Working Paper Modeling technological progress and investment in China: Some caveats

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1 econor Der Open-Acce-Publikaionerver der ZBW eibniz-informaionzenrum Wirchaf The Open Acce Publicaion Server of he ZBW eibniz Informaion Cenre for Economic Felipe, Jeu; McCombie, John Working Paper Modeling echnological progre and invemen in China: Some cavea Working paper, evy Economic Iniue, No. 643 Provided in Cooperaion wih: evy Economic Iniue of Bard College Suggeed Ciaion: Felipe, Jeu; McCombie, John (200) : Modeling echnological progre and invemen in China: Some cavea, Working paper, evy Economic Iniue, No. 643 Thi Verion i available a: hp://hdl.handle.ne/049/57008 Nuzungbedingungen: Die ZBW räum Ihnen al Nuzerin/Nuzer da unengelliche, räumlich unbechränke und zeilich auf die Dauer de Schuzrech bechränke einfache Rech ein, da augewähle Werk im Rahmen der uner hp:// nachzuleenden volländigen Nuzungbedingungen zu vervielfäligen, mi denen die Nuzerin/der Nuzer ich durch die ere Nuzung einveranden erklär. Term of ue: The ZBW gran you, he uer, he non-excluive righ o ue he eleced work free of charge, erriorially unrericed and wihin he ime limi of he erm of he propery righ according o he erm pecified a hp:// By he fir ue of he eleced work he uer agree and declare o comply wih hee erm of ue. zbw eibniz-informaionzenrum Wirchaf eibniz Informaion Cenre for Economic

2 Working Paper No. 643 Modeling Technological Progre and Invemen in China: Some Cavea by Jeu Felipe Aian Developmen Bank, Manila, Philippine and Cambridge Cenre for Economic and Public Policy, Univeriy of Cambridge, U John McCombie Cambridge Cenre for Economic and Public Policy December 200 Thi paper doe no repreen he view of he Aian Developmen Bank, i execuive direcor, or hoe of he counrie ha hey repreen. The auhor are graeful o Dave Dole, Julián Pérez, Aahih Meha, Fan Zhai, and paricipan in a eminar a ingnan Univeriy, Hong ong, China, a well a paricipan a he Chinee Economi Sociey Meeing held in Shanghai July 2 4, 2006, and he Pacific Rim Conference, Beijing, China, January 2 4, 2007, for heir ueful commen on and uggeion for previou draf, one of which appeared a Working Paper No. 7/2005, Cenre for Applied Macroeconomic Analyi, Auralian Naional Univeriy, Canberra, under he ile Aggregae Invemen in he People Republic of China: A Commen. The uual diclaimer applie. Correponding auhor: jfelipe@adb.org. The evy Economic Iniue Working Paper Collecion preen reearch in progre by evy Iniue cholar and conference paricipan. The purpoe of he erie i o dieminae idea o and elici commen from academic and profeional. evy Economic Iniue of Bard College, founded in 986, i a nonprofi, nonparian, independenly funded reearch organizaion devoed o public ervice. Through cholarhip and economic reearch i generae viable, effecive public policy repone o imporan economic problem ha profoundly affec he qualiy of life in he Unied Sae and abroad. evy Economic Iniue P.O. Box 5000 Annandale-on-Hudon, N hp:// Copyrigh evy Economic Iniue 200 All righ reerved

3 ABSTRACT Since he early 990, he number of paper eimaing economeric model and uing oher quaniaive echnique o ry o underand differen apec of he Chinee economy ha muhroomed. A common feaure of ome of hee udie i he ue of neoclaical heory a he underpinning for he empirical implemenaion. I i ofen aumed ha facor marke are compeiive, ha firm are profi maximizer, and ha hee firm repond o he ame incenive ha firm in marke economie do. Many reearcher find ha he Chinee economy can be well explained uing he ool of neoclaical heory. In hi paper, we () review wo example of eimaion of he rae of echnical progre, and (2) dicu one aemp a modeling invemen. We idenify heir horcoming and he problem wih he alleged policy implicaion derived. We how ha economeric eimaion of neoclaical model may reul in apparenly enible reul for miinformed reaon. We conclude ha modeling he Chinee economy require a deeper underanding of i inner working a boh a raniional and a developing economy. eyword: China; Ideniy; Invemen; Neoclaical Model; Toal Facor Produciviy Growh JE Claificaion: C20, E22, E62, O23, P4

4 How much economic analyi i applicable o China? Mo, I believe Gregory Chow (994: 24). INTRODUCTION In hi paper we raie ome queion regarding he mehodology and approache ued o model variou apec of he Chinee economy. In paricular, we queion how an imporan par of he lieraure on China ha advanced ince he early 990. Alhough here i a wide variey of paper uing divere mehodologie and echnique, here i a rand of hi lieraure ha ha aken an approach ha we hink mu be carefully analyzed and evaluaed. By economic analyi in he quoaion above, Chow did no mean any economic analyi, bu orhodox neoclaical economic analyi. In he ame aricle, Chow concluded: The above example have illuraed he propoiion ha mo of exiing economic analyi i applicable o China [ ] Before new ool are developed for China, one hould underand he uefulne a well a he limiaion of he exiing ool (Chow 994: 33; ialic added). 2 Indeed, i eem ha a China become a more marke-oriened economy, many reearcher appear o believe ha he mehod and model of neoclaical economic are he appropriae one o underand he Chinee economy. ikewie, applicaion of he lae economeric echnique o modeling differen apec of he Chinee economy ha become andard. The objecive of hi paper i o dicu if Chow approach oward underanding he Chinee economy i ueful. A many aumpion underlying neoclaical economic (e.g., profi maximizaion; marginal produciviy heory of facor pricing) do no appear o conform o wha i known abou he Chinee economy, in hi paper we dicu wha we view are ome eriou limiaion of a number of he exiing ool. A reader and reearcher of he China economic lieraure, we perceive an almo permanen enion beween he premie inheren in he model of neoclaical economic and heir applicaion o he Chinee economy, ofen puhed hrough core juificaion. For example, Hu and han (997) juificaion for uing One imporan cavea: we do no claim ha all work on China uffer from he problem ha we dicu hi paper. 2 In hi paper Chow argued a follow: The evidence ha uggeed ha he Cobb-Dougla producion funcion fi he daa for Chinee ae-owned indury very well (Chow 994: 25); Thi heory [heory of conumer behavior] appear o be univeral, being applicable o China a well a oher counrie (Chow 994:25). He alo applied he quaniy heory of money and he acceleraor heory o model invemen.

