**3. Results and discussion**

**Table 3** presents the estimation results for the energy demand frontier function. Model A shows the estimation results of (2) and (3). Model B shows the estimation result of the model considering a nonlinear effect in the inefficiency determinant.

First, let us consider the results of Model A. The estimated coefficients show the expected signs, and all variables are statistically significant. Since each variable is a logarithmic variable, the estimated parameter can be interpreted as elasticity. Estimated price elasticity is 0.046 and income elasticity 0.707, indicating that income elasticity significantly exceeds price elasticity. Price elasticity is inelastic and denotes the nature of energy goods as essential goods. The capital-labor ratio and the coefficient on vintage are positive and have reasonable signs. This suggests that there is more energy demand in areas where industries for which mechanization is progressing are located. It also shows that capital investment increases energy demand. The coefficients for cooling degree day are slightly significant, but their magnitude is small. Additionally, the coefficients for heating degree day are not significant. These results show that temperature is a weak determinant of energy demand in the industrial sector.

Next, this study evaluates the estimation results for the factors determining energy efficiency. The capital-labor ratio is positive and reports the expected sign. This indicates that energy efficiency deteriorates with an increase in mechanization. In other words, energy efficiency is lower in regions where numerous industries with large-scale facilities are located. The electrification rate is negative, reporting the expected sign. The results show that an increase in the electrification rate enhances energy efficiency. The coefficient value for the electrification rate is considerably larger than that for the capital-labor ratio. That is, the positive impact


**93**

*βKL*

*βER*

*σu* <sup>2</sup> + *σ<sup>v</sup>*

*σu* 2 /(*σ<sup>u</sup>* <sup>2</sup> + *σ<sup>v</sup>* 2

**Table 4.**

Number of observations

*Estimation results for 1980–2007.*

*Note: \*\* and \* denote significance at the 1 and 5% levels, respectively.*

*Determinants of Energy Demand Efficiency: Evidence from Japan's Industrial Sector*

of installing power facilities and an increase in the electrification rate from office automation are more significant than the negative impact of installing large produc-

Due to these effects, this study estimates Model B, which account for the nonlinear effects of determinants. Statistically, significant values are obtained for the quadratic term of the capital-labor ratio. The sign of the quadratic term is negative. This shows there is a threshold for the impact of the capital-labor ratio on energy efficiency. Specifically, the increase in mechanization improves energy efficiency, but it exacerbates energy efficiency when it exceeds a threshold value. On the other hand, the quadratic terms for electrification are not statistically significant, and the

During the observation period (1990–2010), there was financial crisis in 2008. As the economic depression spreads worldwide from the US, Japan's economic growth rate fell greatly in 2008. This economic downturn had a significant influence on the production system of the regional industry. Hence, when considering result stability, this influence must be considered. Therefore, the analysis period is reset from 1990 to 2007, and Model A and Model B reestimated. **Table 4** shows the reestimation results. Model C represents the result of reestimation of Model A and Model D of Model B. There is no significant difference in the regression coefficients

**Table 5** presents the descriptive statistics for the energy efficiency values of each prefecture, obtained from the estimation results (Model A). An efficiency value of 1 denotes the highest efficiency, while a value below 1 indicates lower energy efficiency. The average energy efficiency value is 0.617 and the median value 0.685. More importantly, a maximum value of 0.950 and a minimum of

*Constant* (*α*) −0.577\*\* (0.044) −0.576\*\* (0.049) *α<sup>P</sup>* −0.063\*\* (0.014) −0.056\*\* (0.014) *α<sup>Y</sup>* 0.709\*\* (0.011) 0.706 \*\* (0.011) *αKL* 0.121\*\* (0.027) 0.118\*\* (0.027) *αIK* 0.073\*\* (0.012) 0.079\*\* (0.012) *αCDD* −0.018 (0.009) −0.018 (0.009) *αHDD* −0.006 (0.008) −0.008 (0.007) *Constant* (*β*) 0.520\*\* (0.051) 0.552\*\* (0.058) *βKL* 0.094\*\* (0.029) 0.091\*\* (0.029)

<sup>2</sup> −0.028\* (0.010) *βER* −0.522\*\* (0.012) −0.543\*\* (0.028)

<sup>2</sup> −0.012 (0.012)

<sup>2</sup> 0.062 \*\* (0.004) 0.063\*\* (0.004)

) 0.648\*\* (0.111) 0.667\*\* (0.106)

846 846

**Model C Model D Coefficient Standard error Coefficient Standard error**

*DOI: http://dx.doi.org/10.5772/intechopen.81482*

nonlinear effects of electrification are not recognizable.

in **Table 4**. Therefore, the results in **Table 3** can be judged as robust.

tive capital equipment.
