Does a small cost share reflect a negligible role for energy in economic production? Testing for aggregate production functions including capital, labor, and useful exergy through a cointegration-based method

Santos, João and Domingos, Tiago and Sousa, Tânia and St. Aubyn, Miguel (2016): Does a small cost share reflect a negligible role for energy in economic production? Testing for aggregate production functions including capital, labor, and useful exergy through a cointegration-based method.

Abstract

Neoclassical models disregard the role of energy in production, equating a factor's output elasticity with its cost share, but failing to explain growth without a residual term. In contrast, ecological economics acknowledges energy's importance in production, regardless of its cost share. The aggregate production function (APF) concept, central to neoclassical theory, is also disputed.

We apply cointegration analysis to test for APFs between output, capital, and labor. We investigate the inclusion of energy inputs, measuring energy's capacity to generate productive work (useful exergy). Plausible APFs must verify cointegration and Granger-causality between output and inputs; and non-negative output elasticities. This method recognizes cases where: a) plausible APFs don't exist; b) energy impacts growth directly; c) energy impacts growth indirectly, through other inputs. We apply the method to Portugal (1960-2009), considering standard and quality-corrected capital and labor measures.

Plausible APFs are rarely obtained for capital-labor models. When they are, the residual growth component is large, and output elasticities disagree with historical cost shares. However, the residual is virtually eliminated for capital-labor-energy models with two cointegration relationships: a) a capital-labor APF, with output elasticities matching historical cost shares; b) a function estimating capital from useful exergy. These models reconcile energy's significance in production with cost-share neoclassical assumptions.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cointegration; Aggregate production function; Cost shares; Solow residual; Useful exergy
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E13 - Neoclassical; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O47 - Empirical Studies of Economic Growth ; Aggregate Productivity ; Cross-Country Output Convergence; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q4 - Energy > Q43 - Energy and the Macroeconomy

References

Aghion, P. & Howitt, P. (2009). The economics of growth. Cambridge, MA: MIT Press.

Amaral, L. (2009). New series for GDP per capita, per worker, and per worker-hour in Portugal, 1950-2007. Working Paper Series. Faculty of Economics. New University of Lisbon.

AMECO. European Commission’s annual macro-economic database. Available online at: http://ec.europa.eu/economy_finance/db_indicators/ameco/index_en.htm. Accessed: 2015-01-10.

Ayres, R. U., & Warr, B. (2005). Accounting for growth: the role of physical work. Structural Change and Economic Dynamics, 16(2), 181-209.

Ayres, R. U., Van den Bergh, J. C., Lindenberger, D., & Warr, B. (2013). The underestimated contribution of energy to economic growth. Structural Change and Economic Dynamics, 27, 79-88.

Barro, R. J., & Lee, J. W. Educational attainment dataset. Available online at: http://www.barrolee.com. Accessed: 2015-06-10.

Caselli, F. (2005). Accounting for cross-country income differences. Handbook of economic growth, 1, 679-741.

Caves, D. W., Christensen, L. R., & Diewert, W. E. (1982). The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica: Journal of the Econometric Society, 50, 1393-1414.

Christensen, L. R., Cummings, D., & Jorgenson, D. (1980). Economic growth, 1947–73: an international comparison. In: J. W. Kendrick and B. N. Vaccara (eds.) New Developments in Productivity Measurement and Analysis (pp. 595-698). The University of Chicago Press, Chicago.

Cleveland, C. J. (1991). Natural resource scarcity and economic growth revisited: Economic and biophysical perspectives. In: Costanza, R. (Ed.), Ecological Economics: the science and management of sustainability, (pp. 289-317). Columbia University Press, New York.

