International Real Business Cycles with Endogenous Markup Variability *

Transcription

1 Federal Reserve Bank of Dallas Globalizaion and Moneary Policy Insiue Working Paper No. 6 hp:// Inernaional Real Business Cycles wih Endogenous Markup Variabiliy * Sco Davis Federal Reserve Bank of Dallas Kevin X.D. Huang Vanderbil Universiy Sepember 2 Absrac The aggregae impac of decisions made a he level of he individual firm has recenly araced a lo of aenion in boh he macro and rade lieraures. We adap he benchmark inernaional real business cycle model o a game-heoreic environmen o add a channel for he sraegic ineracion among domesic and foreign firms. We show how he sum of sraegic pricing decisions made a he level of he individual firm can have significan effecs on he volailiy and cross counry co-movemen of GDP and is componens. Specifically we show ha he addiion of his one channel for sraegic ineracion leads o a significan increase in he cross-counry co-movemen of producion and invesmen, as well as a significan decrease in he volailiy of invesmen and he rade balance over he benchmark IRBC model. JEL codes: L6, E32, F4 * Sco Davis, Research Deparmen, Federal Reserve Bank of Dallas, 22 N. Pearl Sree, Dallas, TX Sco.davis@dal.frb.org. Kevin X.D. Huang, Deparmen of Economics, Vanderbil Universiy, VU Saion B #3589, 23 Vanderbil Place, Nashville, TN kevin.huang@vanderbil.edu. The views in his paper are hose of he auhors and do no necessarily reflec he views of he Federal Reserve Bank of Dallas or he Federal Reserve Sysem.

2 Inroducion The recen aenion o he role of markup variabiliy in he inernaional rade and nance lieraure is quie remarkable. No surprisingly, given ha markup variabiliy provides a wedge beween change in marginal coss and changes in prices, many (bu no all) of hese sudies incorporae endogenous markup variabiliy ino a model wih nominal rigidiies o explain price or exchange rae dynamics. In addiion, some models have employed variable markups o explain eiher naional or inernaional quaniy dynamics, bu hese papers usually focus on he role of markup variabiliy in conjuncion wih endogenous rm enry and exi. 2 This paper consrucs a model o evaluae he role of endogenous markup variabiliy in a ecing inernaional quaniy dynamics. However, unlike mos of he papers in his lieraure, his paper absracs from he role of endogenous rm enry and exi in order o focus speci cally on how sraegic decisions made a he level of he individual rm can aggregae up o have a signi can e ec on he volailiy and inernaional co-movemen of GDP and is componens. Speci cally we will examine how including endogenous markup variabiliy in an inernaional real business cycle model (IRBC) a ecs he relaive volailiy of consumpion, invesmen, ne expors and employmen and he cross-counry correlaion of GDP, consumpion, invesmen, and employmen. These saisics, as presened in Backus e al. (995, henceforh BKK), Chari e al. (22, henceforh CKM) and Ambler e al. (24, henceforh ACZ), are reproduced in able. The able also presens he resuls from he benchmark inernaional real business cycle model in BKK (995). These saisics are chosen speci cally because hese are he key poins where he bench- Dosey and King (25) show how markup variabiliy can a ec in aion dynamics, namely he persisence of in aion and prices. Bouakez (25) develops a model wih markup variabiliy and nominal rigidiies ha can help explain real exchange rae persisence. Sbordone (27) shows he e ec of variable markups on inernaional in aion dynamics. Akeson and Bursein (28) model how markup variabiliy can explain deviaions of inernaional relaive prices from purchasing power pariy. Gus e al. (2) consruc a model where markup variabiliy is responsible for he incomplee pass hrough of exchange rae changes ino impor prices. 2 Cook (22) presens a model where endogenous rm enry and markup variabiliy lead o an increase in cross-counry business cycle co-movemen. Meliz (23) shows how rm heerogeneiy, endogenous rm enry and exi and variable demand elasiciies can explain why some rms expor and ohers only supply he domesic marke. Ruhl (25) uses a similar model o show how endogenous rm enry can a ec he elasiciy of subsiuion beween home and foreign goods. Wih a closed economy model, Jaimovich and Floeo (29) show how variable markups and endogenous rm enry leads o a propagaion mechanism ha can signi canly increase he volailiy of business cycle ucuaions following produciviy shocks. In addiion, Arkolakis and Ramanarayanan (29) show how markup variabiliy and heerogenous rms may be necessary o explain he link beween bilaeral rade and he endogenous ransfer of measured TFP ucuaions. 2

3 mark IRBC model fails o mach he daa. Namely, he model s predicions for consumpion and employmen volailiy are oo low, while hose for invesmen and ne expor volailiy are oo high. Furhermore, he model s predicion for cross-counry consumpion co-movemen is far oo high, and he model predics negaive GDP, invesmen, and employmen correlaion. Table : Volailiy and cross-counry co-movemen of GDP and is componens in he daa and in he benchmark IRBC model. Daa Model BKK (995) CKM (22) ACZ (24) BKK (995) Volailiy relaive o GDP: Consumpion :75 :83 :42 Invesmen 3:27 2:78 :99 Ne Expors :27 : 2:5 Employmen :6 :67 :5 Cross-counry correlaion: GDP :66 :6 :22 :2 Consumpion :5 :38 :4 :88 Invesmen :53 :33 :8 :94 Employmen :33 :39 :2 :78 Many papers have shown how various permuaions of he benchmark IRBC model can help resolve hese discrepancies beween he model and he daa. 3 Wihou doubing he validiy of hese conribuions we propose an addiional channel ha may help resolve hese well known discrepancies beween he benchmark IRBC model and he daa, he channel hrough which he sum of sraegic decisions made a he level of individual rms can have signi can aggregae e ecs. Our work adaps he inernaional real business cycle model of Backus e al. (994) o a game-heoreic environmen. In he model, inermediae goods from home and foreign rms are aggregaed in a discreized Dixi and Sigliz (977) aggregaor funcion. Like in he closed economy model in Yang and Heijdra (993), when deciding is opimal oupu price, he rm akes ino accoun he e ec of is price on he aggregae price level. Thus a sraegic game arises where a rm mus ake ino accoun he impac of is pricing decision 3 See Baxer and Crucini (993) for, among oher hings, a discussion of he role of capial adjusmen coss in increasing he relaive volailiy of consumpion and reducing he relaive volailiy of invesmen. Baxer and Crucini (995), Kehoe and Perri (22), and Heahcoe and Perri (22 and 23) show ha cross-counry consumpion correlaion falls and cross-counry GDP correlaion increases when inernaional asse markes are resriced. Kose and Yi (2), Ambler e al. (22), and Bursein e al. (28) show ha i is possible o raise he level of inernaional business cycle co-movemen by alering he producion process o allow for rade in inermediae inpus in he producion process. 3

