El-hadj Bah* Distortions, structural transformation and the Europe-US income gap

Transcription

1 DOI /bejm B.E. Journal of Macroeconomics 213; 13(1): 1 34 Conribuions El-hadj Bah* Disorions, srucural ransformaion and he Europe-US income gap Absrac: This paper uses a model of srucural ransformaion wih secoral disorions o sudy he convergence of income beween Wesern Europe and he Unied Saes (US). I shows ha in addiion o income effecs and growh differenials in secoral oal facor produciviies (TFP), secoral disorions are imporan for undersanding he reallocaion of resources across secors. Allowing for a growing wedge beween he marginal revenue produc of labor relaive o capial can explain he rapid decline in he manufacuring share of hours for he US ha sared in he 198s. The disorions are also imporan for explaining he pahs of secoral hours for many European counries. However, he disorions lead o a misallocaion of resources across secors, which helps explain why he rapid Europe-US income convergence ha sared in he 195s sopped in he early 198s. Keywords: European cach-up; secoral produciviy; srucural ransformaion; policy disorions. JEL classificaion: E2; O1; O4. *Corresponding auhor: El-hadj Bah, Deparmen of Economics, Universiy of Auckland, Auckland, New Zealand, e.bah@auckland.ac.nz 1 Inroducion This paper uses a model of srucural ransformaion wih secoral disorions o sudy he convergence of income beween Wesern Europe and he Unied Saes (US). From 195 o 1982, he average income per capia for nine European counries increased from 54% o 8% of ha for he US. This relaive income was sill 8% in However, he slowdown in he convergence process was no 1 The counries are Ausria, Belgium, Denmark, Finland, France, Ialy, he Neherlands, Spain and he Unied Kingdom (UK).

2 2 El-hadj Bah experienced in all secors. Secoral sudies find ha he problems are relaed o he slow developmen of marke services in Europe. Hours worked have declined considerably relaive o he US and labor produciviy growh has slowed in ha secor, especially since he mid-199s (Rogerson 28, Inklaar, Timmer, and van Ark 28; van Ark, O Mahoney, and Timmer 28). The aggregae implicaions of he slow growh in marke services depend on he relaive size of he secor and he speed of he reallocaion of resources across secors. This reallocaion process, called srucural ransformaion, accompanies all modern economic developmen pahs. As an economy develops, labor is reallocaed firs from agriculure ino indusry and services and subsequenly from agriculure and indusry ino services. 2 Income and relaive price effecs have been generally used in models o induce a reallocaion of labor across secors. 3 However, closed economy models wih capial accumulaion and no impedimen o resource flow across secors are unable o explain he rapid reallocaion of labor from indusry ino services ha many developed economies experienced in he 198s and 199s (Buera and Kaboski 29; Ungor 211). This paper sudies secoral disorions in a hree-secor model of srucural ransformaion wih capial accumulaion. I show ha ime-varying secoral disorions improve he performance of such a model and lead o a misallocaion of resources across secors ha can explain he slow cach-up of many European economies o he US. Acceleraing he reallocaion of labor ino he service secor, which is relaively less producive han he manufacuring secor, decreases aggregae produciviy and hence slows down he growh of GDP per capia. I use he baseline model of Herrendorf, Rogerson, and Valeninyi (213) and follow Duare and Resuccia (27), Hsieh and Klenow (29) in inroducing he disorion as a wedge beween he marginal revenue produc of labor relaive o capial across hree secors. Tha is, I allow for differences in nominal wages across secors. This wedge is allowed o vary over ime, such ha he model maches he labor reallocaion paerns observed in he daa. This mehodology requires informaion on he pahs of secoral oal facor produciviy (TFP). Such daa are scarce for a large number of counries; herefore, I resric my analysis o OECD counries in he EU KLEMS projec. 2 The processes of srucural ransformaion may differ across counries (Bah 211; McMillan and Rodrik 212). 3 Echevarria (1997), Kongsamu, Rebelo and Xie (21), among ohers, emphasize income effecs, while Baumol (1967), Ngai and Pissarides (27) emphasize relaive price differenials. Gollin, Parene and Rogerson (22, 27), Rogerson (28) and Duare and Resuccia (21) combine boh channels.

3 Disorions, srucural ransformaion and he Europe-US income gap 3 Assuming no disorions, he baseline model is calibraed o mach he srucural ransformaion of he US economy over he period. I find ha non-homoheiciy and TFP growh differenials, compued from secoral daa, allow he model o mach he shares of hours worked in agriculure for he full period. However, for he oher wo secors, he model is unable o replicae he rapid labor reallocaion from indusry ino services ha began in he early 198s. Allowing he disorion in services o grow a 1.5% per year, beginning in 198, generaes pahs of hours ha are very similar o he acual daa and enables he model o mach per capia GDP growh for he period. The calibraed model is hen used o infer he disorions in nine European counries. The mehodology can be summarized as follows. For each counry, I use he daa o calculae differences in secoral TFP relaive o he US in he iniial period and differences in average secoral TFP growh raes. I use he model o deermine he iniial secoral TFP levels and heir growh raes such ha he model maches he iniial GDP per capia relaive o he US and he average per capia GDP growh. The pahs of he disorions in agriculure and services are hen deermined such ha he model maches he pahs of hours in all hree secors. I find ha secoral disorions vary subsanially across counries. For a few counries, agriculural disorions are no necessary for he model o mach he shares of hours in ha secor. Regarding he oher counries, he growh raes are highes for Ausria, Finland and he Unied Kingdom (UK). Regarding he disorion in services, he growh raes vary from for Denmark and Spain o 1.9% per year for he UK. These disorions indicae ha he wedge beween wages in indusry and services has grown over ime, which acceleraed he reallocaion of labor from indusry o services. I provide some empirical evidence ha such widening is aking place. The disorions refer o no only oal labor coss, including axes and labor benefis, bu also policies and regulaions, such as size-dependen policies, access o credi and agriculural policies. The effecs of he growh in he disorions are large. Wih consan disorions, he model predics ha fewer workers would have moved o he service secor. Given ha produciviy is higher in indusry han in services, such a predicion implies ha income would have grown more rapidly. For example, wih consan disorions, he model predics ha he UK s GDP per capia in 27 is 89% of he US level raher han he 81% shown in he daa. This paper is closely relaed o Duare and Resuccia (27), Buera and Kaboski (29). Duare and Resuccia (27) show ha a ime varying wedge beween he wages in services and manufacuring is needed for differences in labor produciviy growh raes o induce he srucural ransformaion pah of Porugal. Buera and Kaboski (29) show ha a sandard model of srucural

