Cobb-Douglas Production Function: The Case of a Converging Economy Dana HÁJKOVÁ – Czech National Bank and CERGE-EI (firstname.lastname@example.org) Jaromír HURNÍK – Czech National Bank, Institute for Economic Studies, Faculty of Social Sciences, Charles University, Prague, and Faculty of Economics and Public Administration, University of Economics, Prague (email@example.com).*
Abstract The Cobb-Douglas production function is often used to analyse the supply-side performance and measurement of a country’s productive potential. This functional form, however, includes the assumption of a constant share of labor in output, which may be too restrictive for a converging country. For example, labor share in the Czech Republic gradually increased over the last decade. In this paper, we test whether this fact renders the application of the Cobb-Douglas production function unreliable for the Czech economy. We apply a more general form of production function and allow labor share to develop according to the empirical data. For the period 1995–2005, we do not find significant difference between the calculation of the supply side of the Czech economy by the Cobb-Douglas production function and a more general production function.
1. Introduction The performance of the supply side of an economy is often identified with the growth rate of potential output. Potential output is not observed in reality, however, and has to be approximated. The use of the production function method for the measurement of potential output growth takes into account different sources of an economy’s productive capacity, namely the contributions of labour, capital and total factor productivity, the latter containing information about technological and allocative efficiency and hence about the supply-side functioning.1 Using the production function, one can discuss changes in the supply-side performance on the basis of the observed simultaneous developments in the quantity of labor, capital and total factor productivity. For instance, an increase in the rate of capital growth accompanied by a rise in trend total factor productivity may signalize some improvement in the supply-side performance. Observing an increase in the rate of the capital growth while trend total factor productivity stagnates, one can, in contrast, deduce that the supply side is functioning ineffectively. The production function thus represents a useful and powerful tool for the macroeconomic analysis and evaluation of the governmental structural policies. The practical application of the production function method requires making certain assumptions, particularly on the functional form of the production technology, returns to scale, and characteristics of the technological progress, as well as of * The views expressed are the views of the authors and may not correspond with the views of the Czech National Bank. The authors would like to thank to anonymous referees for helpful comments 1 This method is regularly used, for instance, by the European Commission (Denis et al., 2006) and by the OECD (Beffy et al., 2006) to assess the productive potential of countries.
Finance a úv r - Czech Journal of Economics and Finance, 57, 2007, no. 9-10
the functioning of markets. The neo-classical two-factor Cobb-Douglas production function with Hicks-neutral technology is frequently used,2 including the assumptions of positive and diminishing marginal products with respect to inputs of labor and capital, constant returns to scale, no unobserved inputs and perfect competition. These assumptions restrict the elasticity of output with respect to labor and capital to values between zero and one and their sum to being equal to one. Given the assumptions, the theoretical technological coefficients are then in practice approximated with the help of the income...