Urban population density and energy conservation: Empirical evidence from 276 cities in China

Abstract

Reducing urban energy consumption is a crucial step towards achieving sustainable urban development. Urban energy plays a fundamental role in urban development, and while previous studies have examined the relationship between population size and energy conservation, the impact of increasing population density on per capita energy consumption (PCEC) remains unclear. To achieve urban energy conservation in China, it is vital to comprehend this significant relationship. This study constructs a spatial regression model to examine the relationship between population density and PCEC using 9 years of balanced panel data from 276 cities to fill a gap in the literature. The results of spatial autocorrelation indicate a significant negative relationship and heterogeneity between population density and PCEC. The results of spatial regression show that for every 1% increase in population density, there is a subsequent increase in PCEC of 0.074%. Our findings suggest that lower PCEC correlation is associated with higher urban population density. This study can be a reference for policymakers seeking new energy conservation strategies for urban development.

1. Introduction

The United Nations established 17 goals in 2015 to bring about global transformation at the Sustainable Development Summit. The General Assembly recognized that energy consumption is responsible for 60% of global greenhouse gas emissions and is the primary contributor to climate change. Comprehending the energy consumption dynamics at the macro level of cities, minimizing energy waste, and establishing sustainable development goals for energy consumption in cities are crucial given that clean energy sources cannot fully replace fossil fuels in the short term. The sustainable development of cities heavily relies on energy conservation and secondary energy use, leading to a reduction in energy consumption and environmental pollution [1,2]. Therefore, reducing the energy consumption of cities is a crucial step toward achieving sustainable urban development.

Energy consumption is increasing steadily alongside China's growing economy and improved living standards. Pollutants from energy consumption are a serious obstacle to sustainable urban development [3]. From 2000 to 2020, China's total energy consumption nearly tripled from 1.409 billion tons of standard coal to 4.557 billion tons. The per capita energy consumption (PCEC), which increased from 1.16 tons to 3.53 tons, has also more than tripled. As of 2020, while China's GDP and energy production growth rates decrease yearly, energy consumption increases. China is a major energy-consuming and carbon-emitting country, due to its heavy reliance on coal [4]. It accounts for approximately 30% of global energy-related carbon monoxide emissions, while the United States only accounts for 15% [5]. In terms of energy conversion efficiency, China's total has increased from 65% to 73.7%; power and heat generation efficiency increased from 36% (in1980) to 46.2% (in 2020). 50% of China's electricity is produced using coal-fired thermal power plants [6]. While fossil and hydro energy have high conversion efficiencies [7], thermal power generation conversion efficiencies only reach 40–50% at best. The energy produced by traditional fossil and nuclear energy used since the industrial revolution is obtained from within the Earth system that is subject to entropy increase in line with the second law of thermodynamics [8]. The consequence is that the burning of fossil and nuclear energy produces carbon dioxide and methane, which further contributes to environmental pollution and atmospheric warming. Although nuclear energy is supposedly less polluting than traditional fossil energy sources [9], it is expensive [10], has high risks, and utilizes limited modern technology. Replacing traditional fossil and nuclear energy with solar energy is difficult economically and technically. Open systems get their energy from the sun, while closed systems get their fossil energy from inside the earth. From a scientific perspective, the industrial revolution introduced a truly revolutionary feature - a significant transition from an open system, primarily reliant on external solar energy, to a closed system driven by internal fossil fuels. This fundamental shift had crucial thermodynamic implications as it adhered strictly to the second law of thermodynamics, necessitating a continuous increase in entropy within a closed system. It can be seen as an ‘upgrade’ from an external, dependable, and sustainable energy source to an internal, unpredictable, and volatile one. A fundamental change to environmental pollution and atmospheric warming caused by fossil fuels and nuclear energy requires a modern energy systems shift from internal closure to external openness. Until then, energy conservation needs to be a major strategy for China to mitigate increasing energy consumption demand [11,12].

According to recent data, China's urbanization rate has risen from 10.64% in 1949 to 63.89% in 2020. This marks a significant milestone as, for the first time since 2007, over half of China's population now resides in cities of varying sizes. Studies show that energy consumption is more concentrated in large cities or megacities and that factors such as urban scale efficiency, technology, and policy can reduce regional energy intensity [13,14]. Smaller cities are less energy efficient and consume more energy. Therefore, the energy consumption patterns differ depending on the urban scale [15,16]. Several studies have explored the scale effects of population on per capita energy consumption, primarily focusing on population size. However, there is a lack of research on the impact of population density on energy consumption. Due to the spatial variability in population density in different cities, few studies have been conducted to characterize population density and PCEC. Therefore, analyzing how population density affects PCEC in different cities is relevant.

