Elasticity of substitution and technical progress: Is there a misspecification problem?

Saltari, Enrico and Federici, Daniela (2013): Elasticity of substitution and technical progress: Is there a misspecification problem?

Abstract

In Saltari et al. (2012, 2013) we estimated a dynamic model of the Italian economy. The main result of those papers is that the weakness of the Italian economy in the last two decades is due to the total factor productivity slowdown. In those models the information and communication technology (ICT) capital stock plays a key role in boosting the efficiency of the traditional capital, and hence of the whole economy. The ICT contribution is captured in a multiplicative way through a weighting factor. The other key parameter to explain the Italian productivity decline is the elasticity of substitution. Recent literature provides estimates of the elasticity of substitution well below 1 -- thus rejecting the traditional Cobb-Douglas production function -- though there is no particular value on which consensus converges. In our opinion, however, these estimates are affected by a theoretical specification problem. More generally, the technological parameters are long run in nature but the estimates are based on short-run data. Our aim is to look more deeply into the estimation procedure of the technological parameters. The standard estimation results present a common fundamental problem of serially correlated residuals so that the standard errors will be under-estimated (i.e. biased downwards). We think that at the root of this problem there are two theoretical issues: the estimated models are static in nature and do not incorporate frictions and rigidities. Our modelling strategy takes into account, though implicitly, adjustment costs without leaving out the optimization hypothesis. Although we cannot in general say that this framework gets rid of the serial correlation problem, the correlation statistics for our model do show that residuals are not serially correlated. Recent literature provides estimates well below 1 -- thus rejecting the traditional Cobb-Douglas production function -- though there is no particular value on which the consensus converges. In our opinion, however, these estimates are affected by a specification problem, which has theoretical roots. The technological parameters are long run in nature but the estimates are based on short-run data: the "real" issue is to bridge this gap. Our aim is to look more deeply into the estimation procedure of the technological parameters. The standard estimation results present a common fundamental problem of serially correlated residuals so that the standard errors will be under-estimated (i.e. biased downwards). We think that at the root of this problem there are two theoretical issues: the estimated models are static in nature and do not incorporate frictions and rigidities. Our modelling strategy takes into account, though implicitly, adjustment costs without leaving out the optimization hypothesis. Although we cannot in general say that these properties get rid of the serial correlation problem, the correlation statistics for our model does show that residuals are not serially correlated.

• Item Type: MPRA Paper
• Language: English
• Keywords: Keywords: CES production function; Elasticity of substitution; Income distribution; Factor-augmenting technical progress and ICT technical change.
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C30 - General; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E22 - Investment ; Capital ; Intangible Capital ; Capacity; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E23 - Production; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O33 - Technological Change: Choices and Consequences ; Diffusion Processes

References

Acemoglu, D. (2008): Introduction to Modern Economic Growth, MIT Press.

Aghion P., and P. Howitt (2009): The Economics of Growth, MIT Press.

Antràs, P. (2004), "Is the US Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of Substitution". Contributions to Macroeconomics, 4, Issue 1, Article 4.

Arrow, K.J., Chenery, H.B., Minhas, B.S., Solow, R.M., (1961):" Capital-labor substitution and economic efficiency". The Review of Economics and Statistics 43, 225--250.

Basu, S., and D. Weil (1998): "Appropriate technology and growth", Quarterly Journal of Economics, 113, 1025-54.

Bergstrom, A. R. (1984): "Monetary, fiscal and exchange rate policy in a continuous time model of the United Kingdom", in P. Malgrange and P. Muet, eds., Contemporary Macroeconomic Modelling. Oxford: Blackwell, 183-206.

Bergstrom, A. R., K. B. Nowman, and C. R. Wymer, (1992): "Gaussian estimation of a second order continuous time macroeconometric model of the United Kingdom". Economic Modelling, 9, 313-351.

Bergstrom, A. R., and K. B. Nowman, (2006): "A Continuous Time Econometric Model of the United Kingdom with Stochastic Trends". Cambridge: Cambridge University Press.

Bergstrom A. R. and C. R. Wymer (1976): "A model of disequilibrium neo-classical growth and its application to the United Kingdom", in A. R. Bergstrom, ed., Statistical Inference in Continuous-Time Economic Models. Amsterdam: North-Holland, 267-328.

Chirinko, R. (2008): "σ: the long and short of it", Journal of Macroeconomics, 30 (2): 671-686.

Chirinko, R., S. M. Fazzari, A. P. Meyer, (1999):" How responsive is business capital formation to its user cost? An exploration with micro data". Journal of Public Economics 74 (October), 53--80.

European Commission (2013): Towards Knowledge Driven Reindustrialisation, European Competitiveness Report.

Colecchia, Alessandra and Paul Schreyer (2001), "The Impact of Information Communications Technology on Output Growth", STI Working Paper 2001/7, OECD, Paris.

Elsby, M. W. L., B. Hobijn, A. Şahin (2013), "The Decline of the U.S. Labor Share", mimeo.