4 on he aggregae price level and hus on all oher rms pricing decisions. 4 The exen o which a rm can in uence he aggregae price level and he prices se by oher rms is deermined by he rm s marke share. A rm wih a higher marke share has greaer marke power, and his greaer marke power allows he rm o charge a higher markup over marginal cos. Cyclical changes in he impor share ha arise in an inernaional real business cycle model as a resul of counry speci c produciviy shocks lead o cyclical changes in domesic and foreign rms marke power and hus cyclical changes in domesic or expor markups. The link beween an increasing marke share of foreign rms and a decreasing domesic markup is well esablished in he empirical lieraure. Tybou (23) provides a survey of ample empirical evidence on how markups generally fall as impor compeiion rises (see, also, Kaics and Peerson, 994; Tribble, 995; Konings and Vandenbussche, 25; Blonigen e al., 27; Chen e al., 29), while Becarello (997) especially emphasizes he empirical signi cance of such markup variabiliy and he impac of impor compeiion a he business cycle frequency. This markup variabiliy in response o a changing impor share reduces he volailiy of ucuaions in GDP, invesmen, and ne expors. In addiion markup variabiliy leads o greaer inernaional co-movemen in producion, invesmen and employmen. The inuiion is as follows. Suppose here is a posiive shock o foreign produciviy. Foreign marginal coss fall. The relaive price of foreign producs decreases. Foreign producers will increase producion and domesic producers will cu producion. Thus he foreign shock leads o volaile business cycle ucuaions and inernaional business cycle divergence. Foreign producers gain marke share a he expense of domesic producers, and hus foreign markups increase while domesic markups fall. These changes in markups cause he relaive price of foreign goods o increase. Thus variabiliy in markups causes a change in relaive prices ha is exacly opposie he change due o he iniial produciviy shock. Home and foreign business cycles will ucuae less han hey would have wihou variable markups. Since home rms nd hemselves a a comparaive disadvanage following he foreign produciviy shock hey cu producion for a period of ime. Therefore he produciviy shock leads o business cycle divergence and negaive bilaeral GDP correlaion. When here is endogenous markup variabiliy, he changes in he markups of home and foreign rms place home rms a less of a comparaive disadvanage and hey reurn o pre-shock levels of producion sooner. Thus wih endogenous markup variabiliy here is less bilaeral 4 We consider boh he cases where his sraegic ineracion arises from rms engaged in quaniy compeiion (Corno) or price compeiion (Berrand). 4

5 business cycle divergence following a counry speci c produciviy shock and higher bilaeral cyclical correlaion. When adding a channel for sraegic ineracion beween domesic and foreign rms o an oherwise ordinary IRBC model, we nd ha sraegic ineracion leads o a nearly 2 percenage poin increase in cross-counry GDP correlaion. In addiion we nd ha crosscounry invesmen and employmen correlaion increase by and 5 percenage poins, respecively. 5 Furhermore, a channel for sraegic ineracion leads o a 5% increase in he relaive volailiy of consumpion, a 5% decrease in he relaive volailiy of invesmen, and an % decrease in he relaive volailiy of ne expors. This paper will proceed as follows. In secion 2 he model is described and a par of he model is solved in order o nd a closed form expression for a rm s elasiciy of demand as a funcion of is marke share. The parameerizaion of he model and he exogenous shock process is described in secion 3. The resuls from he model are presened in secion 4. Firs we log linearize par of he model o provide some inuiion for how markup variabiliy should a ec volailiy and co-movemen. Then we simulae he model o show he quaniaive e ec of endogenous markup variabiliy in an oherwise ordinary IRBC model. Finally, secion 5 concludes. 2 The Model 2. Producion There are wo counries, home and foreign. Foreign variables are wrien wih an aserisk and home variables are no. In he following descripion of he model, foreign equaions are omied for breviy. An aggregae good is used by households for consumpion and invesmen, C and I. This aggregae good, y, is formed hrough he combinaion of domesic and impored nal goods, which are combined in an Armingon (969) aggregaor funcion wih an elasiciy of subsiuion. C + I = y = i h(!) (yd; ) + (!) (ym; ). () where y D; are domesically produced nal goods and y M; are impored nal goods. 5 To pu his in perspecive, in heir seminal paper, Frankel and Rose (998) nd ha he doubling of rade beween wo counries leads o abou an 8 percenage poin increase in bilaeral GDP correlaion and a percenage poin increase in bilaeral employmen correlaion (see also Clark and van Wincoop, 2; Baxer and Kouparisas, 25; Kose and Yi, 26; Calderón e al., 27) 5

6 The demand for domesically produced or impored nal goods as a funcion of aggregae consumpion and invesmen spending is: y D; =! (p ) y (2) p y M; = (!) q y c where p is he price of home nal goods relaive o he price of he home consumpion good, p is he price of foreign nal goods relaive o price of he foreign consumpion good, q is he real exchange rae measured in unis of he foreign consumpion good per unis of he home consumpion good, and c is an iceberg rade cos parameer. Goods shipped inernaionally are subjec o an iceberg rade cos, so when uni of a good is shipped, only c unis arrive. Thus y X; = y M; and ( c) y X; = y M;, where y ( c) X; and are home and foreign expors of nal goods. y X; Final goods, which are o be sold domesically or expored, are produced from he combinaion of value added a he nal goods sage and inermediae inpus. h y D; + y X; = A h y Ky + ( ) (x ) where h y and K y are labor and capial employed in he producion of nal goods, A is a counry speci c oal facor produciviy parameer, x are inermediae inpus, and is he elasiciy of subsiuion beween value added and inermediae inpus in he producion of nal goods. i The demand for inermediae inpus in he producion of nal goods is given by: (3) p x x = ( ) (y D; + y X;) (4) p where p x is he relaive price of inermediae inpus. The inermediae inpu erm x in he producion of nal goods is made up of a combinaion of inermediae inpus from a coninuum of secors j: Z x = x j where x j represens inermediae inpus from secor j. The demand for inpus from secor j is given by: (5) 6

