Value Added and Productivity Linkages Across Countries

K.7 Value Added and Productivity Linkages Across Countries de Soyres, François and Alexandre Gaillard Please cite paper as: de Soyres, François and Alexandre Gaillard (2019). Value Added and Productivity Linkages Across Countries. International Finance Discussion Papers 1266. https://doi.org/10.17016/IFDP.2019.1266 International Finance Discussion Papers Board of Governors of the Federal Reserve System Number 1266 November 2019

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1266 November 2019 Value Added and Productivity Linkages Across Countries François de Soyres and Alexandre Gaillard NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. 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.

alue dded and roductivity inkages cross V A P L A ountries C * F rançois de S oyres† A lexandre G aillard‡ Federal Reserve Board Toulouse School of Economics 1 2019 October , Abstract Whatistherelationshipbetweeninternationaltradeandbusinesscyclesynchronization? Using data from 40 countries, we find that GDP comovement is significantly associated with tradeinintermediateinputsbutnotwithtradeinfinalgoods. Motivatedbythisnewfact,we build a model of international trade that is able to replicate the empirical trade-comovement slope, offering the first quantitative solution for the Trade Comovement Puzzle. The model relies on (i) global value chains, (ii) price distortions due to monopolistic competition and (iii) fluctuations in the mass of firms serving each country. The combination of these ingredientscreatesalinkbetweendomesticmeasuredproductivityandforeignshocksthroughtrade linkages,generatingadisconnectbetweentechnologyandmeasuredproductivity. Finally,we provideempiricalevidencefortheimportanceoftheseelementsingeneratingalinkbetween foreignshocksanddomesticGDP. Keywords: International trade, international business cycle comovement, networks, inputoutput linkages, Solow residual JEL Classification: F 12 , F 44 , F 62 *We are indebted to Thomas Chaney for his invaluable guidance. For their comments, we are grateful to Manuel Amador, Ariel Burstein, Patrick Fève, Simon Fuchs, Christian Hellwig, Rob Johnson, Tim Kehoe, Marti Mestieri, Alban Moura, Franck Portier, Ana-Maria Santacreu, Constance de Soyres, Shekhar Tomar, Robert Ulbricht, Kei-Mu Yi and seminar or workshop participants in many places. Finally, we also thank the Federal Reserve Bank of Minneapolis, where part of this research has been conducted, for their hospitality and ERC grant N°337272–FiNet for financial support. All errors are our own. †Email: francois.m.desoyres@frb.gov;Correspondingauthor. ‡Email: alexandre.gaillard@tse-fr.eu. 1

1 Introduction TheTradeComovementPuzzle(TCP),uncoveredbyKoseandYi( 2001 , 2006 ), referstotheinability of international business cycle models to quantitatively account for the positive empirical rela- 1 tionship between international trade and GDP comovement. Using international real business cycle (IRBC) models, several authors have succeeded to qualitatively replicate the positive link between trade and GDP comovement but fall short of the quantitative relationship by an order 2 of magnitude. This paper has three main contributions. First, it contributes to empirical investigations of the association between bilateral trade and GDP comovement and shows that trade in intermediate inputs is significantly associated with synchronized GDP fluctuations. Second, it proposes a model of trade in both inputs and final goods with monopolistic pricing and firms entry/exit which is able to replicate the observed trade-comovement slope, offering the first quantitative solution of the TCP. Finally, the paper documents the disconnect between technology and measured productivity in presence of markups and extensive margin adjustments and shows that our model generates a trade-Solow Residual slope in line with the data. Empirics. Since the seminal paper by Frankel and Rose ( 1998 ), a large empirical literature has studied cross countries’ GDP synchronization, showing that pairs of countries with stronger trade linkages tend to have more highly correlated business cycles. The paper refines previous 40 10 analysis by constructing a panel dataset of countries consisting of four -years windows 1970 2009 ranging from to , which allows for dyadic as well as time windows fixed effects. In this setting, we document that the positive relationship between trade and GDP-comovement is mostly driven by tradeinintermediateinputs, whereas trade in final good is found insignificant or negative. Those new findings suggest a possible link between global value chains (GVC) and the rising synchronization of GDP across countries. Theory. As discussed in Kehoe and Ruhl ( 2008 ), international production linkages alone do not generate a link between domestic GDP and foreign shocks. With perfect competition and constant returns to scale, firms equalize marginal cost and marginal revenues of imported input, so that changes in the quantity of imported input yields exactly as much benefit as it brings costs. Hence, foreign shocks have an impact on domestic value added only to the extent that they impact the supply of domestic factors. This "negative result" is at the heart of the TCP. We incorporate two ingredients that create an endogenous relationship between domestic productivity and foreign shock through trade linkages. 1 For empirical studies, among many others, see Frankel and Rose (1998), Clark and van Wincoop (2001), Imbs (2004),BaxterandKouparitsas(2005),KoseandYi(2006),Calderonetal.(2007),Inklaaretal.(2008),DiGiovanniand Levchenko(2010),Ng(2010),LiaoandSantacreu(2015),Duvaletal.(2015)andDiGiovannietal.(2016). 2 For quantitative studies, see for instance Kose and Yi (2001, 2006), Burstein et al. (2008), Arkolakis and Ramanarayanan(2009),Johnson(2014)orLiaoandSantacreu(2015). 2

First, when firms choose their price, they do not equalize the marginal cost and the marginal 1988 revenue product of their inputs. As noted previously by Hall ( ) and discussed in Basu and 2002 2014 2014 Fernald ( ), Gopinath and Neiman ( ) or Llosa ( ), this wedge between marginal cost and marginal product of inputs implies that any change in intermediate inputs usage is asso- 3 ciated with a first order change in value added, over and beyond changes in domestic factors. Second, fluctuations along the extensive margin have the potential to create an additional amplification mechanism between domestic productivity and foreign shocks. With love of variety, any variation in the mass of suppliers leads to a first order productivity change. Love of variety is a form of increasing returns to scale: a firm with more suppliers is more efficient at transforming inputs into output, which leads to an increases of value added over and beyond variations in domestic factor supply. Those ingredients create a link between foreign shocks and measured domestic productivity. Quantitative analysis. Motivated by the discussion above, we propose a multi-country dynamic general equilibrium model of international trade in finalgoods and in intermediateinputs that relies on (i) monopolistic competition and (ii) fluctuations in the mass of firms serving each country. We calibrate the model to 14 countries and a composite Rest-Of-the-World and assess its ability to replicate the strong correlation between trade in intermediate inputs and GDP synchronization. Fixed effect regressions on this simulated dataset shows that the model is able to account for the trade-comovement (TC) slope observed in the data mainly through trade in intermediate inputs, a significant improvement compared to previous studies. Decomposing theroleofeachingredient,weshowthattradeinintermediatesaloneisnotsufficienttoreplicate the trade-comovement relationship. The addition of monopolistic pricing and extensive margin adjustments increase the simulated TC slope by a factor seven and improve the model fit. Further empirical evidence. Finally, we provide evidence supporting our modeling assumptions. First, using different measures of monopoly power, we find that countries with higher markups have a GDP that is more systematically negatively correlated with terms-oftrade movements, meaning that they experience a larger GDP decrease when the price of their imports rises. Second, we empirically test the correlation between the extensive and intensive marginsoftradewithcountry-pairGDPcorrelations. Ahigherdegreeofbusinesscyclesynchronizationisassociatedwithanincreaseintherangeofgoodstradedandisnotassociatedwithan 4 increase in the quantity traded for a given set of goods. 3 Relatedtothispoint,Bursteinetal.(2008)showthatifallfirmstakepricesasgiven,achangeintradecostscan affect aggregateproductivity only tothe extent that itchanges the productionpossibility frontier atconstant prices. Thiscanbeinterpretedassayingthatshockstotheforeigntradingtechnologyhavenoimpactonaggregatedomestic productivityifallfirmshaveconstantreturnstoscaleandtakepricesasgiven. 4 This result is in line with the analysis in Liao and Santacreu (2015) which emphasizes the role of the extensive margin. Comparedtothem, weareaddingthepaneldimensionbyperformingfixedeffectregressionwhichallows ustocontrolforcountry-pairfixedeffectsthatcanbecorrelatedwithtradeintensity. Moreover, wealsorelateGDP 3

Relationship to the literature. Starting with Frankel and Rose ( 1998 ), a number of papers havestudiedandconfirmedthepositiveassociationbetweentradeandcomovementinthecross- 5 section. The empirical part of this paper is mostly related to two recent contributions. First, 2015 Liao and Santacreu ( ) is the first to study the link between the extensive margin and GDP and TFP synchronization. Second, Di Giovanni et al. ( 2016 ) uses a cross-section of French firms and presents evidence that international I/O linkages at the micro level are an important driver of the value added comovement observed at the macro level. Their evidence is in line with the 6 findings of this paper. If the empirical link between bilateral trade and GDP comovement has long been known, the underlying economic mechanism of this relationship is still unclear. Using the workhorse IRBC 2006 10 with three countries, Kose and Yi ( ) have shown that the model can explain at most % of the slope between trade and business cycle synchronization, leading to what they called the Trade Comovement Puzzle (TCP). Since then, many papers have refined the puzzle, highlighting ingredients that could bridge the gap between the data and the predictions of classic models. 2008 Burstein et al. ( ) show that allowing for production sharing among countries can deliver tighter business cycle synchronization if the elasticity of substitution between home and foreign 7 2009 intermediate inputs is extremely low. Arkolakis and Ramanarayanan ( ) analyze the impact of vertical specialization on the relationship between trade and business cycle synchronization. Their model with perfect competition does not generate significant dependence of business cycle synchronization on trade intensity, but they show that the introduction of price distortions that react to foreign economic conditions allows their model to better fit the data. Incorporat- 2014 ing trade in inputs in an otherwise standard many-countries IRBC model, Johnson ( ) shows that adding international input-output (I/O) linkages alone is not sufficient to solve the tradecomovement puzzle, but the paper points that such production linkages do synchronize input usage. Compared to those papers, we add firms entry/exit and monopolistic competition and argue that those are key ingredients for the model to deliver quantitative results in line with the 2015 2005 data. Liao and Santacreu ( ) build on Ghironi and Melitz ( ) and Alessandria and Choi 2007 ( ) to develop a two-country IRBC model with trade in differentiated varieties. Compared to this paper, our analysis adds multinational production in a many-country setup which creates a strong interdependency in firms’ pricing and export decisions. We also highlight both comovementtothestandarddeviationofeachmarginandshowthatanincreaseofthevarianceofextensivemargin fluctuationsisassociatedwithhigherGDPcorrelation. 5 Seepaperscitedforinstanceinfootnote2. 6 Relatedly,Ng(2010)usescross-countrydatafrom30countriesandshowsthatbilateralproductionfragmentation hasapositiveeffectonbusinesscyclecomovement. Theconceptofbilateralproductionfragmentationusedisdifferent fromthispaperasittakesintoaccountonlyasubsetoftradeinintermediates,namelyimportedinputsthatarethen furtherembodiedinexports. Moreover,thecrosssectionnatureoftheanalysisdoesnotallowneitherfordyadicnor timewindowsfixedeffects. 7 Intheirbenchmarksimulations,theauthorstakethevalueof0.05forthiselasticity. 4

