Technology Shocks: Novel Implications for International Business Cycles

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 992 January 2010 Technology Shocks: Novel Implications for International Business Cycles Andrea Raffo 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 References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.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/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Technology Shocks: Novel Implications for International Business Cycles Andrea Raffo (cid:3) Board of Governors of the Federal Reserve System First Draft: December 2007. Current version: December 2009. Abstract Understandingthejointdynamicsofinternationalpricesandquantitiesremainsacentral issue in international business cycles. International relative prices appreciate when domestic consumption and output increase more than their foreign counterparts. In addition, both trade(cid:3)owsandtradepricesdisplaysizablevolatility. ThispaperincorporatesHicks-neutral and investment-speci(cid:2)c technology shocks into a standard two-country general equilibrium modelwithvariablecapacityutilizationandweakwealtheffectsonlaborsupply. Investmentspeci(cid:2)c technology shocks introduce a source of (cid:3)uctuations in absorption similar to taste shocks,thusreconcilingtheoryanddata. ThepaperalsopresentsimplicationsforthetransmissionmechanismoftechnologyshocksacrosscountriesandfortheBarroandKing(1984) critiqueofinvestmentshocks. JELClassi(cid:2)cation: E32;F32;F41 Keywords: Backus-Smith puzzle; Investment-speci(cid:2)c technology shocks; International businesscycles. Correspondence: andrea.raffo@frb.gov. I would like to thank M. Bodenstein, V.V. Chari, C. Engel, J. Heath- (cid:3) cote, N. Kocherlakota, S. Leduc, F. Perri, my discussants F. Canova and N. Li, and seminar participants at the 2009NBER-IFMMeetings,2009MGI-CEPRMeetings,2008SEDMeetings,2008EEAMeetings,2008Midwest MacroeconomicMeetings,FederalReserveBoard,GWU,IMF,KansasCityFRB,MinneapolisFRB,Philadelphia FRB,UCLA,UVA,UW-Madison,andtheWorldBankforcommentsandsuggestions. PaulEitelmanandMichelle Olivierprovidedoutstandingresearchassistance. Theviewsexpressedinthispaperaresolelytheresponsibilityof the author and should not be interpreted as re(cid:3)ecting the views of the Board of Governors of the Federal Reserve SystemorofanyotherpersonassociatedwiththeFederalReserveSystem.

1 Introduction SincetheseminalworkbyBackus,KehoeandKydland[1992,1994](BKKhenceforth),general equilibrium models driven by Hicks-neutral technology shocks (or TFP shocks) have provided valuable insights on a wide range of international business cycle features. Notably, the countercyclical behavior of the trade balance is well understood within the realm of these models. Accountingforthejointdynamicsofinternationalpricesandquantities,however,remainsacentral issue of international business cycles. Two features of the data have received much attention in the literature. First, international relative prices tend to appreciate when domestic consumptionandoutputincreasemorethantheirforeigncounterparts.1 Second,bothinternationalrelative pricesandtrade(cid:3)owsarevolatileoverthebusinesscycle.2 Thesestylizedfactsbearimplications for the transmission of shocks across countries, the degree of international risk-sharing, and the sourcesofbusinesscycle(cid:3)uctuations. Thispapershowsthatunderstandingthejointdynamicsofinternationalpricesandquantities requires generating large shifts in domestic absorption relative to output. I then propose a theory that involves an additional source of technological variation (investment-speci(cid:2)c technology or IST shocks), a transmission mechanism with higher short-run response of output to shocks (through changes in the utilization of installed capital), and weak wealth effects on labor supply. Interestingly,thetwofeaturesofdataofinterestturnouttobepropertiesoftheef(cid:2)cientallocation chosenbyasocialplanner. Recent empirical evidence suggests that TFP and IST shocks jointly account for a large fraction of the variation in output and hours over the business cycle.3 In this broader interpretation 1See, for instance, Backus-Smith [1993], Kollman [1995], Stockman and Tesar [1995], Chari, Kehoe and Mc- Grattan[2002],BenignoandThoenissen[2008]andCorsetti,DedolaandLeduc[2008]. 2SeetheoriginalBackus,KehoeandKydland[1994]work,Baxter[1995],Boileau[1999],HeathcoteandPerri [2002],EngelandWang[2008]. 3Early studies on the importance of investment-speci(cid:2)c technology shocks include Greenwood et al. [1988], HansenandPrescott[1993]andGreenwoodetal. [2000]. Morerecently, Fisher[2006]estimatesthatneutraland investment-speci(cid:2)ctechnologyshocksaccountforalmosteightypercentofthevariationofoutputinthepost-1982 period. Justiniano et al. [2008] (cid:2)nd similar results estimating a medium-scale DSGE model that includes several shocksandfrictions. JustinianoandPrimiceri[2008]arguethatchangesinthevolatilityofinvestmentshockscan 1

of technology shocks, investment shocks often drive business cycles. The empirical literature, however, typically abstracts from open economy considerations: one contribution of the paper is to explore the theoretical and quantitative implications of this view of technology shocks for internationalbusinesscycles. From the perspective of the theory, I modify an otherwise standard two-country model (cid:224) la BKK along two dimensions. First, I introduce variable capacity utilization. Hence, technology shocks stimulate output and the accumulation of capital through a more intensive utilization of installed capital. Second, I consider a class of preferences with no intertemporal substitution on laborefforts(GHHpreferences),asinGreenwood,Hercowitz,andHuffman[1988].4 Ishowthat this framework is quantitatively consistent with the empirical properties of international relative pricesandtrade(cid:3)owsdocumented,withoutaffectingthestandardbusinesscycleregularities. Realexchangeratesinthedataappreciatewhendomesticconsumptionishigherthanforeign consumption, leading to a low and often negative correlation between real exchange rates and relative consumption. Therefore, consumption is higher where it is more expensive. Theoretical models produce large and positive correlations between the real exchange rate and relative consumption, as the real exchange rate is tightly linked to the ratio of marginal utilities of consumption. Thestandardtheoryimpliesthatconsumptionishigherwhereveritischeaper,instark contrastwiththedata. TheliteratureoftenreferstothisfailureofthetheoryastheBackus-Smith puzzle(seeBackus-Smith[1993])orconsumption-realexchangerateanomaly(seeChari,Kehoe andMcGrattan[2002]). Fluctuationsinthetermsoftradearealsodif(cid:2)culttoreconcilewithstandardmodelsofinternational business cycles. In the data, the terms of trade tend to appreciate when domestic output increases more than foreign output, as documented in Corsetti, Dedola and Leduc [2007] among others. In the standard models, the terms of trade re(cid:3)ect primarily the relative scarcity in proexplainmostofthechangesinvolatilityofU.S.macroeconomicvariablesduringthepost-warperiod. 4GHH preferences are commonly used in open economy models. See Raffo [2008] for a survey. For an early contribution on the role of variable capacity utilization in the transmission of neutral technology shocks across countries,seeBaxterandFarr[2005]. 2

duction across countries. An increase in domestic production induced by a change in total factor productivity is associated with a depreciation of the terms of trade, as domestic goods are more abundantthanforeigngoodsininternationalmarkets. Last, in the data both net exports and the terms of trade display sizable volatility over the business cycle: net exports are half as volatile as output and the terms of trade are almost twice as volatile as output. In the model, general equilibrium effects introduce a trade-off between the volatility of relative prices and the volatility of trade (cid:3)ows. When the trade structure is de(cid:2)nedbyaconstant-elasticity-of-substitutionaggregatoroverdomesticandforeigngoods,asin Armington[1969],themodelinheritsaninverserelationshipbetweenthevolatilityoftrade(cid:3)ows and international prices. The higher (lower) the elasticity of substitution between traded goods, thelarger(smaller)theresponseofpricestoshocks,whereastheoppositeistrueforquantities. Accountingfortheaforementionedpropertiesofthedatarequireslargechangesinabsorption over the business cycle. The main insight of the paper is that IST shocks provide a plausible source of variation in domestic absorption, since they do not affect directly aggregate ef(cid:2)ciency. In this dimension, they resemble taste shocks. The economy accommodates a positive shift in absorption by (i) increasing production of intermediate goods, (ii) increasing prices, and (iii) increasing imports of goods from abroad. As a consequence, the terms of trade appreciate and the trade balance deteriorates. When IST shocks account for a signi(cid:2)cant fraction of business cycle(cid:3)uctuations,assuggestedbytheempiricalliterature,themodelgeneratesanappreciationof international relative prices during expansions and large volatility of international relative prices andquantities,consistentwiththedata. I then present two implications derived from this theory. The (cid:2)rst is about the direction of terms of trade changes associated with different technology shocks. In response to TFP shocks, the terms of trade primarily re(cid:3)ect relative changes of traded goods production across countries. Thetermsoftradedepreciatewhentheeconomyexpands. InresponsetoISTshocks,incontrast, shiftsindomesticabsorptionaffectdirectlytherelativedemandoftradedgoodsacrosscountries. The terms of trade appreciate when the economy expands. So, these (cid:2)ndings suggest a recon- 3

sideration of the international transmission of technology shocks as typically interpreted in the empiricalliterature.5 The second implication is about domestic comovement. In a frictionless closed economy model, shocks to the marginal ef(cid:2)ciency of investment stimulate labor effort and output through intertemporal substitution of leisure. However, agents choose to postpone consumption as well, resulting in a negative comovement of consumption with labor and investment, which is counterfactual. This observation, originally due to Barro and King [1984], points toward a limited roleofinvestmentshocksinaccountingforbusinesscycle(cid:3)uctuations. Ishowthatthetransmission mechanism exploited in the paper, which relies on variable capacity utilization and weak wealth effects on labor supply, can preserve comovement among domestic variables. Perhaps surprisingly,I(cid:2)ndthatthepossibilityofimportinggoodsfromabroadhasverylittlequantitative impact on comovement. Thus, despite the strong response of output to investment shocks, the benchmarkmodelreproducesthetypicalbusinesscyclefeaturesobservedinthedata. 2 Empirical Motivation Thissectionpresentsthetwomainfactsthatmotivatemystudy: thatinternationalrelativeprices tend to appreciate when domestic consumption and output increase more than abroad; and that both the terms of trade and trade (cid:3)ows are volatile over the business cycle. This section serves also the purpose of discussing related literature on this issue. I later argue that both facts require large movements in absorption - that is, something like a demand shock - and that IST shocks providesuchasourceofvariationsinabsorption. Throughout the paper, international prices are computed as the ratio of foreign prices to domestic prices, both expressed in domestic currency. All statistics refer to HP-(cid:2)ltered series, unless otherwise noted. The Appendix provides more details on the sources and construction of theseries. 5See,forinstance,ClaridaandGal(cid:236)[1994],Corsetti,DedolaandLeduc[2007,2008],EndersandMuller[2009]. 4

