Structural Change and Aggregate Employment Fluctuations in China and the US

Transcription

1 Srucural Change and Aggregae Employmen Flucuaions in China and he US Wen Yao Tsinghua Universiy Xiaodong Zhu Universiy of Torono Firs Complee Draf: December 2017 Absrac One salien feaure of business cycles in developed counries is ha he aggregae employmen is highly procyclical. In China, however, he correlaion of he cyclical componens of aggregae employmen and oupu is close o zero. In his paper, we documen hree new sylized facs: (1) he business cycle properies of employmen a secor level (agriculure and non-agriculure) in China are very similar o hose in he US; (2) employmens in he agriculural and non-agriculural secors are negaively correlaed in boh China and he US; and (3) for boh economies, he agriculure s share of employmen is negaively correlaed wih he real GDP per work in boh secors. These facs sugges ha difference in secor composiion could be an imporan reason for he difference in aggregae employmen flucuaions beween he wo economies. We hen consruc a simple wo-secor growh model wih produciviy shocks and non-homoheic preferences and show ha he model can simulaneously accoun for he secular rend in labor reallocaion away from agriculure and employmen flucuaions a secor level and in he aggregae for boh China and he US. JEL Classificaion: E24, E32, O41 Keywords: Srucural Change, Non-homoheic Preferences, Labor Reallocaion, Aggregae Flucuaions Yao, School of Economics and Managemen, Tsinghua Universiy, yaow@sem.singhua.edu.cn. Zhu, Deparmen of Economics, Universiy of Torono, xzhu@chass.uorono.ca. We would like o hank paricipans a he 2016 PBC- SAIF Conference on Moneary Policy, 2016 Midwes Macro Meeings, 2017 Growh and Insiuion Program Meeing a Tsinghua Universiy, 2017 China Meeing of he Economeric Sociey a Wuhan Universiy, and seminars a several universiies for heir useful commens. Par of he research was done when Xiaodong Zhu was visiing he Shanghai Advanced Insiue of Finance (SAIF), and he hanks SAIF for is hospialiy and financial suppor.

2 1 Inroducion One salien feaure of business cycles in developed counries is ha he aggregae employmen is srongly procyclical. This is no he case in China. The correlaion of he cyclical componens of aggregae employmen and oupu is close o zero. Relaive o oupu, he volailiy of aggregae employmen is also very low. These puzzling facs abou aggregae employmen flucuaions in China are presen even afer we carefully correc for some well-known measuremen problems in he official employmen series. Some ake his as a sign ha here are unique insiuional consrains ha limi he employmen variabiliy in China. While i is rue ha here may be srong employmen rigidiy in he sae-owned enerprises, he labour marke for he non-sae secor in China is quie flexible maybe even more flexible han many developed economies due o minimum regulaions on hiring and firing by non-sae firms. Since he non-sae secor employmen is usually he margin a which he aggregae employmen adjuss over he business cycles, he insiuional consrains on sae-secor employmen canno explain he puzzle In his paper, we argue ha he key o undersanding aggregae employmen flucuaions in China is is economic srucure. We documen hree new sylized facs for he period from 1978 o Firs, he business cycle properies of employmen a secor level (agriculure and non-agriculure) in China are very similar o hose in he US. In paricular, he correlaion of he cyclical componens of nonagriculural employmen and non-agriculural GDP are close o 90 percen in boh counries. Second, employmens in he agriculural and non-agriculural secors are negaively correlaed in boh China and he US. And hird, for boh counries, he agriculure s share of employmen is negaively correlaed wih he real GDP per worker in boh secors. These similariies beween China and he US a secor level sugges ha he key difference beween he wo economies is he size of he agriculural secor. Beween 1978 and 2010, he agriculure s share of oal employmen averaged around 50% in China, bu was always less han 3% in he US. Therefore, he labour reallocaion beween he wo secors could have an imporan dampening effec on aggregae employmen flucuaions in China, bu negligible effec in he US. To invesigae his possibiliy, we consruc a wo-secor growh 1

3 model wih produciviy shocks and non-homoheic preferences, and calibrae i so ha he model can accoun for he secular rend in labour reallocaion from agriculure o non-agriculure in boh China and he US. We hen examine he model s implicaions for he labour marke dynamics a he business cycle frequency. We find ha our calibraed model can indeed accoun for he employmen flucuaions a secor level and in he aggregae for boh China and he US. In paricular, our model implies low employmen-oupu correlaion for China and, a he same ime, high employmen-oupu correlaion for he US. The model we use in he paper is a sandard wo-secor growh model, bu wih non-homoheic preferences proposed by Comin, Lashkari and Mesieri (2015) o accoun for he hird sylized fac we discussed above: For boh China and he US, he agriculure s share of employmen is negaively correlaed wih real income per worker in boh agriculural and non-agriculural secors. This fac suggess he imporance of income effec in deermining labour reallocaion beween secors even for a high income counry like he US. Our paper is relaed o wo srands of lieraure. There is a rapidly growing lieraure on srucural change. See e.g., Caselli and Coleman (2001), Kongsamul, Rebelo and Xie (2001), Ngai and Pissarides (2007), Acemoglu and Guerrieri (2008), and Herrendorf, Rogerson and Valeninyi (2014) for an excellen survey. Mos of he sudies in his lieraure focus on undersanding he sources of srucural change, our paper builds on his lieraure and sudies he business cycle implicaions of srucural change. In paricular, boh Boppar (2014) and Comin, Lashkari and Mesieri (2015) emphasize he imporance of income effec in undersanding he secular rend of labour reallocaon from agriulure o manufacuring and services. We show in his paper ha income effec is also imporan for undersanding aggregae employmen flucuaions a he business cycle frequnecy. Our paper is also relaed o he lieraure on business cycles in China. Brand and Zhu (2000) is one of he firs papers sudying business cycles in China during he reform period. Their focus, however, is on undersanding he relaionship beween GDP growh and inflaion over he business cycles in he 1980s and early 1990s. Chang e al. (2016) is a more recen sudy of business cycles in China, and heir focus is on undersanding he weak correlaion beween invesmen and consumpion in China 2

