The Trade Comovement Puzzle and the margins. of International Trade

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1 The Trade Comovement Puzzle and the margns of Internatonal Trade We Lao and Ana Mara Santacreu Frst Draft: September 2011 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 connecton between trade and output comovement. We propose that nternatonal technology dffuson through trade n varetes may be drvng ths comovement, by ncreasng the correlaton of TFP. Our hypothess s that busness cycles should be more correlated for countres that trade a wder varety of goods rather than larger quanttes of already traded goods. We fnd emprcal support for ths hypothess. When we decompose trade nto ts extensve and ntensve margns, we fnd that the extensve margn explans most of the trade-output and trade-tfp comovement. Ths fndng s strkng gven that the extensve margn only accounts for one thrd of total trade. We then develop a 3-country model of nnovaton and adopton, n whch TFP correlaton ncreases wth trade n varetes, and show wth a numercal exercse that the proposed mechansm ncreases busness cycle synchronzaton wth respect to tradtonal models. Contact: laowecarol@gmal.com; anamara.santacreu@nsead.edu. We apprecate the helpful comments of Antono Fatas, Ana Cecla Feler, Dens Gromb, Ayhan Kose, and semnar partcpants at Insead, NYU, Unversdad Autonoma de Madrd, Georgetown Unversty s McDonough School of Busness, and the Hong Kong Unversty of Scence and Technology. All remanng errors are ours. 1

2 1 Introducton Countres that trade more wth each other tend to have more correlated busness cycles (Frankel and Rose (1998)). Yet, tradtonal nternatonal busness cycle (IBC) models predct a much weaker connecton 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 TFP shocks are more correlated across countres that trade more wth each other. They also show that calbratons of the standard model ncludng ths fact are able to fully capture the output-trade comovement observed emprcally. However, the underlyng mechansms connectng trade and TFP comovement reman unexplaned. We propose that nternatonal technology dffuson through trade n varetes may be drvng TFP comovement. Indeed, a recent lterature shows that technology adopton s able to explan dfferences n TFP growth across countres (Broda, Greenfeld, and Wensten (2006) and Santacreu (2009)). In autarky, a country s TFP depends only on ts domestc technology (Romer (1990)). When, nstead, trade s allowed, TFP also depends on foregn technologes that are emboded n the mported goods. Hence, trade n varetes nduces a process of nternatonal dffuson through whch countres beneft from each others technologcal nnovatons. Based on ths premse, our hypothess s that busness cycles should be more correlated for countres that trade a wder varety of goods rather than larger quanttes of already traded goods. 2 We fnd emprcal support for ths hypothess. We decompose trade ntensty nto ts extensve and ntensve margns and run the Frankel and Rose (1998) regressons on 1 In standard IBC models, drven by productvty shocks, two opposte forces determne the tradeoutput comovement. Frst, more trade leads to more synchronzaton by ncreasng the demand for foregn products ( demand complementarty effect) Second, more ntegraton nduces a stronger reallocaton effect towards the most productve country, decreasng the synchronzaton ( resource-shftng effect). When markets are complete, the latter effect domnates. In addton to the standard channels, a thrd effect has an ambguous sgn: the terms of trade effect. An economy experencng a postve productvty shock benefts from lower prces and ncreases ts market share relatve to foregn economes, reducng the busness cycle synchronzaton. However, foregn economes also beneft from cheaper mports, whch ncreases the busness cycle synchronzaton. Whch effect domnates depends on the elastcty of substtuton between domestc or foregn ntermedate goods, as well as the share of mported ntermedate goods n the foregn economes. 2 Studyng the trade lberalzaton epsode n Inda n 1991, Goldberg, Khandelwal, Pavcnk, and Topalova (2009) and Goldberg, Khandelwal, Pavcnk, and Topalova (2010), show that mports of varetes generate statc and dynamc gans from trade, and ncrease productvty at the plant level. 2

3 both. 3 We fnd that the extensve margn explans most of the trade-output and trade- TFP comovement, whle the ntensve margn plays only a margnal role. Ths fndng s strkng gven that the extensve margn only accounts for one thrd of total trade. The results hold both at hgh and medum frequences. We then develop a three-country model of nternatonal busness cycles wth the followng features. 4 Frst, we assume trade n dfferentated ntermedate and captal goods. 5 Second, the dynamcs of TFP are manly drven by adopton of technologcal nnovatons (Santacreu (2009)). Ths s the key mechansm we propose to explan the trade comovement puzzle. Thrd, two types of costs nduce varatons n trade: ceberg transport costs, whch affect manly the ntensve margn of trade, and entry-regulatons fxed costs, whch affect manly ts extensve margn. Producton nvolves love-for-varety à la Ether (1982) to capture the effect of the extensve margn of trade on growth rates. In each country, a frm produces a non-traded fnal good usng domestc and foregn ntermedate goods (varetes). The effcency of fnal producton s determned by the number of varetes used. In each country, new varetes are ntroduced through an exogenous nnovaton process that allows for spllover effects: frms learn from both domestc and mported ntermedate goods (ths s the so called varety n varety out model n Goldberg, Khandelwal, Pavcnk, and Topalova (2009) and Goldberg, Khandelwal, Pavcnk, and Topalova (2010) ). Domestc nnovatons are mmedately avalable to domestc frms. However, foregn nnovatons must be adopted frst to become productve n the fnal sector, and adopton s modeled as an exogenous process, whch s affected by entry regulaton costs. A decrease n trade costs between two countres ncreases ther blateral extensve margn of trade, nducng technology transfers and an ncrease n ther TFP. In our model, two channels strengthen the correlaton of TFP growth between the two coun- 3 The extensve margn refers to how much trade s drven by the number of products, whereas the ntensve margn refers to the amount of each product that s traded. 4 The choce of a 3-country model s based on Kose and Y (2006) s argument that n a two-country model, one of the countres would be the rest of world and so the model would overstate the mpact of one country on the other. A 3-country model can also help to take the thrd-country effect nto account. 5 The structure of nternatonal trade n the last decade has shfted towards ntermedate and captal goods explanng a hgher share (78% of total trade corresponds to captal (14%) and ntermedate nputs (64%), and only 22% corresponds to consumpton goods). A smlar decomposton n consumpton, captal and ntermedate goods s obtaned when nstead of trade flows one consders the number of goods traded 3

