Estimating Rates of Return on Capital. Gallina Vincelette (PRMED) Apirl 26-30, 2010

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1 Esimaing Raes of Reurn on Capial Gallina Vincelee (PRMED) Apirl 26-30, 2010

2 Rae of Reurn on Capial (RoR) RoR is imporan for applied growh economic work Measures he conribuion of invesmen o economic growh (Solow, 1956), i.e. provides a basis for assessing he conribuion of capial invesmen o he growh process RoR is a key guide for esimaing he opporuniy cos of capial Presens a significan par of growh diagnosics (HRV) Q1: Is invesmen in physical capial low because: (i) he reurn on capial is low, or (ii) he cos of financing is oo high? 2

3 RoR : Definiion RoR (ρ ) is he raio of he value of naional income accrued o capial ( k ) o he value of he naional capial sock ( ) ρ = 3

4 Income Accruing o Capial Toal Capial Income= (Naional Income - Toal Labor Income ) = L Toal Labor Income = (Toal Wages&Salaries + Impued Wages&Salaries) L h = ( p X + = 1 s L UE ) sum of wages and salaries in he naional accouns plus he share of labor in he income of non-incorporaed enerprises ( UE) imes income of he unincorporaed enerprises Impued Wages&Salaries: a fracion of average income ( )generaed by a ypical employee in each secor o accoun for proprieors, parners, selfemployed, and unpaid family members 4

5 Esimaion procedure: Problems Daa in Naional Accouns are usually no in direcly applicable form! The marginal produciviy of labor in he public secor may differ from wages and salaries paid Naional accouns frequenly idenify employee compensaion wih income from labor, which implies ha he income of unincorporaed enerprises is enirely aribued o capial 5

6 Incorporaed Firms Income Accruing o Labor: Example Type I Type II Type III Wages&Salaries (Na.Acc.) 9, , , Number (Na.Acc./Census) 29, , , Average Earnings Unincorporaed Firms Number (Na.Acc./Census) , , Average Earnings Impued Wages&Salaries , Toal Labor Income 9, , ,

7 7 Earnings Direcly Aribuable o Capial Income accruing o capial Share of Naional Income Accruing o Capial (s ) Rule of humb: ~60 percen of he naional income accrues o labor and ~40 percen o capial L UE h s X p s + = =1 ) ( 1 L UE h s X p + = =

8 Esimaing he Sock of Capial Toal capial sock comprises of differen caegories of asses, usually: Fixed Asses Machinery and equipmen Buildings and consrucion Invenory (Land) 8

9 Mehodology Perpeual Invenory Mehod: Ne capial sock for period ( ) is a funcion of he ne capial sock ( -1 ) plus Gross Invesmen (I -1 ) during he year minus depreciaion (D -1 ) = -1 + I -1 D -1 (1) Assumpions: depreciaion mehod has o be chosen level & ime profile of depreciaion rae has o be made iniial capial sock has o be consruced 9

10 Perpeual Invenory Mehod Geomeric depreciaion, δ Perpeual capial sock accumulaion = ( 1 δ ) + 1 I 1 (2) capial sock depreciaes a a consan rae, δ perpeual as all asses par of invenory of capial sock forever Wih infinie number of invesmen periods = i= 0 (1 δ i (3) Wih limied number of invesmen periods ) i I is a weighed sum of pas invesmen, where he weighs are a decreasing funcion of he disance beween he curren period and he invesmen period. = (1 δ ) 1 + i 1 (1 δ ) i= 0 I i (4) 10

11 Esimaing he Iniial Sock of Capial Iniial sock of each ype of reproducible capial: 1 = I /( δ + γ ) Where: I is gross invesmen, δ is he rae of depreciaion, γ is he annual rae of growh of capial sock, and is he capial sock a he beginning of he year capial sock a he beginning of period is calculaed as invesmen in period divided by he sum of he depreciaion rae and he growh rae of he capial sock in period 11

12 Esimaing he Iniial Sock of Fixed Capial Asses 1. Take Gross Invesmen for fixed asses (buildings and consrucion; and machinery and equipmen) o generae capial-sock series (source: Naional Income Accouns) 2. Assume appropriae raes of depreciaion (δ) 3. Assume growh rae of capial sock (γ): in seady sae, invesmen and capial grow a he same rae. 4. Esimae he iniial sock of each ype of reproducible capial: 1 = I /( δ + γ ) 12

