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

Estimates of the Long‐Run Growth Rate of Australia

“…We apply our methodology to Australian productivity database prepared by Diewert and Lawrence (2005, p. 15). The output index is formed by aggregating the quantities of the consumer commodity, government consumption, exports, investment goods, inventory changes and the negative of the 1 This specification has been used by many researchers including Klump and Preissler (2000), Klump et al (2007 and Klump and Saam (2008). import quantity.…”

Balanced‐Budget Rules, Elasticity of Substitution, and Macroeconomic (In)Stability

“…Following the two-step calibration of Klump and Saam (2008), we first choose the values for the economically relevant point, k i , y i , π i , and ψ i . 13 Taking the Cobb-Douglas case with ψ i = 0 (or ε i = 1) as the economically relevant point, we obtain the parameters for the initial CES production function as…”

“…So the effect of factor substitution depends solely on the distribution effect. In the economic relevant case argued by Klump and Saam (2008) where k * > k, we have dτ o /dε < 0 so that the optimal tax rate falls as factor substitution improves in the economy.…”

“…There have been a number of papers that have shown that, when the elasticity of factor substitution can adjust, indeterminacy of the steady-state equilibrium depends on its magnitude. 2 Using the two-step normalization procedure of Klump and Saam (2008), we can identify two separate effects of factor substitution on the balancedbudget rules, namely, the efficiency effect and the distribution effect. 3 The 1 For an excellent exposition of the normalized CES production function, we refer the readers to the survey paper of Klump, McAdam, and Willman (2012).…”

“…Our findings highlight the power of the distribution effect and make a very important point about the concept of normalization used in the literature. Since the work of Klump and Saam (2008), it is well understood that the baseline values of normalization are not chosen arbitrarily. The common practice seems to pick the steady-state values as the baseline values:…”