Cleveland, C. J., Kaufmann, R. K., & Stern, D. I. (2000). Aggregation and the role of energy in the economy. Ecological Economics, 32(2), 301-317.

da Silva, E. G. (2010). Capital services estimates in Portuguese industries, 1977–2003. Portuguese Economic Journal, 9(1), 35-74.

da Silva, E. G. and Lains, P. (2013). Capital formation and long-run growth: Evidence from Portuguese data, 1910-2011. Presented at IBEROMETRICS VI, May 16-17, Facultad de Economia y Empresa, Zaragoza, Spain. Available online at: http://estructuraehistoria.unizar.es/personal/vpinilla/documents/2013.04.04_Iberometrics_Silva.Lains.pdf.

d'Arge, R. C., & Kogiku, K. C. (1973). Economic growth and the environment. The Review of Economic Studies, XL (1), 61-77.

de la Escosura, L. P., & Rosés, J. R. (2009). The sources of long-run growth in Spain, 1850-2000. The Journal of Economic History, 69(04), 1063-1091.

Denison, E. F. (1974). Accounting for United States Economic Growth, 1929-1969. The Brookings Institution Press, Washington, D.C.

Denison, E. F. (1979). Accounting for slower economic growth: the United States in the 1970's. Brookings Institution Press, Washington, D.C.

Diewert, W. E. (1976). Exact and superlative index numbers. Journal of econometrics, 4(2), 114-145.

Dougherty, C. (1991). A Comparison of Productivity and Economic Growth in the G-7 Countries, Ph. D. Dissertation, Harvard University.

Easterly, W., & Levine, R. (2001). What have we learned from a decade of empirical research on growth? It's Not Factor Accumulation: Stylized Facts and Growth Models. The World Bank Economic Review, 15(2), 177-219.

Engle, R. F., & Granger, C. W. (1987). Co-integration and error correction: representation, estimation, and testing. Econometrica: journal of the Econometric Society, 55, 251-276.

Feenstra, R. C., Inklaar, R., & Timmer, M. P. (2015). What is new in PWT 8.1?. University of Groningen (unpublished). Available online at: www.rug.nl/research/ggdc/data/pwt/v81/

Felipe, J., & McCombie, J. S. (2005). How sound are the foundations of the aggregate production function?. Eastern Economic Journal, 31(3), 467-488.

Felipe, J., & McCombie, J. S. (2013). The Aggregate Production Function and the Measurement of Technical Change: Not Even Wrong. Edward Elgar Publishing, Cheltenham.

Gans, J., King, S., Stonecash, R., & Mankiw, N. G. (2012). Principles of economics (5th ed.). Cengage Learning Australia, Melbourne, Australia.

Ghali, K. H., & El-Sakka, M. I. (2004). Energy use and output growth in Canada: a multivariate cointegration analysis. Energy Economics, 26(2), 225-238.

Giraud, G., & Kahraman, Z. (2014). How Dependent is Growth from Primary Energy? Output Energy Elasticity in 50 Countries (1970-2011). Documents de Travail du Centre d’Economie de la Sorbonne, 2014.97, 1-26.

Gross, L. S., & Veendorp, E. C. H. (1990). Growth with exhaustible resources and a materials-balance production function. Natural Resource Modeling, 4(1), 77-94.

Groth, C., Gutierrez-Domenech, M. & Srinivasan, S. (2004). Measuring total factor productivity for the United Kingdom, Quarterly Bulletin, Spring 2004, Bank of England.

Hanushek, E. A., & Woessmann, L. (2012). Do better schools lead to more growth? Cognitive skills, economic outcomes, and causation. Journal of Economic Growth, 17(4), 267-321.

Henriques, S. (2011). Energy transitions, economic growth and structural change: Portugal in a long-run comparative perspective (Vol. 54). Lund University.

Hulten, C. R., & Wykoff, F. C. (1996). Issues in the measurement of economic depreciation introductory remarks. Economic Inquiry, 34(1), 10-23.

INE. Instituto Nacional de Estatística. Available online at: http://www.ine.pt. Accessed: 2015-01-10.

Inklaar, R., & Timmer, M. (2013). Capital, Labor and TFP in PWT8.0. University of Groningen (unpublished). Available online at: http://www.rug.nl/research/ggdc/data/pwt/v80/

Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of economic dynamics and control, 12(2), 231-254.

Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica: Journal of the Econometric Society, 59, 1551-1580.

Jones, C. I. (2002). Introduction to Economic Growth, 2nd ed., W. W. Norton & Company, New York.

Jorgenson, D. W., & Griliches, Z. (1967). The explanation of productivity change. The Review of Economic Studies, 34(3), 249-283.

Jorgenson, D. W., Gollop, F. M., & Fraumeni, B. M. (1987). Productivity and U.S. Economic Growth. Harvard Economic Studies, vol. 159, Harvard University Press, Cambridge, Massachusetts, U.S..

Juselius, K. (2006). The cointegrated VAR model: methodology and applications. Oxford University Press, Cambridge, United Kingdom.

Kaldor, N. (1961). Capital Accumulation and Economic Growth. In: F. A. Lutz, D. C. Hague (eds.), The Theory of Capital: Proceedings of a Conference Held by the International Economic Association, 177–222, St. Martin’s Press, New York.

Kamps, C. (2006). New estimates of government net capital stocks for 22 OECD countries, 1960-2001. IMF staff papers, 120-150.

Kander, A., & Stern, D. I. (2014). Economic growth and the transition from traditional to modern energy in Sweden. Energy Economics, 46, 56-65.

Kander, A., Malanima, P., & Warde, P. (2014). Power to the people: energy in Europe over the last five centuries. Princeton University Press.

Kemfert, C. (1998). Estimated substitution elasticities of a nested CES production function approach for Germany. Energy Economics, 20(3), 249-264.

Kümmel, R., Lindenberger, D., & Eichhorn, W. (2000). The productive power of energy and economic evolution. Indian Journal of Applied Economics, 8(2), 1-26.

Kümmel, R., Strassl, W., Gossner, A., & Eichhorn, W. (1985). Technical progress and energy dependent production functions. Journal of Economics, 45(3), 285-311.

Lindenberger, D., & Kummel, R. (2002). Energy-dependent production functions and the optimization model “PRISE” of price-induced sectoral evolution. International Journal of Thermodynamics, 5(3), 101-107.

Lindenberger, D., & Kümmel, R. (2011). Energy and the state of nations. Energy, 36(10), 6010-6018.

Manuelli, R. E., & Seshadri, A. (2014). Human Capital and the Wealth of Nations. American Economic Review, 104(9): 2736-62.

Newey, W. K., & West, K. D. (1994). Automatic lag selection in covariance matrix estimation. The Review of Economic Studies, 61(4), 631-653.

Ohanian, L. E., & Wright, M. L. (2010). Capital flows and macroeconomic performance: lessons from the golden era of international finance. The American Economic Review, 100(2), 68-72.

Pinheiro, M. (1997). Séries Longas para a Economia Portuguesa pós II Guerra Mundial, Volume I – Séries Estatísticas. Banco de Portugal, Lisboa, Portugal.

Platchkov, L. M., & Pollitt, M. G. (2011). The Economics of Energy (and Electricity) Demand. Working Paper 1116. University of Cambridge Electricity Policy Research Group (EPRG).

Psacharopoulos, G., & Patrinos, H. A. (2004). Returns to investment in education: a further update. Education economics, 12(2), 111-134.

PWT8.1. Penn World Table – Version 8.1. Available online at: http://febwt.webhosting.rug.nl/. Accessed: 2015-04-15.

Robinson, J. (1953). The production function and the theory of capital. The Review of Economic Studies, 21(2), 81-106.

Saunders, H. D. (2008). Fuel conserving (and using) production functions. Energy Economics, 30(5), 2184-2235.

Schreyer, P., Bignon, P. E., & Dupont, J. (2003). OECD Capital Services Estimates: Methodology and a First Set of Results (No. 2003/6). OECD Publishing.

