Multinational Firms and International Business Cycle Comovement

Transcription

1 Multnatonal Frms and Internatonal Busness Cycle Comovement Javer Cravno Unversty of Mchgan Andre A. Levchenko Unversty of Mchgan NBER and CEPR June, 2014 PRELIMINARY Abstract We nvestgate how multnatonal frms spread economc shocks across countres usng a large frm-level dataset that contans ownershp nformaton for 8 mllon frms n 34 countres. We use these data to document two novel emprcal patterns. Frst, foregn afflate and headquarters sales exhbt strong postve comovements: a 10% growth of the headquarters s assocated wth a 2% growth of the afflate. Second, shocks to the source country are almost as mportant as shocks to the destnaton country n explanng varaton n sales growth at the source-destnaton level. We propose a parsmonous quanttatve model to nterpret these fndngs and to evaluate the role of multnatonals for nternatonal busness cycle comovement. Our man result s that for a typcal country par, multnatonals contrbuton to aggregate comovement s lmted. Ths fndng s drven by the fact that observed blateral multnatonal shares tend to be small. We show however that the role of multnatonals can be mportant for some country pars wth strong multnatonal actvty. Furthermore, elmnatng barrers to multnatonal producton down from ther present levels has the potental to decrease the cross-country dsperson n growth rates by 35%. Keywords: nternatonal busness cycle comovement, multnatonal frms JEL Codes: F23, F44 We are grateful to Aaron Flaaen, Jm Hnes, Sebastan Sotelo, Lnda Tesar, semnar partcpants at Indana Unversty and Unversty of Mchgan for helpful suggestons and to Ntya Pandala Nayar and Rsh Sharma for excellent research assstance. Emal: jcravno@umch.edu, alev@umch.edu.

2 1 Introducton Multnatonal frms are a frst-order feature of the world economy: about a quarter of gross output n many developed countres s produced by multnatonals (Alvarez, 2013). Because multnatonals by constructon nvolve producton facltes owned and operated by the same frm n multple countres, a natural conjecture s that the rapd rse of multnatonals n recent decades has had an mpact on the busness cycle comovement across countres. Ths paper uses novel frm level data and a quanttatve mult-country model to examne the role of multnatonal frms n aggregate busness cycle comovement. Our data come from ORBIS, a frm-level database that covers more than 8 mllon frms operatng n 34 countres over the perod. The key feature of the dataset s that t contans nformaton on domestc and foregn ownershp. Hence, for the frst tme n ths context, the operatons of parents and afflates are observed n the same dataset as well as through tme. We explot ths feature to study comovements between parents and afflates and between frms from the same source country. We then develop a conceptual framework to nterpret these comovements and to evaluate how much they contrbute to aggregate busness cycle synchronzaton. We start by documentng a number of stylzed facts about multnatonals presence n the countres n our sample. Multnatonals are a large share of the economy. In the medan country n our sample, foregn multnatonal afflates account for a quarter of aggregate revenues, and ths share exceeds 50 percent n several countres. The actvtes of multnatonals are hghly concentrated. In the medan country the 5 largest foregn frms account fo0 percent of the revenues. Ths suggests that granular shocks that affect the largest multnatonal frms have the potental to affect a sgnfcant fracton of aggregate output n multple countres. We then study comovements between multnatonal afflates and parents, and between frms from the same source country operatng n dfferent destnatons. There s a strong postve correlaton between parents and afflates. Controllng for sourcedestnaton-sector-year fxed effects, the elastcty of afflates growth to parent s growth s about 20%. Ths result s hghly sgnfcant and robust to dfferent samples, fxed effects, and aggregaton methods. To evaluate whether these comovements are drven solely by vertcal producton lnkages, we splt the sample nto sectors that dffer n ther ntermedate nput ntenstes. The results hold for multnatonals operatng n both the manufacturng and the servce sector, although the elastctes n the manufacturng sector are hgher, on the order of 30%. 1

3 We next aggregate multnatonal sales to the source-destnaton level (.e., combned sales of all US multnatonal afflates operatng n the UK), and estmate whether the varaton n source-destnaton growth rates s drven by source or destnaton effects. We fnd that source-specfc shocks are an mportant determnant of blateral growth rates, accountng for about 10% of the varaton n growth rates, compared to 20% accounted for by destnaton shocks. We nterpret ths result as evdence that shocks to the source country are mportant for the varaton n total sales. Our emprcal results thus demonstrate mportant spllovers from source countres to ther foregn afflates. These spllovers are detectable both at the frm and the sourcedestnaton level. In order to assess the quanttatve mportance of these spllovers for aggregate busness cycle comovement, we develop a mult-country quanttatve framework that can be mplemented on the data. In the model, each country produces a fnal good by aggregatng the output of ntermedate producers. These ntermedate producers may be local frms or foregn multnatonal afflates. As standard n much of the lterature on multnatonal producton, the parent transfers technology to ts foregn afflate. 1 As n the more recent quanttatve mplementatons of ths paradgm, the technology transfer s not complete, and thus the foregn afflate does not fully nhert the productvty of the parent. 2 The strength of the technology spllover from the parent to the afflate s a crucal parameter that we estmate n two dfferent ways usng our data. 3 The model llustrates that the extent to whch multnatonals contrbute to the transmsson of shocks across countres s drven by: () what share of the frm s technology shock orgnates n the source vs. the destnaton country; () the dstrbuton of blateral multnatonal shares n the economy; and () general equlbrum effects. We use the model s structural equatons to nterpret our emprcal results, and to calbrate the extent to whch shocks n the source country are transmtted by multnatonals. We estmate that between 20 and 40 percent of the frms shocks orgnate n the source country. The multnatonal producton shares are taken drectly from the data. Fnally, the magntude 1 See, among many others, Helpman (1984); Markusen (1984); Helpman et al. (2004). 2 E.g., McGrattan and Prescott (2009, 2010); Bursten and Monge-Naranjo (2009); Keller and Yeaple (2013); Ramondo and Rodríguez-Clare (2013); Ramondo (2014); Alvarez (2013). 3 The model s setup can be nterpreted more broadly as a reduced form for other types of nterdependences, such as vertcal lnkages. Relatve to a model wth explct nput-output lnkages, our framework gnores the general equlbrum effects of nput producton on factor demands n the nput-supplyng countres. Gven the small observed blateral multnatonal shares, ths s unlkely to apprecably change the man conclusons. At the same tme, t s not (yet) establshed emprcally that the transmsson of shocks through nput trade by multnatonals s a quanttatvely mportant phenomenon. Ramondo et al. (2014) show that US multnatonal afflates abroad sell mostly n the local market, wth the medan afflate havng no shpments to the parent. In our own results, the correlaton between afflate and parent sales occurs even among servce sector frms, for whch nput lnkages are lkely to be much weaker. 2

