Urbanization and energy equity: an urban-rural gap perspective

A high-speed urban expansion in China over the past two decades has been accompanied by a great leap forward for energy consumption. However, such a significant socio-economic transition may increase the potential risk of energy inequality, which deserves special attention. Using China’s provincial panel data covering the periods of 1997–2020, this paper mainly studies the impact of urbanization on urban-rural electricity consumption inequality with a modified STRIPAT model. The results of the Generalized Method of Moments (GMM) estimation show that there is a significant U-shaped relationship between urbanization and urban-rural electricity consumption inequality. The estimated short-run turning point arrives at the urbanization level of around 63.54% and 61.18% for the long-run estimates. We further carry out a regional heterogeneity analysis and then have two interesting findings: firstly, the colder northern region’s turning point (70.95%) arrives later than the south (57.69%). Secondly, the baseline U-shaped relationship remains for developed eastern regions and the estimated turning point is 57.91%, while for the undeveloped midwestern regions, the relationship is not nonlinear but linearly negative. As an extension, we lastly explore the mechanism underlying the U-shaped relationship, and find that the interaction of urbanization’s scale and efficiency effect determines the U-shaped relationship. Our findings remind policymakers that, to narrow the urban-rural development gap, the future preference of energy policy should be dynamically adaptive to varied regions and development stages.


Introduction
Over the past two decades, a significant socio-economic transition has been witnessed in China, with the majority of population moving from the rural to urbanized areas. According to the National Bureau of Statistics, urbanization in China has climbed from 36.22% in 2000 to 64.72% in 2021. Such a high-speed urban expansion has a substantial impact on residents' energy consumption by raising their purchasing power, changing their energy consumption behavior and improving power facilities (Yang et al. 2019). For example, the energy consumption from the residential Responsible Editor: Ilhan Ozturk Lu Wang contributed equally to this work.

Liangguo Luo 17301677679@163.com
Extended author information available on the last page of the article. sector has increased nearly fourfold, from 166.95 million tons of standard coal equivalent (Mtce) in 2000, to 643.80 Mtce in 2020 (Chinese Energy Statistical Yearbook, 2021). However, the great leap forward for energy consumption in China increases the potential risk of energy inequality which is generally defined as uneven accessibility to modern energy services (Shi 2019). In particular, the traditional biofuels consumption of habitants with no electricity access is equivalent to 1.3 million tons of coal, and the indoor pollution arising from it leads to around 0.8 to 1.5 million 45 premature deaths per year in China (WHO, 2016). Access to affordable modern energy services is essential for sustainable development and achieving the Millennium Development Goal (MDG), as it can improve health and reduce time spent gathering firewood, especially for children and women, allowing them to pursue education opportunities and enjoy more leisure time. Given the access to modern energy services is closely related to people's health, education and livelihoods , clarifying the determinants of energy equity and ensuring universal access to modern energy services deserve special attention.
Along with the accelerated urbanization and raising concerns of energy equity in China in recent years, the energy inequality between the urban and rural areas is especially evident both in the quantities of energy used and levels of access to clean and efficient energy (Dou et al. 2021). These disparities stem mostly from the urbanrural differences in income, production and consumption activities, and lifestyles (Nguyen et al. 2019;Taruttis and Weber 2022). For urban areas, high-income households might be inspired to change their lifestyle and use cleaner energy as their income and environmental awareness increases with the rapid urbanization Su et al. 2022). The rural areas, however, have not synchronized with urban counterparts and modernized their energy consumption due to the inadequate energy infrastructure and relatively lower prices of traditional energy. Some rural areas that lack access to modern energy services even maintain the most primitive energy consumption patterns, using firewood as their major daily energy resource . Figure 1 may be informative: in 1997, the urbanization rates of all China's provinces were relatively low and corresponding gaps between urban and rural electricity consumption per capita were quite large. In 2020, most provinces' urbanization increased a lot and corresponding urban-rural electricity consumption gaps undergone tremendous change: some midwestern provinces narrowed their gap, while some developed eastern provinces saw a widening urban-rural gap. Such energy inequality might result in a vicious circle of energy poverty and further contribute to chronic or persistent poverty in the rural areas, which might intimidate the sustainable implementation of China's poverty alleviation resettlement (PAR) program.
The nonnegligible inequality between urban and rural areas in energy consumption has attracted the government's attention; however, few studies have systematically investigated the causal link between urbanization and urban-rural energy equity, especially for the case of China. Existing studies usually discuss and analyze inequality in a monetary perspective rather than from a perspective of energy access and use, although a growing literature has shown that disparities in energy access and use are sometimes starker than inequalities in income (Sovacool and Dworkin 2015;Wu et al. 2017;Bianco et al. 2021). The most related literature on energy consumption may help clarify the factors affecting the energy inequality. Overall, these factors can be categorized into four types (economy, demography, living condition and environmental attitudes) (Li and Leung 2021;Zou and Luo 2019;Al-Shanableh and Evcil 2022;. Also, given the significant regional heterogeneity including geographical and economic differences across China's provinces (Shen et al. 2021), the impact of urbanization on urban-rural energy inequality might be heterogeneous as such regional heterogeneity is closely related to energy users' energy consumption behavior (Xiao et al. 2018;. Nevertheless, the potential heterogeneity has often been ignored in previous studies. In addition, the conflicting "push" and "pull" effects of urbanization on energy use imply that urbanization could both drive residents' energy consumption by increasing their income and shift residents' energy behavior to a lowenergy mode by improving energy efficiency along with urbanization (Ali 2021;Nguyen et al. 2019), which may influence the relationship between urbanization and urbanrural energy equity in different ways. To date, however, very few studies have discussed this impact before.
To fill the academic gaps discussed above, this study first examines the impact of urbanization on urban-rural energy inequality by building a modified STRIPAT model based on a provincial panel data including 30 China's provinces over the period of 1997 to 2020. As China has the highest total electricity output, consumption and installed capacity in the world and electricity consumption closely relates to the promotion of productive opportunities, enterprise growth and employment , the urban-rural electricity consumption inequality is selected as the proxy of energy inequality. Furthermore, this study investigates how the relationship between urbanization and urban-rural energy inequality changes in response to the regional heterogeneity, and explores the potential mechanism underlying that relationship. The contributions of this study lie mainly in the following three aspects: (1) Different from previous studies that focus only on the measurement of energy disparity, we extend the existing literature by further analyzing the nexus between urbanization and energy inequality and the underlying causes of the disparity. This is not only conducive to better understanding the driving factors of energy inequality, but also provides new insights for energy poverty reduction in China.
(2) Most of relevant studies analyze urban-rural inequality in terms of income and monetary measures. We extend existing literature by analyzing it from the perspective of energy inequality, which offers new evidence for balancing the rural and urban development by using a portfolio of energy policies, instead of being limited to monetary policies.
(3) Although the significant regional heterogeneity across China may affect the impact of urbanization on urbanrural energy inequality, the potential heterogeneity has often been ignored in previous studies. We further discuss the regional heterogeneity in the impact of urbanization on energy inequality. This will greatly promote the regional environmental economic research as well as differentiated policies to improve the access to modern energy services across different regions of China.
The rest of the paper proceeds as follows. Section Brief review of the literature and the theoretical background of the testable hypotheses reviews the existing literature. Section Framework and data introduces the model and data. Section Empirical results carries out the empirical estimation and robustness check. Section Heterogeneity analysis performs a heterogeneity analysis analyzing how our results change in response to regional geographical and economic differences. Section Extensions explores the mechanism underlying our baseline results. Section Conclusions concludes.