8 quantitatively and empirically the role of markups and extensive margin fluctuations. Finally, a 2019 complementary approach has been developed by Drozd et al. ( ) which model the dynamics 2012 of trade elasticity in final goods and use GHH preferences. Building on Drozd and Nosal ( ), 3 their quantitative -country model features customers accumulation with matching frictions between producers and retailers. 2 Empirical Evidence 1998 In this section, we update the initial Frankel and Rose ( ) (henceforth, FR) analysis on the relationship between bilateral trade and GDP comovement and we also provide empirical support for the specific role of trade in intermediate inputs in this relationship. Our sample is composed 40 90 of countries , which account for around % of world GDP, and cover the period stretch- 1970 2009 9 ing from to . We use annual data on real GDP at chained PPPs from the th Penn 625 World Table, which is transformed in two ways: (i) HP filter with smoothing parameter . to capture the business cycle frequencies and (ii) log first difference. Trade data come from John- 2017 son and Noguera ( ) who combine data on exports, imports, production, and inputs use to 1970 2009 construct bilateral trade flows from to separating between trade in final good and trade in intermediate inputs within main sectors: agriculture, service, non-manufacturing and 9 manufacturing. We construct a symmetric measure of bilateral trade intensity (hereafter "trade intensity") using the sum of total exports (T ) from country i to j and total imports (T ), i→j j→i such as: Trade = Ti→j +Tj→i , and measures the importance of the trade relationship relative to ij GDPi +GDPj 10 total GDP. In a similar way, we disentangle trade intensity in inputs and final goods by constructing indexes Tradefinal= T i F →j +T j F →i and Trade input = T i I →j +T j I →i by taking into account only the ij GDPi +GDPj ij GDPi +GDPj exports and imports in final and intermediate goods respectively. In practice, as standard in the 11 literature, we take the natural logarithm of both ratios. TheextenttowhichcountrieshavecorrelatedGDPcanbeinfluencedbymanyfactorsbeyond international trade, including correlated shocks, financial linkages, common monetary policies, 8 Intheirmodel,nofirmisbothanimporterandanexporter.Theabsenceofproductionlinkagesmakesitessentially amodeloftradeinfinalgoodonlyinwhichdomesticandforeigngoodsaresubstitutes. This,inturn,createsforces toward negative GDP correlation as is illustrated by the negative association between trade and GDP comovement whentheelasticityofsubstitutionisequalto3.1. 9 WeprovideadditionaldetailsondatasourcesandthelistofcountriesintheonlineappendixA.1. (cid:16) (cid:17) 10 We also used an index defined as Total =max Total Tradeij, Total Tradeij . This measure has the advantage to take ij GDPi GDPj a high value whenever one of the two countries depends heavily on the other for its imports or exports. Both our empiricalandsimulatedresultsholdwhenweusethisindex. 11 Tobemoreprecise,wefirstapplythelogtransformationontradeintensitiesandthenweaverageoverthetime windows. This is motivated by the fact that the original trade data grow exponentially from 1970 to 2009. We also reporttheresultsoftheregressionsusingthelogtransformationonthemeantradeintensitiesinthesupplementary appendix A.3.3. Results are quite similar. In the supplementary appendix A.3.4, we also report the results using the level of trade intensities and show that our findings are robust to this specification. Finally, notice that the log specificationhasalargerexplanatorypower(measuredbytheR2)comparedtoregressionsinlevels. 5

etc. Because those other factors can themselves be correlated with the index of trade proximity in the cross section, using cross-section identification could yield biased results. Indeed, in their seminal paper, FR use cross-sectional variations to evaluate whether bilateral trade intensity correlates with business cycle synchronization, but their specification does not rule out omitted variable bias such as, for example, the fact that neighboring countries have at the same time more correlated shocks and larger trade flows. By constructing a panel dataset and controlling for both country-pair and time windows fixed effects, this paper relates to recent studies that 12 try to control for unobserved characteristics. Therefore, in order to separate the effect of trade linkagesfromotherunobservableelements,weconstructapaneldatasetbycreatingfourperiods 13 of ten years each. Within each time window, we compute GDP correlation (Corr GDP) as well as the average trade intensities defined above. We then estimate two panel data regressions. In the first we follow the existing literature by running linear regression estimation of Corr GDP on the log of trade intensity Trade : ijt ijt Corr GDP = β ln(Trade )+controls +CP +TW +(cid:101) ( 1 ) ijt 1 ijt ijt ij t ijt where i and j denote the two countries and t the time window. In the second, we run the regression on the log of trade intensity disaggregated into final goods and inputs: Corr GDP = β ln(Trade input)+β ln(Tradefinal)+controls +CP +TW +(cid:101) ( 2 ) ijt 1 ijt 2 ijt ijt ij t ijt We finally specify the additional controls that we include (one-by-one) in the analysis. First, we include dummy variables for countries among the European Union (each wave are entitled a different dummy variables) and the Euro Area. Second, we construct two additional measures that capture the effect of trade network (third country effect) and the sectoral composition 14 of trade. Our “third country” index is motivated by the fact that two countries with similar partners could co-move because of their link with common partners. Moreover, our “sectoral” indexcontrolsforchangesinspecialization. Ifshockshaveasectoralcomponent,thentwocountries that tend to specialize over time in the same sectors could have an increase in business cycle comovements over and beyond any direct trade effects. The third index is specified as third (i,j) = 1− 1 ∑ (cid:12) (cid:12) T i→k +T k→i − T j→k +T k→j (cid:12) (cid:12). It measures the degree of simcountry 2 k(cid:54)=i,j(cid:12)∑ T +T ∑ T +T (cid:12) k i→k k→i k j→k k→j ilarity in the geographical distribution of trade shares between country i and country j, and is 12 Di Giovanni and Levchenko (2010) includes country pair fixed effects in a large cross-section of industry-level data with 55 countries from 1970 to 1999 in order to test for the relationship between sectoral trade and output (not value-added) comovement at the industry level. Duval et al. (2015) includes country pair fixed and year effects in a panelof63countriesfrom1995to2013andtesttheimportanceofvalueaddedtradeinGDPcomovement. 13 AddingtimewindowsfixedeffectcontrolsfortherecentriseofworldGDPcorrelationsincethe90s,whichcould beunrelatedtotradeintensity. 14 In the supplementary appendix A.3.2, we also control for sectoral composition of total value added. However, duetomissingdata,thesampleismuchsmaller. 6

equal to 0 if countries i and j have completely separated trade partners while it is equal to 1 if 2 all trade shares are equal. The sectoral composition index is constructed based on -digit SITC (cid:12) T(s) T(s) (cid:12) tradedataassector (i,j) = 1− 1 ∑ (cid:12) i − j (cid:12),with T(s)thetotalexport proximity 2 s∈S (cid:12)∑ T(s) ∑ T(s)(cid:12) i s∈S i s∈S j of country i in the specific sector (or products) s in the set of sectors S. This index controls for the composition of trade and can be thought of as measuring common sectoral specialization within each country-pair: if two countries export exactly the same share of each products, then 1 4 2 the index is equal to . For those two indexes, we use bilateral trade data (SITC REV. ) from the Observatory of Economic Complexity. In columns (1) and (5) of table 1 , we first report results using only within country-pair variations without time window fixed effects (FE). Our estimates are significant and consistent with 48 11 those in the empirical literature (ranging from a trade-comovement slope of about . % and % 15 in log), and show a positive relationship between bilateral trade and GDP correlation. Then, in columns (2) and (6), we run the same regression controlling for aggregate time windows fixed effects. When controlling for both country-pair and time FE, the positive relationship between trade and GDP correlation still holds for HP filter and first differences, but effects are signifi- 16 cantly dampened and about half as large as what is implied without time FE. To have a sense of the magnitude involved, notice that the median change of the log trade intensity between 2000 2009 1970 1979 2 - and - , across all country-pairs, is an increase of factor . According to the 0044 point estimates, this corresponds to an increase in GDP correlation of . . Incolumns(3),(4),(7)and(8)oftable 1 ,weseparatetradeinintermediateinputsfromtrade in final goods. Results highlight a significant positive relationship between GDP correlation and 17 trade in inputs, while trade in final goods is found insignificant. Interestingly, adding time window FE only slightly reduces the correlation between trade proximity in inputs and GDP comovement. Provided that the median increase of the log trade intensity in intermediate goods 2000 2009 1970 1979 184 between - and - isabout . ,theslopecoefficientimpliesanassociatedincrease 0098 18 of GDP correlation of . , a non negligible increase. 15 Frankel and Rose (1998) (FR), estimate an elasticity of nominal GDP comovement to trade intensity of about 4.8%, usingadifferentsetof21countries, timeperiod(1957to1997)andthreeinstrumentalvariables(IV)fortrade intensity: (i)logofdistancebetweencountries,(ii),dummyforcommonborder,(iii)dummyforcommonlanguage. WithaspecificationsimilartoFR,KoseandYi(2006)use21countriesfrom1970-2000andfindanelasticityoftrade intensityandGDPof9.1%usingHP-filteredGDPand7.8%usinglog-difference. Finally,usingthesamemeasurefor trade intensity as in this paper without time window fixed effects, they estimate a coefficient β of about 0.115. In a similarway, LiaoandSantacreu(2015)useIVestimationoverasampleof30countriescoveringtheperiodbetween 1980and2009andfindestimatesbetween0.112(HPfilter)and0.066(FD).InappendixA.3,wealsoprovidesestimates usingthe1970-1990period. 16 See also footnote 1 for papers finding a high and robust association between total trade and business cycle comovementusingcross-sectionalsettings. 17 Di Giovanni and Levchenko (2010) investigate the role of vertical linkages in output synchronization (not value added)usingI/OmatricesfromtheBEA.Theirestimatesimplythatverticalproductionlinkagesaccountforsome30 percentofthetotalimpactofbilateraltradeonthebusinesscyclecorrelation 18 Notice that the estimate using the log of the mean trade intensity in intermediate inputs within time windows impliesanassociatedincreaseofGDPcorrelationof0.091. 7

Table.1. TradeproximityandGDPcorrelation a CorrGDPHPfilter Corr ∆GDP (1) (2) (3) (4) (5) (6) (7) (8) ln(Trade) 0.055∗∗∗ 0.022∗∗ 0.044∗∗∗ 0.027∗∗ (0.007) (0.011) (0.006) (0.011) ln(Tradeinput) 0.054∗∗ 0.053∗∗ 0.055∗∗ 0.042∗ (0.025) (0.024) (0.023) (0.023) ln(Tradefinal) 0.003 −0.030 −0.008 −0.016 (0.022) (0.024) (0.020) (0.023) Country-pair Yes Yes Yes Yes Yes Yes Yes Yes Timewindow No Yes No Yes No Yes No Yes N 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 R2 0.035 0.153 0.037 0.155 0.024 0.141 0.024 0.142 Notes: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Inparenthesis: std. deviation. aWeusefourtimewindowsof10yearseachfrom1970to2009. 2 1 5 We then add our controls in table , where columns ( ) and ( ) report the regression results 2 6 without the additional controls. In columns ( ) and ( ) we show the results with EU and USSR 3 7 4 dummies while in columns ( ) and ( ) we include the third country index. Finally, columns ( ) 8 and ( ) include our index controlling for the sectoral composition of trade. In all specifications, 5 trade in intermediate inputs is shown to be significant at % while trade in final goods is insignificant (or weakly negatively correlated). Notice also that the effect of trade network is also significantandhigh;implyingthatthereisarelationshipbetweenGDPcomovementandthefact that two countries have similar trade partners. 19,20 3 A simple model Forthesakeofexposition,weconsiderhereastaticsmallopeneconomy. Insuchaworld,Kehoe 2008 and Ruhl ( ) (henceforth KR) show that a change in the price of imported inputs has no impact, up to a first order approximation, on measured productivity. Therefore, any change in GDP is due to variations in domestic factors supply. We start by briefly reviewing this result. 19 Results presented here use a fixed effect specification. To discriminate between fixed or random effects, we run aHausmantestwhichdisplayasignificantdifference (p < 0.001), andwethereforerejecttherandomeffectmodel. We also test the need for time-windows effects against the alternative without time-windows FE. The results of a Lagrange multipliers test provide strong support for the model with time-windows fixed effects (p < 0.001). The supplementalappendixprovidesmanyotherrobustnesstestswithalternativedatasetsandtimewindows. 20 The results are also robust to a number of alternative specifications, time periods, time windows, different set of countries (excluding Euro area or European countries), world GDP correlation and an alternative dataset and methodofseparatingintermediatefromfinalgoods. Weprovideanoverviewofthoseresultsintable14inappendix. We also provide in table 12 in appendix results with financial controls. We finally disaggregated further the role of intermediate inputs by main sectors in the supplementary appendix A.3.7, and find that the manufacturing and non-manufacturing industrial sectors play a key role in the positive relationship between trade proximity and GDP correlation. Theseadditionalresultsareprovided. 8

Table.2. TradeproximityandGDPcorrelationwithcontrols CorrGDPHPfilter Corr ∆GDP (1) (2) (3) (4) (5) (6) (7) (8) ln(Tradeinput) 0.053∗∗ 0.059∗∗ 0.060∗∗ 0.061∗∗ 0.042∗ 0.050∗∗ 0.052∗∗ 0.049∗∗ (0.024) (0.024) (0.024) (0.024) (0.023) (0.023) (0.023) (0.023) ln(Tradefinal) −0.030 −0.038 −0.047∗ −0.048∗ −0.016 −0.024 −0.035 −0.033 (0.024) (0.024) (0.025) (0.025) (0.023) (0.023) (0.023) (0.023) sector 0.088 −0.247∗ prox (0.146) (0.138) third 0.307∗∗ 0.305∗∗ 0.400∗∗∗ 0.407∗∗∗ country (0.149) (0.150) (0.141) (0.141) Country-PairFE Yes Yes Yes Yes Yes Yes Yes Yes TimeWindowFE Yes Yes Yes Yes Yes Yes Yes Yes USSR+EUdum. No Yes Yes Yes No Yes Yes Yes N 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 R2 0.155 0.167 0.170 0.170 0.142 0.155 0.159 0.160 Notes: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Inparenthesis: std. deviation. 3.1 The Kehoe and Ruhl (2008) negative result The economy produces a final good y, used for consumption and exports, which is produced by combiningimportedinputs x anddomesticfactorsofproduction (cid:96) (possiblyavector), according to y = F((cid:96),x),where F(.,.)hasconstantreturnstoscaleandisconcavewithrespecttoeachofits arguments. The final good producer chooses domestic factors and imported inputs to maximize profit, taking all prices as given. Optimality requires that factors are paid their marginal product and we have p F ((cid:96),x) = w and p F ((cid:96),x) = p , with p the final good price, p the price of y (cid:96) y x x y x imported inputs x and w the price of domestic factors. Gross Domestic Product is the sum of value added in the country, which is simply the value of final goods minus the value of imported inputs. Importantly, many statistical agencies use base 21 periodpriceswhenvaluingestimatedquantitiesintheconstructionofGDP. Sincepricesarekept constant at their base value, we denote them with the superscript b to emphasize the fact that they are treated as parameter and not as endogenous objects: GDP = pbF((cid:96),x)−pb.x ( 3 ) y x 21 ThePennWorldTablesusedinourempiricalsectionusesbaseperiodprices. TheBureauofEconomicAnalysis usesaFisherchain-weightedpriceindextoconstructGDPattimetrelativetoGDPattimet−1accordingto: GDPt = (cid:32) ∑ k pk t−1 qk t (cid:33)0.5(cid:32) ∑ k pk t qk t (cid:33)0.5 GDP t−1 ∑ k pk t−1 qk t−1 ∑ k pk t qk t−1 wherekindexesallcomponentsofGDP.Intuitively,theFisherindexisageometricaveragebetweentwobaseperiod pricingmethodswherethebasepriceisalternativelythepriceatt−1andatt. 9