4 4 El-hadj Bah ransformaion wih capial accumulaion canno mach he daa for he US. They find ha secoral disorions or secor-specific human capial is needed o improve he performance of he model. The paper is also relaed o a number of sudies ha analyze he role of misallocaion in explaining aggregae oal facor produciviy (TFP) differences across counries. Mos of hese sudies focus on misallocaions across firms, however (Resuccia and Rogerson 28; Alfaro, Charlon, and Kanczuk 29; Hsieh and Klenow 29; Barelsman, Haliwanger, and Scarpea 213). This paper is also relaed o papers ha focus on he secoral composiion of oupu o sudy aggregae oucomes. 4 A number of papers emphasize he role of srucural ransformaion in counries developmen and growh hisories. Gollin, Parene and Rogerson (22, 27) demonsrae he imporance of agriculure in delaying he iniiaion of modern economic growh. Rogerson (28) sudies labor oucomes in Europe and finds ha mos counries failed o develop marke services comparable o ha in he US. Duare and Resuccia (21) analyze he role of secoral labor produciviy and srucural ransformaion on aggregae labor produciviy oucomes across counries. The remainder of he paper is organized as follows. Secion 2 describes he model and characerizes he compeiive equilibrium. Secion 3 calibraes he model o he US economy. Secion 4 uses he calibraed model o infer disorions for European counries. I discuss some of he assumpions in Secion 5 and presen concluding remarks in Secion 6. 2 A hree-secor model of srucural ransformaion This secion develops a hree-secor model of srucural ransformaion, which is characerized as follows. Early in he developmen process, he majoriy of he labor force is engaged in food producion. As food oupu rises, labor moves from agriculure ino indusry and services. This is he firs phase of srucural ransformaion. In he second phase, labor moves from agriculure and indusry ino services. The model presened here assumes a closed economy, and he implicaions of rade are discussed in Secion See, for insance, Cordoba and Ripoll (28), Resuccia, Yang and Zhu (28), Caselli (25), Adamopoulos and Akyol (29), Chanda and Dalgaard (28), Vollrah (29). 5 In his paper, indusry and manufacuring are used inerchangeably. The exac definiion of a secor is presened in he daa appendix.

5 Disorions, srucural ransformaion and he Europe-US income gap Preferences There is an infiniely lived, represenaive household wih preferences for consumpion of he sequence {C }, which is a composie of agriculural consumpion (c a ), manufacuring consumpion (c m ) and service consumpion (c s ). The household is endowed wih iniial capial and one uni of ime supplied o he hree secors of he economy. Lifeime uiliy is given by: β log C, β (, 1) (1) = The composie consumpion good (C ) is a CES aggregaion of he hree secoral goods. ε 1 ε 1 1 ε 1 1 ε 1 ε 1 ε ε ε ε ε ε = ( ) ( ) ( ) µ + µ + µ + a a a m m s s s C c c c c c (2) where c i, μ i. This formulaion is he benchmark specificaion in Herrendorf, Rogerson and Valeninyi (213) and allows boh income and price effecs o play a role. The relaive imporance of hese wo effecs will depend on he calibraion of c and ε. The parameer c is ofen referred o as subsisence agriculure, while i a c is an ad hoc represenaion of home producion. 6 s Technologies All hree secors use Cobb-Douglas producion funcions wih capial and labor as he only wo inpus. 7 I assume idenical capial shares across secors. While his assumpion may be consisen wih he empirical evidence for manufacur- 6 Sudies in he lieraure use boh income effecs (Echevarria 1997; Lainer 2; Caselli and Coleman II 21; Kongsamu, Rebelo, and Xie 21; Gollin, Parene, and Rogerson 22) and price effecs (Baumol 1967; Ngai and Pissarides 27) as key drivers of srucural ransformaion. Acemoglu and Guerrieri (28), insead, inroduce differences in facor shares and capial deepening as he main mechanisms for resource reallocaion. For a more deailed discussion of he main mechanisms of srucural ransformaion, see Herrendorf, Rogerson and Valeninyi (29), Herrendorf, Rogerson and Valeninyi (213). 7 While land is imporan for agriculure, i is ofen assumed o be consan and is normalized o 1. Mos sudies in he lieraure employ his convenien formulaion and rea land as being included in physical capial.

6 6 El-hadj Bah ing and services, i may be a srong assumpion for agriculure (Herrendorf and Valeninyi 28; Herrendorf, Rogerson, and Valeninyi 213). In he Discussion secion, I explore how he resuls are affeced wih a differen capial share in agriculure. Secoral oupu is given by he following: y = Akn ; i= a, m, s (3) α 1 α i i i i where secoral TFPs evolve as follows: A i = A i 1 (1+γ i ). The secoral TFPs will vary across counries, and I will assume consan growh raes for mos of he counries in he quaniaive secion. Oupu from agriculure and services is solely used for consumpion. However, oupu from indusry is used for consumpion (c m ) and invesmen (X ). 8 Aggregae capial (K ) evolves as usual: where δ is he depreciaion rae. K +1 = (1 δ)k +X (4) 2.2 Equilibrium In his secion, I describe how o solve for he compeiive equilibrium of he model economy. Because I use he benchmark model from Herrendorf, Rogerson and Valeninyi (213), I will no presen all of he derivaions; he deails can be found in heir paper The firms problem The represenaive firm in each secor chooses capial and labor o maximize profis. As in Buera and Kaboski (29), I allow firms o face secor-specific disorions o labor inpus relaive o capial. 9 These disorions can resul from size-dependen policies, agriculural policies, access o credi, differences in human capial, infrasrucure, enry coss ec. The problem of firm i = a, m,s is he following: α 1 α max pakn k, n i i i i i i Rki (1 τ ) Wl i i + 8 See he discussions abou his assumpion presened in Secion 5. 9 As heir derivaion shows, we canno separae he effecs of he disorions o capial from he effecs of he disorions o labor. Therefore, my disorions here are on labor relaive o capial.

