, 1999, Policy rules for inflation targeting, in Taylor, 1999. Sbordone, A., 2002, Price and unit labor costs: A new test of price stickiness, Journal of Monetary Economics, 2002, vol. 49(2), pp. 265-292. Smith, A. A., 1993, Estimating nonlinear time-series models using simulated vector autoregressions, Journal of Applied Econometrics, 8, Special issue: Econometric inference using simulation techniques, S63-S84. Svensson, L.E.O., 2000, Open-economy inflation targeting, Journal of International Economics,50, 155-183. Svensson, L.E.O., 2001, The zero bound in an open economy: A foolproof way of escaping from a liquidity trap, Monetary and economic studies, February 2001. Taylor, J. B., 1980, Aggregate dynamics and staggered contracts, Journal of Political Economy, 88, 1-24. Taylor, J.B., 1993a, Macroeconomicpolicyintheworldeconomy: Fromeconometricdesign to practical operation, New York: W.W. Norton. Taylor, J. B., 1993b, Discretion versus policy rules in practice, Carnegie-Rochester Conference Series on Public Policy, 39, 195-214. Taylor, J. B. (ed.), 1999, Monetary policy rules, Chicago: NBER and University of Chicago Press. Taylor, J.B., 2001, The role of the exchange rate in monetary-policy rules, American Economic Review, May, 91,2, 263-267. Wieland, V., 1996, Monetary policy targets and the stabilization objective: A source of tension in the EMS, Journal of International Money and Finance, 15, 95-116. 33

Appendix A.1 Estimation Methodology TheunconstrainedVARsthatweusetosummarizeempiricaloutputandinflationdynamics for the three economies under consideration take the following form, (cid:11) (cid:12) (cid:11) (cid:12) (cid:11) (cid:12) (cid:11) (cid:12) (cid:11) (cid:12) π π π π u q t = A 1 q t−1 +A 2 q t−2 +A 3 q t−3 + u π,t , (A.1) t t−1 t−2 t−3 q,t where q t refers to the output gap and π t to inflation and the error terms u π,t and u q,t are assumed to be serially uncorrelated with mean zero and covariance matrix Σu. We find that a maximum lag length of 3, which corresponds to a maximum contract length of 1 year, is sufficient to capture the observed degree of inflation and output persistence for the economies under consideration. The second stage of the estimation procedure involves the estimation of the structural parameters of the staggered contracts models using the unconstrained VARs as approximating probability models. Of course, the overlapping contracts specifications alone do not represent a complete model of inflation determination. Since the contract wage equations contain expected future output gaps, we need to specify how the output gap is determined in order to solve for the reduced-form representation of inflation and output dynamics for each contract specification. A full-information estimation approach would require estimating all the structural parameters of the complete multi-country model jointly. We take a less ambitious approach and simply use the output gap equation from the unconstrained 30 VAR (the second row in (A.1)) as an auxiliary equation for output determination. Using the output equation from the unconstrained VAR together with the wage-price block, we can solve for the reduced-form inflation and output dynamics under each stag- 31 gered contracts specification. In the case Taylor- and Fuhrer-Moore-Style contracts it is convenient to rewrite the wage-price block in terms of the real contract wage (x−p)t and the annualized quarterly inflation rate π t. The reduced-form of these models is a trivariate constrained VAR. While the quarterly inflation rate π t and the output gap q t are observable variables, the real contract wage (x−p)t is unobservable. Given a maximum contract length of one year this constrained VAR can be written as follows:         (x−p)t (x−p)t−1 (x−p)t−2 (x−p)t−3          π t  = B 1 π t−1 +B 2 π t−2 +B 3 π t−3 +B 0 (cid:7) t , (A.2) q q q q t t−1 t−2 t−3 where (cid:7) t is a vector of serially uncorrelated error terms with mean zero and positive (semi-) definite covariance matrix, which is assumed to be diagonal with its non-zero elements normalized to unity. The coefficients in the bottom row of the B i matrices (i = 0,1,2,3) 30This limited-information approach follows Taylor (1993a) and Fuhrer and Moore (1995a). 31We employ the AIM algorithm of Anderson and Moore (1985), which uses the Blanchard and Kahn (1980) method for solving linear rational expecations models, to compute model-consistent expectations. 34