Brief review of the literature and the theoretical background of the testable hypotheses
Brief review of the literature Energy inequality generally refers to the disparities in individual access to energy (Zhong et al. 2020), indicating that access to (clean) energy is unfairly apportioned among different clusters of the population (Nguyen et al. 2019). To be more specific, although some people have access to an abundance of energy, others struggle to survive because they lack access to clean fuels and technologies for cooking, minimum energy for basic human needs or minimum income for energy spending (González-Eguino 2015). Much attention has been paid to energy inequality due to its consequences for health risks, economic development and environmental issues (González-Eguino 2015; . Specifically, indoor air pollution resulted from inefficient cooking using solid fuels has a negative impact on human health (Awaworyi Churchill and Smyth 2020). (Okushima 2017) found that poor access to modern energy services, especially among lower-income and vulnerable households, resulted in decreasing income and labor productivity, thus leading to underdeveloped economic development. Traditional biomass provides the main source of energy for areas with limited access to clean energy, and its overexploitation increases deforestation, desertification and land-degradation (González-Eguino 2015). It is worth noting that, in China, although access to energy across different segments of the population has become more equal, the gap in consumption levels has grown between urban and rural households . Such urban-rural gap in energy consumption will further restrict sustainable development in China (Fan et al. 2020). Thus, how to effectively control household energy consumption and relieve its inequality is an urgent problem for China.
A strand of literature, most closely related to our research, studies the determinants of residential energy consumption. The existing literature points to mainly four factors (economy, demography, living condition and environmental attitudes) that impact on energy consumption. Firstly, economic factors are the most significant determinants, and among them, GDP per capita, income level and energy price have empirically been examined to be closely associated with residential energy consumption (Saldivia et al. 2020;Huo et al. 2021;Li and Leung 2021). Secondly, other work has emphasized the importance of demographic factors in explaining energy users' consumption. Estiri and Zagheni (2019) and Zou and Luo (2019) and Bello et al. (2021), for example, have empirically examined the importance of age structure, household size and educational attainment. Thirdly, living condition factors affect residential energy consumption through different geographical features and house areas. For example, Al-Shanableh and Evcil (2022) analyzed the Cyprus households' energy consumption based on the survey data, and found that household energy consumption increased with the floor area of house, the year of construction and the type of house per house. Fourthly, environmental attitudes are also found to play a crucial role. Hidalgo-Crespo. J et al. (2022) found that environmental concerns were associated with lower energy consumption using a dataset of household electricity use. Several studies have shown that environmental attitudes and environmental behaviors are related to people's values and values can serve as guiding principles in people's energy behavior (Paco and Lavrador 2017;Achuo and Nchofoung 2022). The great leap forward for energy consumption in China increases the potential risk of energy inequality which deserves special attention; however, previous studies just focus on analyzing the influencing factors of energy consumption. The determinants of energy consumption inequality have not received much attention, and very few studies have systematically investigated the energy inequality in China's case, not to speak of in an urban-rural perspective.
Another strand of literature, most specifically related to our measurement of urban-rural energy consumption inequality, studies how to estimate energy consumption equity. Existing studies primarily use three measurement methods: Lorenz curves and Gini coefficients, Theil index and Atkinson index. The Lorentz curve and Gini coefficients are powerful indicators to measure energy inequality; they are used to reflect the equality status of energy distribution among households (Ma et al. 2021). Jacobson et al. (2005) firstly extended the application of Lorenz curves and Gini coefficients to energy consumption equity. Then, several studies apply this method to assess energy consumption inequality in terms of energy type, enduse demand, regions and climatic zones (Nguyen et al. 2019;. Work by Pakrooh et al. (2020) introduced the Theil index into the energy consumption equity analysis and concluded that Iran's energy consumption inequality was decreasing with years. For the first time, Schlör et al. (2013) used the Atkinson index as an analytical tool to calculate the distribution of energy consumption and used the epsilon parameter to explicitly reveal the inequality aversion of society. Later studies show that applying the Atkinson index could make a significant contribution to science and policy debates on energy equity (Asongu and Odhiambo 2021). To conclude, energy inequality across regions can be measured by using different indexes and the tools should be selected on the basis of the research area and data availability. Based on these measurements of energy consumption equity, some studies also explore its influencing factors including household attributes, regional characteristics and energy policy (Ogwumike and Ozughalu 2015;Wu et al. 2017;Hahn and Metcalfe 2021). For example, Wu et al. (2017) found that the overall inequality of energy consumption varied greatly in terms of household end-use demand and intraregional differences. It can be observed that much attention has been paid to the evaluation of energy inequality and its influencing factors. However, few studies have explored the nexus between energy inequality and urbanization from an urban-rural gap perspective.
Our findings also relate to the literature investigating the relationship between urbanization and energy consumption. Previous research has shown conflicting results, suggesting that the relationship between urbanization and energy use is mixed. On the one hand, urbanization has been identified as a major contributor to the increase in residential energy consumption due to the scale effect of urbanization: the concentration of population, expansion of industrialization and other societal and economic transformation (Wang et al. 2020;Su et al. 2022). For example, Fan et al. (2017) found that urbanization contributed a 15.4% increase in residential energy consumption in China during 1996-2012 but with a diminishing trend over time. Zhang et al. (2016) found that urbanization slowed per capita energy consumption growth in urban areas when compared with rural areas in China. On the other hand, some studies have shown that households could reduce their energy consumption by implementing more efficient heating, cooling and lighting systems or equipment, which can be attributed to urbanization's economies of scale and technological advantages (Shao and Wang 2022). Lin and Zhu (2021) used the panel data of prefecture-level cities and found that urbanization construction had apparent energy-saving effects. Yu (2021) used provincial-level panel data and employed a dynamic spatial panel model to empirically test the ecological effects of urbanization and found that urbanization effectively improved energy efficiency. In addition, some studies also found a reverse causality of the urbanization-energy nexus (Wu et al. 2020;. In brief, the existing evidence on the relationship between urbanization and energy consumption is mixed and inconclusive, which necessitates a comprehensive analysis of how urbanization impacts energy consumption. In addition, although some studies have disclosed that urbanization may have differentiated impacts on urban and rural energy consumption, few further explores the effect of urbanization on urban-rural energy consumption gap. In summary, although several scholars have focused on energy inequality, as outlined in the above literature review, certain research gaps still exist. First, previous studies just focus on estimating energy inequality and investigating urbanization's effect on energy consumption. There is no empirical literature combining the two subjects, which specially studies the relationship between urbanization and electricity consumption inequality, not to speak of the urban-rural electricity consumption inequality. Second, given the significant regional heterogeneity including geographical and economic differences across China's provinces, the impact of urbanization on urban-rural energy inequality might be heterogeneous as such regional heterogeneity is closely related to energy users' energy consumption behavior. However, to the best of our knowledge, very few researchers have discussed the heterogeneity in their empirical analysis. Third, since the existing evidence on the relationship between urbanization and energy consumption is mixed and inconclusive, urbanization may impact on energy inequality in different ways. In other words, the casual mechanism underlying the urbanization-energy nexus should also obtain special attention. However, this issue is often overlooked in previous studies. Poumanyvong and Kaneko (2010) suggested that the impact of urbanization on energy use varied across stages of development. The linear hypothesis adopted by some studies holds that urbanization is the main driving factor of energy consumption. However, the impact of urbanization on energy consumption tends to vary greatly across regions in different urbanization stages (Shahbaz et al. 2020;Papavasileiou 2020). The nonlinear hypothesis is then adopted by more studies. Besides, in the classic Environmental Kuznets Curve (EKC) hypothesis, there is a nonlinear relationship between economic development and environmental problems ). Within our approach, our hypothesis adopts an analogous energy perspective. In order to build our first hypothesis, a reasonable explanation can be possibly attributed to the fact that when the urbanization expands at the early stages, energy consumption pattern in rural area will witness a widespread adoption of the modern energy, and it will be more extensive-oriented, which can be termed as the scale effect of urbanization. However, some urban areas may start switching to more efficient energy due to technological innovation, urban agglomeration and the shift toward knowledge and service-based industries. Then, the urban-rural energy inequality will be narrowed. At the later stage of urbanization, the urban-rural gap will be enlarged because the scale effect of urbanization predominates over the efficiency effect in rural areas, while some modernized urban areas are efficiency-oriented in their energy consumption pattern after the urban-rural convergence in energy consumption.

