IF FACTOR SHARES ARE NOT CONSTANT THEN WE HAVE A MEASURMENT PROBLEM. CAN WE SOLVE IT? Hernando Zuleta

Transcription

1 IF FCTOR HRE RE NOT CONTNT THEN WE HVE MEURMENT PROBEM. CN WE OVE IT? Hernando Zulea ERIE DOCUMENTO DE TRBJO No. 67 goso 2009

2 IF FCTOR HRE RE NOT CONTNT THEN WE HVE MEURMENT PROBEM. CN WE OVE IT? 1 Hernando Zulea Universidad del Rosario merican Universiy in Bulgaria hernando.zulea@gmail.com bsrac Recen evidence show ha facor shares, if properly measured, are far from consan. Moreover, he shares of naural resources and raw labor seem o be negaively correlaed wih income per capia while he share of human and physical capial is posiively correlaed wih income per capia. Now, if facor shares are no consan hen (i) growh accouning exercises rely on a false assumpion and (ii) here is a measuremen problem. The effec ha changes in facor shares have on oupu depend on he relaive abundance of facors and, for his reason, i is necessary o have correc measures. We propose an empirical mehodology o solve he measuremen issue and esimae TFP growh. JE Codes: O11, O30, O41 eyword: Facor hares, Producion Funcion, Measuremen. 1 The findings, recommendaions, inerpreaions and conclusions expressed in his paper are hose of he auhors and no necessarily reflec he view of he Deparmen of Economics of he Universidad del Rosario. 1

3 1. Inroducion The idea ha labor income share is roughly consan, namely, he Cobb-Douglas-aldor paradigm 2, produced imporan consequences in he area of economic growh. lmos all of he lieraure on growh accouning assumes ha he elasiciy of oupu wih respec o capial is consan and concludes ha he major par of economic growh is explained by growh in TFP 1 (see Easerly and evine, 2002; olow, 1957 or oung, 1994 among ohers). Recen empirical work shows ha he Cobb-Douglas-aldor paradigm is no really suppored by he daa. ahn and im (1998) show ha he shares of equipmen, producion workers and non producion workers have clear rends. Blanchard (1997) observes he share of labor decreases in coninenal Europe afer he 80s and suggess ha he reason of such decline may be echnological bias. Oher auhors calculae he income share of reproducible facors (human and physical capial) and no reproducible facors and i urns ou ha he laer is posiively correlaed wih he income level (see rueger, 1999; Caselli and Feyrer, 2007; Zulea, 2008a; urgill, 2009 and Zulea, Parada and Campo, 2008) 3. ddiionally, he variabiliy of facor shares may have differen effecs on oupu depending on he facor abundance of he economy. If he income share of abundan facors is growing he effec of hese changes on he income level is posiive bu if income share of abundan facors is decreasing he effec of hese changes on he income level is negaive. In his paper we propose an empirical mehodology o esimae he correc measures of facor shares. In he nex secion we explain why measuremen is an issue when facor shares are no consan. In he hird secion we presen he mehodology. In he las secion we presen he conclusions. 2 ee Cobb and Douglas (1928) and aldor (1961). 3 In he las decades some auhors revisied he heory of biased innovaions and challenged he Cobb- Douglas-aldor paradigm. Zeira (1998) provides a model of echnological innovaions ha reduce labor requiremens and find ha innovaions are only adoped in counries wih high wages. eaer (2005), Zeira (2006), Pereo y eaer (2007) and Zulea (2008b) among ohers, presen models where he scarciy of no reproducible facors generaes incenives o adop echnologies ha reduce he need of he hese facors. In a marke economy, his ype of echnological change affecs facor income shares in such a way ha he share or reproducible facors is posiively correlaed o he income level of he economy. 2

4 2. Facor hares and Measuremen To illusrae he imporance of correc measures for he facors consider he simples Cobb- Douglas echnology wih wo facors: and. Oupu per worker, y, can be expressed as a funcion of capial per worker k : y k Now, suppose ha here is an increase in he share of capial. The effec of he change in facor shares on income per worker depends on he relaive abundance of capial, y k k Therefore, if k 1 he effec is posiive and if k 1 he effec is negaive. Figure 1 illusraes his fac. y Figure 1 1 k 3. How o solve he problem? For simpliciy consider a producion funcion wih only wo facors: 1 (1) 3