2. Literature review

In recent years, scholars from various fields, including individual behavior and urban planning, have been studying how energy conservation can improve energy intensity and efficiency at both micro and macro levels. This research aims to promote sustainable urban development [17]. Sodiq et al. [18] further emphasized the importance of energy efficiency in sustainable cities, as it helps reduce external dependencies in the energy sector and overall energy consumption. Wu et al. [19] studied the relationship between Internet development and green total factor energy efficiency in China and showed a positive relationship between Internet development and green total factor energy efficiency. Paramati et al. [20] studied the impact of environmental technologies on energy efficiency in 28 countries and found that environmental technologies remarkably reduced energy consumption. Pham et al. [21] proposed a random forest prediction model to predict the energy consumption patterns of buildings. This prediction model can provide energy conservation strategies for building managers. Ko [22] studied the effect of building vegetation on building energy efficiency and found that vegetation significantly reduced building cooling energy and thermal energy consumption. Previous studies have extensively investigated the effects of energy conservation from various angles, including technology, environment, and urban planning. However, a study on energy consumption at the city level indicated that the rise in population and economic growth are the primary drivers of increased energy consumption [23]. Currently, numerous scholars focus on studying the dynamics of urban macro-systems. Their main objective is to understand how social factors, such as population and economy, impact the sustainable development of cities. To advance the research paradigm of urban science, a quantitative approach is adopted to overcome the complex and diverse nature of urban systems. This approach aims to further investigate the existence of a universal and unique urban law or theory [8].

As the population increases, what is the future trend in urban energy consumption? In a multifaceted study of the relationship between population, energy, and other urban elements, Holdren [24] argues that most of the world's population does not have access to adequate energy to meet basic needs. The monetary cost of energy is rising widely, as is the environmental impact of energy supply, becoming a local, regional, and global environmental issue. With the recent rise of low-carbon policies and the increasing national focus on the environment, carbon emissions have become a mainstream trend in studying population and energy consumption. Muhammad [25] studied the relationship between energy consumption and CO2 emissions in 68 countries, showing that CO2 increases as energy consumption increases. Ohlan [26] studied the effect of population density, energy consumption, economic growth, and trade openness on carbon dioxide emissions in India using an autoregressive distributed lagged bounds test for cointegration. The results show a meaningful long-run positive relationship between socio-economic factors and carbon dioxide emissions. Khan et al. [27] used time series data to study the effect between energy consumption and carbon dioxide emissions in Pakistan; they show that Pakistan's carbon dioxide emissions positively correlate with economic growth and energy consumption.

Studies on the dichotomy between population and energy reveal different results. Mazur [28]; Komal and Abbas [29] argue that industrial expansion and population growth increase energy consumption. As energy consumption increases, cities will also emit more pollution. Thus, research on the impact of urban environments on energy consumption is initiated. Woo et al. [30] and Ji et al. [31] argue that the urban microclimate leads to changes in energy consumption. Literature on quantifying temperature changes caused by urban environments and assessing the impact of building energy consumption is limited. Through a mathematical approach, Li et al. [32] find that the heat island effect leads to a median decrease in heating energy consumption by 18.7% and a median increase in cooling energy consumption by 19.0%. In 2022, Singh and Sharston [33] proposed a statistical method to estimate the heat island effect on building energy consumption in the inner city and its relationship to the weather. They show that the heat island effect in hot climates increases annual energy consumption in buildings, while in cold climates, energy consumption decreases.

Conversely, some studies argue that population growth reduces energy consumption because of the city's science and technology [34,35], economic structure [36,37], energy efficiency [38,39], and income [40]. Chun-sheng et al. [41] analyze the quantity and structure of energy consumption in urban and rural areas based on a questionnaire survey and compare the environmental impacts of energy use in both areas. They conclude that population size and income factors promote energy consumption in urban areas. Using an econometric approach, Hu and Fan [42] studied the relationship between urban size and energy use. The results show that per capita energy consumption is observed to be increasing in cities with a population size of less than 1 million, while it is decreasing in cities with a population size of more than 1 million.