4 of the general equlbrum effects depends on a composte parameter that combnes the elastcty of substtuton across ntermedates and the Frsch labor supply elastcty. We use the calbrated model to conduct three quanttatve exercses to measure the mportance of multnatonals for the transmsson of shocks across countres. Frst, we smulate mpulse responses to country and frm-level productvty shocks n each source country, and track the propagaton of these shocks across countres. For the majorty of country pars, the role of multnatonals n the transmsson of shocks s essentally nl, snce blateral multnatonal shares tend to be small. Transmsson of shocks can be mportant for some country pars n whch multnatonals account for a large share of the economy. At the extreme, a productvty shock that ncreases US GDP by 1% ncreases Ireland s GDP by 0.18%. Second, we use the model structure, observed blateral multnatonal producton shares, and our estmates of spllovers to ask, what would be the busness cycle correlaton between each par of countres f the only shocks to the economy were country productvty shocks that are uncorrelated wth each other? Ths exercse s an assessment of how much correlaton can be generated purely by propagaton of shocks through multnatonals under observed levels of multnatonal actvty. It turns out that multnatonals as they stand today can generate almost no busness cycle correlaton: the mean correlaton n our sample of country pars s Ths s of course much too low to account for a non-trval share of nternatonal busness cycle comovement observed n the data. And thrd, we conduct two counterfactual exercses n whch we change the shares of multnatonal frms n the world economy, and study the cross-country dsperson of growth rates under these scenaros. In the frst counterfactual, we ncrease the home bas producton of the fnal good so that there are no multnatonal frms operatng n foregn destnatons. The counterfactual cross-country dsperson n growth rates s 10% larger n ths scenaro than n our benchmark calbraton. In the second counterfactual, we smulate a full ntegraton equlbrum, n whch multnatonals from any source country operate wth the same ntensty n all destnatons. We show that the counterfactual crosscountry dsperson n growth rates s 35% smaller than n our benchmark calbraton. Ths paper contrbutes to three strands of the lterature. The frst s the research agenda on the role of multnatonal frms n the transmsson of nternatonal busness cycles (see, e.g., Bursten et al., 2008; Contess, 2010; Zlate, 2012). 4 Ths lterature has focused manly on the role of wthn-multnatonal trade and vertcal ntegraton for busness cycle syn- 4 Also related s the lterature that explores the role of cross-border vertcal producton lnkages n the nternatonal busness cycle transmsson (see, e.g., Kose and Y, 2001; Arkolaks and Ramanarayanan, 2009; Johnson, 2013), though ths lne of research s not explct on whether the producton lnkages take place wthn frms. 3

5 chronzaton, and has predomnantly employed 2-country models. In contrast, we develop a parsmonous mult-country quanttatve framework that can be drectly taken to the frm-level data. The second s the large lterature on multnatonals and technology transfers (see, among many others, McGrattan and Prescott, 2009; Ramondo and Rappoport, 2010; Keller and Yeaple, 2013). We contrbute to ths lterature by usng frm-level data to estmate the mportance of the parent s technology n the producton functon of the afflates, and apply ths framework to busness cycle transmsson. Fnally, we contrbute to the emprcal lterature on multnatonals and comovement. A number of papers (e.g., Budd et al., 2005; Desa and Foley, 2006; Desa et al., 2009) explore whether parents and afflates are correlated. These papers make no attempt to go from ther estmates to busness cycle comovement between countres. Buch and Lpponer (2005) and Klenert et al. (2012) use sectoral and regonal data to study whether greater multnatonal presence s assocated wth greater comovement. All of these papers feature only one source, or only one destnaton country, and frequently the nformaton on ether the parent or the afflate s lmted. Our work s the frst to study aggregate comovement wth mult-country data n whch parents and afflates are observed wthn the same dataset. In addton, we develop a quanttatve framework to nterpret the emprcal fndngs. The rest of ths paper s organzed as follows. Secton 2 descrbes the data and presents the basc summary statstcs on multnatonals presence. Secton 3 documents blateral and frm-level comovements between multnatonal frms. Secton 4 derves a structural framework to nterpret our emprcal results and to study the aggregate mplcatons of multnatonals for busness cycle comovements and for the transmsson of shocks. Secton 5 descrbes the quanttatve results from the model and counterfactuals, and Secton 6 concludes. 2 Data and summary statstcs The data come from ORBIS, a large cross-country database mantaned by Bureau van Djk. The ORBIS database ncludes nformaton on both lsted and unlsted frms collected from varous country-specfc sources, such as natonal regstres and annual reports. Importantly, t contans nformaton on the global ultmate owner of each frm n the database. Ths nformaton enables us to buld lnks between afflates of the same frm, ncludng cases n whch afflates and the parent are n dfferent countres. Currently, the data are avalable for the perod We collect nformaton on the total 4