4 since he lae 1990s. Neiher of hese sudies examine he relaionship beween aggregae employmen and oupu. He, Chong and Shi (2009) carry ou an exercise of business cycle accouning for China in he spiri of Chari, Kehoe and McGraan (2007). They find ha mos of he flucuaions in aggregae employmen are accouned for by variions in a labour wedge, highlighing he inabiliy of sandard one-secor business cycle models in accouning for he employmen flucuaions in China. Our paper shows ha a sandard wo-secor model wih non-homoheic preferences can accoun for he aggregae employmen flucuaions wihou inroducing a ime-varying labour wedge. There are wo sudies ha are closely relaed o our paper. Da-Rocha and Resuccia (2006) is he firs paper ha documens he low correlaion beween aggregae employmen and oupu in counries wih a large agriculure secor. They use a wo-secor real business cycle model o examine he role of labour reallocaion in accouning for he cyclical behaviour of aggregae employmen. To focus on he cyclical flucuaions, hey assume ha each counry is flucuaing around a seady sae wih a consan employmen share of agriculure. Since srucural change - he secular decline of he agriculure s share of employmen - is a very prominen phenomenon in China during he period we sudy, we hink i is imporan o have a unified model ha can accoun for boh he secular rend of srucural change and he aggregae employmen flucuaions around he rend. In an independne sudy, Soresleern, Tan, Zhao and Ziliboi (2017) also use a wo-secor model o accoun for boh he srucural change and aggregae employmen flucuaions in China. Their model, however, is very differen from ours. They empahsize capial deepening raher han income effec as a driving force for srucural change and labour reallocaion beween he agriculural and non-agriculural secors. We hink heir sudy and ours are complemenary. Before presening our model, we firs discuss in deail he daa and facs abou employmen flucuaions in China and he US. 3

5 2 Daa and Facs For he US, we direcly use he annual secor-level daa on real GDP and employmen from he Groningen Growh and Developmen Cenre s 10-Secor Daabase (Timmer, de Vries and de Vries (2015)), and aggregae he nine secors ouside agriculure ino one non-agriculural secor. For China, he 10-Secor Daabase uses he official employmen seies from China s Naional Bureau of Saisics (NBS) ha are published in he annual China Saisical Yearbook. However, as poined ou by Brand and Zhu (2010), here are wo serious problems wih he NBS employmen series ha need o be deal wih. We discuss nex how we deal wih hese problems and consruc revised annual employmen series for China. Firs, here is a discree upward jump in oal employmen in This jump is due o a change in he official definiion of employmen afer 1990 census ha broadened he coverage of he series. The NBS publishes he employmen daa using he new definiion for he years since 1990, bu sill repors he employmen daa using he old definiion for he years prior o Brand and Zhu (2010) use he 1982 census daa o adjus he employmen daa for he years before 1990 so ha he enire employmen series has a consisen coverage. The official and he revised employmen series are ploed in he lef panel of Figure 1. The second problem of he NBS employmen series is he overesimaion of agriculural employmen. Brand and Zhu (2010) find ha he official agriculural employmen series can be closely approximaed by he Toal Rural Employmen minus he Employmen of he Township and Villiage Enerprises (TVEs). This series clearly overesimaes agriculural employmen because non-agriculural workers in rural privae enerprises and rural individual enerprises (hose ha employ less han eigh employees) are couned as agriculural workers. To beer accoun for employmen in agriculure, we follow Brand and Zhu (2010) and consruc agriculural employmen series as he oal rural employmen minus rural employmens in TVEs, privae enerprises and individual enerprises. The official and he revised agriculural employmen series are ploed in he righ panel of Figure 1. Noe ha his revised agriculural employmen series sill has he same problem as he official oal employmen series for he years prior o To generae a consisen agriculural employmen 4

6 Toal Employmen Figure 1: Agriculure Employmen 7.5 Official Revised Official Agriculure Rural - TVE Revised Agriculure series for he enire period, for each year we firs use he revised agriculural employmen and he official oal employmen o calculae he share of employmen in agriculure; we hen calculae he final revised agriculural employmen as he produc of he share and he revised oal employmen; and finally we calculae he revised non-agriculural employmen as he difference beween he revised oal employmen and he revised agriculural employmen. Figure 2 plos he revised agriculural and non-agriculural employmens and he agriculure s share of oal employmen using he revised daa series. 2.1 Employmen Flucuaions a he Aggregrae Level Given he revised employmen daa for China, we now examine he business cycle properies of aggregae employmen in China and compare hem o hose in he US. Our sample runs from 1978 o 2010 for boh counries. We presen he business cycle properies by calculaing several saisics from he hp-filered ime series. Table 1 repors he relaive sandard deviaion of aggregae employmen o aggregae oupu and he correlaion of aggregae employmen wih aggregae oupu in boh China and he US. All variables are normalized by he size of populaion. From Table 1, we observe wo ineresing sylized facs of aggregae employmen flucuaions in China: 5

