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Energy Demand Model I

  • Nabaz T. KhayyatEmail author
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Part of the Green Energy and Technology book series (GREEN)

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 Cobb-Douglas 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 Elasticity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This chapter introduces the second group of the econometric models estimation, namely the energy demand model. The model is constructed in two forms: The Cobb-Douglas 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 Cobb-Douglas function and then the Translog function. Different econometric tests are conducted to evaluate the estimated Translog function and it superiority in compare to the Cobb-Douglas function.

8.2 The Energy Demand Model not Accounting for Risk

The energy demand model is constructed based on the Eq. ( 3.2) and specified in two forms: The Cobb-Douglas and the Translog function. This will allow for consistency and comparability with the production function part described in Chap.  7. The Translog production function is more flexible than the Cobb-Douglas for many reasons as follows (Pavelescu 2011):
  1. (1)

    It relaxes the assumption of unitary elasticity of substation.

     
  2. (2)

    It relaxes the assumption that all industries have the same production elasticities.

     
  3. (3)

    It is less restrictive due to incorporating flexible functional forms, in which it relaxes the assumptions about the market structure.

     
  4. (4)

    It allows for investigating the possible substitution between the inputs.

     
  5. (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 Cobb-Douglas 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 Cobb-Douglas specification.

The parameter estimates for the pooled energy demand model not accounting for risk reported in Table 8.1. Note that the first part of the table reports the estimated parameters of Cobb Douglas function, whereas the second part (the right side of the table) is the Translog function parameter estimates.
Table 8.1

Parameter estimates for pooled energy demand model (dependent variable is e (energy))

Note The significant levels are as follows: a 99 %, b 95 %, c 90 %

The standard errors are between the parentheses

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 (R2) is equal to (0.867) (compare to 0.80 in case of Cobb-Douglas), 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 F-test 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 F-test statistics, according to Johnston (1984) for comparing the Cobb-Douglas 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 Cobb-Douglas 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 semi-definite as described in Gallant (2008).

The percentage frequency of positive marginal productivities of the estimated Translog energy demand function are as follows (See Table 8.2): Output (0.615), non-ICT capital (0.846), labor (0.330), materials (0.506), value added services (0.792), and ICT capital (0.191), indicating the on average positivity of logarithmic marginal products with respect to output and each input factor of demand is satisfied. The convexity of own price elasticity is also satisfied with (0.881) indicating that more than 88 % of the data points satisfies the convexity condition of own price elasticity in the energy demand model.
Table 8.2

Percentage frequently of positive marginal productivity

Variable

Percentage Frequency

σEP

(Negative values) 0.881

σEY

0.615

σEK

0.846

σEL

0.330

σEM

0.506

σES

0.792

σEI

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, non-ICT 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 semi-definite 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, non-ICT 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 non-neutral technical change which depends on changes in the input over time (Heshmati 1994). Here the non-neutral technical change is interpreted as the rate of substitutability between energy and other inputs. These measures will serve as un-specified technology used with energy inputs (Heshmati and Kumbhakar 2011).

The rate of technical change can be expressed as in the following equation:
$$E_{t} = \frac{{\partial e_{it} }}{\partial t} = \beta_{t} + \beta_{it} t + \sum\nolimits_{j} {\beta_{jt} x_{jit} }$$
(8.1)

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 non-neutral 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 non-neutral 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.

The sample mean value for the rate of technical change as shown in Table 8.3 is equal to (0.037) with the standard deviation of (0.056). It is an evidence of small technical progress (Turnovsky and Donnelly 1984) during the period of study (1970–2007). It can be interpreted as follows: On average, a year later, by the same amount of energy input the output can be produced by 3.7 % more.
Table 8.3

Overall mean energy elasticities (elasticity of energy with respect to output and other inputs)

Variable

Mean

Std. Dev.

σEP

−0.591

0.532

σEY

0.499

0.433

σEK

0.175

0.190

σEL

−0.175

0.410

σEM

0.068

0.596

σES

0.349

0.483

σEI

−0.172

0.191

σET

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

The sample mean of pure and non-neutral components are equal to (0.015) and (0.067), respectively. The positive value of pure component indicates its positive contribution to the rate of technical change. As can be noticed in Fig. 8.1, the pure technical change follows a linear trend, indicating that the demand for energy has increased systematically over time. It reflects the fact that the South Korean economy with its continuous growth over time lead to increase in the demand of energy for its industrialization process. The non-neutral values have decreased dramatically over time indicated its decrease in the positive contribution, which reflects energy saving technology development and change (See Fig. 8.1).
Fig. 8.1

Rate of technical change and its decomposition for energy use

Variability can be observed in the rate of technical change in its non-neutral 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).

The trend in energy saving is shown only in four industries during the period of the study. The non-neutral technical change for food, beverage and tobacco (industry code 3), electrical and optical equipment (industry code 11), wholesale and retail trade (industry code 16), and real estate, renting and business activities (industry code 21). Important implications can be drawn here as follows:
  1. 1.

    The results imply that in these industries the restructure by adopting new, more energy efficient, and productive technology are taken place.

     
  2. 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. 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

The following research questions with their hypotheses are tested based on this model as follows:
  • R1: 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.
    Fig. 8.2

    The mean elasticity of energy with respect to output across sectors

  • 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 Cobb-Douglas 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 Cobb-Douglas 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. Cobb-Douglas 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, non-ICT 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 non-neutral technical change is interpreted as the rate of substitutability between energy and other inputs. These measures will serve as un-specified 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 non-neutral 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

  1. 1.

    Due to unavailability of the inputs prices in the data set, the cross price elasticizes are not computed.

  2. 2.

    For more detail description of the inverted factor demand, see Kumbhakar et al. (2000).

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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Technology Management, Economics, and Policy Program, College of EngineeringSeoul National UniversitySeoulSouth Korea

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