6 sales (turnover) of each frm. Though n prncple ORBIS contans data on more than 100 countres, coverage s extremely uneven, wth most of those countres reportng nformaton on very few frms. In addton, n order to analyze multnatonals we must use the unconsoldated accounts of each frm, snce the consoldated accounts nclude operatng revenue of the foregn afflates. Snce we are nterested n aggregate comovement, t s mportant for us that each country has enough frms to mmc closely the aggregate economy. After extensve checkng of the data, we settled on a sample of 34 countres, for whch n our vew the coverage and data qualty were suffcently good. The sample s domnated by European countres, but ncludes both developed and developng countres, as well as countres outsde of Europe. Table 1 presents the sample of countres along wth some summary statstcs and checks on the qualty of the data. Column 1 reports the total number of frms for each country. The mean number of frms s about 240,000, and the medan s about 130,000. There s a wde range of frm coverage even n our restrcted sample of countres: the country wth the smallest number, Sngapore, has only 2431 frms. Column 2 reports the number of multnatonal frms n each country. Column 3 presents the correlaton between the country s GDP growth rate and the growth rate of aggregate sales of all the contnung frms n ORBIS. We can see that the aggregate growth rate mpled by ORBIS mmcs the GDP growth qute well: the mean correlaton between aggregate growth n ORBIS and GDP growth from the natonal accounts s 0.81, and the medan s Thus, we can make statements about busness cycle correlaton usng our data. Column 4 reports the rato of the total sales of frms n ORBIS to the gross output as reported n other sources. We use two data sources for ths consstency check. For EU countres, the best source of gross output data s EUROSTAT. For countres outsde of the EU, we take gross output data from the UN System of Natonal Accounts. In ths sample of countres, the ORBIS data captures the bulk of aggregate output as reported by natonal statstcal agences. 5

7 Table 1: Sample and summary statstcs 6 Country Number of Frms Number of Multnatonals Correlaton between ORBIS growth and GDP growth Rato of ORBIS revenue to total revenue Country Number of Frms Number of Multnatonals Correlaton between ORBIS growth and GDP growth Rato of ORBIS revenue to total revenue Austra Lthuana Australa Latva Belgum Mexco Bulgara Netherlands Czech Republc Norway Germany Poland Estona Portugal Span Romana Fnland Serba France Sweden Unted Kngdom Sngapore Greece Slovena Croata Slovak Rep Hungary Turkey Ireland Ukrane Italy Unted States Japan Mean Korea, Rep Medan Notes: Ths table reports the sample of countres used n the analyss. It reports the total number of frms and total number of multnatonals n each country, the correlaton between the growth rates of aggregate sales n ORBIS and GDP growth over the perod for whch ORBIS data are avalable ( ), and the rato of combned sales n ORBIS to total gross output reported n EUROSTAT (for EU countres) or UN SNA data (for non-eu countres).

8 Fgure 1: The mportance of multnatonals Notes: Ths fgure reports, for each country, the share of multnatonals n total revenue (lght bars) and the total number of frms (dark bars). Fgure 1 shows the relatve mportance of multnatonals and large frms n the countres n our sample. Nearly 9% of all frms are multnatonals on average, rangng from 0.1% n Japan to 42% n Croata. Multnatonal afflates tend to be larger than domestcallyowned frms, so they comprse hgher shares of total revenue, 29% on average. Once agan there s a wde range, from 2% for Japan to 61% for the Ireland. Indeed, n a number of countres Belgum, Netherlands, Sngapore, Slovaka multnatonal afflates account for more than half of total sales n our data. It could be that multnatonal frms affect aggregate comovement through the granular channel (Gabax, 2011): dosyncratc shocks to ndvdual multnatonals wll appear n aggregate comovement f those multnatonals are suffcently large relatve to the aggregate. Fgure 2 reports the shares of the largest one and fve multnatonal frms n each country. As expected, multnatonals are granular: the top foregn multnatonal afflate accounts for 2.3% of total sales on average, and as much as 10.1%. Indeed, n 13 out of 34 countres, a foregn multnatonal afflate s the sngle largest frm n the economy. Appendx Table A1 presents the matrx of blateral multnatonal shares. It dsplays, n percent, the share of aggregate revenue n the country n the row that s taken up by the frms owned by the country n the column. Thus the dagonal terms, for example, correspond to the share of aggregate revenue that s taken up by domestcally-owned 7

9 Fgure 2: Top Foregn Multnatonal Frms Notes: Ths fgure reports, for each country, the share of largest 5 multnatonals (lght bars) and the share of the sngle largest multnatonals (dark bars) n total sales n each country. frms. The salent feature of the table, mportant for the results below, s that blateral multnatonal shares are small. In the square matrx of 34 sources and destnatons, the mean cross-border revenue share s 0.7%, and the medan s 0.03%. These low averages are drven partly by the fact that many countres n the sample (such as the small perpheral European countres) do not have many of ther own multnatonals. However, even n the G-7 economes, the average outward blateral shares tend to be small. The largest source country, the US, accounts on average for 5.5% of revenue n a foregn destnaton country, followed by Germany (3.7%), the UK (2.9%), and France (2.3%). All of the other source countres have average foregn shares of unde.5%. 3 Emprcal results 3.1 Frm level comovements We now use the frm level data to estmate how the growth rates of afflates are related to the growth rates of parents. In partcular, we run the followng regresson: g ns,t ( f ) = fg s,t ( f ) + ā ns,t + e ns,t ( f ), (1) 8