7 Secor Employmen Figure 2: 0.7 Agriculure Share of Employmen 6 Agriculure Non-agriculure Table 1: Aggregae Momens China US σ (L)/σ (Y ) ρ (L,Y ) The magniude of flucuaions in aggregae employmen is much lower han ha of aggregae oupu in China. This is in sark conras wih he well known fac for he US economy, see Cooley and Presco (1995), where aggregae employmen flucuaes almos as much as he aggregae oupu. 2. Aggregae employmen is acyclical in China: daa shows correlaion of employmen wih oupu close o zero. This is also very differen from he esablished business cycle fac ha he US employmen is srongly pro-cyclical. Figure 3 plos he cyclical movemens of aggregae employmen and aggregae oupu for he wo counries which confirms our observaions. 6

8 0.1 China Daa Figure 3: 0.1 US Daa 0.08 Aggregae Employmen Aggregae Oupu 0.08 Aggregae Employmen Aggregae Oupu Employmen Flucuaions a Secor Level In order o fuher undersand he aggregae facs for China, we now look a he business cycle momens a secor level in China and compare hem o he momens in he US. We will show ha China and he US are acually very similar a secor level. The daa is divided ino agriculural and non-agriculural secors and hp-filered. Panel (A) and (B) in Table 2 show he employmen flucuaions in he wo secors, where subscrip a sands for agriculure and na sands for non-agriculure. Panel (C) documens he labor reallocaion beween secors by calculaing he correlaion of employmens in he wo secors and he correlaions beween he agriculure s share of employmen and secor-level labour produciviies A i, which is measured as he real GDP per worker in secor i, for i = a,na. Three new sylized facs emerge from he momens presened in Table 2: 1. Employmen flucuaions in each secor are very similar beween China and he US. For example, in he non-agriculural secor, he relaive magniude of employmen flucauaion is comparable o ha of he US. Moreover, nonagriculure employmen in China is highly pro-cyclical. In he agriculural secor, he employmen in China also has non-rivial volailiy while he correlaions beween employmen and oupu is low in boh China and he US. 2. The correlaion beween employmen in agriculural secor and non-agriculural 7

9 0.1 China Daa Figure 4: 0.1 US Daa Agriculure Employmen Non-Agriculure Employmen Agriculure Employmen Non-Agriculure Employmen secor is negaive in boh China and he US, as shown in he second column in Table 2 and Figure 4. This negaive correlaion suggess a poenial imporan role of labour reallocaion beween secors in dampening aggregae employmen flucuaions. Of course, he degree o which flucuaions of aggregae employmen are dampened depends on he relaive size of he agriculural secor. Beween 1978 and 2010, he agriculure s share of oal employmen averaged around 50% in China, bu was always less han 3% in he US. Therefore, he labour reallocaion beween he wo secors could have an imporan dampening effec on aggregae employmen flucuaions in China, bu negligible effec in he US. 3. For boh China and he US, he agriculure s share of oal employmen is negaively correlaed wih labour produciviies in boh agriculural and nonagriculural secors. This observaion suggess ha income effec, ha is, he agriculural good has lower income elasiiciy han he non-agriculural good, is an imporan facor for labour reallocaion beween secors. Comin, Lashkari and Mesieri (2015) emphasize he imporance of income effec in undersanding he secular rend of labour reallocaon from agriulure o manufacuring and services. Our fac suggess ha income effec is also imporan for labour reallocaion a he business cycle frequnecy. 8

10 Table 2: Secor Momens China US (A) Non-Agriculure Secor σ (L na )/σ (Y na ) ρ (L na,y na ) (B) Agriculure Secor σ (L a )/σ (Y a ) ρ (L a,y a ) (C) Cross Secor ρ(l a,l na ) ρ( L a L,A a ) ρ( L a L,A na ) Moivaed by hese new sylized facs, we now presen our wo-secor model wih non-homoheic preferences ha we will use o quaniaively accoun for labour marke dynamics in boh he long-run and shor-run. 3 The Model There are wo secors indexed by i = a and na, represening agriculure and nonagriculure, respecively. Each secor produces a consumpion good wih a linear echnology using labour as he only inpu: Y i = A i N i, i = a,na, where Y i, A i and N i are he oupu, labour produciviy and employmen in secor i, respecively. There is a sand-in represenaive household who has preferences over a composie consumpion good C and working ime L. The preferences are represened by a sandard uiliy funcion in he business cycle lieraure, he GHH uiliy funcion ha was firs inroduced by Greenwood, Hercowiz and Huffman 9