The relationship between urban population and energy consumption has been extensively studied. These studies have often revealed positive, negative, and combined relationships when examining the impact of city size, urban land use, and the urban environment on energy consumption. Similarly, the impact of energy consumption on the urban environment has also been explored. However, there is a limited amount of research focused specifically on the relationship between population density and its impact on PCEC (an important indicator reflecting urban population distribution). Population density is mainly used as an explanatory variable in studies on the urban environment and economic development, such as those on the impact of population density on carbon emissions [43,44] air pollution [[45], [46], [47]] and economic development [48]. Population density and energy consumption are often introduced as multiple elements in urban studies, but there is also a mutual influence between the two. Some believe that increasing population density reduces energy consumption. Otsuka [49] uses an econometric approach to study the effect of city and rural population density on energy consumption in Japan and shows that, in general, a more clustered population leads to more energy savings. They reveal that population clustering lowers energy consumption in metropolitan areas, while the dispersed population in rural areas leads to higher energy consumption. Other scholars believe that the higher the population density, the higher the energy consumption. Zarco-Periñán et al. [50] studied the relationship between population density and energy using 50,000 households in Siban and showed that a higher population density raises energy consumption. Using the Population, Affluence, and Technology model, Muzayanah et al. [51] examine the effect of population density on provincial energy, electricity, and fuel consumption in Indonesia. The results show that population density reduces total energy, electricity, and fuel consumption. Thus, the effect of population density on energy consumption is unclear, and the two do not have a clear positive or negative relationship.

This study aims to enrich research into the effect of population density on PCEC factors by examining the effect of urban population density and PCEC in 276 Chinese municipal districts of prefecture-level and above. It attempts to clarify whether the expansion of urban population density in China under current conditions reduces PCEC. We then discuss the spatial relationships and linear effects of urban population density on PCEC, ultimately aiming for reference implications for energy conservation and stable development of cities in Chinese from the perspective of population density. The current literature lacks extensive studies on the impact of population density on energy consumption, with limited use of regression models for analysis. Our contribution stands out due to our large sample size (276 cities) and long time span (9 years).

3. Data and methods

3.1. Data collection

We used 276 prefecture-level municipal districts in China as the study units. Data are obtained from the China Statistical Yearbook and the China City Statistical Yearbook. We also use the Statistical Yearbook of each province and city and the annual statistical bulletin of each city to search for missing data. As for the few missing years, we take linear interpolation to supplement the data. The landscape data for constructed land was obtained from Landsat's annual land cover product (https://zenodo.org/record/5816591#.Y4tSTBZByMp). The population density data for the study was calculated from satellite remote sensing data, i.e., the ratio of resident population to built-up land area in the municipal area.

3.2. Research framework

The following are the main elements in the research framework we constructed (Fig. 1). First, to identify PCEC clusters and outlier locations, we show the spatial distribution characteristics and spatial autocorrelation results of PCEC. Then, we analyze the distribution difference pattern of population density. Next, we build a regression model for the effect of population density on PCEC, with PCEC and population density as the dependent and explanatory variables, respectively. To avoid missing variables, we selected six control variables. To analyze the relationship between population density and PCEC, we compared four models: ordinary least squares (OLS), spatial lag model (SLM), spatial error model (SEM), and spatial Durbin model (SDM). Our analysis considered three main components: significance, direction, and intensity. After comparing the results, we determined the best-fit and discussed the findings.

Fig. 1.

Research framework.

3.3. Variable selection

3.3.1. Dependent variable: PCEC

Using relevant literature, we have chosen the PCEC in the municipal area as our dependent variable. Our analysis divides energy consumption into three categories: society-wide electricity consumption, gas, and liquefied petroleum gas (LPG). We have excluded cities that lack society-wide electricity consumption, but have retained those without gas and LPG, since the share of society-wide electricity consumption in urban energy consumption is substantial. Liquefied petroleum gas and natural gas are not the main sources of energy for a city, while electricity consumption is the main energy consumption of a city. And we exclude a small number of cities, which has a negligible effect on the results. To calculate the total energy consumption of electricity, gas, and LPG, we utilize conversion coefficients from the China Energy Statistics Yearbook (Table 1). The PCEC can be calculated using the standard coal conversion factor by using Eq. (1):

$$Pce{c}_{it}=\frac{E{y}_{it}\times 0.1299+C{g}_{it}\times 1.33+Lp{g}_{it}\times 1.7143}{R{P}_{it}}$$ (1)

where, Pcec is the PCEC, Ey is the electricity consumption, Cg is the gas consumption, Lpg is the LPG consumption, and Rp is the total resident population in the municipal area. i denotes different prefecture-level cities and t denotes the year.