coincide exactly with the coefficients of the output gap equation of the unconstrained VAR, with the B 0 coefficients obtained by means of a Choleski decomposition of the covariance matrix Σu. The reduced-form coefficients in the upper two rows of the B i matrices, which are associated with the determination of the real contract wage and inflation, are functions ofthestructuralparameters(f i ,γ,σ (cid:1)x )aswellasthecoefficientsoftheoutputgapequation of the unconstrained VAR. In fitting the constrained VAR we employ the indirect inference methods proposed by Smith (1993) and Gouri´eroux, Monfort and Renault (1993) and developed further in Gouri´eroux and Monfort (1996) to estimate the structural parameters f i, γ and σ (cid:1)x . Indirect inference is a simulation-based procedure that provides a precise way of comparing a model to the data by comparing key characteristics, which themselves are quantities 32 that require estimation via an auxiliary model. In our case, the aim of the estimation procedure is to find values of the structural parameters such that the degree of inflation persistence exhibited by the structural model matches the persistence in the inflation data as summarized by the inflation equation of the unconstrained VAR models discussed above. An advantage of this indirect inference procedure is that the approximating probability model (the unconstrained VAR) does not require controversial identifying assumptions. Furthermore, since the VAR parameters also determine the autocovariance functions of inflation and output, matching those parameters is essentially equivalent to matching the autocorrelations and cross-correlations of the VAR. In this sense, indirect inference based on the estimated parameters of the unconstrained VAR model is an efficient and robust way to make use of the relevant information contained in the data. By contrast, informal model calibration techniques, but also methods-of-moments based estimation, typically rely onasmallsetofoftensubjectivelychosenstandarddeviationsandautocorrelationsdirectly inferred from the data. Of course, one cannot always directly match the parameters of the constrained VAR model (A.2) with the parameters of the unconstrained VAR model (A.1) because the constrained model also includes the real contract wage, which is unobservable. Instead, we first simulate the constrained VAR to generate “artificial” series for the real contract wage, the inflation rate and the output gap for given values of the structural parameters and the 33 parametersofthereduced-formoutputgapequation. Inasecondstep, wethenfittheunconstrained VAR model to the inflation and output gap series generated in this manner and match the simulation-based estimates of the inflation equation as closely as possible with the empirical estimates by searching over the feasible space of the structural parameters. 32Formally, indirect inference provides a rigorous statistical foundation for data-based calibration techniques,whichhavebecomeincreasinglypopularinmacroeconomicmodellinginrecentyears. Theprocedure itselfincludingitsasymptoticproperties,isdiscussedindetailintheappendixoftheworkingpaperversion of Coenen and Wieland (2000). There, we also provide a comparison to the maximum-likelihood methods used by Taylor (1993a) and Fuhrer and Moore (1995a). 33All that is needed for simulation are three initial values for each of these variables and a sequence of randomshocks. Inestimationweusesteady-statevaluesasinitialconditions. Wedropseveralyearsofdata from the simulations so as to avoid an estimation bias due to these initial conditions. 35

A.2 The Data Figure A: The Data for the United States, the Euro Area and Japan Output Gap Inflation Rate 12.00 25.0 8.00 20.0 4.00 15.0 0.00 10.0 −4.00 5.0 −8.00 0.0 −12.00 −5.0 1975 1980 1985 1990 1995 2000 1975 1980 1985 1990 1995 2000 Year Year Short−Term Nominal Interest Rate Real Effective Exchange Rate 25.0 −3.0 20.0 −3.5 15.0 −4.0 10.0 −4.5 5.0 −5.0 0.0 −5.5 −5.0 −6.0 1975 1980 1985 1990 1995 2000 1975 1980 1985 1990 1995 2000 Year Year Notes: Solid line: United States. Dashed line: Euro Area. Dot-dashed line: Japan. 36

A.3 Additional Estimation Results Table A: Estimated Contracting Specifications with Restrictions on Contract Weights s γ σ (cid:1)x p-value(d) Taylor Wage Contracts United States(a,b) 0 0.0093 0.0053 < 10−13[5] (0.0056) (0.0002) Euro Area(a,c) 0.0456 0.0115 0.0038 0.3186[4] (0.0465) (0.0053) (0.0005) Japan(a,b) 0.0086 0.0178 0.0080 0.0083[4] (0.0153) (0.0055) (0.0004) Fuhrer-Moore Wage Contracts United States(a,b) 0 0.0118 0.0034 0.6426[5] (0.0041) (0.0002) Euro Area(a,c) 0.0742 0.0212 0.0024 0.2602[4] (0.0245) (0.0048) (0.0003) Japan(a,b) 0.0771 0.0048 0.0044 0.0049[4] (0.0284) (0.0046) (0.0006) Notes: (a) Simulation-basedindirectestimatesusingaVAR(3)modelofquarterlyinflationandtheoutput gap as auxiliary model. Estimated standard errors in parentheses. (b) Output gap measure constructed using OECD data. (c) Inflation in deviation from linear trend and and output in deviation from loglinear trend. (d) Probability value associated with the test of overidentifying restrictions. Number of overidentifying restrictions in brackets. 37

Table B: Estimated Aggregate Demand Equations for the Closed Economies δ 1 δ 2 δ 3 φ σ (cid:1) p-value(e) d United States(a,b) 1.2297 -0.1063 -0.2586 -0.1436 0.0072 0.5455[5] (0.0678) (0.1141) (0.0864) (0.0454) Euro Area(a,c,d) 1.0398 0.0510 -0.1183 -0.0832 0.0054 0.3114[5] (0.0985) (0.0774) (0.0678) (0.0695) Japan(a,b) 0.9374 -0.0815 0.0068 0.5733[7] (0.0237) (0.0498) Notes: (a) GMM estimates using a constant, lagged values (up to order three) of the output gap, the quartely inflation rate and the short-term nominal interest rate. The weighting matrix is estimated by means of the Newey-West (1987) estimator with the lag truncation parameter set equal to the maturity implied by the definition of the long-term nominal interest rate minus one. Estimated standard errors in parentheses. (b) Output gap measure constructed using OECD data. (c) Output measured in deviation from log-linear trend. (d) For the euro area, the German long-term real interest rate has been used in the estimation. Similarly, German inflation and short-term nominal interest rates have been used as instruments. (e) Probability value associated with the test of overidentifying restrictions. Number of overidentifying restrictions in brackets. 38