4 tres: a drect channel workng through the tradtonal demand-supply spllover effect, and an ndrect channel that affects TFP through the nternatonal dffuson of technologes emboded n the varety of traded goods. Models that gnore the extensve margn of trade do not capture ths ndrect channel. Fnally, we perform a numercal exercse n whch we change the blateral trade ntensty by varyng transport costs (both varable and fxed). The exercse shows that modellng explctly the extensve margn of trade, generates hgher busness cycle synchronzaton than standard nternatonal bussness cycle models. Several strands of lterature have tackled the trade comovement puzzle. Frst, and as mentoned earler, Kose and Y (2006) document that TFP shocks are more correlated across countres that trade more wth each other, but they do not model explctly ths mechansm. Others emphasze the role of ntermedate nputs n ncreasng plant-level productvty after trade lberalzaton (e.g., Goldberg, Khandelwal, Pavcnk, Topalova (2009, 2010), Kugler and Verhoogen (forthcomng), Manova and Zhang (2011)). Our paper bulds upon ths lterature by proposng a mechansm through whch TFP s more correlated across pars of countres that trade a wder varety of goods. Our man nnovaton s to dsentangle the effect of the extensve margn and ntensve margn of trade on the comovement of TFP growth and output growth. Another strand of lterature studes the role of vertcal lnkages, both emprcally (D Govann and Levchenko (2009) and Bursten, Kurz, and Tesar (2008)), and theoretcally (Arkolaks and Ramanarayanan (2009)). Ths lterature also explores the role of traded ntermedate nputs. However, they study amplfcaton effects arsng from multple stages of producton. For example, D Govann and Levchenko (2009) fnd that sectors that trade more wth each other have more correlated cycles. Our analyss allows for a smple form of vertcal lnkages, and shows that ths channel alone cannot fully capture the trade-comovement observed emprcally. Fnally, Drozd and Nosal (2008) propose that a low elastcty of substtuton between domestc and foregn ntermedate goods at busness cycle frequences can partly explan the trade-output comovement. In ther model, frctons n the short-run to generate a low prce elastcty that s compatble wth the hgh long-run elastcty of substtuton 4

5 observed n the data. Ths model can capture 50% of the correlaton between trade and output comovement found n the emprcal studes. However, the emprcal evdence of ths mechansm s not well-establshed. The paper s organzed as follows. Secton 2 updates the Frankel and Rose regressons for output comovement up to 2009, for a sample that ncludes developed and developng countres. Secton 3 analyzes the relatonshp between output-comovement and TFP comovement and performs the Frankel and Rose regressons usng the blateral correlaton of TFP growth as the dependent varable. In Secton 4, we decompose the blateral trade ntensty on the extensve and ntensve margns of trade and regress both the output and TFP comovement varables on the two margns of trade. Secton 5 presents the model, whch s calbrated n Secton 6. Fnally, Secton 7 concludes. 2 Frankel and Rose revsted We frst update the Frankel and Rose (1998) regresson up to Our updated sample spans from 1980 Q1 to 2009 Q4, and covers 30 countres (20 OECD countres, and 10 developng countres). Countres n our sample consttute about 75% of world GDP and 73% of world trade (as of year 2009). 6 The country lst can be found n the Appendx. Followng Frankel and Rose (1998), we study the relatonshp between two key varables: blateral trade ntensty and blateral correlatons of real economc actvty. Two dfferent proxes are used to measure blateral trade ntensty. The frst one reles only on nternatonal trade data: 7 w t = (X,t + M,t )/(X t + X t + M t + M t ) where X,t s the total nomnal exports from country to country durng perod t, and X t s the aggregate nomnal exports to all countres from country. M denotes 6 We use the total PPP Converted GDP(G-K method, at current prces n mlons I$) collected from the Pen World Table to calcuate the GDP shares. For the trade shares, data are collected from IMF Drecton of Trade Statstcs database. 7 The blateral trade data used to calculate trade ntensty are obtaned from the Internatonal Monetary Fund s Drecton of Trade data set. 5

6 mports. 8 We calculate the blateral correlaton between real GDP n country and country to measure real actvty correlaton at tme t. For the OECD countres, the real GDP data are obtaned from OECD quarterly natonal account database (seres name: VOBARSA, Mllons of natonal currency, volume estmates, OECD reference year, annual levels, seasonally adusted). For the other countres, the quarterly real GDP data are taken from IMF Internatonal Fnancal Statstcs, the GDP Volume seres (2005=100). 9 The output data are transformed n three dfferent ways. Frst, we apply the Hodrck- Prescott ( HP ) flter (usng the tradtonal smoothng parameter of 1600) to the real GDP seres. Second, we take frst-dfferences of natural logarthms of the real GDP data to calculate the output growth rate. Fnally, we apply the Band-Pass flter on the real output to remove the hgh frequency varatons but retan frequences between 32 and 120 quarters. The frst two ways to de-trend the varables am to capture busness cycle frequences, whle the thrd ams to capture medum-term busness frequences (Comn and Gertler (2006)). 10 After approrately transformng the data, the blateral correlatons for real actvty are estmated between two countres over a gven span of tme. We begn by splttng our sample perod nto sx subsamples of 5 years each, between 1980 and For 30 countres, there are a total of 2610 observatons (435 n the cross secton and 6 n the tme seres). Takng the output growth rate as an example, we estmate the cor- 8 An alternatve ndex of trade ntenstes s calcuated as w 2 t = (X,t + M,t )/(GDP t + GDP t ) The nomnal GDP data (annul ndex n natonal currency) are collected from IMF Internatonal Fnancal Statstcs. Because the trade data are n US dollars, we use offcal exchange rate(perod average; when offcal exchange rate s not avalable, market exchange rate s used nstead) to transform the nomnal GDP n natonal currency nto USD denomnated data. It s dffcult to say whch ndexs more approprate to measure blateral trade ntenstes.therefore we conduct our study usng both measures. Our results are robust to both measures of trade ntensty. We only report the results for models usng w 1 t n ths paper. The tables usng w 2 t as regressors are avalable upon request. 9 For earler sample perods, quarterly data are not avalable for some emergng markets. We then nterpolate annual ndex (also from IFS) assumng real GDP s constant every quarter wthn a year. For robustness check, we try regressons usng shorter sample perod durng whch quarterly GDP data are avalable for all economes, and the results are consstent wth what we obtan from the full sample analyss. The results are avalable upon request. 10 The motvaton for usng the Band-pass flter wll become more clear later. 11 To accommendate possble measurement error, we also calculate parwse output correlatons for the entre sample perod. The regresson results are very smlar to what we obtaned usng 5-year correlatons. The tables are avalable upon request. 6