Table 1.

Reference coefficients for various energy sources converted to standard coal.

Types of energy	The discount factor for standard coal
Electricity	0.1229 kgce/kWh
Liquefied petroleum gas	1.7143 kgce/kg
Gas	1.330kgce/cu.m

Note: The reference coefficient in energy discounted standard coal is from the China Energy Statistical Yearbook.

3.3.2. Explanatory variable: urban population density

Previous studies on population density in prefecture-level cities were limited by the lack of data on the area of construction land. The City Statistical Yearbook only provides information on construction land in municipal districts, leaving out data for prefecture-level cities. In order to overcome this limitation, we utilized satellite remote sensing data to extract the construction land of prefecture-level cities, thus improving the accuracy of the calculated population density. Population density is expressed as equation (2):

$$P{d}_{it}=\frac{Pop{u}_{it}\times Ur{b}_{it}}{Con{s}_{it}}$$ (2)

where Pd is the population density, popu is the resident population of the prefecture-level city, Urb is the urbanization rate, and Cons is the construction land of the prefecture-level city. i denotes different prefecture-level cities and t denotes the year.

3.3.3. Control variables

Drawing on previous studies, we mainly consider economic-related variables that affect PCEC to enhance the model's credibility. We use per capita GDP to express the per capita economic level. Some studies have concluded that per capita GDP and energy consumption are positively related [52]. Research has demonstrated the correlation between population income and energy consumption. The average wage of urban unit workers on duty (AVWAG) serves as a measure of the overall income level of the population. Generally, higher income levels are associated with increased purchase of household appliances and subsequent energy consumption [53]. Total retail sales of social consumer goods (TRSCG) are a direct representation of domestic consumption demand. Increased consumption can lead to the purchase of energy-consuming appliances and other bulk goods, thereby positively impacting energy consumption [54]. As energy demand primarily comes from the secondary sector, we can measure industrial energy consumption using the proportion of secondary industry value added to GDP (SIGDP). It is worth noting that any increase in the secondary sector will have a positive impact on energy consumption [55,56].

3.4. Research methods

3.4.1. Spatial autocorrelation analysis

The global Moran's I can be analyzed to characterize the overall look spatial distribution of PCEC [57], and the global Moran's I is calculated as Eq. (3) and Eq. (4):

$$I=\frac{\sum _{i=1}^n\sum _{j=1}^n{w}_{ij}\left(x_i-\bar{x}\right)\left(x_j-\bar{x}\right)}{S^2\sum _{i=1}^n\sum _{j=1}^n{w}_{ij}}$$ (3)

$$S^2=\frac{\sum _{i=1}^n{\left(x_i-\bar{x}\right)}^2}{n}$$ (4)

where I is the global Moran index; x_i (x_j) is the PCEC of the i-th (j-th) city, W_ij is the spatial weight matrix of different cities, and the distance between cities is set to 1 within the threshold distance and 0 above that distance. The Z value can determine the degree of spatial clustering of PCEC. The expression for the value of Z is Eq. (5):

$$Z\left(I\right)=\frac{I-E\left(I\right)}{\sqrt{Var\left(I\right)}}$$ (5)

where Var(I) denotes the number of variances, and E(I) is the mathematical expectation of urban PCEC. A larger absolute value of Z indicates a more significant positive (negative) spatial positive (negative) correlation of urban PCEC. The closer the absolute value of Z to zero indicates that the results are not significant, implying that the PCEC is distributed randomly in space.

3.4.2. Ordinary least squares

For the purpose of comparative analysis, we utilize four models: SEM, SLM, SDM, and OLS variations and improvements. These models are correlated and based on OLS, allowing us to examine their differences and similarities. OLS requires no covariace between independent variables and does not regard the interaction between PCEC in spatially adjacent cities, so it can be used to analyze the relationship between population density and PCEC [58]. The expression of OLS is Eq. (6):

$$y_{it}={\beta }_j{X}_{it}+{\alpha }_i+{\gamma }_t$$ (6)

Where i is 276 prefecture-level cities, t represents the time series from 2011 to 2019, j denotes the coefficients of different variables.; y is the explanatory variable of the urban PCEC; X is the influencing factor of PCEC; β denotes the regression coefficient of the six influencing factors. α denotes city fixed (CF), γ denotes time fixed (TE).