5 growh accouning i mo unconvincing from a mehodological poin of view. Afer aing ha he eimae of produciviy growh for China may be biaed in eiher direcion if here are deviaion from he aumpion impoed by he adoped mehodology hey coninue: However, ince hi mehodology i widely ued in udying ource of economic growh for member of he Organizaion for Economic Cooperaion and Developmen, he newly indurialized economie of Ea Aia, and many developing counrie wih divergen income level and economic rucure, i i of inere cerainly a a fir ep, o apply he ame analyi o he Chinee economy o obain wha could be viewed a a benchmark eimae (Hu and han 997: 08); ee Felipe and McCombie (200, 2002). Oher ime, auhor need o juify pervere finding. For example, Blanchard and Giavazzi (2005: able 4) ummarize variou eimae of oal facor produciviy (TFP ) growh for China. They indicae ha hee eimae are abou 3% per year ince reform ared, bu ha TFP growh appear o have lowed ignificanly in recen year. The auhor, however, explain ha he finding of a low TFP growh i compaible wih a very high GDP growh: The implicaion of hi compuaion hould no be however ha here i no echnological progre in China. The aumpion underlying he compuaion i ha facor are paid heir marginal produc. If, in fac, capial ha been miallocaed, hen conrary o hi aumpion, he marginal produciviy of capial in hoe ecor where here ha been exceive invemen could be negaive. Therefore, he righ way o inerpre he compuaion i ha, while echnological progre i urely preen, i i parly offe by capial miallocaion. Blanchard and Giavazzi 2005: ; ialic added) Alhough he profeion ha advanced a grea deal in erm of aking queion abou he performance of he Chinee economy, i ha no been advanced enough in erm of aking if he peculiariie of he Chinee economy demand radically differen heoreical (and perhap empirical) approache. Cerainly, hi i no o ay ha China economi have no dicued wheher he peculiariie of he Chinee economy call for a pecific approach. Qin (2000), for example, provided an in-deph review of he ae of macro-modeling in raniion economie wih pecial reference o China and raied eriou concern. Thi omewha unforunae endency in recen year o apply andard neoclaical model o he udy of he Chinee economy i reinforced by he applicaion of he lae 2

6 economeric refinemen, in paricular he analyi of uni roo and coinegraion in ime-erie analye. Thi ha led, a ime, o he ue of ereoyped heorie camouflaged in complicaed echnical device. The concluion, in our view, i ha a number of China economi eem o believe ha he model ued mu explain Chinee economic behavior adequaely imply becaue he reul obained are apparenly good. Thi aiude involve an elemen of inrumenalim, he view ha (realiic) aumpion do no maer in evaluaing a model; wha maer i i predicive abiliy. To dicu he implicaion of hee problem, we review hree example of how modeling and eimaing echnical progre and invemen in China ha proceeded. In ecion 2, we review he mehod propoed by Wan (995) and Chow (993) o quanify echnical progre. In ecion 3, we dicu he pecificaion of he neoclaical model of invemen propoed by He and Qin (2004). We argue ha hee empirical exercie can be inerpreed a approximaion o accouning ideniie. Indeed, we hall how ha expreion almo idenical o he model derived in hee paper can be obained by rewriing he income accouning ideniy according o which value-added equal he wage bill plu oal profi. I i for hi reaon ha he expreion hee auhor eimaed appear o work empirically and hu produce eemingly enible reul. However, for being approximaion o ideniie, eimaion of hee model canno, herefore, rejec he null hypohee ha hey purpor o e. We conclude ha if knowledge abou he Chinee economy i o improve, China economi have o pay eriou aenion o he heorie and aiical echnique ha hey ue: no only do hey have o be relevan o he Chinee realiy, bu alo heir eing ha o allow aiical rejecion. 2. THE MEASUREMENT OF TECHNICA PROGRESS IN CHINA In hi ecion, we dicu wo aemp a eimaing he rae of echnical progre in China which, in differen way, uffer from he problem menioned in he inroducion, namely, he belief ha neoclaical economic can explain Chinee economic behavior, and ha he mehod ued are no more han approximaion o an accouning ideniy. The fir one i ha of Wan (995) and he econd one i ha of Chow (993). 3

7 2. Wan Meaure of Technical Progre Wan (995) propoed a eemingly aumpion-free nonparameric approach o eimae he rae of TFP growh. The raionale behind Wan mehod wa wo-fold. Fir, he poined ou quie correcly ha he derivaion of he radiional growh accouning equaion depend on aumpion uch a profi maximizaion and perfec compeiion. Thee are, mo probably, inappropriae for a cenrally planned economy like China. Second, Wan claimed ha he convenional approach require he explici inroducion of ime in he producion funcion. Thi, in he word of he auhor, preclude he poibiliy of udying cro-ecional echnical change (Wan 995: 309). A i well known, he andard mehod o eimae he growh rae of TFP he proxy for he growh of echnical progre i o aume an aggregae producion funcion, ypically wih Hick-neural echnological progre, A F(, ), where denoe oupu, i employmen, i he ock of capial, A i he level of echnology, and he ubcrip denoe ime. In growh rae, he producion funcion become = Ŷ λ + α ˆ + α ˆ =, where he ymbol ^ denoe he growh rae of he correponding variable, α and α are he elaciie of oupu wih repec o labor and capial (repecively), and λ i he rae of Hick-neural echnical progre. Auming profi maximizaion and compeiive marke, he facor elaiciie are equal o he correponding facor hare in oupu and hu he previou equaion become Ŷ = λ + ˆ + ˆ, where and and capial hare in oupu, repecively. From here, λ can be eimaed reidually a λ = Ŷ ˆ ˆ. are he labor In order o avoid hee problem and define echnical change (TE ) appropriaely, Wan (995) drew he ioquan of he producion funcion wih oupu 0 a he bae year (ee figure ). The oal co (TC ) of producing he oberved level of oupu 0 i definiionally given by = +, where w i he average wage rae, denoe employmen, r i he uer 0 TC0 = w00 r0 0 co of capial, and i he ock of capial, wih all value meaured in real erm. Ioquan and ioco line inerec a poin a ( 0, 0 ). Poin b (, ) repreen he oberved oupu given by anoher producion funcion, where he funcional form ha changed becaue of echnical change. A b, = TC = w + r. Finally, a poin c ( 2, 2 ) he ame level of oupu a a b 4