Fact 1: International relative prices tend to appreciate when domestic consumption and output increasemorethanforeignconsumptionandoutput. Figure 1 presents business cycle components of the U.S. trade-weigthed real exchange rate and of U.S. consumption relative to an aggregate of its major trading partners’ consumption6. The chart shows that there is negative relationship between the two variables (the correlation is -0.18). Hence,increasesinU.S.consumptionrelativetoforeignconsumptionareassociatedwith increasesinU.S.CPIrelativetoforeignCPI(i.e. appreciationsoftherealexchangerate). [PleaseinsertFigure1here] This feature of the data has been originally documented in Backus and Smith [1993], and doesnotapplyexclusivelytotheUnitedStates. Corsetti,DedolaandLeduc[2007],forinstance, report that the median value for this correlation among OECD countries is -0.30. The negative relationship between relative consumption and real exchange rates represents a central puzzle of international data, since consumption smoothing implies exactly the opposite relationship betweenthetwoquantities. Forsimplicity,assumethattherearetwoagents,home(H)andforeign (F),andassetmarketsarecomplete. Optimalityrequiresequalizationof(real)marginalutilities, or ePF UF RER = ct (1) PH / UH ct Under the assumption that the utility function is logarithmic in consumption, (1) implies that the correlation between the real exchange rate and relative consumption is one. More generally, equalization of (marginal utility of) consumption requires that consumption is higher where it is cheaper. This result is preserved if one considers a production economy where the utility function includes leisure and is non-separable, as in a standard model (cid:224) la BKK. Chari, Kehoe and McGrattan [2002] note that this anomaly is robust to many deviations from the standard 6BusinesscyclecomponentsarederivedusingChristiano-Fitzgeraldband-pass(cid:2)lterandexcludingfrequencies higherthanoneandahalfyearsandlowerthaneightyears. 5

model and holds "in any model with complete asset markets, regardless of the frictions in the goodsandlabourmarketslikestickyprices,stickywages,shippingcosts,andsoon." The negative correlation between the real exchange rate and relative consumption is often interpreted as evidence of low international risk-sharing. Corsetti, Dedola, and Leduc [2007] propose a model with incomplete asset markets where productivity shocks have large uninsurable wealth effects through international prices, depending on the trade elasticity and the persistence of shocks7. Kollmann [2009] accounts for the Backus-Smith correlation with a model whereasigni(cid:2)cantfractionofagentshasnoaccesstoassetmarkets. StockmanandTesar[1995], instead,emphasizetheroleoftasteshockstogetherwithnon-tradedgoodsasanalternativeexplanation of the consumption-real exchange rate anomaly8. Notwithstanding the general problems of identifying structural disturbances, taste shocks appear to suffer the most from this criticism. Nevertheless, both lines of research suggest that absent a mechanism that either directly or indirectly generate signi(cid:2)cant shifts in domestic absorption, models driven by productivity shocks will have a hard time accounting for the observed movements in the real exchange rate and relativeconsumption. The cyclical behavior of the terms of trade and relative output is also puzzling from the perspective of standard theories. Figure 2 plots business cycle components of the U.S. terms of tradeandU.S.GDPrelativetoanaggregateofitsmajortradingpartners’output. [PleaseinsertFigure2here] Once again, the data suggests that the U.S. terms of trade appreciate at times of expansion in domestic production relative to foreign production. The correlation between the two variables is 7BenignoandThoenissen[2008]showthatastandardtwo-countrymodelwithincompletemarketsandanontradedsectorcanreproducetheconsumption-realexchangerateanomaly. Theirsetup,however,generatesinternationalpricesthatarelessvolatilethaninthestandardBKKmodel. TheenvironmentstudiedinCorsetti,Dedola,and Leduc[2007]issuccessfulinreproducingthevolatilityofinternationalrelativepricesobservedinthedata,atleast forlowvaluesofthetradeelasticity. 8SeealsoHeathcoteandPerri[2009]forasimilarapproachbasedonpreferenceshocks. 6

-0.36, and it is -0.20 for the median OECD country (see Corsetti, Dedola, and Leduc [2007] for recentevidence). From the perspective of the theory, this feature of the data is also puzzling. Let us return to our simple example and assume that the two agents have endowments of an agent-speci(cid:2)c good but consume a bundle of the both goods. In this environment, any positive shock to the home outputimpliesadeclineofitspriceandacorrespondingincreaseinthepriceoftheforeigngood. The intuition for this result relies on a relative scarcity argument: positive shocks to the supply of one good induce an increase in the demand for the other good. The subsequent appreciation of the terms of trade, whose strength depends on the elasticity of substitution between goods, has implications for risk-sharing and the transmission of shocks across countries. As pointed out by Cole and Obstfeld [1991], the movements in the terms of trade supports consumption for the agent that did not experience an increase in the supply of its good, thus providing insurance against idiosyncratic shocks. Heathcote and Perri [2002] (cid:2)nd that in a two-country model (cid:224) la BKK the allocation obtained in a bond economy is very close to the social planner solution, thus quantitatively con(cid:2)rming the robustness of this mechanism. The data, however, provide no support for this mechanism, suggesting that models need to generate shifts in absorption that induceexpansioninproductiontogetherwithappreciationofthetermsoftrade. Fact2: Internationalrelativepricesandtrade(cid:3)owsarevolatileoverthebusinesscycle. Table 1 presents the standard deviation of the terms of trade and trade (cid:3)ows (measured as real net exports over GDP) relative to the standard deviation of output for a sample of OECD countries. As indicated by their median values, the terms of trade are about twice as volatile as outputwhereastrade(cid:3)owsarehalfasvolatileasoutput. Hence,bothinternationalquantitiesand pricesarequitevolatile. [PleaseinsertTable1here] ThebottompartofTable1presentssimulationresultsobtainedfrombenchmarkBKKmodel wherecyclesaredrivenbyTFPshocksandwithcapitaladjustmentcostscalibratedtoreproduce 7

the volatility of investment relative to output. Two (cid:2)ndings emerge. First, the BKK model delivers very little volatility in trade variables, accounting for almost none of the empirical volatility of trade (cid:3)ows and about one third of the volatility of the terms of trade. While the dynamics of trade(cid:3)owsinthemodelre(cid:3)ectstheincentivestoinvestacrosscountries("makehaywhenthesun shines"), Table 1 suggests that quantitatively this mechanism does not generate suf(cid:2)cient reallocation of resources across countries as in the data. Second, general equilibrium considerations introduce a trade-off between the volatility of trade prices and the volatility of traded quantities. Consider for simplicity our two-agents example presented above. When the consumption bundle is assumed to be a CES aggregator, as the literature typically does, then the terms of trade are a function of the import ratio that depends on the trade elasticity9. As goods become more complement (low trade elasticity), technology shocks induce a larger response in relative prices onlybymakingtheresponseofquantitiesevenmoremuted. Ontheotherhand,asgoodsbecome more substitute (high trade elasticity), the response of trade (cid:3)ows increases at the expense of the variabilityininternationalrelativeprices. In her contribution to the Handbook of International Economics, Baxter [1995] identi(cid:2)es the lackofvolatilityofnetexportsandthetermsoftradegeneratedbygeneralequilibriummodelsas amajorchallengefortraditionalbusinesscycletheory. Boileau[1999]incorporatestradeincapitalgoodsintoanotherwisestandardtwo-countrymodel(cid:224)laBKKtoaccountforthesevolatilities. However,hismodeldoesnotgenerateothertypicalfeaturesofinternationalbusinesscycles,such as the countercyclicality of net exports, and does not address Fact 1. More recently, Engel and Wang [2008] considers a model with trade in both capital and durable goods. Their model provides valuable insights in accounting for the volatility of trade variables and countercyclical net exports. However, the terms of trade and the real exchange rate are negatively correlated in their model,indicatingthattheirapproachwouldlikelyhavedif(cid:2)cultiesinaccountingforFact1. 9Theimportratioisde(cid:2)nedastheratioofimportsrelativetooutputexcludingexports. 8

3 The Economy Consider two countries (i = 1,2) of equal size populated by identical in(cid:2)nitively lived agents. The representative agent in each country maximizes lifetime utility (V ) de(cid:2)ned over sequences it ofconsumptionof(cid:2)nalgoods(C )andhoursworked(N ) : it it 1 V = E (cid:12)tU(C ;N ) (2) it 0 it it t=0 X whereE referstotheexpectationconditionalontheinformationavailableattimezero. Thetime 0 endowmentisnormalizedtooneandthediscountfactorissuchthat0 < (cid:12) < 1. Themomentary utilityfunctiontakesthefunctionalform [C N(cid:23)]1 (cid:13) (cid:0) U(C;N) = (cid:0) (3) 1 (cid:13) (cid:0) as proposed by Greenwood, Hercowitz and Huffman [1988] (so called GHH preferences). Parameters are such that > 0;(cid:13) > 0; and (cid:23) > 1: Benhabib et al. [1991] show that this utility function can be obtained analytically as a reduced form case from a model that includes home activities10. Raffo[2008]showsthatintwo-countrymodels(cid:224)laBKKthesepreferencesgenerate suf(cid:2)cientvolatilityinconsumptionsothattherealtradebalanceiscountercyclical,asinthedata. As in a Ricardian model of international trade, each country specializes in the production of one intermediate good (j = A;B). The production of the intermediate good output (Y ) is it carriedoutaccordingtoaCobb-Douglasproductionfunctionthatusescapitalservicesandlabor, whichareimmobileacrosscountries: Y = ezit(u K )(cid:18)N1 (cid:18) (4) it it it it(cid:0) where z is an exogenous neutral technology shock. Capital services consist of the stock of it installedphysicalcapital(K )andtherateofcapacityutilization(u ). Theresourceconstraints it it 10Theparametricassumptionsare: (cid:23) = 1and(cid:13) = 1:Inaddition,capitalandlaborareperfectsubstitutesinthe production of the home good. When shocks are assumed to be trend-stationary, GHH preferences are consistent with balanced growth under the assumption that productivity in the home sector grows at the same rate as market productivity. 9

associatedwithintermediategoodsproductioninthetwocountriesare A +A = Y (5) 1t 2t 1t and B +B = Y (6) 2t 1t 2t Intermediatesarethencombinedineachcountrytoproducegoodsdestinedto(cid:2)nalabsorption followingtheArmingtonaggregator: 1 $ A1 (cid:11) +(1 $ )B1 (cid:11) 1 (cid:11) i = 1 i it(cid:0) (cid:0) i it(cid:0) (cid:0) G (A ;B ) = (7) it it it 8 (cid:2) (cid:3) > < (1 $ )A1 (cid:11) +$ B1 (cid:11) 1 1 (cid:11) i = 2 (cid:0) i it(cid:0) i it(cid:0) (cid:0) where $ i > 0.5 determines the > : hom(cid:2)e bias in the compositio(cid:3)n of domestic absorption. The parameter (cid:27) = 1 denotes the elasticity of substitution between intermediate goods. Domestic (cid:11) absorptionisallocatedto(cid:2)naldomesticconsumptionandinvestment(I ) it C +I = G (A ;B ) (8) it it it it it Capitalaccumulationevolvesaccordingtothelawofmotion K = [1 (cid:14)(u )]K +evitI +(cid:9)(:) (9) it+1 it it it (cid:0) where(cid:9)(:)isaconvexadjustmentcost. Theeconomyincursnocostofchangingcapitalinsteady stateandthefunction(cid:9)(:)isincreasinginthelevelofcapital,hence(cid:9)(K ) = 0;(cid:9)(:) > 0and ss 0 (cid:9)(:) > 0:AsinGreenwoodetal. [1988],capitaldepreciation(cid:14)(u )isanincreasingandconvex 00 it function of the utilization rate: (cid:14) 0 (u it ) > 0;(cid:14) 00 (u it ) > 0. The term evit represents investmentspeci(cid:2)c technical change, as in Greenwood, Hercowitz and Krusell [2000] and Fisher [2006]. This formulation implies that IST shocks affect the productivity of new capital goods, but they donotchangetheproductivityofinstalledcapital. TheshockprocessisassumedtobeVAR(1): Zt = (cid:10)Zt 1 +(cid:15) t (10) (cid:0) E((cid:15) (cid:15) ) = (cid:6) (11) t 0t 10

where Zt = [z 1t ;z 2t ;v 1t ;v 2t ] and (cid:15) t = ["z 1t ;"z 2t ;"v 1t ;"v 2t ]: (cid:10) is a 4x4 matrix governing the persistence and spillover of the shocks. (cid:6) is the variance-covariance matrix associated with VAR process. Both(cid:10)and(cid:6)aresymmetricacrosscountries. Trade variables in country 1 are de(cid:2)ned as follows. Net exports over GDP are the difference betweenrealexportsandrealimportsrelativetorealoutput11 A B 2t 1t RNX = (cid:0) (12) 1;t Y 1t Relative prices can be derived from the (cid:2)rst order conditions associated with the optimization problem. The terms of trade, de(cid:2)ned as price of imports relative to exports, are computed from themarginalrateofsubstitutionintheArmingtonaggregator: 1 @G (A ;B )=@B 1 $ A (cid:27) 1 1 1 1 1 1t TOT = = (cid:0) (13) 1t @G (A ;B )=@A $ B 1 1 1 1 1 (cid:20) 1t(cid:21) Therealexchangerateisproportionaltotheratioofmarginalutilities: U RER = C2;t (14) 1;t U C1;t 4 Parameterization Table2reportstheparametersusedinthecalibrationofthebenchmarkexperiment. [PleaseinsertTable2here] The discount factor is 0.99, consistent with a real interest rate in steady state of about 1 percent. Thecoef(cid:2)cientofrelativeriskaversion((cid:13))is2. ThecurvatureparameterintheGHHpreferences ((cid:23)) is set to 1.64, so that the implied Frisch elasticity is the same as in the isoelastic preferences consideredbyBKK(about1.5). 11Exports,importsandoutputareevaluatedusingsteadystateprices. 11

