Working Paper Series. The Trade Comovement Puzzle and the Margins of International Trade. Wei Liao and Ana Maria Santacreu

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1 RESEARCH DIVISION Workng Paper Seres The Trade Comovement Puzzle and the Margns of Internatonal Trade We Lao and Ana Mara Santacreu Workng Paper A November 2014 FEDERAL RESERVE BANK OF ST. LOUIS Research Dvson P.O. Box 442 St. Lous, MO The vews expressed are those of the ndvdual authors and do not necessarly reflect offcal postons of the Federal Reserve Bank of St. Lous, the Federal Reserve System, or the Board of Governors. Federal Reserve Bank of St. Lous Workng Papers are prelmnary materals crculated to stmulate dscusson and crtcal comment. References n publcatons to Federal Reserve Bank of St. Lous Workng Papers (other than an acknowledgment that the wrter has had access to unpublshed materal) should be cleared wth the author or authors.

2 The Trade Comovement Puzzle and the Margns of Internatonal Trade We Lao and Ana Mara Santacreu September 2014 Abstract Countres that trade more wth each other tend to have more correlated busness cycles. Yet, tradtonal nternatonal busness cycle models predct a much weaker lnk between trade and busness cycle comovement. We propose that fluctuatons n the number of varetes embedded n trade flows may drve the observed comovement by ncreasng the correlaton among tradng partners total factor productvty (TFP). Our hypothess s that busness cycles should be more correlated between countres that trade a wder varety of goods. We fnd emprcal support for ths hypothess. After decomposng trade nto ts extensve and ntensve margns, we fnd that the extensve margn explans most of the trade TFP and trade output comovement. Ths result s strkng because the extensve margn accounts for only a fourth of the varablty n total trade. We then develop a two-country model wth heterogeneous frms, endogenous entry, and fxed export costs, n whch TFP correlaton ncreases wth trade n varetes. A numercal exercse shows that our proposed mechansm ncreases busness cycle synchronzaton compared wth the levels predcted by tradtonal models. Contact: laowecarol@gmal.com; anamara.santacreu@nsead.edu. We apprecate the helpful comments of Roger Farmer, Antono Fatas, Ana Cecla Feler, Delfm Gomes, Dens Gromb, Jean Imbs, Ayhan Kose, Lnda Tesar, and Jaume Ventura as well as those of semnar partcpants at NYU, Unversdad Autonoma de Madrd, Georgetown Unversty s McDonough School of Busness, the Hong Kong Unversty of Scence and Technology, Cty Unversty of Hong Kong, Copenhagen Busness School, the Seventh Annual Workshop on Macroeconomcs and Global Interdependence (MGI), the Second Jont Macro Workshop (Pars), Tel-Avv Unversty, Hafa Unversty, SED 2012, EEA-ESEM 2012, the IMF, Georgetown Unversty, and the Federal Reserve Bank of Sant Lous. We are very grateful to Fabo Ghron and Marc Meltz for sharng ther Matlab codes and to Jonas Hepertz and Rondy Wong for excellent research assstance. All remanng errors are ours. The vews expressed n ths paper do not necessarly represent those of the IMF or ts board of drectors. The authors acknowledge fnancal support from a EUROPLACE grant. 1

3 1 Introducton Countres that trade more wth each other tend to have more strongly correlated busness cycles (Frankel and Rose (1998); Clark and Van Wncoop (2001); Baxter and Koupartsas (2005); Kose and Y (2006)). However, tradtonal nternatonal busness cycle (IBC) models predct only a weak lnk between trade and output comovement. 1 Kose and Y (2006) propose several solutons to what they call the trade comovement puzzle. In partcular, they fnd that () total factor productvty (TFP) shocks are also more correlated across countres that trade more wth each other and () calbratons of the standard model that account for ths fact are able to capture fully the trade output comovement observed emprcally. Yet, the underlyng mechansms that connect trade and TFP comovement reman unexplaned. We hypothesze that fluctuatons n the number of goods (or varetes) embedded n trade flows may be one of the forces drvng TFP comovement and thereby output comovement. Indeed, research has shown that low-frequency fluctuatons of trade n varetes can explan dfferences n TFP growth across countres (Broda, Greenfeld, and Wensten (2006); Goldberg, Khandelwal, Pavcnk, and Topalova (2010); Santacreu (2009)). One nterpretaton of these fndngs s that technology s embedded n new goods created through nnovaton. 2 Under autarky, a country s TFP depends only on domestc technology. Wth nternatonal trade, however, TFP depends also on foregn technologes embedded n mported goods. 3 Thus trade n varetes nvolves the nternatonal dffuson of technologes, whch enables countres to beneft from each others nnovatons. Ghron and Meltz (2005) analyze the effect of hgh-frequency fluctuatons n the extensve margn of trade on real aggregate varables. These authors report that when trade flows vary, ether across countres or wthn a country over tme, so does the number of goods emboded n those trade flows. Based on ths premse, our hypothess s that busness cycles are more correlated for countres that trade a wder varety (though not necessarly a greater quantty) of goods. 4 1 In the standard IBC model (Backus, Kydland, and Kehoe (1995)), whch s drven by productvty shocks, two opposng forces determne the trade output comovement. Frst, more trade leads to more synchronzaton by ncreasng the demand for foregn products (demand complementarty effect). Second, greater ntegraton nduces a stronger reallocaton effect toward the most productve country, lessenng synchronzaton (resource-shftng effect). When markets are complete, the latter effect domnates. In addton to these standard channels, a thrd channel the terms of trade effect has an ambguous sgn. An economy experencng a postve productvty shock benefts from lower prces and so ncreases ts market share relatve to other economes, whch reduces busness cycle synchronzaton. Yet foregn economes also beneft from cheaper mports, whch ncreases synchronzaton. Whch effect domnates depends on the elastcty of substtuton between domestc or foregn ntermedate goods as well as on the share of mported ntermedate goods n the foregn economes. 2 Bursten and Meltz (2011) show how nnovatve actvtes at the frm level amplfy productvty dfferences between exporters and nonexporters. 3 Goldberg, Khandelwal, Pavcnk, and Topalova (2009) and Goldberg, Khandelwal, Pavcnk, and Topalova (2010) study Indas s (1991) trade lberalzaton and show that mports of varetes generate statc and dynamc gans from trade whle ncreasng productvty at the plant level. 4 Both theoretcal and emprcal work have hghlghted how the number of goods embedded n trade flows vares wth the busness cycle. Ghron and Meltz (2005) and Alessandra and Cho (2007) argue that the extensve margn of trade should not be gnored when studyng trade flows. There s emprcal evdence for endogenous fluctuatons n avalable US domestc varetes (Ghron and Meltz (2007)). Other papers that document new varetes beng ntroduced n the US economy n conuncton wth the busness cycle nclude Axarloglou (2003), Bernard, Jensen, Reddng, and Schott (2007), and Broda and Wensten (2007). 2