8 (i.e., = 2 ) i produced auming he ame level of echnology a a a. In oher word, he increae in oupu from 0 o 2 i enirely he reul of increaed inpu. Technical change i defined a he difference beween he co of producing oupu 2 a c uing he ame echnology a a a, and he co of producing wih a differen echnology, bu wih he bae-year facor price, i.e., w 0 and r 0. Thu, uing he co ideniie, he increae in oal efficiency i given by TE = ( w0 2 + r0 2 ) ( w0 + r0 ). Conequenly, hi definiion of echnical change i he aving in co reuling from he need o ue le inpu a b compared wih wha would have been ued a c a a reul of benefi of echnical progre. Since = w02 + r0 2 i no direcly obervable, Wan aumed 2 = γ0 and 2 = γ 0, where γ i ome conan. Then i follow ha, wih conan reurn o cale, he only aumpion Wan claim i i neceary o make i, 2 = γ0. Thi implie ha TE = ( w0 γ 0 + r0γ 0 ) ( w0 + r0 ). Wan meaure of he rae of echnical progre (or oal facor produciviy) a he raio of TE over year one oupu ( ) i (ince γ = 2 /0 and 2 = ): TE ( / ) ( w00 + r0 0 ) ( w0 + r0 ) ( w + w ) 0 = () where TE denoe echnical efficiency and meaure he aving in co reuling from he need o ue le inpu due o he benefi of echnical progre, and all he variable on he righ-hand ide are obervable. I i imporan o noe ha Wan did no ue he marginal produciviy condiion, made no aumpion abou he ae of compeiion, and ha parameer uch a he elaiciy of ubiuion did no even play an indirec role in hi calculaion. The reaon, a we hall how, i ha Wan derived hi reul imply from he manipulaion of he Naional Income and Produc Accoun (NIPA) accouning ideniy, according o which value-added ( ) equal he wage bill (W ) plu profi ( Π ), ha i, W + Π. A algebraically, W w and Π r and r are he average wage rae and he ex po average profi rae, hen,, where w W + Π w + r (2) 5

9 6 Thi accouning ideniy doe no depend on any ae of compeiion, or on he marginal produciviy heory of facor pricing, and i no derived from Euler heorem. Hence i i no a behavioral relaionhip; he ymbol denoe ha expreion (2) i rue by definiion. We can expre now he NIPA ideniy in growh rae a: r w y ˆ ˆ ˆ ˆ ˆ (3) where he ymbol ^ denoe he growh rae of he correponding variable in he ideniy and / ) w ( / W and r / ) / ( Π are he labor and capial hare in oupu, repecively. Expreion (3) can be rewrien a: y r w λ + ˆ ˆ ˆ ˆ ˆ (4) However noe ha Wan definiion of oal facor produciviy growh, equaion (), can be rewrien a: ) ( ) ( ) ( ) ( ) ( r r w w r w r w r w TE + = + + = + = (5) or r w r r r w w w TE ˆ ˆ ] ) / [( ] ) / [( = + = (6) where / ) ( w and / ) ( r are he facor hare. Equaion (6) i equivalen o expreion (4), he accouning ideniy. 3 3 Thi i rue excep for he fac ha he growh rae of he wage and profi rae are defined a 0 X ) / X X ( inead of 0 0 X ) / X X (. Thi i cerainly a minor iue. There i alo he iue of he difference beween he ex po profi rae and he uer co of capial. On hi, ee Felipe and McCombie (999, 2007)

10 Figure. Wan Meaure of Technical Change wihou Relaive Facor Price Change Capial b c 2 2 = 0 0 a _ w 0 _ w _ w 2 r 0 r r abor The dicuion above lead o he concluion ha Wan approach i problemaic and hu i canno be referred o a new in any way. Wan ared off by wriing he value-added accouning ideniy and he imply ranformed i ino an equivalen form. However, ince one canno infer anyhing abou he rae of echnical change olely from an ideniy, i mu be concluded ha hi mehod uffer from eriou limiaion. 2.2 Chow Eimaion of Technical Progre We move o a differen ype of criique. I i an exenion of he argumen in ecion 2., which we ake o i logical concluion. In a well-known paper o China peciali, Chow (993) eimaed Cobb-Dougla aggregae producion funcion for he Chinee economy (for he oal economy and ecor) and eimaed he rae of oal facor produciviy growh for Hi reul yielded he imporan concluion ha echnical progre had been aben in China during In a more recen paper, Chow (2006) ued he ame mehod (i.e., eimaion of 7