7 x j = pj p x! x (6) where p j is he relaive price of inermediae goods from secor j. The inermediae good from secor j is formed by combining rm speci c varieies from N home rms and N foreign rms in secor j. We use he convenion ha rms denoed i = ; :::; N are home rms and hose denoed i = N + ; :::; N + N are foreign rms: x j = N+N P i= x j (i) where x j (i) is he inermediae good from rm i in secor j. Firm i can supple o eiher he home or he foreign marke. (7) For noaional clariy, suppose ha x j D; (i) and xj X; (i) are he quaniies ha he rm supplies o he home and foreign markes, respecively. For each of hese goods he rm charges a price p j D; (i) and p j X; (i). The demand from he home marke for he inermediae good from rm i in secor j is: x j D; (i) = pj D; (i) p j! x j (8) and he demand in he foreign marke for he inermediae good from he same rm is: x j X; (i) = c q ( p j X; (i) c) p j! x j (9) Again we see ha raded inermediae inpus are subjec o an iceberg rade cos. The price of he inermediae good from secor j, p j, is given by: 2 p j P = 4@ N p j D; (i) i= + N+N P i=n+ p j X; q (i)! 3 A5 c () The oal quaniy sold by rm i in secor j for boh he domesic and foreign markes is produced from a combinaion of domesic capial and labor. x j D; (i) + xj X; (i) = A h j (i) K j (i) () where h j (i) and K j (i) is labor and capial employed by rm i in secor j, A is an exogenous counry speci c produciviy shock, and is a xed cos which ensures ha rms earn zero 7

8 pro in he seady sae Households The one represenaive household per counry derives uiliy from consumpion and leisure. The household in he home counry maximizes expeced lifeime uiliy given by: E P =o h( h ) (C ) i where is he coe cien of relaive risk aversion and h = h y + R (2) NP h j (i) dj is aggregae labor supplied by he domesic household o boh nal goods producion, h y, and o inermediae goods producion from all rms i in all secors j, R NP h j (i) dj. We assume ha inernaional asse markes are complee. We can model his by assuming households share one worldwide budge consrain: i= i= C + I + q (C + I ) = w h + r K + R NP i= j (i) dj + q w h + r K + R NP i= j (i) dj where w is he home wage rae (in erms of he home consumpion good), r is he renal rae of home capial, K = K y + R NP K j (i) dj, and j (i) = p j D; (i) xj D; (i) + pj X; (i) xj M; (i) i= w h j (i) r K j (i) is he pro a ime of he home rm i in secor j. Finally, he home capial sock evolves according o he following: (3) where is he one-period depreciaion rae of capial. K + = ( ) K + I (4) 2.3 The rm s maximizaion problem Firm i in secor j, wih i N, chooses p j D; (i), pj X; (i), xj D; (i), and xj M (i) = ( c) x j X; (i) o solve he following saic maximizaion problem: max p j D; (i) xj D; (i) + pj X; (i) xj M; (i) w h j (i) r K j (i) (5) This pro can be rewrien as: max p j D; (i) MC x j D; (i) + ( c) pj X; (i) MC x j X; (i) MC (6) 8

9 where MC = w r. A We assume a su cien degree of marke segmenaion such ha rms can price o marke, i.e. he rm is able o se a di eren price for goods sold domesically versus hose ha are expored. If rms are engaged in quaniy compeiion hen he rm chooses domesic and expor quaniies according o: x j D; (i) = argmax p j D; (i) x j D; (i) x j X; (i) = argmax ( c) p j X; (i) x j X; (i) MC x j D; (i) (7) MC x j X; (i) subjec o he inverse demand funcions: p j D; (i) = x j D; (i)! x j p j X; (i) = q ( c) x j x! ( c) x j X; (i) x j p x (8)!! x j p x x Thus he domesic and expor elasiciies of demand faced by he rm are: " d (i) = " x (i) = sj D; (i) + sj D; (i) (9) sj X; (i) + sj X; (i) where s j D; (i) = p j D; (i) xj (i) P N p j D; (i) xj (i) + N+N P i= i=n+ s j X; (i) = p j X; (i) xj (i) P N (i) + N+N P p j X; i= (i) xj i=n+ p j X; (2) (i) xj (i) p j D; (i) xj (i) 9

10 are an inermediae good rm s marke shares in he home and foreign markes. If insead rms engaged in price compeiion he demand elasiciies would be he following: " d (i) = s j D; (i) + s j D; (i) (2) " x (i) = s j X; (i) + s j X; (i) Deails of he soluion o he rm s problem and he derivaion of hese elasiciies can be found in he appendix. The impac of sraegic ineracion among rms and how ha can a ec rm markups is highlighed by equaions (9) and (2). Sraegic ineracion occurs when a rm akes ino accoun he e ec of is pricing decision on he aggregae price level, and hus on he pricing decision of oher rms. If he aggregae price level increases afer a rm raises is price hen oher rms will follow sui and raise heir prices as well. Thus he rm ha is able o signi canly in uence he aggregae price level and hus he pricing decisions of oher rms has greaer marke power and will maximize pro s by charging a higher markup. In equaions (9) and (2), he elasiciy of demand for he oupu from rm i is a convex combinaion of he echnological elasiciy of subsiuion beween rms in he same secor and he elasiciy of subsiuion beween secors. As he rm s marke share increases, he weigh on he elasiciy of subsiuion beween secors increases, and hus he elasiciy of demand for he oupu from rm i decreases. If rm i is small compared o he res of he marke and hus is marke share, s j D; (i), is close o zero, hen when seing is price he rm does no ake ino accoun he e ec of is decision on oher rms. Thus when he marke is made up of many small rms here is no channel for sraegic ineracion and each rm s demand elasiciy reduces o. 3 Parameerizaion The model s parameers and heir benchmark values are found in able 2. is he elasiciy of subsiuion across inermediae inpus from di eren rms. We se his elasiciy equal o. This is done o mach he convenion in his lieraure 6 and ensure ha in he exreme case of aomisic rms (N + N! ), rms charge a seady sae markup of abou %, which is common in he lieraure wih imperfec compeiion and aomisic rms. 6 Akeson and Bursein (28) use an elasiciy of in a similar model.