4 We proceed n three steps. Frst, we fnd emprcal support for ths hypothess. We update the trade output and trade TFP comovement regressons and fnd results n lne wth the lterature. We then decompose trade ntensty nto ts extensve and ntensve margns. We fnd that the former explans most of the trade TFP and trade output comovement whle the latter plays only a margnal role. These results hold both at hgh and at medum frequences. 5 In partcular we fnd that, whle holdng the ntensve margn constant, a doublng of the medan extensve margn of trade s assocated wth an ncrease n the blateral TFP correlaton of about 0.06 and n the blateral GDP correlaton of about When we hold the extensve margn constant, n contrast, doublng the medan ntensve margn of trade s assocated wth a decrease n the blateral TFP correlaton of about 0.01 and an ncrease of the blateral GDP correlaton of about These estmates are statstcally sgnfcant only for the extensve margn of trade. Our fndng that the extensve margn explans most of the trade TFP and trade output comovement s strkng because that margn accounts for only a fourth of the varablty of blateral trade ntensty observed n the data. Ths suggests that countres tradng a hgher number of products (a hgher level of the extensve margn) and not more of each product (a hgher level of the ntensve margn) exhbt a greater amount of TFP comovement and output comovement. Second, we llustrate our emprcal results wth a well-establshed model that explans how shocks to productvty generate movements n the extensve margn that affect output comovement across pars of countres. In ths model, the hgher s the steady-state level of the extensve margn between two countres, the stronger s the effect that productvty shocks have on the comovement of busness cycles through fluctuatons n that margn. We buld upon Ghron and Meltz (2005) and Alessandra and Cho (2007) to develop a two-country IBC model wth the followng addtonal features. 6 Frst, there s captal and endogenous labor supply. Second, there s trade n dfferentated ntermedate goods (varetes). 7 Thrd, the dynamcs of TFP are manly drven, both at low and hgh frequences, by the number and average productvty of domestc and foregn varetes; ths s the mechansm we propose to explan the trade comovement puzzle. 8 Fourth, varatons n trade are nduced by ceberg transport costs (whch affect manly the ntensve margn of trade) and the fxed export costs assocated wth entry regulatons (whch affect manly the extensve margn). In each country, a frm produces a nontraded fnal good usng domestc and foregn varetes. Producton nvolves love of 5 Comn and Gertler (2006) show that there are strong procyclcal movements n emboded technologcal change, research and development (R&D), and TFP over the medum term; there s also strong comovement between output and embedded technologcal change both at hgh and medum frequences. These authors argue that the strong medum-term procyclcalty of TFP can be explaned by endogenous productvty. The dea s to ntroduce mechansms va whch nvestments n resources lead to greater future productvty. 6 Kose and Y (2006) argue that, n a two-country model, one of the countres would be the rest of the world and so the model would overstate the mpact of one country on the other; hence a three-country model s needed to accommodate the thrd-country effect. Although we agree that ths s the rght approach when calbratng to a partcular par of countres, our paper focuses on whether the mechansm s stronger for pars of countres wth tghter trade lnkages. As wll become clearer n the quanttatve exercse, we show that pars of countres wth stronger trade lnkages have more correlated TFP and output. 7 Durng the last decade, the structure of nternatonal trade has shfted toward ntermedate and captal goods: 78% of total trade corresponds to captal (14%) and ntermedate nputs (64%), and only 22% corresponds to consumpton goods. A smlar decomposton nto consumpton, captal, and ntermedate goods s obtaned when one consders the number of goods traded rather than trade flows. 8 In Appendx D we provde evdence of hgh-frequency movements n the extensve margn of trade that track closely the hgh-frequency movements n TFP and GDP. There we focus on the case of the Unted States and Chna. 3

5 varety à la Ether (1982), so producton effcency (.e., TFP) ncreases wth the number and average productvty of varetes used. Intermedate producers are heterogeneous n productvty as well as face sunk costs of entry nto the domestc market and fxed costs of servng the foregn market. In the model, each frm s assocated wth a dfferent varety. Forward-lookng frms formulate entry and export decsons based on ther expected future profts. Only a subset of the most productve frms serves the foregn market, a fact that generates varatons n the extensve margn of trade across pars of countres. Exogenous shocks to aggregate productvty alter the composton and average productvty of domestc and foregn varetes n each country. We consder only those TFP shocks that are uncorrelated across countres whle focusng on the correlaton between the endogenous component of countres TFP. Two channels strengthen the correlaton of GDP growth rates between tradng partners. The frst channel s the tradtonal demand supply spllover effect, whch s present n standard IBC models but quanttatvely too small to explan the trade output comovement observed n the data. A second (albet less drect) channel results from entry, at busness cycle frequences, nto domestc and foregn markets. Followng a postve transtory shock to domestc TFP, domestc fnal producers ncrease ther demand for foregn ntermedate goods, whch n turn ncreases foregn output; ths s the standard demand supply channel. In addton, however, hgher productvty nduces entry nto both domestc and foregn markets. Indeed, the country experencng a postve productvty shock exports varetes, each of whch has a hgher average productvty, and these exports ncrease each tradng partner s endogenous TFP. Hgher TFP ncreases output both drectly through the producton functon and ndrectly by ncreasng even more the demand for ntermedate goods, whch amplfes the demand supply channel present n the standard IBC model. The strength of the endogenous TFP effect s hgher when export fxed costs are lower. An mportant predcton of our model one that allows us to llustrate our emprcal results s that countres wth hgher steady-state levels of the extensve margn also exhbt greater propagaton of shocks due to changes n ths margn. In other words, the mportance of the extensve margn s evdent not only at the steady-state level but also wth respect to the transmsson of shocks across countres. We descrbe the emprcal evdence that establshes ths result. In partcular, we show that pars of countres wth a hgher extensve margn (as measured by the number of traded varetes) exhbt a greater varablty n ths margn and also that ths s true at dfferent frequences. In a thrd step we conduct a quanttatve analyss to llustrate the man mechansms of the model. Toward ths end, we frst use mpulse response functons to analyze how trade n varetes amplfes the effect of an exogenous TFP shock to one country on the output growth of ts tradng partner. Second, we smulate the model for artfcal pars of countres that dffer n ther ceberg transport costs and n ther fxed costs of export. We compute the correlatons among output growth, TFP growth, average trade ntensty, and the extensve and ntensve margns of trade; we then reproduce the same exercse as n our emprcal analyss. Ths exercse allows us to recover the trade output and the trade TFP coeffcents mpled by the model, whch we compare wth the coeffcents mpled by the data. We fnd that addng heterogeneous frms and fxed costs to the standard IBC model mproves sgnfcantly the trade output and trade TFP coeffcents n comparson wth the the standard model. 4