11 aggregae producion funcion) and emphaized he validiy of he procedure. However, a we hall how, he mehod i problemaic. Chow (993) fied aggregae Cobb-Dougla producion funcion θ θ = Ao exp( λ ) ε, where i a ime rend and 2 ε i he diurbance erm, o daa for Chinee oal oupu and five ecor (agriculure, indury, conrucion, ranporaion, and commerce). Here, λ meaure he annual rae of TFP growh. Afer carefully compiling daa on income, employmen, and capial, Chow fir ran variou regreion (wih differen eimae of he capial ock) for oal oupu daa excluding he year 958 o 969. Thi i due o he aumpion ha he year were abnormal due o he grea upheaval of he Grea eap Forward movemen and he Culural Revoluion (he number of obervaion wa hu reduced from 28 o 7). Chow argued ha o exclude he year from 958 o 969 in eimaing an aggregae producion funcion i a reaonable and rewarding procedure (Chow 993: 82). In oher word, Chow argued ha during he Culural Revoluion, China wa no on he producion poibiliy fronier. Hence, obervaion from ha period hould no be aken a reflecing he ame producion funcion a obervaion from oher period. From he aiical poin of view, however, hi can be viewed a an exercie in daa mining. Even hough hee excluded year aw a collape in oal oupu (he value in 962 wa only 64% of he value of 959) followed by a rapid recovery (966 wa 77% of he 962 value), hi hould no affec he parameer of he producion funcion, if indeed he daa were eimaing he laer. The fall in he flow of he ervice of inpu hould lead o a decline in oupu ha hould be cloely prediced by he producion funcion. 4 Indeed, figure 2 for he conrucion ecor how uch decline. Chow argued ha if a reader ill wihe o queion he excluion of hee year, my anwer i ha i i inereing o find ou how abnormal he excluded year are if he remaining year up o 980 are aumed normal year [ ] Daa are provided in hi paper for any reader who wihe o 4 Borenzein and Ory (996), urpriingly, juify Chow approach on he following ground: One approach i o ee which combinaion of oupu, labor, and capial, are conien wih he hypohei of a able aggregae producion funcion. On hi bai, Gregory C. Chow (993) exclude he period from 958 (when he Grea eap Forward began) o 969 (he fir year of poiive growh following he end of he Culural Revoluion), finding ha for he remaining year, combinaion of (log of) oupu and capial per worker are fairly cloe o a raigh line (Borenzein and Ory 996: 225; ialic added). 8

12 elec ome oher year a abnormal o draw her own concluion (Chow 993: 82 2; ialic in he original). 5 Figure 2. Oupu, Capial Sock, and Employmen: China Conrucion Secor 8 7 Oupu Capial Sock Employmen Daa Source: Chow (993). ogarihmic cale Chow work uffer from wo relaed problem. Fir, i ha been known for decade ha aggregae producion funcion can be juified heoreically only under exremely rericive aumpion. For pracical purpoe, hi mean ha hey do no exi (Felipe and Fiher 2003, 2006). Economi coninue uing hem becaue i eem ha a ime hey yield eemingly enible reul in empirical eimaion. Thi i, implicily, Chow (2006: 92) argumen. Chow (2006: 9) elf-reaurance ha hi reul are meaningful becaue hey agree wih Mankiw, Romer, and Weil (992) finding i alo dubiou, for hey eimaed he eady-ae oluion of Solow model, unrelaed o Chow exercie (on hi, ee Felipe and McCombie 2005). 6 Thi poin i no ju an obcure heoreical reul wihou implicaion for empirical work. On he conrary, i undermine he whole raionale for eimaing aggregae producion 5 I i worh noing ha omehing imilar happened o Cobb and Dougla in heir pioneering udy. There, hey eimaed heir producion funcion for However, hey noed ha aw a fall in oupu of ju under 30%, and aw a recovery of a imilar magniude. However, in hi cae, if he la hree year are dropped from he regreion, i yield very poor reul. Only he regreion wih he complee period yield enible reul. See Felipe and Adam (2005). 6 Holz (2006: 96), in hi reply o Chow (2006), queioned he exience of an economy-wide aggregae producion funcion. Holz wa clearly referring o he aggregaion problem in producion funcion. Peronal correpondence wih Caren Holz. 9

13 funcion and inerpreing heir reul (i.e., coefficien, elaiciy of ubiuion) in he andard manner. The econd concern wih Chow work provide an explanaion for why, depie he fac ha aggregae producion funcion do no exi, hey appear o work a ime in empirical work. I can be hown, pace Chow, ha here i no need o eliminae any year whaoever o obain excellen eimae of he Cobb-Dougla producion funcion. The reaon i ha he regreion Chow eimaed (Cobb-Dougla aggregae producion funcion ) can be derived a an algebraic ranformaion of he NIPA accouning ideniy, expreion (2). A an implicaion, we hall how ha Chow (993) argumen abou he lack of oal facor produciviy growh in he Chinee economy during i he reul of a peculiar mipecificaion problem. I can be hown ha a form ha reemble a Cobb-Dougla producion funcion can be eaily derived from he NIPA ideniy, expreion (2). Thi ideniy in growh rae i expreion (3), above. Suppoe now, fir, ha in China facor hare were conan during he period under conideraion; and econd, ha wage and profi rae grew a conan rae (i.e., he um of he growh rae of he wage and profi rae, each weighed by i facor hare, i a conan). Thi implie ha expreion (3) become: λ + (7) ŷ ˆ + ˆ where λ wˆ + rˆ. If we inegrae expreion (5) and ake he ani-logarihm we obain A exp( λ ) (8) o Thi expreion, and hi i he key iue, i no he Cobb-Dougla producion funcion, bu he NIPA ideniy rewrien under he wo aid aumpion abou he facor hare and he wage and profi rae. Thi decepively imple argumen explain wha Chow (993) did and he reaon why he wa led o believe ha neoclaical producion heory can explain growh and produciviy in China. Before we go ino more deail abou he argumen and i far-reaching implicaion, le ake a look a he four regreion in able for he Chinee conrucion ecor, eimaed uing Chow (993) daa e. 0

14 The fir regreion reproduce Chow (993: able XII) reul. Thi regreion wa eimaed for , bu eliminaing he year 96, 962, and 968. The aiical inignificance of he ime rend (alo found in imilar regreion for oher ecor of he economy) led Chow o he concluion ha here had no been any poiive echnological progre in China during he period analyzed. The econd regreion wa eimaed uing he complee period provided by Chow (993) in hi paper and wihou eliminaing a ingle year. The problem wih hi regreion i ha he ock of capial bear a negaive ign, hence i could no be acceped. Thi i he problem Chow encounered and puaively olved by arguing ha he Culural Revoluion wa an anomalou period, and for hi reaon he year correponding o hi period had o be excluded from he analyi. Nowihanding he reul, i i worh indicaing ha he proxy for he rae of echnical progre, he ime rend, i aiically ignifican. However, he aiical inignificance of he logarihm of he capial ock, which occurred in a number of oher ecor (afer eliminaing cerain year), ugge a mipecificaion of he regreion.