Hypothesis 1 (H1)
In line with the EKC hypothesis, urbanization and urban-rural energy inequality exhibit a U-shaped curve.
To better understand the development of the above testable hypotheses, we provide the theoretical channels to justify the evolution prior to and after the threshold level. The urban environmental transition theory mainly discusses the types of urban energy-related environmental issues and their evolution (Cole et al. 2021). It implies that urbanization in the initial stage promotes the vigorous development of construction industry and energy consumption, which can be seen as the scale effect. It is suggested that urbanization and industrialization are the main socio-economic driving forces of energy inequality between urban and rural areas (Sikder et al. 2022). Chang-hong et al. (2006) concluded that the industrialization in the process of urbanization promoted energy consumption because citizens' energy demand was boosted by the industrialization, especially the development of power equipment manufacturing industry. Meanwhile, power facilities are improved and thus energy users are more accessible to energy consumption. However, such scale effect may affect urban and rural energy consumption in different ways. The causes are twofold: on the one hand, energy consumption pattern in rural area has experienced much more dramatic changes than urban areas. The most significant shift is the popular adoption of the modern energy and the reduce in the usage of traditional energy. On the other hand, some urban areas may start switching to more efficient fuel sources due to technological innovation, urban agglomeration and the shift toward knowledge and service-based industries, which helps reduce energy consumption in urban areas (Topcu and Tugcu 2020). It implies that when the urbanization expands at the early stages, the gap in residential energy consumption between urban and rural will be narrowed.

Hypothesis 2. (H2)
At the early stage of urbanization, the urban-rural energy inequality will be narrowed.
Ecological modernization theory emphasizes not only economic modernization but also social and institutional transformations in explaining the effects of modernization on the environment (Toke 2022). In this theory, urbanization is the process of social transformation regarded as one important indicator of modernization. Although urban energy-related environmental problems may increase at the early stage, further modernization can minimize such problems, as societies come to realize the importance of environmental sustainability, seeking for improved environmental regulations, technological progress and structural change along with urbanization (Liu et al. 2018). In other words, urbanization in the mature stage promotes the sustainable development which has a restraining effect on energy consumption as a result of the population agglomeration, environmental improvement and technological advance, which can be termed as the efficiency effect of urbanization (Franco et al. 2017). Research done by Liu (2009) suggests that enhancement of energy efficiency coupled with the acceleration of the process of urbanization could help in sustainable development, and such energy efficiency effect plays an important role in decreasing urban residential energy consumption at the aggregate level. However, for rural areas, it should be noted that the efficiency effect might be lagged due to the level of rural modernization has lagged far behind the level of industrialization and urbanization (Zheng 2018). The main focus of China's current rural energy system construction is still on eliminating energy poverty, and the government still keeps increasing the investment on construction of the power grid and other energy infrastructure. In other words, after the urban-rural convergence in energy consumption, the urban-rural energy gap might be enlarged because the scale effect of urbanization predominates over the efficiency effect in rural areas, while some modernized urban areas are efficiency-oriented in their energy consumption pattern.