7 relaton between output growth for two countres and over each subsample perod as corr( y t, y t ). The nternatonal trade data s at annual frequency, thus the trade ntenstes are calculated for each year, then we take natural logarthms. To match the frequency of blateral output correlatons, we take average of log trade ntenstes n each of the sx subsamples. We run the followng regresson, for the three measures of output (growth rates, HP-flter and BP-flter): corr( y t, y t ) = α + βlog(w t ) + ε t The results are broadly consstent wth the lterature and robust to the ncluson of nstrumental varables. 12 Table 1 collects the results for updated Frankel&Rose regresson usng dstance as IV. We fnd that doublng the sze of trade ntensty leads to a 0.05 hgher correlaton of output growth (0.12 HP-fltered output and 0.15 BP-fltered output). Table 1. Output correlaton and the trade ntensty:iv (2SLS) regresson Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(y hp,y hp ) Coef. corr( y, y ) Coef. corr(y bp,y bp ) Coef. log(w ) 0.139*** log(w ) 0.081*** log(w ) 0.240*** (0.009) (0.006) (0.015) Constant 1.095*** Constant 0.634*** Constant 1.506*** (0.052) (0.033) (0.085) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). Use log dstance as IV. 3 Trade comovement and TFP In ths secton we re-run Frankel and Rose (1998) regresson usng blateral correlatons of TFP as the dependent varable. Kose and Y (2006) fnd that TFP shocks are more correlated across countres that trade more wth each other. 12 The natural nstrument for trade ntensty, as used by the lterature, s dstance. 7

8 Fgure 1 shows the correlaton between blateral correlaton of TFP growth and our measuere of trade ntensty. Panel A shows a strong correlaton between the two varables. We splt the sample of countres n three dfferent ways: North-North, North- South and South-South. The relaton s stronger for North-South trade (Panel B). We then test emprcally whether countres that trade more wth each other have more correlated TFP. TFP n our paper s calculated as the Solow resdual n a standard Cobb-Douglas producton functon. For each country, takng logs of the producton functon: log(z t ) = log(y t ) α log(n t ) (1 α)log(k t ) (1) Where z t denotes the TFP, y t s the real ncome, n t measures the total employment, and k t represents the real physcal captal stock. We take the gross-fxed captal formaton data from the IFS and employment ndex from IFS and OECD database. 13 The physcal captal s constructed usng the perpetual nventory method wth a constant quarterly deprecaton of 2.5%, assumng the ntal captal stock s zero. The labor share of ncome n GDP, α, s set to be 0.64 for ndustralzed countres and 0.5 for emergng markets followng the lterature. 14 We replcate the steps from Secton 2 and transform TFP n three dfferent ways: quarter-to-quarter growth rates, HP- fltered TFP and BP-fltered TFP. Then we estmates the blateral correlatons of the TFP for country and durng each of the sx subsamples. We run the followng regresson, for the three measures of TFP (growth rates, HP-flter and BP-flter): corr( T FP t, T FP t ) = α + βlog(w t ) + ε t The results are consstent wth the lterature and robust to the ncluson of nstrumen- 13 For OECD countres, the gross-fxed captal formaton data are seres named VOBARSA(Mllons of natonal currency, volume estmates, OECD reference year, annual levels, seasonally adusted); the employment data s from OECD Labour Force Statstcs (MEI) Dataset (All persons, Index OECD base year 2005=100, s.a.). For other countres, the data are from IFS database. The gross-fxed captal formaton data are deflated by GDP deflator (2005=100, also from IFS database) to obtan the real captal formaton data. For countres and perods when quarterly data are not avalable, we nterpolate annual ndex assumng constant volume every quarter wthn a year. For robustness check, we fnd excludng the perods when quarterly data are not avalable does not affect our results. 14 As a robustness check, we also calculate TFP for emergng markets usng the same labor share as for ndustralzed couantres. It does not affect our results. 8

9 tal varables. 15 Quanttatvely, the correlaton between and trade ntensty s stronger at medum term frequences (BP-flter measure) than at busness frequences. Ths fndng suggets that to match quanttatvely the trade comovement found by Frankel and Rose (1998), we need mechansms that operate manly n the medum term. Table 2. TFP correlaton and the trade ntensty Panel 1: HP-fltered TFP Panel 2: TFP growth Panel 3: BP-fltered TFP corr(t f p hp,t f p hp ) Coef. corr( t f p, t f p ) Coef. corr(t f p bp,t f p bp ) Coef. log(w ) 0.064*** log(w ) 0.043*** log(w ) 0.131*** (0.008) (0.005) (0.012) Constant 0.563*** Constant 0.386*** Constant 1.274*** (0.046) (0.030) (0.067) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). Use log dstance as IV. 4 Trade comovement and the margns of trade In ths secton, we depart from standard emprcal studes on the totaltrade comovement puzzle, and dsentangle the effect of the blateral extensve and ntensve margns of trade on our two measures of real actvtes: GDP and TFP. As n prevous sectons, we explore the relatonshp, both at busness frequences (usng growth rates and the HPflter) and at medum frequences (usng the BP-flter). It has been argued by several authors n the lterature that the EM of trade does not vary sgnfcantly at the busness cycle frequency (Kehoe and Ruhl (2003)). For that reason, we follow Comn and Gertler (2006), and remove the hgh frequency varatons of the data. We use blateral trade data at the 6-dgt level of dsaggregaton (Harmonzed System) from the UNcomtrade database and calculate the two margns of trade followng two dfferent methodologes. Frst we perform the Hummels and Klenow (2005) decomposton; then as robustness checks we count the number of varetes as the measure 15 Drozd and Nosal (2008) replcate a smlar regresson 9