10 Table 2: Afflate-Parent Comovement All Manufacturng Servces f 0.278*** 0.213*** 0.389*** 0.303*** 0.270*** 0.210*** (0.0053) (0.0064) (0.015) (0.032) (0.0055) (0.0065) Obs N. mult R FE No Yes No Yes No Yes Notes: Standard errors clustered at the parent level n parentheses. ***: sgnfcant at the 1% level. Ths table presents the results of estmatng equaton (1). FE refers to source destnaton sector year fxed effects. where g ns,t ( f ) s the sales growth rate of frm f from source country, operatng n destnaton country n n sector s, g s,t ( f ) growth rate of frm f s parent n the source country, and ā ns,t are source destnaton sector year fxed effects. We run equaton (1) on the sample of frms that are foregn afflates (so that the growth rate of the parent, g s,t ( f ) exsts), poolng observatons across years. Standard errors are clustered at the parent level. The results are presented n Table 2. We report results from a smple bvarate regresson wth no fxed effects, as well as the results from ncludng the fxed effects. There s a strong postve correlaton between afflates and parents across all the specfcatons. The second panel of the table shows that the correlaton s larger for frm whose headquarters s n the manufacturng sector, although the last panel shows there s a strong postve correlaton even for frms wth headquarters n servces. These results are robust to a varety of alternatve approaches to estmaton: year-by-year, ncludng domestc afflates, dfferent sets of fxed effects. We do not report those robustness checks to conserve space. 3.2 Blateral comovements The results above reveal strong nterdependence at the frm level. It may be that ths nterdependence s drven by transmsson of dosyncratc shocks wthn frms, that averages out on aggregate. Fgure 2 provdes an ndcaton that even these dosyncratc shocks are unlkely to average out, gven the granular nature of multnatonal actvty. Nonetheless, we would lke to establsh that there s a common component to the combned overall sales of multnatonals from a partcular country. We thus estmate the contrbuton of 9

11 source and destnaton specfc shocks to the varaton n the blateral growth rates: g n,t = s,t + d n,t + a n,t. (2) Equaton (2) wrtes the growth rate g n,t of total sales of frms owned by country operatng n country n (.e., the growth rate of the total sales of all =US multnatonals operatng n n =UK) as a functon of the source effect s,t that s common to all frms owned by worldwde, the destnaton effect d n,t that s common to all frms from all countres sellng n market n, and an dosyncratc term a n,t. Ths decomposton of a cross-secton of data nto dfferent types of shocks draws on a common approach n macroeconomcs (see, e.g., Stockman, 1988, and the lterature that followed), but to our knowledge has never been appled to foregn multnatonal operatons to establsh the exstence of a source country shock. The emprcal model (2) s estmated by regressng observed growth rates g n,t on source and destnaton fxed effects (when carred out year-by-year), or source-year and destnaton-year effects (when carred out n a pooled sample of years). There s a large amount of varaton n the sze of source-destnaton pars. Smaller n pars tend to have fewer frms and thus tend to be more volatle. To account for ths fact, the observatons are weghted by the nverse of the Herfndahl ndex of sales shares n an n par. Table 3 reports the results. Source effects account for about 10% of the varaton n the cross-secton of source-destnaton growth rates, compared to 19% for the destnaton shocks. The table reports the F-statstcs and p-values assocated wth the hypothess that the source effects as a group are zero. As a group, they are hghly sgnfcant n explanng the varaton n the data Implcatons for aggregate growth rates We now provde a decomposton of country-level growth rates to understand the contrbuton of source vs. destnaton shocks to the dsperson n aggregate growth rates. We can wrte the aggregate growth rate n country n as: g n,t = Â w n,t g n,t = Â w n,t [a n,t + s,t ] + d n,t, (3) where w n,t denotes the share of country n 0 s revenues generated by frms from country. We can express country n s growth rate relatve to the average growth rate as: g n,t ḡ t = A n,t + S n,t + D n,t (4) 10

12 Table 3: Importance of source and destnaton effects Source Destnaton Part. R 2 F-stat. p-val. Partal R 2 F-stat p-val Mean Medan Pooled Notes: Ths table reports the results of estmatng equaton (2). The frst column reports the partal R 2 assocated wth the source and destnaton effect. The second column reports the F-statstc assocated wth the hypothess that all of the source/destnaton effects are zero, and the thrd column reports the p-value assocated wth that hypothess test. The results are reported year-by-year as well as pooled across years. In the pooled estmaton uses source-year and destnaton-year effects. 11

13 Table 4: Decomposton of cross-sectonal varance of aggregate growth rates Year s 2 g n,t s 2 S n,t s 2 D n,t s 2 A n,t Covarances Mean Medan Notes: Ths table reports the results of decomposton (5). The frst column reports cross-sectonal varance of the aggregate growth rates. The rest of the columns report the components due to source, destnaton, and dosyncratc varances, and the covarance terms. 1 where A n,t  w n,t a n,t N  n  w n,t a n,t s the aggregaton of all of the dosyncratc 1 shocks; S n,t  w n,t [s,t s,t ] Nn  n  w n,t [s,t s,t ] s the aggregaton of all the source shocks, and D n,t d n,t dt s the destnaton effect. In these expressons, we denote by x t 1 N  x n,t the average of a varable across all destnatons. Equaton (4) states that dfferences n the growth rate of country n relatve to the world average are drven by: () dfferences n the orgn of the frms operatng n country n vs. the rest of the world, S n,t ; () dfferences n the destnaton shock n country n vs the rest of the world, D n,t ; or () dfferences n the country par shocks between pars that nclude country n vs the average par, A n,t. We now use the decomposton n equaton (4) to wrte the cross sectonal varance of growth rates n any year t as: sg 2 n,t =  (g n,t ḡ t ) 2 n = ss 2 n,t + sd 2 n,t + sa 2 n,t + 2  (S n,t A n,t + D n,t A n,t + D n,t S n,t ). (5) n Ths cross-sectonal varance s a measure of busness cycle comovement between countres: a low varance mples a hgh level of synchronzaton, and vce versa. Ths measure of dsperson can be decomposed addtvely nto the dsperson due to source shocks ss 2 n,t =  n Sn,t 2, due to destnaton shocks s2 D n,t =  n Dn,t 2, due to dosyncratc shocks sa 2 n,t =  n A 2 n,t, and all the combned covarance terms. The results of ths varance decomposton are presented n Table 4. Most of the 12