7 Disorions, srucural ransformaion and he Europe-US income gap 7 where τ are he secoral disorions. i Normalizing he price of manufacuring o one, he firs-order condiion wih respec o labor leads o: 1+ τ p y y 1+ τ p y a a a m s s s = = = W. 1+ τ n n 1+ τ n m a m m s Le he disorions in agriculure and services relaive o manufacuring be: 1+ τ 1+ τ a s τ = and τ =. This formulaion of he wedge is similar o he barrier a 1 + s τ 1 τ m + m o services used by Duare and Resuccia (27) and he disorions in Hsieh and Klenow (29) for lower-digi indusries. The wo firs-order condiions become: τ p y y p y a a m s s n = n = τ n = W. (5) a s a m s p y y p y a a m s s = = = R. (6) k k k a m s Combining hese equaions wih he marke-clearing condiions for capial (k a +k m +k s = K ), we ge: τ a k k k K a s m n = τ, s n = = n (7) a s N n n a s where N =. τ + n + m τ This shows ha he capial-labor raios differ across a s secors and ha he differences may vary overime. Using equaion (7), we obain he relaive prices of agriculure and services: a m α 1 Am p = τ, a a (8) A p A τ (9) α 1 m =. s s As These wo equaions show ha relaive prices are proporional o he inverse of he secoral TFP raios. Therefore, if here are growh differenials in secoral

8 8 El-hadj Bah produciviy, he relaive prices will change over ime, which leads o subsiuion beween goods. Growh in he disorions will also cause changes in he relaive prices. For insance, rapid growh in τ s decreases he growh of he relaive price of services, which implies a subsiuion away from he manufacured good for services. Anoher way o hink abou his is ha as labor in services becomes cheaper, he service secor will employ increasingly more people Household s problem The problem of he household is o selec he invesmen and consumpion levels of each good o maximize is lifeime uiliy subjec o he budge consrain: max β U( c, c, c ) = a m s s. p c + c + p c + K = (1 δ+ R ) K + W. a a m s s + 1 The F.O.C are he following: ε ε ε µ ( c c ) C = λ p, a a a a (1) C ε ε ε µ ( c ) C = λ, m m (11) C ε ε ε µ ( c + c ) C = λ p, s s s s (12) C where λ is he Lagrange muliplier. Combining (1) (12), we obain: where P is a price index given in he following way: λ 1 = λ β(r +1 δ), (13) 1 P, C = λ (14) 1 1 ε 1 ε 1 ε µ µ µ a a m s s P = [ ( p ) + + ( p ) ]. (15)

9 Disorions, srucural ransformaion and he Europe-US income gap 9 We can derive he following equaions: 1 ε 1 ε 1 ε µ µ a m s m PC A A P = =, c µ A µ A µ m m a m s m p ( c c ) p a a a a = µ a PC P 1 ε, (16) (17) p ( c + c ) p s s s s = µ s PC P 1 ε. (18) The marke-clearing condiions for goods for agriculure and services can be rewrien in he following way: c = y = A K n a a a a τ N a α, (19) c = y = A K n s s s s τ N s α. (2) From equaions (13) and (14), we obain he Euler equaion: PC P C 1 1 = β( R + 1 δ). (21) Combining he marke-clearing condiions, we obain he dynamic equaion of he economy: K = (1 δ) K + Y PC + pc p c, (22) + 1 s s a a where Y = p a y a +y m +p s y s. We observe ha hese wo equaions resemble he Euler and dynamic equaions for capial for a one-secor growh model, wih he excepion ha he erm pc p c is no included. I can be shown ha a generalized balanced growh s s a a pah (GBGP), defined as an equilibrium pah such ha he renal rae of capial is consan, exiss if: pc p c =. (23) s s a a

10 1 El-hadj Bah When ε < 1 and he secoral TFP growh raes differ, here will be srucural ransformaion in he generalized balanced growh pah. If condiion (23) does no hold, here will be an asympoic GBGP. 1 Nex, le us examine how he disorions, non-homoheiciy and relaive prices lead o labor reallocaion across secors. As already discussed, non-consan disorions lead o varying relaive prices and differences in he capiallabor raios. Boh of hese channels lead o labor reallocaion across secors. To simplify he exposiion for he income and price effecs, le us se he disorions in boh secors o one. We hen can derive he labor shares of agriculure and services by combining equaions (17 2). n a ε 1 ε P p µ C + c µ PC a a p a a a P ca α α α A K A K A K a m a = = + (24) n s ε 1 ε P p µ C c µ PC s s p s s s P cs α α α AK A K AK s m s = =. (25) Moreover, le us assume ha γ a > γ m > γ s. From he equaions above, we can observe he facors driving labor ou of agriculure and ino services. Firs, he subsisence parameer ( c ) ensures ha, a iniially, labor is allocaed o agriculure. However, as he agriculural secor becomes more producive and aggregae capial increases, he subsisence erm plays a lesser role. This observaion is consisen wih he findings of Dennis and Iscan (29). Overime, he relaive price of agriculure declines, and his decline drives labor ou of ha secor. Regarding services, we can see from equaion (18) ha p s c s /P C is increasing in p s if ε < 1. Since γ m > γ s, he relaive price of services is increasing, and labor will reallocae ino he secor, as equaion (25) shows. However, he preference parameer ( c ) decreases he amoun of labor ha is s allocaed o services. The inuiion is ha some services are produced a home, and we allocae less marke work o his secor. The role of non-homoheiciy decreases as he economy becomes wealhier. The wo channels above have been a feaure of mos recen models of srucural ransformaion. Therefore, one may wonder why he secoral wedges are needed in his model wih capial o mach he labor pahs in he US and oher 1 See Herrendorf, Rogerson, and Valeninyi (213) for a deailed discussion of his issue.

