Evaluating and Optimizing Residential Electricity Price Tiers Considering Income Redistribution Equity Under Cross-Subsidies Mechanisms

Abstract

The inequitable redistribution of electricity price cross-subsidies constitutes a critical issue, as it compromises the implementation efficiency of tiered electricity pricing (TEP) policies and impedes the equalization of basic public services in the power sector. Drawing on residential TEP data from Hebei Province spanning 2016 to 2020, this paper employs the Gini coefficient method and reveals that high-income residential users receive substantially larger electricity price cross-subsidies than their low-income counterparts. Overall, the degree of such inequality has been rising annually. Furthermore, both high-income and low-income groups exhibit greater inequity in subsidy allocation relative to the middle-income group. Against this backdrop, this paper proposes a more rational tiering framework for TEP by adopting the rank-sum ratio (RSR) method, thereby identifying a viable pathway for residential users across all income brackets to share electricity costs equitably. This research contributes to the sound management of electricity price cross-subsidies, mitigates the inequity in subsidy distribution, and guides residents toward rational electricity consumption behaviors.

1. Introduction

The current TEP policy not only effectively enhances residents’ energy-saving awareness—with more pronounced energy-saving behaviors among high-income groups—but also facilitates the rational allocation of power resources to a certain extent. Furthermore, the electricity price cross-subsidy policy alleviates the financial burden of residential electricity consumption and ensures access to basic electricity for ordinary residents, thereby safeguarding their essential energy needs [1,2,3,4].

However, electricity price cross-subsidization exhibits issues of inequitable distribution, an excessively large scale, and uneven allocation, which undermine energy conservation efforts [5]. Sun et al. [6] note that the current subsidy policy suffers from insufficient precision and targeting, meaning that low-income groups, the most subsidy-needy population, fail to receive the financial support to which they are entitled. Li et al. [7] and Li et al. [8] have identified that in developing countries, inequities in cross-subsidization lead to poorer-quality electricity public services for low-income residents, whereas high-income households tend to access higher-quality service provision. Pu et al. [9] demonstrate that in China, despite a higher overall level of cross-subsidization in the more economically developed eastern regions, the degree of “reasonable cross-subsidization” (i.e., cross-subsidies aligned with policy objectives and social equity) is lower compared to the central and western regions. Sherwin et al. [10] find that while the electricity price subsidy mechanism can raise residents’ living standards by 30%, it also leads to a significant increase in electricity consumption.

To enhance subsidy efficiency and curtail ineffective subsidy allocations, several studies have explored approaches to appropriately address the issue of electricity price cross-subsidization. First, the target population of subsidies must be clearly defined. Lin et al. [11] argue that cross-subsidization should be targeted and tailored to the socioeconomic characteristics of the intended beneficiaries, which not only reduces total subsidy expenditure but also narrows the consumption disparity among different resident groups. Second, cost reduction should be prioritized in policy design. Liu et al. [12] highlight that prior to formulating an electricity price cross-subsidization framework, policymakers must fully consider the subsidy’s target population and scope, accurately calculate and reasonably allocate associated costs, and conduct a comparative analysis with the existing subsidy scheme.

The implementation of a rational tiered pricing mechanism represents the primary challenge to address in the design and operation of a TEP system [13]. The design of scientific tiering must incorporate objective factors including residents’ electricity consumption patterns, household electricity affordability, income distribution, electricity price multipliers, and climatic conditions [14]. Furthermore, the scientific tiering approach must fully reflect distributive equity. In the selection of tiered pricing methods, Wang takes residential income as the basis for grouping and uses the population coverage of each electricity consumption bracket as the criterion for defining electricity consumption tiers [15]. Zhu et al. [16] regard residents’ dissatisfaction as an optimization objective for electricity tiering, while Ci et al. [17] adopt the rank-sum ratio (RSR) method, which classifies electricity consumption tiers based on differences in residential electricity consumption across income groups. Liu et al. [18] estimated the theoretical values of the first and second electricity consumption tiers at both the national and regional levels by constructing counterfactual scenarios and applying the cross-sectional threshold model and Stone–Geary function. With regard to the determination of electricity consumption tiers, Liu et al. [13] theoretically constructed a price optimization model for incremental TEP under the constraint of individual carbon trading. Wu [19] and Liu et al. [20] designed an optimization model for TEP tailored to different policy objectives, employing the method of sufficient statistics and integrating multiple influencing factors. Chu et al. [21] incorporated time-of-use (TOU) electricity pricing into the calculation of TEP, integrated these two-tiered mechanisms, and established an optimal TOU electricity pricing scheme.

