Calibration of Normalised Ces Production Functions in Dynamic Models

Abstract

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

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“…In particular, results are relatively sensitive to variations of σ 1 . Therefore, we have calibrated the CES production function to a specific baseline point (Klump and Saam, 2008). As standard value, we choose σ 1 = 0.5, which is in line with the literature on CGE models (see for example Burniaux et al, 1992;Babiker, 2001;Burniaux and Truong, 2002;Paltsev et al, 2005;Edenhofer et al, 2010).…”

A Growth Framework Using the Constant Elasticity of Substitution Model

“…It follows from (13) that the MRS is independent of both the total factor of productivity and the output per worker. Also, for 1 γ > , (13) implies that MRS → +∞ as k → +∞ . For 1 γ < , (13) implies that MRS 0…”

The Identification of Directed Technical Change Revisited

“…In most empirical applications, normalization is necessary to rescale this point to the data or vice versa. The choice of the point of normalization is not trivial (see Klump and Saam (2008)). Current practice in empirical work is to use either initial values or minima of data, or geometric averages for inputs and outputs and the arithmetic average of the capital share.…”

“…David and van de Klundert (1965) were the first to introduce directed technical change into an econometric estimation of this function. With better understanding of the formal properties of the CES function achieved, i.a., by the contributions by de La Grandville (1989), Klump and de La Grandville (2000) and Klump and Saam (2008) on normalization, it was possible to more systematically reveal the properties of the nonlinear CES estimation with directed technical change. Using Monte Carlo simulations, León-Ledesma, McAdam and Willman (2010 and forthcoming) show that the normalized systems approach is superior to other approaches in identifying the highly nonlinear CES function.…”