Hypothesis 3. (H3)
At the later stage of urbanization, the urban-rural energy inequality will be enlarged.

Framework
In this paper, we explore the relationship between urbanization and urban-rural electricity consumption inequality using a modified STRIPAT model which was first proposed by Rosa and Dietz (1998). Because the urbanrural electricity consumption inequality, as our research subject, does burden China's urban and rural areas with different environmental pressures, it is reasonable to use the STRIPAT model to guide our analysis, which relates environmental pressures (or environmental impacts) to population, affluence (GDP per capita) and technology. The environmental pressure loaded by urban and rural China is where E irt and E iut is the electricity consumption of province i at times t for rural and urban areas; P and A denote population and affluence, respectively; e represents the random error term and includes the technology shock, which accords with previous work 1 ; a is the constant term; and b and c are the elasticities of P and A. To capture urbanrural electricity consumption inequality, we take the ratio of urban area's electricity consumption per capita to the rural where E iut /P iut E irt /P irt represents the urban-rural electricity consumption inequality; P iut P irt is the ratio of urban population to the rural, which can also be seen as an indicator of urbanization level; A iut A irt is the ratio of urban affluence to the rural, standing for the urban-rural income inequality; and the last two terms, , can be regarded as other socioeconomic shocks on electricity consumption, which explain why elasticities of P and A for the urban and rural are different. For example, China's rural areas are often with more elderly dwellers because the young move to cities for jobs, and the elderly have a stronger demand of electricity consumption for heating and lighting. Thus, this demographic difference between urban and rural areas may produce different elasticities. For convenience of analysis, we incorporate such socioeconomic shocks into X it , so Eq. 3 can be briefly expressed as where I neq it is the electricity consumption inequality of province i at times t; Urba is the urbanization level; I nco is the urban-rural income inequality; and X denotes other socioeconomic factors affecting electricity inequality. In addition, because geographical, economic and demographic features all vary across China's provinces, we introduce v i to capture province-specific characteristics. Following previous work, all variables are in logarithmic form to eliminate possible heteroscedasticity 2 .
In the following empirical part, to measure the dependent variable, China's provincial urban-rural electricity consumption inequality, we introduce the Theil index. The Theil index is a popular measurement for inequality, which was firstly proposed by Sastry and Theil (1969). We also take the ratio of urban electricity consumption per capita to the rural as another measurement for urban-rural electricity consumption inequality, which learns from Dong and Hao (2018)'s measurement of China's provincial income disparity. The two measurements have been broadly used in the research on measuring the economy and society inequality. We will use the Theil index in the baseline estimation and then use the ratio form for the robustness checks. The calculation methods of the Theil index and ratios are where Y it is the total electricity consumption of province i at times t; X it is the total population of province i at times t; Y jt is the electricity consumption of area j at times t; X jt is the population of area j at times t; and it represents urban areas if j=1 and rural areas if j=2; e iut and e irt is the urban and rural electricity consumption per capita at times t in province i. In addition, for ratios, some of its logarithmic term is below 0 because some provinces' rural electricity consumption per capita will exceed the urban at a certain time. To better depict the inequality after the rural's outstripping the urban, we take the absolute value of these ratios.
Equation 5 can be transformed into a dynamic model by adding lags of the dependent variable to the right side of Eq. 5. Compared with static models, the dynamic model is chosen because its advantage in estimating both long-run and short-run elasticities.
Many empirical studies 3 have found an Environmental Kuznets Curve (EKC) relationship between urbanization and environmental impacts. Intuitively, we further modify the model by adding the quadratic term of urbanization to capture the potential non-linear relationship between urbanization and electricity consumption inequality. Finally, Eq. 9 will guide our following empirical analysis.

Data
The dataset is a balanced panel which contains observations of 30 China's provinces 4 over periods of 1997-2020, with a sample of 720 observations. The provincial level data are obtained from China Statistical Yearbook, China City Statistical Yearbook, China Regional Statistical Yearbook, China Industrial Statistical Yearbook, China Energy Statistical Yearbook and Statistical Yearbooks of each province. Especially, the data of provinces' yearly electricity consumption are collected from each provinces' annual balanced sheet of electricity consumption, which annually records urban and rural electricity consumption of all China's regions and provinces. In addition, all economic variables are deflated based on the CPI of 2020. The dependent variable, China's provincial urban-rural electricity consumption inequality, is measured by two methods: the Theil index and ratio form. The key independent variable, the urbanization level, is proxied by four indicators: the ratio of urban population to the rural, region's urban population to total population, the proportion of region's non-agricultural population and road network density. The first one is set by our modified STRIPAT model and will be used in the baseline estimation. The latter three variables are the alternative specifications of urbanization, which will be employed in the robustness checks. In addition, we also measure urban-rural income inequality by the ratio of urban GDP per capita to the rural.
Besides the above variables directly derived from the STRIPAT model, this paper includes other socioeconomic variables affecting urban-rural electricity consumption inequality. We firstly consider urban-rural education gaps because energy users' energy consumption patterns relatively depend on their human capital level. The urbanrural education gap is defined as the ratio of urban residents' average years of school attainment to the rural. 5 Secondly, the annual provincial infrastructure construction funds, which include investments on electricity facilities, can improve the electricity production and power transmission efficiency. And this improvement will further relieve region's electricity disparity, especially for the rural China. Thus, we incorporate infrastructure construction funds into the analysis. Thirdly, the price of residential energy is closely related to electricity consumption, and therefore affects urban and rural electricity consumption patterns. So the price index of residential energy is taken as another independent variable. Lastly, we are also interested in how climates across China's regions influence local urban-rural electricity consumption inequality. To investigate this relationship, this paper divides China into five zones according to their specific climatic features, and each climatic zone will be treated as a binary variable in the estimation. 6  Table 1 reports the descriptive statistics of all these variables. To intuitively display the relationship between urbanrural electricity consumption inequality and urbanization, we picture the scatter diagram of electricity consumption inequality against the urbanization rate and draw a fitness line in Fig. 2. As it shows, the line of best fit has a U-shaped curve and it implies that urban-rural electricity consumption inequality has a U-shaped relationship with urbanization. To more precisely investigate the relationship between urbanization and urban-rural electricity consumption inequality, some intricately detailed estimation will be employed in the following section.