In summary, existing studies have proposed TEP categorization approaches to address cross-subsidy issues in TEP, based on residential income, disparities in residential electricity consumption, and policy objectives. However, no studies have explored TEP categorization from the perspective of comprehensively considering disparities in residential electricity consumption and the fairness of income redistribution via cross-subsidization. The 20th National Congress of the Communist Party of China (CPC) emphasized the importance of improving the multi-level social security system and elevating the equalization level of basic public services. As electricity is a basic public good, studying the tiered pricing policy from the perspective of the fairness of income redistribution via cross-subsidization is of great significance for enhancing the equalization level of public power services and advancing the energy revolution.

The remainder of this paper is organized as follows. Section 2 introduces the research methods. It defines the core calculation models, elaborates the fundamental principles of the Dagum Gini coefficient and the rank-sum ratio (RSR) method, and explores the inherent coupling and complementary mechanisms between the two approaches. Section 3 describes the data sources and presents a descriptive analysis. It clarifies the data origins, core variable settings, and calculation criteria. This chapter also uses descriptive statistics to examine temporal trends and group differences in residential electricity consumption and power tariff cross-subsidies. Section 4 conducts an empirical analysis of tiered electricity pricing optimization. It applies the Dagum Gini coefficient to decompose and measure unequal cross-subsidy distribution and to identify key characteristics of allocation imbalance. The rank-sum ratio method then optimizes the tier settings, and multiple tests verify the rationality and equity of the revised scheme. Section 5 discusses the findings. It interprets the formation mechanisms and driving factors of unbalanced cross-subsidy distribution based on the empirical results. This chapter compares the findings with those of previous studies to highlight their theoretical contributions and practical implications. It also acknowledges the research limitations and proposes directions for future exploration. Section 6 draws conclusions and presents policy implications. It summarizes the major research outcomes. Considering winter heating demand and local policy conditions in northern China, this chapter proposes targeted measures to restructure tiered electricity pricing, adjust thresholds dynamically, and improve supporting mechanisms. The results provide scientific insights for the equitable and refined enhancement of residential tiered electricity pricing systems.

2. Research Methods

This study takes residential electricity consumption data from Hebei Province (2016–2020) as a case study, applies the Gini coefficient method to calculate and analyze electricity price cross-subsidization and the income distribution effects among residential users in different income groups. It reveals the trends and causes of unfair income redistribution via cross-subsidization during the implementation of the TEP policy, and proposes a rational TEP categorization approach using the rank-sum ratio (RSR) method. The aim is to identify effective approaches to ensure that various user groups bear electricity costs fairly; finally, the inter-group and intra-group Gini coefficient methods are used to verify whether this categorization approach guarantees the relative fairness of subsidies among different user groups.

2.1. Cross-Subsidy Mechanism

Power market cross-subsidy is an income redistribution mechanism driven by price regulation. Regulators set differentiated electricity tariffs for various user groups. Industrial and commercial users pay tariffs that exceed marginal supply costs, thereby generating surplus revenue. This revenue offsets the structural losses incurred by residential and agricultural users, whose tariffs fall below marginal costs, in order to meet policy objectives such as providing affordable electricity to households.