Let us now compute the first order change in GDP when the Terms-of-Trade (≡ p ) change: x dGDP ∂(cid:96) ∂x = pbF ((cid:96),x) + (pbF ((cid:96),x)−pb) ( 4 ) dp y (cid:96) ∂p ∂p y x x x x x (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) FactorSupplyEffect Input-OutputEffect 4 The first term in equation ( ) captures the value added change due to variations in factor supply. Quantitatively, this terms depends on the degree of complementarity between foreign 22 and domestic inputs as well as on the elasticity of factor supply. The second term captures the direct impact that changes of imported input usage have on GDP. With perfect competition, profit maximization insures that p F ((cid:96),x) = p when using current prices. When base period y x x prices pb and pb are close to their current value, 23 this term vanishes. In such a model, any first y x order change in GDP following a terms of trade shock is solely driven by variations in domestic factor supply. This is the negative result presented in KR: when firms take prices as given, profit maximization insures that the marginal benefit of using an additional unit of imported input x (p F ((cid:96),x)) is equal to its marginal cost (p ). Up to a first order approximation, foreign y x x technological shocks affect real GDP only through a change in factor supply. In other words, the 24 measured productivity is not affected by foreign shocks. 4 Equation ( ) encapsulates in a simple way the reasons why standard IRBC models cannot generate a quantitatively important link between trade linkages and GDP comovement. In models with perfect competition and constant returns to scale, the change in GDP after a foreign shock is solely driven by variations in domestic factors supply. Such a change, in turn, is disciplined by (i) the elasticity of labor supply and (ii) the complementarity between domestic and 25 foreign inputs. 3.2 Markups and love of variety Consider now a variant of the economy described above with an additional production step: inputsareimportedbyacontinuumofintermediateproducerswithalinearproductionfunction m = x. Critically, we now add two new elements: ( 1 ) a price wedge for intermediate producers µ > 1 so that the price of intermediates m is given by p = µ× p , and ( 2 ) love of variety in the m x 22 TheroleofcomplementarityisdiscussedatlengthinBursteinetal.(2008)orinBoehmetal.(2015). 23 WithaFisherchain-weightedpriceindexintheconstructionGDP,baseperiodpricesarealwaysclosetocurrent prices. 24 Note that an important part of the reasoning rests upon the fact that GDP is constructed using constant base prices. Ifthepricesusedtovaluefinalgoodsandimportedinputsweretochangeduetotheshock,onewouldhave anadditionalterminequation(4). 25 If domestic and foreign inputs are strongly complement, any shock that increases foreign input usage also rises demandfordomesticinputs,whichincreasesGDP.However,asshowninJohnson(2014),complementarityinproductionfactorsaloneisnotsufficienttosolvetheTCP.Moreprecisely,Johnson(2014)showsthatcrosscountryproduction synchronizesinputusageandourpapertakesthisinsighton-boardandfurthershowsthatinputsynchronizationcan alsoleadtoGDPsynchronizationwhenoneaddsmarkupsandextensivemarginadjustments. 10

26 final good production technology in the form of a Dixit-Stiglitz aggregation of intermediates. The production function in the final good sector is:   σ M σ−1 (cid:90) σ−1 y = F((cid:96),I) with I =  m σ di ( 5 ) i 0 Thisproductionfunctiondisplayslovefofvariety: foragivenamountoftotalimports,thelarger the mass of input suppliers M, the higher the amount of final production obtainable. For each variety m , there is a producer with a linear technology using imports only: i ∀ i ∈ [0,M], m = x ( 6 ) i i All intermediate producers are completely symmetric and we denote by m their (common) production and by x their (common) import levels. The bundle I can then be simply expressed as I = Mσ/(σ−1)m and the price index dual to the definition of the bundle is P = M1/(1−σ)p , m which is also equal to F ((cid:96),I), the marginal productivity of the input bundle in final good pro- I duction. Finally, taking the derivative of GDP with respect to p while keeping prices constant x at their base period value, we obtain: (cid:18) (cid:19) dGDP ∂(cid:96) ∂m ∂M 1 ∂M = pbF ((cid:96),I) + M + m .(µ−1)pb + pb m ( 7 ) dp y (cid:96) ∂p ∂p ∂p x σ−1 m ∂p x x x x x (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) FactorSupplyEffect MarkupEffect Entry/ExitEffect 7 4 Equation ( ) is the counterpart of ( ) in a model with extensive margin adjustments and wheresomedomesticfirmsarenotpricetakers. Thesetwoelementscreatealinkbetweenforeign shocksanddomesticrealGDPvariations,overandbeyondanychangeindomesticfactorsupply. First, the existence of a price wedge µ > 1 means that the first term does not vanish. With m(cid:48)(p ) < 0, a decrease in the price of imported inputs leads to an increase in GDP. When firms x are price setters and earn a positive profit, the marginal revenue generated by an additional unit of imported input x is larger than its marginal cost p . Hence, cheaper inputs means more sales, x more profit and more value added. Moreover, any change in the mass of firms M also impacts domestic value added. One can model many reasons why the mass of producing firms would change, including a free entry 4 conditionasinthequantitativemodelinsection . Achangeinthenumberofpricesettingfirms gives a time varying element to the effect described above, triggering a greater reaction of GDP 26 In many models, the elasticity of substitution in the CES aggregation governs at the same time the markup chargedbymonopolisticcompetitorsandthedegreeofloveofvariety. Inordertoclearlydifferentiatethesheereffect ofmarkupfromtheloveofvariety,weassumeherethatthemarkupµcantakeanyvalue,includingthecasewhere µ=σ/(σ−1). 11

after a foreign shock, independently of the love of variety which is captured by the parameter σ. Overall, the key idea governing this term can be expressed as follows: firms that charge a markup have a disconnect between the marginal cost and the marginal revenue product of their inputs. Thedifferencebetweenthesetwoisaccountedasvalueaddedintheformofprofits. Any change in input usage leading to a change in profits triggers a change in value added. Second, when σ < +∞ , another effect arises. When the production function exhibits love of variety,anychangeinthemassofsuppliersimpliesanadditionalreactionfortheinputbundleI. 27 If the decrease of p is accompanied by an increase in the mass of producing firm, the bundle x I increases not only because each intermediate producer produces more, but also because an increase in the mass of firms mechanically increases I even for a fixed amount of intermediates. With love of variety, a producer that has access to more suppliers can produce more output for the same level of input. In other words, the set of feasible combinations of output I, and M (cid:82) inputs m di = X is not independent of the mass of producers M: a change of M shifts the i 0 production possibility frontier. Interestingly, this channel is at work independently of the price distortion channel discussed previously. Even in the absence of monopoly pricing, the sheer fluctuation in the mass of producing firms coupled with a love of variety creates a link between import price and GDP fluctuation. Finally, note that the introduction of markups and love of variety allows GDP to change over andbeyondchangesinthedomesticfactorsofproduction. Usingagrowthaccountingperspective, this means that the introduction of these two elements makes measured domestic productivity change after a foreign shock, even though technology is unchanged. Two countries that have important trade flows in intermediate inputs should then have correlated measured TFP (i.e. the Solow Residual), a prediction we test in the data in section 6.3 and which our quantitative model is able to reproduce. 4 A Model of International Trade with Cross-Border Input Linkages We develop a many-country international business cycle model with trade in final and interme- 2005 2007 diate goods. The model is related to Ghironi and Melitz ( ) and Alessandria and Choi ( ), extended to multiple asymmetric countries and intermediate goods crossing borders multiple times. In contrast to a standard IRBC framework, the model features monopolistic competition 28 and firms entry/exit. As we will show, the combination of international I/O linkages, price distortions and extensive margin adjustments provide a quantitative solution to the TCP. 27 Ifthemassoffirmsispinneddownbyafreeentrycondition,theincreaseinprofitsofeachintermediateproducer whenthepriceofimportedinputgoesupleadstoaincreaseinthemassoffirms. 28 Alternatively,themodelpresentedherecanbethoughtofasanextensionoftheIRBCmodelpresentedinJohnson (2014)withtwonewelements: markupsandextensivemarginadjustments. Itisalsorelatedtothestaticsmallopen economymodelinGopinathandNeiman(2014) 12

4.1 Consumption and Labor Supply Consider a multi-period world economy with many countries (i,j ∈ {1,...,N}). In each country, there is a representative consumer who consumes final goods and supplies labor L for i,t production. Consumers’ utility function is: (cid:34) +∞ (cid:32) (cid:16) (cid:17) L1+ν (cid:33)(cid:35) U = E ∑ βt log CF −ψ i,t ( 8 ) 0 0 i,t i 1+ν t=0 with C i F ,t = (cid:32) ∑ ω i F(j)ρ 1 F ·C j ρ ,i F ρ , F − t 1 (cid:33) ρF ρF −1 and C j,i,t =   (cid:82) c j,i,t (s) σj σ − j 1 ds   σi σ − i 1 ( 9 ) j s∈ΩF j,i,t where ψ is a scaling parameter, ν the inverse of the Frisch elasticity of labor supply and σ i i the elasticity of substitution between different varieties of final goods originating from country i. ωF(j) is the share of country j in the consumption bundle of country i, with ∑ωF(j) = 1, and i i j ΩF is the endogenous set of firms from country j that serve the final good market in country j,i,t i. 29 Finally, ρF is the final goods Armington elasticity of substitution. Final good price indices are defined as: P i F ,t = (cid:32) ∑ ω i F(j)· (cid:16) P(cid:101) j F ,i,t (cid:17)ρF ρF −1 (cid:33) ρF ρF −1 and P(cid:101) j F ,i,t =    (cid:90) pF j,i,t (s) σi σ − i 1 ds    σi σ − i 1 ( 10 ) j s∈ΩF j,i,t where pF (s) is the price charged by firm s in the set ΩF when selling in the final good market j,i,t j,i,t in country i. As we will see below, given our assumptions, firms charge the same price in both final and intermediate good markets in a given country. 30 The agent chooses consumption, investment and labor, subject to the budget constraint: PF (C +K −(1−δ)K ) = w L +r K −T ( 11 ) i,t i,t i,t+1 i,t i,t i,t i,t i,t i where we introduced the term T which captures potential trade imbalance in country i (T < i i 0, corresponds to a trade deficit meaning that country i consumes more than the value of its 29 Aswewillseebelow, givenourassumptions, thesetoffirmsservingthefinalgoodandtheintermediateinput marketinanycountrywillbeidentical. 30 Note that the right hand side of this equation include firms’ profits since, as explained below, firms pay entry costsusingdomesticlabor. ItshouldthenbeunderstoodthatL includesbothproductionand“entrycost”workers. i,t Moreover,animplicitassumptionofthebudgetconstraintaboveisthatinvestmentinthecapitalstockisdoneusing theaggregatedconsumptiongood. 13