10 for the extensve margn of trade. The two sets of measures delver smlar results. Hummels and Klenow (2005) use Feenstra and Markusen (1994) methodology to ncorporate new varetes nto a country s mport prce ndex when preferences are C.E.S. In ths settng, the mport prce ndex s effectvely lowered when the set of goods expands. When comparng export prces for a country relatve to a reference country requres an adustment for the sze of each exporter s goods set. The adustment used by Hummels and Klenow (2005) s the extensve margn. For the case when s shpments to are a subset of k s shpments to, the extensve margn s defned as : EM = m I p k m x k m m I p k m x k m where I s the set of observable categores n whch country has postve exports to. The reference country k (whch n our case s the rest of the world) has postve exports to n all I categores. The extensve margn s a weghted count of categores relatve to k categores. If all categores are of equal mportance, then the extensve margn s smply the fracton of categores n whch exports to (categores are weghted by ther mportance n k exports to ). 16 The correspondng ntensve margn compares nomnal shpments for and k n a common set of goods. It s gven by: IM = m I p m x m m I p k m x k m (2) IM equals nomnal exports relatve to k nomnal exports n those categores n whch exports to. The rato of country exports to wth respect to country k exports to equals the product of the two margns. OV = EM IM (3) where OV s the overall trade from country to country relatve to trade from the 16 Ths s dfferent than usng count data to compute the EM and IM. We wll use count data for robustness check later, and we conclude that the results are very smlar. 10

11 rest of the world to country. Takng logs, we obtan the followng expresson log(ov ) = log(em ) + log(im ) (4) We use the formulas above to compute the contrbuton of both margns of trade to overall trade and obtan that, for the average country, the IM accounts for more than 75% of the overall trade. Next, we classfy the 5-dgt goods n 3 categores: consumpton, ntermedate and captal goods, and regress the correlaton of our three measures of output aganst the log of the rato of country to country k exports to for ntermedate and captal goods. ρ( y t, y t ) = β OV log(ov,t ) + ε m,t (5) Snce trade s an endogenous varable, we run nstrumental varables regressons, usng dstance as the nstrument for overall trade. Our results are consstent wth the results obtaned n the updated Frankel and Rose (1998) regresson. Table 3. Instrumental varables (2SLS) regresson Only use captal and ntermedate goods to calculate OV Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(y hp,y hp ) Coef. corr( y, y ) Coef. corr(y bp,y bp ) Coef. log(ov ) 0.115*** log(ov ) 0.067*** log(ov ) 0.197*** (0.006) (0.004) (0.010) Constant 0.851*** Constant 0.492*** Constant 1.084*** (0.028) (0.017) (0.045) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). Use log dstance as IV. We then analyze the contrbuton of the dfferent margns of trade on output comove- 11

12 ment by runnng the followng regressons: ρ( y t, y t ) = β EM log(em,t ) + β IM log(im,t ) + ε,t (6) We need to fnd nstruments for the extensve and ntensve margns of trade. In a trade model wth varable and fxed trade costs, the IM s manly affected by the ceberg transport cost, whereas the EM s manly affected by the fxed cost to enterng a new market. Therefore, we use dstance as the nstrument for the ntensve margn. For the extensve margn, we followhelpman, Meltz, and Rubnsten (2008) who use countrylevel data on the regulaton costs of frm entry, collected and analyzed by Dankov, La Porta, Lopez-de-Slanes, and Shlefer (2002). These entry costs are measured va ther effects on the number of days, the number of legal procedures, and the relatve cost (as percent of GDP per capta) needed for an entrepreneur to legally start operatng a busness. Our ndcator of par-wse trade costs n constructed by addng both the mportng and exportng entry regulaton costs. In partcular, we use the relatve costs as a percentage of GDP per capta, so that these cost measures can be compared across countres. 17 By constructon, these blateral varables reflect regulaton costs, that predomnantly affect the fxed costs of trade and should not depend on the volume of exports to a partcular country. We then we run an IV regresson of the correlaton of both TFP and GDP on the extensve and ntensve margns of trade. We fnd that the EM has a postve and sgnfcant effect on the comovement of busness cycles across pars of countres for the three measures of output, whereas the IM has a lower and non-sgnfcant effect. The results are stronger when the BP-flter s used n the analyss. Indeed, the coeffcents double wth respect to the case n whch HP-fltered or growth GDP s used, ndcatng a stronger relatonshp between busness cycle synchronzaton and nternatonal trade at medum-term frequences. 17 Helpman, Meltz, and Rubnsten (2008) use as an alternatve the number of days and procedures as a measure of entry costs, but fnd that the ontly defned ndcator varable had substantally more explanatory power. In addton, entry regulaton costs could be correlated wth the varable trade cost dstance. However, Helpman, Meltz, and Rubnsten (2008) add country fxed effects n the frst stage regresson and show that ths s not the case. 12

