Estimating Rates of Return on Capital

Transcription

1 Esimaing Raes of Reurn on Capial Gallina Vincelee and Frizi oehler (PRMED) Augus 27, 2009 The World Bank ~ yiv, Ukraine 1

2 Rae of Reurn on Capial (RoR ) provides a basis for assessing he conribuion of capial invesmen o he growh process is a key guide for esimaing he opporuniy cos of capial 2

3 RoR : Imporan for applied growh economic work Measures he conribuion of invesmen o economic growh (Solow, 1956) Presens a significan par of counry-level diagnosics analysis of impedimens o growh: ey Quesion: Is invesmen in physical capial low because: (i) he reurn of capial is low, or (ii) he cos of financing is oo high? 3

4 4 RoR : Definiion RoR (ρ ) is he raio of he value of naional income accrued o capial ( k ) during he year o he value of he naional capial sock a he beginning of he year ( ) where a is he share of capial in income Therefore:

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 Income Accruing o Capial Toal Capial Income = (Naional Income - Toal Labor Income ) L Toal Labor Income = (Toal Wages&Salaries + Impued Wages&Salaries) L h 1 ( p X s L UE ) 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 6

7 Income Accruing o Capial Obaining esimaes of : Or dynamic capial shares of income as repored in na. accouns 'rule of humb' assumes a consan capial share of income of 0.4 regress capial shares repored by Bernanke and Gurkaynak (2001) on he value added share of indusry and region dummies regress capial shares repored by Gollin (2002) on region dummies In he case of Ukraine: we obain four esimaes of a and use hem o calculae four ses of Income Accruing o Capial 7

8 8 Income Accruing o Capial Share of Naional Income Accruing o Capial Income accruing o capial L UE h s X p ) ( 1 L L UE h s X p 1

9 Capial Shares of Income Toal Income Accruing o Capial ear Rule of humb Capial Share (B&G Region Dummies) Capial Share (Gollin Region Dummies) Capial Share (dynamic) Rule of humb Capial Share (B&G Region Dummies) Capial Share (Gollin Region Dummies) Capial Share (dynamic) E E E E E E E+11 9

10 Esimaing Income Accruing o Capial: Ukraine 140,000 Income Accruing o Capial consan 2001 LCU, mln 120, ,000 80,000 60,000 40,000 20, Rule of humb Capial Share (B&G Region Dummies) Capial Share (dynamic) 10

11 Esimaing he Sock of Capial Toal capial sock comprises of differen caegories of asses, usually: Fixed Asses Machinery and equipmen Buildings and consrucion Invenory 11

12 Mehodology Perpeual Invenory Mehod: Ne capial sock a he beginning of he period ( +1 ) is a funcion of he ne capial sock ( ) plus yearly Gross Invesmen (I ) minus depreciaion (D ) +1 = + I D (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 12

13 Perpeual Invenory Mehod: Assumpions Geomeric depreciaion ( 1 ) 1 Differen deprecaion raes δ across he ypes of invesmen considered I Iniial Sock of Capial ( 1 ) 1 I i ) 1 ( 1 ) 1 (1 i I i I ( ) 13 (5)

14 Esimaing Iniial Sock of Fixed 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) and of economic growh (γ) 3. Esimae he iniial sock of each ype of reproducible capial: 1 I /( ) 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 14

15 Esimaing Capial Sock in Transiion Economies Upward bias in recorded values of capial socks prior o 1990, because par of old capial does no conribue any longer o he producion process and is sill in he records Esimae old Sovie capial sock: µ share of unusable capial and old depreciaion rae of old capial ), old ( 1 ) 0 (1 old Izyumov and Vahaly (2008) esimae (i) 1989 capial sock using daa from Goskomsa; (ii) 1991 capial sock using PIM 0.05; 0.3 Esimae new capial sock (from 1992 unil year ) old, new I n (1 new n 0 ) n 15

16 Toal Economy old capial depreciaion of old capial oal enering capialsock depreciaion of capial sock 16 gross capial formaion (invesmen) depreciaion of invesmen old & new capial - a he beginning of he year E E E E E E E E E E E E E E E E E E E E E E E E+11 Noe: SSCU series Capial sock deflaed ino consan 2001 LCU; GCF - SSCU series Invesmen in fixed capial deflaed ino consan 2001 LCU; depreciaion 5% Source: SSCU

17 Esimaing Capial Sock: Ukraine 1,000,000 Capial Sock consan 2001 LCU, mln 900, , , , , , , , , Old & new capial a beginning of year gross capial formaion (invesmen) Noe: SSCU series Capial sock deflaed ino consan 2001 LCU; GCF - SSCU series Invesmen in fixed capial deflaed ino consan 2001 LCU; depreciaion 5% Source: SSCU 17

18 Esimaing Sock of Invenories Inv Inv 0 [ n0 Inv n Inv n /( GDP GDPn )] * GDP 1 Inv Rerieve Ne Invenory Accumulaion from Naional Accouns Calculae Marginal Invenory/GDP= Ne Invenory Accumulaion /Change in GDP [Ukraine= 10.35%] Apply raio [10.35%] o iniial year GDP and esimae Iniial Invenory Sock Derive Invenory Sock by adding Ne Invenory Changes o Iniial Sock of Invenory for each year afer 18

19 Esimaing Invenory Sock: Ukraine 35,000 Invenory Sock consan 2001 LCU, mln 30,000 25,000 20,000 15,000 10,000 5, , ,000 ne invenory change Invenory sock a beginning of year 19

20 20 The Rae of Reurn on Capial 1. Esimae Toal Capial Sock = Σ[Fixed Capial) ; (Invenories) ] 2. Naional Income Accruing o Capial or 3. Esimae he rae of reurn (ρ ) ) ( 1 L UE h s X p

21 Raes of Reurn on Capial: Ukraine Rule of humb Capial Share (B&G Region Dummies) Capial Share (dynamic) Average RoR (over dynamic shares, rule of humb and B&G) 21

22 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 Goskomsa. (2006). Goskomsa (Rossa), annual: Rossiiskii Saisicheskii Ezhegodnik (Russian Saisical Annual). Sae Commiee for Saisics/Federal Saisical Service: Moscow. Harberger, A. C. (1972). On Esimaing he Rae of Reurn o Capial in Colombia. Proec Evaluaion: Colleced Papers, S

23 Seleced References 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 Izyumov, A., & Vahaly, J. (2008). Old Capial vs. New Invesmen in Pos-Sovie Economies: Concepual Issues and Esimaes. Comparaive Economic Sudies, 50, pp 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