11 (1988), U = C B 1 + σ L1+σ. Here σ > 0 is he inverse of he Frisch labour supply elasiciy and B is a imevarying labour supply parameer ha is used o capure he demographic facors (e.g., age srucure and gender composiion of he labour force) ha affec average household s labour supply decisions. Following Comin, Lashkari and Mesieri (2015), he composie consumpion C is defined implicily by he following equaion: (ϕ a ) 1 C µ a 1 c 1 a + (ϕ na ) 1 µ na 1 C c 1 na = 1, where ϕ a, ϕ na, µ a, µ na and are all posiive consans. The parameer ϕ i represens he household s preference weigh on consumpion good in secor i (ϕ a + ϕ na = 1), µ i measures he income elasiciy of consumpion good i and is he elasiciy of subsiuion beween he wo consumpion goods. The impliciy uiliy funcion is a generalizaion of he sandard CES uiliy funcion by allowing for poenially differen income elasiciies for he wo consumpion goods. If µ a = µ na = 2, hen he uiliy funcion is reduced o he sandard CES uiliy funcion. If µ a < µ na, he income elasiciy is smaller for he agriculural good han for he nonagriculural good. As a resul, relaive demand for he agriculural good declines wih income. Noe ha for he implici uiliy funcion for C o be monoon and concave, we need boh µ a and µ na o be less han one if > 1 and greaer han one if < 1. (See he foonoe 12 of Comin, Lashkari and Mesierie (2015)). 3.1 Social Planner s Problem Since we assume ha here is no fricion nor exernaliy in he economy, he compeiive allocaion is he same as he social opimal allocaion, which is he soluion o he following social planner s problem: [ max {N C B ]} c a, c na,l a,l na, C 1 + σ L1+σ subjec o (ϕ a ) 1 C µ a 1 c 1 a + (ϕ na ) 1 µ na 1 C c 1 na = 1, (1) 10

12 c a = A a L a, (2) c na = A na L na, (3) L a + L na = L. (4) Here, N is he populaion size and L i = N i /N is he raio of employmen in secor i o oal populaion (i {a,na}). In he Appendix A, we show ha he opimal consumpion, c a and c na, and working ime L saisfy he following equaions: c a = ( ϕ a A 1 a c na = ( ϕ a A 1 a C µ a 1 ϕ a A ac µ a 1 + ϕ na A 1 na C µ na 1 ϕ na A nac µ na 1 C µ a 1 + ϕ na A 1 na C µ na 1 ), (5) 1 ), (6) 1 ( (1 ) ϕ a A 1 a L = ( B (µ a 1)ϕ a A 1 a C µ a 1 C µ a 2 ) + ϕ na A 1 na C µ na (µ na 1)ϕ na A 1 na C µ na 2 ) 3.2 Equilibrium Employmen, Consumpion and Oupu 1 σ. (7) From he goods marke clearing condiions, (2) and (3), and equaions (5) and (6), we have, L a = ( ϕ a Aa 1 L na = ( ϕ a A 1 a C µ a 1 ϕ a A 1 a C µ a 1 + ϕ na A 1 na C µ na 1 ϕ na A 1 na C µ na 1 C µ a 1 + ϕ na A 1 na C µ na 1 Hence he aggregae employmen o populaion raio is ( L = L a + L na = ϕ a A 1 a C µ a 1 ), (8) 1 ). (9) 1 ) + ϕ na A 1 na C µ 1 na 1 1, (10) 11

13 and he secor employmen shares are l a L a L = l na L na L = ϕ a A 1 a ϕ a A 1 a Equaion (11) can also be wrien as ϕ a A 1 a C µ a 1 + ϕ na A 1 na C µ, (11) na 1 C µ a 1 ϕ na A 1 na C µ na 1 + ϕ na A 1 na C µ. (12) na 1 C µ a 1 l a L a L = ( ) ϕ a Aa 1C µ a µ na ϕ na A na ( ) 1 + ϕ a Aa 1C µ a µ na ϕ na A na, (13) which shows ha he agriculure s share of employmen is affeced by wo facors, he relaive produciviy of agriculure A a /A na and he aggregae consumpion per capia C. The firs facor represens he subsiuion effec and he second facor he income effec. The subsiuion effec depends on wheher is smaller or larger han one. If is less han one, he agriculure s share of employmen is a decreasing funcion of he agriculural secor s produciviy and an increasing funcion of he non-agriculural secor s produciviy. The opposie is rue if is greaer han one. Therefore he subsiuion effecs of he wo secor s labour produciviy on he agriculural secor s employmen is in he opposie direcions as long as he value of is no equal o one, in which case here is no subsiuion effec. However, in Table 3 we have documened ha he cyclical componen of he agriculure s share of employmen is negaively correlaed wih he cyclical componens of real labour produciviy in boh secors, suggesing ha he second facor, income effec, is also imporan for labour reallocaion a he business cycle frequency. If µ a < µ na, hen he agriculure s share of employmen is a decreasing funcion of he aggregae consumpion. Since labour produiviies in he agriculural and non-agriculural secors boh have posiive impac on he aggregae consumpion, hey boh have a negaiv effec on he agriculure s share of employmen. Equaion (10) and (7) can be combined o yield he following equaion for he 12