13 Esimaing Sock of Invenories 1. Rerieve Ne Invenory Accumulaion from Naional Accouns 2. Calculae Marginal Invenory-o-GDP raio Alernaively, use anoher (similar) counry s average Marginal Invenory-o-GDP raio 3. Apply his raio o he iniial year GDP o esimae he Iniial Invenory Sock 4. Derive Invenory Sock series by adding Ne Invenory Changes o Iniial Sock of Invenory for each year afer 13

14 The Rae of Reurn on Capial 1. Esimae Toal Capial Sock = Σ[Fixed Capial) ; (Invenories) ] 2. Naional Income Accruing o Capial = 1 L UE 3. Esimae he rae of reurn (ρ ) h = ( p X + s ) ρ = L 14

15 Checks and Adusmens: Depreciaion Check 1. Compare he depreciaion (δ FA = δ consrucion & buildings + δ machinery & equipmen) across each group of fixed asses o he depreciaion from naional accouns (δ Naional Accouns) 2. If esimaes are on he lower side, reduce depreciaion (e.g. by 20%, i.e. δ consrucion & buildings = 2% and δ machinery & equipmen = 5%) 3. If esimaes are on he higher side, increase depreciaion 4. Esimae new capial sock for each group of fixed asses 5. Perform depreciaion checks again and compare o he adused naional accouns depreciaion 15

16 RoR Accouning Decomposes changes in RoR ino changes in capial sock and in income accruing o capial Explains how much of he change in RoR can be aribued o (i) changes in he income accruing o capial; (ii) he changes in he capial sock Back o he HRV diagnosic ree

17 Seleced References Bai, C.-e., Hsieh, C.-T., & Quian,. (2006). The Reurn o Capial in China. Brookings Paper on Economic Aciviy, S Barro, R. J., & Lee, J. (Sepember 2000). Inernaional Daa on Educaional Aainmen: Updae and Implicaions. NBER working paper No Bernanke, B. S., & Gürkaynak, R. S. (July 2001). Is Growh Exogenous? Taking Mankiw, Romer, and Weill Seriously. NBER Working Paper No. 8365, S Blades, D. (1998). Measuring depreciaion. paper presened a he second meeing of he Camberra Group on Capial Sock Saisics, Paris. OECD. Caselli, F., & Feyrer, J. (May 2007). The Marginal Produc of Capial. The Quarerly Journal of Economics, S Dey-Chowdhury, S. (Sepember 2008). Perpeual Invenory Mehod. Economic & Labor Marke Review, S Ferreira, A. L. (Augus 2008). On he Differences Beween he Marginal Produc of Capial Across Counries. Universiy of Sao Paulo, Deparmen of Economics, FEARP, Brasil. Gollin, D. (April 2002). Geing Income Shares Righ. The Journal of Poliical Economy, S Harberger, A. C. (1972). On Esimaing he Rae of Reurn o Capial in Colombia. Proec Evaluaion: Colleced Papers, S Izyumov, A., & Vahaly, J. (Augus 2007). New capial accumulaion in ransiion economies: implicaions for capial-labor and capial-oupu raios. Economic Change and Resrucuring, S

18 Seleced References amps, C. (2004, April). New Esimaes of Governmen Ne Capial Socks for 22 OECD Counries IMF Working Paper, pp Meinen, G., Verbies, P., & de Wolf, P.-P. (July 1998). Perpeual Invenory Mehod: Service Lives, Discard Paerns and Depreciaion Mehods. Saisics Neherlands, Deparmen of Naional Accouns. Narodnoye hozyaisvo SSSR, (1989). Sae commiee for Saisics: Moscow. OECD. (2001). Measuring Capial: Measuring of Capial Socks, Consumpion of Fixed Capial and Capial Services. OECD. Priche, L. (2000, December). CUDIE (Cumulaed, Depreciaed, Invesmen Effor) Is No Capial. Journal of Economic Growh, pp Sachs, J., & Warner, A. (1995). Economic Reform and he Process of Global Inegraion. Brookings Papers on Economic Aciviy, No 1, pp oung, A. (Augus 1995). The Tyranny of Numbers: Confroning he Saisical Realiies of he Eas Asian Growh Experience. The Quarerly Journal of Economics, S