13 Table 4. Instrumental varables (2SLS) regresson wth EM and IM Usng Klenow and Hummels decomposton method Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(y hp,y hp ) Coef. corr( y, y ) Coef. corr(y bp,y bp ) Coef. log(em ) 0.309*** log(em ) 0.196*** log(em ) 0.593*** (0.042) (0.027) (0.036) log(im ) log(im ) log(im ) (0.021) (0.013) (0.036) Constant 0.644*** Constant 0.354*** Constant 0.662*** (0.059) (0.037) (0.101) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). log dstance and log of entry cost as IVs. Smlarly, we nvestgate the contrbuton of the dfferent margns of trade on TFP comovement by runnng the followng regresson: ρ( T FP t, T FP t ) = β EM log(em,t ) + β IM log(im,t ) + ε,t (7) Agan, we use ceberg transport cost and fxed cost as nstrumental varables n above regresson. Smlar to what we fnd from output-trade comovement analyss, the results show that only the extensve margn has a postve and sgnfcant effect on the comovement of TFP across borders, whle the IM has a negatve or a non-sgnfcant effect Smlar results on the effect of changes of trade costs on the dfferent margns of trade have been obtaned by Dutt, Mhov, Van Zandt, and Ossa (2011) n the context of the WTO. They show that the effect s almost exclusvely on the extensve product margn of trade, whle t has a neglgble or even a negatve mpact on the ntensve margn. 13

14 Table 5. TFP correlaton on EM and IM Usng Klenow and Hummels decomposton method Panel 1: HP-fltered TFP Panel 2: TFP growth Panel 3: BP-fltered TFP corr(t f p hp,t f p hp ) Coef. corr( t f p, t f p ) Coef. corr(t f p bp,t f p bp ) Coef. log(em ) 0.275*** log(em ) 0.181*** log(em ) 0.557*** (0.037) (0.024) (0.062) log(im ) * log(im ) * log(im ) ** (0.018) (0.012) (0.030) Constant 0.215*** Constant 0.154*** Constant 0.568*** (0.051) (0.034) 0.568*** Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). log dstance and log of entry cost as IVs. The emprcal evdence suggests that to understand the connectons between nternatonal trade and busness cycle synchronzaton we should look at the extensve margn of trade. At the same tme, we need a model n whch ceberg transport costs and fxed costs generate the necessary varaton for the IM and EM of trade flows. 5 The model 5.1 Fnal Producton In each country = 1,...,I, a perfectly compettve frm, henceforth fnal producer, uses traded ntermedate goods, both domestc and foregn, to produce a non-traded fnal good. We ntroduce the standard Armngton assumpton of goods beng dfferentated by source of exports, that s, countres exogenously specalze n dfferent sets of goods. As t s standard n the lterature, we defne a varety n as an ntermedate good produced n country n. Intermedate products are combned accordng to the CES producton functon 14

15 Y t = ( M n=1 ˆ A nt =0 ) σ (b n t)(xn t) σ 1 σ 1 σ d where Y t s the quantty of fnal good produced n country, A nt s the number of ntermedate goods that country mports from country n, b n t are the so-called Armngton weghts and represent the share of country s spendng on ntermedate good from country n, xn t s the quantty of varety n mported by country, σ > 1 s the elastcty of substtuton across varetes (whch are perfect substtutes when σ ). The fnal producer chooses x n t to maxmze hs proft Π t = P t Y t M ˆ A nt n=1 =0 p n tx n td where p n t s the prce of varety n that s sold n country, and P t s the prce ndex for the fnal good, whch takes the CES form P t = ( I n= ˆ A nt =1 (b n t) σ ( ) 1 1 σ p ) 1 σ n t d and b n t s the expendture share n varety n. Ths mples the followng demand for varety n x n t = (b n t) σ ( p n t P t Total spendng by country on varety n s ) σ Y t 5.2 Intermedate Producton In each country n = 1,..., I a contnuum of monopolstcally compettve frms produce a good usng labor and captal accordng to a Cobb-Douglas producton functon y n t = (k n t ) α (l n t ) 1 α where y n t s the quantty of good that country n produces, k n t s the amount of captal that s rented to the households, and l n t s the amount of labor employed to produce that quantty, wth the share of captal on output α (0,1). Note that all ntermedate 15

16 producers n a country have the same productvty, rrespectve of the good they produce. The frm chooses amount of l n t and k n t to mnmze w nt l n t + R nt k n t s.t y n t = (k n t ) α (l n t ) 1 α To solve the problem, assume L = w nt l n t + R nt k n t λ[y n t (k n t ) α (l n t ) 1 α ] F.O.C. L l n t : w nt λ(1 α) y n t l n t = 0 L k n t : R nt λα y n t k n t = 0 Where λ = mc n t Therefore w nt = mc n t (1 α) y n t l n t R nt = mc n t α y n t k n t and mc n t = ( w nt 1 α )1 α ( R nt α )α Intermedate producers take the demand by fnal producers, determned n the last secton, and set a prce that s a constant mark-up over that cost. Prces can dffer across countres. Markets are segmented due to ceberg transport costs: for products shpped from country n to n, the transport cost s dn > 1, wth d = 1. We use mgc n t to 16

17 denote the margnal cost, mc n t = d nmc n t Frm n country n wll maxmze π n t = (P n t mc n t)x n t s.t. x n t = ( ) p σ n t Y t P t F.O.C x n t + (P n t mc n t) x n t P n t = 0 Where Therefore x n t P n t = σ(p n t) σ 1 P σ t Y t P n t = σ σ 1 mc n td n 5.3 Emboded Technologcal Progress: Innovaton and Adopton Innovaton: Let Z nt denote the stock of domestc developed technology n country n, also the total number of ntermedate producers n country n at tme t, and Z wt = M n=1 Z nt the total number of technology avalable n the whole world. New technologes arrve exogenously to the economy accordng to the followng process: Z nt+1 = Z nt (1 + ā)exp(ε z nt) and ε z nt = ρ n ε nt 1 + u nt Notce that Z nt+1 Z nt -1 grows at ā n steady state. 17