14 equilibrium value of aggregae consumpion C. ( (1 ) ϕ a A 1 a ( B (µ a 1)ϕ a A 1 a C µ a 1 C µ a 2 ( = ϕ a A 1 a ) + ϕ na A 1 na C µ na (µ na 1)ϕ na A 1 na C µ na 2 C µ a 1 ) 1 σ ) + ϕ na A 1 na C µ 1 na 1 1 (14) Equaions (8), (9) and (14) can be used o solve for he equilibrium employmen and oupu in he wo secors as follows. Given he preference parameers and he real labour produciviies in he wo secors, A a and A na, equaion (14) can be used o solve for C. Given C, equaions (8) and (9) can be used o solve for L a and L na. Finally, GDP per capia in he wo secors can be calculaed as Y a = A a L a and Y na = A na L na and, when he labour produciviiy levels are normalized so ha he relaive price of agriculure a = 0 is 1, he aggregae GDP per capia is simply Y = Y a + Y na. Nex, we discuss how we calibrae he values of he preference parameers. 4 Calibraion We se σ = 0.6 so ha he Frisch elasiciy of labour supply is 1.7, a value used by Greenwood, Hercowiz, and Huffman (1988) and many ohers in he business cycle lieraure. For he res of he model parameers, we calibrae heir values so ha when here is no produciviy shock, he model maches he long-run rends of srucural change and aggregae employmen rae in China over he sample period of 1978 o We use he hp-filer o filer ou he rends of he agriculural employmen o populaion raio, he oal employmen o populaion raio and he labour produciviies in he wo secors. Because of he non-homoheic preferences, he agriculure s share of employmen is affeced by he relaive produciviy beween he wo secors as well as he level of produciviies. Given ha he produciviy is an index and is level depends on he normalizaion, we rea he iniial produciviy level 13

15 of agriculure secor, A 0, as a free parameer and choose is value along wih he preference parameers ϕ a,, µ a, µ na o mach he rend of he agriculure s share of employmen. To be specific, le x denoe he hp-filered rend componen of any variable x. Firs, for any = 0,1,...,T, given he rend aggregae employmen rae L and rend labour produciviies A a and A na in he daa, we can solve he rend aggregae consumpion C (A 0,ϕ a,, µ a, µ na ) as an implici funcion of he parameers A 0,ϕ a,, µ a, µ na from equaion (10), L = ( ( ) 1 ( ) 1 A0 ϕ a A a C µ a 1 A0 + ϕ na A na C µ na 1 A a0 A a0 ) 1 1 Then, from (11), we can wrie he rend of agriculure s share of employmen as. ϕ a ( A0 A a0 A a ) 1C µ a 1 (A 0,ϕ a,, µ a, µ na ) l a (A 0,ϕ a,, µ a, µ na ) = ( ) ϕ A0 1C ( ) µ a A a 1 A a a0 (A 0,ϕ a,, µ a, µ na ) + ϕ A0 1C µ na A na 1 A na a0 (A 0,ϕ a,, µ a, µ na ) Finally, we choose (A 0,ϕ a,, µ a, µ na ) o minimize he following loss funcion (i.e., non-linear leas square): T =0 { [la (A 0,ϕ a,, µ a, µ na ) l a ] 2 }. In our model, B in he uiliy funcion is exogenously given o capure he longrun changes in aggregae employmen rae due o demographic facors. For any given value σ and he calibraed values of (A 0,ϕ a,, µ a, µ na ), we choose B so ha he model implied rend of aggregae employmen rae maches ha in he daa. 14

16 Tha is, we choose B o solve he following equaion ( ( ) (1 ) ϕ A0 1C µ a A a 1 A a a0 L = ( ) B ((µ a 1)ϕ A0 1C µ a A a 1 A a a0 ( ) ) + ϕ A0 1C 1 µ na A na 1 A na a0 ( ) + (µ na 1)ϕ A0 1C µ na A a 1 A na a0 ) Table 3 summarizes he calibraion resuls. The calibraed value of he elasiciy of subsiuion () is less han one, implying ha he subsiuion effec is such ha he agriculure s share of employmen is negaively relaed o he agriculure s relaive produciviy. This is consisen wih he heoreical assumpion of Ngai and Pissarides (2007) and he finding of Herrendorf, Rogerson and Valeninyi (2013). The calibraed value of µ a is less han ha of µ na, implying ha he income effec is such ha he agriculure s share of employmen is negaively relaed o he labour produciviies in boh secors. Table 3: Benchmark Calibraion Parameer Descripion Value ϕ a average employmen share of agriculure 0.11 elasiciy of subsiuion beween wo goods 0.47 µ a income elasiciy of agriculural good 1.57 µ na income elasiciy of non-agriculural good 3.76 σ inverse of Frisch elasiciy of labour supply 0.6 A 0 iniial produciviy level σ Figure 5 displays he rends of he agriculure s share of employmen and aggregae employmen rae from boh he model and he daa. Our calibraed model maches perfecly he rend of aggregae employmen rae by consrucion, and maches he rend of he agriculure s share of employmen very well. We nex urn o he cyclical properies of our calibraed model when here are shocks o produciviies in he wo secors. 15

17 Agriculure Employmen Share: Trend Figure 5: Long Run Trend - China China Daa Model Aggregae Employmen Rae: Trend China Daa Model Benchmark Resuls Table 4 presens he resuls of simulaing our calibraed model. We feed he model wih he acual labour produciviies series from he daa, A a and A na, = 0,1,...,T. We filer he simulaed ime series from he model using he hp-filer in he same way as we filer he daa series o exrac he cyclical componens of he ime series. The firs and second columns of Table 4 presen he business cycle saisics calculaed from China s daa and he simulaed ime series from he model. Panel A shows he relaive sandard deviaions of he aggregae employmen o oupu and he correlaion beween he aggregae employmen and oupu, Panel B he secor level correlaions and relaive sandard deviaions, and Panel C he correlaion beween secor employmen and he correlaion of he agriculure s share of employmen wih secor labor produciviies. Figure 6 compares he simluaed employmen from model wih he daa for boh secors. Overall, he model does a good job in maching boh aggregrae and secor momens in he daa. From Panel A, we see ha he model produces a relaive volailiy of aggregae employmen of 0.13, which is very close o 0.11 in he daa. The model also generaes a correlaion of employmen and oupu close o zero, indicaing ha employmen is acyclical. When we look a business cycle facs a secor level from Panel B, he model shows employmen in boh secor flucuaes a lo, wih he rel- 16