11 is he elasiciy of subsiuion beween goods from di eren secors. parameer equal o :. We se his Again his is similar o Akeson and Bursein (28) and an elasiciy of subsiuion close o one ensures ha secoral expendiure shares are roughly consan. is he elasiciy of subsiuion beween home and foreign nal goods. As discussed in Anderson and van Wincoop (24), in he rade lieraure, his elasiciy is commonly esimaed as somewhere beween 5 and. However he inernaional macro lieraure nds ha his elasiciy needs o be low, around :5, in order o mach he variabiliy of he real exchange rae. Ruhl (25) aemps o jusify hese di eren esimaes of he same elasiciy in a model wih endogenous rm enry. Since we do no consider he role of endogenous rm enry in his model, we follow he convenion in he inernaional macro lieraure and se his elasiciy o :5. The nex six parameers:, he exponen on leisure in he Cobb-Douglas uiliy funcion,, he coe cien of relaive risk aversion,, capial s share of income,, he discoun facor,, he capial depreciaion rae, and, he elasiciy of subsiuion beween value added and inermediae inpus in he producion of nal goods, are all se o values commonly found in he real business cycle lieraure. The benchmark xed cos parameer,, from he rm s producion funcion, is se such ha rms earn zero pro in he seady sae. The nex wo parameers deermine he marke share of foreign rms in eiher he marke for nal goods or he marke for inermediae inpus. The rade cos parameer c a ecs boh he relaive cos of foreign nal goods and he cos of foreign inermediae goods, alhough he purpose of his parameer is o deermine he seady sae marke share of foreign inermediae goods rms. By seing he rade cos parameer equal o :59, he seady sae marke share of foreign rms in he marke for inermediae inpus is equal o 25%. The parameer! describes he exogenous home bias for domesically produced nal goods. This parameer is se o :733 o ensure ha afer accouning for rade coss, he seady sae share of foreign goods in he household s consumpion baske is equal o 25%. The seady sae domesic markup is equal o 2%. Wih his seady sae domesic markup, he number of rms, N, can be backed ou of he elasiciy expressions in (9) and (2). 7 7 d " = d, or alernaively " d = d +. Under quaniy compeiion, " d = " d, d N ( m) + N ( m) ( m)( hus N = ) :Under price compeiion, " d = ( m), hus N = ( m)( ) (" d ) where m is he seady sae marke share of for- N ( m) + N eign rms in he inermediae goods marke. ( " d )

12 Finally, in his real business cycle model, ucuaions in oal facor produciviy drive business cycle ucuaions. The A and A variables in () are exogenous counry speci c shocks ha evolve according o he following VAR() process: " A + A + # " # " :9 = :9 where var(" ) =var(" ) = :6 2 and corr(" ; " ) = :25 A A # " + " " # 4 Resuls 4. Qualiaive e ec of variable markups To see how variable markups a ec he cyclical ucuaions in producion and aggregae oupu, consider he log linearizaion of he demand funcion for inermediae goods from domesic rms in (8): ^x D; = ^p D; + ^p + ^x (22) Noe ha he secoral superscrips j have been omied for clariy. If we log linearize he price index in (), hen he secoral price level ^p can be expressed as: ^p = Ns D; (^p D; ) + N s X; ^p X; + ^q (23) where s D and s X, de ned in an earlier secion, are a home inermediae good rm s marke shares in he home and foreign markes, respecively. Since he N home inermediae goods rms and he N foreign inermediae goods rms are idenical, N s X; = m is he marke share of foreign rms in he marke for inermediae goods, and Ns D; = m is he marke share of domesic rms. Subsiuing equaion (23) ino (22) yields he following: ^x D; = m ^q + ^p X; ^p D; + ^x (24) The domesic price is simply equal o a markup over he domesic marginal cos of producion, p D; = + D; MC. The foreign expor price is equal o a markup muliplied by he foreign marginal cos of producion, p X; = + X; MC. Afer log-linearizing hese pricing formulas, he log-linearizaed demand funcion in (24) is: 2

13 ^x D; = m ^q + X ^ + X; + M ^C X D ^ + D; M ^C + ^x (25) D where D and X are he seady sae values of he domesic and expor markups. Suppose ha here is an exogenous change in he foreign marginal cos of producion, MC. Equaion (25) shows ha he elasiciy of domesic demand wih respec o changes in foreign marginal cos is: ^x D; M ^C = m ^q M ^C + X + X ^ X; M ^C Suppose markups are consan, hen ^ X; M ^C rewrien as: ^x D; M ^C = m ^q M ^C + = ^ D; M ^C + D + D ^ D; M ^C M ^C M ^C! + ^x M ^C (26) =. Then he elasiciy in (26) can be M ^C M ^C! + ^x M ^C Therefore equaions (26) and (27) show how he variabiliy of markups can a ec he o be he change in elasiciy when he vari- cyclical ucuaions in oupu. De ne ^x D; M ^C abiliy of markups is aken ino accoun: 8 ^x D; M ^C = m X + X (27) ^ X; M ^C D ^ D; + D M ^C In his model, he markup is an increasing funcion of marke share. Therefore when foreign coss decrease, foreign producers gain marke share in he domesic marke and hus heir markup rises, ^ X; M ^C (28) <. Similarly when foreign cos decrease, domesic producers lose marke share and hus heir markup increases, M ^C >. This implies ha ^x D; M ^C The key resul from his paper is summarized in equaion (28). Markup variabiliy should lead o less business cycle volailiy and greaer inernaional business cycle correlaion. Suppose here is a posiive shock o foreign produciviy. Foreign marginal coss fall, and he relaive price of foreign producs decreases. Foreign producers will increase producion and domesic producers will cu producion. Thus he foreign shock leads boh business cycle volailiy and inernaional business cycle divergence. Foreign producers will gain marke share a he expense of domesic producers, and hus foreign markups increase while domesic markups fall. These changes in markups cause he 8 This expression for ^x D; M ^C rae wih respec o changes in foreign marginal coss, and he elasiciy of home gross oupu, ^ D; <. is an approximaion. Oher elasiciies like he elasiciy of he real exchange ^x M ^C ^q M ^C, he elasiciy of home marginal coss,, should all be a eced by he variabiliy of markups. M ^C M ^C, 3