production). Optimality yields the standard Euler equation and labor supply: (cid:34) (cid:32) (cid:33)(cid:35) 1 1 r = β E × i,t+1 +(1−δ) ( 12 ) C t C PF i,t i,t+1 i,t w 1 ψ Lν = i,t ( 13 ) i i,t PF C i,t i,t 4.2 Production In any country i, production is performed by a continuum of firms with heterogeneous productivity, defined as the product of an idiosyncratic component ϕ and a country specific component Z . In all countries, productivity ϕ follows a Pareto distribution with shape parameter γ. Firms i,t produce with a Cobb-Douglas technology using labor (cid:96) (ϕ), capital k (ϕ) and intermediate i,t i,t inputs I (ϕ) bought from other firms from their home country as well as from abroad. The i,t intermediate input index in country i, I , is a CES aggregation of country specific bundles M , i,t j,i,t with an intermediate goods Armington elasticity ρI. To introduce a rationale for markups and for love of variety, each country specific bundle is itself a CES aggregation of many varieties, with 31 the elasticity of substitution σ. The production function is: j Q i,t (ϕ) = Z i,t .ϕ . I i,t (ϕ)1−ηi −χi . (cid:96) i,t (ϕ)χi . k i,t (ϕ)ηi ( 14 ) with I i,t (ϕ) = (cid:32) ∑ ω i (j)ρ 1 I M j ρ ,i I ρ , − I t 1 (cid:33) ρI ρ − I 1 and M j,i,t =    (cid:90) m j,i,t (s) σi σ − i 1 ds    σi σ − i 1 ( 15 ) i s∈Ω j,i,t where ωI(j) is the share of country j in the production process of country i, with ∑ωI(j) = 1, i i j and ΩI is the endogenous set of firms based in j and serving the intermediate input market in j,i,t country i. Similarly to the final good market, we have P i I ,t = (cid:32) ∑ ω i I(j)· (cid:16) P(cid:101) j I ,i,t (cid:17)ρI ρ − I 1 (cid:33) ρI ρ − I 1 and P(cid:101) j I ,i,t =    (cid:90) p j I ,i,t (s) σi σ − i 1 ds    σi σ − i 1 ( 16 ) j s∈ΩI j,i,t and P i IB = χ i −χi ×η i −ηi ×(1−η i −χ i )(ηi +χi −1)× (cid:16) P i I ,t (cid:17)1−ηi −χi ×w i χ ,t i ×r i η , i t ( 17 ) where P denotes the price of the country-pair specific bundle M and PIB is the unit cost of j,i,t j,i,t i,t the Cobb Douglas bundle aggregating I , k and (cid:96) (called the input bundle) and represents the i,t i,t i,t price of the basic production factor in country i. pI (s) is the price charged by any firm s in the j,i,t 31 Thisparametergovernsboththemarkupchargebyfirmfromcountry jandthedegreeofloveofvariety. 14

set ΩI when selling in the intermediate input market in country i. 32 j,i,t To be allowed to sell its variety to a country j, a firm from country i must pay a fixed cost fc ij (labeled in unit of the input bundle) as well as a variable (iceberg) cost τ . Firms choose which ij countries they enter (if any), affecting both the level of competition and the marginal cost of all firms in the country. As will be clear below, profits are strictly increasing with productivity ϕ so that equilibrium export decisions are defined by country-pair specific thresholds ϕ above i,j,t whichfirmsfromi finditprofitabletopaythefixedcost fc andservethefinalgoodandintermediij ateinputsmarketsincountry j. Finallythereisanoverheadentrycost fE, sunkattheproduction i stage, to be paid before firms know their actual productivity. Based on their expected profit in all markets, firms enter the economy until the expected value of doing so equals the overhead entry cost. This process determines the mass of firms M . i,t 4.3 Equilibrium Wespecifytheequilibriumconditionsofthemodelbyintroducing X theaggregateconsumers’ i,t revenue and S the total firms’ spendings (including bilateral fixed costs payments to access all i,t markets)incountryi. Givenprices,totaldemandfacedbyfirm ϕ isgivenbythesumofdemand stemming from both the final good and the intermediate input markets: (cid:32) pF (ϕ) (cid:33)−σi (cid:32) P(cid:101)F (cid:33)−ρF ωF(i)X ∑ i,j,t i,j,t j j,t q (ϕ) = i,t P(cid:101)F PF PF j i,j,t j,t j,t 18 ( ) (cid:32) pI (ϕ) (cid:33)−σi (cid:32) P(cid:101)I (cid:33)−ρI ωI(i)(1−η −χ )S ∑ i,j,t i,j,t j j j j,t + P(cid:101)I PI PI j i,j,t j,t j,t where the summation is done over all markets that are served by a firm with productivity ϕ. Firms choose their price to maximize profits. Since the price elasticity of demand is constant, they charge a constant markup over marginal cost. For a firm from country i, the only elasticity that is relevant for pricing is σ, capturing the fact that firms compete primarily with other i firms coming from their home country since their individual pricing decision has no impact 33 onthecountry-specificpriceindexineverymarket. Asaresult, firmschargethesamemarkup in the final and intermediate good markets, and we have: pF (ϕ) = pI (ϕ) = p (ϕ) and i,j,t i,j,t i,j,t P(cid:101)F = P(cid:101)I = P(cid:101) . The marginal cost of a firm with productivity ϕ in country i is PIB/(Z ϕ) i,j,t i,j,t i,j,t i,t i,t 32 TheexactexpressionsoftheseobjectsarestandardandcanbefoundinthesupplementaryappendixB. 33 With a finite number of firms, elasticities σ, ρI and ρF would all appear in the pricing strategy. In such a case, i every firm would take into account the fact that its own price has an impact on the unit cost of the corresponding country-specificbundle. Therefore,whendecreasingitsprice,afirmwouldattractmoredemandcomparedtofirms fromitsowncountrybutalsoincreasetheshareoftotaldemandthatgoestoeveryotherfirmsfromitscountry. 15

and its optimal price in country j is: σ PIB p (ϕ) = τ i i,t ( 19 ) i,j,t ij σ −1Z ϕ i i,t 1980 2003 2005 Unlike in the canonical Krugman ( ), Melitz ( ) or Ghironi and Melitz ( ) models, one needs to jointly solve for all prices in the economy. Through PIB, the price charged by firm ϕ i,t in country i depends on the prices charged by all firms supplying country i (both domestic and foreign) which in turn depend on the prices charged by their suppliers and so on and so forth. Determining prices requires solving jointly for all country-pair specific price indexes P(cid:101) . i,j,t The definitions of price indexes give rise to a simple relationship between the price of the country i specific bundle at home, P(cid:101) , and its counterpart in country j, P(cid:101) : i,i,t j,i,t (cid:32) (cid:33)σi−γi−1 ϕ 1−σi P(cid:101) = τ i,j,t ×P(cid:101) ( 20 ) j,i,t ij i,i,t ϕ i,i,t where ϕ defines the threshold of idiosyncratic productivity ϕ above which firms from i serve i,j,t country j. Intuitively, the ratio between the price of a country specific bundle in two different markets depends on the relative iceberg costs as well as the relative entry thresholds. Using this relation in the definition of price indexes in every country yields a system of N equations which jointly defines all inner price indexes:   (cid:32) (cid:33) σj−γj−1 1−ρI1−ηi −χi (P(cid:101) )1−ρI = µ   ∑ ωI(j)τ ϕ j,i,t 1−σj P(cid:101)    ( 21 ) i,i,t i  i  ji ϕ j,j,t  j j,j,t 34 withµ dependingonentrythresholds,themassoffirmsandparameters. Forgiventhresholds i 35 and mass of firms, this system admits a unique non-negative solution. Turning to export strategies, the productivity thresholds above which firms from country i serve market j are implicitly defined by: PIB π (ϕ ) = i,t .fc for all i,j ∈ {1,...,N} ( 22 ) i,j,t i,j,t Z ij i,t where π (ϕ) is the variable profit earned by a firm with productivity ϕ in market j. Similar i,j,t to Ghironi and Melitz ( 2005 ), the fixed cost fc is paid in units of the basic production factor in ij 34 µ1 1 − − ρ σ I i = γϕ i σ , i i, − t γi−1 M (cid:18) σi w i χ ,t i×r i η , i t 1 (cid:19)1−σi i γi −(σi −1) i,t σi −1χ i χi×η i ηi×(1−ηi −χi )1−ηi−χi Zi,t 35 FollowingKennan(2001)anddenotingG k =(P(cid:101)i,i,t )1−ρI andGtheassociatedN×1vector,itsufficestoshowthat the system is of the form G = f(G) with f : RN → RN a vector function which is strictly concave with respect to eachargument,whichisobviousaslongas0<η +χ <1. k k 16

36 country i deflated by aggregate technology Z. Finally, the mass of firms is determined by the free entry condition defined as: w Π = M i,t .fE for all i ( 23 ) i,t i,t Z i i,t where fE is labeled in units of labor and Π denotes aggregate profits of all firms in country i i,t i. Following Eaton and Kortum ( 2005 ), we can show that Π is proportional to total revenues. i,t Defining R the total sales of all firms from country i, we have: i,t Lemma 1. : Total profits in country i are proportional to total revenues: σ −1 Π = i R ( 24 ) i,t i,t γ σ i i Proof: see Appendix B. Closing the model involves standard market clearing conditions for capital, labor and goods. Labor can be used either for production (L p ) or for the entry cost (Le ) so that L = L p +Le . i,t i,t i,t i,t i,t WithCobb-Douglasproduction,consumer’srevenues X areequaltothesumofthepaymentto i,t productionworkers χ S , rentfromcapital η S , totalfirms’profits Π (which, atthefree entry i i,t i i,t i,t equilibrium, is completely used to pay the entry cost fE), and potential trade imbalances −T . i i,t Total revenues of all firms from i are: (cid:32) (cid:33)1−ρF (cid:32) (cid:33)1−ρI R = ∑ P(cid:101) i,j,t ωF(i)X + P(cid:101) i,j,t ωI(i)(1−η −χ )S ( 25 ) i,t PF j j,t PI j j j j,t j j j And total exports (the sum of final goods and intermediate inputs exports) from i to j is defined as (cid:32) (cid:33)1−ρF (cid:32) (cid:33)1−ρI P(cid:101) P(cid:101) T = i,j,t ωF(i)X + i,j,t ωI(i)(1−η −χ )S i→j PF j j,t PI j j j j j,t j,t Using X = w L +r K −T = (η +χ )S +Π −T , the good market clearing condii,t i,t i,t i,t i,t i,t i i i,t i,t i,t tion writes: (cid:32) (cid:33)1−ρF (cid:32) (cid:33)1−ρI R = ∑ P(cid:101) i,j,t ωF(i) (cid:104) (η +χ )S +Π −T (cid:105) + P(cid:101) i,j,t ωI(i)(1−η −χ )S ( 26 ) i,t PF j j j j j j PI j j j j j j,t j 36 Inevery market, entryoccurs untiltheprofit oftheleast productivefirms isequalto thefixedcost ofaccessing themarket. DenotingbyX totalfinalgoodspendingbyconsumers(X =w L +r K −T ),wehaveforanyi i,t i,t i,t i,t i,t i,t i,t   1 and j: ϕ i,j,t = (cid:18) τ ijσi σ − i 1 P Z i i I , , t B t P(cid:101) 1 i,j,t (cid:19) × (cid:16) P(cid:101)i,j,t/P j I ,t (cid:17)1−ρI ω j I(i)(1− σi η f i c j j − (P χ i I j ,t B )S / j Z + i, (cid:16) t ) P i,j,t/P j F ,t (cid:17)1−ρF ω j F(i)Xj,t  σi−1 . 17

Furthermore, using lemma 1 above and the fact that R = S +Π , we get: i,t i,t i,t (cid:18) (cid:19) σγ −σ +1 S = i i i R i,t i,t σγ i i Replacing Π and S as a function of R , equation ( 26 ) can be written as: i,t i,t i,t (cid:32) (cid:33)1−ρF (cid:34) (cid:35) R = ∑ P(cid:101) i,j,t ωF(i) (η j +χ j )·(σ j γ j −σ j +1)+σ j −1 R −T i,t PF j σγ j,t j,t j j,t j j 27 ( ) + ∑ (cid:32) P(cid:101) i,j,t (cid:33)1−ρI ωI(i)(1−η −χ ) (cid:18) σ j γ j −σ j +1 (cid:19) R PI j j j σγ j,t j j,t j j Which can be expressed in compact form as:     R T 1 1 M·   . . .   = − (cid:16) (WF)(cid:48)◦PF (cid:17)  . . .   ( 28 )     R T N N Where ◦ is the element-wise (Hadamard) product and WF is the weighting matrix associated with final good aggregation and is defined as WF = ωF(j). PF is a matrix defined by PF = ij i i,j,t (cid:18) (cid:19)1−ρF P(cid:101)i,j,t . Moreover, the matrix M is defined at any time t as: PF i,t (cid:32) (cid:33)1−ρF P(cid:101) (η +χ )(σγ −σ +1)+σ −1 M =I − i,j,t ωF(i) j j j j j j i,j,t i,j PF j σγ j,t j j 29 ( ) (cid:32) P(cid:101) (cid:33)1−ρI (cid:18) σγ −σ +1 (cid:19) − i,j,t ωI(i)(1−η −χ ) j j j PI j j j σγ j,t j j Setting w = 1, implying S = L p /χ , provides a unique solution for all variables by solving 1 1 1 1 12 13 21 togethertheinvestmentEulerequation( ),thelaborsupplyequation( ),thepricesystem( ), 22 28 23 the threshold system ( ), the Revenue system ( ) and the Free Entry system ( ). GDP definition. In the data, GDP is constructed using base prices and quantity estimates. In order to be as close as possible to the method used in the construction of the data used in the 37 empirical analysis, we define GDP using steady state prices as base prices. GDP is obtained by deflating nominal spending using steady-state price indices that are corrected from product 37 Inthedata,GDPisdefinedusingtheFisheridealquantityindexwhichisageometricmeanoftheLaspeyresand Paascheindices. Hence,forallperiodst,thebaseperiodpriceisageometricmeanbetweenperiodtandperiodt+1. 18