18 aive volailiy of agriculure employmen o be 0.82 and non-agriculure employmen o be The non-agriculure employmen is srongly procyclical, as in he daa. However, for he agriculural secor, employmen is negaively correlaed wih oupu in he model and slighly posiive in he daa. The model-implied negaive correlaion beween employmen and oupu in he agriculural secor obviously implies ha he correlaion beween agriculural employmen and agriculural labour produciviy is srongly negaive. We explain below ha his is due o a srong income effec. Panel C shows he labor reallocaion beween he wo secors. The correlaion of employmens in he wo secors is -0.83, as in he daa, indicaing srong reallocaion beween secors. Moreover, he model implies ha he agriculure s share of employmen is negaively correlaed wih labor produciviy in boh secors. When he labor produciviy in agriculure secor increases, relaive price of agriculure good falls. Given ha agriculural and non-agriculural goods are complemens, subsiuion effec leads o a fall of he agriculure s share of employmen. In addiion, higher agriculural labor produciviy also raises aggregae consumpion. Because µ a < µ na, he income effec is such ha he agriculure s share of employmen declines. Thus, boh subsiuion and income effecs lead o negaive correlaion beween he agriculure s share of employmen and labor produciviy. This explains why he model implies a very srong negaive correlaion of When he labor produciviy in non-agriculure secor increases, he relaive price of agriculure good rises and he subsiuion effec is such ha he agriculure s share of employmen increases. The income effec sill leads o a fall of he agriculure s share of employmen. Overall, he income effec dominaes, leading o a correlaion of In summary, he model economy maches he daa for he Chinese economy well. In pariculare, i generaes high employmen-oupu correlaion in he nonagriculural secor and low employmen-oupu correlaion in he aggregae. I s implicaions for labour reallocaion beween secors is also broadly consisen he daa. In he following secion, we show ha our model can replicae he business cycle facs in he US as well. 17

19 Table 4: Model Momens - China China Daa Model (A) Aggregae σ (L)/σ (Y ) ρ (L,Y ) (B) Wihin Secor σ (L a )/σ (Y a ) σ (L na )/σ (Y na ) ρ (L a,y a ) ρ (L na,y na ) (C) Cross Secor ρ(l a,l na ) ρ( L a L,A a ) ρ( L a L,A na ) Agriculure Employmen: Cycle Figure 6: 0.1 Non-Agriculure Employmen: Cycle 0.08 China Daa Model 0.08 China Daa Model

20 6 Model s Implicaions for he US For he US economy, we keep he preference parameers ϕ a,, µ a, and µ na a he same values as in our benchmark calibraion for China. Recall ha, from equaions (15) and (16), he level of he aggregae conusmpion maers for he level of he agriculure s share of employmen due o he non-homoheic preferences, and he aggregae consumpion depends on he produciivy level A 0. Therefore, we recalibrae A 0 o mach he level of he agriculure s of employmen in he US economy. The lef panel of Figure 7 shows a sriking resul ha wih he same preference parameers, our model can mach well he srucural change rend in he US: he agriculure s share of employmen declines from 2.9% in 1978 o 1.3% in Agriculure Employmen Share: Trend Figure 7: Long Run Trend - US US Daa Model Aggregae Employmen Rae: Trend US Daa Model We also keep he value of σ he same as in he benchmark calibraion for China and recalibrae B, = 0,1,...,T, o mach he rend of aggregae employmen rae in he US. Table 5 compares he simulaed model momens wih he US daa and shows ha our model does a good job in replicaing he US business cycles. From Panel A, we see ha he model can generae highly procyclical aggregae employmen: he correlaion beween aggregae employmen and aggreggae oupu is However, he model produces a relaive employmen volailiy han is lower han he daa. This problem is common for sandard real business cycle model, as poined 19

21 ou by Cooley and Presco (1995), ha wihou addiional labor marke fricions hese models have difficuly in generaing sizable employmen variaions. Panel B and C illusrae he secor level correlaions and labor reallocaions across secors. I is worh emphasizing ha he model is able o produce a negaive correlaion beween he wo secors employmens and negaive correlaions of he agriculure s of employmen wih labor produciviies in boh secors. Table 5: Model Momens - US US Daa Model (A) Aggregae σ (L)/σ (Y ) ρ (L,Y ) (B) Wihin Secor σ (L a )/σ (Y a ) σ (L na )/σ (Y na ) ρ (L a,y a ) ρ (L na,y na ) (C) Cross Secor ρ(l a,l na ) ρ( L a L,A a ) ρ( L a L,A na ) Overall, despie being highly sylized, our model economy wih he same preference parameers can mach well he daa from boh China and US. We show ha our model wih he highlighed mechanism is imporan in undersanding he business cycle flucuaions in boh US and China. 7 Sensiiviy Analysis In his secion we carry ou some sensiiviy analysis. 20