14 relaive price of foreign goods o increase. Thus variabiliy in markups causes a change in relaive prices ha is exacly opposie o he change due o he iniial produciviy shock. Home and foreign business cycles will be less volaile and will diverge less han hey would have wihou variable markups. This sequence of evens is illusraed in gures and 2. Figure plos he response of home and foreign marginal cos and he response of home domesic markups and foreign expor markups o a posiive foreign produciviy shock. The doed line in each plo refers o he pah of markups and GDP when markups are consan. Figure 2 plos he price of domesically produced inermediae goods in he home marke and he price of foreign inermediae goods in he home marke, as well as home and foreign GDP. The doed line in each impulse response diagram refers o he version of he model where markups are held consan over he cycle, and he solid line refers o he version of he model where markups are variable over he cycle and arise from rms engaged in quaniy compeiion, as in (9). 9 The op row of impulse response diagrams in gure shows how he posiive foreign TFP shock causes home marginal coss o increase and foreign marginal coss o decrease. However when his happens, foreign rms gain marke share a he expense of domesic rms. The boom row in he gure shows ha when markups vary over he cycle, foreign rms will increase heir markup in he home markup and domesic rms will cu heir markup. The op row in gure 2 shows how he price of domesically produced inermediae inpus should rise and he price of foreign inermediae inpus should fall following he foreign TFP shock. However he gure shows ha he price change is smaller if markups vary over he cycle. Home inermediae goods prices sill rise and foreign inermediae goods prices sill fall, bu no as much under variable markups as under consan markups. Therefore domesic producion is higher and foreign producion is lower han i would have been wihou variable markups. Endogenous markup variabiliy means ha he iniial negaive response o home GDP is less negaive, and he iniial posiive response of foreign GDP is less posiive, leading o less volaile responses in home and foreign GDP following he foreign TFP shock. Home rms nd hemselves a a comparaive disadvanage following he foreign produciviy shock and hus hey cu producion for abou 6 quarers. Therefore he produciviy shock leads o business cycle divergence and negaive bilaeral GDP correlaion, which is a feaure of many IRBC models wih complee inernaional asse markes. When here is endogenous markup variabiliy, he changes in he markups of home and foreign rms place home rms a less of a comparaive disadvanage and hey reurn o pre-shock levels of producion afer abou quarers. Thus wih endogenous markup variabiliy here is less bilaeral business cycle divergence following a counry speci c produciviy shock and 9 In boh cases he seady sae markup is 2%. 4

15 bilaeral correlaion should be higher. 4.2 Quaniaive impac of variable markups 4.2. Business Cycle Volailiy The volailiy of GDP and is componens as calculaed from simulaions of he model are presened in able 3. The rs wo rows of he able presen he sandard deviaion of real GDP. The remaining rows in he able lis he relaive sandard deviaion of he componens of GDP (and labor inpu). In he able, he daa for each enry is compued wice, once in he model assuming ha markups are held consan over he cycle, and once in he model assuming ha markups are allowed o vary over he cycle. The rs column of he able presens he resuls from he benchmark parameerizaion, as described in secion 3. The share of foreign rms in boh he inermediae and nal goods markes is se o 25%. Inermediae goods rms charge a 2% markup in heir home marke, rms are engaged in quaniy compeiion, inernaional asse markes are complee, and preferences are non-separable in consumpion and leisure. Under he benchmark parameerizaion of he model, he sandard deviaion of real GDP is 3:25% when markups are held consan and 3:6% when markups are allowed o vary. Thus allowing markups o vary over he cycle leads o a nearly 6% reducion in GDP volailiy. The able also shows ha allowing markups o vary leads o a nearly 6% increase in he relaive volailiy of consumpion from :44 o :47, no enough of a change o fully reconcile he IRBC model s predicions abou consumpion volailiy wih he volailiy observed in he daa (see able ) bu de niely a signi can move in he righ direcion. Anoher well known feaure of he IRBC model is ha wihou invesmen adjusmen coss, he model s predicions for invesmen and ne expor volailiy is way oo high. Table 3 shows ha he inclusion of endogenous markup variabiliy leads o a 5% fall in invesmen volailiy and an % fall in ne expor volailiy. However he model canno help resolve he discrepancy beween he IRBC model s predicion abou employmen volailiy and ha observed in he daa. The model consisenly predics a relaive volailiy of employmen ha is below ha observed in he daa. However he able shows ha he inroducion of endogenous markup variabiliy acually reduces he relaive volailiy of employmen, and hus markup variabiliy canno help resolve he well known discrepancy beween he model and he daa in regards o he relaive volailiy of employmen. The remaining columns in he able calculae he same saisics from model simulaions bu under alernaive parameerizaions. The second column repors he resuls when rms 5

16 are engaged in price compeiion, he hird column repors he resuls for a 25% seady sae markup, he fourh column repors he resuls for a 5% seady sae markup, he fh column repors he resuls from a model where he only asse raded inernaionally is a non-coningen bond, and he sixh column repors he resuls from he model where preferences are separable in consumpion and labor e or. The e ec of markup variabiliy on he volailiy of GDP and is componens remains he same under he alernaive parameerizaions. In fac, he e ec is enhanced when rms are engaged in price compeiion or he seady sae markup is high. When markups are small, markup variabiliy sill has an e ec on volailiy, bu he e ec is smaller. Similarly he e ec of markup variabiliy is slighly reduced when asse markes are resriced. Lasly, he resuls are largely una eced by he subsiuabiliy of leisure and consumpion in he uiliy funcion. The e ec of markup variabiliy as he marke share of foreign rms increases The quaniaive resuls in able 3 are calculaed assuming ha in he seady sae foreign rms supply 25% of he inermediae goods used in he home counry. The qualiaive resuls earlier in his secion, speci cally equaion (28), suggess ha he quaniaive e ec of markup variabiliy should be increasing in he marke share of foreign inermediae goods rms. In his secion we will examine he e ec of an increasing foreign marke share on business cycle volailiy. The sandard deviaion of GDP as calculaed from model simulaions for di eren seady sae foreign marke shares is presened in gure 3. The gure presens he resuls from he model assuming markups are held xed over he cycle and assuming ha markups are variable over he cycle. The gure con rms he predicion from equaion (28) ha he role of variable markups in reducing GDP volailiy is increasing in he marke share of foreign rms. The e ec of markup variabiliy on he relaive volailiy of he componens of GDP are presened in gure 4. The gure con rms he resuls ha are presened in able 3. Endogenous markup variabiliy has a posiive e ec on he relaive volailiy of consumpion and a negaive e ec on he relaive volailiies of invesmen, ne expors and employmen. Furhermore, his e ec of markup variabiliy is increasing in he marke share of foreign rms Inernaional Business Cycle Co-movemen Similarly, markup variabiliy has a sizeable e ec on inernaional business cycle co-movemen. The resuls from calculaing he cross-counry correlaion of GDP and is componens in he model wih and wihou markup variabiliy are lised in able 4. 6