5 4 Where is oal income, is physical capial is raw labor. Noe ha facor shares have he subindex, namely hey are variables no parameers. Now, given ha facor shares vary, he relaive abundance of facors becomes very imporan and, for his reason, i is necessary o have correc measures of capial and labor. The parameers and play his role. If 1 hen he economy is capial abundan. a. The Mehodology assuming away facor augmening echnological change. Differeniaing equaion 1, (2) ) 1 ( Now define (3) ) 1 ( The variable in equaion 3 is he olow residual. Now, from equaions 2 and 3 i follows ha he olow residual is no only TFP growh. The olow residual includes biased echnological change: (4) Define o equaion 4 can be rewrien (5) Therefore, he reduced form o be esimaed is he following, (6) C C 1 0 Where C 0, C 1.

6 Therefore, his mehodology allows us o idenify he correc measures of facors per worker. Finally, combining he previous resuls wih equaion 1 and aking logs we ge (7) log log log log( ) We also know ha log log 0 log(1 C0 ). Therefore, we can define log log log(1 C0 ) log so ha equaion 7 can be wrien as log( ). Therefore, we can also idenify he iniial level of TFP muliplied by he 0 correc measure of labor. b. Wha if here is labor augmening or capial augmening echnological change? We assume ha here is facor augmening echnological change and he rae of echnological change is consan. Equaion 2 becomes (2) Where and (1 ), (1 ), are, respecively, capial and labor augmening echnological change. Equaions 4 and 5 becomes (4) (1 ),, (5),0 1,0 5

7 Therefore, he reduced form o be esimaed is he following, (6) C0 C1 C2 Where C 1 1, C 2 and C 0. Therefore, we can idenify he correc measures of facors per worker, he difference beween capial augmening and labor augmening echnological change and he sum of neural plus labor augmening echnological change. References cemoglu, Daron (2002) "Direced Technical Change" he Review of Economic udies, 69 (4) Boldrin, Michele and evine, David. (2002) " Facor aving Innovaion" Journal of Economic Theory, 105 (1), Caselli, Francesco and Feyrer, James (2007) "The Marginal Produc of Capial" Quarerly Journal of Economics, vol. 122(2), , 05. Cobb C W and Douglas P H (1928) " Theory of Producion", merican Economic Review, 18 (upplemen), Dunning, J.H. (1998), Explaining Inernaional Producion ondon: Unwin Hyman. Gollin, D., (2002) Geing Income hares Righ, Journal of Poliical Economy, 110 (2), rueger, lan (1999) "Measuring abor's hare" merican Economic Review, 89 (2), Heckscher, Eli F., (1919) The Effec of Foreign Trade on he Disribuion of Income, Ekonomisk Tidskrif aldor, N., (1961), Capial ccumulaion and Economic Growh, In F uz and DC Hague, eds., The Theory of Capial, New ork, Marin s Press. ennedy, Charles (1964), "Induced Bias in Innovaion and he Theory of Disribuion", Economic Journal, XXIV, Pereo, Piero and eaer, John "ugmenaion or Eliminaion?", working paper 2006, hp://ideas.repec.org/p/deg/conpap/c011_060.hml urgill, Brad (2009) Cross-counry Variaion in Facor hares and is Implicaions for Developmen ccouning working Papers 09-07, Deparmen of Economics, ppalachian ae Universiy. oung,., (1995). The Tyranny of Numbers: Confroning he aisical Realiies of he Eas sian Growh Experience. Quarerly Journal of Economics, 110: Zeira, Joseph. (1998) "Workers, Machines and Economic Growh." Quarerly Journal of Economics, 113 (4), pp Zeira, Joseph, (2005) "Machines as Engines of Growh," CEPR Discussion Papers

8 Zulea, Hernando, (2007) Why labor income shares seem o be consan, Journal of Inernaional Trade & Economic Developmen, 16 (4), Zulea, Hernando, (2008a) n Empirical Noe on Facor hares, Journal of Inernaional Trade & Economic Developmen, 17 (3), Zulea, Hernando, (2008b) Facor aving Innovaions and Facor Income hares, Review of Economic Dynamics, 11 (4), Zulea, Hernando; Parada, Julian y Campo, Jacobo (2008) "Capial Naural, Capial Humano y Paricipación de los Facores. Una Revisión de los Méodos de Medición del Crecimieno Económico," DOCUMENTO DE TRBJO , UNIVERIDD DE RORIO - FCUTD DE ECONOMÍ. 7