Baseline results
The above Eq. 7 guides our following empirical analysis and it is a dynamic panel model. To relieve potential endogenous problems, this paper also employs the first difference GMM (Arellano and Bond 1991) and system GMM model (Arellano and Bover 1995;Blundell and Bond 1998), which are for "small T and large N" panel models. The first difference GMM can eliminate fixed effects and avoid endogenous problems by taking variables' lag-terms as the instrumental variables. However, problems −10-0 • C), hot summer and cold winter areas (the coldest mean monthly dry-bulb temperature: 0-10 • C; the hottest mean monthly dry-bulb temperature: 25-30 • C), hot summer and warm winter areas (the coldest mean monthly dry-bulb temperature: >10 • C; the hottest mean monthly dry-bulb temperature: 25-30 • C), and temperate areas (the coldest mean monthly dry-bulb temperature: 0-13 • C; the hottest mean monthly dry-bulb temperature: 18-25 • C). For the distribution of climatic zones, please see Fig. 4.
of weak instruments will arise as a result of too many instrumental variables if the time series T is large enough.
Based on a new assumption that the first differences of instrumental variables are not correlated with the fixed effects, Arellano and Bover (1995) build system GMM model which simultaneously estimates the original equation and first differencing equation. Such treatment can reduce some bias of using the first difference GMM model. The system GMM estimator also allows the introduction of more instruments, which can dramatically improve estimation efficiency (Roodman 2009). Before the empirical estimation, a pre-test of unit root test is conducted to make sure that the series of panel data are stationary. Covariate-Augmented Dickey Fuller (CADF) test (Hansen 1995) is used to examine whether variables are stationary at levels. The CADF test has the null hypothesis of unit root. Table 2 shows that all variables are stationary at levels whether with the intercept or with the intercept and   Table 3 reports the result of benchmark estimation which uses the Theil index as the dependent variable. As noted previously, the first difference GMM and system GMM methods are employed to relieve potential endogenous problems and corresponding estimation results are shown in columns (3) and (4). To ensure the effectiveness of GMM estimation, we also conduct the FE and POLS estimation as a comparison, which are reported in columns (1) and (2). The validity of GMM estimates is determined by the Sargan test and AR (2) test. The results of the Sargan tests and Arellano-Bond tests are reported on the bottom of Table 3. The Sargan test is performed to examine the effectiveness of the instrument variables used in the GMM models and the null hypothesis of this test assumes that the instrumental variables are valid. The Arellano-Bond test is conducted to verify the existence of second-order autocorrelation in residuals, which is a presumption of the GMM model. The results of Sargan tests reveal that the instruments set is valid and AR(2) test results accept the null hypothesis of no autocorrelation of the second order in residuals, which verifies the validity of GMM estimation. Moreover, Arellano and Bond (1991) concluded that a consistent and reasonable GMM estimator should not be significantly higher than the OLS estimator or significantly lower than the FE estimator. Our results show that most of the GMM estimators are slightly lower than the POLS's and higher than the FE's, which further confirms the effectiveness of our GMM estimation.
As baseline estimation result shows in Table 3, there is a significant U-shaped relationship between urbanization and urban-rural electricity consumption inequality, and the estimated turning point 7 arrives at the urbanization level of 59.27% and 63.54% for columns (3) and (4). This finding indicates that the urban-rural electricity consumption inequality shifts from a downward trend to an upward trend when the urbanization rate is around 60%, which is consistent with our first hypothesis regarding the impact of urbanization on energy equity. It should be noted that the above empirical result is based on the autoregressive distributed lag model (ADL) 8 and its estimated coefficients reflect the short-run effects. Following George Halkos (2013), we further estimate the long-run effects of each independent variable by making the short-run coefficients be divided by the difference between 1 and the coefficient of lagged dependent variable. Because the estimation using GMM models is more accurate and reliable, we just estimate the long-run estimates using the short-run coefficients of first difference GMM and system GMM. The results of long-run effects are reported in columns (5) and (6), and the following discussion is based on the long-run estimates.
The long-run coefficients on urbanization in columns (5) and (6) in Table 3 indicate that there is a significant long-run U-shaped relationship between urbanization and urban-rural electricity consumption inequality. The estimated turning 7 Following traditional literature on Environmental Kuznets Curve (EKC), the formula for calculating the turning point via regression coefficient is as follows: -coefficient of the linear term/(2*coefficient of the squared term). After this calculation has been performed, an exponential transformation of the calculated turning point is needed due to the logarithmic transformation of the variable in the baseline regression. 8 In the standard ADL model, the regressors may include lagged values of the dependent variable and current and lagged values of one or more explanatory variables. For our empirical model in this paper, the number of the lagged terms of independent variables is automatically determined by our setting of the GMM model. Note: Standard errors in parentheses; * * * , * * and * represent significance at the 1%, 5% and 10% levels, respectively point arrives at the urbanization level of around 60% (58.96% and 61.18% for columns (5) and (6), respectively), which is quite similar to the estimated short-run coefficients in Table 3. For this U-shaped relationship, we find evidence of two opposite impacts from the scale effect and efficiency effect emerging in urbanization. The urban environmental transition theory suggests that urbanization in the initial stage promotes the vigorous development of construction industry and energy consumption (Cole et al. 2021), which can be seen as the scale effect. In other words, the scale effect is the pull effect of urbanization to both urban and rural residents' electricity consumption, which can be attributed to that the industrialization in the process of urbanization promotes energy consumption with the development of power equipment manufacturing industry and improved grid systems. However, such scale effect may affect urban and rural energy consumption in different ways. Specifically, in the early course of urbanization, the scale effect is dominant and it has a stronger push to rural electricity consumption than to the urban, which helps to decrease the gap between urban and rural electricity consumption. In line with such idea, the data from the China National Energy Administration shows that rural electricity consumption per capita, especially after 2000, grows much more rapidly than urban. Ecological modernization theory finds that societies come to realize the importance of environmental sustainability, seeking for improved environmental regulations, technological progress and structural change in the mature stage of urbanization (Toke 2022). It suggests that urbanization in the mature stage promotes the sustainable development which has a restraining effect on energy consumption as a result of the population agglomeration, environmental improvement and technological advance, which can be termed as the efficiency effect of urbanization. However, the efficiency effect may be much more prominent in urban areas than rural areas because, in the late course of urbanization, urban environment and resources are burdened with much more pressure caused by the large population inflow. We will further detailedly investigate the scale and efficiency effect to urban and rural electricity consumption in Section 3. There are also several other interesting findings. Firstly, our estimates show that the urban-rural education gap is positively associated with the urban-rural electricity consumption inequality. Individuals from an under-privileged background in rural areas may use less efficient energy resources such as wood; however, as education levels rise, these individuals have the opportunity to replace relatively primitive energy generating fuels with the cleaner energy serviced by an efficient electricity grid. In other words, rural energy users will shift their energy consumption pattern from a high-energy-consumption way to an energy-efficient way when they are better educated, and thus these better educated rural energy users gradually replace their traditional biomass consumption with relatively cleaner electricity consumption, which helps to decrease the urban-rural electricity consumption inequality. Secondly, the infrastructure construction fund is negatively associated with the urban-rural electricity consumption. The intuition behind how the infrastructure construction affects energy consumption is relatively straight forward. By improving the infrastructure construction in the rural grid system, rural energy users will be much more accessible to electricity consumption and then consume more than before. Thirdly, the price index of residential energy is positively related to the urban-rural electricity consumption inequality. For this positive relationship, Nesbakken (1999) found fuels' price was the dominant factor affecting households' energy consumption, so when fuels' price rises, the relatively poorer rural households who are more sensitive to the rising fuels' Note: Standard errors in parentheses; * * * , * * and * represent significance at the 1%, 5% and 10% levels, respectively price will switch to consume more primitive energy. However, for urban energy users, their electricity elasticity of demand is much smaller than the rural counterparts due to their urbanized energy consumption structure and limited access to primitive energy.