3.4.3. Spatial regression model

In the SLM, the explanatory variable is influenced by itself or other explanatory variables from the region or surrounding regions. Therefore, the SLM considers the spatial correlation of the dependent variable, which is expressed in this study as the influence of the independent variables of the urban surrounding areas on the urban PCEC [59,60]. The expression of the SLM is Eq. (7):

$$y_{it}=\rho \sum _{j=1}^n{w}_{ij}+{\beta }_j{X}_{it}+{\alpha }_i+{\gamma }_t$$ (7)

where ρ represents the spatial autoregressive coefficient value. W_ij represents the spatial weights.

SEM considers the spatial correlation in the random disturbance term, which is expressed in this study as the effect of the random error on urban PCEC, thus, expressing the correlation in space [61]. The expression of SEM is Eq. (8):

$$y_{it}=\lambda \sum _{j=1}^n{w}_{ij}{\phi }_{it}+{\beta }_j{X}_{it}+{\alpha }_i+{\gamma }_t$$ (8)

where φ is the error term affecting the independent variable in urban PCEC.

SDM is a combined extended form of SDM and SEM, considering both the spatial relationship in the dependent variable and the spatial relationship in the independent variable, that can be interpreted in this paper as the urban PCEC is influenced not only by the PCEC of the neighboring cities but also by the independent variable of the neighboring cities [62], the expression of SEM is Eq. (9):

$$y_{it}=\rho \sum _{j=1}^n{w}_{ij}+\lambda \sum _{j=1}^n{w}_{ij}{\phi }_{it}+{\beta }_j{X}_{it}+{\alpha }_i+{\gamma }_t$$ (9)

In Equation (7), each symbol is similar to the description for Equations (5), (6).

4. Results and discussion

4.1. Spatial variation characteristics in PCEC and population density

The manual breakpoint method divides the PCEC into five classes. In Fig. 2, from 2011 to 2019, the concentration of cities in the first rank decreases, and the other four ranks are increasing year by year, with a smaller increase in the number of cities in the fifth rank.

Fig. 2.

Number of cities corresponding to the per capita energy consumption interval.

Note: In Fig. 2, the years from the inner ring to the outer ring are 2011,2013,2015,2017, and 2019 in that order.

To observe the spatial dispersion in PCEC, we use the manual breakpoint method of ArcGIS 10.7 to visualize the spatial pattern in PCEC (Fig. 3). From 2011 to 2019, PCEC is increasing year by year and shows a clear spatial clustering feature.

Fig. 3.

Spatial variation of PCEC. (a), (b), (c), (d) and (e) represent the spatial distribution of PCEC in 2011, 2013, 2015, 2017 and 2019, respectively.

The PCEC of different cities may affect each other; hence, we use spatial autocorrelation to analyze the distribution characteristics of PCEC. In Table 2, in 2019, the global spatial autocorrelation of PCEC is calculated with Moran's I of −0.025, P = 0.000, and Z value of −10.271. Moran's I was negative from 2011 to 2019 with a significant P value, indicating a negative spatial correlation between PCEC in each year. The analyzed fruits of other years still satisfy the spatial negative correlation feature. In Fig. 4, in 2019, the local Moran value of PCEC is −0.019; the P value is 0.001. The results indicate that neighboring cities may influence the urban PCEC. In addition, in Fig. 4, from 2011 to 2019, the PCEC of various cities are primarily concentrated in the second quadrant (low-high agglomeration area) and the fourth quadrant (high-low agglomeration area). This finding suggests that there are considerable spatial variations in PCEC among cities, indicating significant spatial heterogeneity.

Table 2.

Global autocorrelation results for variables.

Variables	PCEC			Population density
year	I	Z value	P value	I	Z value	P value
2011	−0.015	−5.815	0.000	−0.193	−92.809	0.000
2013	−0.017	−6.525	0.000	−0.207	−100.020	0.000
2015	−0.017	−6.765	0.000	−2.00	−96.580	0.000
2017	−0.019	−7.325	0.000	−0.199	−95.824	0.000
2019	−0.025	−10.271	0.000	−0.203	−97.759	0.000

Fig. 4.

