Macroeconomic impacts of energy productivity: a general equilibrium perspective

Abstract

This study aims to enhance our understanding on the macroeconomic effects of autonomous energy efficiency improvement. We adopt a global computable general equilibrium model assuming future energy efficiency improvement until 2040 follows historical trends at a regional level including the USA, European Union, Japan, Russia, China, India, and Brazil over the period of 1995–2009. Results show that the global GDP would increase by 1.3% from 2015 to 2040, without making any regions worse off, if energy efficiency in all economic activities other than energy production gradually reaches 10% higher in 2040 than a baseline scenario. However, economy-wide rebound effects on energy use accumulate over time and vary from 55 to 78% across regions in 2040. The additional energy efficiency improvement by the same percentage for fossil and non-fossil energy pushes a stronger downward pressure on fossil fuel prices than on renewable prices, thus discouraging the share of renewables in the energy mix. We conclude that energy efficiency policy needs to be aligned with renewable and climate targets to control its rebound effect on energy use and related emissions.

Appendix

This appendix can be found from Appendix A of Wei and Liu (2017).

A brief description of the GRACE model

GRACE is a recursively dynamic computable general equilibrium (CGE) model. The model finds a static general equilibrium solution for a year given exogenous settings, which can be updated over time. In this version, key intertemporal exogenous settings include supply and productivity of labor and capital stock at the beginning of a year. In the BAU scenario, regional productivity of labor and capital stock is updated over time and their values are calibrated to obtain the exogenous regional GDP growth. Regional labor supply changes over time at the same rates of regional growth of population size. In the beginning of a year other than the base year, regional capital stock is adjusted by deducting depreciation of the existing capital stock and adding new capital stock generated from previous year investments, which are financed by total savings from all regions. In mathematical form, we have:

$$ {K}_{r,t+1}=\left(1+\delta \right){K}_{r,t}+{I}_{r,t} $$

(A1)

where K_{r, t} is the available capital stock in a region r at the beginning of a year t; δ is the depreciation rate of 4% annually for all regions; and I_{r, t} is the investments in a region r during a year t. Regional investments (I_{r, t}) are financed by a common pool of global savings, which is the sum of regional savings. For each region, we assume that if capital stock grows at a region-specific growth rate of capital stock (${\hat{K}}_r$), then at a given time s, investors would expect a constant rate of return to capital. Hence, the expected rate of return to capital (R_{r, s + h}) in an instantaneous time h > 0 is only related to the change in capital stock other than the region-specific growth:

$$ \frac{R_{r,s+h}}{R_{r,s}}={\left(\frac{K_{r,s+h}}{K_{r,s}\times {e}^{{\hat{K}}_r\cdot h}}\right)}^{-\sigma } $$

where σ > 0 is elasticity of the expected rate of return with respect to the capital stock, which is assumed 10 in the GRACE model. Differentiation with respect to h on both sides yields:

$$ \frac{{\dot{R}}_{r,s+h}}{R_{r,s+h}}=-\sigma \times \left(\frac{{\dot{K}}_{r,s+h}}{K_{r,s+h}}-{\hat{K}}_r\right) $$

where the “.” above a variable represents the derivative with respect to time. The above expression can be rewritten as:

$$ \frac{{\dot{R}}_{r,t}}{R_{r,t}}=-\sigma \times \left(\frac{{\dot{K}}_{r,t}}{K_{r,t}}-{\hat{K}}_r\right) $$

(A2)

By assuming t = s + h. A discrete version of the above Eq. A2 is:

$$ \frac{\varDelta {R}_{r,t}}{R_{r,t}}=\frac{R_{r,t+1}-{R}_{r,t}}{R_{r,t}}=-\sigma \times \left(\frac{K_{r,t+1}-{K}_{r,t}}{K_{r,t}}-{\hat{K}}_r\right) $$

By using Eq. A1, we have:

$$ \frac{\varDelta {R}_{r,t}}{R_{r,t}}=-\sigma \times \left(\frac{I_{r,t}}{K_{r,t}}+\delta -{\hat{K}}_r\right) $$

(A3)

Which is adopted in GRACE to allocate global investments to regions by equalizing the changes in regional rates of return to capital, i.e., for any two regions r and rr,

$$ \varDelta {R}_{r,t}=\varDelta {R}_{rr,t} $$

Hence, the allocation of investments across regions does not depend on the elasticity of the expected rate of return with respect to the capital stock (σ).

In the end of a year, total returns to capital of all regions are allocated to regions proportional to shares of regional savings at the beginning of the year. After receiving its share of returns to capital and other income (labor income and various taxes), a region allocates a fixed share of its income for global savings, which is then used for global investments. The other part of the regional income is proportionally allocated for private and public consumptions.

International trade is modeled through a nested constant elasticity of substitution (CES) function (Fig. 12). The parameters starting with small letter “e” indicate the elasticities of substitution at the level where they stay. An Armington good combines domestic production and an aggregate of imports from all other regions. Exceptions of the elasticities are made for the following sectors: (a) refined oil (eARM = 6), (b) electricity (eARM = 0.5; eIMP = 0.3), and (c) gas and coal (eIMP = 4). With the trade of a good, the importing country pays a fixed unit cost to the international transport sector. The international transport is provided by a Cobb-Douglas composite of regional transport services.

Fig. 12

Armington aggregate of bilateral imports. The parameters starting with small letter “e” indicate the elasticities of substitution at the level where they stay

Figure 13 illustrates the economic activities of a region. Together with intermediate inputs of goods and services, available productive resources—capital, labor, and natural resources—are utilized to produce goods and services, which can export to other regions and meet final demand for domestic private and public consumption and investments together with imported substitutes. Investments form new capital for the next period. As by-products, greenhouse gas emissions accompany with these economic activities. CO₂ emissions from fossil fuels are linked to fossil fuels used by producers and households by fixed emission factors.

Fig. 13

Economic activities of a region

Sectoral production is simulated by two types of nested CES functions. One type is illustrated in Fig. 14 for production of primary energy, i.e., crude oil, coal, and gas. To highlight the dependence on natural resources, the top level is a combination of the natural resource (RES) and an aggregate of remaining inputs. At the middle level, the remaining inputs are a Leontief composite of intermediate goods and value added, where the value-added combines capital (CAP) and labor (LAB).

Fig. 14

Production structure of primary energy goods. The parameters starting with small letter “e” indicate the elasticities of substitution at the level where they stay

The other type of production functions (Fig. 15) is for goods and services other than the primary energy. The top level is a Leontief composite of intermediate inputs other than energy and an aggregate of value added and energy inputs (VA Energy). The next level is a combination of value added and energy inputs. The value added is further a combination of capital and labor. The energy inputs are a combination of electricity (ELC) and other energy inputs as a Cobb-Douglas aggregate of crude oil (CRU), coal (COL), refined oil (REF), and gas (GAS).

Fig. 15

Production structure of goods/services other than primary energy. The parameters starting with small letter “e” indicate the elasticities of substitution at the level where they stay

Figure 16 illustrates the demand structures of consumers and investors. At the top level, substitution can be made between energy and the other goods (non-energy). At the bottom level, the energy combines five energy goods and the non-energy combines all the other goods.

Fig. 16

Final demand structure in GRACE-EL. The parameters starting with small letter “e” indicate the elasticities of substitution at the level where they stay