Robustness checks
In the following analysis, we will examine whether our baseline findings remain robust to a number of alternative specifications and sample divisions.

Another measurement of electricity inequality
So far, we have measured the urban-rural electricity consumption inequality by the Theil index. Another measurement, the ratio of urban electricity consumption per capita to the rural, is employed to assess whether baseline results remain. The set of the ratio is where e iut and e irt is the urban and rural electricity consumption per capita at times t in province i. In addition, for ratios, some of its logarithmic term is below 0 because some provinces' rural electricity consumption per capita will exceed the urban at a certain time. To better depict the inequality after the rural's outstripping the urban, we take the absolute value of these ratios. Table 4 reports the results of using the ratio of urban electricity consumption per capita to the rural as the dependent variable. The results are generally similar to our baseline results, and the U-shaped relationship between urbanization and urban-rural electricity consumption inequality remains unchanged. Specifically, the estimated turning point is 60.18% in column (1), which quite approximates the baseline estimation.

Other measurements of urbanization
Recall that our model defines urbanization as the ratio of urban population to the rural. Urbanization can also be measured by the ratio of region's urban population to region's total population and the proportion of region's non-agricultural population, which are two popular measurements of urbanization in relevant studies. Additionally, we use province's road network density as another alternative of urbanization. The validity of road density has been verified by many researches on urbanization. For example, Rudel and Richards (1990) found that regions with better traffic were often with more rapid urbanization while less developed transportation system impeded regions' urbanization. Next, we consider whether our baseline results are sensitive to these different measurements of urbanization.
Columns (2)-(4) in Table 4 replace urbanization with the ratio of region's urban population to region's total population, the proportion of region's non-agricultural population and road network density, respectively. Each of the three is based on the system GMM model. The coefficients of columns (2) to (4) show that the U-shaped relationship does not change when we employ different measurements of urbanization.

Sample divisions
Our baseline results imply that the turning point of the U-shaped relationship arrives at the urbanization rate of 60%. To assess how urban-rural electricity consumption inequality changes before and after the turning point, we split sample periods into two parts : 1997-2008 and 2009-2020. The reason why we select the year 2008 as the breakpoint is that some eastern provinces' urbanization rate has approximately reached 60%, which is around the turning point. In addition, this treatment can also ensure that two new samples all have enough observations for our GMM estimation.
Columns (5) and (6) in Table 4 report the results of sample divisions. The coefficient of sample 1997-2008 (column (5)) suggests a significantly negative relationship between urbanization and urban-rural electricity consumption inequality. In contrast, for sample 2009-2020, the relationship is nonsignificant. We suppose that in sample 2009-2020, some eastern provinces' rural electricity consumption per capita outweighs the urban, leading its coefficients being nonsignificant. In other words, urbanization's overall decreasing effect on urban-rural electricity consumption inequality may be vitiated after the relationship between urbanization and urban-rural electricity consumption inequality turning to be positive for some developed eastern provinces. Thus, the results of sample divisions indirectly confirm the U-shaped relationship between urbanization and urban-rural electricity consumption inequality.

Heterogeneity analysis
One might be concerned that unobserved regional heterogeneity might bias our estimates. The regional heterogeneity includes geographical and economic differences between China's provinces. These differences are closely related to energy users' electricity consumption, and impact on urbanization's effect on the urban-rural electricity consumption inequality. We next explore in more detail how the U-shaped relationship responses to the regional heterogeneity.

Geographical differences
Energy users' consumption pattern closely relates to local geographic and climatic features. In the case of China, geographically, the separation between the north and south is defined by the border which runs along the Qingling Mountains from Sichuan through the southern Shaanxi Province eastwards along the Huai River ending in the Pacific. Generally, the south is warmer and wetter in climate than the north. This explains why there is no heating system in southern China. Also, northern China is much richer in coal resources than the south. We suppose these differences in geographic and climatic features might affect locals' daily electricity consumption pattern. We then examine the impact of such geographical division on the relationship between urbanization and urban-rural electricity consumption inequality.
Given that grouped regressions based on the division will cause the loss of observations, this paper takes the varying coefficient model. This model helps to examine how regression coefficients change over regions with different geographical divisions without losing observations. The empirical specification is as follows (11) where, The results are presented in Table 5. Columns (1) and (3) report the short-run estimates, and (2) and (4) report the long-run estimates. They are both based on the system GMM model. The coefficients on urbanization and urbanization 2 imply that the U-shaped relationship remains significant for both the south and north. As the long-run estimates show, northern region's turning point arrives later than the south, specifically, it is around the urbanization rate of 70.95% and the south is around 57.69%. The reason to interpret the different turning points of the south and north is as follows: northern Chinese, especially in the rural, is more used to consuming coals for daily heating and cooking due to northern China's abundant coal supplies. For example, according to the National Energy Administration, more than 90% of northern rural areas still use bulk coals for winter heating in 2017. This means that northern energy users' transformation from the coal-consumption-habit to the electricity-consumptionhabit might be much harder. Besides, backward power facilities of northern rural areas make the transformation more difficult. Southern China, by contrast, has weaker heating demand due to its warmer climate. Also, the relatively developed power facilities of southern rural areas make rural habitats more accessible to electricity consumption.