Local Moran scatters plot of PCEC. (a), (b) and (c) represent localized Moran scatter plots for PCEC in 2011, 2015 and 2019, respectively.

Fig. 5 shows the growth level and population density level of the PECE. The bottom and top of the rectangular box represent the 25th and 75th percentiles, and the horizontal line in the middle of the box is the median line. The upper whisker line represents the maximum value and the lower whisker line represents the minimum value. In Fig. 5, the maximum population density in 2011 exceeds 5000 people per square kilometer and the overall trend in population density is characterized by a slight decrease. On the contrary, the level of energy consumption per capita has an increasing trend and is increasing year by year.

Fig. 5.

PECE and population density description. (a) and (b) represent boxplots of population density and PCEC in 2011, 2013, 2015, 2017 and 2019, respectively.

4.2. The effect of population density on PCEC based on OLS

To study the degree of influence of population density on PCEC and the direction of influence, we construct regression models to analyze the factors influencing PCEC. Before conducting the regression analysis, we perform a multiple covariance test to detect the covariance among the independent variables. Table 3 shows that the variance influence factor values of the independent variables are less than 10, indicating no cointegration between them. In other words, each variable can be included in the regression model.

Table 4.

OLS and its fixed effects results.

	(1)	(2)	(3)
Variables	OLS	CF	TE
lnPD	−0.108***	0.218*	−0.053
	(-5.81)	(1.76)	(-1.48)
lnPEGDP	1.282***	0.583***	0.905***
	(30.14)	(6.79)	(16.45)
SIGDP	−0.029***	−0.032***	−0.001
	(-20.80)	(-20.32)	(-0.52)
lnAVWAG	0.680***	1.332***	0.352***
	(6.34)	(9.71)	(3.25)
lnTRSCG	−0.276***	0.153***	−0.077***
	(-10.80)	(3.96)	(-2.92)
lnGPA	0.089***	−0.005	0.024*
	(5.38)	(-0.27)	(1.72)
Constant	−7.513***	−13.132***	−4.425***
	(-6.91)	(-8.75)	(-4.08)
Observations	2484	2484	2484
R2	0.520	0.465	0.624
Number of city	276	276	276

Note：t-statistics in parentheses, ***, **, and * represent the 0.01, 0.05, and 0.1 significance levels, respectively.

Table 3.

Descriptive statistics for each variable.

Variables	definition	Unit	Min	Max	VIF
lnPCEC	Per capita energy consumption	tce/104 people	3.995	10.85
lnPD	Population density	104 people/square kilometers	−3.332	1.711	1.17
lnPEGDP	Per capita GDP	yuan/person	8.773	12.15	2.64
SIGDP	Secondary industry value added as a proportion of GDP	%	6.330	89.34	1.48
lnAVWAG	Average wage of urban unit workers on duty	yuan/person	9.753	11.45	2.10
lnTRSCG	Total retail sales of social consumer goods	104 yuan	5.367	18.71	3.76
lnGPA	Green patent acquisition	pcs	0	8.844	4.21

The results in Table 4 show that the estimated coefficient from the estimated urban population density is negative, indicating that the increase in urban size has a negative effect on energy intensity. Hence, as the population density increases, PCEC decreases. The results indicate that for every 1% increase in population density, PCEC decreases by 0.121%.

4.3. The effect of population density on PCEC based on a spatial regression model

Previous econometric models do not consider the location information in the variables when analyzing population density on PCEC. However, we introduce spatial weights to the variables, OLS, SEM, SLM, and SDM model analysis with Stata software and then select the best-fit. The weights are constructed using the fixed distance method, with the distance threshold set at 350 km. Table 5 shows that the R² of SDM is significantly larger than that of OLS, SLM, and SEM, indicating that SDM fits best.

Table 5.

Comparison of OLS, SLM, SEM, and SDM.

	(4)	(5)	(6)
Variables	SLM	SEM	SDM
lnPD	−0.029*	−0.056***	−0.034**
	(-1.73)	(-2.63)	(-2.05)
lnPEGDP	1.085***	1.169***	1.115***
	(29.00)	(29.43)	(30.30)
SIGDP	0.005***	0.005***	0.005**
	(2.77)	(2.63)	(2.49)
lnAVWAG	0.235**	0.288***	0.265***
	(2.52)	(2.90)	(2.86)
lnTRSCG	−0.266***	−0.234***	−0.271***
	(-12.06)	(-10.00)	(-12.28)
lnGPA	0.116***	0.116***	0.113***
	(8.09)	(8.03)	(7.86)
Observations	2484	2484	2484
R2	0.298	0.370	0.422
Number of city	276	276	276

Note：t-statistics in parentheses, ***, **, and * represent the 0.01, 0.05, and 0.1 significance levels, respectively.