15 Table. Producion Funcion for China Conrucion Secor Eimaion Period ear Eliminaed Chow (993) , 962, 968 c ln ln (2.93) Thi paper None.873 (4.46) Thi paper None (2.43) Thi paper None (0.80) Source: Auhor eimaion uing Chow (993) daa e Noe: -aiic in parenhee. Daa: Chow (993) (-0.) (3.90) (7.02) (7.43) 0.42 (5.70) 0.44 (6.6) (2.26) (-0.08) 0.42 (8.7) (8.37) (.92) (.8) The hird regreion in able ha been alo eimaed for he full period and alo wihou excluding a ingle year. The difference i ha now hi regreion include he variable, which i no an exponenial ime rend bu he funcion, = in( 2 ) + in( 3 ) + in( 4 ) + co( ) co( 2 ) co( 3 ) + co( 5 ) + log( 2 ), where in denoe he ine funcion, co he coine funcion, log i he logarihmic funcion, and repreen ime. The regreion wa alo eimaed for differen ubperiod (954 80, he ame a Chow, hown in he la row) o e i robune. The predicive failure e, recurive eimae, and Chow abiliy e indicae no rucural break and able coefficien. Moreover, he eimaed coefficien reemble, a in Chow regreion, he facor hare. Finally, he coefficien of aiically ignifican. Why hee ubanial difference in reul and why he rigonomeric funcion? The derivaion of equaion (8) above indicae ha if i were eimaed wih he coefficien unrericed, i hould have o work very well empirically provided facor hare are i approximaely conan and wage and profi rae grow a conan rae, ha i, if λ wˆ + rˆ. In oher word, if hee wo aumpion happen o be correc in China, and one ge daa on 2

16 oupu, labor, and capial, eimaion of o θ θ 2 = A exp( λ ) ε will yield a very high fi (cloe o one), θ and θ 2. Thi i excluively becaue of he underlying accouning ideniy. Mo likely, facor hare in China have been ufficienly conan (ee oung 2000: able XXIII) for purpoe of economeric eimaion, a facor hare do no flucuae widely from period o period. Therefore, if eimaion of he Cobb-Dougla funcion o θ θ 2 = A exp( λ ) ε did no reul in a good approximaion o he ideniy (econd regreion in able ) i wa mo likely becaue he econd aumpion (ha wage and profi rae grew a a conan rae) wa incorrec. Thi i very plauible a i i unlikely ha λ wˆ + rˆ i a conan. Hence, he approximaion of λ hrough he linear rend wa erroneou and led o he biaed eimae ha reuled when all year were included in hi regreion. Thi wa caued by a mipecificaion error, hough no in he uual ene in economeric, bu in he ene of chooing an incorrec approximaion o he income ideniy. Wha can be done? Reurning o expreion (3), if we make only he aumpion ha facor hare are conan, ubiuion ino expreion (3) and inegraion yield (aking anilogarihm) o A w r, an even more general approximaion o he accouning ideniy han expreion (8), a i only depend on one aumpion, he conancy of facor hare. The previou argumen imply ha he way o improve upon Chow poor reul when all year are included i o earch for he correc approximaion o w r (or ln w + ln r in logarihm) a a funcion of ime (bu no a linear rend). Given ha hi variable mo likely flucuae cyclically around an upward rend in he cae of China, a rigonomeric funcion probably would do a beer job, a indeed wa he cae (he variable above), which led o he approximaion o he ideniy. Thi way, he laer (ricly peaking, a very good approximaion o i) wa recovered. I mu be reed ha he whole exercie i poinle from an economic poin of view a all i being eimaed i an ideniy, or an approximaion o i. To complee he argumen i i imporan o emphaize ha he funcion i imply a rigonomeric funcion of ime whoe only purpoe i o rack he movemen of r. 7 w 7 A word of cauion: he expreion n n i no a perfec approximaion o he accouning ideniy. The perfec approximaion would involve perhap more complicaed erm (and hour in fron of he compuer). The main purpoe of he exercie i o how inuiively why Chow exercie and concluion are queionable. Beide, we do no have he wage and profi rae erie o conruc he full ideniy. 3

17 Nohing in neoclaical economic indicae ha he funcion of ime in he producion funcion (which uppoedly capure echnical progre) ha o be linear; lineariy i merely a convenien aumpion. Figure 3 plo ( ) for 34 period (952 85), where i he eimae of (ee hird regreion in able ). 0.4 Figure 3. Funcion (0.034 ) Noe: = in( ) + in( ) + in( ) + co( ) co( ) co( ) + co( ) log( ) and i he eimaed coefficien (ee hird regreion in able ). Chow argued ha i i eay o explain why here wa no echnical change in China before he reform ared. There i no reaon o aume ha echnical progre occurred during he period up o 980. Economic co-operaion wih he Sovie Union ended in he 960. Wihou incenive from privae enerprie, where could echnological progre have come? I have found no heory o uppor he aerion ha cenral planning will produce echnological progre (Chow 993: 84). The ame daa, however, could equally ell anoher ory, namely, one of rapid echnological progre, bu where a fa growh of he labor force, ogeher wih he exience of urplu labor, led o a iuaion where he weighed average of he growh rae of he wage and he implied profi rae did no increae markedly over ime. The reader may wonder how we came up wih uch complicaed rigonomeric funcion. Thi wa he reul of rial and error. nowing ha we were earching for an approximaion o he accouning ideniy, we graphed ln θ ln θ 2 ln for differen value of θ and θ 2. I i a erie wih an upward rend ha flucuae. Thi indicaed ha we were looking for a rigonomeric funcion. 4