variety effects, such that: GDP = P (cid:91) F,ss X i,t + ∑ P(cid:100)ss T i→j,t − ∑ P(cid:100)ss T j→i,t ( 30 ) i,t i P(cid:99)F i,j P(cid:100) j,i P(cid:100) j i,j,t j j,i,t i,t (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) Consumption+Investment Totalexports(final+inputs) Totalimports(final+inputs) where we defined P(cid:100) i,j,t = (cid:16) M i,t .(ϕ i,j,t )−γi (cid:17)1/(σi −1) P(cid:101) i,j,t and P(cid:99) i F ,t = (cid:32) ∑ ω i F(j)· (cid:16) P(cid:100) j,i,t (cid:17)ρF ρF −1 (cid:33) ρF ρF −1 in j 38 order to be consistent with the way actual data are collected. 5 Calibration The model is calibrated to 14 countries and a composite Rest-Of-the-World for the time period 1980 1990 78 - . As compared to our empirical sample, it represents around % of total trade flows, 79 % of total trade in final goods and 77 % of total trade flows in intermediate goods. 39 With N countries,thereare4×N2+4N+5parameterstodetermine,towhichonemustaddparameters 40 relative to the technological shocks. 5.1 Parameterization We set β = 0.99 and we choose ν = 1, leading to a Frisch elasticity of 1. We set the value of the macro (Armington) elasticity ρI and ρF to be equal to unity, which is in the range of the 2004 024 35 literature. For instance, Saito ( ) provides estimations from . to . for the Armington elasticity. 41 There is also a theoretical convenience to use ρI = ρF = 1, as it allows the model to takethesameformasothernetworkmodelssuchasAcemogluetal.( 2012 ). Wesetparametersψ i in each country to replicate the relativedifference of working age population with a normalization 13 42 ensuring an average capital-output ratio of in the model. Markups and Value Added Shares. Concerning the micro elasticities, we set a value of σ = i 38 Sincebothconsumers’utilityandproductionfunctionshaveaCEScomponent,itiswellknownthattheassociated price indexes can be decomposed into components reflecting average prices (captured by statistical agencies) and productvariety(whichisnottakenintoaccountinnationalstatistics). SeeFeenstraandMarkusen(1994)orGhironi andMelitz(2005)foradiscussionofthis. 39 The set of countries is: Australia, Austria, Canada, Denmark, France, Germany, Ireland, Italy, Japan, Mexico, Netherlands,RoW,Spain,UnitedKingdomandUnitedStates. 40 For each country-pair (i,j), we specify values for ωF(j),ωI(j) (each with N×(N−1) values), τ and fc. For i i ij ij everycountryiwehave(η +χ),ψ, fE,T ,σ andγ. Thesetofcommonparametersisgivenbyχ/(χ +η),ν,β,ρI i i i i i i i i i i andρF. Ontopofthese,wealsoneedtosetthevolatility,covarianceandauto-correlationofthetechnologyshocksin allcountries. 41 Feenstraetal.(2014)studiesthemacroandmicroelasticitiesforfinalgoodsandreportsestimatesbetween-0.29 and4.08fortheArmingtonelasticity. Theyfindthatforhalfofgoodsthemacroelasticityissignificantlylowerthan themicroelasticity,evenwhentheyareestimatedatthesamelevelofdisaggregation. 42 ThisnormalizationhasnoinfluenceontheresultsbecauseFOCsareindependentfromthisparameter. 19

σ = 5, ∀iinthebaselinesimulation. AndersonandvanWincoop( 2004 )reportavailableestimates 3 10 2003 forthemicroelasticityintherangeof to . FollowingBernardetal.( ),GhironiandMelitz 2005 38 2016 ( )chooseamicroelasticityof . andrecently,paperssuchasBarrotandSauvagnat( )or 2015 Boehmetal.( )arguethatfirms’abilitytosubstitutebetweentheirsupplierscanbeverylow. This choice leads to markups of 25%. The aggregate profit rate, however, is only of 17.4% since 7 firms have to pay fixed cost in order to access any market. In Section , we consider alternative 43 elasticities for σ, and defer discussion of those cases till then. We set the Pareto Shape of the i firm-specific productivity distribution to γ = σ −0.4, as in Fattal Jaef and Lopez ( 2014 ). i i Thevalueaddedshare,η +χ ,foragivencountryi,arecalibratedusingcostofintermediates i i and total sales as observed in the WIOD database at the 2 -digits sector level. Specifically, (1− η −χ ) = cost_intermediatess, represents the share of intermediate inputs in total costs in a given i,s i,s total_saless sector. We use the fact that total sales = µ ×total cost with µ the markups in country i. s i s i Therefore, we fix (η +χ ) = 1− cost_intermediatess σi . With σ = 5, the implied mean values of i,s i,s total_saless σi −1 i η +χ ,weightedbythesectorimportanceintotalsales,rangefrom 0 . 31 to 0 . 45 fortheconsidered i i countries(wesetthevalueforRoW tothemeanvalue),whichseemstobeconsistentwithvalues 2015 reported in Halpern et al. ( ). Finally, the capital and labor shares in value added are fixed at 2/3 and 1/3 respectively. Entry costs. The sunk entry cost fE in each country are computed from the Doing Business i 44 Indicators. We measure the relative entry fixed costs by using the information on the amount of time required to set up a business in the country relative to the US, where we normalize fE in US ordertogeneratearatiooftotalnumberoffirmsdividedbytheworkingpopulation, M,ofabout L 12 22 24 %. Thisismotivatedbythefactthatthereareabout - millionsofnon-employerbusinesses 55 and . millions of employer businesses in the US, while the working age population represents 180 45 around millions of individuals during the considered period. As shown later, the results are not sensitive to this specification. Trade frictions. The variable (iceberg) trade costs for each country-pairs, τ > τ , are ij ii taken from the ESCAP World Bank: International Trade Costs Database, where we normalize τ = ii 43 Weforinstancerecalibratethemodelwithheterogeneouselasticitiesofsubstitutionacrossvarieties,σ,basedon i twomeasures: theDeLoeckerandEeckhout(2018)markupestimatesandaPriceCostMarginapproach. Asshown insection7,theintroductionofheterogenousmarkupsmakesitpossibletostudytheroleofmarketpowerinshaping thecorrelationbetweentermsoftradeandGDP,inlinewithempiricalevidence. 44 The World Bank’s Doing Business Initiative collected data on regulations regarding obtaining licenses, registering property, hiring workers, getting credit, and more. See http://doingbusiness.org/data/exploretopics/ trading-across-borders and http://doingbusiness.org/data/exploretopics/starting-a-business. Unfortunately,duetodatalimitations,weuseobservationavailablein2015. However,asshownlater, fE playsalittlerolein i thecorrelationbetweentradeandGDPcomovement. 45 This is also close to the 12% self-employment rate usually reported for the US between 1990 and 2000 (BLS). Results are not sensitive to this assumption. We provide a comparison of this rate and the self-employment rate in eacheconomyinthesupplementaryappendixC. 20

46 1. This database features symmetric bilateral trade costs in its wider sense, including not only international transport costs and tariffs but also other trade cost components discussed in 2004 2008 Anderson and van Wincoop ( ). Similar to Helpman et al. ( ), we assume domestic fixed costs fc = 1 for every country i. We set the values for the fixed costs of exporting from country ii i to country j, fc > 1 for i (cid:54)= j, in line with Di Giovanni and Levchenko ( 2013 ) using the Trading ij Across Borders module of the Doing Business Indicators. Specifically, we choose the number of days it takes to export to a specific country relative to the number of days it takes to supply in 1 47 the home country (normalized to in the model). Steady-State Trade Flows and Imbalance. Data relative to bilateral flows in final goods and intermediate inputs, {TI /GDP,TF /GDP}, are sufficient to identify the shares ωI(j) j→i i j→i i i and ωF(j). Similar to our empirical part, we use trade data from Johnson and Noguera ( 2017 ) i dis-aggregated into final and intermediate goods. Moreover, since complete financial autarky is inconsistentwiththetradebalancesobservedinthedata,wecalibratethemodeltradeimbalance {T ,...,T } to match steady-state trade imbalances relative to GDP, and then hold those nominal 1 N imbalances constant during the simulation. Finally, to be as close as possible to the data used in the empirical analysis, we construct estimates by deflating the nominal spending by the price index that do not take into account love of variety, as described in section 4.3. By taking all of this information, the model steady state matches relative bilateral trade flows and relative trade imbalances exactly. Aggregate Technology Process. The level of GDP comovement in our simulations is driven both by correlated technology shocks and by the transmission of those shocks across countries via trade linkages. In the model, Z is the country-specific technology process which is not i,t 63 properly measured in the data by the Solow Residual (see section . for a discussion on this). We take a different route and set the cyclical properties of (Z) to replicate observed GDP i i=1,...,N properties. To calibrate the variance-covariance matrix and the persistence of those technology shocks, we set the off diagonal elements (the covariance terms) so that the average correlation of GDP in the model matches exactly the one observed in the data, which is 0.27 for the selected 1980 1999 countries in - . We then calibrate the volatility (the diagonal elements of the covariance matrix) so that the model replicates exactly the observed GDP volatility (de-trended using HPfilter) in every country. This allows us to generate GDP fluctuations in the simulated economy 48 that are similar to those observed in the data. It is informative to note that, in order to match an observed international GDP correlation of 0.27, the correlation of technology shocks is only 46 Seeathttp://artnet.unescap.org/. 47 ThisapproachmeansthatthefixedcostassociatedwithtradefromFrancetotheUSisthesameastheonefrom GermanytotheUS.Onemustkeepinmind,however,thattheicebergvariablecostwilldiffer. 48 Recallthatthegoalofthisexerciseisnottoexplainthelevelofcomovementacrosscountries,butitsslopefollowing achangeintradeintensities. 21

0.189, with cross-country propagation through trade making up for the gap between technology 49 and GDP correlations. In this sense, through the lens of our model, propagation through trade explains about a third of international comovement. Finally, we set a common value for auto-correlation of shocks so that the GDP series generated bythemodelisexactly0.8,whichistheaverageGDPauto-correlationinthedata. Onelastdetail regarding the simulation is that we parameterize the variance of the shocks to the Rest-of-the- World based on median GDP value in the data and the RoW covariance terms are set to 0 . Table 3 reports the list of parameters. All targeted moments are perfectly matched. Table.3. Parametersofthemodel. Parameter Symbol Value Moment/Source A.Fixedparameters Discountfactor β .99 Annualdiscountrateof4% Laborcurvature ν 1.0 Frischelasticityof1.0 LaborSupplyScaling ψ [5.4e−5,0.16] Relativeworkingagepopulation i Laborshare χ /(χ +η) 2/3 67%ofdomesticvalueadded i i i Argmintonelasticities ρI,ρF 1.0 Saito(2004),Feenstraetal.(2014) Microelasticityofsubstitution σ,∀i 5.0 Markupof25%,profitrateof17.4% i Sunkentrycost fE/fE [0.4-3.9] DoingBusinessDatabase-WorldBank i US Fixedtradecost fc [3.3-18] DoingBusinessDatabase-WorldBank ij Icebergtradecost τ [1-2.8] ESCAP-WorldBank ij Paretoshape γ σ −0.4 FattalJaefandLopez(2014) i i Parameter Symbol Value Maintarget A.Steadystates Inputsspendingweights ωI(j) insup. app. Importsharesininputs i Finalgoodsspendingweights ωF(j) insup. app. Importsharesinfinalgoods i Tradeimbalance {T,...,T } insup. app. TradeimbalanceoverGDP i N B.Simulation: Technologyprocess PersistencyofTechno. shocks ρ .77 Avg. GDPauto-correlation Z Std. ofTechno. shocks σ (i) [.0012,.0050] GDPvolatility(de-trended) Z CovarianceofTechno. shocks σ (i,j),∀i (cid:54)= j .189 Avg. GDPcorrelationof0.27 Z 6 Results 2 Followingourempiricalfindingsinsection ,weexaminethemodel’sabilitytomatchtheaggregateTCslope. Theanalysisfocusonthreequestions: (i). IsthemodelabletogenerateaTCslope of the same magnitude as in the data? (ii). What are the role of price distorsions and extensive margin in generating this TC slope? (iii). What is the quantitative importance of trade and TFP correlation in generating the observed level of GDP co-movement? 49 Indeed, when we calibrate the model with zero trade flows for all country pairs, then GDP correlation is very closetothecorrelationoftechnologyshocks,asshownintable5. Thisisnotsurprisingsinceinsuchacase,theworld isessentiallyacollectionofislandthatdonotinteractwithoneanother. 22