17 As discussed in he inroducion, bilaeral GDP, invesmen, and employmen correlaion is far oo low in he benchmark IRBC model wih complee inernaional asse markes and no invesmen adjusmen coss. Furhermore, bilaeral consumpion correlaion in he model is oo high compared o ha observed in he daa. In he benchmark case of his model, he correlaion beween he wo counries GDP ucuaions is abou 8% when markups are held consan over he cycle. When markups are allowed o vary, his correlaion coe cien increases o abou 4%. Thus endogenous markup variabiliy leads o a 2 percenage poin increase in cross-counry GDP correlaion. Similarly allowing markup variabiliy leads o an percenage poin increase in invesmen co-movemen and a 5 percenage poin increase in cross-counry employmen co-movemen. Thus he inclusion of endogenous markup variabiliy parially resolves he well known puzzle ha in he benchmark IRBC model, GDP, invesmen and employmen correlaion is oo low. However he model does no help resolve he puzzle abou bilaeral consumpion correlaion being oo high. The inroducion of endogenous markup variabiliy leads o abou a percenage poin increase in cross-counry consumpion correlaion. While ha is he opposie of wha is needed o resolve he discrepancy beween he model and he daa, he e ec of markup variabiliy on cross-counry consumpion correlaion is abou one order of magniude smaller han he e ec on GDP, invesmen, or employmen correlaion, so i is safe o say ha endogenous markup variabiliy doesn have much of an e ec on cross-counry consumpion correlaion. The remaining columns in he able presen he model s simulaed correlaion coe ciens under alernaive parameerizaions. The resuls hold under he various parameerizaions, and in some cases are enhanced. For insance, when markup variabiliy arises from rms engaged in price compeiion, cyclical markup variabiliy leads o a 6 percenage poin increase in GDP co-movemen, a 4 percenage poin increase in invesmen co-movemen, and a nearly 2 percenage poin increase in he cross-counry employmen correlaion. The e ec of markup variabiliy as he marke share of foreign rms increases The e ec of increasing foreign marke share on cross-counry GDP correlaion is presened in gure 5. The gure shows ha he gap beween correlaion in he model wih variable markups and ha in he model wih consan markes is increasing in he foreign marke share. As prediced in equaion (28), as foreign rms occupy a greaer share of he home inermediae goods marke, allowing markups o vary over he cycle should have a greaer quaniaive e ec on he cross-counry co-movemen of business cycles. The e ecs of variable markups on cross-counry GDP correlaion of he componens of GDP is presened in gure 6. This gure con rms he resuls from able 4 and shows ha 7

18 markup variabiliy has a sizable posiive e ec on cross-counry invesmen and employmen co-movemen. The gure also shows ha he e ec of markup variabiliy is increasing in he marke share of foreign inermediae goods rms Using command-basis GDP insead of real GDP As discussed in Kehoe and Ruhl (28), when he erms of rade are volaile, real GDP may no accuraely measure he purchasing power of an economy. In he model, real GDP is measured as: GDP = C P C + I P I + X P X where C, I, X, M are he nominal values of home consumpion, invesmen, expors, and impors, and P C, P I, P X, P M are he de aors for consumpion, invesmen, expors and impors. As demonsraed by Kehoe and Ruhl, he acual purchasing power of an economy should insead be measured wih as command-basis GDP, also referred o as gross domesic income (GDI): GDI = C P C + I P I M P M + X M P M Noice ha he only di erence beween he wo measures is ha he nominal value of expors is de aed by he impor price de aor in he measure of GDI bu he expor price de aor in he measure of GDP. The reason he command-basis GDP measure is a beer measure of purchasing power is ha X M measures he nominal ne income from inernaional rade. By de aing his nominal ne income by he impor price de aor, you can measure he acual quaniy of goods and services from abroad ha an economy was able o purchase wih his ne income from inernaional rade. Algebraically, he only di erence beween he measure of real GDP and command-basis GDP is ha in he measure of command-basis GDP, he nominal value of expors is divided by he erms of rade. Thus if he erms of rade is relaively sable, ucuaions in real GDP should be similar o ucuaions in command-basis GDP. However if he erms of rade ucuae, and are posiively correlaed wih ucuaions in expors, hen command-basis GDP should be less volaile and have greaer inernaional co-movemen ha ucuaions in real GDP. The resuls from simulaions of he model where we calculae he momens of command- GDP insead of real-gdp are presened in ables 5 and 6. The able shows ha in his model where business cycles are driven by produciviy shocks, ucuaions in command-gdp are less volaile and display higher inernaional correlaion han ucuaions in real GDP, 8