6 Taken together, our results suggest that () much of the trade TFP and trade output comovement can be explaned by the extensve (but not the ntensve) margn of trade and () the nternatonal transmsson of shocks through trade n varetes s a plausble explanaton for these relatonshps. Several strands of lterature have tackled the trade comovement puzzle. Kose and Y (2006) document that TFP shocks are more strongly correlated across countres that trade more wth each other. Other researchers emphasze the role of ntermedate nputs n ncreasng plant-level productvty after a trade lberalzaton (e.g., Goldberget al. 2009, 2010; Kugler and Verhoogen (2009); Manova and Zhang (2011)). Juvenal and Santos Montero (2010) fnd that cross-country correlatons n technology consttute one of the man drvers of the trade comovement puzzle. The man nnovatons n our paper are dsentanglng the effects of the extensve and ntensve margns on the comovement of TFP growth and output growth and proposng a mechansm to explan the mportance of the extensve margn of trade. As Kose and Y (2006) pont out, the puzzle addressed n ths paper dffers from standard puzzles n the IBC lterature (e.g., the output and consumpton puzzles). In that lterature, the correlaton puzzle concerns the nablty of standard nternatonal busness cycle models to generate a rankng of crosscountry output and consumpton correlatons that matches the data. The trade comovement problem concerns the nablty of these models to generate a strong change n output correlatons from changes n blateral trade ntensty. Another strand of lterature studes the role of vertcal lnkages, both emprcally (Bursten, Kurz, and Tesar (2008); D Govann and Levchenko (2009); Ng (2010); Johnson (2011)) and theoretcally (Arkolaks and Ramanarayanan (2009)). Much as n our paper, that research emphaszes the amplfyng effect of traded ntermedate goods. However, the amplfcaton reported by these authors s drven by the multstage nature of producton whereas here t s drven by fluctuatons n the extensve margn of trade. Drozd and Nosal (2008) argue that a low elastcty of substtuton between domestc and foregn ntermedate goods (at busness cycle frequences) can explan, n part, the trade output comovement. In ther model, frctons n the short run generate a low prce elastcty that s compatble wth the hgh long-run elastcty of substtuton observed n the data. Although that model captures as much as half of the correlaton (between trade and output comovement) found n emprcal studes, the mechansm by whch ths occurs has not been well establshed emprcally. Fnally, the papers of Alessandra and Cho (2007) and Fattal-Jaef and Lopez (2010) extend the framework of Ghron and Meltz (2005) by addng captal and adustment costs to the hgh-frequency fluctuatons n the extensve margn of trade; they fnd that the addton of captal dampens the effect of the extensve margn on busness cycle comovement. We follow that modelng strategy. Yet nstead of analyzng the model s tme-seres propertes of the model, we examne ts cross-sectonal propertes. Our goal s to determne whether ncreases n blateral trade generate an ncrease n busness cycle comovement that s consstent wth prevous emprcal fndngs. The mechansm that we propose can 5

7 be vewed as an alternatve explanaton to complement the emprcal and theoretcal lterature that has addressed the trade comovement puzzle. Our paper proceeds as follows. Secton 2 decomposes blateral trade ntensty nto ntensve and extensve margns of trade and shows that much of the observed comovement s due to the latter margn. Secton 3 presents our model and explans the proposed mechansm, and Secton 4 conducts a quanttatve analyss. Secton 5 concludes. 2 Trade Output Comovement and the Margns of Trade In ths secton, we dsentangle the effects of extensve and ntensve margns of blateral trade on both GDP and TFP comovement. Ths approach s a departure from the lterature, whch nvestgates only the relatonshp between total blateral trade and the comovement of output. We update Frankel and Rose (1998) wth respect to a 30-country sample (20 OECD countres and 10 developng countres) spannng the perod from 1980Q1 through 2009Q4. Ths sample accounts for nearly 75% of world GDP and 73% of world trade. 9 The output data are transformed n three ways: () Hodrck Prescott (HP) flterng of real GDP (wth smoothng parameter 1600); () frst-dfferencng of natural logarthms to calculate the output growth rate; and () band-pass (BP) flterng to remove hgh-frequency varatons (whle retanng frequences between 32 and 116 quarters). The frst two transformatons capture busness cycle frequences and the thrd captures medum-term busness cycles (Comn and Gertler (2006)). We then calculate the blateral correlaton of real GDP over sx (nonoverlappng) fve-year ntervals, between 1980 and 2009, for each of the three resultng measures. 10 We use blateral trade data at the 5-dgt level of dsaggregaton (SITC Rev. 3) from the UN Comtrade database and calculate the two margns of trade usng the Hummels and Klenow (2005) decomposton. Ths s the hghest level of dsaggregaton at whch data exst for a large sample of countres and a long perod of tme. 11 Hummels and Klenow (2005) use the Feenstra and Markusen (1994) methodology to ncorporate new varetes nto a country s mport prce ndex when preferences reflect constant elastcty of substtuton (CES). The extensve margn (EM) s defned as a weghted count of country s mported varetes from country relatve to ts mported varetes from country k. If s shpments to are a subset of 9 The country lst s gven n Appendx E as Table E It has been argued by several authors that the extensve margn of trade does not vary sgnfcantly at hgh frequences (see, e.g., Kehoe and Ruhl (2003)). Hence we follow Comn and Gertler (2006) and remove hgh-frequency varatons n the data. 11 As a robustness check, we count the number of varetes to obtan the extensve margn of trade (normalzed by the number of varetes exported by the rest of the world). The count data represents a partcular case of the Hummels and Klenow decomposton n whch each varety s assgned the same weght. The two measures yeld smlar results. 6