14 cross-sectonal varance n growth rates s drven by the cross-sectonal varance of the destnaton-specfc shocks. Ths s not surprsng: examnng (3), t s mmedate that the destnaton shock apples to all the frms operatng n n, whereas the source and dosyncratc shocks are dversfed across all the source countres. Note, however, that for the medan year, a quarter of the cross-sectonal varance n growth rates s accounted for the cross-sectonal varance of S n,t. Ths shows that dfferences n the orgn of the frms operatng n dfferent destnaton countres s an mportant source of cross-country dsperson n growth. The contrbuton of S n,t to the varance can be small f ether: () the source shocks s,t do not dffer across countres, or; () the source shocks s,t do dffer across countres, but the sets of frms operatng n each country s smlar that s, the same multnatonals account for a large share of sales n dfferent countres. We come back to ths pont n the next secton when we use ths decomposton to evaluate how multnatonal affect the dsperson of growth rates across countres. 4 A structural framework for nterpretng the data The precedng emprcal results underscore two key features of the data. Frst, there s sgnfcant comovement between multnatonal parents and ther foregn afflates. Ths comovement s detectable n overall source-destnaton sales. Second, there s a large amount of heterogenety across sources, destnatons, and country pars n the extent of multnatonal presence. Ths suggests that the mpact of multnatonal frms on busness cycle comovement wll dffer mportantly across country pars. These two features of the data nform the desgn of the quanttatve mult-country model that we use to study the mplcatons of the emprcal fndngs for aggregate cross-country comovements. After settng up the theoretcal framework, we crcle back to the emprcal results n Secton 3 and nterpret them through the lens of the model. 4.1 Model Prelmnares We consder a world economy wth multple countres ndexed by and n. Each country produces an homogeneous fnal good usng ntermedate nputs. In each country, ntermedate producers from dfferent countres produce dfferentated goods that are combned nto the fnal good by a CES aggregator. The output of the ntermedate producers cannot be traded nternatonally. We focus on the model s predctons for aggregate output and productvty, whch, as we explan below, are ndependent of the 13

15 nternatonal asset market structure. Technologes and market structure country n s gven by: Q n,t = The producton functon of the fnal good n each "  1 r A n,t Q r n,t # r, (6) where Q n,t s a bundle of the output produced by frms from source country that operate n country n, and r denotes the elastcty of substtuton across goods produced by frms from dfferent source countres. A n,t s a source-destnaton specfc productvty parameter, whch we normalze to  A n,t = 1 for each n. Thus, the producton functon s an Armngton aggregator of goods produced by frms owned by varous countres, ncludng domestcally owned and operated frms. Cost mnmzaton by fnal good producers mples: Q n,t = A n,tp r n,t P r n,t Q n,t, (7) where P n,t s the prce ndex n country n for the bundle of goods produced by frms from source country, and P n,t = "  A n,t P 1 # 1 r 1 r n,t (8) s the aggregate prce ndex n country n. In turn, the ntermedate output bundle Q n,t aggregates the output of all the frms from source country operatng n n: Q n,t = " # r  Q n,t ( f ) r, f 2W n where W n s the set of frms from country that operate n destnaton n and Q n,t ( f ) s the output of frm f. It follows that the prce ndex for the ntermedate nput bundle s P n,t = "  f 2W n P 1 r n,t ( f ) # 1 1 r. (9) 14

16 Each frm operates a lnear technology that uses labor n the destnaton country as the only nput of producton. Followng the lterature on multnatonal producton and technology transfers, we assume that the multnatonal s technology can be partally shared across all destnaton countres. 5 In partcular, the output of the frm s gven by: Q n,t ( f ) = Z n,t ( f ) L n,t ( f ), (10) f n,t where Z n,t ( f ) = Z f,t ( f ) Z1 ( f ) s a frm-destnaton specfc productvty component. Ths producton functon mples that a fracton (1 f) of the productvty of the frm s specfc to a partcular destnaton n whch the frm operates, whle the remanng f s shared across destnatons. 6 Ths s the only potental source of aggregate comovement n the model. The demand for frm s f product s gven by: Q n,t ( f ) = P r n,t ( f ) P r n,t Q n,t. (11) Frms are monopolstcally compettve, so proft maxmzaton mples a constant markup over margnal cost: Preferences P n,t ( f ) = r W n,t Z n,t ( f ). (12) Consumers n country n get utlty from consumpton and dsutlty from supplyng labor accordng to the GHH preferences (Greenwood et al., 1988): u (C n,t, L n,t ) = Â d t y 0 n C n,t t ȳ Lȳ n,t. Utlty maxmzaton mples the followng labor supply: L n,t = apple Wn,t P n,t 1 y 1, (13) where y ȳ ȳ 1 > 1. As s well known, under GHH preferences the labor supply s ndependent of wealth effects. We explot ths property to derve predctons for output that are ndependent of the nternatonal asset market structure. 5 See for example McGrattan and Prescott (2009, 2010), Ramondo and Rappoport (2010), Keller and Yeaple (2013), Ramondo (2014). 6 The assumpton that the productvty n the source and destnaton are combned by a Cobb-Douglas aggregator s not crucal. Appendx A.1 derves the equatons under CES aggregaton of productvtes, and shows they are the same to a frst-order approxmaton. 15