The share of labor in production (1 (cid:18)) is 0.64. Consistent with long-run values for the United (cid:0) States, the import share is 15 percent, which pins down the home bias in domestic absorption ($). Thespeci(cid:2)cationofthedepreciationfunctionfollowsGreenwoodetal. [1988]: (cid:20) (cid:14)(u) = u! (15) ! t Icalibratetheparameters(cid:20)and! asfollows. The(cid:2)rstorderconditionwithrespecttou andthe t lawofmotionofcapital,bothevaluatedinthesteadystate,implythetworelationships Y (cid:18) = (cid:20)u! 1K (16) (cid:0) u and (cid:20) I u! = (17) ! K I set the long-run quarterly depreciation rate to 0.025, as implied by the average investment-tocapital ratio, and the long-run utilization rate to 0.75, which is the average value in the U.S. data. Given that investment is about 25 percent of output, the solution to equations (16) and (17) determinesthevaluesof! and(cid:20): Thetradeelasticityinthebenchmarkcaseisequalto0.5.Thisvalueisintherangeoftheestimates reportedinHooper,JonhsonandMarquez[2000]forG-7countries. HeathcoteandPerri[2002], usingatime-seriesapproach,estimateavalueof0.9. Inthebaselinecalibration,Corsetti,Dedola, and Leduc [2007] estimate the trade elasticity using method of moments targeting the empirical volatility of the real exchange rate. In their bechmark case - given the calibrated value for the shareofthedistributionsector-theimpliedtradeelasticityfallsbelow0.5. Turningtotheshockprocess,IapproximateISTshockswiththechangesintherelativeprice between investment and consumption, as it is often assumed in the literature12. However, in 12The relationship between IST shocks in a two-sector model and changes in the relative price of investment is exactundersome(quiterestrictive)assumptions, namelyequalfactorsharesinproductionandnoimpedimentsin thereallocationofinputsacrosssectors. Nevertheless,itiswidelyusedintheempiricalliterature. SeeGuerrieriet al. [2009]foraninterestingquantitativeanalysisofthisissue. 12

estimatingthedynamiceffectsofTFPandISTshocksfortheUnitedStates,Fisher[2006]argues that neglecting quality adjustments in the investment price de(cid:3)ator has important quantitative implications for his estimates. Hence, Fisher constructs an investment price series alternative to the NIPA de(cid:3)ators which uses the quality-adjusted indices for equipment and software (E&S) producedbyCumminsandViolante[2002]13. Unfortunately,thereislittleavailabilityofqualityadjustedE&Sde(cid:3)atorsforothereconomies,andinmanycasesitisevendif(cid:2)cultto(cid:2)ndquarterly series for such de(cid:3)ators. Nonetheless, the relative price of equipment, when available, appears to share similar properties to the corresponding series for the United States. For instance, Figure 3 presents the business cycle component of the relative price and the real share of equipment investmentobtainedfromNationalAccountsforAustralia,Canada,Italy,andtheUnitedStates14. There is a clear negative relationships between the two series in the United States, as previously documented in Greenwood, Hercowitz and Krusell [2000] and Fisher [2006]. This pattern holds intheothereconomiesaswell,withcorrelationsof-0.36inAustralia,-0.16inCanada,and-0.38 inItaly. Motivated by this observation, I calibrate the statistical properties of neutral and investmentspeci(cid:2)c technology shocks to reproduce the evidence provided by Fisher for the United States. In particular, I target two statistics in this exercise. First, the relative variance of the two domestic technology shocks is set so that the IST shock explains about 50 percent of the variance of output and the TFP shock 25 percent of it. Hence, these shocks together account for 75 percent of the overall variation of output. Notably, Justiniano et al. [2008] (cid:2)nd very similar results by estimating a structural DSGE model that includes several shocks and frictions. Second, the correlation between innovations of the two technological shocks is set so that the model gener- 13The classical reference on this point is Gordon [1989], who (cid:2)rst showed the empirical relevance of taking into account quality adjustments for durable equipment. Cummins and Violante [2002] extend Gordon’s work by producingquality-adjustedpriceindexesfor24categoriesofE&Sfrom1947to2000. Onarelatedpoint,Gortetal. [1999]arguethatinvestmentinstructuresisalsosubjecttosigni(cid:2)canttecnhologicalimprovementnotcapturedby thestandardaccountingprocedures. 14Therealshareofinvestmentisthequantityofequipmentinunitsofcapitalrelativetogrossdomesticproduct inconsumptionunits. Thecyclicalcomponentisobtainedbyapplyingaband-pass(cid:2)lterthatexcludesfrequencies higherthan18monthsandlowerthaneightyears. 13

atescountercyclicalrelativepriceofinvestmentwithineachcountry,consistentwiththeevidence provided in Figure 3. As for the remaining parameters, the calibration assumes that both neutral and investment-speci(cid:2)c shocks are persistent with some moderate spillover across countries, as intheoriginalBKKarticle. 5 Findings This section introduces the main (cid:2)ndings of the paper. Sections 5.1 presents the quantitative performance of the model and Section 5.2 explores the core economic mechanism by means of impulse response analysis. Section 5.3 and 5.4 derive implications from the theory with respect to the response of international prices to technology shocks and the Barro-King [1984] critique ofinvestmentshocksrespectively. 5.1 Model Simulations Table 3 reports HP-(cid:2)ltered statistics for the data, the benchmark economy, and variations of the benchmark economy. The United States represents the home country, while the foreign country is constructed by aggregating series for Canada, EU-15 and Japan. These countries altogether account for more than half of U.S. trade over the sample considered. The appendix provides details about the data sources and the construction of the foreign aggregate. In all tables, net exportsrefertotherealnettradeingoodsandservicesrelativetoGDP. [PleaseinsertTable3here] The(cid:2)rstcolumnpresentsthepropertiesofthedata. SinceIusethequality-adjustedseriesfor therelativepriceofinvestmentconstructedbyFisher[2006],thesampleisrestrictedtotheperiod 1983-200015. Nevertheless,theshortersampledoesnotaffectthestandardbusinesscyclefeatures 15Inhisanalysis,Fisher[2006]splitsthesamplein1983toaccountfortheabruptincreaseintheaveragedecline oftheinvestmentprice. SeealsoJustinianoandPrimiceri[2008]onthesameissue. 14

reported in the literature. In terms of volatility, consumption is less volatile than output (with a ratio of standard deviations of 0.7) whereas investment is almost three times more volatile than output. Thus, overall domestic absorption is more volatile than output, a central observation for understandingmovementsininternationalpricesandquantities. Turningtoinputsofproduction, labor - measured as total hours of work - is less volatile than output while capacity utilization is more volatile than output. The measure of capacity utilization is constructed by the Board of Governors and is published in the release G.17. As for the trade variables, the volatility of net exportsfortheUnitedStatesisaboutone-thirdthevolatilityofoutput. Thisvalueisinthelower range of the distribution presented in Table 1, but remains consistent with sizable (cid:3)uctuations in trade (cid:3)ows over the business cycle. Finally, international relative prices are more volatile than output,withtherealexchangeratemorevolatilethanthetermsoftrade. Intermsofcorrelations,alldomesticvariablesarestronglyprocyclical. Further,consumption, hours worked and investment comove over the business cycle, yet another stylized feature of the data. This last observation is often dif(cid:2)cult to reproduce in multi-sector models with supply shocks,astheseshocksinducereallocationofresourcestothemostef(cid:2)cienttechnology. Inthedata,netexportsarenegativelycorrelatedwithoutput(-0.43).16 Thisstatisticindicates that countries borrow from international capital markets in good times, different from the implications of standard consumption smoothing theory. As originally documented by Backus and Smith [1993], the correlation between the real exchange rate and relative consumption is negative (-0.23). Similarly, the correlation between the terms of trade and relative output is negative (-0.17). Hence, international relative prices appreciate when domestic consumption and output arehigherthanabroad. The second column in Table 3 - labelled "Benchmark Economy" - presents the main quantitative (cid:2)ndings of the paper. In terms of volatility (relative to output), the model reproduces the standard deviations of consumption, investment, and domestic absorption. Hours worked are 16See, for instance, the original BKK articles, Heathcote and Perri [2002], Raffo [2008], and Engel and Wang [2008]. 15

somewhat less volatile than in the data, but more so than in a typical international real business cycle model. Capacity utilization is also somewhat less volatile than in the data, although in this casethedatamightoverstatethevolatilityofutilizationasitisconstructedusinginformationonly from the manufacturing, mining and utilities sectors. The model also generates procyclical consumption, hours worked, and investment as well as comevement among these variables. Thus, the usual domestic business cycle properties are unaffected by the introduction of IST shocks, variablecapacityutilizationandGHHpreferences. Thebenchmarkeconomyreproducesremarkablywellthemainfeaturesofinternationalquantities and prices. First, the model can reproduce simultaneously the high volatility of trade (cid:3)ows andinternationalrelativeprices. Thevolatilityoftrade(cid:3)owsincreasesbyafactoroffourrelative tothestandardBKKmodel(seeTable1),anditisevenslightlylargerthanintheU.S.data(0.37 vs 0.28), although the value for the United States is in the lowest range among OECD countries. Notably, the model reproduces about 90 percent of the empirical volatility of the terms of trade. RelativetoastandardBKKmodel,thetermsoftradeinthebenchmarkeconomyarealmostthree times more volatile (see again Table 1). Therefore, the model can account for Fact 2. The main failureinthisrespectisthelowervolatilityoftherealexchangeraterelativetothetermsoftrade (and,asaconsequence,relativetothedata). Thisresultisnotsurprising: absentdeviationsfrom the law of one price, the consumption real exchange rate is a linear transformation of the terms of trade. Recent work by Atkeson and Burstein [2008] shows that the producer(cid:150)price based real exchange rate empirically is also more volatile than the terms of trade, suggesting that the practice of pricing-to-market is widespread among exporters. These authors incorporate imperfect competition with variable markups and trade cost into a model of international trade to generate pricing-to-market and large deviations from relative purchasing power parity. Embedding a richer market structure as in Atkeson and Burstein [2008] into the benchmark economy should notaffectthemainmacroeconomicimplicationsofthemechanismproposedhere,butIleavethis projecttofutureresearch. 16