11 Disorions, srucural ransformaion and he Europe-US income gap 11 counries while similar models wih only labor do a good job of maching he daa (Duare and Resuccia 21). I should emphasize ha all closed economy models wih capial and no secoral disorions or human capial fail o mach he daa (Buera and Kaboski 29; Ungor 211), because during laer periods, only he subsiuion effec plays a role and capial is reinforcing he effec of he secoral TFP in decreasing he demand for labor. For example, assume ha here is an increase in service produciviy. The relaive price of services decreases, as does he price index; however, capial and, hence, aggregae consumpion increase. The decrease in he relaive price of services leads o higher consumpion of ha good, as can be seen from equaion (18), which would increase he demand for labor in services. However, he increase in service TFP and capial reduces he demand for labor [equaion (25)], which leads o a smaller increase in he share of labor in services. This addiional channel is no presen in a model wih only labor. The sraegy for compuing he equilibrium allocaions follows Hayashi and Presco (28). Firs, I assume ha afer 27, he secoral TFP growh raes are consan. Then, I derend he model and use a shooing algorihm o compue he equilibrium pah given he iniial capial. 3 Calibraion o he US economy In his secion, I calibrae he model o he US economy for he period. The sources and deails of he daa series are provided in he Appendix. 3.1 Parameer values The model is calibraed o mach he US srucural ransformaion and per capia GDP growh from 195 o 27, assuming ha he disorions are consan and equal o one. The model period is 1 year. The naural counerpar for he labor inpu in he model is secoral shares of hours worked. The parameer values o be deermined are c, c, β, δ, ε, α and µ and he ime series for A a s i a, A m, A s and iniial capial. The capial share α is se o.33, as esimaed by Herrendorf and Valeninyi (28). Choosing values for he produciviy levels A i(i = a, m, s) amouns o choosing unis; herefore, I normalize he produciviy levels o 1 in 195. I use daa for secoral value added, secoral capial and hours o compue secoral TFPs. I hen use he average growh raes for he period o deermine he secoral TFP series See he Appendix for addiional deails.

12 12 El-hadj Bah Table 1 Calibraed parameers. Parameer Value Targe and commens A a 1 A m 1 Normalizaion A s 1 γ a 2.2% γ m 1.6% Calculaed from secoral daa γ s 1% ca.12 Shares of hours in Ag in 195 cs.12 Shares of hours in Serv. in 195 α.33 Lieraure β.96 4% Ineres rae δ 5% Average invesmen rae of 22.3% ε.1 μ 1.1 Long erm labor reallocaion across secors μ 2.12 μ 3.87 k o 4.65 Capial-oupu raio in 195 I use he sandard value for β of.96, which corresponds o an ineres rae of 4%, and calibrae δ o mach he average capial-oupu raio for he US. The iniial capial sock is seleced o mach he capial-oupu raio in 195. The nonhomoheic parameers c a and c are calibraed o mach he iniial shares of s hours worked in agriculure and services. The remaining parameers, he weighs ( μ i ) and he elasiciy of subsiuion (ε) beween goods, govern he long-erm labor reallocaion across secors. Herrendorf, Rogerson, and Valeninyi (29) argue ha for value added consumpion, ε is very low if no zero. I se i o.1 for he benchmark calibraion and will subsequenly conduc a sensiiviy analysis. The weighs of he differen goods are se o mach he long-erm shares of hours worked in he hree secors. I use.1 for agriculure and.12 for manufacuring. 12 Table 1 summarizes he calibraed parameer values. 3.2 Srucural ransformaion of he US economy This secion provides some insighs ino how well he calibraed model fis he US daa. I use he calibraed model o compue per capia GDP and he secoral 12 The corresponding values in Herrendorf, Rogerson, and Valeninyi (29) are.1.2 and.15.18, respecively.

13 Disorions, srucural ransformaion and he Europe-US income gap 13 A GDP per capia Model Daa B Ag-Model Ind-Model Serv-Model Ag-Daa Ind-Daa Serv-Daa GDP per capia growh Share of hours Figure 1 US srucural ransformaion wihou disorions. shares of hours for he US economy for he period and compare hem wih he daa series. 13 Firs, I discuss he case wih no disorions (τ i = 1), and hen, I show ha incorporaing a wedge in he nominal wages beween services and manufacuring improves he fi of he model. Figure 1 plos GDP per capia and he changes in he shares of hours prediced by he model. 14 This figure shows ha he compued secoral TFP growh raes and he calibraion allow he model o mach per capia GDP growh very closely. The model also does a very good job of replicaing he shares of hours in agriculure. Recall ha he only arge was he iniial share and he weigh of he agriculural good seleced o mach he long-erm rend. For he oher wo secors, he model fis he daa closely unil he lae 197s. Beginning in he mid-198s, he daa reveal a sharp decline in he manufacuring share of hours ha is no well replicaed by he model. This discrepancy beween he model and he daa has been observed by oher researchers, moivaing hem o search for addiional facors for labor reallocaion beween manufacuring and services (Buera and Kaboski 29; Ungor 211). As explained earlier, he inroducion of capial slows down he reallocaion of labor and capial across secors when he income effec becomes small. The discrepancy noed above also occurs for he reallocaion of capial. From he secoral daa for capial ha are used o calculae he secoral TFPs, I compue 13 The daa series has been filered o focus on low frequency ime series. 14 I use he prices in 195 o compue GDP per capia for all periods.