17 Equlbrum Combnng equatons (9) and (12) we can wrte the real wage as: " # 1 W n,t = P n,t r   A n,t Z n,t ( f ) r 1 f 2W n (14) where W n s the set of frms that are actve n country n. Proft maxmzaton mples that aggregate revenues are proportonal to total labor payments:  P n,t Q n,t = P n,t Q n,t = r W n,tl n,t, (15) whch n combnaton wth (14) and (13) permts expressng the aggregate producton functon as: Q n,t = "  A n,t Z n,t ( f ) r 1 # y. (16) For smplcty, we assume that the fnal good s homogeneous across countres and can be freely traded. We use the fnal good as the numerare of the world economy and set ts prce equal to P W t = P n,t = 1 8n. 7 Ths mpes that aggregate sales growth s equvalent to growth of real output Q n,t. Aggregate growth n country n s gven by: g n,t = y  apple an,t  w n,t ( f ) + z n,t ( f ). (17) f 2W n where lower-case varables to denote growth rates, and w n,t ( f ) P n,t( f )Q n,t ( f ) P n,t Q n,t = A n,tz n,t ( f ) ()  A n,t Z n,t ( f ) denotes the share of country n 0 s revenues generated by frm f from source country. In the specal case where the destnaton shock s common across frms, z n,t ( f ) = z n,t, equaton (17) becomes: () g n,t = y  w n,t [a n,t + f () z,t ] + y (1 f) z n,t, (18) w where, z,t =  n,t ( f ) f 2Wn w z n,t,t ( f ), and w n,t P n,tq n,t P n,t Q n,t revenues generated by frms from source country. denotes the share of country n s Equaton (18) s the key equaton that encapsulates the role of multnatonals n bus- 7 The assumpton that the fnal good s homogeneous s not crucal. Appendx A.1 derves the equatons under the assumpton that country-specfc goods are mperfect substtutes, and shows that the results go through. 16

18 ness cycle comovement. It states that growth n country n depends on ts own productvty shock, z n,t, and a weghted average of the productvty shocks z,t to all countres that have frms operatng n country n. Because foregn multnatonal afflates nherts part of the shock that ht the parent z,t, ther presence mples that productvty and output of countres wll be postvely correlated even f true domestc TFP z n,t s not. Ths equaton connects our framework to the nternatonal busness cycle lterature n the tradton of Backus et al. (1995, henceforth BKK). The canoncal BKK model has no multnatonals, but t typcally must assume that TFP shocks across countres are correlated. Equaton (18) provdes a possble mcrofoundaton for ths correlaton. The equaton llumnates the key parameters and quanttes that wll drve the strength of the shock transmsson through multnatonals. The frst s the strength of spllovers, f. The more foregn afflates nhert the source country productvty, the more comovement there wll be n the aggregate. The second s the multnatonal shares, w n,t. Larger shares wll mply more comovement, snce more of the shocks are shared. Fnally, the combnaton of parameters y captures the strength of general equlbrum effects that occur n response to a partcular productvty shock z,t. It regulates how the rest of the economy responds to a shock n a partcular country. We now nterpret the emprcal results n Secton 3 n lght of ths conceptual framework, and use these results to dsentangle the dfferent shocks and dscplne the model. 4.2 Interpretng afflate-parent comovements The emprcal results n Secton 3.1 can be gven a structural nterpretaton and used to estmate the share of the frm s technology that gets transferred across destnatons, f. Usng equatons (11) and (12), frm f sales n destnaton n can be wrtten as: where Ā n,t W 1 r n,t ths n growth rates as: P n,t ( f ) Q n,t ( f ) = Ā n,t Z n,t ( f ), h P r n,t Q r. n,t Usng the functonal form for Zn,t ( f ) we can wrte g n,t ( f ) = ā n,t + () fz,t ( f ) + ()(1 f) z n,t ( f ). The growth rate of the frm n ts home country s: g,t ( f ) = ā,t + () z,t ( f ). 17

19 Substtutng we obtan: g n,t ( f ) = ã n,t + fg,t ( f ) + e n,t ( f ), (19) where ā n,t ã n,t fã,t and e n,t ( f ) ()(1 f) z n,t ( f ). Equaton (19) states that, after controllng for source-destnaton-year effects, the coeffcent on the parent s growth rate s can be nterpreted as f. Hence, our emprcal results n Table 2 mply that the share of a frm s productvty that s transferred across countres s approxmately 20% (f 0.2). 4.3 Interpretng source and destnaton specfc shocks We now use the model s mplcatons for aggregate source-destnaton growth rates g n,t to nterpret our emprcal results n Secton 3.2 under the assumpton that destnaton shocks are common across frms (.e. z n,t ( f ) = z n,t ). Combnng expressons (7), (12), (8), and (16) we can wrte the total revenues by multnatonals from source country operatng n country n as: f() where S,t = Z h f() P n,t Q n,t = A n,t S,t D n,t,,t s a term common to all frms from source country and D n,t = y r+1 y(1 f) Zn,t s a term common to all frms operatng n destnaton coun- Â A n,t Z,t try n. Expressed n growth rates, ths s gven by: g n,t = s,t + d n,t + a n,t, (20) whch s dentcal to the decomposton (2) estmated n Secton 3.2. Equaton (20) provdes a structural nterpretaton for the source and destnaton dummes estmated n Secton 3.2. The fact that a sgnfcant fracton of the varaton of the blateral growth rates s accounted for the source dummes, as reported n Table 3, mples a role for the transmsson of technology from the source country, f > 0. We now use these structural equatons to develop an alternatve method to pn down the parameter f. 18