Turning to the cross-correlations, the model generates negative correlations between the real exchangerateandrelativeconsumptionaswellasbetweenthetermsoftradeandrelativeoutput. Hence, the model can also account for Fact 1. Remarkably, the Backus-Smith correlation characterizes the ef(cid:2)cient allocation chosen by a social planner facing IST shocks and non-separable preferences. This last observation suggests that the Backus-Smith correlation is not necessarily evidenceinfavoroftheroleofincompletemarketsinthetransmissionofshocksacrosscountries, asoftenadvocatedintheliterature. [PleaseinsertTable4here] Arethemodel’simplicationsfortherelativepriceofinvestmentreasonablevis-(cid:224)-visthedata? Table 4 addresses this issue as follows. First, the table presents the moments targeted in the calibrationoftheshockprocess. Then,itdocumentsempiricalpropertiesofFisher’srelativeprice of investment in terms of volatility and correlations, and compares them with the corresponding moments implied by the model. Given that the latter moments are not used in the calibration, theyprovideanadditionaltesttothemechanismproposedbythetheory. ThetopportionofTable4reportsthestatisticstargetedinthecalibrationoftheshockprocess, namely the variance decomposition of GDP and the correlation between the investment price and GDP reported in Fisher [2006]. In the benchmark economy, (domestic) IST shocks explain almost half of the variance of GDP whereas TFP shocks account for only a quarter of it. In addition, the relative price of investment is negatively correlated with GDP, which is consistent withtheideathatshockstothesupplyofinvestmentareimportantoverthebusinesscycle. The bottom portion compares other empirical moments of the investment price series with the corresponding moments implied by the model. In the data, the investment price series is almost as volatile as GDP, is quite persistent (with a (cid:2)rst-order autocorrelation of 0.85), and is positively correlated with trade variables (net exports and the real exchange rate). The model reproduces these features quite well. The volatility of the investment price is slightly above its 17

empirical counterpart, but remains below the volatility of output. The investment price is also quitepersistentandpositivelycorrelatedwithtradevariables. In sum, three quantitative implications emerge from this exercise. First, when IST shocks explainalargefractionofthevariationofoutput,internationalrelativepricesandtrade(cid:3)owsare about as volatile as in the data. Second, the real exchange rates and the terms of trade appreciate when domestic consumption and output increase more than foreign consumption and output. Third, the introduction of IST shocks does not affect the standard features of business cycles in termsofvolatility,cyclicality,andcomovementofdomesticvariables. 5.2 Inspecting the Mechanism: Impulse Response Analysis ThissectionillustratesthetransmissionmechanismofISTshocksinthebenchmarkeconomyby means of impulse response analysis17. The main insight of the paper is that investment-speci(cid:2)c technology shocks introduce a source of (cid:3)uctuations in domestic absorption that does not directlyaffecttheaggregateproductionfunction. Therefore,ISTshocksresembleatypicaldemand shock, similar to the preference shocks considered in Stockman and Tesar [1995] or Heathcote and Perri [2009]. Differently from these papers, however, the data provide more discipline in modellingISTshocksandthestructuralinterpretationofISTshocksappearslesscontroversial. [PleaseinsertFigure4here] As shown in the (cid:2)rst row of Figure 4, a positive IST shock generates an investment boom associated with an expansion in consumption, leading to a large increase in domestic absorption. In turn, this increase in domestic absorption has three implications for the supply-side of the economy, which can be easily read from the resource constraint of the economy (recall that an IST shockcorrespondstoachangeinthepriceofinvestmentrelativetoconsumption): C +e vtI = G ezt(u K )(cid:18)N1 (cid:18) NX (18) t (cid:0) t a t t t(cid:0) (cid:0) t 17For simplicity, I do not discuss the case of a TFP shock as the features introduced in the model do not affect qualitativelytheresponseofthemaineconomicvariablestothisshock. 18

First,domesticproductionexpandsbacauseofhighercapitalservices,achievedthroughincreases in utilization rates. The consequent shift in the marginal product of labor schedule encourages workerstopostponeleisure,thusleadingtoastrongresponseofaggregatehoursworked(middle panels in Figure 4). Second, production ef(cid:2)ciency requires moving resources from the foreign countryintothedomesticcountry,sinceproducinginvestmentgoodsinthehomecountryisnow more productive. Therefore, an IST shock is associated with a trade de(cid:2)cit ((cid:2)rst panel in the last row of Figure 4). Finally, provided that (cid:2)nal goods are intensive in domestically-produced intermediates, the increase in domestic absorption makes domestic output more expensive and the relative value of intermediate goods in terms of (cid:2)nal goods increases (G ). Thus, the terms a oftradeappreciatewhendomesticproductionexpands,asinthedata. As discussed before, the planner chooses an allocation characterized by a negative relationship between the real exchange rate and relative consumption. Hence, the Backus-Smith correlationinthisenvironmentisarequirementofproductionef(cid:2)ciency. Themechanicsofthisresult canbeunderstoodbyanalyzingthelog-linearexpressionoftherealexchangerate: R[ER = U U (19) t C2;t (cid:0) C1;t = (cid:13)[((cid:11) c (cid:11) n ) ((cid:11) c (cid:11) n )] b C 1b;t N 1;t C 2;t N 2;t (cid:0) (cid:0) (cid:0) Ef(cid:2)ciency requires that the marginal ubtility of cbonsumptionbis equalbized across agents in the two countries. After a positive IST shock, the stronger response of hours worked relative to consumption (Figure 4) determines an increase in the marginal utility of consumption in the home country. This is so because, as the IST shock triggers a sharp increase in the marginal product of capital, the opportunity cost associated with an extra unit of current consumption is very high. Under standard preferences, the consumer would indeed postpone consumption and leisure. Under GHH preferences, consumption increases, but less than labor input. As for foreign marginal utility, the wealth effects associated with this shock induce a stronger increase inconsumptionthaninhoursworked,leadingtoadeclineinthemarginalutilityofconsumption. 19

This mechanism relies on two essential features of the utility function, namely the nonseparabilitybetweenconsumptionandleisure,andtheabsenceofwealtheffectsonlaborsupply. The role of the (cid:2)rst element is straightforward, as under the separable utility function the real exchange rate is perfectly correlated with the ratio of consumption. Section 6.1 below explores inmoredetailtheroleofshort-runwealtheffectsonlaborsupply. 5.3 On the Transmission of Productivity Shocks and International Prices A large and growing literature investigates the (conditional) response of international prices to structural shocks generating business cycles. In the Mundell-Fleming-Dornbusch (MFD) tradition, an increase in money supply results in a rise in output and a real depreciation of the currency. Similarly, a positive supply shock increases output together with a depreciation of international prices. Demand shocks increase output together with an appreciation of international prices. Starting from these theoretical (cid:2)ndings, Clarida and Gal(cid:236) [1994] estimate VARs - identi- (cid:2)ed with long-run restrictions - that include the bilateral real exchange rate of the United States with Germany, Japan, Canada, and the United Kingdom as a variable. They (cid:2)nd that demand and monetary shocks account for most of the (cid:3)uctuations of the real exchange rate and that the impulseresponsesobtainedfromthedataprovidesupportfortheMFDtransmissionmechanism. Interestingly, they de(cid:2)ne demand shocks as "capturing shocks to home absorption relative to foreignabsorption." More recently, Corsetti, Dedola and Leduc [2007, 2008] (cid:2)nd that shocks to productivity are associated with expansions of output, appreciation of international prices, and deterioration of the trade balance. Their empirical strategy relies on structural VARs as well, identi(cid:2)ed with either long-run restrictions or sign restrictions. Since their theoretical framework is the standard international real business cycle model (cid:224) la BKK, they interpret these (cid:2)ndings as evidence in favor of incomplete markets triggering large changes in relative wealth across countries. In this environment, changes in relative prices amplify wealth disparities. Similarly, Enders and Muller [2009] estimate bivariate VARs and (cid:2)nd evidence that in the United States the terms of trade 20

appreciatefollowingapositiveproductivityshocks. Thispaperprovidestwomaininsightsontherelationshipbetweenstructuralshocksandinternationalrelativeprices. First,itshowsthattheconditionalresponseofinternationalrelativeprices to technology shocks depends critically on the type of technology shocks considered. IST and TFP shocks are associated respectively with an appreciation and a depreciation of international relativeprices. Second,itprovidesanexplanationfortheappreciationofinternationalpricesduring periods of economic expansion that does not rely on large changes in relative wealth across countries, is driven by what looks like a demand shock, and yet originates from an improvement inthetechnicalef(cid:2)ciencyofproducingofinvestmentgoods. Figure5presentstheimpulseresponseofthetermsoftradeandoutputtoaTFPshock(dotted line)andaISTshock(solidline). Giventhestronglinkbetweenoutputandhoursworkedimplied by GHH preferences, the impulse responses of output are very similar to the impulse responses oflaborproductivity. Forconvenience,Iplotonlytheformer. [PleaseinsertFigure5here] As shown in Figure 5, TFP shocks are associated with a depreciation of the terms of trade whereasISTshocksinduceanappreciationofthetermsoftrade. Bothtechnologyshocksgenerate an expansion in economic activity (and an increase in labor productivity). Hence, the transmission mechanism of the two technology shocks through international prices is very different. Thelog-linearexpressionforthetermsoftradeprovidestheintuitionforthis(cid:2)nding: T[OT = ’ y G +(y y ) (20) 1t 1t 1t 1t 2t (cid:0) (cid:0) h (cid:16) (cid:17) i where both ’ = 1 (cid:0)im 2im and = 2(cid:27)(1 1 im) are b positbive coef(cid:2) b cients b and, under standard parameter (cid:0) values,’ > 1:Notably,thisderivationdependsonlyontheproductionstructureoftheeconomy, whiletheformoftheutilityfunctionisirrelevant. 21

Changes in the terms of trade re(cid:3)ect two offsetting forces. The term (y y ) says that 1 2 (cid:0) changes in relative production across countries alter directly the relative scarcity of goods in the b b international markets. After an increase in domestic output, foreign output becomes more expensive and the terms of trade depreciate. Under this mechanism, the terms of trade provide insurance against country-speci(cid:2)c shocks, as movements in relative prices offset movements in relative outputs. This result was (cid:2)rst noted by Cole and Obstfeld [1991] in an endowment economy, and subsequently con(cid:2)rmed quantitatively by Heathcote and Perri [2002] in a two-country modelwithproduction(cid:224)laBKK. Theterm y G re(cid:3)ectsprimarilyshiftsindomesticabsorptionrelativetodomesticout- 1 1 (cid:0) put. Investme(cid:16)nt-speci(cid:2)(cid:17)c technology shocks trigger an expansion in domestic absorption relative b b to foreign absorption, which raises both domestic output and domestic prices. Hence, the terms oftradeappreciateandthetradebalancedeteriorates. This discussion provides interesting empirical implications for the international transmission of productivity shocks and the sources of business cycle (cid:3)uctuations. A negative correlation betweenthetermsoftradeandoutputisoftenconsideredprimafacieevidencethatdomesticfactors otherthanshockstototalfactorproductivityareanimportantdeterminantofinternationalprices, as in Clarida and Gal(cid:236) [1994]. My analysis supports this view, but provides a different interpretation about the sources of (cid:3)uctuations in absorption, since in my model they originate from investment-speci(cid:2)c technology shocks. In addition, and differently from the approach taken by Corsetti et al. [2008] or Enders and Muller [2007], the appreciation in international prices generated by the model is consistent with an ef(cid:2)cient allocation of resources, and does not depend on the presence of incomplete asset markets. In other words, international prices in this environment do not amplify the wealth effects associated with productivity shocks, and risk is fully sharedacrosscountries. Finally,despiteitswidespreaduse,thisanalysisquestionstheuseofVARsidenti(cid:2)edthrough long-run restrictions to recover the impulse response functions of international prices to technology shocks. As extensively discussed in Fisher [2006], when technology shocks other than 22