14 14 El-hadj Bah he reallocaion of capial in each secor as he ending share minus he iniial share. The daa show small changes in all hree secors. For agriculure and indusry, he shares declined by 3. and 3.38 percenage poins, respecively. Thus, he shares of services increased by 6.8 percenage poins. Clearly, wih he large increase in he shares of services in erms of value added, labor and consumpion in he las 57 years, he model predics much greaer reallocaions of capial. According o he model, he shares for agriculure and indusry declined by 6.8 and 4.11 percenage poins, respecively. Thus, qualiaively, he model is consisen wih he daa, bu i predics larger changes in capial. Because he daa for secoral capial may have measuremen errors, we can use he predicions for labor produciviy o assess he performance of he model wih respec o capial reallocaion. If he model predics secoral labor produciviy and labor reallocaion correcly, i mus also predic capial reallocaion correcly. This es is imporan for European counries ha will be analyzed laer, as we do no have daa for secoral capial. The average growh raes of labor produciviy ha are prediced by he model are 3.44%, 2.45% and 1.86% for agriculure, indusry and services, respecively; he corresponding averages from he daa are 3.36%, 2.35% and 1.5%, respecively. Thus, he predicions of he model are quie closed o he daa. The model also predics he relaive prices of agriculure and services, which reflec he differences beween he secoral TFP growh raes. The relaive price of agriculure declined by 1% per year, on average, and he relaive price of services grew by.6%. Using he Groningen 1-secor daabase, he corresponding growh raes beween 1971 and 2 are 1% and.9%, respecively. Therefore, he model maches he decline in he price of agriculure bu underpredics he growh in services. Inroducing a wedge beween he wages in services and manufacuring allows he model o mach he pahs of hours in hose wo secors. I assume ha he disorion is consan and equal o one beween 195 and 1979 bu ha i grows a a consan rae of 1.5% from 198 o 27. Figure 2 shows he new srucural ransformaion pah for he US. The model no only sill maches per capia GDP growh bu also now maches he shares of hours in all hree secors. As for he growh raes of labor produciviy by secor, he model now predics slighly higher growh raes in agriculure and indusry, wih no change in services; he respecive growh raes are 3.69%, 2.69% and 1.86%. The disorion makes labor less expensive in services compared o manufacuring, leading more workers o be reallocaed from manufacuring ino services. The capial inensiy herefore increases in manufacuring, while i decreases in services. Using secoral daa for he US, I find ha he average hourly wage in services relaive o manufacuring in 27 is 94% and ha he capial-labor raio in services relaive o manufacuring has declined. Overall, he disorions in

15 Disorions, srucural ransformaion and he Europe-US income gap 15 A 3.5 B.8 GDP per capia Model Daa Ag-Model Ind-Model Serv-Model Ag-Daa Ind-Daa Serv-Daa GDP per capia growh Share of hours Figure 2 US srucural ransformaion wih disorions in services. services improve he performance of he model in maching he srucural ransformaion of he US economy since Disorions and srucural ransformaion across counries In his Secion, I use he calibraed model o sudy he srucural ransformaions for nine OECD counries and quanify he disorions in agriculure and services. 15 The selecion of counries is based on daa availabiliy. The only source ha harmonizes secoral daa across counries is EU KLEMS. The daa coverage is limied o OECD counries beginning in 1971 or Mehodology From he daa, I compue he average growh rae of TFP in each secor. However, hese growh raes canno be used direcly in he model because hey come from differen producion funcions and daa ses. For insance, he average growh rae of aggregae real value added ha is used in he compuaion of he TFP 15 Bah and Brada (29) use a similar model o assess he produciviy cach-up in 1 ransiion counries in Easern Europe. 16 Deails concerning he daa and compuaion mehods are presened in he appendix.

16 16 El-hadj Bah growh rae for he UK is 2.6%, while he average growh rae of GDP from he Penn World Tables (PWT) is 2.87%. 17 Moreover, he EU KLEMS daa decompose capial ino informaion and communicaion echnology (ICT) and non-ict and ake ino accoun labor composiion. In addiion, he capial shares vary over ime and are no equalized across secors. For all hese reasons, I do no use he compued average growh raes direcly; insead, I use hem o deermine he growh differenials across secors. The nex sep is o find he iniial secoral TFPs and non-homoheic parameers for each counry. We know ha he iniial secoral TFP and non-homoheic parameers deermine he iniial allocaion of hours. As argued by Duare and Resuccia (27, 21), c and c canno be invarian o large changes in produciviy a s for agriculure and services. Similar o heir procedure, from equaion (25), I impose cs ha is invarian across counries. Because of he differences in he iniial AK α s agriculural shares of hours, imposing a similar condiion for c a is problemaic. For he UK, he agriculural share of hours was 3% in 1971, bu i was 22% in Ialy. Selecing agriculural TFP o mach such shares will imply ha he UK is much more producive han he US, while Ialy is much less producive. As in Duare and Resuccia (27), I selec c o mach he iniial agriculural share of hours. a The Groningen cener esimaed secoral TFPs relaive o he US in 1997 for a number of OECD counries. I use he secoral TFP growh raes from EU KLEMS o deermine he relaive TFPs in 1971 or For he same reasons as saed above, using hese esimaes direcly will no allow he model o mach some aspecs of he daa. Specifically, I scale he iniial secoral TFP levels up or down such ha he model maches he iniial GDP per capia relaive o he US. 18 Because I employ a common scaling facor, his procedure amouns o using he daa o deermine he differences in iniial secoral TFP levels and using he model o deermine he corresponding levels. Wih he iniial TFP levels and preference parameers seleced as described above, he model may sill no predic he share of hours in services. Therefore, I selec he iniial disorion in services (τ s1 ) such ha he model maches he share of hours for ha secor. If here is a discrepancy beween he ime pahs of secoral shares of hours in he model and he daa, I selec he growh raes of he disorions in agriculure and services such ha he model follows he daa closely. Iniial capial is chosen o mach he capial-oupu raio, compued using invesmen daa from he Penn World Tables. 17 Such discrepancies are also presen for oher counries. 18 The US secoral prices in 195 are used o compue he GDP per capia for all counries.