18 Thi analyi lead u o queion Chow overall concluion abou he lack of echnical progre in China. Even auming ha China aggregae producion funcion exi, we have hown ha one doe no need o eliminae cerain year from he regreion o obain good reul, including a aiically ignifican eimae of he proxy for he rae of echnical progre. Second, under he premie ha he aggregae producion funcion doe no exi, Chow exercie can be viewed a imply one for he earch of a good approximaion o he income accouning ideniy. I may well be ha echnical progre in China beween he 950 and 980 wa zero. Our poin i imply ha he mehodology ued by Chow i no uied o anwer hi queion. 3. THE NEOCASSICA MODE OF INVESTMENT In hi ecion we furher elaborae upon he ame wo heme, i.e., he problem poed by he underlying accouning ideniy and he queion of wheher or no he neoclaical model ui he Chinee condiion, in he conex of modeling invemen in China. In a recen paper, He and Qin (2004) (ee alo Song e al. [200]) have made a worhy aemp a anwering he imporan and difficul queion of wha are he driving force behind China fa-growing domeic invemen. Thi i a very complex ak given ha modeling invemen ha alway been a very hard underaking, which in he cae of China i compounded by he fac ha he counry ha been in a ae of raniion for abou 30 year. Hence i i no clear which heoreical approach one hould follow. The Polih economi Michal alecki (97) once commened ha: The deerminaion of invemen deciion by, broadly peaking, he level and rae of change of economic aciviy [ ] remain he pièce de réience of economic alecki (97: 65). ear laer, Blanchard ill fel he ame way: The dicrepancy beween heory and empirical work i perhap nowhere in macroeconomic o obviou a in he cae of he aggregae invemen funcion (Blanchard 986). 3. Chinee Buine Secor Invemen He and Qin (2004) divided Chinee domeic invemen ino buine ecor invemen ( I B ) compoed of ae-owned enerprie, collecive-owned enerprie, and privae enerprie and governmen invemen ( I G ). Following Song, iu, and Ping (200: 232), He and Qin (2004) 5

19 argued ha in he ligh of he fac ha China invemen yem ha changed profoundly ince he raniion proce began, and ha he buine moive of mo Chinee firm have become more marke-oriened ince he 990, i i appropriae o model I B by he orhodox facorinpu demand model (He and Qin 2004: 03). By hi, he auhor mean he neoclaical model of invemen (ee Jorgenon 963). In hi ecion we dicu he modeling of I B. Regarding governmen invemen ( I G ),He and Qin (2004) modeled i a a mixure of policy arge and upply-ide conrain. We review hi in he nex ecion. In he neoclaical heory of invemen (Jorgenon 963), oupu and he co of capial are he variable deermining he opimal capial ock, while invemen repreen he adjumen from he acual o he opimal (deired) capial ock. Jorgenon aumed ha firm chooe heir long-run deired capial ock ( B ) by opimizing heir facor demand ubjec o a conan reurn-o-cale Cobb-Dougla producion funcion (he aumpion abou he form of he producion funcion i no a crucial feaure of he model). Thi lead o he fir-order condiion = θ ( / r), where θ i he elaiciy of oupu () wih repec o capial, and r i B he uer co of capial. Deired invemen ( I B ) follow he equaion I B ) + = ( δ, where δ i he conan depreciaion rae. From he fir-order condiion and he moion of invemen i i eay o derive he baic equaion ued o model buine invemen, namely: = Δ I B θδ I B θδ r (9) r where he ymbol Δ denoe he difference in he value of a variable beween wo conecuive period. He and Qin (2004) argue ha hi equaion reemble a andard error correcion model (ECM), where he erm in quared bracke implie he long-run relaionhip I B = θδ. r Moreover, he auhor argue ha conidering he poibiliy ha he Chinee buine-ecor invemen may alo be affeced by he governmen policie, we exend ha equilibrium relaion by adding governmen direc invemen a a new explanaory variable (He and Qin 2004: 04). α α Thu, he hypoheized long-run relaionhip become I θδ r 2 ( I ) 3 B =, which in α G 6

20 logarihm i ln I B = α 0 + α ln + α 2 ln r + α 3 ln I G, wih expeced eimae α 0 = ln(θδ ), α =, and α =. 2 For economeric purpoe, hi long-run relaionhip wa embedded in a dynamic pecificaion of equaion (9), o which an error erm wih he andard aumpion wa added: d d 0i i j j 2 j j i= j= 0 j= 0 j= 0 d Δ ln I α 0 + α Δ ln I + α Δ ln + α Δ ln r + α Δ ln I + λe + ε (0) = d 3 j G j 2 3 where E = I θδ α r α ( I ) α denoe he diequilibrium erm (he ECM erm) and ε i he B G diurbance. The equaion wa eimaed wih quarerly daa uing he acual value of invemen (ha i, for pracical purpoe, all variable ued were he acual value, wihou he aerik) for he period 994Q4 200Q4. The auhor howed ha he eimaed model paed he andard diagnoic e (auocorrelaion, normaliy, heerocedaiciy, and funcional form) and hey could no rejec he hypohei ha α =, and α 2 =. Baed on he good economeric reul obained He and Qin (2004: 0) concluded ha he long-run oluion derived from heir alleged model ugge rongly ha aggregae buine invemen demand i now largely marke-driven in he PRC. 3.2 Once Again, he Underlying Accouning Ideniy To ee he problem wih equaion (9), above, conider fir he definiion of he capial hare ( ) in oupu (which i obviouly par of he accouning ideniy (2)), namely, Π /, where Π r denoe oal profi (urplu in he NIPA erminology), wrien a he produc of he average ex po profi rae ( r ) ime he ock of capial ( ), and i GDP. From here i follow ha: r () 7