Economic differences
There are numerous empirical studies show that economic level is an important determinant of residential energy consumption patterns. So it is reasonable to suppose that regions with different economic levels may have differentiated relationship between urbanization and urban-rural electricity consumption inequality. To investigate such heterogeneity of regional economic disparity, we divide China into two regions: the developed east and undeveloped midwest. 9 Based on that division, the developed east includes 12 provinces (areas), and the undeveloped midwest includes 18 provinces (areas). About the empirical specification, we follow the above varying coefficient models Columns (5) and (7) in Table 5 report the short-run estimates, and (6) and (8) report the long-run estimates. As is clear from Table 5, the long-run coefficients show that the U-shaped relationship between urbanization and urban-rural electricity consumption inequality is valid for developed eastern regions; however, for the undeveloped midwest, the relationship is not nonlinear but negative linearly. This difference results from the economic disparity between eastern and midwestern regions. In particular, richer eastern regions' urbanization is much faster than Standard errors in parentheses; * * * , * * and * represent significance at the 1%, 5% and 10% levels, respectively midwestern regions. 10 For the undeveloped midwest, its urbanization has not yet come to the turning point and its urban-rural electricity consumption inequality decreases with the development of urbanization. Meanwhile, for the developed east, the estimated long-run turning point is at the urbanization rate of 57.91%, which is close to our baseline results (60%).
10 According to China's National Bureau of Statistics, in 2018, the urbanization rate of some eastern provinces (Shanghai, Beijing, Tianjin, Guangdong, Jiangsu and Zhejiang) is more than 70%, while it is still below 50% for some western provinces (Yunnan, Gansu and Guizhou).

Extensions
The most important finding so far is that there is a U-shaped relationship between urbanization and urbanrural electricity consumption inequality. However, it is empirically unclear how urbanization impacts on urbanrural electricity consumption inequality and what the mechanism underlying such U-shaped relationship. To address this question, we carry out an analysis introducing the scale effect and efficiency effect. As we mentioned above, the U-shaped relationship can be theoretically explicated by two effects of urbanization: the scale and efficiency effect. Succinctly, the scale effect is the pull effect of urbanization on both urban and rural Fig. 3 The mechanism flowchart residents' electricity consumption, and the efficiency effect helps save electricity consumption by the improved energy efficiency. It should be noted that the two effects might change over the urban and rural due to China's urban-rural dual economic system. 11 About China's urban-rural dual economic system, two comments are in place. First, it limits the free move from the rural to urban by implementing a strict household registration system. Second, it widens the social and economic gap between rural and urban citizens by implementing different disposal mechanisms of resources. 12 According to Wei and Gong (2019), the "two systems" has undergirded not only China's industrialization, but also urbanization and rural-urban dynamics. Therefore, urbanization may have differentiated effects on urban and rural energy consumption pattern. Then, we will analyze the scale and efficiency effect from the rural and urban perspective, independently. The relevant mechanism is shown in Fig. 3.
Firstly, we use electricity consumption per capita as the dependent variable and carry out regressions based on the system GMM for the urban and rural samples. Results are shown in columns (1) and (2) in Table 6, and all estimations pass both Sargan and AR test. The most striking difference between the results of urban and rural samples is the magnitude of coefficients on urbanization. For urban samples, a 1% increase in urbanization rate raises electricity consumption per capita by 16.9%, reported in column (1). The corresponding coefficient for rural samples is 27.8%. This difference implies that there is a more rapid rise in rural electricity consumption along with urbanization. Some examples can be informative: according to the State Statistical Bureau, among 2008 to 2011, the yearly electricity consumption growth rate of rural areas was about 12-14%, while it was about 8.9-11% for urban areas. One way of seeing the difference in magnitude is that the scale effect of rural areas might be much bigger than urban areas and it predominates over the efficiency effect. 11 Kuang (2012) note that China's rural-urban dual society system is instituted by its unique Hukou system. This system causes inequalities in social status between permanent urban and rural residents, and discrimination against rural-to-urban migrants is thus prevalent. 12 Urban education and infrastructure are almost supported by national finance while a considerable part of rural funds is supported by themselves. This differentiated system further results in the urban-rural human capital gap and separates rural industry from urban industry.
To examine such conjecture, this paper will further quantify the scale and efficiency effect, and investigate their specific impacts on urban and rural electricity consumption.
In order to estimate the scale and efficiency effect, we need to find ways to define the two effects at first. For the scale effect, Chang-hong et al. (2006) concluded that the industrialization in the process of urbanization promoted electricity consumption. The reason is that citizens' electricity demand is boosted by the industrialization, especially the development of power equipment manufacturing industry. Meanwhile, power facilities are improved and thus energy users are more accessible to electricity consumption. So we define the scale effect as the industrialization rate, which is estimated as the ratio of industrial production to GDP. For the efficiency effect, it mainly refers to the technical advances and efficiency improvement. We define the efficiency effect as the energy intensity, also known as the ratio of GDP to final energy consumption.
Following the empirical method of Zhang (2019), we introduce urbanization rate's interactions with the industrialization rate and energy intensity to depict shocks of scale and efficiency effect on urban and rural electricity consumption. The empirical specification is where Electricity it is the electricity consumption per capita of region i at time t; Urbanization it is the urbanization rate of region i at time t; I ndustrial it and I ntensity it are the industrial rate and energy intensity, respectively, and their interactions with urbanization are Urbanization it × I ndustrial it and Urbanization it × I ntensity it , which captures the scale and efficiency effect. It represents urban areas if i = 1 and rural areas if i = 2.
Columns (3) and (4) show the results of scale effects for urban and rural areas. As for rural areas, the positive coefficient on the interactions (Urbanization it × Note: Urbanization * Energyintensity is the interaction term between urbanization and energy intensity; Urbanization * I ndustrial is the interaction term between urbanization and industrial rate; Standard errors in parentheses; * * * , * * and * represent significance at the 1%, 5% and 10% levels, respectively. I ndustrial it ) is significant at 1 percent, which is reported in column (4). This estimate points out the fact that the electricity consumption of China's rural energy users increases with the industrialization in the process of urbanization. In contrast, as column (3) shows, the coefficient on the interaction term is nonsignificant. The reason may be that urbanization's pull effect on urban electricity consumption is vitiated by the improving energy efficiency. Another explanation is that with the development of industrialization, urban habitants' lifestyle is gradually transformed into an "industrial mode", which means work takes up more of their time, and thus workers' daily household electricity consumption is reduced. Therefore, the mix of pull and restraining effect eventually leads to the nonsignificant relationship. Columns (5) and (6) in Table 6 report the results of the efficiency effect for urban and rural energy consumption. Overall, it provide evidence in supporting of our second hypothesis. The estimates also show that the efficiency effect on urban and rural electricity consumption is different. In the case of urban electricity consumption, the coefficient on the interaction (Urbanization it × I ntensity it ) is significantly negative. However, for rural electricity consumption, such relationship is nonsignificant. The reason may be that the efficiency effect might be lagged due to the level of rural modernization has lagged far behind the level of industrialization and urbanization (Zheng 2018). The main focus of current rural energy system construction is still on eliminating energy poverty, and the government still keeps increasing the investment on construction of the power grid and other energy infrastructure. In contrast, research done by Liu (2009) suggests that the enhancement of energy efficiency coupled with the acceleration of the process of urbanization could help in sustainable development, and such energy efficiency effect plays an important role in decreasing urban residential energy consumption at the aggregate level. This finding is consistent with our third hypothesis regarding the efficiency effect of urbanization. As discussed above, the scale and efficiency effect change over urban and rural areas. We believe that the scale effect, especially the scale effect of rural areas, is dominant before the turning point. Thus, urban-rural electricity consumption inequality is decreasing at this stage. After the turning point, the negative efficiency effect of urban areas causes electricity consumption drop off. However, at the same time, rural areas' electricity consumption keeps increasing. Eventually, the rural electricity consumption of some provinces exceeds the urban. That interaction of scale and efficiency effect is probably a mechanism for the Ushaped relationship between urbanization and urban-rural electricity consumption inequality.