This study employs the Price-Gap Approach proposed by the International Energy Agency to quantify the income transfer associated with cross-subsidies. Specifically, the method measures the deviations between actual regulated tariffs and cost-reflective benchmark tariffs (i.e., tariffs based on marginal supply costs) to calculate both the absolute amount and the relative intensity of the cross-subsidy.

$$\left\{\begin{array}{l}{S\mathrm{ub}}_{\mathrm{i}}=(M_i-P_i)\times Q_i\\ D{S\mathrm{ub}}_{\mathrm{i}}=(M_i-P_i)/M_i\end{array}\right.$$

(1)

In the above equation, $Su{b}_i$ denotes the amount of cross-subsidization for residential customers, $DSu{b}_i$ denotes the degree of cross-subsidization. A positive $DSu{b}_i$ indicates residential electricity underpricing, meaning that residents receive implicit subsidies. A negative value signifies overpricing, implying that residential users provide subsidies to the power system. Larger absolute values of $DSu{b}_i$ indicate more severe price distortion and a more pronounced redistributive effect of the cross-subsidy mechanism.; $M_i$ denotes the cost of electricity, which is the base price of electricity for residential customers, The benchmark electricity cost (CNY/kWh) comprises the provincial weighted average power purchase price, the regulated transmission and distribution tariff (including integrated line losses) for the corresponding voltage level, and the legally mandated governmental funds and surcharges; $P_i$ denotes the actual price of electricity for residential customers; and $Q_i$ denotes the actual electricity consumption of residential customers.

2.2. Gini Coefficient Method

Power tariff cross-subsidies essentially act as an implicit form of income redistribution. Evaluating their fairness requires quantitative tools that can measure unequal resource allocation. The Dagum Gini coefficient serves as a classic welfare economics method for depicting relative gaps in the distribution of residential subsidies. Researchers have widely applied this indicator to measure disparities in income, property, consumption, and living standards [22].

This indicator possesses distinct theoretical merits that align well with our research scope. First, it maintains solid consistency with fundamental economic theories. Built on the Lorenz curve, the Gini coefficient quantifies inequality by calculating the area ratio between the absolute equality line and the actual distribution curve. Larger distribution gaps correspond to higher Gini values [22,23]. The coefficient ranges from 0 to 1. Values closer to 0 reflect fairer income redistribution from power tariff cross-subsidy policies, while values approaching 1 indicate poorer policy fairness.

Second, the Gini coefficient supports international comparison and standardized evaluation. Major global institutions, including the World Bank and the International Energy Agency, adopt this index to assess the distributional effects of energy subsidies. The United Nations Development Programme (UNDP) sets 0.4 as the warning threshold for income disparity, thereby providing an objective criterion for judging the redistribution fairness of power tariff cross-subsidies.

Third, this method offers strong scalability. Unlike the Theil index, which captures only overall inequality, the Dagum Gini coefficient decomposes total inequality into within-group inequality, between-group inequality, and transvariation [24]. This decomposition allows us to identify the sources and contribution degrees of unfair subsidy distribution across and within power consumption groups. Accordingly, this study applies the Gini coefficient approach to examine inequality in the income redistribution driven by power tariff cross-subsidies.

$$G_T={\displaystyle \frac{{\displaystyle \sum _{j=1}^k{\displaystyle \sum _{h=1}^k{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_h}\left|S{\mathrm{ub}}_{ji}-S{\mathrm{ub}}_{hr}\right|}}}}}{2n^2\overline{Sub}}}$$

(2)

The calculation method of the Gini coefficient is referred to the literature of Dagum [25], as shown in Equation (2). Where $G_T$ is the overall Gini coefficient, n is the number of samples, u denotes the average value of electricity price cross-subsidies enjoyed by all sample users, k denotes the number of groups clustered according to electricity consumption after processing the sample overall, $Su{b}_{ji}$ and $Su{b}_{hr}$ denote the electricity price cross-subsidies enjoyed by any user in groups of j and h (j = 1, 2, …, k, h = 1, 2, …, k), $n_j$ and $n_h$ denote the number of sample users in subgroups j and h.

