Energy intensity in Guangdong of China (2006–2015): A spatial dynamic general equilibrium econometric model

This paper investigates the effects of population, investment, urbanization, industrial structure, policy instrument, and enterprise size on energy intensity in Guangdong, China. A dynamic optimal theoretical framework is utilized and empirical results are reported using panel data from 2006 to 2015. The fixed effects models and spatial fixed effects models both show that population, investment, urbanization, and enterprise size decrease energy intensity, but industrial structure and policy instrument drive it up; population, investment, urbanization, and enterprise size increase the energy consumption and economic output, but industrial structure and policy instrument decrease them, China; the energy intensity has significant spatial spillover effect that should be considered in Guangdong, China.

T A B L E 1 Summary of recent literature review for energy consumption and economic growth

| THEORETIC FRAMEWORK
One objective is to derive a theoretical framework that connects urbanization and energy intensity and is based upon an optimal allocation that maximizes household's intertemporal utility function (U). This intertemporal model will be connected to energy consumption through investments in energy infrastructure, so the utilitarian intertemporal utility function (W) can be expressed as follows: (1) where θ represents utility discount rate, C t denotes numeraire consumption, and over T number of years. We assume the utility function is isoelastic form with a constant parameter γ: The optimization problem is expressed as below: Under a constrained optimization format, we turn our attention to the constraints. First is a constraint on the numeraire consumption is based on the income accounting identity: where I t denotes all investment (private and public) that is outside the energy generation industry at year t and G t denotes government investment on energy infrastructure at year t. Investment is the change in the economy's capacity of capital as follows: Hence, plugging Equation (4) into Equation (3), we obtain the following equation: Writing this identity in discrete-time form, we have the following equation where δ is the depreciation rate.
The constraint for numeraire consumption is: So, the change of capital stock can be derived from Equations (6) and (7): The production function is assumed to be represented in Cobb-Douglas (C-D) form for each year t: where K t is capital, E t is energy utilized in production, and L t is labor. The parameters of Equation (9) are restricted as: a b d 0 < < 1, 0 < < 1, 0 < < 1 and a b d + + = 1. The second constraint comes from the capacity of energy production due to available infrastructure. To do so, we use F t to represent capacity of energy infrastructure at year t. The capacity of energy infrastructure (F t + 1 ) at year (t + 1) is composed of annual investment on energy infrastructure (G t ) and the value of remaining stock of energy infrastructure. A convenient way of modeling the latter is to assume that the value of remaining stock of energy infrastructure at the end of year t is F where the depreciation rate is π. Therefore, we define value of changes in the capacity of energy infrastructure as follows: Finally, the amount of energy consumption, E t , is treated as an increasing functional of the capacity of energy infrastructure and other factors (ε t ) so that E fF = ε , t t t where f is the transfer coefficient representing how many percentage of energy stock can be effectively used. Therefore, we have the following setup for an optimal control problem as follows: Hence, we form the current Hamiltonian Function as follows: The first order conditions are given in the following equations: The solutions of the optimal control model above is as follows: Plugging Equations (14) and (16) into Equation (15), we obtain: According to E f F = ε t t t , we obtain the optimal energy consumption function as follows: If we let β = bf π θ δ ε + − t , then the energy consumption function can be expressed as: E βY = t t . Therefore, there should be a parameter B satisfies that In terms of Equation (9), we can obtain the following equation: So, if we plug Equation (20) into Equation (19), we obtain: Therefore, Furthermore, let Equation (21) Finally, we plug Equation (21) into Equation (20), then get the following equation: 3 | DATA AND EMPIRICAL METHODS

| Econometric models
So as to estimate coefficients in Equations (21)-(23) and capture the fixed effects on city and time, I extend Equation (21) and get the equation: X ′ it is the covariate vector, α i captures all unobserved, time-constant factors that affect lnY it , which is individual fixed effect. The year effect, μ t , is also treated as a parameter to be estimated. u it is the error term. And then we also get the extension form from Equation (22): Similarly, we extend Equation (23) into the following form: Furthermore, if we measure the spatial spillover effect, Equation (24) can be extended into the spatial fixed effects model: ε it is the residual for Equation (27) and w′ i is the ith row of the spatial weight matrix W. ρ ≠ 0 is an unknown parameter which specifies the strength of correlation between colocated provinces. Error term ε it represents unobservable factors excluding spatial spillover effects. In terms of W, if city i and city j have a common border, then w = 1 ij , otherwise w = 0 ij . And the diagonal elements are 0, that is, w w = … = = 0 nn 11 , which means that the distance between the same city is 0.
Similarly, the spatial fixed effects forms of Equations (25) and (26) are as below, respectively:

| Data and description statistics
To get the estimations from Equations (24)

| EMPIRICAL RESULTS
The Hausman test is performed before the regression in Table 4. Table 4 shows that the p values of accept the null hypothesis of random effects are <0.1, so the fixed effects models should be selected. Table 5 shows urbanization is significantly negative associated with energy intensity. Besides, population and investment are also significantly and negatively associated with it, which is against the finding of Li and Lin (2015). The proportion of primary industry and secondary industry are significantly positively associated with it, while the effect of the eleventh 5-year plan on energy intensity is significantly positive.
However, the coefficients in other two regressions are significantly opposite with those in the first regression, but the impacts of sl and hl on GDP and energy consumption are significantly positive, which is nonsignificant.

| Extension: Spatial econometric analysis
In this section, we consider the spatial spillover effect. Table 6 illustrates that the absolute values of the coefficients across the three regressions are significantly less than those in the fixed effects models, which means the fixed effects models overestimate the impact of covariate variables. Especially, the coefficients of spatial autogressive items across these three models are significantly positive. It means that the spatial spillover effects are obvious and should be considered.
In terms of the variable sl, after considering spatial dependence, the effect of it on energy intensity becomes significantly negative, which is the same with the conclusion from Salim and Shafiei (2014) and Ren, Wang, Wang, and Liu (2015).

| CONCLUSIONS AND FURTHER DISCUSSION
In this paper, we provide a framework to conduct theoretical and empirical research demonstrating how population, investment, urbanization, industrial structure, and enterprise size affect energy intensity, energy consumption, and economic performance by setting up the dynamic optimization models and design the fixed effects models and spatial fixed effects models using panel dataset from Guangdong, China. Based on the theoretical framework, the empirical results demonstrate three findings: (a) Population, investment, urbanization, and enterprise size decrease energy intensity, but industrial structure and policy instrument drive it up; (b) population, investment, urbanization, and enterprise size increase the energy consumption and economic output, but industrial structure and policy instrument decrease them, China; and (c) the energy intensity has significant spatial spillover effect that should be considered in Guangdong, China.
Finally, this study has limitations that include: (a) The theoretical model assumes utility optimization and general equilibrium, (b) the specification of econometric model does not consider macroeconomic factors such as interest rates, and (c) important uncertainties referring to the export and import between cities, energy market structures, and decarbonizing technology are not included in the empirical models.

ACKNOWLEDGMENT
This study is financially supported by National Ten Thousand Outstanding Young Scholar Program (W02070352) and China National Social Science Foundation (19FJYB050). Note: Standard errors in parentheses. ***p < .01 **p < .05 *p < .1