22 Aggregae labour supply parameer B. Since he long run change of aggregae employmen rae is deermined by demographic facors, which are no he ineres of our paper, we used exogenous B o mach he rend of aggregae employmen rae in our calibraion. We now es he robusness of our model by imposing a consan B. In paricular, we use B o mach he long run average of aggregae employmen rae, which is 0.55 for China from 1978 o This gives a value of 0.45 for B. Table 6 shows he simulaion resuls, where he second column is our benchmark resul and he hird column is he robusness check when B is a consan. By comparing he second and hird column of he able, we see ha holding B consan barely affecs he business cycle properies of our model. All he conclusions from our benchmark model carry hrough. Elasiciy of labour supply. The parameer σ governs he elasiciy of labor supply, which affecs direcly he aggregae employmen volailiy. In line wih he lieraure, we choose his parameer o be 0.6 in our benchmark calibraion. We now check he sensiiviy of our model o his parameer by changing he value of σ and recalibraing our model o he same arge. In he fourh and fifh columns of Table 6, we repor he simulaion resuls from he model for differen values of σ. I can be seen ha higher labor elasiciy, or lower value of σ, implies higher aggregae employmen volailiy. Aggregae employmen remains acyclical for differen values of σ. While here is some differences in he resuls across differen value of σ, he properies of secor-level flucuaions and he labour reallocaion beween he wo secors of he benchmark model sill hold. Idenical income elasiciy for boh goods. The parameer µ i conrols he income elasiciy of good i, which we argue is imporan in undersanding he reallocaion of labour across secors. Our benchmark calibraion gives µ a < µ na, implying a negaive income effec on agriculure employmen share. We now suppress he income effec by leing he income elasiciy of he wo goods be he same. To be specific, we se hem o be he average of benchmark values of µ a and µ na, i.e., µ a = µ na = Case 4 in Table 6 displays our simulaion resuls. Panel A shows, wihou income effec, he model produces a highly procyclical aggregae employmen whereas daa shows acyclical aggregae employmen. Panel C shows ha when only he subsiuion effec is presen, he model produces a 21

23 posiive correlaion beween agriculure s share of employmen and non-agriculure labor produciviy, which is conray o he daa. This exercise shows he imporance of non-homoheic preference in explaining he employmen dynamics. CES preferences. To compare wih he sandard CES preferences, we now se µ a = µ na = 2. We recalibrae he model following he sraegy used by Da- Rocha and Resuccia (2004). Specifically, we choose a value of 0.5 for ϕ a o mach he average of he agriculure s share of employmen, which is 0.5 in he daa, a value of 8 for σ o mach he relaive volailiy of aggregae employmen o oupu of 0.11, and finally a value of 0.27 for o mach he relaive volailiy of agriculure employmen o non-agriculure employmen of Case 5 in Table 6 shows he simulaion resuls. Comparing wih he benchmark case, he CES case needs a much lower labour elasiciy of 0.1 in order o mach he relaive volailiy of aggregae employmen, and i also implies a highly procyclical employmen series, which conradics he daa. The srong procyclical propery of he aggregae employmen seems o be a general feaure of he CES preferences. In Appendix B, we presens simulaion resuls wih differen values for he preference parameers, hey all show a srong procyclical employmen series. 1 A he secor level, wihou income effec, he CES model produces wrong sign of correlaion beween he agriculure s share of employmen and non-agriculure produciviy. 8 Conclusion The cyclical behavior of aggregae employmen differs significanly beween China and he US. This sharp difference a he aggregae level conceals similar behavior of cyclical employmen a secor level. We argue ha he main difference beween China and he US is he size of he agriculural secor. We show ha a simple wosecor growh model wih produciviy shocks and non-homoheic preferences can simulaneously accoun for he secular rend of srucural change and employmen 1 Da-Rocha and Resuccia (2004) also uses he CES preferences, bu hey inroduce an expos produciviy shock in agriculure ha helps o lower he correlaion beween he aggregae employmen and oupu. In he version of heir model wihou he expos agriculural produciviy shock, he correlaion of employmen and oupu is

24 Table 6: Sensiiviy Analysis China Daa Benchmark Case 1 Case 2 Case 3 Case 4 Case 5 Consan B σ = 0.1 σ = 2 µ a = µ na CES (A) Aggregae σ (L)/σ (Y ) ρ (L,Y ) (B) Wihin Secor σ (L a )/σ (Y a ) σ (L na )/σ (Y na ) ρ (L a,y a ) ρ (L na,y na ) (C) Cross Secor ρ(l a,l na ) ρ( L a L,A a ) ρ( L a L,A na ) flucuaions a he business cycle frequency in boh China and he US. 23