TFP are considered, this methodology is robust to the extent that the responses to the different technology shocks are suf(cid:2)ciently similar.18 Figure 5, and the theoretical mechanism discussed so far, suggest that this condition is likely to be violated, as the sign of the impulse responses of international prices depends on the type of technology shock considered. Hence, not including the relative price of investment in VARs might lead to a mistaken inference in terms of the conditionalresponseofinternationalpricestoshocks. 5.4 On the Barro-King [1984] Critique The benchmark economy presented in this paper preserves the typical features of domestic business cycles, including the comovement of consumption with hours worked and investment. This result is less trivial than it might appear, since models where investment shocks provide significant contribution to business cycle (cid:3)uctuations often generate weak or even negative comovement.19 Barro and King [1984] originally observed that in a simple neoclassical framework, shifts to aggregate investment raise output and the interest rate, but lower consumption, which contrasts with the typical pattern of business cycles. The intuition for this argument relies on an intertemporalsubstitutionmechanism,whichcanbeinferredfromtheresourceconstraint: C +e vtI = Y (K ;L ) t (cid:0) t t t t After a positive investment shock (a decline in e vt), agents increase labor efforts to expand (cid:0) production and allocate more resources to capital accumulation. At the same time, however, today’sconsumptionisveryexpensiveandagentsincreasesavingthroughinvestment. Thus,this mechanismgeneratesnegativecomovementofconsumptionwithhoursworkedandinvestment. In principle, this issue could disappear if we allow borrowing from international capital mar- 18ThereaderisinvitedtoconsultFisher[2006,page420],foraformalstatisticalde(cid:2)nitionoftheseconditions. 19Thispointisaconsequenceofthetwo-sectorinterpretationofthemodel. Providedthatonlytechnologyshocks generatebusinesscycles,reallocationofresourcesacrosssectorsimpliesnegativecomovement. 23

kets,asforeigntradeloosensthedomesticresourceconstraint: C +e vtI +NX = Y (K ;L ) t (cid:0) t t t t t After a positive investment shock, agents can now increase imports, thus reducing the need to sacri(cid:2)ceconsumption. I next investigate quantitatively this point. Figure 6 presents the impulse response of consumption and leisure to a IST shock in a neoclassical economy closed to foreign trade and in the benchmark economy presented in the paper. I also plot the response of these variables in the standard BKK model, in order to assess the impact on comovement of relaxing the resource constraint through foreign trade. For the closed economy experiment and the BKK experiment, capital adjustment costs are calibrated to target the volatility of investment relative to output, the shock process is the same as in the benchmark economy, preferences are isoelastic, and capacity utilizationis(cid:2)xed.20. [PleaseinsertFigure6here] The RBC impulse response con(cid:2)rms the (cid:2)ndings of Barro and King [1984]. After a positive IST shock, labor efforts increase, consumption drops, and the economy expands production in order to accumulate capital. Consumption moves in opposite direction relative to hours worked and investment. In the BKK model, the response of consumption remains weakly negative, suggesting that foreign trade provides only limited support to domestic consumption. In the eyes of the planner, shocks speci(cid:2)c to the production of investment goods encourage a reallocation of resources to the most ef(cid:2)cient location. Hence, as for TFP shocks, investment shocks stimulate importsofgoodsmainlyto(cid:2)nanceinvestmentbooms. Thetransmissionmechanismadoptedinthebenchmarkeconomyhastwodistinctivefeatures. First, variable capacity utilization implies that investment shocks have a larger short-run impact 20Fortheclosedeconomycase,Isetthepersistenceparameterequaltothelargesteigenvalueimpliedbytheopen economyprocess. 24

on output. After an investment shock, the increase in capital utilization shifts the schedule of the marginal product of labor, triggering an increase in the real wage and hours of work. Nevertheless, this mechanism alone would not be suf(cid:2)cient to generate comovement as increasing the income effect of shocks provides incentives to enjoy both consumption and leisure. With GHH preferences, there is an additional intratemporal effect that creates substitution away from leisure towards consumption, as labor supply responds only to substitution effects. Benhabib et al. [1991] show that under a few parametric assumptions ((cid:23) = 1 and (cid:13) = 1), GHH preferences represent a limiting case for a two-sector model that incorporates home and market productions, perfectsubstitutabilitybetweentechnologiesandstandardisoelasticpreferences.21 Hence,leisure inthebenchmarkeconomyistobeinterpretedasthesumofhoursspentinhomeproductionand leisure activities. After a shock to market technologies, the response of leisure activities is no different from the isoelastic utility case, while consumers reduce considerably home work and home consumption in favor of market work and market consumption. As a consequence, market work and market consumption are strongly positively correlated whereas home and market activitiesarenegativelycorrelated.22 The ability of the model to reproduce the comovement among domestic variables bears additional implications for the cyclical properties of the trade balance. As mentioned above, net exports are countercyclical in the data, indicating that countries borrow from abroad at times of expansion in economic activity. This observation implies that absorption is more volatile than output. Infact,startingfromtheidentity DA = Y NX (cid:0) 21Raffo [2008] (cid:2)nds that the parametric assumptions for GHH preferences commonly adopted in the literature ((cid:23) = 1:64and(cid:13) = 2)areequivalent,quantitatively,toalowerelasticityofsubstitutionbetweenhomeandmarket technlogies. Benhabibetal. [1991]showalsothatthestandardcaseofisoelasticpreferencescorrespondstoaunit elasticityofsubstitutionbetweenhomeandmarkettechnologies. 22Thereislargeamountofevidenceonthenegativecorrelationbetweenhomeandmarketactivites. Forinstance, servicesthataresubstitutesforhomeproductionarestronglyprocyclical,suchasrestaurants,child-care,andcleaningservices. Time-surveysprovideasimilarpictureintermsoftheallocationoftimeoverthebusiness-cycleorthe life-cycle. SeeBenhabibetal. [1991]andRaffo[2008]. 25

and,computingthevarianceofbothsidesoftheequality,yields Var(DA) = Var(Y)+Var(NX) 2Cov(NX;Y) (21) (cid:0) Expression(21)showsthatcountercyclicalnetexportsareanindicationthatdomesticabsorption (cid:3)uctuatesmorethanoutputoverthebusinesscycle. However,bythesamelogic,thevolatilityof absorptiondependsonthecomovementbetweenconsumptionandinvestment Var(DA) = Var(C)+Var(I)+2Cov(C;I) Therefore, provided that models can generate the volatility of consumption and investment observedinthedata,thecomovementbetweenthesevariablesisintimatelyrelatedtothecyclicality of net exports through the volatility of absorption. Table 5 presents simulations for the three economiesanalyzedabove. [PleaseinsertTable5here] The top panel presents the volatility of consumption, investment and absorption relative to output. All models generate reasonable volatilities for these variables, yet they have very different implications for absorption. For the closed economy case, absorption shares the same propertiesofoutput,byconstruction. Intheopeneconomymodels,however,thevolatilityofabsorption is much higher than output only in the benchmark economy. The middle panel presents the correlation of consumption with labor and investment and the correlation of net exports with output. As anticipated in the impulse response analysis, investment shocks in closed economies generate negative comovement between consumption and investment, which is counterfactual. In a two-country model (cid:224) la BKK, this issue is somewhat alleviated but it not fully resolved. Remarkably,inbothexperimentsinvestmentshocksaccountforaverysmallfractionofthevariation of output (bottom panel), and yet no comovement is preserved. Turning to the correlation of net exports with output, this statistic is positive in the BKK model with IST shocks and negative in the benchmark economy, con(cid:2)rming quantitatively our previous intuition. In sum, the 26

inability of models with investment shocks to generate comovement between consumption and investment affects the cyclical properties of the trade balance, a stylized feature of international businesscycles. 6 Features of the Model: A Discussion This section presents a discussion of the features of the benchmark economy that are not commonlyadoptedintwo-countrymodels(cid:224)laBKK.First,IinvestigatetheroleofGHHpreferences by comparing simulations against three alternative utility functions, namely the isoelastic utility function adopted in BKK, the utility function proposed in Jaimovich and Rebelo [2009] and a utilityfunctionwithexternalhabitinconsumption. Next,Iinvestigatetheroleofvariablecapacityutilization. Finally,Ipresentsomediscussiononthequantitativeimpactofthetradeelasticity. 6.1 Utility Function The absence of wealth effects on labor supply embedded in GHH preferences might appear an unappealingfeatureofthemodel,asitimpliesalargevalueforthelaborsupplyelasticity. Alarge amount of literature provides estimates for this parameter, but disagreement on the appropriate valuethatshouldbeusedformacromodelsremains. Althoughourpreviousdiscussionregarding the home production interpretation of GHH preferences mitigates these concerns, it is still of interesttoinvestigatethequantitativeimportanceoftheabsenceofwealtheffectsonlaborsupply formy(cid:2)ndings. Forthispuropose,the(cid:2)rstthreevariationsofthebenchmarkeconomypresented inTable3summarizetheresultsobtainedbyadoptingalternativeutilityfunctions. Following BKK, the literature usually assumes that utility is non-separable in consumption andleisure,andisoelastic: [C(cid:22)(1 N)(cid:22)]1 (cid:13) (cid:0) U(C;N) = (cid:0) (22) 1 (cid:13) (cid:0) The share parameter (cid:22) is equal to 0.34, so that in steady state agents allocate 30 percent of their time endowment to market activities. The curvature parameter (cid:13) is set to 2.0 as in the 27

benchmarkcase. Notably,when(cid:13) = 1thisutilityfunctioncorrespondstoacaseofunitelasticity ofsubstitutionbetweenhomeandmarketactivities. This economy performs remarkably well in terms of business cycle statistics. Overall, the model reproduces the usual empirical regularities in terms of domestic volatilities and correlations, and net exports are weakly countercyclical. International relative prices and net exports display volatilities much closer to the data than in a standard BKK model (see Table 1). In addition, the correlation between the terms of trade and relative output is close to zero, con(cid:2)rming the role played by investment shocks in shifting relative absorption across countries. However, the model performs poorly with respect to the Backus-Smith puzzle and, to a lesser extent, the comovementofconsumptionwithlaborandinvestment. The(cid:2)rstfailurecanbeexplainedbynoting the low volatility of hours relative to output (0.41): the response of labor to shocks is muted, andtherisk-sharingconditionisprimarilydeterminedbyrelativemovementsinconsumption. In termsofcomovement,theBarro-Kingcritiquediscussedearlierapplies,butcomovementamong consumption,hoursandinvestmentisonlyweak,notnegative. Thepossibilityofvaryingcapital services through the capacity utilization rate is quantitatively an important factor for generating positivecorrelations(seeTable5forcomparison). The experiment with BKK preferences emphasizes the importance of the wealth effects on labor supply for the Backus-Smith condition. How large do these wealth effects need to be? I nextconsidertheutilityfunctionproposedbyJaimovichandRebelo[2009]: [C N(cid:23)X ]1 (cid:13) U(C ;N ) = t (cid:0) t t (cid:0) (23) t t 1 (cid:13) (cid:0) where X = C(cid:17)X1 (cid:17) (24) t t t(cid:0)1 (cid:0) The parameter (cid:17) is such that 0 (cid:17) 1: These preferences nest as limiting cases two classes (cid:20) (cid:20) of preferences commonly used in the business cycle literature. When (cid:17) = 0, (23) reduces to the GHH utility function adopted in the benchmark economy and the wealth effects on labor supply are zero. When (cid:17) = 1, on the other hand, (23) reduces to the class of preferences discussed in 28