6.1 Baseline Experiment To assess the model ability to replicate the correlation between trade and GDP-comovement, we 5000 simulate a sequence of , shocks (identical across each configuration) and record the correlation of logged and HP-filtered GDP as well as the average index of logged trade proximity in intermediate inputs and final goods. As the objective is to use within country-pair variations, we then recalibrate the spending shares ωI(j) and ωI(j) for all country-pairs i and j with differi i ent targets for trade proximity across countries, decreasing and increasing the targeted imports 10 in intermediate inputs relative to GDP by % and then decreasing and increasing the targeted 10 5 imports in final goods relative to GDP by % (this amounts to experiments, including the baseline simulation). 50 This gives rise to a panel dataset of 14×13/2 = 91 country-pairs (excluding RoW) for each of the 5 configurations, hence a total of 455 observations. 51 . We then use this simulated dataset to estimate the model-implied TC slope, controlling for country-pair fixed 4 effects, as we did in the empirical analysis. Table shows the results. Table.4. TradeComovementSlope: DataversusModel Dependentvariable: CorrGDPHP Data Model Tradeindexmeasure (1) (2) (3) (4) Measure Variable Bench. ρF =1 ρF =1.05 (cid:16) Ti↔j (cid:17) ln(Trade Input ) 0.054** 0.053** 0.051*** 0.065*** GDPi +GDPj ln(Trade Final ) 0.003 −0.030 0.017*** 0.007*** max (cid:16) Ti↔j , Ti↔j (cid:17) ln(Trade Input ) 0.050*** 0.052** 0.052*** 0.065*** GDPi GDPj ln(Trade Final ) 0.004 −0.032 0.016*** 0.005** CountryFE Yes Yes Yes Yes TimewindowsFE No Yes - - Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. 70 The benchmark model generates a realistic trade comovement slope of about . %, comparable to the range of values [4.8%−11%] reported in the literature for different set of countries, time periods and specifications. Turning to the relative importance of intermediate inputs rela- 3 tive to final goods, we find that trade in inputs has times the explanatory power of that of final 70 goods and account for % of the total trade comovement slope. Our simulated slope with trade in intermediate inputs is close to one estimated from the data, and this hold for the two measures of trade proximity usually considered in the literature. In the data, the trade comovement slope associated with trade in final goods is found small and insignificant, a feature that can be obtained in our model by using a higher final goods Armington elasticity of ρF = 1.05, as shown 4 4 in table , column ( ). 50 The model results are not very sensitive to the percent increase of trade flows between experiment, suggesting thattheimpactoftradeonGDP-comovementisfairlylinearinthemodel. 51 Each configuration can be thought as a different time-window, except that we do not need to add controls for eachconfigurationinthemodel,asweonlychangetradeintensitiesbetweenexperiments. 23

6.2 Decomposition - Role of the ingredients To assess the role of each ingredient in the quantitative results, we then turn off one by one the key elements of the model, namely movements in the number of firms supplying each market 5 and price distorsions. Results are gathered in table . Table.5. Decompositionoftherolesofpricedistorsionsandtheextensivemargin. Model Benchmark ρF =1 Highelasticity ρF =1.05 TC-Slope a GDPcorrb TC-Slope a GDPcorrb Input Final Input Final Data(withCP&TWFE) 0.053** -0.030 0.270 0.053** -0.030 0.270 I/Olinkages+Markups+EM 0.051*** 0.017*** 0.270 0.065*** 0.007*** 0.258 I/Olinkages+Markups 0.024*** 0.005*** 0.229 0.026*** 0.002*** 0.225 I/Olinkages 0.007*** 0.005*** 0.212 0.007*** 0.004*** 0.210 ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Inparenthesis: std. deviation. aThetradeindexesusedinthoseexperimentsare(T i→j +T j→i )/(GDP i +GDP j ). bAverageloggedandHPfilteredGDPcorrelationfortheselectedsample. ThesoleadditionofpricedistortionstoanotherwisestandardIRBCmodelwithI/Olinkages 0007 0024 increasesthetradecomovementslopeforinputsfrom . to . ,whiletheamplificationcom- 005152 ing through the fluctuation in the mass of firms increases the slope further to . . Turning to the implied GDP correlation, adding price distortions and adjustments along the extensive mar- 58 gins imply an overall non negligeable increase in the average GDP correlation by . percentage points relative to the model featuring only I/O linkages. Notice that those findings are robust to a higher Armington elasticity of ρF = 1.05. Overall, the key insight emerging from this analysis is that adding GVC to an otherwise standard IRBC model is not sufficient to solve the TCP, 2014 as shown in Johnson ( ). However, a model combining GVC with markups and extensive adjustments can provide the first quantitative solution to the TCP. 6.3 Solow Residual and Technology 3 In section , we showed how the introduction of two elements, extensive margin adjustments and market power, creates a link between foreign shocks and domestic productivity (usually measured as the the Solow Residual), even with fixed technology. More precisely, our model predicts that an increase in trade flows in input synchronizes Solow residual (SR) fluctuations (cid:16) (cid:17) (cid:16) (cid:17) across countries. Defining SR as: SR = log(GDP )− ηi log(K )− χi log(L ) we it it ηi +χi it ηi +χi it 6 present in table the relationship between SR and trade intensity in inputs and final goods as 52 ThisisincontrastwithempiricalfindingsinGopinathandNeiman(2014),whoarguethattheextensivemargin plays a small role in explaining the Argentine trade collapse. We provide new evidence of the role of extensive margininsection7,whereourempiricalanalysisembedsanumberofdifferentcountriesandassessadjustmentsof theextensivemarginoveramuchlongertimehorizon(10yearsinourempiricalspecification)aswellaswithineach timewindows. 24

estimated from the data and in our simulations. Both in the data and in our baseline calibration, an increase of trade in inputs is associated with an increase in SR comovement by a factor of 6 relativetotradeinfinalgoods. Quantitatively,ourmodelisabletoreproducearealistictrade-SR slope. As expected, this association is absent in a model without markups and extensive margin adjustments and is decreasing in σ. Table.6. Model: trade-TFPcomovementslope a ExactTechno. (Z) SolowResidual(SR)c Trade-SRslopec corrb ACF corrb ACF σSR Inter. inputs final σZ Data(withTW+CPFE) - - 0.228 0.639 - 0.055** -0.044* Baseline(σ =5.0) 0.189 0.77 0.246 0.736 2.709 0.037*** 0.007*** I/Olinkages+Markups 0.189 0.77 0.213 0.775 1.906 0.016*** -0.002*** I/Olinkagesonly 0.189 0.77 0.196 0.774 2.008 -0.001*** -0.001*** Highmarkup(σ =4.0) 0.189 0.77 0.282 0.726 3.765 0.063*** 0.013*** Lowmarkup(σ =6.0) 0.189 0.77 0.230 0.743 2.552 0.025*** 0.004*** Highelasticity(ρF =1.05) 0.189 0.77 0.237 0.737 2.716 0.044*** 0.000 aSimulationsarebasedontheexactsamesequenceofshocksZ. bcorrcorrespondtotheaveragecross-countrycorrelation. cDataonSRareconstructedusingPennWorldTablesasSR =log(rgdpo)−αlog(rnna)−(1−α)log(emp∗ ij hc), with emp, hc and rnna variables corresponding to employment, human capital and capital stock and α=1/3. CorrelationandACFarecomputedusingthesamesampleofcountriesasinthemodelfrom1970 to1999. ResultsoftheTrade-SRslopearerobustusingfirstdifferenceandwhenaddingtradedummiesas showninappendixA.4. Using our simulations, we can also compare the cyclical properties of Z and SR. When measuring productivity as the change in GDP that is not explained by movements of capital and labor,fluctuationsin SR donotonlycapturechangesintechnology,butalsocapturefluctuations of profits and adjustments along the extensive margin. As a result, the baseline implied average SR correlation of about 0 . 246 is much larger than the one implied by the underlying technology process (Z) ( 0 . 189 in all experiments). The difference simply reflects the endogenous synchronization of SR through trade, due to profits and extensive margin movements. SR is also much more volatile and less auto-correlated than Z, with a ratio of standard deviations larger than 3 , showing that SR is potentially a poor proxy for calibrating technology shocks. 6.4 Robustness checks and business cycle properties Our results are robust to a number of alternative specifications. Changing the value of parameters γ does not change the implied slope. In contrast, ν has a more significant impact on the i magnitude of the overall trade comovement slope, while preserving the relative importance of final goods versus intermediate inputs. We also test the model with ρ = 0.95. As expected, F in that case, trade in final goods generates more GDP comovements as compared to the benchmark. The level of trade frictions in the calibrated steady state {τ , fc, fE} do not affect the ij ij ij 25

implied TC slope. Regardless of the initial level of those trade frictions, increasing trade proximity is associated with the same reaction for GDP comovement. We also conduct robustness on the specified technology processes {Z}. We first use the observed estimated covariance matrix i of standard TFP data computed as the Solow residual in Penn World Tables (∑ (cid:101)). While this approach is sometimes used in the literature, it leads to overshooting the level of cross-country GDP correlation. Results regarding the TC slope remain similar to the benchmark calibration. In order to better assess the implications of the trade channel, we also simulate the model under the counterfactual assumption that technology shocks are uncorrelated across countries and set theoff-diagonalelementsofthecovariance-variancematrixtozero(i.e. cov(Z ,Z ) = 0,∀i (cid:54)= j). i,t j,t Under all those alternative specifications, the implied TC slope is large and significant, with a much larger association with trade in intermediate inputs. We provide all the detailed results in 7 table . 8 Finally, we report business cycle properties in table . By comparing the first three columns, wefindthataddingextensivemarginandpricedistortionsleadstoanincreaseininvestmentand consumption volatility relative to GDP, while keeping other properties unchanged. Interestingly, our baseline calibration features a higher cross-country correlation of GDP than consumption, 1992 implying that the model is not subject to the Backus et al. ( )’s consumption correlation 53 puzzle. Another dimension worth looking at is the volatility of extensive margin adjustments as measured by the standard deviation of the (log) number of exporters. Compared to the data, 54 our model tends to be conservative as it slightly under-predicts the volatility of this margin. The last column of the table shows the Business Cycle properties when the covariance matrix of technology shocks are calibrated using the Solow Residual from Penn World Tables. Such a calibration leads to strong overshooting in terms of GDP, consumption and investment volatility as well as all cross-country correlations. 7 Model Mechanisms and Empirical Relevance Inthissection,wefurtherinvestigatetheroleoffirms’entry/exitandmarkupsinthemodeland test their empirical relevance. 7.1 The Role of Extensive Margin of Trade We first study the role of extensive margin (EM) and intensive margin (IM) fluctuations on the correlation between trade and GDP comovement. We conduct two empirical tests. First, in line 53 Thesocalled“BKKconsumptioncorrelationspuzzle”referstothefactinstandardmodels,consumptionismore correlatedacrosscountriesthanoutput,whichisatoddswiththedata. 54 Notethatintroducinglifecyclepropertiesinfirms’behavior,suchas“longtermfixedcosts”insteadofper-period fixed costs, would only widen the gap with the data as such elements tend to give more persistence to exporting decisions. 26

Table.7. Robustnesscheck a TC-slope Experiment Parameterchange GDPcorr Inter. inputs Finalgoods Baseline - 0.270 0.051*** 0.017*** A.Modelparameter Highparetoshape γ = σ −0.3 0.271 0.052*** 0.017*** i i Lowparetoshape γ = σ −0.5 0.270 0.051*** 0.017*** i i LowFrischelasticity ν =0.75 0.295 0.067*** 0.025*** HighFrischelasticity ν =1.25 0.257 0.043*** 0.013*** LowCESElasticity ρF =0.95 0.276 0.065*** 0.022*** B.Tradefrictions Icebergcosts +10% 0.270 0.051*** 0.017*** Fixedcosts +10% 0.270 0.051*** 0.017*** C.Productivityprocess EstimatedTFPshocks ∑(cid:101) 0.347 0.038*** 0.013*** Uncorrelatedtechno. shocks cov(Z ,Z ) =0,∀i (cid:54)= j 0.030 0.025*** 0.008*** i,t j,t D.Tradeimbalance Notradeimbalance T =0, ∀i 0.273 0.050*** 0.017*** i E.Referenceperiodfor{ωI,ωF} Cobb-Douglas ρF =1.0 1990-2000 0.340 0.088*** 0.034*** CESspecification ρF =1.05 1990-2000 0.316 0.119*** 0.012** aThesimulationsarebasedontheexactsamesequenceofshocks,underthefivevariationsoftrade indexesusedinthebenchmark. 2015 2005 with Liao and Santacreu ( ), we use the Hummels and Klenow ( ) (HK) decomposition and investigate the relation between the average and the volatility within each time window of the EM and IM of trade intensities between different time windows and GDP comovement. 2015 Compared to Liao and Santacreu ( ), we use a different identification strategy and a broader 55 set of countries over a longer period. Second, we use the recent Exporter Dynamics Database (EDD) from the World Bank with measures for the EM and IM that directly report the number of active exporters as well as the average trade value per exporter. This allows us to directly test if the average and the volatility of the number of exporters is associated with higher GDP 2 synchronization. As in section , we aim to handle the heterogeneity between countries that are closer each other, and who experience common macro policies using fixed effects. EM-IM HK decomposition. Building on Feenstra and Markusen ( 1994 ) and Hummels and 2005 Klenow( )(HK),weusedatafromtheNBERUnitedNationsTradeDatacoveringtheperiod 1962 2000 2001 2014 from to and the UN COMTRADE data for the period from to . We use the 55 LiaoandSantacreu(2015)useasetof30countriesovertheperiodfrom1980-Q1to2009-Q4whileweuse38countriesfrom1971to2010(wedropCzechoslovakia,Estonia,Russia,SloveniaandSlovakiaduetolackofobservations). 27