17 Disorions, srucural ransformaion and he Europe-US income gap 17 The procedure can be summarized as follows. Iniial capial is chosen o mach he capial-oupu raio in he iniial period. I choose c o mach he iniial a cs agriculural shares of hours, and c is chosen such ha is consan across s α AK counries. The daa are used o deermine he iniial secoral TFP differences, and he levels are chosen such ha he model maches he iniial GDP per capia relaive o he US. The secoral TFP growh differenials are derived from he daa, and he acual growh raes are chosen such ha he model maches he observed per capia GDP growh rae. The iniial disorion in services is chosen o mach he iniial service share of hours, and he growh raes of he wo disorions are chosen such ha he model replicaes he ime pahs of secoral shares of hours. s 4.2 Comparing secoral TFP pahs Before discussing he disorions, I analyze he pahs of secoral TFP for he nine European counries relaive o he US. Recall ha he relaive TFPs esimaed by he Groningen cener are scaled such ha he model maches he iniial GDP per capia relaive o he US. 19 Moreover, given he differences in he growh raes from he daa, he acual TFP growh raes are chosen o mach he average growh rae of GDP per capia. The arges and predicions of he model are shown in Table 2. As we can see from he able, he model maches he arges very closely. Table 2 European arges. Counry Average growh GDP/capia Iniial GDP/capia rel. o US Iniial capial o GD raio Daa Model Daa Model Daa Model Ausria Belgium Denmark Finland France Ialy Neherlands Spain UK If heir iniial esimaes include disorions, hey will appear here. However, hese are he bes esimaes available.

18 18 El-hadj Bah A 1.1 B Ag. TFP relaive o he US Ind. TFP relaive o he US Agriculure Indusry C Serv. TFP relaive o he US AUT BEL DNK FIN FRA ITA NLD ESP UK Services Figure 3 Relaive secoral TFP across counries. Noe: This figure plos TFP relaive o US by secor for all nine EU counries. The iniial relaive TFPs compued from he daa were scaled up or down o mach iniial GDP per capia relaive o he US. Also, he average growh raes from he daa were used o compue growh differenials and he model was used o infer he acual growh raes in order o mach average growh of GDP per capia. Figure 3 plos he relaive produciviies in he hree secors from 1981 o Panel (A) presens he relaive TFPs in agriculure. The iniial produciviies vary from a low of 43% for Ialy o 85% for Belgium and he Neherlands. The produciviy of all counries grew more rapidly han ha of he US, wih a very rapid cach-up for Spain and Ialy. 2 The simulaions for Finland, Ialy and he UK begin in 1971, bu in his graph, I provide a common saring dae o faciliae he comparison.

19 Disorions, srucural ransformaion and he Europe-US income gap 19 As panel (B) shows, he iniial TFPs in indusry were close o he US level. In fac, few counries were more producive han he US in Among all he counries, five caugh up o he US, while he oher four fell behind. Neverheless, mos counries are above 9% of he US level in 27. We observe a differen paern in Panel (C), where all counries began below he US level for services and fell behind over ime. The larges decline occurred in Ausria, where he relaive service TFP declined by more han 2 percenage poins. A comparison of relaive TFPs across secors demonsraes ha he ranking changed over ime. Iniially, mos counries were relaively he leas producive in agriculure, followed by services and hen indusry. However, wih he cach-up in agriculure and he decline in services, mos counries were relaively more producive in agriculure han in services by 27. Throughou he period, mos of he counries achieved heir highes produciviy level in indusry. This paern is documened by Duare and Resuccia (21) for labor produciviy. Mos counries (developed and developing) no only were relaively less producive in services in he 195s bu also failed o cach up o he US over ime. By conras, mos counries were able o cach up o he US over ime in agriculure and indusry. 4.3 Secoral Disorions and Labor Reallocaions Wihou any disorions in he reallocaion of resources across secors, he secoral TFP series discussed above canno explain he pahs of labor shares ha are observed in he daa. Firs, he model predics ha more workers are in services in he iniial period because he difference in TFP beween secors is no large enough. Second, he growh differenial beween indusry and services underpredics he labor reallocaion from indusry o services. Recall ha only subsiuion effecs play an imporan role a laer sages of he srucural ransformaion process. Wih disorions in agriculure and services, he model is able o mach he labor allocaions in he daa very closely. For each counry, τ a1 = 1, and τ s1 is chosen for he model o mach he iniial secoral shares of hours in services. The growh raes of he wo disorions are chosen for he model o replicae he pahs of labor shares. Figure 4 shows ha he model closely maches he pahs of labor shares over he full period for all counries. Compared o he US, he European counries have a high share of hours in agriculure and a lower share in services in he iniial period. The differences are paricularly sark for Finland, Ialy and Spain. This implies a high iniial disorion in services. In Table 3, I presen he inferred disorions. The iniial τ s ranges from.65 for Ialy o 1.28 for Denmark. Recall ha in he model,

20 2 El-hadj Bah A B C Ausria Belgium D E F Finland France G H I Neherlands Spain Denmark Ialy Unied Kingdom Figure 4 Srucural ransformaion wih disorions in Europe. Noe: This figure plos secoral shares of hours for each counry. The disorion τ a1 = 1 bu can grow over ime is 2 words for some counries. τ s1 is se o mach iniial service shares of hours and is allowed o grow over ime is 2 words. τ s = W m /W s. Therefore, he resuls indicae ha he wage in indusry is 35% lower han ha in services for Ialy, while i is 22% higher for Denmark. Again, he magniudes of he disorions are explained by he iniial differences in TFP and he shares of hours in indusry and services. In 1971, he shares of hours in Ialy were 38% in indusry and 39% in services. The corresponding relaive secoral TFPs were 83% and 93%, respecively, of ha of he US. These resuls