King, Plosser and Rebelo (1988), for which wealth effects on labor supply tend to be negative (i.e. thewealtheffectinducedbyanincreaseinthewagerateimpliesanincreaseinconsumption andleisure). The simulation reported in Table 3 assumes that (cid:17) = 0.10:23 Despite the very weak short-run wealth effects associated with this low value of (cid:17); the risk-sharing condition implies a correlation between the real exchange rate and the ratio of consumption across countries close to zero. Therefore, weak wealth effects on labor supply are quantitatively important to generate the Backus-Smith correlation. When (cid:17) = 0.10 the model can still account for the volatility of international prices and trade (cid:3)ows, and for the negative correlation between the terms of trade and relative output. Finally, the performance of the model in terms of comovement is also unaffected.24 Last, I consider the case of external habit persistence in consumption, which is commonly usedintheempiricalmacroeconomicliterature. Theutilityfunctiontakestheform: (C dC )1 (cid:13) (1 N )1 (cid:13) t t 1 (cid:0) t (cid:0) U(C t ;N t ) = (cid:0) (cid:0) + (cid:0) (25) 1 (cid:13) 1 (cid:13) (cid:0) (cid:0) with 0 < d < 1. The simulation assumes that d = 0:8 and (cid:13) = 1. Similarly to the case with BKK preferences, this model performs quite well with respect to usual business cycle properties as well as the volatility of international prices and quantities. The correlation between the terms of trade and relative output is positive, but very low. Once again, the main failure of the model consistsinitsinabilitytoreproducetheBackus-Smithregularityandstrongcomovementamong omesticvariables. Fromthelog-linearexpressionfortherealexchangerateunderexternalhabit: R[ER = A[(c c ) d(c c )] (26) 1;t 2;t 1;t 1 2;t 1 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) where A = (cid:13) and d is the habit persistence parameter.25 The habit persistence parameter has 1 d b b b b (cid:0) 23Jaimovic and Rebelo [2009] report that when (cid:17) = 0:10 and no news shocks are considered, their two-sector modelgeneratesectoralcomovement. 24Simulationsresults(notshown)suggestthatthisisstillthecaseevenforspeci(cid:2)cationsinwhichwealtheffects onlaborsupplyaresizable: when(cid:17) =0.5,thecorrelationsofconsumptionwithinvestmentandlaborare0.56and 0.58respectively. 25Theutilityfunctionisnowseparableinleisure,andlabordoesnotentertheexpressionoftherealexchangerate. 29

two effect on the real exchange rate. First, it reduces the impact of deviations in consumption from steady state. Second, it increases the response of the marginal utility of consumption, as if we were to increase the risk-aversion parameter. Nevertheless, no value of d could generate a negativecorrelationbetweenrealexchangerateandrelativeconsumption. In terms of comovement, the model with habit persistence performs similarly to the case with BKK preferences, although the correlation between consumption and hours is still slightly negative. Variablecapacityutilizationremainsaquantitativelyimportantfeaturefortheseresults. Lastly,itremainstoverifywhatimplicationsthesealternativeprefecencespeci(cid:2)cationscarry for the relative price of investment (Table 4). In all cases, the relative price of investment turns out to be more volatile than in the data. Its volatility is about twice as large as in the data for Jaimovic-Rebelo preferences and is more than three times larger in the habit case. All three models perform like the benchmark economy in terms of autocorrelation of the relative price of investmentandcross-correlationwithtradevariables. In sum, these experiments suggest that a general equilibrium model that incorporates TFP and IST shocks together with variable capacity utilization can account for the volatility of internationalquantitiesandprices(Fact2)andgenerateweakcorrelationsbetweenthetermsoftrade andrelativeoutput. However,these(cid:2)ndingsrequireaconsiderablylargervolatilityoftherelative priceofinvestmentthanobservedinthedata. Thefunctionalformoftheutilityfunctionappears tobequantitativelyimportantfortheBackus-Smithcorrelation,aswealtheffectsonlaborsupply limittheresponseofhourstoshocks. 6.2 Variable Capacity Utilization Variablecapacityutilizationrepresentsthesecondfeatureintroducedinthebenchmarkeconomy as it allows to endogenously vary capital services through an intensive margin. I next explore quantitativelytheimportanceofthisfeature. The "Fixed Capacity" experiment in Table 3 reports simulation for the benchmark economy with constant capacity utilization. The shock process is calibrated as in Section 4, and the corre- 30

lationbetweeninnovationsissettoreproduceanegativecorrelationbetweentherelativepriceof investment and output. However, under no reasonable parameterization for the relative volatility ofTFPandISTinnovationsthemodelwasabletoreproducethevariancedecompositiontargeted inthebenchmarkeconomy. Hence,Idecidedtoleavethisparameterunchanged. This economy performs well in terms of the usual business cycle statistics and the cyclical correlation of net exports with output. The volatilities of net exports and the terms of trade (Fact 2)arealsowellreproducedbythemodel. Thecorrelationbetweenthetermsoftradeandrelative outputisnegative,andtheBackus-Smithcorrelationisslightlynegative. Hence,thisspeci(cid:2)cation brings the model close to account for Fact 1 as well. Consumption is positively correlated with hours worked and investment, as in the data. Notably, IST shocks account for only 4 percent of thevariationofoutputinthisexperiment,whereasTFPshocksaccountfor80percentofbusiness cycle(cid:3)uctuations. This last observation con(cid:2)rms that variable capacity utilization essentially allows demandlike shocks to stimulate output. The (cid:2)rst order conditions that characterize the optimal choice of capacityutilizationandofhoursworkedare: @G (A ;B ) e v1t (cid:20)u! 1K = 1t 1t 1t (cid:18)ez1tu (cid:18) 1K(cid:18)N1 (cid:18) (27) (cid:0) 1t(cid:0) 1t @B 1t (cid:0) 1t 1t(cid:0) 1t (cid:0) (cid:1) @G (A ;B ) (cid:29)N(cid:29) 1 = 1t 1t 1t (1 (cid:18))ez1tu(cid:18) K(cid:18)N (cid:18) (28) 1t(cid:0) @B (cid:0) 1t 1t 1(cid:0)t 1t Equation (27) states that the marginal cost of increasing capacity utilization has to equal its marginalbene(cid:2)tintermsofproduction. Themarginalcostdependsontwocomponents. Changes inthepriceofinvestment(e v1t)induce(cid:2)rmstoinvestmoretoreplaceinstalledcapital. Theterm (cid:0) (cid:20)u! 1K represents the cost of increasing depreciation from current levels. Equation (28) is 1t(cid:0) 1t t(cid:0)he intratem(cid:1)poral condition equating the marginal rate of substitution between consumption and leisuretothemarginalproductoflaborunderGHHpreferences. With constant capacity utilization (u = u ), IST shocks change the incentives to invest t ss only through the price effect. Shifts in the MPL are small, and output increases only because 31

of changes in labor input. As implied by the variance decomposition of output (Table 4), the elasticityofoutputtotheseshocksisverysmallandbusinesscycle(cid:3)uctuationsaremostlydriven byproductivityshocks. Conversely,thevolatilityofpricesincreases,asmarketclearingrequires largerresponsesinprices. When capacity utilization can vary, the planner increases the short-run response of output to IST shocks using capital more intensively. The additional reduction in the marginal cost of depreciation translates into a larger shift of the MPL schedule,inducing a larger increase in hoursworked. Therefore, variable capacity utilization represents the main transmission mechanism of IST shocks to output. Absent this channel, the model still performs reasonnably well in terms of reproducing Fact 1 and Fact 2, although it requires a larger volatility of the relative price of investment compared to the data (Table 4). The issue of domestic comovement does not arise, sinceTFPshocksdominatebusinesscycle(cid:3)uctuations. 6.3 Trade Elasticity Thereisalotofuncertaintyabouttheappropriatevalueforthetradeelasticityforbusinesscycle studies. In their original work, BKK set this parameter equal to 1.5, referring to J. Whalley [1985]. Morerecently,Hooperetal. [2000]reportestimatesforG7countriesinarangebetween 0.1 and 2. Heathcote and Perri [2002] estimate a value of 0.9 for this elasticity. CDL [2008] use a model (cid:224) la BKK that includes a distribution sector which lowers the implied trade elasticity. WhentheyestimateviaGMMmethodsthetradeelasticity,they(cid:2)ndavaluebelow0.5. Incontrasttothebusinesscycleliterature,generalequilibriumtrademodelsadoptlargetrade elasticities. Yi [2003] shows that, with an elasticity of about 12, these models match the large growthininternationaltrade(cid:3)owsafteratradeliberalization. Ruhl[2005]providesaninteresting perspective on these disparities, by arguing that the source of variation in prices and quantities across the two models is fundamentally different: temporary shocks for business cycle models, permanent changes for trade models. He then builds a model with entry and exit that is able to 32

reconcilethisdiscrepancyandestimatesahighfrequencytradeelasticitycloseto1. Based on this discussion, Table 4 presents simulations in which the trade elasticity is equal to 1.5, the value considered in the original BKK work. The usual business cycle properties, including comovement, are preserved. In terms of relative standard deviations, the volatility of trade (cid:3)ows increases but international prices are less volatile than output. In the data, however, international prices are typically more volatile than output. Expression (20) provides once again guidanceinunderstandingthisresult: alargertradeelasticityisassociatedwithalowerresponse ofthetermsoftradetochangesinrelativesupplyanddemandofintermediategoods. Ifintermediate goods are more substitutes, changes in productivity will have higher impact on quantities thanprices.26 Hence,lowtradeelasticityappearsanimportantfeaturetoaccountforFact2. Turning to the cross-correlations, the correlation between the terms of trade and relative output remains negative and the correlation between real exchange rate and consumption is close to zero. Thus, the model can still account reasonably well for Fact 1. This last (cid:2)nding provides support for the mechanism presented, especially in light of the fact that (i) TFP shocks in this experiment account for a large fraction of the variation of output, and (ii) the volatility of the relativepriceofinvestmentisonlyslightlyhigherthaninthedata. Overall, this analysis con(cid:2)rms that the trade elasticity remains a key parameter to account for the volatility of international prices, as previously documented in the literature (see, for example, Heathcote and Perri [2002] and CDL [2008]). The performance of the model improves dramatically when the trade elasticity is lower than one. The model can still account for the correlation between international prices and relative consumption and output, without requiring unrealisticallyhighvolatilityintherelativepriceofinvestment. 7 Conclusions International relative prices appreciate when domestic consumption and output increase more than abroad. In addition, the terms of trade and trade (cid:3)ows are quite volatile. These two central 26Inthelimitingcase,theeconomyreducestoaonegoodmodelandthetermsoftradedonotmoveatall. 33

featuresofinternationaldatabearimplicationsforrisk-sharing,thetransmissionofshocksacross countries,andthesourcesofbusinesscycle(cid:3)uctuations. This paper (cid:2)nds that a two-country model that incorporates neutral as well as investmentspeci(cid:2)ctechnologyshocks,variablecapacityutilizationandweakwealtheffectsonlaborsupply can account for the aforementioned features of the data. IST shocks introduce a source of (cid:3)uctuations in domestic absorption that does not change aggregate production possibilities, like a tasteshock. Outputexpands,domesticpricesincrease,thetermsoftradeappreciateandthetrade balancedeteriorates. The mechanism proposed in this paper is close to Stockman and Tesar [1995], since an additional source of variations in absorption (IST shocks) is used to generate realistic dynamics in international relative prices. However, IST shocks appear less controversial than taste shocks, as both theory and data provide more discipline in embedding these shocks into the model. For instance,Charietal. [2009]arguethatshockstototalfactorproductivity,investment-speci(cid:2)ctechnologyandmonetarypolicyarearguablystructuralshocksonwhichtherehasbeenconvergence inmacroeconomics. CumminsandViolante[2002]andFisher[2006]documentthelong-runand cyclical properties of the real price of investment, often used as a proxy for investment-speci(cid:2)c technologyshocks. The(cid:2)ndingsofthepaperpointtowardsatleasttwointerestingresearchavenues. First,Ishow that the response of international prices to technology shocks depends on the type of technology shocks considered, since their transmission mechanism is very different. Further empirical work on this issue appears a natural development. Second, IST shocks have potentially interesting implications for the cyclical properties of stock prices in open economies27. Boldrin, Christiano and Fisher [2001] build a model that incorporates these shocks together with habit persistence and constraints to the reallocation of factors across sectors which is able to account for several asset prices features of the United States. Their work, however, does not consider international trade. Coeurdacier, Kollmann, and Martin show that in a two-country model with IST shocks 27IthankNanLiforraisingthiscommentinherdiscussion. 34

can provide valuable insights on the lack of international diversi(cid:2)cation observed in the typical investorportfolio. Ileavetheinvestigationoftheseissuestofutureresearch. 35