Table.8. BusinessCycleStatistics: DataandModels.a Statistics Datab,c NoMarkup/EM NoEM Baseline SRasTechno. Shocks Averagestandarddeviation(%) GDP 1.38 0.90 0.84 1.38 6.49 Nb. Exp. (annual) 2.44 - - 1.54 6.43 StandarddeviationrelativetoGDP Consumption 1.03 0.18 0.26 1.19 1.29 Investment 3.21 3.66 5.65 7.72 8.22 Nb. Exp. 1.61 - - 1.09 1.09 Internationalcontemporaneouscrosscorrelations GDP 0.27 0.21 0.23 0.27 0.35 Consumption 0.16 0.27 0.29 0.26 0.41 Investment 0.25 0.20 0.21 0.25 0.33 ContemporaneouscorrelationswithGDP GDP(-1) 0.80 0.80 0.82 0.80 0.80 Consumption 0.69 0.66 0.77 0.82 0.82 Investment 0.77 0.99 0.98 0.98 0.94 aAllstatisticsarecomputedusinglogtransformationandHP-filter. Recallthatthebaselinemodeltargets aninternationalcontemporaneouscrosscorrelationsofabout0.27andaGDPauto-correlationof0.80. bAll statistics refer to the mean values in the data from 1980Q1 - 1999Q4, except for the log number of exporterswhichiscomputedusingtheEDDfrom1997to2014. c WeusetheEDDtoestimatethestandarddeviationoftheHP-filtered(withλ=6.25)andloggedannual numberoffirmsexportingfromacountryitoacountry jbetween1997to2014. Noticethatamongthe91 country-pairsinthemodel,ourestimatesarebasedon30country-pairspresentintheEDD. 2 4 bilateral trade flows as categorized under the SITC (rev. , -digits) classification. This choice is 56 made because of the longer period covered by this classification. Using the HK decomposition, we construct the Extensive and Intensive margins of trade for each directed pair of country (i → j). 57 Since those measures are not symmetric within every country-pair we sum, for each country pair (i,j), the margins from i to j and from j to i. We then compute the average and the standard deviation of those measures within each time window and run: Corr GDP = β ln(EMHK)+β ln(IMHK)+CP +TW +(cid:101) ( 31 ) ijt 1 ijt 2 ijt ij t ijt Corr GDP = β ln(std(EMHK) )+β ln(std(IMHK) )+CP +TW +(cid:101) ( 32 ) ijt 1 ijt 2 ijt ij t ijt 1 2 Results are gathered in table 9 (columns ( ) and ( )) and show that the correlation between the extensive margin of trade and GDP comovement is positive and significant for the two specifications. This result is particularly striking given that most of the variation in trade is explained by variations along the intensive margin. 58,59 56 IntheonlineappendixA.4.5,wealsoshowthatourresultsareconsistentwithafinerHS(6-digits)classification. 57 SeeinAppendixformoredetailsontheHKdecomposition. 58 Performing a Shapley value decomposition of total trade on the intensive and extensive margins, one finds that only one fourth of the total variance is explained by the variation of the extensive margin. Those results are in line withthesimilaranalysisinLiaoandSantacreu(2015). 59 Theresultsarerobustwhenaddingdummiesforcountriesinthe2000EuroAreaorwithinthedifferentwavesof 28

EM-IM decomposition using firms data. As an additional experiment, we use the recent Exporter Dynamics Database (EDD) from the World Bank in order to test whether a change in the number of exporters (EM) and a change in the average value added per exporter (IM) within different time windows are correlated with changes in GDP comovement. This database provides measures of micro-characteristics of the export sector; number of exporters (their size and growth), their dynamics in terms of entry, exit and survival, and the average unit prices of the 70 1997 2014 products they trade, across countries from to . In order to study the correlation between the extensive and intensive margins on GDP correlations, we average the GDP (trans- 3 formed with log and HP-filter) correlations between country-pairs at quarterly frequency over 5 1997 160 time-windows of years, starting in -Q . Due to the lack of coverage of the EDD relative to our sample of countries, we use the only reported information of a reference country within a 61 country-pair as direct measure for the EM and the IM. We first estimate the role of the EM using as indicator the number of new exporters net of exiting firms between country i and country j, normalized by the total number of exporters. For the IM, we use the natural logarithm of the average value added per exporter. (cid:104)Entry - Exit(cid:105) (cid:16)(cid:104) value (cid:105) (cid:17) Corr GDP = β +β ln +CP +TW +(cid:101) ( 33 ) ijt 1 2 ij t ijt Nb Exp ijt exporter ijt 9 3 1 Table , column ( ), summarizes the results. Point estimates imply that an increase of % of the 35 number of new net exporters is associated with an increase in GDP correlation of about . %. 62 On the contrary, we find that the IM correlates negatively with GDP correlation. We then 4 investigate in column ( ) whether more variability along the extensive and intensive margins are associated with more GDP correlation within the considered time-windows. We regress: (cid:16)(cid:104) value (cid:105) (cid:17) Corr GDP = β ln(std nb exp )+β ln std +CP +TW +(cid:101) ( 34 ) ijt 1 ijt 2 exporter ijt ij t ijt Results feature a positive and significant relationship between variations in the number of exportersandGDPcorrelation,whilevariationsalongtheintensivemarginisnegativelycorrelated with GDP comovement. This again suggests a potential key role of the extensive margin in generating GDP comovement as opposed to the variation along the intensive margin. The role of the EM and IM in the model. In order to capture the respective role of EM and theEuropeanUnion(1970,1980,1990). 60 OECDGDPatquarterlyfrequencyisnotavailableforallthecountries. Wethereforereducethesample. Further detailsareprovidedintheonlineappendixA.1androbustnessesareconductedintheonlineappendixA.4. 61 Forinstance,thedatabasecontainsinformationaboutexportsfromBelgiumtomanydestinations,butthereisno informationaboutBelgium’simports. Itisthereforenotpossibletocomputesymmetricmeasures. 62 We point out that those results are robust to the period excluding the crisis (1997 - 2006) and to alternative measures, such as the number of new entrants surviving at longer horizons (one, two or three years) and using FD GDPcorrelationsasshowninasupplementaryappendixA.4. 29

IM in the model, we perform similar analysis on our simulated dataset. The extensive margin is constructed as the number of firms producing goods in a specific international submarket (i,j), while the intensive margin is computed as the average production by exporter, such as: EM = M φ −γi +M φ −γj and IM = 1 T j→i + 1 T i→j ( 35 ) ijt i ij j ji ijt 2 M φ −γj 2 M φ −γi j ji i ij wheretheindextreferstodifferentconfigurations(i.e. todifferentsteady-stateswhereonlytrade 63 5 9 proximity as been changed). We then estimate in column ( ) of table the relative correlation 32 of those measures (averaged and log transformed as in ( )) with changes in GDP comovement 6 in the five configurations described in section . Moreover, to investigate the importance of each margin’s volatility , we also compute the standard deviation of those measures as ln(std(EM) ) ijt andln(std(IM) ) ineachconfigurationandregressthosemeasuresonGDPcorrelationforeach ijt 6 9 country-pairs in column ( ) of table . Consistent with our empirical findings, both average EM and the volatility of EM fluctuations are associated with a significant increase in GDP cor- 7 8 relation. Finally, we also show in columns ( ) and ( ) the relationship between measures using the HK decomposition and SR comovement and we report the corresponding results using the 9 10 64 modelincolumns( )and( ). Consistentwithpreviousfindings,SRcomovementispositively correlated with the extensive margin in the data and in the model. Table.9. GDPandSolowResidual(SR)correlationsandthemarginsoftrade a CorrGDPHPfilter CorrSRHPfilter ijt ijt HKindexes EDDmeasures Model(base.) HKindexes Model(base.) Avg. Std. Avg. Std. Avg. Std. Avg. Std. Avg. Std. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) EMmeasure 0.046∗ 0.060∗∗∗ 3.480∗∗∗ 0.109∗ 0.070∗∗∗ 0.089∗∗∗ 0.075*** 0.014 0.045∗∗∗ 0.053∗∗∗ (0.026) (0.021) (1.285) (0.065) (0.012) (0.004) (0.028) (0.020) (0.009) (0.002) IMmeasure −0.019 −0.020∗ −0.038 −0.022 0.002 0.033∗∗∗ 0.010 −0.005 0.007 0.025∗∗∗ (0.011) (0.012) (0.163) (0.043) (0.010) (0.001) (0.020) (0.012) (0.007) (0.001) CPFE Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes TWFE Yes Yes Yes Yes - - Yes Yes - - N 2,357 2,356 135 135 455 455 2,235 2,231 455 455 R2 0.083 0.086 0.586 0.558 0.253 0.630 0.204 0.201 0.169 0.730 Notes: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Inparenthesis: std. dev. Avg. referstospecificationswhereweassessthelinkbetweenGDP/SRcomovementandtheaverageofeachmargin in different configuration. Std. refers to specifications where we assess the link between GDP/SR comovement and thevolatility(standarddeviation)ofeachmarginineachconfiguration. aWe use EDD data from 1997 to 2014 for EDD measures, UN COMTRADE data from 2001-2010 and NBER United NationsTradeDatafrom1971to2000fortheHKdecomposition. 63 Thisexercicecanbecomparedtoourempiricalexperimentswherewecomputetheaverageextensiveandintensivemarginsinagiventime-windowsandtheassociatedGDPcomovementinthissametime-windows. 64 We do not use the EDD here because there is not sufficient data to construct the SR at quarterly frequency for mostcountries. With5yearstime-windows,usingannualdatatocomputebilateralcorrelationisnotreliable. 30

7.2 The Role of Markups Inthebenchmarkmodel,wemadetheassumptionofhomogeneousmicroelasticitiesofsubstitution between goods across countries with σ = 5, ∀i. In this section, we first test the implication i ofhigher(i.e. lowerσ)andlower(i.e. higherσ)pricedistorsionsonthetradecomovementslope. i i We then relax the homogeneous assumption and introduce heterogenous market power across countries. This allows us to test the direct implications of price distortions on GDP comovement through trade. To do so, we simulate the model with heterogenous σ estimated from the data i using two different estimates. We first use Price Cost Margin (PCM) as an estimate of markups within each industry, which measures the difference between revenue and variable cost. Second, 2018 65 we use direct markup estimates from De Loecker and Eeckhout ( ). In each experiment, we center the heterogenous markups {σ ,...,σ } around the baseline value σ = 5. Table 10 presents 1 N the results when we implement the two different estimates. Table.10. Theroleofpricedistorsions a TC-slope Experiment Elasticity Markup GDPcorr Inter. inputs Finalgoods Data(withCP&TWFE) - - 0.270 0.053** -0.030 Baseline σ =5.0 25% 0.270 0.050*** 0.017*** Highmarkups σ =4.0 33% 0.311 0.080*** 0.025*** Lowmarkups σ =6.0 20% 0.253 0.038*** 0.014*** Heterogenousmarkups,PCM σ ∈ [3.20,5.65] [22%,45%] 0.269 0.050*** 0.017*** i Heterogenousmarkups, σ ∈ [3.68,6.07] [20%,37%] 0.277 0.055*** 0.018*** i DeLoeckerandEeckhout(2018) aThe simulations are based on the exact same sequence of shocks, under the five variations of trade indexes usedinthebenchmark. As expected, an increase in markups leads to a higher TC slope for intermediate and a lower TC slope for final goods. Quite surprisingly, adding heterogeneous markups centered around the value of σ = 5 does not change substantially the implied trade comovement slope, which suggeststhataccountingforcross-countryheterogenousmarkupsdoesnotchangetheaggregate strength of international propagation. Moreover, it should be noticed that the estimated trade comovement slopes in the literature vary quite a lot depending on the sample and the time 48 11 66 period, ranging from . % to %. A feature that our model can rationalize through different market power over time and across countries. Finally, we assess the role of markups in generating a link between terms of trade and GDP fluctuations. Our model predicts that markups play an important role to make GDP react to 5 foreign shocks, as shown in the decomposition in table . To find empirical support for the role 65 WeprovidedetailsonthetwomeasuresinappendixA. 66 For instance, we find a TC-slope of about 8.1% using the period 1970-1990 for trade in inputs, as shown in the supplementalappendixA.3. Using20-yearstimewindows,wefindaslopeof7.4%. 31