8 k s shpments to, then the extensve margn s EM = m I p k m x k m m I p k m x k m ; (1) here I I s the set of observable varetes for whch country has postve exports to, and I s the set of all varetes. The reference country k (n ths case, the rest of the world) has postve exports to n all I varetes. The terms p k m and x k m are (respectvely) the prce and quantty of varety m exported by the reference country k to country. The ntensve margn (IM) smlarly compares nomnal shpments for country and country k wth respect to a common set of goods: IM = m I p m x m m I p k m x k m. (2) The rato of country s exports to country wth respect to country k s exports to country, whch we refer to as overall trade and denote by OT, equals the product of the two margns; thus takng logs yelds log(ot )=log(em )+log(im ). (3) We classfy the 5-dgt goods nto three categores (consumpton, ntermedate, and captal goods) and then compute the margns of trade for each category for the perod We perform a varance decomposton of the trade ntensty nto the varablty of the ntensve and extensve margns of trade; we fnd that, on average, the ntensve margn accounts for nearly 75% of the varaton of overall trade. We then regress the correlaton of our three measures of output correlaton aganst the logarthm of country s exports to country relatve to country k s exports to country whle ncludng only ntermedate and captal goods: 12 corr( y t, y t )=β 0 + β OT log(ot,t )+ε m,t. (4) We run nstrumental varable (IV) regressons usng dstance as the nstrument for overall trade. The results, reported n Table 1, are consstent wth those obtaned n prevous studes: countres that trade more wth each other tend to have more correlated output growth. 12 We nclude only ntermedate and captal goods n order to capture the noton that the transfer of technology emboded n these types of goods may help explan the busness cycle comovement. In the next secton we present a model n whch only ntermedate and captal goods are traded across countres. Regressons that nclude also consumpton goods delver smlar results. 7

9 Table 1: Output correlaton and overall trade HP-fltered output Output growth BP-fltered output corr(y HP,y HP ) Coeff. corr( y, y ) Coeff. corr(y BP, y BP ) Coeff. log(ot ) 0.114*** log(ot ) 0.066*** log(ot ) 0.197*** (0.011) (0.006) (0.023) Constant 0.847*** Constant 0.490*** Constant 1.077*** (0.051) (0.029) (0.104) Notes: Two-stage least-squares (2SLS) IV regresson usng log dstance as the IV. Standard errors are reported n parentheses. *** denotes sgnfcance at the 1% level. The next step s to analyze the contrbuton of each margn of trade to output comovement. We do ths va the followng regresson: corr( y t, y t )=β 0 + β EM log(em,t )+β IM log(im,t )+ε,t. (5) Instruments are needed for both margns of trade. We follow Chaney (2008) and Helpman, Meltz, and Rubnsten (2008) n usng both entry costs and dstance between the two countres as nstruments. Our nstrumental varables are presumed to be correlated wth blateral trade ntensty, but we can assume that they are not nfluenced by other condtons that affect the blateral correlaton of actvty. The dea s that the ntensve margn s affected manly by the ceberg transport cost (a varable cost) whereas the extensve margn s affected manly by the cost of enterng a new market (a fxed cost). We therefore use dstance as an nstrument for the ntensve margn; to nstrument the extensve margn, we use country-level data on the regulaton costs of frm entry as measured by Dankov, La Porta, Lopez-de Slanes, and Shlefer (2002). These entry costs are measured n terms of ther effects on the number of days, the number of legal procedures, and the relatve cost (as a percentage of GDP per capta) requred for an entrepreneur to start operatng a busness. Our ndcator of parwse trade costs s constructed by addng the mportng and exportng relatve cost as a percentage of GDP per capta. 13 One problem wth ths approach s that entry regulaton costs mght be correlated wth the varable trade cost affected by dstance; however, we follow Helpman, Meltz, and Rubnsten (2008) and add country fxed effects to the frst-stage regresson to show that ths s not the case. Furthermore, the frst-stage regresson results show that our nstrumental varables are strong. Table F.2 (n Appendx F) reports the weak dentfcaton test results from the frst-stage regressons, whch demonstrate the strength of our proposed nstruments for each frst-stage equaton. The adusted R- squared ranges from 14% to around 40%, whch shows that the nstruments can explan a szable share of the varaton n our endogenous varables. More mportantly, the Cragg Donald F-statstc exceeds the Stock Yogo weak dentfcaton test crtcal values by substantal margns at all the conventonal 13 The blateral extensve margn between country and s computed as the sum of the extensve margns for the two countres and. Therefore, the entry regulaton cost used as an nstrument s blateral and s computed as the sum of the entry cost for the mporter and the exporter; t vares by source and destnaton but not over tme. The same remarks apply to dstance, a varable used n the emprcal lterature as an nstrument for trade ntensty. 8