To further explore the disparities in income redistribution between and within groups, the Gini coefficient can be decomposed as follows:

$$G_{jj}={\displaystyle \frac{\frac{1}{2u_j}{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_j}\left|Su{b}_{ji}-Su{b}_{jr}\right|}}}{n_j^2}}$$

(3)

$$G_{jh}={\displaystyle \frac{{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_h}\left|Su{b}_{ji}-Su{b}_{hr}\right|}}}{n_j{n}_h(\overline{Su{b}_j}+\overline{Su{b}_h})}}$$

(4)

$G_{jj}$ is the intra-subgroup Gini coefficient, denotes the intra-group Gini coefficient when residential electricity consumption is in group j; $G_{jh}$ is the inter-group Gini coefficient, denotes the inter-subgroup Gini coefficient of residential electricity consumption in different groups.

$$\left\{\begin{array}{l}{G}_w={\displaystyle \sum _{j=1}^k{G}_{jj}{p}_j{s}_j}\\ G_{nb}={\displaystyle \sum _{j=2}^k{\displaystyle \sum _{h=1}^{j-1}{G}_{jh}}}(p_j{s}_h+p_h{s}_j)D_{jh}\\ G_t={\displaystyle \sum _{j=2}^k{\displaystyle \sum _{h=1}^{j-1}{G}_{jh}}}(p_j{s}_h+p_h{s}_j)(1-D_{jh})\end{array}\right.$$

(5)

$G_w$ is the contribution of intra-subgroup differences, which represents the distributional gap of electricity price cross-subsidies enjoyed by users in j(h) electricity consumption group. $G_{nb}$ is the difference contribution between groups, $p_j=n_j/n$ is the ratio of the number of sample users in subgroup j to the number of all sample users, and $s_j=n_j{u}_j/nu$ is the ratio of the electricity price cross-subsidies enjoyed by sample users in subgroup j to the electricity price cross-subsidies enjoyed by all sample users. $G_t$ is the ultra-high density contribution rate, reflecting the phenomenon of cross-overlap and reflecting the relative gap situation. Among them:

$$D_{jh}={\displaystyle \frac{d_{jh}-p_{jh}}{d_{jh}+p_{jh}}}$$

(6)

$$\left\{\begin{array}{l}{d}_{jh}={\displaystyle {\int }_0^{\infty }d{F}_j}(y){\displaystyle {\int }_0^y(y-x)}d{F}_h(x)\\ p_{jh}={\displaystyle {\int }_0^{\infty }d{F}_h(y)}{\displaystyle {\int }_0^y(y-x)}d{F}_j(x)\end{array}\right.$$

(7)

$D_{jh}$ is the relative influence between the sample users in groups j and h. $d_{jh}$ represents the weighted average of the absolute value of the positive difference in the degree of cross-subsidy between groups j and h. y(x) in Equation (7) represents the amount of cross-subsidy in group j(h), and F(x) is the cumulative distribution function. $p_{jh}$ represents the weighted average of the absolute value of the negative difference in the degree of cross-subsidy between groups j and h.

2.3. Rank-Sum Ratio Method

The optimal design of power tariff cross-subsidies is a multi-criteria decision-making problem. Policymakers must balance multiple objectives, including fairness, efficiency, and policy feasibility. The rank-sum ratio (RSR) method is a comprehensive non-parametric statistical evaluation tool. This study selects this method based on three theoretical considerations.

First, this approach is well suited to the inherent characteristics of the data distribution. Residential electricity consumption data generally follow a strongly right-skewed distribution. Heterogeneous factors, including income level, climatic conditions, housing area, and consumption habits, lead to substantial differences across individual samples. Conventional parametric statistical methods, such as analysis of variance (ANOVA) and regression models, require data to satisfy normal distribution and homogeneity of variance. In contrast, the RSR method conducts statistical analysis based on rank values and imposes no constraints on the population distribution. It is highly robust to outliers and suits research scenarios characterized by highly heterogeneous residential electricity consumption behaviors [16,17]. Second, this method offers strong capabilities for multi-dimensional comprehensive evaluation. Optimizing electricity pricing tiers requires considering multiple indicators, including power consumption distribution, electricity expense burden ratio, and the Gini coefficient. The rank-sum ratio method converts multi-dimensional indicators into dimensionless rank-sum ratios. It standardizes and integrates indicators with diverse dimensions and attributes, and eliminates biases arising from subjective weight assignment [26]. Third, this method ensures accurate and feasible tier classification. It determines grouping schemes based on the internal structural features of sample data and generates repeatable outcomes. This feature distinguishes it from the analytic hierarchy process and other approaches that rely on subjective expert judgment. This method not only performs sample classification but also ranks tier performance and estimates probabilities [27]. Considering the research object and available data in this study, factors such as income, environmental conditions, electricity expenditure, and consumption habits lead to significant heterogeneity in residential electricity consumption. Therefore, the data conditions in this paper satisfy the requirements for applying the rank-sum ratio method to investigate the optimal number of pricing tiers. The calculation steps of the rank-sum ratio method are as follows:

Step 1 involves selecting relevant indicators. Select indicators that effectively capture variations in residential electricity consumption, as this choice critically affects the accuracy of the final classification.

Step 2 entails calculating the rank of each indicator. In statistics, the rank is an ordinal number, represented by $R_{ij}$, where i is the year (i = 1, 2, …, 5), j is the index (j = 1, 2, …, 5), m represents the total number of years, and n is the total number of indicators. The calculation method is as follows. If an indicator is of the beneficial type, apply Formula (8):

$$R_{ij}=1+(n-1){\displaystyle \frac{X_{ij}-\min \left\{X_j\right\}}{\max \left\{X_j\right\}-\min \left\{X_j\right\}}}$$

(8)

If the indicator is a cost type, apply Formula (9):

$$R_{ij}=1+(n-1){\displaystyle \frac{\max \left\{X_j\right\}-X_{ij}}{\max \left\{X_j\right\}-\min \left\{X_j\right\}}}$$

(9)

Step 3 consists of calculating the rank-sum ratio $RS{R}_{\mathrm{i}}$ based on the ranks obtained, then sorting these ratios in ascending order.

Step 4 involves calculating the frequency of each group, along with the cumulative frequency ${\displaystyle \sum f}$, the average rank $\overline{R}$, and the cumulative frequency distribution P for each group. The cumulative frequency distribution is then converted to derive the probit value: the corresponding probit Y is obtained by consulting a probit table, after which the regression equation is fitted:

$$\widetilde{RSR}=\mathrm{a}+b{P}_{\mathrm{robit}}$$

(10)

Step 5 is to calculate the estimated RSR value $\widetilde{RSR}$ using Formula (10), followed by implementing the grading procedure. Subsequently, Bartlett’s test for homogeneity of variance is conducted sequentially; a significant result indicates that the final grading method is optimal.

2.4. Complementary Mechanisms of the Gini Coefficient and Rank-Sum Ratio Methods

This study couples the Dagum Gini coefficient and the rank-sum ratio (RSR) method to construct a dual-layer empirical analysis framework. The two methods do not simply overlap; instead, they form endogenous complementarity across four dimensions: mathematical logic, evaluation hierarchy, statistical properties, and policy orientation. This coupling compensates for the inherent limitations of each individual model at the methodological level.

Specifically, the Dagum Gini coefficient traces structural inequality in subsidy distribution and identifies the sources of distributional unfairness [28]. The RSR method conducts multi-objective constrained optimization to determine rational tier boundaries. This method calculates optimal tier thresholds under multiple constraints including equity, efficiency and cost. The two methods jointly establish a closed-loop paradigm spanning diagnosis and optimization. The complementary mechanisms are explained from four perspectives below.

First, deep coupling in mathematical logic: static tracing and dynamic optimization form a closed loop. From the perspective of mathematical logic, the Dagum Gini coefficient, based on the Lorenz curve, structurally decomposes the continuously distributed subsidy amounts. It quantifies the contributions of within-group disparity, between-group disparity, and transvariation, thereby precisely locating the institutional causes of imbalance in subsidy distribution. For example, it can clearly answer: under the current tiered electricity pricing, to what extent do high-consumption users “capture” subsidies, and how severe is the insufficient coverage for low-income groups? However, the Gini coefficient is essentially a static inequality measurement tool. It can only “diagnose” the current situation and lacks the ability to “prescribe” solutions. The RSR method differs. It transforms multidimensional indicators such as fairness, efficiency, and cost into dimensionless rank-sum ratios based on non-parametric rank transformation, and solves for the optimal electricity pricing tier thresholds through sorting and classification. It belongs to the category of dynamic constrained optimization models and can answer: “Given the constraints, what should the tier cutoffs be?” Therefore, the structural pain points identified by the Gini coefficient (e.g., excessively high subsidies for third-tier users) can directly serve as constraints or weighting criteria in the optimization process of the RSR method. The two thus form a mathematical closed loop of “problem identification to quantitative solution,” rather than operating as independent analyses.

