Energy Demand in Industry pp 129150  Cite as
Energy Demand Model I
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Abstract
This chapter introduces the second group of the econometric models estimation, namely the energy demand model. The model is constructed in two forms: The CobbDouglas and the Translog function to allow for consistency and comparability. It is worthy of mentioning that the estimated energy demand is a derived demand, the variable of energy is considered as one of the input factors of production. The energy demand is, therefore, derived from the demand for the industry’s output. Since the demand for energy depends on the output level, the possible substitutability between energy and other inputs is allowed by production technology and energy price.
Keywords
Energy Demand Technical Change Energy Price Demand Response Output ElasticityThis chapter introduces the second group of the econometric models estimation, namely the energy demand model. The model is constructed in two forms: The CobbDouglas and the Translog function to allow for consistency and comparability. It is worthy of mentioning that the estimated energy demand is a derived demand, the variable of energy is considered as one of the input factors of production. The energy demand is, therefore, derived from the demand for the industry’s output. Since the demand for energy depends on the output level, the possible substitutability between energy and other inputs is allowed by production technology and energy price. The demand behavior and the potential policy variables are specified in short run and long run in their elasticities. In the short run, the behavioral specifications and the policy variables such as imposed taxes must consider that demand responses can only take the form of saving and alter in utilizing capital, while in the long run as the size and technological characteristics of the capital stock become variable, the characteristics and the degree of availability of new technologies as well as substitutability or complementarity become applicable. The partial derivative of the energy demand function with respect to time along with the elasticity of energy with respect to time is calculated to capture the rate of technical change. Due to presence of heterogeneity across the industries under this study, the estimated models have been corrected for heteroskedasticity. The heteroskedasticity standard errors are reported instead of the original ones. According to the results, the South Korean industrial sector exhibits a technological progress with increase in the returns to scale. Only few industries have witnessed restructuring by adopting new, more energy efficient, and productive technology. The findings reveal that although the substitutability between ICT capital and energy is feasible and proved in this model, the high technology industries still lack behind in implementing energy saving program.
8.1 Introduction
As explained in previously, the demand for energy is a derived demand. The variable of energy is considered as one of the input factors of production. The energy demand is, therefore, derived from the demand for the industry’s output. Since the demand for the energy depends on the output level, the possible substitutability between energy and other inputs is allowed by production technology and energy price.
This chapter will provide details about the estimation procedure of the energy demand function not accounting for risk. The model is estimates by applying first the CobbDouglas function and then the Translog function. Different econometric tests are conducted to evaluate the estimated Translog function and it superiority in compare to the CobbDouglas function.
8.2 The Energy Demand Model not Accounting for Risk
 (1)
It relaxes the assumption of unitary elasticity of substation.
 (2)
It relaxes the assumption that all industries have the same production elasticities.
 (3)
It is less restrictive due to incorporating flexible functional forms, in which it relaxes the assumptions about the market structure.
 (4)
It allows for investigating the possible substitution between the inputs.
 (5)
It allows for implementing nonlinear relations between the explanatory variables and the dependent variable through the use of square and interaction terms.
Thus, the Translog production function is used to measure the elasticities of substitution, technical change, and the total factor productivity growth . For the mentioned reasons the CobbDouglas function will not be considered for the energy demand analysis. The only reason of reporting it is to show the robustness of the Translog function and its superiority relative to CobbDouglas specification.
Parameter estimates for pooled energy demand model (dependent variable is e (energy))
Due to the presence of functional forms , it is difficult to directly interpret the estimated coefficients, thus, different measures will be provided to interpret the estimated coefficients such as input and output elasticities and the rate of technical change measures.
8.3 The Overall Performance
The model’s coefficient of determination (R^{2}) is equal to (0.867) (compare to 0.80 in case of CobbDouglas), it implies that more than 86 % of variations in the data can be explained using this model. The standard error (MSE), as another measure of goodness of fit with a value of (0.414) indicates that the observations on average are little over 4 point away from the mean. In other words, there is relatively not high rate of dispersion of the data around the mean. The model consists of 45 explanatory variables (the intercept, the variables and their quadratic and interactions with other variables), in which, 34 variables (76 %) are statistically significant, 26 of them are highly significant with 99 % level of significance.
The value of Ftest statistics (equal to 130.97) is large and statistically significant at a 99 % level. It is large enough to reject the null hypothesis that all explanatory variables are zero, and the overall model accounts for a significant portion of the variability in the dependent variable (Fai and Cornelius, 1996). The Ftest statistics, according to Johnston (1984) for comparing the CobbDouglas and the Translog based on Eq. ( 7.3) is equal to (14.335), which is larger than the critical value at 99 %. This implies the superiority of Translog over CobbDouglas form (Press et al. 1994).