21 Disorions, srucural ransformaion and he Europe-US income gap 21 Table 3 Agriculure and service disorions. Counry Agriculure Services Growh% (period) Iniial Growh (period) Ausria 1.5 (82 7) (86 7) Belgium (95 7) Denmark Finland 1.8 (79 7).7.6; 1.4;.8 a France (86 7) Ialy 1.3 (82 7) (94 7) Neherlands (89 7) Spain..95. UK 1.6 (8 7) (8 7) a For Finland, here are hree sub-periods: 76 91, 92 1, and 2 7. show why a high level of disorion is required o mach he shares of hours in services. 21 There is also subsanial variaion in he growh raes of he disorions for boh agriculure and services. For agriculure, Belgium, Denmark, France and Spain had no disorion. For he oher counries, he growh raes were below 1.5% for Ausria, he Neherlands and Ialy bu above ha for he UK and Finland. Regarding services, only wo counries (Denmark and Spain) had a consan disorion. The growh raes ranged from 1.1% o 1.9% for he oher counries. The growh raes of he disorions are driven by he TFP growh differenials and labor reallocaion paerns in indusry and services. For example, in he UK, he iniial shares of hours were 46% in indusry and 51% in services. By 27, he respecive shares were 2% and 78%. Thus, here was a subsanial reallocaion of labor ino services (+27 percenage poins) even hough he secoral TFP growh differenial was only 1.43 percenage poins. Therefore, a high iniial disorion is needed in services, and he disorion mus grow a a high rae. As for he US, I compare he secoral averages of he labor produciviy growh raes ha are prediced by he model wih hose from he daa o assess he performance wih respec o capial reallocaion. Figure 5 plos he growh raes in he daa versus he model for each secor. Qualiaively, he predicions of he model are consisen wih he daa. We can also see ha many daa poins are close o he 45 degree line, especially for manufacuring. 22 Thus, he model wih disorions is consisen wih he daa. 21 Noe ha errors in he esimaes of secoral TFP in he daa will affec he magniude of he disorions inferred from he model. 22 The fi for he counerfacuals below is worse, indicaing ha he disorions do no hinder he capial reallocaion.

22 22 El-hadj Bah A 6 Agriculure B 5 Indusry Model ITA UK BELDNK NLD ESP FRA FIN AUT Model ESP ITA NLD DNK UK BEL FRA AUT FIN Daa Daa C 3 Services Model 2 1 ITA DNK NLD UK ESP BEL FRA FIN AUT Daa Figure 5 Labor produciviy growh: Daa vs. model. Noe: This figure plos he labor produciviy growh raes by secor for all nine EU counries from he daa and he model. The growh raes from he daa are calculaed from EU KLEMS. 4.4 Counerfacuals In his Secion, I conduc a simple experimen o highligh he role of he disorions. Assuming ha he disorions are consan over ime, I presen he predicions of he model for labor reallocaions and cach-up o he US in erms of GDP per capia. Figure 6 plos he pahs of he secoral shares of hours for all counries when τ a and τ s are held consan. Wih he excepion of Denmark

23 Disorions, srucural ransformaion and he Europe-US income gap 23 A B C Ausria D E F G H I Finland Neherlands Belgium France Spain Denmark Ialy Unied Kingdom Figure 6 Srucural ransformaion wihou disorions in Europe. Noe: This figure plos secoral shares of hours for each counry. The disorions are held consan from he iniial period. and Spain, all oher counries would have had much more labor in indusry and much less labor in services. The declines in agriculure were he larges in Finland ( 18 percenage poins) and Ialy ( 17 percenage poins). Absen growh in he disorions, he model would have implied respecive declines of 2 and 18 percenage poins for Finland and Ialy. The declines in manufacuring shares of hours in he daa vary from 2 percenage poins in Spain o 25 percenage poins in he UK. Mos oher counries had declines of approximaely 1 percenage poins. The model wih consan

24 24 El-hadj Bah disorion, especially in services, predics very lile reallocaion ou of indusry. For insance, he model predics a decline of 1 percenage poins for he UK compared o he 25 percenage poins in he daa. As he service secor is generally less producive han he manufacuring secor, a small reallocaion of labor ou of indusry would have implied a much more rapid income cach-up o he US. In Figure 7, I show he pahs of GDP per capia relaive o he US, for he baseline model, he counerfacuals and he daa. A B C GDP/Capia relaive o he US GDP/Capia relaive o he US Ausria Finland GDP/Capia relaive o he US Belgium D E F GDP/Capia relaive o he US France G H I GDP/Capia relaive o he US Neherlands GDP/Capia relaive o he US Spain GDP/Capia relaive o he US GDP/Capia relaive o he US GDP/Capia relaive o he US Denmark Ialy Unied Kingdom Figure 7 GDP per capia relaive o he US. Noe: This figure plos he pahs of GDP per capia relaive o US for each counry. The doed line represens he daa, he solid line represens he model wih growing disorions and he dashed line represens he counerfacual where disorions are consan.

25 Disorions, srucural ransformaion and he Europe-US income gap 25 Firs, i is clear ha mos counries do no cach up over he full period. Ausria, Belgium, Ialy and he Neherlands ended he period a almos he same levels of GDP per capia relaive o he US. Absen growh in he disorions, hese counries would have been able o cach up o he US o some exen. For example, Ausria began a 87% of he US in 1981 and ended a 89% of he US in 27. Wih consan disorions, he GDP per capia for Ausria would have been 95% of ha for he US. The counries wih he larges gains relaive o he US were Finland and he UK. The gain for Finland would have been 2 percenage poins raher han he 12 percenage poins in he daa and he benchmark model. For he UK, he GDP per capia would have increased o 89% of ha for he US (+21 percenage poins) raher han 81% (+13 percenage poins). Denmark and France los ground relaive o he US by 2.4 and 8.5 percenage poins, respecively. A consan disorion was sufficien o mach he labor reallocaions across secors for Denmark bu no for France. If he disorion in services was consan, France would have los 6.8 percenage poins. Overall, he graphs indicae ha he growh in he disorions acceleraed he labor reallocaion ou of indusry and slowed he income cach-up of he European counries o he US. 4.5 Evidence for Disorions Throughou he quaniaive exercises, I have shown ha disorions ha creae wedges beween secoral nominal wages, especially in services, are imporan for he model o mach he reallocaion paerns observed in he daa. The key is for he wedges o grow over ime. The disorions can resul from size-dependen policies, agriculural policies, access o credi, differences in human capial, infrasrucure, enry coss, axes, labor regulaions ec. Guner, Venura, and Xu (28) discuss size-dependen policies ha affec secors differenly. For example, in some European counries, small reailers are proeced from compeiion from large reailers, and employmen proecion laws (hiring, firing, using emporary workers, ec.) ofen depend on he size of he firm. These laws creae he ypes of disorions ha are emphasized in his model. However, caaloguing and quanifying he effecs of hese laws is a difficul ask. Insead, I employ he labor cos measure from he OECD STAN daabase o indicae wheher relaive labor coss vary over ime. The daabase noes ha he labor cos measure covers a significan par of oal labor coss such as wages and salaries; bonuses; paymens in kind relaed o labor services (e.g., food, fuel, housing); severance and erminaion pay and employers conribuions o pension schemes, casualy and life insurance and workers compensaion.