10 szes; ths, too, shows that our nstruments are strong. The results are robust to alternatve measures of EM and IM. We next run IV regressons of the output comovement on the extensve and ntensve margns of trade for all measures of output. We fnd that the extensve margn has a postve and sgnfcant effect on GDP comovement whereas the ntensve margn s statstcally nonsgnfcant (see Table 2). The results are stronger for the BP flter. Indeed, the coeffcents n ths case are double those found wth respect to ether the HP flter or GDP growth, whch ndcates that the relatonshp between busness cycle synchronzaton and nternatonal trade s stronger at medum-term frequences. There are two man reasons why nstrumental varables are requred. Frst, we must deal wth the omtted varable problem. For nstance, a lnked exchange rate polcy between trade partners can rase both trade ntensty and output correlaton. Usng nstruments wll help us dentfy the effect of trade patterns on output correlaton. The second reason for usng IVs s that trade data may be recorded wth measurement error. If the ntensve margn s measured wth much larger error than s the extensve margn, then a multple lnear regresson of GDP correlaton on EM and IM wll result n underestmatng the IM s coeffcent; usng nstrumental varables helps correct such a bas. Measurement error n the data could also result n large standard devatons for the estmators. However, as seen n Table 2, ths s not a problem n our estmaton for two reasons: () the standard error of the coeffcent for the extensve margn s small; and () even though the standard error of the coeffcent for the ntensve margn s large relatve to the pont estmates, the upper bound of the resultng 95% confdence nterval for the ntensve margn s much lower than the extensve margn s coeffcent. Fnally, we address the ssue of multcollnearty between the margns of trade. The extensve and ntensve margns are ndeed postvely correlated. But snce the correlaton s only about 0.43, multcollnearty should not be a concern. We also calculate the varance nflaton factor (VIF) and fnd that t s only 1.25; tradtonally, only VIFs of at least 10 are problematc. Table 2: Output correlaton and the margns of trade HP-fltered output Output growth BP-fltered output corr(y HP,y HP ) Coeff. corr( y, y ) Coeff. corr(y BP, y BP ) Coeff. log(em ) 0.309*** log(em ) 0.196*** log(em ) 0.593*** (0.075) (0.053) (0.189) log(im ) log(im ) log(im ) (0.035) (0.025) (0.091) Constant 0.644*** Constant 0.354*** Constant 0.662*** (0.100) (0.072) (0.250) Note: Two-stage least-squares (2SLS) IV regresson usng log dstance as the IV. Standard errors are reported n parentheses. *** denotes sgnfcance at the 1% level. Next we study the relaton between nternatonal trade and total factor productvty. Kose and Y (2006) fnd that TFP shocks are more correlated across countres that trade more wth each other. We calculate TFP as the Solow resdual n a standard Cobb Douglas producton functon. 9

11 We then test whether countres that trade more wth each other have more correlated TFP. Just as for the case wth output data, we transform TFP n three ways (quarter-to-quarter growth rates, HP- and BP-fltered TFP) before computng the blateral correlatons durng each of the sx fve-year ntervals. The results are reported n Table 3 and are consstent wth those obtaned n Secton 2. Table 3: TFP correlaton and overall trade HP-fltered TFP TFP growth BP-fltered TFP corr(tfp HP,TFP HP ) Coeff. corr( TFP, TFP ) Coeff. corr(tfp BP, TFP BP ) Coeff. log(ot ) 0.055*** log(ot ) 0.037*** log(ot ) 0.106*** (0.009) (0.006) (0.013) Constant 0.453*** Constant 0.308*** Constant 1.029*** (0.042) (0.028) (0.058) Note: Two-stage least-squares (2SLS) IV regresson usng log dstance as the IV. Standard errors are reported n parentheses. *** denotes sgnfcance at the 1% level. Fnally, we nvestgate the contrbuton of the dfferent margns of trade on TFP comovement va the followng regresson: corr( TFP t, TFP t )=β 0 + β EM log(em,t )+β IM log(im,t )+ε,t. (6) We fnd that the extensve margn has a postve and statstcally sgnfcant effect on the comovement of TFP but that the ntensve margn has a small (negatve) effect that s not sgnfcant (see Table 4). 14 Table 4: TFP correlaton and the margns of trade HP-fltered TFP TFP growth BP-fltered TFP corr(tfp HP,TFP HP ) Coeff. corr( TFP, TFP ) Coeff. corr(tfp BP, TFP BP ) Coeff. log(em ) 0.305*** log(em ) 0.205*** log(em ) 0.610*** (0.076) (0.056) (0.119) log(im ) log(im ) log(im ) 0.109* (0.035) (0.027) (0.057) Constant 0.188* Constant 0.131* Constant 0.495*** (0.099) (0.078) (0.160) Note: Two-stage least-squares (2SLS) IV regresson usng log dstance as the IV. Standard errors are reported n parentheses. *** (*) denotes sgnfcance at the 1% (10%) level. The ntensve margn of trade explans the largest part (75%) of the overall varablty n trade ntensty. However, the extensve margn of trade explans most of the varablty n the parwse correlaton 14 Smlar results on the effect of trade cost changes on the two margns of trade are obtaned by Dutt, Mhov, and Van Zandt (2011) n the context of the Wold Trade Organzaton. These authors show that such changes affect the extensve margn of trade almost exclusvely and have a neglgble (or negatve) effect on the ntensve margn. 10

12 of output growth (80%) and of TFP growth (57%). 15 As a robustness check, we repeat the regressons of output growth correlaton and TFP correlaton on the extensve and ntensve margns for varous categores of the traded goods namely, captal, ntermedate goods, and nonntermedate (consumpton) goods. Tables F.7.1 and F.7.2 report the results. We also performed regressons usng the Harmonzed System (HS) classfcaton as an alternatve to the SITC classfcaton; these results are reported n Tables F.8.1 and F.8.2. Fnally, we analyzed the results for dfferent levels of dsaggregaton of the trade data (3- and 5-dgt codes); see Tables F.9.1 and F.9.2. for the results. Hummels and Klenow (2005) remark that, at lower levels of dsaggregaton, t s expected that some varety dfferences wll be relegated to the ntensve margn of trade. Our results are broadly consstent wth that ntuton, showng smaller coeffcents for EM at the 3-dgt than at the 5-dgt level. For all the regressons descrbed so far, coeffcents for the extensve margn are both statstcally and economcally sgnfcant; ths s n contrast to the nsgnfcant and small coeffcents found for the ntensve margn. Taken together, the emprcal results reported n ths secton ndcate that countres tradng more at the extensve than at the ntensve margn have more correlated TFP growth and also more correlated output growth. These emprcal results nvolve the levels of the margns of trade. A greater level of extensve margn s assocated wth a greater output growth and TFP growth synchronzaton. In the next secton, we extend the standard nternatonal busness cycle model to account for both margns of trade and then show how the mechansm proposed n the extended model can amplfy the effect of a TFP shock on busness cycle comovement. 3 The Model We buld on the work of Ghron and Meltz (2005) and Alessandra and Cho (2007) n developng a two-country model of heterogeneous frms that face both fxed and varable trade costs; we extend ther framework to generate varatons n TFP through the extensve margn of trade. Unlke the orgnal model, n whch consumers derve ther utlty from CES Dxt Stgltz preferences, the model developed here treats preferences as a separable functon of aggregate consumpton and labor (thus allowng for endogenous labor supply) and ntroduces the CES aggregator on the producer sde of the economy. In ths sense we examne the effect that mported ntermedate goods have on TFP rather than ther effect on welfare. 16 Tme s dscrete and s ndexed by t = 0,1,... The two countres are Home and Foregn, ndexed by n=h,f. 15 Standard OLS regressons delver smlar results: the effect of the extensve margn s postve and statstcally sgnfcant whereas the effect of the ntensve margn s negatve or statstcally nsgnfcant. 16 We descrbe the mplcatons of our modelng choce n Appendx B. 11