8 Appendix A. Linearization GiventhattheArmingtonaggregatorishomogenousofdegreeone,itslog-linearizedversionis28 (cid:22) (cid:22) (cid:22) G a(cid:22) G b a b ^ ^ G(:) = a^ + b = (1 im )a^ +im b (A.1) (cid:22) 1 (cid:22) 1 1 1 1 1 G G (cid:0) d whereimistheimportshare. MarketclearingconditionforgoodA,equation(4),yields y^ = (1 im )a^ +im a^ (A.2) 1 1 1 1 2 (cid:0) Combining(A.1)and(A.2)weobtaintheexpressionforrealnetexports ^ ^ n\xqty = y^ G = im a^ b (A.3) 1 1 1 2 1 (cid:0) (cid:0) h i whichisthedifferencebetweenexportsandimportsevaluatedatsteadystateprices. Thelinearapproximationofequation(9)de(cid:2)ningthetermsoftradeis 1 ^ p = a^ b (A.5) 1 1 (cid:27) (cid:0) h i Combining(A.2),(A.3),(A.5)anditsanbalogousforcountry2weobtainequation(12)inthetext p^= (cid:17) (cid:30) y G +(y y ) (A.6) 1 1 1 2 (cid:0) (cid:0) h (cid:16) (cid:17) i where(cid:17) = 1 and(cid:30) = 1 2im1: b b b b 2(cid:27)(1 im1) (cid:0)im1 (cid:0) 9 Appendix B. Data DatafortheU.S.arefromtheBureauofEconomicAnalysis(BEA)NationalIncomeandProduct Account(NIPA).Realvariablesrefertos.a.a.rseriesofchained2000dollars. Thesamplecovers the years 1970:Q1 to 2007:Q3. Following the OECD classi(cid:2)cation, investment includes both private and government investment. Consumption is the sum of private and public consumption. Thetermsoftradearetheratiooftheimportstotheexportspricede(cid:3)ators,whereeachde(cid:3)ators 28Inwhatfollows,ahatdenotespercentagedeviationsfromsteadystateandabardenotessteadystatevalues. 36

is constructed as the ratio of nominal over real trade exports and imports. The real exchange rate is the real broad trade-weighted exchange value of the US$, indexed to March 1973=100. Data are provided by the Federal Reserve Board, Foreign Exchange Rates, G.5 (405). Monthly data are converted to quarterly by taking the average of each month in the quarter. The series is availablestarting1973:Q1. Laborinputistheproductofhoursandtheemploymentrate. Hoursare"Non-FarmBusiness Hours"fromtheBureauofLaborStatistics(BLS)ProductivityandCostRelease. Employmentis "Total Non-Farm Employees" from the BLS publication (cid:147)The Employment Situation(cid:148). Monthly data, in thousands, are converted to quarterly data by taking the average of each month in the quarter. Population15-64isfromtheBureauoftheCensus,CurrentPopulationreports. CapacityUtilizationdatais(s.a.) percentofcapacityforTotalIndustryprovidedbytheBoard of Governors of the Federal Reserve System. Monthly data are from the Industrial Production and Capacity Utilization G.17 (419) Summary Table. Monthly data are converted to quarterly databytakingtheaverageofeachmonthinthequarter. Series for the construction of the rest-of-world aggregate (ROW) are from the OECD Quarterly National Account (QNA). Rest-of-world is de(cid:2)ned as Canada, Japan, and the 15 European Union countries (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Spain, Sweden and the United Kingdom), which are the major trading partner over the sample considered. Including Mexico did not affect the results. GDPandGDPcomponentseriesforthesecountriesareaggregatedbysummingtheOECDmeasure VPVOBARSA (millions of US$, volume estimates and (cid:2)xed PPPs, at constant 2000 prices, s.a.a.r). 37

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Table1. Volatility: NetExportsandTermsofTrade StandardDeviation x NetExports TermsofTrade Australia 0.62 2.76 Belgium 0.86 1.24 Canada 0.58 1.32 Denmark 0.81 0.95 Finland 0.62 1.09 France 0.49 2.04 Germany 0.20 2.39 Italy 0.96 3.10 Japan 0.39 4.02 theNetherlands 0.62 0.93 NewZealand 0.78 1.64 Portugal 0.77 1.84 Spain 0.79 3.54 Sweden 0.58 1.27 UnitedKingdom 0.47 1.35 UnitedStates 0.25 1.72 Median 0.62 1.68 BKK[1994] -Benchmark 0.08 0.53 -HighElasticity 0.14 0.19 StandarddeviationsrelativetothestandarddeviationofGDP.Statistics x refertoHP-(cid:2)lteredquarterlydatafortheperiod1980Q1-2007Q4. 43

Table2. BenchmarkParameters Preferences (cid:12) =0.99 (cid:13) =2.0 (cid:23) =1.64 Production (cid:18) =0.36 (cid:20) =0.0525 ! =1.404 Trade (cid:27) =0.5 im =0.15 ShockProcess 0.906 0.088 0.00 0.00 0.088 0.906 0.00 0.00 (cid:10) =2 3 0.00 0.00 0.906 0.088 6 0.00 0.00 0.088 0.906 7 6 7 4 5 0.012 0.003 -0.016 0.000 0.003 0.012 0.000 -0.016 (cid:6) =10 3 2 3 (cid:0) (cid:3) -0.016 0.000 0.073 0.019 6 0.000 -0.016 0.019 0.073 7 6 7 4 5 44

Table3. BusinessCyclesStatistics VariationsoftheBenchmarkEconomy Benchmark BKK JR Habit Fixed HighTrade Statistic Data Economy Utility Utility Utility Capacity Elasticity y Standarddeviations z Consumption 0.72 0.67 0.69 0.60 0.67 0.74 0.73 Investment 2.88 2.84 2.89 2.85 2.86 2.86 2.84 Domesticabsorption 1.13 1.14 1.06 1.11 1.04 1.17 1.15 Hoursworked 0.88 0.61 0.41 0.56 0.68 0.61 0.61 Capacityutilization 1.82 1.18 1.73 1.28 2.23 - 1.16 Netexports 0.28 0.37 0.19 0.32 0.19 0.39 0.47 Termsoftrade 1.49 1.30 1.09 1.25 1.36 1.61 0.84 Realexchangerate 3.56 0.91 0.76 0.90 0.96 1.13 0.59 Cross-correlations BetweenGDPand Consumption 0.78 0.94 0.82 0.93 0.80 0.94 0.96 Investment 0.93 0.90 0.86 0.92 0.88 0.87 0.79 Hoursworked 0.86 1.00 0.73 0.94 0.10 1.00 1.00 Capacityutilization 0.82 0.79 0.75 0.78 0.42 - 0.79 Netexports -0.43 -0.55 -0.26 -0.45 -0.17 -0.57 -0.25 BetweenConsumptionand Investment 0.76 0.72 0.45 0.75 0.43 0.66 0.65 Hoursworked 0.58 0.94 0.20 0.90 -0.08 0.94 0.96 Betweentermsoftrade andrelativeGDP -0.17 -0.68 0.12 -0.53 0.12 -0.44 -0.21 Betweenrealexchangerate andrelativeconsumption -0.23 -0.41 0.98 -0.04 0.64 -0.05 0.09 y StatisticsarebasedonloggedandHP-(cid:2)lteredU.S.quarterlydatafortheperiod1983Q1-2000Q4. StandarddeviationsofthevariablesaredividedbythestandarddeviationofGDP. z 45

Table4. RelativePriceofInvestmentfortheModels VariationsoftheBenchmarkEconomy Benchmark BKK JR Habit Fixed HighTrade Statistic Data Economy Utility Utility Utility Capacity Elasticity y Statisticstargetedinthebenchmarkcalibration Contributiontobusinesscycles TFP 0.27 0.22 0.22 0.25 0.24 0.80 0.37 IST 0.53 0.47 0.59 0.47 0.59 0.04 0.43 Cross-correlations BetweenInvestment PriceandGDP -0.52 -0.42 -0.46 -0.40 -0.51 -0.41 -0.29 Statisticsimpliedbythemodel Standarddeviations z InvestmentPrice 0.80 0.94 1.83 1.37 2.60 1.42 1.04 Autocorrelation InvestmentPrice 0.85 0.70 0.69 0.70 0.69 0.70 0.70 Cross-correlations BetweenInvestmentPriceand Netexports 0.18 0.55 0.58 0.58 0.50 0.56 0.59 Realexchangerate 0.26 0.57 0.33 0.52 0.22 0.50 0.53 y Statisticsfortherelativepriceofinvestmentarecalculatedusingquality-adjustedinvestmentpriceseries asconstructedbyFisher[2006]. StatisticsfortheothervariablesarebasedonloggedandHP-(cid:2)lteredU.S. quarterlydatafortheperiod1983Q1-2000Q4. StandarddeviationoftheinvestmentpriceseriesdividedbythestandarddeviationofGDP. z 46

Table5. OntheBarro-King[1984]Critique Experiment: -Sameshockprocessasinthebenchmarkeconomy -Adjustmentcosttocapital U.S. RBC BKK Benchmark Statistic Data Model Model Economy Standarddeviation z Consumption 0.72 0.69 0.67 0.67 Investment 2.88 2.89 2.86 2.84 Domesticabsorption 1.13 1.00 1.04 1.14 Cross-correlations Betweenconsumptionand Investment 0.78 -0.12 -0.03 0.72 Hoursworked 0.86 -0.45 -0.23 0.94 BetweenGDPand NetExports -0.43 - 0.23 -0.55 Contributiontobusinesscycles TFP 0.27 0.86 0.80 0.22 IST 0.53 0.13 0.07 0.47 StandarddeviationofseriesdividedbythestandarddeviationofGDP. z 47

Figure 1. U.S. Real Exchange Rate and Relative Consumption 000000......111111000000000000 000000......000000222222555555 00000.....000005555500000 00000.....000001111133333 0000....000000000000 0000....000000000000 ---000...000555000 ---000...000111333 --00..110000 --00..002255 RReeaall EExxcchhaannggee RRaattee RReellaattiivvee CCoonnssuummppttiioonn

Figure 2. U.S. Terms of Trade and Relative Output 000000......111111000000 000000......000000222222555555000000 00000.....0000055555 00000.....00000111112222255555 0000....00000000 0000....0000000000000000 ---000...000555 ---000...000111222555 --00..1100 --00..00225500 TTeerrmmss ooff TTrraaddee RReellaattiivvee OOuuttppuutt