Gandolfo, G. (1981): Qualitative Analysys and Economteric Estimation of Continuous Time Dynamic Models, North-Holland.

Gandolfo, G., and P. C. Padoan (1990): "The Italian continuous time model. Theory and empirical results". Economic Modeling, 7, 91-132.

Hicks, J. R., (1963): The Theory of Wages, second ed. MacMillan & Co., London (first edition published in 1932).

Jorgenson, D., M. S Ho, and K. J Stiroh (2004). "Will the U.S. Productivity Resurgence Continue?". Current Issues in Economics and Finance 10, no. 13, 1-7.

Kaldor, N. (1961), "Capital Accumulation and Economic Growth," in F.A. Lutz and D.C. Hague, eds., The Theory of Capital, St.Martins Press, 177--222.

Karabarbounis, L. and B. Neiman (2013):"The Global Decline of the Labor Share", mimeo.

Klump R., P. McAdam and A. Willman (2008):"Unwrapping some euro area growth puzzles: Factor substitution, productivity and unemployment",Journal of Macroeconomics, 30 (2): 645-66.

Klump R., P. McAdam and A. Willman (2012): " The Normalized CES Production Function: Theory and Empirics", Journal of Economic Surveys, 26, 769 - 799.

Klump R. and O. de La Grandville (2000): "Economic growth and the elasticity of substitution: Two theorems and some suggestions", The American Economic Review, 90, 282-91.

Klump R. and H. Preissler (2000): "CES Production Functions and Economic Growth", Scandinavian Journal of Economics, 102, 41-56.

Klump, R. and Saam, M. (2008): "Calibration of normalised CES production functions in dynamic models", Economics Letters, Elsevier, 99(2), 256-259.

Knight, M. D. and C. R. Wymer (1978): "A macroeconomic model of the United Kingdom". IMF Staff Papers, 25, 742-78.

La Grandville, O. de (1989): "In quest of the Slutsky diamond", American Economic Review, 79, 468-481.

La Grandville, O. de (2009): Economic Growth: A Unified Approach. Cambridge: Cambridge Cambridge University Press.

León-Ledesma, M. A., P. McAdam and A. Willman (2010):" Identifying the Elasticity of Substitution with Biased Technical Change", The American Economic Review, 100(4):1330--1357.

Miyagiwa, K. and Papageorgiou, C. (2007): "Endogenous aggregate elasticity of substitution", Journal of Economic Dynamics and Control, vol. 31(9), 2899-2919.

Nelson, R. R. (1965):" The CES Production Function and Economic Growth", The Review of Economics and Statistics, Vol. 47, No. 3, 326-28.

Mallick, D. (2012):"The role of the elasticity of substitution in economic growth: A cross-country investigation", Labour Economics 19 (2012) 682--694.

Papageorgiou C. and M. Saam (2008): "Two-level CES Production Technology in the Solow and Diamond Growth Models", Scandinavian Journal of Economics, 110(1), 119-143.

Pereira, C. (2003). "Empirical Essays on the Elasticity of Substitution, Technical Change, and Economic Growth." Ph.D. dissertation, North Carolina State University.

Robinson, J., (1933): The Economics of Imperfect Competition. MacMillan & Co., London (reprinted 1959).

Rowthorn R. (1999) , "Unemployment, Capital-Labor Substitution, and Economic Growth", Cambridge Journal of Economics, 23, 413-425.

Saltari, E., C. Wymer, D. Federici and M. Giannetti (2012), "Technological adoption with imperfect markets in the Italian economy, Studies in Nonlinear Dynamics & Econometrics, 16, 2.

Saltari, E., C. Wymer and D. Federici. (2013). "The impact of ICT and business services on the Italian economy, Structural Change and Economic Dynamics, 25, 110--118.

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

Stiroh, K. J. (2002): "Information Technology and the U.S. Productivity Revival: What Do the Industry Data Say?",The American Economic Review, 92(5), 1559-1576.

Timmer, M.P. and van Ark, B. (2005):" Does information and communication technology drive EU-US productivity growth differentials?", Oxford Economic Papers, 57(4), pp. 693--716.

Turnovsky, S. J. (2002):" Intertemporal and intratemporal substitution and the speed of convergence in the neoclassical growth model", Journal of Economic Dynamics and Control, 26, 1765--1785.

Wymer, C. R. (1972): "Econometric estimation of stochastic differential equation systems", Econometrica, 40, 565-77.

Wymer, C. R. (1996): "The role of continuous time disequilibrium models in macroeconomics", in Barnett, W.A., G. Gandolfo and C. Hillinger, eds., Dynamic Disequilibrium Modeling, Cambridge: Cambridge University Press.

Wymer, C. R. (1997): "Structural non-linear continuous-time models in econometrics", Macroeconomic Dynamics, 1, 518-48.

Wymer, C. R. (2006): WYSEA: Systems estimation and analysis reference and user guide, mimeo.