20 4.4 Estmatng productvty spllovers wth source-destnaton data We can now relate the estmates for the source and destnaton specfc shocks to the spllover parameter f. In partcular, the model structure mples that we can wrte the destnaton-specfc shock as: d n,t = apple y 1  w n,t [a n,t + s,t ] + y 1 f f s n,t. (21) Foregn productvty shocks z affect the destnaton effect n country n through two dfferent channels. On the one hand, these changes affect compettveness n country n h f() 1 through  A n,t Z,t (.e. n response to an ncrease n Z, frms from all other source countres wll sell less n country n due to ncreased competton). On the other hand, these shocks affect the real wage (and real aggregate output) n country through h y f()  A n,t Z,t (.e. n response to an ncrease n Z, aggregate demand n country n wll ncrease, ncreasng the sales of all frms operatng n country n). In the case of r 1 = y these two effects exactly offset each other, and the destnaton effect s ndependent of changes n foregn technologes. We can use the relaton between source and destnaton shocks n equaton (21) to pn down the parameter f. Usng the notaton from Secton we can wrte: D n,t = apple y 1 [A n,t + S n,t ] + y 1 f f S n,t own (22) where Sn,t own 1 hs n,t N  n s n,t captures the devaton of country n 0 s source shock from the average source shock. In partcular, note from equaton (22) that the destnaton effect s lnked to the source effect Sn,t own through the parameter f and a term capturng general equlbrum effects. Takng squares n equaton (22), averagng across countres, and solvng for f we obtan: Where s 2 Ft 1 N  n h y f = y+1 r D n,t [A n,t + S n,t ] s s,t s s,t + s Ft (23) 2, and s 2 s,t 1 N  n that n the specal case of = ȳ, obtan s 2 Ft = s2 dt = 1 N  n D 2 n,t. S own n,t 2. Note Equatons (22) and (23) use the model structure to connect observables s,t, d n,t, and a n,t estmated n Secton 3.2 to the two key model parameters, y/(r each value of y/(r 1) and f. For 1) we can thus use (22) and (23) and the estmated s,t, d n,t, and a n,t 19

21 Table 5: Estmated f based on source-destnaton data Year y = 1 y = 2 y = Mean Medan Notes: Ths table reports estmates of f usng blateral data followng equaton (23). Each column represents the estmate under an alternatve value of the GE parameter y. to pn down f. The basc ntuton for ths appoach can be gleaned from (23). Ignorng the general equlbrum effects, t says that f s pnned down by the relatve varances of the estmated source and destnaton effects. If the data tell us that source effects have a lot of varablty, ths mpled that spllovers are hgh. At the other extreme, f the source effects had no varance, ths would mply absence of spllovers, f = 0. y Table 5 presents the mpled spllovers for dfferent values of. The estmates of f range from 0.3 to 0.5, wth a central tendency of about 0.4. Ths s hgher than, but not too dssmlar from, the frm-level estmates n Secton Quanttatve results We now have the theoretcal structure, the estmates of the key parameter, and the data to carry out a quanttatve assessment of multnatonals role n the nternatonal busness cycle transmsson. Ths secton performs three exercses. The frst s an mpulse response exercse desgned to answer the queston, how much does a productvty shock n one country change output n another? The second s a counterfactual correlaton exercse, that answers the queston, f all the countres productvty shocks were uncorrelated, how much correlaton would the busness cycles exhbt across countres under the current levels of multnatonal actvty? And thrd, how much do multnatonals contrbute to observed dsperson n cross-country growth rates, and how much would that dsper- 20

22 son fall f ntegraton ncreased further? 5.1 Transmsson of shocks across countres We now use our parameterzed model to evaluate how productvty shocks to any source country spread across countres. From 18, the response of output to a productvty shock n any source country s gven by: where I n=n 0 g n z = y [w n f + (1 f) I =n ] (24) s an ndcator functon that equals 1 f n = n 0 and 0 otherwse. We can express the response n country n as a fracton of the effect of the shock n the source country as: g n z / g z = w n f w f + (1 f) n 6=. (25) Equaton (3) answers the queston, how much does aggregate output n country n change when output n country goes up by 1? It s mmedate that the answer depends on two key quanttes: the magntude of the spllover f, and the extent of country s multnatonal presence n n, w n. If ether of these s large, there wll be more nterdependence between and n. There s no smulaton requred to compute these mpulse responses. Instead, they are computed drectly from the data on w n and estmated f. Snce there are 34 countres n the sample, there are cross-border mpulse responses. Fgure 3 shows the mpulse responses to source specfc shocks for all possble country pars. We use f = 0.4 and w n s for 2011 to construct the fgure. Each square n the fgure represents the mpulse response n destnaton n to a shock to productvty n source country, z, relatve to the response n the source country, as n (25). We can nterpret each square of the fgure as the percent change n country n GDP to a shock that ncreases GDP n country by one percent. We omt the entres on the dagonal (they are all tautologcally 1) to facltate the presentaton. The fgure shows that shocks to the productvty of most source countres do not have bg aggregate consequence n most destnatons. Ths reflects the fact that the blateral shares w n n equaton (25) are small for most country pars. In more than half of all source-destnaton pars, the mpact s exactly zero, reflectng the absence of multnatonals from most sources n most destnatons. Among the nonzero pars, the mean and me- 21

23 Fgure 3: Response (n %) to a source shock that rases source country output by 1% dy d /dy s USA UKR TUR SVK SVN SGP SWE SRB ROU PRT POL NOR NLD MEX LVA LTU KOR JPN ITA IRL HUN HRV GRC GBR FRA FIN ESP EST DEU CZE BGR BEL AUS AUT Source SVK TURUKRUSA ROU SRBSWESGPSVN MEX NLDNORPOLPRT ITA JPNKORLTULVA GBR GRCHRVHUNIRL DEU ESTESPFINFRA AUT AUSBELBGRCZE Destnaton Notes: Ths fgure dsplays the change n aggregate output of each destnaton that accompanes a change n source output equal to 1. dan mpact s about 0.011, that s, an ncrease n a source country output of 1% changes foregn output by about one-hundredth of that amount. However, ths low amount of transmsson on average masks a number of outlers. US, Germany, and UK have the hghest average outward mpact, at 0.022, 0.015, and respectvely. About 20 country pars have mpulse response coeffcents of above 0.03, wth the maxmum coeffcent of between US and Ireland. 22