13 3.1 Producton and Consumpton In each country, a frm produces a nontraded fnal good usng domestc and foregn ntermedate goods (varetes). Producton nvolves love of varety as n Ether (1982), so producton effcency (.e., TFP) ncreases wth the number and average productvty of varetes used. In ths sense, TFP s endogenous. An exogenous TFP shock provdes the only source of uncertanty n the model. Each ntermedate good s produced by a monopolstcally compettve frm usng labor and captal. The nontraded fnal good s then sold to households that consume, supply labor and captal, and save Intermedate Producton We extend Ghron and Meltz (2005) s model of ntermedate producton by addng captal and endogenous labor supply. 17 In each country n=h,f, the total labor supply (L nt ) and total captal supply (K nt ) are employed by a contnuum of monopolstcally compettve frms (henceforth, ntermedate producers) to produce ntermedate goods ndexed by [0,N nt ], where N nt represents the mass (or, alternatvely, the number) of avalable products. Aggregate labor productvty s ndexed by Z nt ; ths represents the effectveness of one unt of Home labor and follows the frst-order autoregressve process log(z nt )=ρ n log(z n,t 1 )+u nt, (7) where ρ n (0,1) and u nt N(0,σu). 2 Frms are heterogeneous n producng wth dfferent technologes ndexed by relatve productvty z. A domestc frm wth relatve productvty z has a total factor productvty of Z nt z. The technology of each ntermedate producer s gven by the Cobb Douglas producton functon y t (z)=zz t k t (z) (1 α) l t (z) α, (8) where α (0,1) s the labor ncome share; here k t (z) and l t (z) represent (respectvely) the captal nput and labor nput used by ntermedate frm z. Frms choose k t (z) and l t (z) to mnmze the producton cost ω nt l nt (z)+r k ntk nt (z) subect to the technology constrant (8). All the varables are expressed n real terms. That s: ω nt W nt /P nt s the real wage, where W nt s country n s nomnal wage and P nt s the prce ndex (to be 17 Fattal-Jaef and Lopez (2010) develop a smlar model. We depart from ther modelng strategy n terms of how the endogenous labor supply s ntroduced. 12

14 defned later); and r k nt = R k nt/p nt s the real rental prce of captal, where R k nt s the nomnal rental prce of captal. The frst-order condtons of the ntermedate producers are ω nt = mc nt (z)α y t(z) l t (z), (9) r k nt = mc nt (z)(1 α) y t(z) k t (z) ; (10) here mc nt (z) s the real margnal cost of producng one unt of ntermedate good by frm wth productvty z. The expresson for mc t (z) s mc nt (z)= 1 ( ωnt ) ( α r k ) 1 α nt. (11) zz t α 1 α Note that the margnal cost for each frm s dentcal except for the dosyncratc productvty z. As n Meltz (2003), frms pror to entry are dentcal and must ncur sunk costs (to enter the market) of f E effectve labor unts, gven by ω nt f E /Z nt unts of the fnal good. We vew these costs as product development costs or fxed costs of nnovaton. Upon entry, frms draw ther productvty level z from a common dstrbuton G(z) wth support on [z mn, ); thereafter, the relatve productvty level remans fxed. All frms produce n every perod untl they are ht wth an exogenous death shock δ (0,1) that s ndependent of the frm s productvty level. Intermedate producers can serve both ther domestc and export markets. Exportng s costly. We consder two types of trade costs: an ceberg transport cost τ 1 that affects manly the ntensve margn of trade; and a fxed entry cost f X, whch s measured n unts of effectve labor, that affects manly the extensve margn of trade. In real terms, the fxed costs are ω nt f X /Z nt and are pad perodby-perod. For a multcountry model the fxed costs would be blateral, and we could nterpret them as entry regulaton costs (Helpman, Meltz, and Rubnsten (2008)) or as the costs of adaptng a product to the foregn market s specfcatons, establshng networks for marketng and dstrbuton, and learnng about bureaucratc and admnstratve procedures n the new market (Alessandra and Cho (2007)). All frms take as gven the demand by the fnal producer n each country n=h,f and then set a prce that reflects a constant markup over margnal cost. Prces may dffer across countres because markets are segmented owng to the ceberg transport cost τ for products shpped to the foregn market. Let p D nt and p X nt denote (respectvely) the nomnal domestc and export prces of a frm n country n. Prces, n real terms (relatve to the prce ndex n the destnaton market), are then gven by ρ D nt = θ θ 1 mc nt(z), and ρ F nt = Q 1 t θ θ 1 mc nt(z)τ t ; (12) 13

15 here Q t e tpt P t s the real exchange rate and θ 1 θ s the constant markup (wth θ to be defned shortly). Gven the fxed export costs, frms wth low productvty levels z may decde not to export n any gven perod. Frms decompose ther total profts π nt (z) nto what they earn n the domestc market π D nt(z) and from export sales π X nt(z). The total profts n countres n at tme t are thus gven by π nt (z)=πnt(z)+i D nt(z)π x nt(z) X (13) wth Int(z)=1 x f frm z exports and 0 otherwse. In every perod there s a mass Nnt D of domestc frms producng n country n. Among these frms, Nnt X =(1 G(z X nt))nnt D sell ther product to the foregn market. A frm exports as long as ts productvty remans above the cutoff level z X nt = nf { z : πnt(z)>0 X } Fnal Producton In each country n=h,f, a perfectly compettve frm (henceforth, fnal producer) uses a composte of traded ntermedate goods both domestc and foregn to produce a nontraded fnal good accordng to the CES producton functon (ˆ ) θ/(θ 1) Y nt = (y nt (z)) (θ 1)/θ dz, (14) z Ω t where, Ω s the set of avalable ntermedate goods (both domestc and foregn), θ > 1 s the symmetrc elastcty of substtuton across ntermedate goods. The CES component ntroduces a love-of-varety effect: when expendtures y nt (z) are held constant, usng a wder range of varetes corresponds to ncreased productvty (Ether 1982). The fnal producer chooses y nt (z) to maxmze ts proft: here P nt s the prce ndex for the fnal good and takes the form ˆ Π nt = P nt Y nt p nt (z)y nt (z)dz; (15) z Ω t (ˆ ) 1/(1 θ) P nt = (p nt (z)) 1 θ dz. (16) z Ω t Observe that the prce ndex faced by the fnal producer s decreasng n the number of varetes. The demand by the fnal producer of each ntermedate good s ( ) pnt (z) θ y nt (z)= Y nt. (17) P nt 14

