Using a normalized CES function with factor-augmenting technical progress, we estimate a supply-side system of the U.S. economy from 1953 to 1998. Avoiding potential estimation biases that may have occurred in earlier studies and putting a high emphasis on data consistency, we obtain robust results not only for the aggregate elasticity of substitution but also for the parameters of labor and capital augmenting technical change. We find that the elasticity of substitution is significantly below unity and that technical progress shows an asymmetrical pattern where the growth of labor-augmenting technical progress is exponential, while that of capital is hyperbolic or logarithmic. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

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We examine inconsistencies and controversies related to the use of CES production functions in growth models. First, we show that not all variants of CES functions commonly used are consistently speci®ed. Second, using a simple growth model, we ®nd that a higher elasticity of substitution leads to a higher steady state and makes the emergence of permanent growth more probable. It is also pointed out that the effect of a higher elasticity of substitution on the speed of convergence depends on the relative scarcity of the factors of production. Finally, we discuss possible explanations of variations in the elasticity of substitution.

The elasticity of substitution between capital and labor and, in turn, the direction of technical change are critical parameters in many fields of economics. Until recently, though, the application of production functions with specifically non‐unitary substitution elasticities (i.e., non‐Cobb–Douglas) was hampered by empirical and theoretical uncertainties. As recently revealed, ‘normalization’ of production‐technology systems holds out the promise of resolving many of those uncertainties. We survey and assess the intrinsic links between production (as conceptualized in a production function), factor substitution (as made most explicit in Constant Elasticity of Substitution functions) and normalization (defined by the fixing of baseline values for relevant variables). First, we recall how the normalized Constant Elasticity of Substitution function came into existence and what normalization implies for its formal properties. Then we deal with the key role of normalization in recent advances in the theory of business cycles and of economic growth. Next, we discuss the benefits normalization brings for empirical estimation and empirical growth research. Finally, we identify promising areas of future research.

Die Dis cus si on Pape rs die nen einer mög lichst schnel len Ver brei tung von neue ren For schungs arbei ten des ZEW. Die Bei trä ge lie gen in allei ni ger Ver ant wor tung der Auto ren und stel len nicht not wen di ger wei se die Mei nung des ZEW dar.Dis cus si on Papers are inten ded to make results of ZEW research prompt ly avai la ble to other eco no mists in order to encou ra ge dis cus si on and sug gesti ons for revi si ons. The aut hors are sole ly respon si ble for the con tents which do not neces sa ri ly repre sent the opi ni on of the ZEW.Download this ZEW Discussion Paper from our ftp server:ftp://ftp.zew.de/pub/zew-docs/dp/dp06078.pdf Non-technical summaryBasic models of economic dynamics are used to analyse how capital accumulation and technology influence economic growth and income distribution. A central element of such a model is the production function. It relates the economy's input of capital and labour to its total output. The production function with a constant elasticity of substitution (CES) represents a commonly used functional form. The elasticity of substitution is a parameter that can be thought to reflect an economy's overall flexibility. It has been estimated in a number of empirical studies. The CES function has two more parameters. Current practice of choosing them in applications of dynamic models can lead to arbitrary and inconsistent results. Based on the concept of normalisation introduced by Klump and de La Grandville (2000), we develop a method that chooses them using empirical values of the income share of capital, the ratio of capital to output, and the elasticity of substitution. We illustrate the method with an example from the Ramsey growth model. Abstract Normalising CES production functions in the calibration of basic dynamic models allows to choose technology parameters in an economically plausible way. When variations in the elasticity of substitution are considered, normalisation is necessary in order to exclude arbitrary effects. As an illustration, the effect of the elasticity of substitution on the speed of convergence in the Ramsey model is computed with different normalisations. Calibration of Normalised CES Production Functions in Dynamic Models

In this paper, we seek to re-establish the link between the CES production function and neoclassical growth theory. We did so in three dimensions. First, we reviewed the increasing importance of the CES technology in modern dynamic macroeconomics, in expanding not only theory but also in addressing important policy questions. Second, we argued that the importance of the CES function in growth theory is intimately linked to 'normalization'. Finally, we examined the data congruence between CES functions and recent growth patterns in US and euro-area economies, where we apply CES functions with factor-augmenting and time-varying technical progress.

ABSTRACT. This paper extends the Lucas (1978, The Bell Journal of Economics 9(2), 508-523) analysis of firm size by taking into account a normalised aggregate CES production function. In a general equilibrium framework it is proved that there is an inverse relation between the elasticity of substitution and average firm size. If interpreted together with the fact that richer countries are characterised by a higher elasticity of substitution, this result can explain why the recent literature finds a positive association between the importance of SMEs in an economy and its stage of development, but seems to fail in finding causality between the two. Both have a common origin: a high value of the elasticity of substitution. This paper also provides a first empirical test of the theory proposed using crosscountry data from both developed and developing countries.KEY WORDS: average firm size, general equilibrium models, neoclassical growth models, CES function.JEL CLASSIFICATION: C65, E13, L11.

Die Dis cus si on Pape rs die nen einer mög lichst schnel len Ver brei tung von neue ren For schungs arbei ten des ZEW. Die Bei trä ge lie gen in allei ni ger Ver ant wor tung der Auto ren und stel len nicht not wen di ger wei se die Mei nung des ZEW dar.Dis cus si on Papers are inten ded to make results of ZEW research prompt ly avai la ble to other eco no mists in order to encou ra ge dis cus si on and sug gesti ons for revi si ons. The aut hors are sole ly respon si ble for the con tents which do not neces sa ri ly repre sent the opi ni on of the ZEW.Download this ZEW Discussion Paper from our ftp server:ftp://ftp.zew.de/pub/zew-docs/dp/dp06078.pdf Non-technical summaryBasic models of economic dynamics are used to analyse how capital accumulation and technology influence economic growth and income distribution. A central element of such a model is the production function. It relates the economy's input of capital and labour to its total output. The production function with a constant elasticity of substitution (CES) represents a commonly used functional form. The elasticity of substitution is a parameter that can be thought to reflect an economy's overall flexibility. It has been estimated in a number of empirical studies. The CES function has two more parameters. Current practice of choosing them in applications of dynamic models can lead to arbitrary and inconsistent results. Based on the concept of normalisation introduced by Klump and de La Grandville (2000), we develop a method that chooses them using empirical values of the income share of capital, the ratio of capital to output, and the elasticity of substitution. We illustrate the method with an example from the Ramsey growth model. Abstract Normalising CES production functions in the calibration of basic dynamic models allows to choose technology parameters in an economically plausible way. When variations in the elasticity of substitution are considered, normalisation is necessary in order to exclude arbitrary effects. As an illustration, the effect of the elasticity of substitution on the speed of convergence in the Ramsey model is computed with different normalisations. Calibration of Normalised CES Production Functions in Dynamic Models