24 5.2 Country par growth correlatons and multnatonal shares Ths secton derves how much covarance/correlaton n aggregate output would be generated by the presence of multnatonals n a world where the only shocks are shocks to country-level productvtes z that are uncorrelated across countres. Under these condtons, (18) mples that the covarance of aggregate growth rates between any par of countres n, n 0 s gven by cov (q n,t, q n 0,t) = Notng that s,t = f (r cov (q n,t, q n 0,t) = h y " 2 cov  1) z,t, we can wrte ths as: f (1 w n,t s,t + 1 f f s nt,  w 0 n 0,ts 0,t + 1 f 0 f f)  w n,t cov (z,t, z n 0 t) + f (1 + f 2   w n,t w 0 n 0,tcov (z,t, z 0,t) + cov (z n, z n 0) 0 s n 0 t! f)  w n 0,tcov (z nt, z,t ) # apple y 2.. (26) Under the assumpton that cov (z n,t, z n 0,t) = 0 for n 6= n 0 we can wrte: cov (q n,t, q n 0,t) = " f (1 # apple y f)[w n 0 n,t + w nn 0,t] + f 2  w n,t w n 0,t 2 s 2 z, (27) where s 2 z s the varance of z. Under the same assumptons, we can wrte the varance of q n,t as: where Q 2 n of countres s then: apple y var (q n,t ) = Q 2 n h f 2  w 2 n,t + 2f (1 f) w nn,t + (1 f) 2. The correlaton between any par r n,n 0 = f (1 f)[w n 0 n,t + w nn 0,t] + f 2  w n,t w n 0,t. (28) Q n Q n 0 Note that whle the covarance n equaton (27) depends on the sze of the general equlbrum effects (captured by [y/(r 2 s 2 z, 1)] 2 ) and the varance of the shocks s 2 z, the correlaton s a functon only of the degree of spllovers, f, and the multnatonal shares, w n. Table 6 presents the correlatons predcted by the model. Consstent wth our results 23

25 Table 6: Predcted and actual correlatons r n,n 0 Mean St.Dev. Mn Max Counterfactual Data Notes: Ths table reports summary statstcs for aggregate correlatons. The row labeled Counterfactual reports the results for correlatons computed usng equaton (28). The row labeled Data reports the actual correlatons of aggregate output n ORBIS, from the prevous secton, the predcted correlatons tend so be small. The mean s only 0.01, and 95% of all the blateral correlatons are below There are some outlers, however. Ireland has a predcted correlaton of 0.25 wth the US and 0.12 wth the UK. Netherlands has a predcted correlaton wth the US of For the sake of comparson, the bottom row presents the actual aggregate output correlatons n ORBIS. As s wellknown, correlatons are much hgher n the data. We conclude that n a large majorty of country pars, transmsson of shocks through multnatonals n and of tself cannot generate anythng close to observed output correlatons. 5.3 Predcted and counterfactual comovements In ths secton we further nvestgate the effect of multnatonals on output comovements by studyng the predcted comovements n our model. We frst use our estmates of f, a n,t, and s,t to compute predcted growth rates n our model usng equatons (4), (22) and the defntons of S n,t and A n,t. To measure the extent to whch multnatonals contrbute to busness cycle synchronzaton, we wll focus on the cross-sectonal dsperson n country-level growth rates as our measure of comovements (see Secton 3.2.1). We then conduct two sets of counterfactual exercses to nvestgate how multnatonals contrbute to these comovements. Throughout ths secton, we wll focus on the specal case where y = 1 (the destnaton shocks are ndependent of the general equlbrum effects). Changng multnatonal shares In the frst set of counterfactuals, we ask how the crosscountry dsperson n growth rates would look lke f multnatonal shares where dfferent. We focus on two polar opposte counterfactuals: () No multnatonals and () Full Integraton. Under No Multnatonals, we change the values of the w n s so that wn,t NM = 1 f = n, wn,t NM = 0 f 6= n. That s, the only frms producng n country are country frms. Under Full Integraton we change the w n s so that wn,t FI = w,t FI = N 1 ÂN n w n,t. 8 That s, the producton shares of frms of all source coun- 8 Note that  w,t = 1 N  n  w n,t = 1. 24

26 tres s the same n every country, and equal to the average share of each country across destnatons observed n the data. In each of the counterfactual exercses ndexed by c = {NM, FI}, we compute the counterfactual components S c n,t, Ac n,t, Dc n,t usng estmated s,t and a n,t as: Sn,t c =  wn,t c s,t A c n,t =  wn,t c a n,t D c n,t = y + 1 r 1 N  n  1 N  n  w c n,t s,t (29) w c n,t a n,t A c n,t + S c n,t + y 1 f f S n,t own. and use them to compute the counterfactual growth rates g c n,t and varances sc g n,t from equatons (4) and (5). Table 7 reports the actual and counterfactual dsperson of growth rates for every year n our sample. The second column shows that the standard devatons of growth rates produced by the model are somewhat hgher but strongly related to those n the data. Column 3 reports the standard devaton of growth rates under the No multnatonals counterfactual. Note from equaton (29) that the dsperson of Sn,t c s hgher under ths scenaro, snce multnatonals are not there to spread the source shocks across countres. We see that for the medan year, the standard devaton of growth rates would ncrease by 10% n the absence of multnatonals. Column 4 reports the standard devaton of growth rates under the Full Integraton counterfactual. Note from equaton (29) that n ths case S c n,t = 0 (snce w n s constant across destnatons). Source shocks are completely shared across destnatons under full ntegraton, hence, dfferences do not contrbute to the dsperson n growth rates. As a consequence, the dsperson n growth rates s sgnfcantly smaller under ths scenaro. For the medan year, the standard devaton of growth rates would ncrease by 35% f all barrers to multnatonals are elmnated. Changng Spllovers In the second set of counterfactuals, we mantan the observed multnatonal shares and change the strength of spllovers from multnatonals to f c. In ths case we can compute the counterfactual components as: 25