18 where T nt s the total number of technologes avalable for producton n country (nnovators learn from what they have produced and from what they have mported), and u nt s a whte nose. In steady state, we wll have g z = T nt Z wt ā Adopton: New technologes become productve only when they are adopted. A nt = ε nt(z nt A nt) We assume that the adopton process s nstantaneous wthn a country but t takes tme across countres. That s, once a new technology arrves to the economy, t s mmedately ready to be used by the fnal producers n that country. However the dffuson of technologes to a foregn country follows a random process εnt, whch s the rate at whch a good that has been nvented by country n s adopted by country, ε nt = ε n A nt Z nt exp(e nt) where ε n s a country-par specfc parameter that reflects entry regulaton costs or barrers to adopton. A hgher value for ths parameters mples lower regulaton costs. In steady state, the rate of dopton s determned unquely by the entry regulaton costs. In steady state, g a = A nt+1 A nt A nt = ( A nt )( Z nt Z nt A 1) = 1 A nt nt Z nt Therefore g a = g z 5.4 Households In each country = 1,...,M, a representatve household consumes a non-traded fnal good, supples labor, captal and saves. The household maxmzes the lfe-tme expected 18

19 utlty functon subect to the budget constrant U t (C t,c t+1,...) = E t s=t β s (log(c s ) Lψ+1 s ψ + 1 ) P t C t + P k ti t = ω t L t + Π T t + R t K t where C t s consumpton, β (0,1) s the dscount factor, P t s the prce ndex, ω t s the wage, L t s labor supply, Π T t are the frms profts, R t s the rental prce of captal, P k t s the prce of captal, K t s the supply of captal, whch s accumulated through the standard law of moton K t = (1 δ)k,t 1 + I t Let L = s=t β s (log(c s ) Lψ+1 s ψ + 1 ) λ t[ω t L t +Π T t +R t K t P t C t Q t (K t (1 δ)k,t 1 )] F.O.C. C,t+1 C t = λ t λ t+1 P t P,t+1 L ψ t = λ t w t Q t = λ t+1 λ t [R t+1 + (1 δ)q t+1 ] 19

20 5.5 Market Clearng Condtons Resource Constrant Fnal output s used for consumpton, nnovaton and adopton. Y t = C t + I t Trade Balance There s fnancal autarky n the model. Therefore, trade s balanced every perod, and the total value of exports n one country has to equal the total value of mports. M ˆ A nt =1 =0 p n tx n td = Intermedate goods market clearng Labor market clearng y n t = L nt = M ˆ A nt =1 =0 ˆ Znt =0 M ˆ An t p n tx n td. n=1 =0 x n td l n t d 6 The Equatons n equlbrum 6.1 Equlrum Z nt x nt = M =1 A ntx nt (8) x nt = ( P nt P t ) 1 σ X t (9) W nt l nt = (1 α)x nt σ 1 σ (10) R nt k nt = α x nt σ 1 σ (11) 20

21 mc nt = ( w nt 1 α )1 α ( R nt α )α (12) P nt = σ σ 1 mc ntd n (13) X nt = C nt + I nt (14) 1 P nt I nt = K n,t+1 (1 δ)k nt (15) M n A ntx nt = M n A n tx n t (16) Z nt = Z nt ε z nt (17) A nt = ε nt(z nt A nt) (18) εnt = ε n A nt exp{e Z nt} (19) nt P nt = ( M =1 A n t(p n t) 1 σ ) 1 1 σ (20) L ψ nt = w nt C nt (21) C n,t+1 C nt = β R n,t+1 + (1 δ)p n,t+1 P nt (22) L nt = Z nt l nt (23) 21

22 K nt = Z nt k nt (24) 6.2 Shock Process ε z nt = ρ z nε z nt 1 + uz nt + ā (25) e nt = ρ n e n,t 1 + u nt (26) Both u z nt and u nt are normally dstrbuted. 7 Experments In ths secton, we perform a smple numercal exercse to understand how the mechansms of our model work. Ths s not a proper calbraton exercse, whch we wll explore n a more complete verson of the paper. Instead, we now consder a verson wth exogenous growth, n whch the number of nnovatons and adopted varetes remans constant n steady state. As a result, n steady state every country adopts all the varetes nnovated n the world, and there s convergence both n the levels and n the growth rates across countres. We follow prevous studes and set values for the standard parameters (σ, φ,δ, α), and then we vary the parameters correspondng to ceberg transport costs, τ = d 1, and the rate of adopton ε between two countres (hgher ε mples lower fxed entry cost). Changes n these parameters nduce varatons on both margns of trade: the ceberg transport cost affects manly the ntensve margn, whle the rate of adopton (the nverse of entry cost)affects manly the extensve margn of trade. We compute changes n the correlaton of GDP growth per par of countres, changes n the blateral trade ntensty and the correspondng changes n the blateral extensve and ntensve margns of trade that are nduced by changes n ether the ceberg transport costs (τ) or the fxed entry costs (nverse of the adopton rateε). In Table 6, we see that reductons n trade costs, ether ceberg transport costs or fxed entry costs, both ncrease the par-wse correlaton of output growth and the blateral trade ntensty. Changes n 22

23 τ (rows) affect manly the ntensve margn of trade, whereas changes n ε (columns) affect manly the extensve margn of trade. Table 6. Decrease n transport costs ε = 0.2 ε = 0.6 ε = 0.8 Corr_y TI EM IM Corr_y TI EM IM Corr_y TI EM IM τ = τ = Table 7 shows the effect of a decrease n the ceberg transport costs from τ = 0.2 to τ = 0, and for dfferent rates of technology adopton, measured by ε. For a gven rate of adopton ε, both the correlaton of output growth and the trade ntensty ncrease, but manly through the ntensve margn of trade. The extensve margn of trade also ncreases, and the effect s stronger for hgher rates of adopton. Ths suggests that pars of countres wth faster adopton rates (hgher ε) wll experence hgher ncreases n the output growth comovement after a decrease n transport costs. Table 7. Decrease n ceberg transport costs (τ = 0.2 to τ = 0) Corr_y TI EM IM ε = ε = ε = In Table 8, we analyze the effect of a decrease n entry regulaton costs (.e. an ncrease n the rate of adopton) from ε = 0.2 to ε = 0.6, for dfferent values of the ceberg cost. Both the par-wse correlaton ncreases and trade ntensty ncrease, manly drven by the extensve margn of trade. The mpact seems to be ndependent of the level of ceberg costs. Changes n trade nduced by changes n the entry regulaton costs have an mportant effect on synchronzng busness cycles through the extensve margn. Models that gnore ths margn mss an mportant channel through whch cycles are synchronzed across countres. 23