19 however he e ec of endogenous markup variabiliy is unchanged. Endogenous markup variabiliy has he same qualiaive and quaniaive e ec on business cycle volailiy and inernaional co-movemen even when we consider ucuaions in command-gdp. The volailiy and cross-counry correlaion of command GDP as he marke share of foreign inermediae goods rms changes is presened in gures 7 and 8. Again, using command basis GDP insead of real GDP leads o a level shif in he volailiy and cross-counry correlaion, bu he ne e ec of inroducing endogenous markup variabiliy is unchanged. 5 Summary and Conclusion This paper inroduces sraegic ineracion among rms and endogenous markup variabiliy ino he inernaional real business cycle model. Speci cally his paper shows how his sraegic ineracion among individual rms can have a signi can e ec on aggregae quaniies a he business cycle frequency. The inuiion here is simple. Due o sraegic ineracions among rms, a rm s marke power is posiively relaed o is marke share. Following a produciviy shock in an inernaional real business cycle model, here is a change in he relaive prices of home and foreign produced goods ha leads o a change in rm marke shares. We nd ha he inroducion of sraegic ineracion and he resuling markup variabiliy ino he IRBC model leads o abou a 5% decrease in GDP volailiy, a 5% increase in he relaive volailiy of consumpion, and a 5% and % decrease in he relaive volailiies of invesmen and he rade balance, respecively. Furhermore his sraegic ineracion among rms leads o a nearly 2 percenage poin increase in bilaeral GDP correlaion and a and 5 percenage poin increase in he crosscounry correlaion of invesmen and employmen. This paper s ino he young bu growing lieraure ha applies he microeconomic issue of endogenous markup variabiliy o macroeconomic quesions. Mos, bu no all, papers incorporaing endogenous markup variabiliy sudy macroeconomic issues relaed o prices and exchange raes. This paper shows ha he e ec of sraegic ineracion on aggregae quaniies is no rivial. The e ec of markup variabiliy on oher quesions peraining o quaniies and producion allocaion is a promising avenue for furher research. 9

20 References Ambler, Seve, Emanuela Cardia, and Chrisian Zimmermann, 22, Inernaional ransmission of he business cycle in a muli-secor model, The European Economic Review 46, , Inernaional business cycles: Wha are he facs?, Journal of Moneary Economics 5, Anderson, James E., and Eric vanwincoop, 24, Trade coss, Journal of Economic Lieraure 42(3), Arkolakis, Cosas, and Ananh Ramanarayanan, 29, Verical specializaion and inernaional business cycle syncronizaion, The Scandinavian Journal of Economics, Armingon, P.S., 969, A heory of demand for producs disinguished by place of producion, IMF Sa Papers 6, Akeson, Andrew, and Ariel Bursein, 28, Pricing o marke, rade coss, and inernaional relaive prices, The American Economic Review 98, Backus, David K., Parick J. Kehoe, and Finn E. Kydland, 994, Dynamics of he rade balance and he erms of rade: The j-curve?, The American Economic Review 84, , Inernaional business cycles: Theory and evidence, in: T.F. Cooley, ed., Froniers of Business Cycle Research) Baxer, Marianne, and Mario J. Crucini, 993, Explaining saving invesmen correlaions, The American Economic Review 83, , Business cycles and he asse srucure of foreign rade, Inernaional Economic Review 36, Baxer, Marianne, and Michael A. Kouparisas, 25, Deerminaes of business cycle comovemen: a robus analysis, Journal of Moneary Economics 52, Beccarello, Massimo, 997, Time series analysis of marke power: Evidence from g-7 manufacuring, Inernaional Journal of Indusrial Organizaion 5, Blonigen, Bruce A., Benjamin H. Liebman, and Wesley W. Wilson, 27, Trade policy and marke power: The case of he us seel indusry, NBER Working Paper No Bouakez, Hafedh, 25, Nominal rigidiy, desired markup variaions, and real exchange rae persisance, Journal of Inernaional Economics 66, Bursein, Ariel, Chrisopher Kurz, and Linda Tesar, 28, Trade, producion sharing, and he inernaional ransmission of business cycles, Journal of Moneary Economics 55,

21 Calderon, Cesar, Albero Chong, and Erneso Sein, 27, Trade inensiy and business cycle synchronizaion: Are developing counries any di eren?, Journal of Inernaional Economics 7, 2 2. Chari, V.V., Parick J. Kehoe, and Ellen R. McGraan, 22, Can sicky price models generae volaile and persisen real exchange raes, Review of Economic Sudies 69(3), Chen, Naalie, Jean Imbs, and Andrew Sco, 29, The dynamics of rade and compeiion, Journal of Inernaional Economics 77(), Clark, Todd, and Eric vanwincoop, 2, Borders and business cycles, Journal of Inernaional Economics 55, Cook, David, 22, Marke enry and inernaional propogaion of business cycles, Journal of Inernaional Economics 56(), Dixi, Avinash K., and Joseph E. Sigliz, 977, Monopolisic compeiion and opimum produc diversiy, The American Economic Review 67, Dosey, Michael, and Rober G. King, 25, Implicaions of sae dependen pricing for dynamic macroeconomic models, Journal of Moneary Economics 52, Frankel, Je rey A., and Andrew K. Rose, 998, The endogeneiy of opimum currency area crieria, The Economic Journal 8, Gus, Chrisopher, Sylvain Leduc, and Rober J. Vigfusson, 2, Trade inegraion, compeiion, and he decline in exchange rae pass-hrough, Journal of Moneary Economics 57(3), Heahcoe, Jonahan, and Fabrizio Perri, 22, Financial auarky and inernaional business cycles, Journal of Moneary Economics 49, , Why has he U.S. economy become less correlaed wih he res of he world?, The American Economic Review (Papers and Proceedings) 93, Jaimovich, Nir, and Max Floeo, 28, Firm dynamics, mark-up variaions, and he business cycle, Journal of Moneary Economics 55, Kaics, Michelle, and Bruce Peersen, 994, The e ec of rising impor compeiion on marke power: A panel daa sudy of us manufacuring, Journal of Indusrial Economics 42, Kehoe, Parick J., and Fabrizio Perri, 22, Inernaional business cycles wih endogenous incomplee markes, Economerica 7, Kehoe, Timohy J., and Kim J. Ruhl, 28, Are shocks o he erms of rade shocks o produciviy, Review of Economic Dynamics (4),

22 Konings, Jozef, and Hylke Vandenbussche, 25, Anidumping proecion and he markups of domesic rms, Journal of Inernaional Economics 65(), Kose, M. Ayhan, and Kei-Mu Yi, 2, Inernaional rade and business cycles: Is verical specializaion he missing link?, The American Economic Review, (Papers and Proceedings) 9, , Can he sandard inernaional business cycle model explain he relaion beween rade and comovemen?, The Journal of Inernaional Economics 68, Meliz, Marc J., 23, The impac of rade on inra-indusry reallocaions and aggregae indusry produciviy, Economerica 7(6), Ruhl, Kim J., 25, Solving he elasiciy puzzle in inernaional economics, mimeo, Universiy of Texas - Ausin. Sbordone, Argia M., 27, Globalizaion and in aion dynamics: The impac of increased compeiion, NBER Working Paper No Tribble Jr., Romie, 995, Domesic marke power, he ransnaional indusry cycle, and he meris of free versus fair rade, Inernaional Advances in Economic Research, Tybou, James, 23, Plan and rm-level evidence on new rade heories, in: Eun Kwan Choi, James Harrigan, eds, Handbook of Inernaional Trade) Yang, Xiaokai, and Ben J. Heijdra, 993, Monopolisic compeiion and opimum produc diversiy: Commen, The American Economic Review 83,