21 The ymbol denoe ha expreion (9) i rue by definiion, in he ene ha i i an accouning ideniy, no a behavioral relaionhip. 8 ikewie, define he law of moion of he ock of capial a: I + ( δ ) (2) which obviouly i alo an accouning ideniy. By rewriing expreion (2) for invemen, ubiuing for he ock of capial from ideniy (), and auming only ha he capial hare i conan (i.e., = ), we obain I + δ (3) r r r Finally, ubracing I from boh ide yield: I I ΔI Δ I δ (4) r r The obviou poin behind expreion (4) i ha i i idenical o equaion (9), he one pecified by He and Qin (2004). I mu be reed ha expreion (4) i an accouning ideniy ha ha been derived a a ranformaion of wo oher accouning ideniie. The only aumpion made o derive expreion (4) i ha he capial hare i conan ( = ), omehing ha can be verified or refued very eaily. The concluion i ha expreion (4), like all near auologie, i conien wih any macroeconomic daae and herefore i no ueful for eing heorie. 8 ikewie, he labor hare in oupu can be wrien a W /, where W denoe he oal wage bill. The laer can be wrien a he produc of he average wage ( w ) rae ime employmen ( ), ha i, W w. I hould be clear ha any yem of conien accoun (e.g., he Naional Income and Produc Accoun [NIPA] of any counry, including hoe of China, from which he facor hare can be inferred) provide oupu () a he um of he oal wage bill (W) plu oal profi ( Π ), ha i + Π. Hence, i i arihmeically poible and W correc o expre oupu a w + r. The fac ha ome counrie do no collec daa ha allow he conrucion of W + Π doe no undermine he heoreical argumen. Neverhele, hi i no he cae of China. 8

22 Provided he capial hare i (ufficienly) conan, economeric eimaion of expreion (4) a: ΔI b Δ + b2 I + ζ (5) r r where ζ = δ, will be a poinle exercie ince one know, ex ane, ha he reul will be b = and b 2 = (he uppoed peed of adjumen o he long-run equilibrium in an error correcion model!), and a perfec aiical fi (here i no error erm of any kind). 9 Cerainly, if he aumpion abou he conancy of he capial hare were incorrec, hen eimaion of expreion (5) uing andard regreion mehod (e.g., OS, IV) would no yield a perfec fi, and he eimaed parameer would diverge from he heoreical value. Bu uch reul would only mean ha capial hare i no ufficienly conan. 0 The general argumen abou expreion (5) would remain valid. The concluion i ha he hypohei ha expreion (3) i a good explanaion of invemen in China can never be rejeced aiically; hence, i canno be poulaed a a model o explain invemen behavior becaue i i no falifiable. He and Qin (2004), however, did no obain a perfec fi when hey eimaed heir model. Thi i becaue hey did no eimae equaion (9). A noed above, hey eimaed equaion (0), which include lag of he variable, and eimaed an error correcion model. Thi led o he inroducion of imporan difference wih repec o he original model, equaion (9). Moreover, He and Qin (2004) inroduced governmen invemen ( I G ) ino he pecificaion. Summing up, in our view, He and Qin (2004: 0) concluion ha he long-run oluion derived from heir alleged model ugge rongly ha aggregae buine invemen demand i now largely marke-driven in he PRC i unwarraned. The concluion of hi ubecion i ha 9 Of coure, no acual daa e will diplay a perfec conancy of he facor hare. For economeric purpoe, hi condiion mu be underood a roughly conan. 0 The general expreion wihou auming ha capial hare i conan i: I + ( ) + δ. r r r r There i a ligh concepual difference worh menioning. In neoclaical pecificaion, auhor ue he uer co of capial inead of he profi rae. The concepual difference i dicued in Felipe and McCombie (2007). 9

23 he Auoregreive Diribued ag (AD) he auhor eimaed i only vaguely relaed o he heoreical framework ha hey argue underlie i, namely, he neoclaical model of invemen. While he auhor ared by auming a relaionhip derived from hi heory, he equaion hey end up eimaing i o differen ha virually ha no relaionhip wih he model. Hence, i i impoible o inerpre i Modeling Chinee Governmen Secor Invemen Given he lack of a ound heory o model he Chinee governmen ecor invemen, he auhor ake a very imple approach. They propoe he long-run relaionhip: T ln I G = β 0 + β ln GR + β 2 ln( / ) + β 3u (6) where I G i he deired level of governmen invemen, T T oupu, i he long-run rend of oupu hu ( / G R i governmen revenue, i acual ) meaure he deviaion of acual oupu from i long-run rend and u i he unemploymen rae, wih expeced ign β > 0, β 2 < 0, and β 3 > 0. A in he cae of he buine-ecor invemen, hi hypoheized long-run relaionhip i inered ino a dynamic equaion in growh rae. Again, empirically, acual value (wihou aerik) were ued. Depie ha he auhor did no model governmen ecor invemen according o he neoclaical model hey ried o inerpre he reul wihin he framework of neoclaical heory, a we hall ee. A key apec of equaion (6) i ha i conain he long-run rend of oupu T, which i T unobervable and hence ha o be eimaed. The auhor argue ha hey define a he ymbolically marke-driven Cobb-Dougla producion funcion wih conan reurn o cale o θ θ reflec he long-run propec T = A (He and Qin 2004: 05, ialic added). Thi i cerainly a mo unuual definiion of a producion funcion and here i no explanaion of wha i mean. The procedure followed o eimae funcion ln( ln A + θ ln( / ) T i he andard one of he fiing producion / ) = and hen uing he fied value (Ŷ ) o approximae he T long-run rend. 2 For empirical purpoe, He and Qin (2004) ued alo an auoregreive diribued lag pecificaion wih a view o pliing hor- and long-run dynamic. Wha i 2 For a imilar procedure ee Heyen and Zebreg (2003). 20

