A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics van der Werf, Edwin Working Paper Production Functions for Climate Policy Modeling: An Empirical Analysis Kiel Working Paper, No. 1316 Provided in Cooperation with: Kiel Institute for the World Economy (IfW) Suggested Citation: van der Werf, Edwin (2007) : Production Functions for Climate Policy Modeling: An Empirical Analysis, Kiel Working Paper, No. 1316, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: http://hdl.handle.net/10419/17841 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. 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Any comments on working papers should be sent directly to the author. Production functions for climate policy modeling: an empirical analysis∗ Edwin van der Werf† Abstract Quantitative models for climate policy modeling differ in the produc- tion structure used and in the sizes of the elasticities of substitution. The empirical foundation for both is generally lacking. This paper estimates the parameters of two-level CES production functions with capital, labour and energy as inputs, and is the first to systemati- cally compare all nesting structures. Using industry-level data from 12 OECD countries, we find that the nesting structure where capital and labour are combined first, fits the data best, but for most coun- tries and industries we cannot reject that all three inputs can be put into one single nest. These two nesting structures are used by most climate models. However, while several climate policy models use a Cobb-Douglas function for (part of the) production function, we reject elasticities equal to one, in favour of considerably smaller values. Fi- nally we find evidence for factor-specific technological change. With lower elasticities and with factor-specific technological change, some climate policy models may find a bigger effect of endogenous techno- logical change on mitigating the costs of climate policy. JEL Classification: O13, Q32, Q43, Q55 Keywords: Climate policy, input substitution, technological change ∗I am grateful to Daan van Soest and Sjak Smulders for their help and useful discus- sions. In addition I thank Katie Carman, Anne Gielen and Johannes Voget for discussions and comments. †Corresponding author. Kiel Institute for the World Economy, D¨usternbrooker Weg 120, 24105, Kiel, Germany. Phone: +49 431 8814 468. Email: Edwin.vanderWerf@IfW- Kiel.de 1 1 Introduction The recent literature on the long run effects of climate policy focusses on the alleviating effect of endogenous technological change on the costs of climate policy. That is, it studies the welfare gains from research and development or from learning-by-doing effects when the economy faces some form of climate policy, compared to a scenario without endogenous technological change. Next to investing in new technologies, applied climate policy models allow firms to react to price changes, caused by climate policy, through input sub- stitution, e.g. shifting away from energy towards capital or labour. Since the endogenous changes in technology are themselves determined by the price changes and the substitution possibilities – the easier it is to substitute away from energy, the smaller may be the need to invest in energy-saving technologies –, it is important that the substitution possibilities in applied climate policy models are not only empirically founded, but also disentan- gled from changes in the production isoquant that come from technological change: too high or too low elasticities may lead to under- or overestimates of the effects of endogenous technological change. In addition, the results of simulations without technological change are sensitive to the elasticity of substitution. Indeed, Jacoby et al. (2004) found that, in the MIT EPPA model, the elasticity of substitution between energy and value-added (the capital-labour composite) is the parameter that affects the costs of ”Kyoto forever” for the U.S. economy the most. Unfortunately, in most applied dynamic climate policy models, neither the production structure nor the accompanying elasticities of substitution have an empirical basis. The current paper therefore estimates production functions for climate policy models. We study all possible production struc- tures, while taking into into account that both substitution possibilities and technological change affect the production possibilities frontier. In applied climate policy models the ease with which one can substitute 2 one input for another is generally represented by elasticities of substitution. As they generally use constant elasticity of substitution (CES) production functions with capital, labour and energy as inputs, applied climate models can choose between different structures for the production function. For example, capital and energy can be combined first using a two-input CES function with a specific elasticity of substitution, and subsequently this com- posite can be ’nested’ into another CES function, where it is combined with labour (with possibly a different elasticity). Table 1 presents an overview of the production structures, elasticities of substitution and types of technological change of some dynamic models that simulate the effect of climate policy on the economy. The table shows that the nesting structure differs between the various papers. Moreover, 3 out of 10 models do not nest at all and treat all inputs at the same level. A second observation is that in all models but one, capital is in the same nest as labour. One could nevertheless argue that capital and energy should be combined first, as is done in the GREEN model (Burniaux et al., 1992), since (physical) capital and energy generally operate jointly. When we look at the elasticities of substitution in Table 1, we see that models use different values for the elasticities of substitution, even when they use the same nesting structure. In addition, many models use the knife-edge case of a unit elasticity and hence neutral technological change in (part of) the production function. When the elasticity of substitution is equal to one, the CES function reduces to a Cobb-Douglas function, in which case relative factor productivity is unaffected by technological change. Hence the choice for a unit elasticity greatly affects the role of technological change in model simulations. The way in which technological change enters the production function differs as well (we define technological change as a change in the position or shape of the production isoquant, for a given elasticity of substitution). 3 Table 1: Nesting structure and elasticities of substitution for several models Author(s) Nesting structurea Elasticitiesb Techn. changec Bosetti et al. (Forthcoming) (KL)E σK,L = 1; σKL,E = 0.5 exog. TFP; endog. energy-specific d Burniaux et al. (1992) (KE)L σK,E = 0 or 0.8; σKE,L = 0 or exogenous 0.12 or 1 Edenhofer et al. (2005) KLE σK,L,E = 0.4 endog. factor-specific Gerlagh and Van der Zwaan (2003) (KL)E σK,L = 1; σKL,E = 0.4 endog. energy-specific Goulder and Schneider (1999) KLEM σK,L,E,M = 1 endog. TFP Kemfert (2002) (KLM)E σKLM,E = 0.5 endog. energy-specific 4 Manne et al. (1995) (KL)E σK,L = 1; σKL,E = 0.4 exogenous Paltsev et al. (2005) (KL)E σK,L = 1; σKL,E = 0.4 − 0.5 exogenous Popp (2004) KLE σK,L,E = 1 endog. energy-specific e Sue Wing (2003) (KL)(EM) σK,L = 0.68 − 0.94; σE,M = 0.7; endog. TFP σKL,EM = 0.7 a (KL)E means a nesting structure in which capital and labour are combined first, and then this composite is combined with energy with a different elasticity of substitution. (KLE) means that all inputs are in a single-level CES function. b σi,j is the elasticity of substitution between inputs i and j and σij,k is the elasticity of substitution between the composite of inputs i and j on the one hand, and input k on the other. c TFP = Total Factor Productivity growth. d Lower elasticities for old capital, higher elasticities for new capital. e Elasticities taken from Cruz and Goulder (1992). Focussing on endogenous technological change, we see that four of the models in Table 1 use energy specific technological change, two models use total factor productivity (TFP) growth (both at the industry level), and only one model uses factor-specific technological change. In sum, dynamic climate policy models differ along three dimensions: nesting structure, the sizes of the elasticities, and the way in which techno- logical change affects marginal productivities. Surprisingly, the production functions used by the models in Table 1 generally lack empirical foundation.