8.4 Regularity Conditions Test
To test for the regularity conditions monotonicity and quasi concavity, the Translog function must satisfy the positivity of logarithmic marginal products with respect to each input factor of production (the input elasticities). In addition to the own price elasticity , in case of the factor demand the property of convexity is required to have negative values of own price elasticities (Morey 1986). In the case of energy demand, the curvature can be tested. It requires that the other inputs and the output elasticity matrix be negative semidefinite as described in Gallant (2008).
Percentage frequently of positive marginal productivity
Variable  Percentage Frequency 

σ_{EP}  (Negative values) 0.881 
σ_{EY}  0.615 
σ_{EK}  0.846 
σ_{EL}  0.330 
σ_{EM}  0.506 
σ_{ES}  0.792 
σ_{EI}  0.191 
The Curvature condition in the energy demand model is also evaluated. The Eigen values of the elasticities are mixed in sign. The sample average elasticities for price, output, nonICT capital, labor, materials, value added services, ICT capital, and time trend are (−2.71), (2.16), (−0.73), (1.05), (−0.12), (0.03), (0.081), and (0.038), respectively, indicating negative semidefinite values. As a result, the second regularity condition is also satisfied (Moss et al. 2003). However, the sign of ICT capital does not alter with the sign of time variable, indicating that the curvature property does not hold globally for all bundle of inputs (Sauer et al. 2006).
8.5 The Elasticities of Energy Demand
The demand behavior and the potential policy variables can be classified as short run and long run in their elasticities. In the short run, the behavioral specifications and the policy variables such as imposed taxes must consider that demand responses can only take the form of saving and alter in utilizing capital, while in the long run as the size and technological characteristics of the capital stock become variable, the characteristics and the degree of availability of new technologies as well as substitutability or complementarity become applicable (Hartman 1979).
The energy demand elasticities have been estimated econometrically by many scholars aiming at specifying causal relationships between energy and economic growth (See for example: Agnolucci 2009; Apostolakis 1990; Berndt and Wood 1975; Bhattacharyya and Timilsina 2009; Kamerschen and Porter 2004; Pindyck 1979; Polemis 2007). However, despite its importance for policy driven tools, there is little literature that estimate the elasticity of energy demand for the industrial sector using panel data set (Adeyemi and Hunt 2007; Liu 2004).
The energy demand elasticity is calculated as the derivative of energy use with respect to energy price, output, nonICT capital, labor, materials, value added service, ICT capital, and time trend. These elasticities are short run elasticities reflecting the percentage changes in energy use in response to one percent changes in respective explanatory variables of energy price, output, and other inputs (ceteris paribus). The elasticity with respect to time indicates percentage changes in energy use when time elapses with one year. In the production theory it is labeled as the rate of technical change (Kumbhakar et al. 2000). A negative rate of technical change will suggest energy saving, whereas a positive value suggests energy using technology employment for given level of output.
The elasticities of energy with respect to various inputs are calculated at each point of the data to allow variations in the responsiveness of industries in their energy use. It should be mentioned that the individual coefficients of the Translog energy demand function does not have direct interpretation alone (Pavelescu 2011). Therefore, the total elasticity must be computed at the mean of the data or at certain levels. These elasticities vary over time and industry. The sign of elasticity of energy demand with respect to energy price rate is expected to be negative, and the output elasticity to be positive, while others depending on their sign show the substitutability (negative) and complementarity (positive) relationships with energy use.^{1}
The input elasticities of substitution are evaluated at the mean per year, industry, and industry’s characteristics. They are all reported in Appendix A. It is worthy of mentioning that energy demand model is an inverted factor demand model, which is very similar to a cost model.^{2} However, here the dependent variable is a partial cost but the structure of the function and interpretation of the elasticities are somewhat similar. In this study, the returns to scale (which is 1/cost for elasticity of output) will not be discussed due to difficulties in interpreting technological scale.
8.6 The Rate of Technical Change
The partial derivative of the energy demand function with respect to time along with the elasticity of energy with respect to time are calculated to capture the two of the rate of technical change components, namely, the pure technical change, which depends only on time, and the nonneutral technical change which depends on changes in the input over time (Heshmati 1994). Here the nonneutral technical change is interpreted as the rate of substitutability between energy and other inputs. These measures will serve as unspecified technology used with energy inputs (Heshmati and Kumbhakar 2011).
This is equal to the partial derivative of the energy demand function with respect to time. The pure technical change which represents the effect of knowledge advancement over time is considered as an indicator of knowledge development. It refers to the shift in the energy requirement function over time. The nonneutral component suggests that a shift in the energy use over time is not neutral. The magnitude of the rate of change is affected by utilizing other factors of production and their relationships with energy such as complementarity (positive sign) and substitutability (negative sign). Furthermore, the nonneutral component captures the cost reduction effects by applying inputs price changes and substitution. A possible interpretation is that industries replace energy with other production factors.
