Substitutability and the Cost of Climate Mitigation Policy

Abstract

We explore how and by how much the values of elasticities of substitution affect estimates of the cost of emissions reduction policies in computable general equilibrium (CGE) models. We use G-Cubed, an intertemporal CGE model, to carry out a sensitivity and factor decomposition analysis. The decomposition analysis determines the contributions of changes in average abatement costs and changes in baseline emissions to the change in total mitigation costs. The latter has not previously been considered. Average abatement cost rises non-linearly as elasticities are reduced. Changes in the substitution elasticities between capital, labor, energy, and materials have a greater impact on mitigation costs than do inter-fuel elasticities of substitution. The former have more effect on business as usual emissions and the latter on average abatement costs. As elasticities are reduced, business as usual emissions and GDP growth also decrease so that there is not much variation in the total costs of reaching a given target across the parameter space. Our results confirm that the cost of climate mitigation policy is at most a few percent of global GDP.

Appendix: The G-Cubed Model

G-Cubed has some important features that make it particularly suitable for our analysis. G-Cubed has various tiers of nesting on the production and consumption sides, which allows us to explore the substitutability of the economy at different levels (see Fig. 7). In the following, we describe the features of the model that are most relevant to our sensitivity analysis. McKibbin and Wilcoxen (1999, 2013) provide a more complete description of the model. There are twelve production sectors where the top tier level of production is modeled as a CES function of capital, labor, energy and materials:

$$\begin{aligned} Q_i =A_i^o \left( {\sum \limits _{j=K,L,E,M} \left( {\delta _{ij}^o } \right) ^{\frac{1}{\sigma _i^o }}\left( {A_j^o X_{ij} } \right) ^{\frac{\sigma _i^o -1}{\sigma _i^o }}} \right) ^{\frac{\sigma _i^o }{\sigma _i^o -1}}, \end{aligned}$$

(5)

where $Q_{i}$ is the output for sector i, the $X_{ij}$ are the inputs for sector $i; A_{i}^{O}, \sigma _{i}^{O}$, and $\delta _{ij}^{O}$ are parameters that reflect technology, elasticity of substitution, and input weights, respectively. Particularly, $A_{j}^{O} (j=K, L, E, M)$ is the factor-specific technology parameter at the top tier. The energy $(X_{iE})$ and materials $(X_{iM})$ inputs in (1) are also modeled as CES functions of component energy carriers and materials:

$$\begin{aligned} X_{iE} =\left( {\sum \limits _{j=1,\ldots ,6} \left( {\delta _{ij}^E } \right) ^{\frac{1}{\sigma _i^E }}\left( {X_{ij}^E } \right) ^{\frac{\sigma _i^E -1}{\sigma _i^E }}} \right) ^{\frac{\sigma _i^E }{\sigma _i^E -1}} \end{aligned}$$

(6)

where $X_{,iE}$ is the aggregate energy used in sector i. The $X_{ij}^{E}$ represent outputs of the six energy producing sectors including: electricity, crude oil, coal, petroleum, natural gas and its utility; $\sigma _{i}^{E}$ and $\delta _{ij}^{E}$ are inter-fuel elasticity and input weights parameters, respectively. Similarly the aggregate material input is a CES aggregate of the outputs from the six “materials” producing sectors of the economy. Materials in fact include transportation and services inputs. Each of these lower tier inputs—both materials and energy—are a CES aggregate of domestic and imported commodities where the elasticity of substitution is the Armington elasticity.

Fig. 7

Production and consumption structure in G-Cubed. a Production nesting. b Consumption structure

In addition to the twelve ordinary industrial sectors, there are also a capital goods production sector, which has a similar nesting, with $\sigma ^{OR}$ and $\sigma ^{ER}$ being the elasticity parameters in the two tiers.⁶

In common with most studies using G-Cubed, the major sources of technological change are in the form of labor augmenting technical change and autonomous energy efficiency improvement (AEEI) (McKibbin and Wilcoxen 1999; McKibbin et al. 2008). Our assumptions about the rates of labor productivity growth and AEEI are documented in Tables 10 and 11. These technological change parameters have an impact on both the BAU projections of GDP and emissions as well as on the costs of mitigation. The relative price of labor and energy will regulate the energy consumption and emissions paths over time. The higher the prices of other factors of production are relative to the price of energy in the BAU projection, the higher mitigation costs will be. Labor augmentation and capital-energy substitution can increase the amount of electricity produced per unit input of fossil fuels over time up to some limit of productivity as assumed.

Table 10 Labor productivity assumptions

Table 11 Autonomous energy efficiency improvement (AEEI) assumptions

On the household side, the representative household utility function is given by:

$$\begin{aligned} U_t =\int _t^\infty \left( {\hbox {ln}C\left( s \right) +\hbox {ln}G\left( s \right) } \right) e^{-\theta \left( {s-t} \right) }ds \end{aligned}$$

(7)

where C is aggregate consumption and G is government consumption, which is intended to measure the provision of public goods; $\theta$ is the rate of pure time preference. Aggregate consumption C also has two layers of CES nesting: one is the top tier nesting of household capital, labor, energy, and materials; the lower tier consists of inter-fuel nesting for energy (with elasticity $\sigma ^{EH}$) and nesting for material goods (with elasticity $\sigma ^{MH}$). Therefore, the top tier consumption aggregate is as follows:

$$\begin{aligned} C=\left( {\sum \limits _{j=K,L,E,M} \left( {\delta _{Cj}^C } \right) ^{\frac{1}{\sigma _C^{OH} }}\left( {X_{Cj} } \right) ^{\frac{\sigma _C^{OH} -1}{\sigma _C^{OH} }}} \right) ^{\frac{\sigma _C^{OH} }{\sigma _C^{OH} -1}} \end{aligned}$$

(8)

in which $\sigma _{C}^{OH}$ and $\delta _{Cj}^{C}$ are the elasticity of substitution between the 12 consumption goods and the corresponding weights parameters, respectively. The elasticities: $\sigma _{i}^{O}, \sigma _{i}^{E}, \sigma ^{OR}, \sigma ^{ER}, \sigma ^{OH}$, and $\sigma ^{EH}$ are the parameters of interest in our sensitivity analysis.

We set the rate of time preference to 2.2 % and the annual growth rate of effective labor in the steady state to 1.8 %.⁷ Since the quantity and value variables in the model are scaled by the number of effective labor units, the growth rate of effective labor units appears in the discount factor. These quantity and value variables must be converted back to their original form (McKibbin and Wilcoxen 2013). Since utility is in a log-linear form as in Eq. (7), the elasticity of marginal utility is 1 and our discounting rule is consistent with the modified Ramsey discounting rule in climate economic modeling (e.g. Tol 2011). Therefore, G-Cubed assumes that the long-term real interest rate converges to 4 % at the steady state, which is comparable to the discount rate of 4.3 % in Nordhaus (2007)’s DICE model. This rate is used in computing the net present value of mitigation costs in our study.

The G-Cubed model also features macro-economic characteristics such as partly rational expectations, price stickiness, and a central bank policy rule. These distinctive features that most recursive CGE models do not have, give the model rich short-run dynamics and make the model more suitable for short to medium term scenario analysis. While long-run consequences are the usual focus of climate scientists, the short-run to medium run (two to three decades) dynamics are probably more relevant to policy-makers and economists. G-Cubed also features a comprehensive representation of international trade, which is important for issues in a global context, such as climate change.