ofmarkup,wedepartfromadirecttestofthemodelandtestthefollowinghypothesis: countries where markups are high experience a larger decrease in GDP when experiencing an increase in their terms-of-trade. For this, we compute the correlation of GDP with the terms of trade and regress this correlation on markups estimates, such that: Corr(GDP , ToT) = β Markup.Index +Country +TW +(cid:101) ( 36 ) it 1 it i t it 11 Table gathers the results for the two measures of markup estimates and the implied slope 67 in the model. We first show the results of pooled cross-section analysis and then perform fixed effect regression and add time dummies to control for time-window specific factors that might affect the correlation of GDP and terms-of-trade. We also run the exact same regression with the model generated data using σi as markup index and using variations in σ. Results using the σi −1 i modelgenerateddatashowthatcountrieswithhighermarkupsalsoexperiencealargerdecrease in their GDP when the relative price of their import rises, consistent with observed data. Table.11. MarkupsandGDP-ToTcorrelation Corr(ln(GDPHP),ln(ToTHP)) i i Data Model Markupmeasure PCM a DeLoeckerandEeckhout(2018)b Markupindex -1.151 -2.650** -0.756*** -0.495* -0.527*** (0.967) (0.911) (0.187) (0.289) (0.090) CountryFE Yes Yes Yes Yes Yes TimewindowsFE No Yes No Yes - N 43 43 80 80 112 R2 0.066 0.322 0.132 0.232 0.260 ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Inparenthesis: std. deviation. aWeusetwotime-windowsfrom1971-2010over22countriesreportedinappendix. bWeusethreetime-windowsfrom1980-2009for29countriesreportedinappendix. 8 Conclusion This paper analyzes the relationship between international trade and business cycle synchronization across countries. We start by refining previous empirical studies and show that higher trade in intermediate input is associated with an increase in GDP comovement, while trade in final good is found insignificant. Motivated by this new fact, we propose a model of trade and 2 3 business cycle with (i) global value chains, ( ) monopolistic pricing and ( ) firms’ entry/exit. All elements are necessary for foreign shocks to have a first order impact on domestic productivity 67 Data on real GDP and terms of trade at the annual frequency are both taken from the OECD database and are HPfilteredtocapturebusinesscyclefrequencies. Wealsousefirstdifferencedataandresultsareconsistentwithour findingsusingHP-filter,asshowninthesupplementaryappendixA.5.2. 32

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Where I is the set of observable categories in which j has a positive shipment to m and I is the jm set of all categories exported by the reference country. We normalize both measures by the sum of GDP of the two countries. A.2 Markup measures Markups. Insection 7 ,weusedtwodifferentmarkupindexestimates. Wefirstusedaggregated 2018 70000 micro markups estimated by De Loecker and Eeckhout ( ). They use micro data of , 134 1980 2016 firms in countries from to and estimate aggregate average markups using a costbased approach. This method defines markups as the ratio of the output price to the marginal costs,andthereforereliessolelyoninformationfromthefinancialstatementsoffirms(salesvalue andcostofgoodssold). Aggregatingallfirmsspecificmarkupsforeachcountry,DeLoeckerand 2018 Eeckhout( )provideadetailedandcomparablemeasureofmarketpowerbetweencountries. 29 1980 201668 The sample that we use from their estimates includes countries from to . Second, we use Price Cost Margin (PCM) as an estimate of markups within each industry 22 1971 201069 1969 using data from countries from to . Introduced by Collins and Preston ( ) and widely used in the literature, PCM is the difference between revenue and variable cost (the sum of labor and material expenditures, over revenue): PCM = Sales−Laborexp.−Materialexp. Sales DataattheindustrylevelcomefromtheOECDSTANdatabase,anunbalancedpanelcovering 107 34 1970 2010 sectors for countries between and . Due to missing data for many countries in 22 70 theearliestyears,werestricttheanalysisfor countries. WecomputePCMforeachindustrycountry-year and then construct an average of PCM within each country-year by taking the sales-weighted average of PCM over each industry. Finally, the average PCM for a given time window is simply the mean of country-year PCM over all time periods. A.3 Trade comovement slope with financial controls We provide additional robustness of the trade comovement slope using financial controls. To do this,weconstructtwoadditionalindexescapturingthefinancialinterconnectionoftwocountries. First, we construct an index of financial integration (FI) using Foreign Direct Investment (FDI) data, as follows: FI = FDIi→j,t +FDIj→i,t. Second, we use the total bilateral cross-border claims ijt GDPit +GDPjt (including bank and non-bank sectors for all maturities) from the consolidated banking statistics 68 Thelistofcountriesis:Austria,Belgium,Canada,Colombia,Denmark,Finland,France,Germany,Greece,Ireland, Iceland, Indonesia India, Israel, Italy, Japan, Korea, Luxembourg, Mexico, the Netherlands, New Zealand, Norway, Portugal,SouthAfrica,Spain,Sweden,Switzerland,Turkey,theUnited-KingdomandtheUnited-States. 69 Thelistofcountriesis: Austria,Belgium,Canada,Denmark,Finland,France,Germany,Greece,Ireland,Iceland, Israel,Italy,Japan,Korea,Luxembourg,Mexico,theNetherlands,Portugal,Spain,Sweden,theUnited-Kingdomand theUnited-States. 70 ForGermany, dataareavailableonlyfrom1991onward(afterthereunification), whichiswhythetotalnumber ofobservationintheregressionsis43. 37

from the Bank for International Settlement to construct an index of financial proximity (FP) between a country i and j: FP = Ci→j,t +Cj→i,t , where here C refers to total cross-border ijt GDPit +GDPjt i→j,t claims from country i to country j. 12 Table summarizes the results with financial controls. Except for the specification using correlation of first difference GDP together with financial proximity index, the results are shown to be robust to the inclusion of financial controls. Using a larger sample including high and low 2019 income countries, World Bank ( ) show consistent findings. Table.12. Trade-GDPcorrelation,Disaggregatedtrade,controlswithfinancialvariables CorrGDPHPfilter Corr∆GDP (1) (2) (3) (4) (5) (6) (7) (8) ln(Tradeinput) 0.170∗∗∗ 0.177∗∗∗ 0.298∗∗∗ 0.312∗∗∗ 0.067 0.074 0.202∗ 0.186∗ (0.065) (0.063) (0.097) (0.095) (0.075) (0.074) (0.104) (0.098) ln(Tradefinal) −0.006 −0.048 −0.367∗∗∗ −0.351∗∗∗ 0.074 0.036 −0.340∗∗∗ −0.316∗∗∗ (0.057) (0.057) (0.092) (0.094) (0.063) (0.067) (0.093) (0.095) ln(FP) 0.039∗∗ 0.027 (0.016) (0.019) ln(FI) −0.022 −0.036∗ (0.020) (0.021) thirdcountry 0.322 −0.319 0.400 0.429 (0.301) (0.502) (0.330) (0.612) Country-PairFE Yes Yes Yes Yes Yes Yes Yes Yes TimeWindowFE No Yes Yes Yes No Yes Yes Yes EU+USSRdum. Yes Yes Yes Yes Yes Yes Yes Yes N 1,030 1,030 728 728 1,030 1,030 728 728 R2 0.425 0.432 0.440 0.443 0.343 0.347 0.350 0.355 Notes: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Inparenthesis: std. deviation. A.4 Trade comovement slope using Solow Residual correlation 91 The Solow Residual in the data is constructed using the PWT . using the variables of real GDP (rgdpo), real capital stock (rnna), total employment (emp) and the index of human capital per employee (hc), such that: SR = log(rgdpo)−αlog(rnna)−(1−α)log(emp∗hc), with α = 1/3. ij With this method, we can compute the SR for up to 592 country-pairs over 4 time-windows. 13 Completeresultsofthetrade-SRcomovementslopeareshownintable ,wherepointestimates are positive and significant for intermediate inputs. Results hold for both HP-filter and first difference. A.5 Sensitive analysis of main empirical results 14 We provide in table sensitive analysis concerning our main results of the trade-comovement slope. Details of those results are provided in the supplementary appendix. 38

Table.13. TradeandSolowResidualcorrelationwith10yearstimewindows CorrSRHPfilter Corr ∆SR (1) (2) (3) (4) (5) (6) ln(Tradetotal) 0.010 0.013 (0.012) (0.012) ln(Tradeinput) 0.055∗∗ 0.066∗∗∗ 0.054∗∗ 0.064∗∗∗ (0.025) (0.025) (0.025) (0.024) ln(Tradefinal) −0.044∗ −0.044∗ −0.040∗ −0.040∗ (0.024) (0.024) (0.024) (0.024) Country-PairFE Yes Yes Yes Yes Yes Yes TimeWindowFE Yes Yes Yes Yes Yes Yes URSS+EUdum. No No Yes No No Yes N 2,367 2,367 2,367 2,367 2,367 2,367 R2 0.213 0.215 0.235 0.208 0.210 0.228 Notes: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Inparenthesis: std. deviation. Table.14. Sensitiveanalysis: TC-slope Coefficient on Coefficient on GDP Countries Period TW CP trade in in- trade in final Filter |Obs. puts goods Sampleselection WholeSample 0.053∗∗ −0.030 HP 40|2,900 1970-2009 Yes Yes 20yearsTW 0.074∗∗ −0.054 HP 40|1,450 1970-2009 Yes Yes ExcludingEUCP 0.056∗∗ 0.005 HP 40|2,280 1970-2009 Yes Yes ExcludingUSSR 0.064∗∗ −0.006 HP 34|2,244 1970-2009 Yes Yes AlternativeTW 0.081∗∗∗ 0.014 HP 34|2,244 1970-1999 Yes Yes Alternativecontrolsforsectoralcomposition 4DigitsSITC 0.058∗∗ −0.045∗ HP 36|2,520 1970-2009 Yes Yes ISICclassification 0.059∗∗ −0.045∗ HP 36|2,520 1970-2009 Yes Yes 1DigitAgg. sectors 0.088 −0.044 HP 38|1,291 1970-2009 Yes Yes Alternativeindexes level(trade)a 33,96∗ −34.92 HP 40|2,900 1970-2009 Yes Yes log(mean(trade)) 0.044∗ −0.027 HP 40|2,900 1970-2009 Yes Yes (cid:16) (cid:17) max Ti↔j , Ti↔j 0.052∗∗ −0.032 HP 40|2,900 1970-2009 Yes Yes GDPi GDPj STANdata 0.209∗∗ −0.107 HP 20|760 1995-2014 Yes Yes Notes: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Inparenthesis: std. deviation. a WeprovidetheresultsusingEUandUSSRdummiessinceaddingthosecontrolssubstantially reducethesignificanceoftradeinfinalgoods. 39

B Theoretical appendix – proof of Lemma 1 Reminder of Lemma 1. : Total profits in country i are proportional to total revenues: σ −1 Π = i R i i γ σ i i Proof: For simplicity, we write the proof in the Cobb-Douglas case with σ = σ and γ = γ, i i although it extends immediately to a more general CES case, and we omit the time subscript. First, since firms charge a constant markup σ/(σ−1), variable profits are a fraction 1/σ of total revenues and total profits net of fixed costs for all firms in i are Π = Ri −∑FC , where FC i σ i→j i→j j is the sum of fixed cost payment from all firms from country i serving market j. Then, note that total fixed cost payment for all firms in country i is: +∞ (cid:90) PB PB FC = M fc × i ×γϕ −γ−1×dϕ = M f i ×ϕ −γ i→j i ij Z i ij Z i,j i i ϕi,j For all i,j, total revenues (sales) from i to j can be written as: R = M (cid:90) +∞(cid:32) τ σ PB i 1 (cid:33)1−σ × (cid:104)ω j I(i)S j + ω j F(i)X j(cid:105) ϕσ−1g(ϕ)dϕ i,j i ij σ−1 Z i P(cid:101) i,j P j I P j F ϕ i,j = γM i × (cid:18) τ σ PB i (cid:19)1−σ × (cid:104)ω j I(i)S j + ω j F(i)X j(cid:105) ϕ σ−γ−1 γ−(σ−1) ij σ−1 Z PI PF i,j i j j Next, using the expression for ϕ , we get i,j γM PB γ R = i ×σfc i ϕ −γ = ×σFC i,j γ−(σ−1) i,j Z i,j γ−(σ−1) i→j i Combining those expressions, we get (cid:32) (cid:33) ∑ γ−(σ−1) ∑ γ−(σ−1) FC = × R = ×R i→j i,j i γσ γσ j j Using this expression of ∑FC in the definition of profits completes the proof. i→j j 40