26 26 El-hadj Bah Labor coss in indusry relaive o services AUT BEL DNK FIN FRA ITA NLD ESP Figure 8 Labor coss in indusry relaive o services. Noe: This figure plos labor coss of indusry relaive o services for each counry. The values have been normalized o one in he firs period o highligh he changes over ime. Figure 8 plos he labor coss per hour in indusry relaive o services for he period for eigh of he counries in my sample. 23 I is clear ha he wedge is growing over ime and ha here are differences across counries. However, he growh raes in he model are generally higher han he wedge ploed here, which is no surprising as he daa only represen one componen of he disorions considered in he model. 5 Discussion 5.1 Inernaional Trade The model used here assumes a closed economy, and I quanify he necessary disorions for he model o mach he secoral shares of hours for OECD counries. However, inernaional rade may play a role in he srucural ransformaion process. 24 Uy, Yi, and Zhang (213) show ha increased produciviy growh in manufacuring in one counry can lead o an invered U-shaped paern for he labor shares in ha counry and a seady decline in oher counries. For insance, an increase in manufacuring produciviy in China can lead o a decline in manufacuring labor shares for counries such as he US, Korea and Japan (Coleman II 23 The series has been normalized o one in 1995 o focus on he growh of he wedge. 24 See, for example, Masuyama (29), Coleman II (27), Uy, Yi, and Zhang (213), Tombe (212), Huang (211), Ungor (211), among ohers.

27 Disorions, srucural ransformaion and he Europe-US income gap 27 Trade balance/gdp AUT BEL DNK FIN FRA ITA NLD ESP UK US Figure 9 Trade balance relaive o GDP. Noe: This figure plos he pahs of rade balance relaive o GDP for he US and he 9 EU counries. The series have been filered o focus on he rend. 27, Ungor, 211) bu an increase in he shares for China. 25 While his is plausible, i is difficul o quaniaively evaluae he effecs of his channel. Huang (211) include he negaive rade balance for he US in a similar hree-secor model o show ha such a model can explain he decline in he shares of hours worked in indusry. Specifically, he assumes ha y m TB = c m +x, where TB is he oal rade balance ha was hen replaced wih he rade balance as a share of GDP in he simulaion. Noe ha his formulaion is similar o using a disorion in manufacuring oupu and using he rade balance o measure he disorion. Overall, heories in he lieraure predic ha counries wih deerioraing rade balances will experience a more rapid decline in he labor shares for indusry and a higher growh rae in he service disorion. In Figure 9, I plo he rade balance as a share of GDP for he period. The larges declines in he rade balance occur in Spain, he US and he UK. While maching he declines for he UK and he US required rapid growh in he disorion, a consan disorion was sufficien o mach he labor shares for Spain. Moreover, counries such as Finland, he Neherlands and Ausria have posiive and growing rade balances, while heir service disorions grow a high raes, which is inconsisen wih he 25 Large exporers, such as Germany, Japan and Korea, also have large manufacuring labor shares.

28 28 El-hadj Bah heoreical predicions. Therefore, he inroducion of rade in my model does no eliminae he need for he disorions, as emphasized here when looking a he srucural ransformaion paerns of a large se of counries. 5.2 Capial Shares In he baseline model, I assume ha he capial shares are equalized across secors. However, he empirical evidence shows ha he assumpion is no valid for agriculure. Esimaes of capial shares for agriculure are approximaely.5 for he US. There are few implicaions from using his value for agriculure and mainaining he equaliy of capial shares for indusry and services a.33 for an economy wih consan disorions. Wihou changing he non-homoheiciy parameers c and c, he model implies a lower iniial share of hours in agriculure and a larger share in services. The iniial share in agriculure declines a s from 8.4% o 4.7%. Overall, we will have a sligh decrease in GDP growh (from an average of 2.12% o 2.9%) because US agriculure is more producive han US services. If I recalibrae c and c o mach he iniial shares, he higher capial a s share implies ha here is a more rapid reallocaion of labor from agriculure. However, by 27, he model predics only a very sligh decline in he agriculural shares of hours. Herrendorf and Valeninyi (28) find ha he capial shares for final expendiures are nearly idenical beween indusry and services. In erms of value added, he shares depend on how we rea buildings. If we include housing capial, services will be more capial inensive. In his case, he model would predic ha labor reallocaes from services ino manufacuring, which conrass wih wha is observed in he daa (Herrendorf, Rogerson, and Valeninyi 213). Defining he shares as such would hus imply higher disorions. 5.3 Invesmen This model assumes ha all invesmen comes from he manufacuring secor; however, his assumpion may be inconsisen wih he daa for more recen years. Par of informaion echnology, which has grown remendously since he early 199s, is from he service secor. However, i is exremely difficul o separae invesmen by source given he available daa even for he US. Moreover, assuming ha par of invesmen comes from services grealy complicaes he soluion mehodology of he model. Righ now, he soluion mehodology uses a forward shooing algorihm wih wo dynamic equaions in aggregae capial and