Schröer, G., & Stahlecker, P. (1996). Ist die gesamtwirtschaftliche Cobb-Douglas-Produktionsfunktion eine Kointegrationsbeziehung? Empirische Analyse vor und nach der Wiedervereinigung/Is the Macroeconomic Cobb-Douglas Production Function a Cointegration Relationship? Empirical Analysis Before and After German Reunification. Jahrbücher für Nationalökonomie und Statistik, 513-525.

Schwert, G. W. (2002). Tests for unit roots: A Monte Carlo investigation. Journal of Business & Economic Statistics, 20(1), 5-17.

Serrenho, A. C., Warr, B., Sousa, T., Ayres, R. U., & Domingos, T. (2016). Structure and dynamics of useful work along the agriculture-industry-services transition: Portugal from 1856 to 2009. Structural Change and Economic Dynamics, 36, 1-21.

Smulders, S., & De Nooij, M. (2003). The impact of energy conservation on technology and economic growth. Resource and Energy Economics, 25(1), 59-79.

Solow, R. M. (1957). Technical change and the aggregate production function. The Review of Economics and Statistics, 39, 312-320.

Sraffa, P. (1975). Production of commodities by means of commodities: Prelude to a critique of economic theory. Cambridge University Press, Cambridge.

Stern, D. I. & Kander, A. (2010). The Role of Energy in the Industrial Revolution and Modern Economic Growth, CAMA Working Paper Series, WP1/2-11.

Stern, D. I. (1997). Limits to substitution and irreversibility in production and consumption: a neoclassical interpretation of ecological economics. Ecological Economics, 21(3), 197-215.

Stern, D. I. (2000). A multivariate cointegration analysis of the role of energy in the US macroeconomy. Energy Economics, 22(2), 267-283.

Stern, D. I. (2011). The role of energy in economic growth. Annals of the New York Academy of Sciences, 1219(1), 26-51.

Stresing, R., Lindenberger, D., & Kümmel, R. (2008). Cointegration of output, capital, labor, and energy. The European Physical Journal B, 66(2), 279-287.

Timmer, M. P., Inklaar, R., O'Mahony, M., & Van Ark, B. (2010). Economic growth in Europe: a comparative industry perspective. Cambridge University Press. Cambridge, United Kingdom.

Tintner, G., Deutsch, E., Rieder, R., & Rosner, P. (1977). A production function for Austria emphasizing energy. De Economist, 125(1), 75-94.

US Energy Information Administration (US EIA) (2011). Energy Consumption, Expenditures, and Emissions Indicators Estimates, Selected Years, 1949-2011. US Energy Information Administration: Annual Energy Review 2011. Available online at: http://www.eia.gov/totalenergy/data/annual/pdf/sec1_13.pdf

Van Ark, B. (2014), Total factor productivity: Lessons from the past and directions for the future, National Bank of Belgium, Working Paper Research No 271, October.

van den Bergh, J. C., & Nijkamp, P. (1994). Dynamic macro modelling and materials balance: Economic-environmental integration for sustainable development. Economic Modelling, 11(3), 283-307.

Wallis, G. (2009). Capital Services Growth in the UK: 1950 to 2006. Oxford Bulletin of Economics and Statistics, 71(6), 799-819.

Warr, B. S., & Ayres, R. U. (2010). Evidence of causality between the quantity and quality of energy consumption and economic growth. Energy, 35(4), 1688-1693.

Warr, B., Ayres, R., Eisenmenger, N., Krausmann, F., & Schandl, H. (2010). Energy use and economic development: A comparative analysis of useful work supply in Austria, Japan, the United Kingdom and the US during 100years of economic growth. Ecological Economics, 69(10), 1904-1917.

Whalley, J., & Zhao, X. (2013). The contribution of human capital to China's economic growth. China Economic Policy Review, 2(01), 1350001.

Young, A. (1995). The Tyranny of Numbers: Confronting the Statistical Reality of the East Asian Growth Experience, Quarterly Journal of Economics, 110, 641–680.