24 inereing i he reul obained for he elaiciy of oupu wih repec o capial: θ =0.95. Since he auhor hough ha here wa omehing wrong wih hi reul, hey experimened (He and Qin 2004: 2) and eled for a no much differen value of θ =0.85. Given he auhor aemen ha hi parameer i normally found o be well below 0.5 in mo marke economie (He and Qin 2004: 2), i eem ha wha hey mean by a ymbolically marke-driven producion funcion i imply a producion funcion uch ha when eimaed he reul are conien wih he exience of compeiive marke, ha i, ha he facor elaiciie equal he facor hare in he NIPA. 3 The NIPA of he advanced counrie repor a capial hare in he neighborhood of Why he auhor did no obain a value of θ cloe o he capial hare i eay o explain, a he reaon i he ame a ha oulined in ecion 2.2, in he conex of Chow (993) work. I eem odd ha he poulaed producion funcion doe no include any variable o accoun for echnological progre (preumably a very imporan facor in China during he period of eimaion, 994Q4 200Q4), no even he andard exponenial ime rend, i.e., = Aexp( λ) θ θ ε. We conjecure ha he reaon i poor economeric reul a a conequence of he fac ha he linear rend provide a bad approximaion o he weighed average of he growh rae of he wage and profi rae. Hence He and Qin (2004) had o ele for a producion funcion which, alhough in neoclaical erm mied an imporan feaure of he Chinee economy (echnical progre), i had, a lea, facor elaicie ha could be explained. For purpoe of He and Qin (2004) work, our argumen implie ha if hey had ued he correc approximaion o he ideniy, he fied value of oupu from he aggregae producion funcion (Ŷ ) would have o be (almo) idenical o he acual value of oupu, hence Ŷ T T, and deviaion from rend ( ), i.e., he oupu gap, hould be very cloe o zero. A corollary of hi reul i ha he producion funcion approach o eimaing poenial oupu and he oupu gap i a queionable mehod. 3 The empirical evidence, however, doe no corroborae hi aemen (ee Sylo-abini 995). In general, eimaion of Cobb-Dougla funcion wih ime-erie daa lead o poor reul (ee he dicuion in ecion 2.2). The implauible reul ha ofen appear wih ime-erie daa eimaing he imple Cobb-Dougla wih a ime rend i a well-known problem o hoe who eimae producion funcion; ee alo Felipe and Adam (2005). 2

25 4. CONCUSIONS Thi paper ha delved ino he general queion of he validiy of he neoclaical heory o model echnical progre and invemen in China. Our overall aemen i ha hi i a very problemaic roue. In he hree cae analyzed here, he equaion ued in he analyi have led o apparenly enible reul for miinformed reaon. The reaon i ha hey can be inerpreed a approximaion o accouning ideniie. Chow, quoed in he inroducion o hi paper, argued ha before new ool are developed for China, one hould underand he uefulne a well a he limiaion of he exiing ool. Perhap uch ime ha arrived. We are convinced ha furher effor are clearly needed. I here any alernaive? One view, raher nihiliic, i ha here i no way ou, a aggregae echnical progre and invemen are problemaic concep due o he aggregaion problem in producion funcion (Felipe and Fiher 2003, 2006). I ha been known for decade ha he condiion o heoreically derive an aggregae producion funcion are o ringen ha i i difficul o believe ha real economie can aify hem. On he quanificaion of he role of echnological progre, he neoclaical aggregae producion funcion, wih i emphai on pliing he alleged conribuion of facor accumulaion and echnical progre o overall oupu growh i an avenue ha hould be dicarded (Sco 989; Nelon 973, 98, 998). Moreover, imulaion analye by Felipe and McCombie (2006) how ha he rue rae of echnical progre, eimaed wih phyical daa, differ ubanially from he rae of TFP growh, calculaed wih aggregae daa in value erm. The laer i imply, a uually eimaed, a meaure of change in diribuional income. Alhough he above i a poiion ha we fundamenally believe i correc, perhap here are ome oher opion ha allow reearcher o gain ueful inigh. Eimaion of echnical progre hould once-and-for-all abandon he neoclaical framework (eiher growh accouning exercie or eimaion of aggregae producion funcion). The recen work of Haumann, Hwang, and Rodrik (2007) and Hidalgo e al. (2007) i a welcome advance (he laer uing nework heory) oward underanding how counrie progre by looking a he produc ha hey expor uccefully and he capabiliie needed o do o. A meaure of he ophiicaion of a counry expor bake ha proven o be a good predicor of fuure growh: conrolling for iniial income, counrie wih a more ophiicaed expor bake (alo iniially) grow faer. 22

26 Hidalgo e al. (2007) argue ha developmen ha o be underood a a proce of accumulaing more complex e of capabiliie and finding pah ha creae incenive for hoe capabiliie o be accumulaed and ued. To hi purpoe hey inroduce a new analyical ool called he produc pace. Abdon e al. (200), Felipe, umar, and Abdon (200), and Felipe e al. (200) ue i o udy China performance and how ha he progre ha he counry ha een for decade canno be explained wihou underanding how i ranformed, upgraded, and diverified i expor bake; hi could be done only hrough he maering of more complex capabiliie. On modeling invemen in China, a le radical view i o conider aggregae invemen a a meaningful economic concep, bu hen model i ouide he realm of neoclaical economic. Effor mu be developed oward: (i) incorporaing elemen from developmen heory ha apply o he Chinee economy; (ii) incorporaing he role of expecaion, a crucial apec of any realiic model of capial accumulaion (e.g., ee Heye 995); and (iii) incorporaing he role of profi a a ource of invemen. alecki (97) emphaized he imporance of reinveed profi a a ource of invemen, profi rae (in paricular, he difference beween he expeced rae of profiabiliy and he inere rae), and capaciy uilizaion. 4 The idea ha invemen depend upon profi i among he olde of macroeconomic relaion. If indeed China privae ecor i behaving more like a marke economy, hen urely a proxy for he profiabiliy of invemen (e.g., he average profi rae) and profi hemelve will play an imporan role in modeling invemen (e.g., Sun 998). 4 For eimae of profiabiliy for China, ee Holz (2002). 23

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