Table 5 illustrates the results of SDM. Population density has a negative effect on PCEC, indicating that for every 1% increase in population density, PCEC decreases by 0.039%. Comparing the model results reveals that the model fit of SDM is better than OLS, and the population density has the same direction of influence on energy consumption. This indicates that the PCEC decreases as the population becomes more concentrated, primarily due to the agglomeration benefits of the city, energy efficiency, technological development, and energy policies. In Table 5, the effect of population density on PCEC is significant. In addition, Per capita GDP, SIGDP, and Green patent acquisition have a significance of less than 0.05, indicating that the selected indicators are reliable. Per capita GDP, SIGDP, AVWAG, and Green patent acquisition positively affect PCEC.

4.4. Robustness test

First, by using four models of OLS, SLM, SEM, and SDM select Euclidean distance as the spatial weight matrix. To ensure the reliability of the results, we use SDM as a base and select other matrices to test the robustness of the results, which are the adjacency matrix, the inverse distance matrix, and the inverse distance square matrix. The population density coefficients of adjacency matrix, the inverse distance matrix, and the inverse distance square matrix are −0.048, −0.038, and −0.029. The coefficients are in the same direction compared to the population density coefficients of the Euclidean distance, indicating that the results of the study are robust.

Second, we perform the analysis using a reduced sample. We eliminate all cities located in land border provinces; hence, the number of cities is reduced from 276 to 215. The coefficients of OLS, SLM, SEM, and SDM are −1.01, −0.044, −0.053, and −0.054, respectively, and the R² of SDM is higher than OLS, SLM, and SEM. The results show that SDM is still a better fit than OLS, SLM, and SEM, and population density has a significant negative effect on PCEC. In the model comparison between 276 and 215 cities, the control variables of both have the same direction of influence on PCEC, which verifies the robustness of the study's results. In conclusion, both tests prove that the choice of SDM is robust.

4.5. Discussion

The spatial distribution characteristics show that PCEC in the eastern coastal region are generally higher than those in other regions, which is consistent with China's eastern region's developed economy and concentrated population. All factors are correlated and closely related [63]. The spatial autocorrelation analysis shows that PCEC has significant spatial clustering characteristics, indicating that the high PCEC of cities may be related to the PCEC of neighboring cities.

The study identified six independent variables that influence urban PCEC and developed a research framework and regression model. The models compared were OLS, SLM, SEM, and SDM, with SDM being determined as the best-fit. The results of the best-fit indicate that spatial errors and spatial lag can impact regression results when analyzing the influencing factors of urban PCEC. Furthermore, the SDM model better aligns with theoretical expectations compared to the traditional linear regression model. The spatial regression model includes a spatial weight matrix, whereas the general linear regression model does not. The findings from the analysis of global spatial autocorrelation and local spatial autocorrelation indicate that the presence of negative spatial correlation in PCEC does not necessarily imply negative spatial correlation between population density and PCEC. Therefore, the SDM model aligns better with the theoretical expectation.

According to the SDM model results, there is a negative correlation between population density and PCEC. This means that as population density increases, the amount of PCEC required decreases. This is because compact urban layouts, which are often found in high-density cities, require less PCEC. Additionally, an increase in urban population density can lead to agglomeration effects, as noted in previous studies [64,65]. Compact cities also have the added benefit of being more energy-efficient [66]. Per capita GDP, SIGDP, AVWAG, and TRSCG are the four control variables that positively affect PCEC. SIGDP denotes the contribution of industry to economic development, and since energy consumption mainly comes from the secondary sector, the positive coefficient of SIGDP aligns with theoretical expectations [67]. Based on previous findings and research theories, there are four main theories and hypotheses on the relationship between energy consumption and economic growth: the growth hypothesis (which suggests a positive relationship between energy consumption and economic growth), unidirectional causality, bidirectional causality, and a neutral relationship between energy use and economic growth [68]. These studies discuss the general contribution of a single amount of energy consumption (electricity, oil, coal, natural gas, etc.) versus aggregate energy to economic growth. Our results indicate that GDP per capita has a positive effect on energy consumption per capita (energy consumption per capita in aggregate), which supports the growth hypothesis of energy consumption. The positive impact of AVWAG on PCEC may be attributed to the higher living standards and increased consumption potential of residents, which aligns with the theoretical expectations of Román-Collado and Colinet [69]. Our findings at the municipal level indicate a positive relationship, where green innovation leads to an increase in energy consumption per capita. In contrast, Jiang et al. [70] conducted a study using both firm and provincial levels and found that energy consumption promotes green innovation, while green innovation reduces energy consumption. However, it is important to note that green innovation technologies in China are still in the developmental stage, which may explain the insignificant effect of these technologies in reducing energy consumption [71]. Additionally, it is worth mentioning that the results of our study only explain the positive impact of total green patent acquisition on per capita energy consumption, as obtaining accurate data on green energy patents at the municipal level is challenging.