Figure 3. Equipment over the Business Cycle UUnniitteedd SSttaatteess CCaannaaddaa 0.030 0.090 00..006600 00..009900 0.060 00..006600 00..004400 0.020 0.030 00..003300 00..002200 0010 0000 00.000000 0.000 -0.030 -0.020 -0.060 -0.040 -0090 1Q- 4891 1Q- 5891 1Q- 6891 1Q- 7891 1Q- 8891 1Q- 9891 1Q- 0991 1Q- 1991 1Q- 2991 1Q- 3991 1Q- 4991 1Q- 5991 1Q- 6991 1Q- 7991 1Q- 8991 1Q- 9991 1Q- 0002 1Q- 1002 1Q- 2002 1Q- 3002 1Q- 4002 Canada 0.030 0.090 0.060 0.020 0.030 0.010 0.000 -0.030 0.000 -0.060 -0.010 -0090 1Q- 389 2Q- 489 3Q- 589 4Q- 689 1Q- 889 2Q- 989 3Q- 099 4Q- 199 1Q- 399 2Q- 499 3Q- 599 4Q- 699 1Q- 899 2Q- 999 3Q- 000 4Q- 100 1Q- 300 2Q- 400 United States 0.060 0.090 0.060 0.040 0.030 0.020 0.000 0.000 -0.030 -0.020 -0.060 -0.040 -0.090 -0.060 -0.120 1Q- 4891 1Q- 5891 1Q- 6891 1Q- 7891 1Q- 8891 1Q- 9891 1Q- 0991 1Q- 1991 1Q- 2991 1Q- 3991 1Q- 4991 1Q- 5991 1Q- 6991 1Q- 7991 1Q- 8991 1Q- 9991 1Q- 0002 1Q- 1002 1Q- 2002 1Q- 3002 1Q- 4002 Canada 0.030 0.090 0.060 0.020 0.030 0.010 0.000 -0.030 0.000 -0.060 -0.010 -0.090 -0.020 -0.120 Real Price Real Share 1Q- 3891 2Q- 4891 3Q- 5891 4Q- 6891 1Q- 8891 2Q- 9891 3Q- 0991 4Q- 1991 1Q- 3991 2Q- 4991 3Q- 5991 4Q- 6991 1Q- 8991 2Q- 9991 3Q- 0002 4Q- 1002 1Q- 3002 2Q- 4002 United States 0.060 0.090 0.060 0.040 0.030 0.020 0.000 0.000 -0.030 -0.020 -0.060 -0.040 -0.090 -0.060 -0.120 Real Price Real Share Italy Australia 0.030 0.060 0.090 0.200 0.150 0.020 0.030 0.060 1Q- 4891 1Q- 5891 1Q- 6891 1Q- 7891 1Q- 8891 1Q- 9891 1Q- 0991 1Q- 1991 1Q- 2991 1Q- 3991 1Q- 4991 1Q- 5991 1Q- 6991 1Q- 7991 1Q- 8991 1Q- 9991 1Q- 0002 1Q- 1002 1Q- 2002 1Q- 3002 1Q- 4002 Canada 0.030 0.090 0.060 0.020 0.030 0.010 0.000 -0.030 0.000 -0.060 -0.010 -0.090 -0.020 -0.120 Real Price Real Share 1Q- 3891 2Q- 4891 3Q- 5891 4Q- 6891 1Q- 8891 2Q- 9891 3Q- 0991 4Q- 1991 1Q- 3991 2Q- 4991 3Q- 5991 4Q- 6991 1Q- 8991 2Q- 9991 3Q- 0002 4Q- 1002 1Q- 3002 2Q- 4002 United States Real Price Real Share 0.090 0.200 0.150 0.060 0.100 0.030 0.050 0.000 0.000 -0.030 1Q- 2Q- 3Q- 4Q- 1Q- 2Q- 3Q- 4Q- 1Q- 2Q- 3Q- 4Q- 1Q- 2Q- 3Q- 4Q- 1Q- 2Q- Australia 0.030 0.060 0.020 0.030 0.010 0.000 0.000 -0.030 -0010 -0060 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 1Q- 0.060 0.090 0.060 0.040 0.030 0.020 0.000 0.000 -0.030 -0.020 -0.060 -0.040 -0.090 -0.060 -0.120 Italy 1Q- 4891 1Q- 5891 1Q- 6891 1Q- 7891 1Q- 8891 1Q- 9891 1Q- 0991 1Q- 1991 1Q- 2991 1Q- 3991 1Q- 4991 1Q- 5991 1Q- 6991 1Q- 7991 1Q- 8991 1Q- 9991 1Q- 0002 1Q- 1002 1Q- 2002 1Q- 3002 1Q- 4002 Canada 0.030 0.090 0.060 0.020 0.030 0.010 0.000 -0.030 0.000 -0.060 -0.010 -0.090 -0.020 -0.120 Real Price Real Share 1Q- 3891 2Q- 4891 3Q- 5891 4Q- 6891 1Q- 8891 2Q- 9891 3Q- 0991 4Q- 1991 1Q- 3991 2Q- 4991 3Q- 5991 4Q- 6991 1Q- 8991 2Q- 9991 3Q- 0002 4Q- 1002 1Q- 3002 2Q- 4002 United States Real Price Real Share 0.090 0.200 0.150 0.060 0.100 0.030 0.050 0.000 0.000 -0.030 -0.050 -0.060 -0.100 -0.090 -0.150 1Q- 3891 2Q- 4891 3Q- 5891 4Q- 6891 1Q- 8891 2Q- 9891 3Q- 0991 4Q- 1991 1Q- 3991 2Q- 4991 3Q- 5991 4Q- 6991 1Q- 8991 2Q- 9991 3Q- 0002 4Q- 1002 1Q- 3002 2Q- 4002 Australia 0.030 0.060 0.020 0.030 0.010 0.000 0.000 -0.030 -0.010 -0.060 -0.020 -0.090 -0.030 -0.120 Real Price Real Share 1Q- 4891 1Q- 5891 1Q- 6891 1Q- 7891 1Q- 8891 1Q- 9891 1Q- 0991 1Q- 1991 1Q- 2991 1Q- 3991 1Q- 4991 1Q- 5991 1Q- 6991 1Q- 7991 1Q- 8991 1Q- 9991 1Q- 0002 1Q- 1002 1Q- 2002 1Q- 3002 1Q- 4002 0.060 0.090 0.060 0.040 0.030 0.020 0.000 0.000 -0.030 -0.020 -0.060 -0.040 -0.090 -0.060 -0.120 Italy Real Price Real Share 1Q- 4891 1Q- 5891 1Q- 6891 1Q- 7891 1Q- 8891 1Q- 9891 1Q- 0991 1Q- 1991 1Q- 2991 1Q- 3991 1Q- 4991 1Q- 5991 1Q- 6991 1Q- 7991 1Q- 8991 1Q- 9991 1Q- 0002 1Q- 1002 1Q- 2002 1Q- 3002 1Q- 4002 Canada 0.030 0.090 0.060 0.020 0.030 0.010 0.000 -0.030 0.000 -0.060 -0.010 -0.090 -0.020 -0.120 Real Price Real Share 1Q- 3891 2Q- 4891 3Q- 5891 4Q- 6891 1Q- 8891 2Q- 9891 3Q- 0991 4Q- 1991 1Q- 3991 2Q- 4991 3Q- 5991 4Q- 6991 1Q- 8991 2Q- 9991 3Q- 0002 4Q- 1002 1Q- 3002 2Q- 4002 United States Real Price Real Share 0.090 0.200 0.150 0.060 0.100 0.030 0.050 0.000 0.000 -0.030 -0.050 -0.060 -0.100 -0.090 -0.150 1Q- 3891 2Q- 4891 3Q- 5891 4Q- 6891 1Q- 8891 2Q- 9891 3Q- 0991 4Q- 1991 1Q- 3991 2Q- 4991 3Q- 5991 4Q- 6991 1Q- 8991 2Q- 9991 3Q- 0002 4Q- 1002 1Q- 3002 2Q- 4002 Australia 0.030 0.060 0.020 0.030 0.010 0.000 0.000 -0.030 -0.010 -0.060 -0.020 -0.090 -0.030 -0.120 Real Price Real Share 1Q- 4891 1Q- 5891 1Q- 6891 1Q- 7891 1Q- 8891 1Q- 9891 1Q- 0991 1Q- 1991 1Q- 2991 1Q- 3991 1Q- 4991 1Q- 5991 1Q- 6991 1Q- 7991 1Q- 8991 1Q- 9991 1Q- 0002 1Q- 1002 1Q- 2002 1Q- 3002 1Q- 4002 0.060 0.090 0.060 0.040 0.030 0.020 0.000 0.000 -0.030 -0.020 -0.060 -0.040 -0.090 -0.060 -0.120 Italy Real Price Real Share 1Q- 4891 1Q- 5891 1Q- 6891 1Q- 7891 1Q- 8891 1Q- 9891 1Q- 0991 1Q- 1991 1Q- 2991 1Q- 3991 1Q- 4991 1Q- 5991 1Q- 6991 1Q- 7991 1Q- 8991 1Q- 9991 1Q- 0002 1Q- 1002 1Q- 2002 1Q- 3002 1Q- 4002 Canada 0.030 0.090 0.060 0.020 0.030 0.010 0.000 -0.030 0.000 -0.060 -0.010 -0.090 -0.020 -0.120 Real Price Real Share 1Q- 3891 2Q- 4891 3Q- 5891 4Q- 6891 1Q- 8891 2Q- 9891 3Q- 0991 4Q- 1991 1Q- 3991 2Q- 4991 3Q- 5991 4Q- 6991 1Q- 8991 2Q- 9991 3Q- 0002 4Q- 1002 1Q- 3002 2Q- 4002 United States Real Price Real Share

Figure 4. Impulse Response to a IST Shock IInnvveessttmmeenntt CCoonnssuummppttiioonn DDoommeessttiicc AAbbssoorrppttiioonn 2255 55 1100 2200 44 88 1155 33 66 1100 22 44 55 11 22 00 00 00 11 55 99 1133 1177 2211 2255 2299 3333 3377 11 55 99 1133 1177 2211 2255 2299 3333 3377 11 55 99 1133 1177 2211 2255 2299 3333 3377 OOuuttppuutt VVaarriiaabbllee CCaappaacciittyy HHoouurrss WWoorrkkeedd 1100 1122 55 1100 88 44 88 66 33 6 4 2 4 2 1 2 0 0 0 1 5 9 13 17 21 25 29 33 37 1 5 9 13 17 21 25 29 33 37 1 5 9 13 17 21 25 29 33 37 Net Exports Price of Output Real Exchange Rate 4 1 6 4 2 0.5 2 0 0 1 5 9 13 17 21 25 29 33 37 1 5 9 13 17 21 25 29 33 37 0 1 5 9 13 17 21 25 29 33 37 -2 -0.5 -2 -4 -1 -4

Figure 5. Technology Shocks and Terms of Trade TTeerrmmss ooff TTrraaddee OOuuttppuutt 88 88 66 66 44 44 22 22 00 00 1 5 9 13 17 21 25 29 33 37 -2 -2 1 5 9 13 17 21 25 29 33 37 -4 -4 -6 -6 -8 -8 IST TFP IST TFP

Figure 6. On the Barro-King [1984]: Impulse Responses IIIIIIIIIRRRRRRRRRFFFFFFFFFsssssssss tttttttttooooooooo IIIIIIIIISSSSSSSSSTTTTTTTTT SSSSSSSSShhhhhhhhhoooooooooccccccccckkkkkkkkk::::::::: CCCCCCCCCooooooooonnnnnnnnnsssssssssuuuuuuuuummmmmmmmmppppppppptttttttttiiiiiiiiiooooooooonnnnnnnnn 000000000.........555555555 00000000........44444444 00000000........33333333 00000000........22222222 0000000.......1111111 0000000 1111111 3333333 5555555 7777777 9999999 11111111111111 11111113333333 11111115555555 11111117777777 11111119999999 22222221111111 22222223333333 22222225555555 22222227777777 22222229999999 33333331111111 33333333333333 33333335555555 33333337777777 33333339999999 -------0000000.......1111111 ------000000......222222 ------000000......333333 RRRRRRBBBBBBCCCCCC BBBBBBKKKKKKKKKKKK BBBBBBEEEEEENNNNNNCCCCCCHHHHHHMMMMMMAAAAAARRRRRRKKKKKK IIIIIRRRRRFFFFFsssss tttttooooo IIIIISSSSSTTTTT SSSSShhhhhoooooccccckkkkk::::: LLLLLaaaaabbbbbooooorrrrr 00000.....66666 00000.....55555 0000....4444 0000....3333 0000....2222 000...111 000 111 333 555 777 999 111111 111333 111555 111777 111999 222111 222333 222555 222777 222999 333111 333333 333555 333777 333999 --000..111 --00..22 RRBBCC BBKKKK BBEENNCCHHMMAARRKK