Second, nested complementarity in evaluation hierarchy: macro-level structural diagnosis integrates with micro-level tier implementation. The two methods form a nested structure of “macro, meso, and micro” levels in their evaluation hierarchy. The Dagum Gini coefficient primarily operates at the macro and meso levels. On the one hand, it measures the overall inequality of subsidy distribution across all residential users (macro level). On the other hand, it decomposes the contributions of disparities between different electricity consumption groups and identifies institutional allocation barriers between groups (meso level). This allows researchers to judge the policy defects of the current tiered electricity pricing from an overall institutional perspective, rather than relying on isolated or local observations. The RSR method descends to the micro-level regulatory layer. It focuses on heterogeneous characteristics of individual household electricity consumption (such as consumption distribution and electricity expenditure burden ratio), and determines tier divisions and calibrates tier cutoffs based on the intrinsic distribution of the sample rather than subjective settings. This solves the practical problem that the “one-size-fits-all” tier division of traditional tiered pricing deviates from actual consumption distributions and misclassifies user groups. The complementarity between the two lies in the following: the macro-level structural judgments provided by the Gini coefficient (e.g., “between-group disparity accounts for more than 90% of total inequality”) define constraint boundaries for the micro-level tier optimization of the RSR method. That is, the optimization cannot undermine the basic between-group fairness lower bound. Conversely, the tier classification results obtained from the RSR method can be re-evaluated by the Gini coefficient to verify whether they have improved overall and between-group inequality. This creates a hierarchical verification and feedback mechanism, rather than having the two methods work in isolation.

Third, statistical complementarity: parametric precision integrates with non-parametric robustness. From a statistical perspective, the two methods complement each other in addressing the complex characteristics of residential electricity consumption data, which are skewed, heterogeneous, and contain extreme values. The Dagum Gini coefficient is a parametric measurement method. It is highly sensitive to continuous subsidy amounts and can precisely capture small distributional differences, making it suitable for quantifying detailed gaps in welfare distribution. However, the cost of this sensitivity is that the Gini coefficient is susceptible to extreme outliers and has limited adaptability to skewed distributions. In residential electricity consumption data, high-consumption users may receive subsidy amounts far above the mean, and such extreme values can significantly inflate the Gini coefficient, potentially masking the true distribution among low- and middle-income groups. The RSR method is the opposite. It is a typical non-parametric method that does not require the data to follow a normal distribution or satisfy homogeneity of variance. It performs analysis based on rank ordering rather than raw values, thereby naturally mitigating the influence of extreme high or low consumption samples and demonstrating strong data robustness. However, this robustness also has a cost: rank transformation discards some fine-grained information contained in the raw values. The practical benefit of combining the two is as follows. The Gini coefficient provides precise measures of subsidy disparities, but its results undergo cross-validation through the robustness of the RSR method. Meanwhile, the tier classification results from the RSR method can be subjected to sensitivity tests using the Gini coefficient, for example, by examining whether the Gini coefficient changes dramatically after excluding extreme samples. This two-way verification of precision and robustness provides greater confidence in the empirical findings than any single method alone.