Conclusions
This paper focuses on exploring the impact of the urbanization on energy equity from an urban-rural perspective. The baseline results of this paper demonstrate that a longrun U-shaped relationship exists between urbanization and urban-rural electricity consumption inequality, and the estimated turning point arrives at the urbanization level of around 60%. This result is consistent with the findings of the research on the relationship between urbanization and energy consumption, which finds that the impact of urbanization on energy consumption tends to vary greatly across regions in different urbanization stages (Shahbaz et al. 2020;Papavasileiou 2020). Besides, our findings also accord with the classic Environmental Kuznets Curve (EKC) hypothesis that there is a nonlinear relationship between economic development and energy-related environmental problems ). In addition, our mechanism analysis finds that at the early stage of urbanization, the urbanrural energy inequality will be narrowed due to the stronger scale effect of urbanization in rural areas. This supports the urban environmental transition theory which finds that urbanization in the initial stage promotes the vigorous development of construction industry and energy consumption and then become the main socio-economic driving forces of energy inequality between urban and rural areas (Sikder et al. 2022). Our mechanism analysis also finds that at the later stage of urbanization, the urban-rural energy inequality will be enlarged as a result of a prominent efficiency effect of urbanization on urban electricity consumption. This is consistent with the ecological modernization theory which emphasizes that although urban energy-related environmental problems may increase at the early stage, further modernization can minimize such problems, as societies come to realize the importance of environmental sustainability, seeking for improved environmental regulations, technological progress and structural change along with urbanization (Liu et al. 2018). In summary, the results in our study could be comparable with the previous findings arguing that the impact of urbanization on energy consumption tends to vary greatly across regions in different urbanization stages.
The above findings also provide some important policy implications. First, the energy policy should be a dynamic policy which could be adaptive to varied regions and development stages. Specifically, the future policy preference for developing nations where rapid urbanization and industrialization is occurring should be given more to improve rural habitats' accessibility to modern energy service, which helps to relieve the gap between rural and urban development. Given the unbalanced development across different provinces, China should continue to consolidate energy infrastructure construction in the undeveloped regions. Second, in the long term, the seeking for environmental sustainability requires improved environmental regulations, technological progress and structural change along with urbanization. To meet energy users' long-term demand for more efficient energy at the later stage of urbanization, it is greatly important that developed nations should build sustainable energy infrastructure systems and improve their efficient use. It is also critical for all nations to formulate appropriate energy policies to promote energy efficiency and to accelerate the switch to low carbon energy, decoupling environmental impact from economic growth in the longer run. Third, the fact that energy equity is also closely related to educational attainment and fuels' price reminds policymakers that the design of energy policy should incorporate other policy packages. In this way, these integrated sub-policies support and complement each other to realize the policy objective. For example, the government should enhance the energy-related knowledge of energy users to adopt modern energy for consumption. Besides, fuels' price is the dominant factor affecting households' energy consumption, so policymakers could regulate energy users' consumption structure by employing some price-oriented policies.
Although the results in our study could be comparable with the previous findings, however, this research has certain drawbacks. First, the transformation of energy use is a complicated process which is influenced by many factors, and the form of urban expansion, urban density, urban population structure are yet to be included. While these may also potentially influence energy use and emissions, their inclusion is beyond the scope of the current paper. Future research considering these and other factors would then help advance the knowledge of urbanization impacts. Second, this paper evaluated the relationship between urbanization and energy equity merely from the perspective of electricity consumption. However, the indicator system for the energy equity can be improved and the results will be more reliable if future research is built in other perspectives. Third, this study used provincial data and could only provide insights into practice at the level of provincial areas and could not be refined at the municipal level. One possible direction for future work is to use more detailed county data, even micro-data to study the urban-rural gap.