24 8 Concluson Table 8. Increase n adopton rate ε = 0.2 to ε = 0.6 Corr_y TI EM IM τ = τ = TO BE WRITTEN Appendx A Solvng the model We re-wrte the model n real terms so that n each country the nomnal varables are normalzed by P Nt The equatons to solve the model are: 1. Demand by fnal producers (Y t ): y nt = (b nt) σ ( p n t P t ) σ Y t (where p nt s really p nt P 3t and P t P 3t 2. Prce of ntermedate producers (p nt): p nt = σ σ 1 (mc ntd n) 3. Margnal cost for ntermedate producers (mc nt): mc n t = ( Rk nt α )α ( w nt 1 α )1 α 4. Demand for captal by ntermedate producers (R k nt): p nty nt = αr k ntk nt 5. Total demand for captal (k nt): K nt = A ntk nt 6. Demand for labor by ntermedate producers (w nt ): p nty nt = (1 α)w nt l nt 7. Total demand for labor (l nt): L nt = A ntl nt 8. Investment (K nt ): I t = K t (1 δ)k,t-1 9. Output (I nt ): Y t = C t + I t 24

25 10. Consumpton (C nt ): 1 C,t+1 β C t = P t P,t+1 R,t Labor supply (L nt ): P t C t = w t L φ t 12. Law of moton for prce of captal (Pt k ): Pk t = Rk,t+1 +Pk,t+1 R t 13. Non-arbtrage condton (R t ): R t = R k t 14. Trade balance (we get the prces from here) (P t ): I =1 A nt p ntxnt = I n=1 An t pn t xn t ; Prces: P t = ( I n= A ( )) 1 nt p 1 σ nt Prces are determned by the trade balance equaton 15. Innovaton (Z t ): Z t = α R T,t 1exp(g z ε t ) 16. Adopton (A nt ): A nt = ε nt (Z nt A nt ) wth ε nt = ε n exp(u nt ) We need to wrte the model n a statonary way. In steady state, ε nt s constant, and Z nt and A nt grow at the same rate g z. Consumpton and nvestment grow at the same rate of fnal output, whch grows at A nt Z nt = ε n g a +ε n Z (1+g z ) T = α R σ σ 1 g z. Other ratons n steady state are: I K = g k + δ R = 1+g c β g k = g y Algorthm to compute relatve prces: From prce equaton, demand for ntermedate producers and trade balance equaton. Statonarzed varable to use: P ntx nt P t Y t A nt Z 3t 25

26 We are gong to start wth an exogenous growth model, that s, we assume that the number of varetes remans constant n steady state, whch mples that n steady state all countres end up adoptng all the varetes. Ths s easy to do the log-lnearzaton of the model because the only trend that we need to take care of s the dsemboded technology trend. Log-lnearzed model and Steady State: 1. x nt = (1 σ)(p nt p t ) 2. p nt = mc nt + d nt 3. x nt = r k nt + k nt 4. K nt = (k nt + a nt ) A nk n K n 5. x nt = w nt + a nt 6. L nt = (l nt + a nt ) A nl n L n 7. (g k + δ)i nt = (1 + g k )K n,t+1 + (1 δ)k nt 8. c,t+1 c t + g t = r t w 3t + w 3,t+1 9. c t = w t + φl t 10. r t = r k t 11. r t + P k R p k t = rk,t+1 + P k R p k,t+1 wth P k R k = 1 R 1 and R = 1+g c β 12. z,t+1 = t t + ε t 13. t t = z t + (I 1) n a nt 14. a n,t+1 = a nt + ε n (z nt a nt ) A 15. n x n A P Y (a nt + x nt ) = n x n n P n Y n (a nt + x nt ) P ny n P Y 16. Algorthm based on: expresson for P and expresson for x n and trade balance equaton. 26

27 Appendx B: Tables 27

28 Table 9. Instrumental varables (2SLS) regresson wth EM and IM Usng Count Data Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(y hp,y hp ) Coef. corr( y, y ) Coef. corr(y bp,y bp ) Coef. log(em ) 0.348*** log(em ) 0.229*** log(em ) 0.701*** (0.063) (0.041) (0.108) log(im ) log(im ) log(im ) * (0.056) (0.036) (0.095) Constant 1.528*** Constant 0.954*** Constant 2.502*** (0.166) (0.108) (0.284) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). log dstance and log of entry cost as IVs. Table 10. TFP correlaton on EM and IM Usng Count Data Panel 1: HP-fltered TFP Panel 2: TFP growth Panel 3: BP-fltered TFP corr(t f p hp,t f p hp ) Coef. corr( t f p, t f p ) Coef. corr(t f p bp,t f p bp ) Coef. log(em ) 0.362*** log(em ) 0.241*** log(em ) 0.744*** (0.061) (0.041) (0.100) log(im ) *** log(im ) *** log(im ) *** (0.054) (0.036) (0.088) Constant 1.303*** Constant 0.867*** Constant 2.759*** (0.162) (0.107) (0.262) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). log dstance and log of entry cost as IVs. 28

29 Table 11. Instrumental varables (2SLS) regresson wth EM and IM Usng Klenow and Hummels decomposton method Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(y hp,y hp ) Coef. corr( y, y ) Coef. corr(y bp,y bp ) Coef. log(em ) +log(em ) 0.155*** 0.098*** 0.296*** (0.029) (0.018) (0.049) log(im ) +log(im ) (0.014) (0.009) (0.024) Constant 0.644*** Constant 0.354*** Constant 0.662*** (0.080) (0.051) (0.136) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). log dstance and log of entry cost as IVs. 29