This study has some limitations. First, determining the high and low intervals of population density and PCEC was challenging due to the lack of strict criteria. Therefore, the natural breakpoint method was used for ranking. Second, data for a few cities were difficult to obtain, resulting in their exclusion from the SDM. Third, the study only examines six variables, despite the complex and diverse factors that affect PCEC. Future research should approach the influencing factors from a different perspective. Fourth, the study's findings only demonstrate a correlation between population density and PCEC - cities with higher population densities have lower PCEC. This correlation should be interpreted with caution, as it is only marginally significant. The study does not offer a precise explanation for the observed effect, and determining a reasonable range of population density is not feasible. It is important to note that accurately determining the exact effect of population density on PCEC is challenging due to the involvement of multiple variables. The impact of population density on PCEC is believed to be non-linear, meaning that there is a turning point where the PCEC either decreases or increases. However, factors such as city size, socio-economics, and other variables make it difficult to identify this non-linear effect across a large number of different cities. Therefore, it is not feasible to determine a precise and reasonable population density.

The current results suggest that in order to address the issue of PCEC in future urban constructions, relevant authorities should focus on building compact cities and strictly controlling the expansion of construction land to increase urban population density. Future research could comprehensively examine this problem and identify the optimal population density range to provide practical and effective policy guidance for urban energy consumption using specific power mechanism data.

5. Conclusions and policy implications

5.1. Conclusions

This study examines the impact of population density on PCEC in 276 Chinese cities by analyzing the direction and intensity of the influence. A spatial regression model is constructed using one explanatory variable and six control variables from nine years of balanced panel data. Unlike general regression models, spatial regression enables us to explore the spatial perspective of the impact of population density on PCEC and adding the distance factor to enrich the model. The results show that cities with higher population density have an advantage over cities with lower population density in terms of energy consumption and energy conservation potential.

The PCEC has significant spatial autocorrelation characteristics, suggesting that the PCEC of neighboring cities impacts the PCEC of cities. SDM is used to analyze the relationship between population density and PCEC. The SDM model results indicate a significant negative relationship between population density and PCEC. In addition, TRSCG negatively affect PCEC, which aligns with theoretical expectations.

5.2. Policy implications

This study has important policy implications. It suggests that cities should avoid disorderly expansion of construction land to mitigate negative effects. Increasing the population density of cities without expanding urban land construction to increase the economic growth rate leads to the waste of construction land and energy use. Therefore, relevant policies can reasonably control the expansion of municipal building land and bring energy conservation benefits to the city from a density perspective. Second, one potential solution is to build compact cities. Urban compactness can improve traffic and energy accessibility within the city limits. Additionally, developing three-dimensional cities (High-rise buildings, underground buildings) and increasing plot volume ratio can expand the population capacity per unit area, resulting in energy-saving benefits. it is crucial to enhance the capacity of energy infrastructure and introduce advanced energy conservation products to ensure sufficient energy supply in densely populated cities.

Data availability statement

The data that support the findings of this study are available in [Academic Exchange Platform for Urban Livability, Housing and Sustainablity] at [http://39.108.95.102:2233/teamen.html].

CRediT authorship contribution statement

Yang Wang: Writing – review & editing, Writing – original draft, Funding acquisition, Conceptualization. Guiquan Sun: Writing – original draft, Visualization, Methodology, Investigation, Data curation. Yingmei Wu: Supervision, Formal analysis. Shaojian Wang: Project administration, Methodology. Xiaoli Yue: Validation, Software, Resources. Hong'ou Zhang: Project administration, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.