16 3.1.3 Households In each country n=1,...,m, a representatve household consumes the fnal good, supples labor and captal, and saves. The household maxmzes ts lfetme expected utlty functon, subect to the budget constrant ( µ C U t = E t β s ns (1 L ns ) 1 µ ) 1 γ, (18) s=t 1 γ B nt+1 + Q t B n t+1+ η 2 B2 nt+1+ η 2 Q tb 2 n t+1 +C nt+ I nt = = ω nt L nt + r k ntk nt + Π T nt+ R nt B nt + Q t R n tb n t+ T nt (19) for n n and n,n = {H,F}. Here C nt s consumpton; β (0,1) s the dscount factor; γ s the ntertemporal elastcty of substtuton; and µ s the share of consumpton n the household s utlty; ω nt s the real wage; I nt s nvestment; Π T nt are the total profts of all frms n country n, to be defned n detal later; B nt+1 denotes holdngs of home bonds and B n t+1 denotes holdngs of foregn bonds; η 2 B2 nt+1 s the cost of adustng holdngs of home bonds and η 2 B2 n t+1 s the cost of adustng holdngs of foregn bonds (n unts of foregn consumpton); T nt s the fee rebate, taken as gven by the household and equal to η 2 B2 nt+1 + η 2 Q tb 2 n t+1 n equlbrum; and R nt s the rsk-free rate of return. The household s decson problem s to choose consumpton, labor and captal supply, and domestc and foregn bonds to maxmze (18) subect to (19). The law of moton for captal s I nt = K nt+1 (1 δ k )K t, (20) where δ k (0,1) s the rate of deprecaton of captal. The frst-order condtons of the consumers are 1 µ µ C nt = ω nt (1 L nt ); (21) ( Cnt C nt+1 ) 1 ( C µ nt(1 L nt ) 1 µ C µ nt+1 (1 L nt+1) 1 µ ) 1 γ = β(r k nt+1 +(1 δ k)). (22) (1+ηB nt+1 )Cnt 1 ( µ C nt (1 L nt ) 1 µ) 1 γ ( = βc 1 µ nt+1 C nt+1 (1 L nt+1) 1 µ) 1 γ Rnt+1, (23) (1+ηB n t+1)cnt 1 ( µ C nt (1 L nt ) 1 µ) 1 γ ( = βc 1 µ nt+1 C nt+1 (1 L nt+1) 1 µ) 1 γ Rnt+1. (24) 15

17 3.2 Frm Entry and Ext and the Export Decson In every perod there s an unbounded mass of prospectve entrants n both countres. Entrants are forward lookng and maxmze profts π nt (z)=π D nt(z)+i x nt(z)π X nt(z). All these profts are expressed n real terms n unts of the fnal producton good: π X nt(z)= { πnt(z)= D 1 ( ρ D θ nt (z) ) 1 θ Ynt ; (25) (Q t /θ) ( ρnt(z) X ) 1 θ Yn t ω nt f Xt /Z nt f frm z exports, (26) 0 otherwse. Once agan, n n. As n Meltz (2003), we defne the average productvty levels that allow us to summarze all the nformaton on the productvty dstrbutons that s relevant for the macroeconomc varables. Thus we wrte and z Xt = [ˆ ] 1/(θ 1) z D = z θ 1 dg(z) z mn (27) [ˆ 1 ] 1/(θ 1) z θ 1 dg(z). (28) 1 G(z Xt ) z Xt Prospectve entrants n perod t compute the present dscounted value of ther expected stream of profts: ṽ nt = E t s=t+1 [β(1 δ)] s t d ns. (29) Entry occurs untl the average frm value ṽ t s equal to the entry cost. The free-entry condton s ṽ nt = ω nt f E Z nt. (30) We assume that entrants at tme t do not begn producng untl tme t+ 1. Therefore, the number of domestcally produced varetes s gven by N D nt =(1 δ)(n D n,t 1+ N E n,t 1) (31) and the total number of varetes avalable for fnal producton n country n n every perod t s N nt = N D nt+ N X nt. The budget constrant s now 16

18 B nt+1 + Q t B n t+1+c nt + I nt = ω nt L nt + r k ntk nt + Π T nt+ R nt B nt + Q t R n tb n t, (32) where Π T nt = ( d nt + ṽ nt ) N D nt x nt ṽ nt N nt x n,t+1. Households n each country hold two types of assets: () shares n a mutual fund of domestc frms and () domestc and foregn rsk-free bonds. We use x t to denote the share n the mutual fund of Home frms held by the representatve home household enterng perod t. 3.3 Parameterzaton of Productvty Draws Productvty s assumed to be Pareto dstrbuted wth lower bound z mn and shape parameter k>θ 1; thus, G(z)=1 (z mn /z) k. From ths assumpton we obtan the average domestc and export cutoffs, z D n = vz mn (33) and z X nt = vz X nt, (34) [ k 1/(θ 1). where v= k (θ 1)] The fracton of exported ntermedate goods s Nnt X Nnt D ( ) = z k ) X k k k/(θ 1) mn ( z nt. (35) k (θ 1) Observe that, wth all else held constant, the number of exported varetes s ncreasng n the extent of domestc entry and s decreasng n the average export cutoff value. 3.4 Aggregate Accountng and Closng the Open Economy In equlbrum B nt+1 + B nt+1 = 0, (36) B n t+1+ B n t+1 = 0. (37) 17