Overall mean energy elasticities (elasticity of energy with respect to output and other inputs)
Variable  Mean  Std. Dev. 

σ_{EP}  −0.591  0.532 
σ_{EY}  0.499  0.433 
σ_{EK}  0.175  0.190 
σ_{EL}  −0.175  0.410 
σ_{EM}  0.068  0.596 
σ_{ES}  0.349  0.483 
σ_{EI}  −0.172  0.191 
σ_{ET}  0.037  0.056 
Puret  0.015  0.047 
Nonnt  0.067  0.126 
RTS  2.938  1.279 
TFP  0.015  0.098 
Growth of output  0.096  0.113 
Variability can be observed in the rate of technical change in its nonneutral component across industries and across different characteristic of industries (See Tables 8.4, 8.5, 8.6, 8.7, 8.8, 8.9 and 8.10). Only five industries are exhibiting technical regress, these are mining and quarrying (industry code 2), food, beverage and tobacco (industry code 3), wood and cork (industry code 5), machinery and NEC (industry code 10), and manufacturing, NEC and recycling (industry code 13).
 1.
The results imply that in these industries the restructure by adopting new, more energy efficient, and productive technology are taken place.
 2.
Only electrical and optical equipment industry is considered as a high technology industry among the four industries mentioned above. This implies that the high technology industries still lack behind in implementing energy saving program although the substitutability between ICT capital and energy is feasible and already proved by estimating the energy demand model in this chapter.
 3.
The high rate of energy saving technical change implies that these industries have experienced strong competitive pressure within the industries or encounter competition against countries with cheaper energy supply.
8.7 Hypotheses Testing

R_{1}: What is the impact of energy use on the production level in the South Korean Industrial sector?
From the results reported in Table 8.3, the mean elasticity of energy with respect to output is equal to (0.499) with the standard deviation of (0.433). A possible interpretation is that with a 10 % increase in output level, the energy use will be increased by 4.99 %. By looking at the figures of the mean elasticity of energy with respect to output across the industries, one can notice the variability of the level of energy used in the production level across the industries (See Fig. 8.2). As a result, the evidence supports the alternative hypothesis that there is a significant and a positive impact of energy use on the production level in the industrial sector for South Korea. 
R2: Is there any factor substitution pattern between energy and other inputs of production in the South Korean industrial sector?
Based on the results reported in Table 8.3, one can evaluate the mean elasticities signs, the sign for the elasticity of energy with respect to each input specifies whether this input on average is substitute (negative sign) or complement (positive sign). Accordingly, the negative signs of the elasticities of energy with respect to labor and ICT capital indicate that these two inputs may substitute the level of energy use in the production. Hence, the hypothesis stating that ICT capital and labor are substituting energy in the South Korean industrial sector is accepted. However across industries, the sign of the mean elasticity of energy with respect to the different inputs are differed, indicating substitutability and complementarity of these inputs across industries.
8.8 Summary
The second group of models estimated is the energy demand model based on the inverted factor demand or input requirement function. Here again as in the previous chapter, the model is estimated firstly by the CobbDouglas then by the Translog functional form. Different econometric tests are conducted for the choice of the models and evaluation. It is found that the Translog function is superior to the CobbDouglas for its flexibility due to the use of functional forms and explanatory power.
Due to the presence of heterogeneity across the industries under the study, the two models for the energy demand (i.e. CobbDouglas and Translog) have been corrected for heteroskedasticity. The heteroskedasticity standard errors are reported instead of the original ones.
As mentioned previously, the estimated coefficients of the Translog specification cannot be directly interpreted due to the presence of functional forms . Therefore, the energy demand elasticity is calculated, it is calculated as the derivative of energy use with respect to energy price, output, nonICT capital, labor, materials, value added service, ICT capital, and time trend. These elasticities are short run elasticities reflecting the percentage changes in energy use in response to one percent change in respective explanatory variables of energy price, output, and other inputs (ceteris paribus). The elasticity with respect to time indicates percentage changes in energy use when time elapses with one year. In the production theory it is labeled as the rate of technical change.
The partial derivative of the energy demand function with respect to time along with the elasticity of energy with respect to time are calculated to capture the rate of technical change The nonneutral technical change is interpreted as the rate of substitutability between energy and other inputs. These measures will serve as unspecified technology used with energy inputs. The magnitude of the rate of change is affected by utilizing other factors of production and their relationships with energy such as complementarity (positive sign) and substitutability (negative sign). Furthermore, the nonneutral component captures the cost reduction effects by applying inputs price changes and substitution. A possible interpretation is that industries replace energy with other production factors.
Footnotes
References
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