30 Table 12. Instrumental varables (2SLS) regresson wth EM and IM Usng Klenow and Hummels decomposton method Panel 1: HP-fltered TFP Panel 2: TFP growth Panel 3: BP-fltered TFP corr(t f p hp,t f p hp ) Coef. corr( t f p, t f p ) Coef. corr(t f p bp,t f p bp ) Coef. log(em ) +log(em ) 0.138*** 0.091*** 0.279*** (0.025) (0.017) (0.042) log(im ) +log(im ) * (0.012) (0.008) (0.021) Constant 0.215** 0.154** 0.568*** (0.071) (0.047) (0.118) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). log dstance and log of entry cost as IVs. Table 13. Instrumental varables (2SLS) regresson wth EM and IM Usng count data Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(y hp,y hp ) Coef. corr( y, y ) Coef. corr(y bp,y bp ) Coef. log(em ) +log(em ) 0.355*** 0.237** 0.736*** (0.106) (0.073) (0.194) log(im ) +log(im ) * * * (0.108) (0.074) (0.197) Constant 2.097*** Constant 1.340*** Constant 3.731*** (0.440) (0.301) (0.805) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). log dstance and log of entry cost as IVs. 30

31 Table 14. Instrumental varables (2SLS) regresson wth EM and IM Usng count data Panel 1: HP-fltered TFP Panel 2: TFP growth Panel 3: BP-fltered TFP corr(t f p hp,t f p hp ) Coef. corr( t f p, t f p ) Coef. corr(t f p bp,t f p bp ) Coef. log(em ) +log(em ) 0.365** 0.249** 0.793*** (0.118) (0.080) (0.221) log(im ) +log(im ) * * ** (0.120) (0.081) (0.224) Constant 1.870*** 1.269*** 4.095*** (0.488) (0.331) (0.914) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). log dstance and log of entry cost as IVs. Table 15. Output correlaton and the trade ntensty normalzed by GDP: IV (2SLS) regresson Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(y hp,y hp ) Coef. corr( y, y ) Coef. corr(y bp,y bp ) Coef. log(w ) 0.123*** log(w ) 0.071*** log(w ) 0.213*** (0.006) (0.004) (0.010) Constant 0.977*** Constant 0.565*** Constant 1.304*** (0.030) (0.019) (0.055) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). Use log dstance as IV. Trade ntenstes are measured by w 2 t = (X,t + M,t )/(GDP t + GDP t ). 31

32 Table 16. Output correlaton and the trade ntensty normalzed by GDP: IV (2SLS) regresson Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(t f p hp,t f p hp ) Coef. corr( t f p, t f p ) Coef. corr(t f p bp,t f p bp ) Coef. log(w ) 0.057*** log(w ) 0.038*** log(w ) 0.117*** (0.005) (0.003) (0.008) Constant 0.510*** Constant 0.349*** Constant 1.164*** (0.027) (0.018) (0.044) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). Use log dstance as IV. Trade ntenstes are measured by w 2 t = (X,t + M,t )/(GDP t + GDP t ). Table 17. Output correlaton and the trade ntensty:iv (2SLS) regresson Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(y hp,y hp ) Coef. corr( y, y ) Coef. corr(y bp,y bp ) Coef. log(w ) 0.186*** 0.121*** 0.220*** (0.011) (0.007) (0.020) Constant 1.331*** 0.845*** 1.363*** (0.060) (0.037) (0.111) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). Use log dstance as IV, trade ntensty s normalzed by total blateral trade, and averaged over Blateral correlatons are calculated usng sample from 1985 to

33 Table 18. TFP correlaton and the trade ntensty:iv (2SLS) regresson Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(t f p hp,t f p hp ) Coef. corr( t f p, t f p ) Coef. corr(t f p bp,t f p bp ) Coef. log(w ) 0.091*** 0.064*** 0.108*** (0.011) (0.008) (0.014) Constant 1.306*** 1.196*** 1.431*** (0.063) (0.045) (0.079) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). Use log dstance as IV, trade ntensty s normalzed by total blateral trade, and averaged over Blateral correlatons are calculated usng sample from 1985 to Table 19. Instrumental varables (2SLS) regresson wth EM and IM Usng Klenow and Hummels decomposton method Panel 1: HP-fltered output Panel 2: Output growth Panel 3: BP-fltered output corr(y hp,y hp ) Coef. corr( y, y ) Coef. corr(y bp,y bp ) Coef. log(em ) 0.232*** 0.167*** 0.205** (0.035) (0.023) (0.063) log(im ) (0.017) (0.011) (0.031) Constant 0.662*** Constant 0.375*** Constant 0.721*** (0.099) (0.065) (0.176) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). log dstance and log of entry cost as IVs. Trade ntensty s normalzed by total blateral trade, and averag over Blateral correlatons are calculated usng sample from 1985 to

34 Table 20. Instrumental varables (2SLS) regresson wth EM and IM Usng Klenow and Hummels decomposton method Panel 1: HP-fltered TFP Panel 2: TFP growth Panel 3: BP-fltered TFP corr(t f p hp,t f p hp ) Coef. corr( t f p, t f p ) Coef. corr(t f p bp,t f p bp ) Coef. log(em ) 0.266*** 0.211*** 0.244*** (0.035) (0.026) (0.041) log(im ) *** *** * (0.017) (0.013) (0.020) Constant 0.651*** 0.686*** 0.808*** (0.098) (0.074) (0.114) Note: Standard errors n parentheses. Sgnfcance at the 1% (5%) level s ndcated by ( ). log dstance and log of entry cost as IVs. Trade ntensty s normalzed by total blateral trade, and averag over Blateral correlatons are calculated usng sample from 1985 to

35 Table 21. Country Lst Developed Countres Australa Austra Canada Denmark Germany Fnland France Greece Ireland Italy Developng Countres Chna Hong Kong, SAR Inda Argentna Brazl Korea Phlppnes Sngapore Indonesa Malaysa Japan Netherlands New Zealand Norway Portugal Span Sweden Swtzerland Unted Kngdom Unted States Source: UN classfcaton 35

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