25 Appendix A Derivaion of Formulas The FOCs of he social planner s maximizaion problem wih respec o L a and L na are: C c a A a B L σ = 0 (15) From equaion (1), we have C c na A na B L σ = 0 (16) (µ a 1)(ϕ a ) 1 c 1 a C µ a 1 C + (µ na 1)(ϕ na ) 1 c 1 c a + ( 1)(ϕ a ) 1 c 1 na C µ na 1 a C µ a 1 = 0, C c a Thus, we have where (µ a 1)(ϕ a ) 1 c 1 a C µ a 1 D = (µ a 1)(ϕ a ) 1 c 1 a C + (µ na 1)(ϕ na ) 1 c 1 c na + ( 1)(ϕ na ) 1 c 1 1 c 1 µ a 1 C na C µ na 1 c na na C µ na 1 = 0. C = (1 )(ϕ a) a C, (17) c a D 1 c 1 µ na 1 C = (1 )(ϕ na) na C, (18) c na D C µ a 1 + (µ na 1)(ϕ na ) 1 c 1 na C µ na 1, (19) Subsiuing equaions (17) and (18) ino (15) and (16), respecively, and solving for c a and c na, we have he following: ( ) (1 )Aa c a = ϕ a D B L σ C µ a 1, (20) c na = ϕ na ( (1 )Ana D B L σ Subsiuing hese wo equaions ino (1) we have ) C µ na 1. (21) ( ) (1 1 ( ) )Aa ϕ a D B L σ C µ a 1 (1 1 )Ana + ϕ na D B L σ C µ na 1 = 1, 24

26 which implies ha ( D B L σ 1 ) 1 ( ) ϕ a A 1 a C µ a 1 + ϕ na A 1 na C µ na 1 ( = ϕ a A 1 a = 1, ) + ϕ na A 1 na C µ 1 na 1 1. (22) D B L σ C µ a 1 1 Subsiuing (22) ino (20) and (21) and solving for c a and c na yield he soluion in equaions (5) and (6).. Subsiuing (5) and (6) ino (19) and simplifying yields he following: From (22), hen, we have D = (µ a 1)ϕ a A 1 a ϕ a A 1 a ( (1 ) ϕ a A 1 a L = ( B (µ a 1)ϕ a A 1 a C µ a 2 C µ a 1 C µ a 1 C µ a 2 + (µ na 1)ϕ na A 1 + ϕ na A 1 na C µ na 1 na C µ na 2 ) + ϕ na A 1 na C µ na (µ na 1)ϕ na A 1 na C µ na 2. ) 1 σ. (23) B Sensiiviy Analysis for CES Preferences In Table 7, we show he simulaion resuls for CES preferences wih differen combinaions of σ and. Table 7: CES Preferences China Daa σ = 0.6 σ = 2 σ = 8 = 0.5 = 1.5 = 0.5 = 1.5 = 0.5 = 1.5 (A) Aggregae σ (L)/σ (Y ) ρ (L,Y ) (B) Wihin Secor σ (L a )/σ (Y a ) σ (L na )/σ (Y na ) ρ (L a,y a ) ρ (L na,y na ) (C) Cross Secor ρ(l a,l na ) ρ( L a L,A a ) ρ( L a L,A na )

27 References [1] Acemoglu, Daron, and Veronica Guerrieri Capial Deepening and Non-Balanced Economic Growh. Journal of Poliical Economy, 116, [2] Boppar, Timo Srucural Change and The Kaldor Facs in a Growh Model wih Relaive Price Effecs and Non-Gorman Preferences. Economerica 82 (6), [3] Brand, Loren, and Xiaodong Zhu Redisribuion in a Decenralized Dconomy: Growh and Inflaion in China under Reform. Journal of Poliical Economy 108 (2), [4] Brand, Loren, and Xiaodong Zhu Accouning for China s Growh. Universiy of Torono Working Paper No [5] Caselli, Francesco and Coleman, Wilbur John, II The US Srucural Transformaion and Regional Convergence: A Reinerpreaion. Journal of Poliical Economy 109, [6] Chang, Chun, Kaiji Chen, Daniel F. Waggoner, and Tao Zha Trends and Cycles in China s Macroeconomy. NBER Macroeconomics Annual 30, [7] Chari, V. V., Parick J. Kehoe, and Ellen R. McGraan Business Cycle Accouning." Economerica 75, [8] Cooley, Thomas F., and Presco, Edward C Economic Growh and Business Cycles. in he Froniers of Business Cycle Research, edied by Thomas F. Cooley, Princeon Universiy Press. [9] Comin, Diego, Danial Lashkari, and Mar Mesieri Srucural Change wih Long-run Income and Price Effecs. NBER Working Paper No [10] Da-Rocha, José M., and Diego Resuccia The Role of Agriculure in Aggregae Business Cycles. Review of Economic Dynamics 9, [11] Greenwood, Jeremy, Zvi Hercowiz, and Gregory Huffman Invesmen, Capaciy Uilizaion, and he Real Business Cycle. American Economic Review 78 (3). [12] He, Qing, Terence Tai-Leung Chang, and Kang Shi Wha accouns for Chinese Business Cycle? China Economic Review 20, [13] Herrendorf, Berhold, Richard Rogerson, and Akos Valeninyi Growh and Srucural Transformaion." in he Handbook of Economic Growh, Volume 2. Elsevier. [14] Kongsamu, Piyabha, Sergio Rebelo and Danyang Xie Beyond Balanced Growh. Review of Economic Sudies, 68(4), pp [15] Ngai, L. Rachel and Chrisopher A. Pissarides Srucural Change in a Mulisecor Model of Growh. American Economic Review, 97,

28 [16] Soresleen, Kjeil, Bo Zhao, and Fabrizio Ziliboi Flucuaing Like China: Business Cycles during Srucural Change. Unpublished. [17] Timmer, Marcel P., Gaaizen de Vries, and Klaas de Vries Paerns of Srucural Change in Developing Counries. in he Rouledge Handbook of Indusry and Developmen. pp Rouledge. 27