23 A Technical Appendix A. The household s maximizaion problem The household will maximize he expeced presen value of lifeime uiliy, (2), subjec o heir budge consrain in (3), and capial accumulaion equaion, (4). Under complee inernaional nancial markes, he home and foreign households problems are solved as one maximizaion problem subjec o one worldwide budge consrain and wo capial accumulaion equaions: L = E P =o h ( h ) (C ) i + h( h ) (C ) i w h r K R C + I + q (C + I ) NP j (i) dj q w h r K i= (K + ( ) K I ) K+ ( ) K I R NP i= j (i) dj C A The rs order condiions wih respec o C ; C ; h ; h ; I ; I ; K + and K + are: h = ( ) ( h ) (C ) i (C ) (29) h q = ( ) ( h ) (C ) i (C ) h w = ( h ) (C ) i ( h ) h w q = ( h ) (C ) i ( h ) = q = = ( ) r + = ( ) r +q + 23

24 A.2 The rm s maximizaion problem Firm i in secor j will choose a prices and quaniies o maximize pro given by: j (i) = p j D; (i) xj D; (i) + pj X; (i) xj M; (i) w h j (i) r K j (i) (3) This pro can be rewrien as: j (i) = p j D; (i) MC x j D; (i) + ( c) pj X; (i) MC x j X; (i) MC (3) where MC = A w r. A.2. Quaniy Compeiion The rm engaged in quaniy compeiion will choose quaniies x j D; (i) and xj X; (i) o maximize (7) subjec o he inverse demand funcions in (8). Afer subsiuing he inverse demand funcion ino he pro maximizaion problem, he rm s univariae maximizaion problem o choose x j D; (i) is: x j D; (i) = argmax x j D; (i) 8 : xj D; (i) x j! x j x! p x 9 = MC A x j D; (i) ; The individual rm s choice of x j D; (i) can in uence oal producion wihin secor j, xj, bu no he quaniy of inermediae inpus from all secors x or marginal cos, MC. Using he fac ha ha d ln x j d ln x j D; + (i) = ( m ) N x jd; (i) x j D; (i) he rs order condiion of he rm s problem is: x j x j (x ) p x j j D; (i) (x ) p j D; (i) x j C A = MC (32) Subsiue he inverse demand funcion in (8) ino his rs order condiion and noe d ln x j = ( m d ln x j D; (i) ) = N sj D;, hen he price se by he rm engaging in quaniy compeiion is: 24

25 p j D; (i) = ( sd ) + sd MC (33) Thus he domesic elasiciy of demand for he rm engaged in quaniy compeiion is: " d = sd + sd A.2.2 Price Compeiion The rm engaged in price compeiion will choose prices p j D; (i) and pj X; (i) o maximize: p j D; (i) = argmax p j D; (i) p j D; (i) p j X; (i) = argmax ( c) p j X; (i) p j X; (i) MC x j D; (i) (34) MC x j X; (i) subjec o he following demand funcions: x j D; (i) = p j D; (i)! p j x j X; (i) = ( c) q ( p j p x p j X; (i)! x (35) c) p j!! p j x p x Afer subsiuing he demand funcion ino he maximizaion problem, he rm s univariae maximizaion problem o choose is domesic price, p j D; (i), is: p j D; (i) = argmax p j D; (i) ( p j D; (i) MC p j D; (i) p j! p j p x! x ) (36) The individual rm s choice of p j D; (i) can in uence secoral prices, pj, bu no he aggregae price of inermediae inpus, p x, or he quaniy of inermediae inpus from all secors, x, or marginal cos, MC. he rs order condiion of he rm s problem is, making noe of 25

26 he fac ha d ln p j d ln p j D; (i) = ( m ) N = s D; : p j D; (i) = sd + s D ( s D ) + s D MC (37) Thus he domesic elasiciy of demand for he rm engaged in price compeiion is: " d = s D + s D 26

27 Table 2: Parameer Values Symbol Value Descripion elasiciy of subsiuion across inermediae goods producing rms : elasiciy of subsiuion across di eren secors :5 elasiciy of subsiuion across home and foreign nal goods :7 weigh on leisure in he uiliy funcion 2 coe cien of relaive risk aversion :36 capial s share of income :99 discoun facor :25 capial depreciaion rae :5 elasiciy of subsiuion beween value added and inermediae inpus :5 coe cien on value added in he producion funcion for nal goods :32 xed cos parameer (benchmark) c :59 rade cos parameer! :733 exogenous preference for impored goods in he nal goods aggregaor funcion d 2% seady sae domesic markup 27

28 Table 3: Sandard deviaion of GDP and is componens as calculaed by he model wih and wihou variable markups. Variaions on he benchmark economy Benchmark Price High Low Incomplee Separable : economy Compeiion Markups Markups Markes Preferences Sandard deviaion of GDP (%): Consan Markups 3:254 3:252 3:3 3:26 2:762 2:762 3:62 3: 3:2 3:4 2:75 2:6 Relaive sandard deviaion of: Consumpion: Consan Markups :445 :445 :444 :446 :65 :32 :47 :479 :483 :458 :69 :34 Invesmen: Consan Markups 3:63 3:62 3:543 3:668 3:72 3:85 3:4 3:4 3:275 3:57 2:986 3:672 Ne Expors: Consan Markups :76 :77 :79 :724 :386 :776 :636 :629 :596 :685 :347 :699 Expors: Consan Markups :92 :93 :8 :24 :954 :24 :37 :37 :8 :75 :942 :82 Impors: Consan Markups :3 :3 :9 :42 :94 :68 :74 :78 :45 :3 :93 :4 Labor: Consan Markups :53 :54 :499 :528 :47 :48 :483 :476 :456 :54 :399 :454 28