19 The current account s defned as CA nt = B nt+1 B nt + Q t (B n t+1 B n t). (38) Combnng the domestc and foregn aggregate budget constrants, we have an equlbrum verson of trade balance An equvalent equaton to the trade balance condton s CA nt + Q t CA n t = 0. (39) B nt+1 + Q t B n t+1 = = R nt B nt + Q t R n tb n t+ 1 2 (ω ntl nt + r k ntk nt Q t (ω n tl n t+ r k n t K n t)) (ND nt d nt Q t N D n t d n t) 1 2 (NE ntṽ nt N E n tṽn t) 1 2 (C nt+ I nt Q t (C n t+ I n t)). (40) 3.5 Market Clearng The market clearng condtons for labor and captal are, respectvely, L nt = N D nt ( r k ) 1 α ( nt α ( ) ) (1 α)(ωnt rnt k ) α θ θ ω nt (1 α) θ 1 A Znt θ 1 ( ) ( z D θ 1Ynt nt + Nx nt Nnt D ) ( z x nt) θ 1 τt 1 θ Qt θ Y n t f E n f x n + Nnt E + Nnt x (41) Z nt Z nt K nt = N D nt where A ( 1 α ) α ( 1 1 α) 1 α. ( ωnt (1 α) r k ntα ( ) ( z D θ 1Ynt nt + Nx nt Nnt D ) α ( ( ) ) (1 α)(ωnt rnt k ) α θ θ θ 1 A Znt θ 1 ) ( z x nt) θ 1 τt 1 θ Qt θ Y n t (42) The fnal good n each country s used for consumpton and nvestment, Y nt = C nt + I nt. (43) The demand for domestc and foregn varetes s equal to the supply: ỹ nt = ỹ D nt+ ỹ X nt, (44) 18

20 where ỹ D nt =N D nt( ρ D nt ) θ Ynt, ỹ X nt =N X nt( ρ X nt Q t ) θ Yn t. Analogous equaltes hold for the foregn economy. 3.6 Equlbrum For all n = {H,F}, a general symmetrc equlbrum n ths economy s defned as consstng of an exogenous stochastc sequence {Z nt }, an ntal vector {Z n0,n D n0,k n0,b n0 }, a set of parameters {θ,δ,δ k,α,β,z mn,τ, µ, f E, f X,η} that are common across countres, a set of parameters {ρ n } that dffer across countres, an aggregate sequence of prces and wages {Q t,p nt,ω nt,rnt,r k nt } t=0, a set of prces{ ρ nt, D ρ nt} X t=0 for ntermedate goods, a sequence of aggregate quanttes{y nt,i nt,b nt,ỹ nt }, quanttes of ntermedate goods{ỹ D nt,ỹ X nt} t=0, a number of ntermedate goods{ne n,t,nnt} X t=0, domestc and export cutoff values{ z D n, z X nt} t=0, sequences of profts and value{π nt, d nt,ṽ nt } t=0, and laws of moton {Nnt,Z D n,t+1 } such that the followng condtons hold. (The equatons are gven n Appendx A.) The state varables satsfy the laws of moton. The endogenous varables solve the producer and household problems. Feasblty s satsfed by the market-clearng condtons. Prces are such that markets clear. We focus on a statonary equlbrum that conssts of statonary decson rules and prcng rules that are functons of the economy s state. Ths state s completely descrbed by the dstrbuton of each ndvdual ntermedate producer state varable (z) and of each TFP shock Z nt. 3.7 The Mechansm In ths secton, we explan the workngs of our model s mechansm that generates the endogenous comovement of TFP growth across countres. We analyze the formula for TFP n steady-state, to focus on the effect of the extensve margn of trade. From equaton (14) t follows that total factor productvty depends on the number of domestc and foregn ntermedate goods used for fnal producton. Usng the average frm varables (27) and (28), we can show that TFP n steady-state n our model has two components. 18 The frst s an exogenous component determned by the aggregate productvty 18 In steady-state there s trade balance and the countres are symmetrc. 19

21 shock Z nt. The second s an endogenous component that depends on: () the number of ntermedate goods used for fnal producton, both domestc N D nt and foregn N X nt; () the average productvty of each of these ntermedate goods, respectvely z D n and z X nt; () relatve prces as derved from the terms of labor mc n t /Z n t mc nt /Z nt, the real exchange rate Q t, and the ceberg transport cost τ t ; and (v) the elastcty of substtuton θ between domestc and foregn goods. Factors () and () correspond to the extensve margn of trade, and () corresponds to the ntensve margn of trade. Factor () affects both margns. Thus, 19 the average TFP n country n,n ={H,F} can be wrtten as = Z θ 1 nt T FP nt = N D nt( z D nt ) θ 1+ N x n t ( zx n t )θ 1 τ 1 θ Q θ 1 t ( ωn t ω nt ) α ( r k n t r k nt ) 1 α(zn t Z nt ) 1 θ 1 ( L p nt Countres are symmetrc n steady-state; thus, mc nt = mc n t and Q t = 1. Furthermore, n steady state, Z nt = 1. The expresson for TFP becomes = ([ N D n T FP n = L nt ) α (45) ) D θ 1+ ( z n N x n ( z x n )θ 1 τ 1 θ]) ( θ 1 1 L p) α n (46) L n The mechansm that we propose n the model to reproduce the trade output comovement through endogenous TFP works as follows. A postve transtory aggregate productvty shock n the Home economy generates a demand supply spllover effect whereby domestc fnal producers demand more foregn ntermedate goods, ncreasng output n the Foregn economy. Ths s the channel present n the standard IBC model, but we know from Kose and Y (2006) that t alone cannot explan the trade output comovement observed n the data. Our model ncorporates an addtonal channel that operates by ncreasng TFP comovement across the tradng partners. The postve aggregate shock nduces entry n the domestc market because expected future profts of the potental entrants ncrease (.e., the domestc economy becomes more attractve to new busnesses). Frst, va the law of moton (31), there s an ncrease n N D H,t that ncreases the domestc component of TFP n the Home economy. Second, there s an ncrease n the number of exported varetes of the economy experencng the postve TFP shock, whch ncreases the endogenous component of TFP n the Foregn economy. The nternatonal transmsson effect s stronger the lower s the fxed export cost between the two countres. Low fxed export costs ncrease the steady-state value of endogenous TFP that s explaned by the extensve margn, whch n turn amplfes the transton effects of a postve productvty shock. One should bear n mnd that the effect of endogenous TFP on fnal output s both drect (through the producton functon) and ndrect (through a hgher demand for ntermedate goods that amplfes the demand supply channel, present n the standard IBC model). 19 See Appendx B for the dervaton. 20