Fourth, two-way balancing in policy orientation: fairness as a rigid constraint cooperates with comprehensive benefit optimization. At the policy application level, the two methods represent respectively “fairness-first” and “efficiency-first” policy logics, and their coupling achieves two-way balancing rather than a simple compromise. The core function of the Dagum Gini coefficient is to provide a rigid fairness constraint. It offers a set of quantifiable bottom-line indicators. For example, an overall Gini coefficient exceeding 0.4 enters the internationally recognized “inequality warning zone,” and an excessively high contribution rate of between-group disparity indicates serious institutional allocation defects. In the policy optimization process, any tier scheme must not significantly worsen these fairness indicators. This prevents excessive sacrifice of low-income groups’ welfare in pursuit of economic efficiency or administrative convenience. The RSR method aims to maximize comprehensive benefits. Within the fairness constraint boundaries set by the Gini coefficient, it solves for the optimal tier scheme by balancing multiple dimensions, including economic cost, operational efficiency, and policy feasibility. For instance, it can select the tier threshold that minimizes the subsidy leakage rate without increasing the overall Gini coefficient. The two-way balancing mechanism can be summarized as follows: the Gini coefficient defines the lower bound of fairness (i.e., “no worse than this”), and the RSR method searches within this bound for the best possible comprehensive solution. This approach is more operational and verifiable than merely emphasizing the slogan of “balancing fairness and efficiency,” and provides a quantifiable technical pathway for the long-term improvement of the cross-subsidy system in tiered electricity pricing.

3. Data Sources and Analysis

The raw data on residential electricity consumption presented in this study were sourced from State Grid Hebei Electric Power Co., Ltd. [29] for the period of 2016 to 2020, with a total sample size of 590,285 households. The sales electricity prices for residential and agricultural electricity, calculated under the independent transmission and distribution tariff mechanism, were used as the benchmark prices in this study. Owing to policy-related factors, minor discrepancies exist in the transmission and distribution tariffs, which fail to fully reflect the actual cost of electricity supply. The sales benchmark electricity prices are based on the following policies: Notice of the Hebei Provincial Price Bureau on the Transmission and Distribution Tariffs of the Hebei Provincial Power Grid (2017–2019), Notice of the Hebei Provincial Price Bureau on Relevant Matters Concerning the Rational Adjustment of the Electricity Price Structure, and Notice of the Ministry of Finance on the Cancellation and Adjustment of Certain Government Funds. The actual electricity price adopted refers to the actual average electricity price implemented subsequent to the TEP policy, where the actual average electricity price is equivalent to the ratio of total electricity costs to total electricity consumption. Descriptive statistical analyses of the data are presented in

Table 1. Descriptive statistical analysis.

Year	2016	2017	2018	2019	2020
Sample size	117,931	118,211	118,178	118,127	117,838
Average electricity price (CNY/kWh)	0.527	0.52	0.506	0.501	0.495
Average electricity consumption (kWh)	1561.71	2187.33	2737.35	2990.17	3232.88
Average electricity charge (CNY)	823.02	1137.41	1385.1	1498.08	1600.28
Average electricity price cross-subsidy (CNY)	122.95	279.46	538.34	661.59	777.21
Minimum electricity price cross-subsidy (CNY)	−1047.6	−503.58	−762.85	−314.94	−496.22
Maximum electricity price cross-subsidy (CNY)	8219.14	11,236.67	12,348.18	12,601.57	13,650.07
Standard deviation of cross-subsidy (CNY)	376.67	638.32	1083.99	1244.66	1360.02
The proportion of samples with negative electricity price cross-subsidy to total samples (%)	0.54%	0.10%	0.03%	0.06%	0.03%
Per capita disposable income (CNY)	19,725.4	21,484.1	23,445.7	25,664.7	27,135.9

.

The data presented in Table 1 indicate that the average residential electricity consumption increased by a factor of 1.07 over the five-year period. Given that the annual growth rate of average residential electricity consumption outpaced that of average electricity charges, and that electricity consumption is inversely proportional to electricity prices and directly proportional to electricity charges, the calculated average electricity price exhibited an overall downward trend over the five years: it decreased by 6.46%, falling from 0.527 CNY/kWh in 2016 to 0.495 CNY/kWh in 2020. The increase in average residential electricity consumption can be attributed to economic growth, rises in residents’ overall disposable income, increased demand for material living standards, household size, and seasonal weather conditions. Meanwhile, the cross-subsidy in average electricity prices has risen year-on-year, with the subsidy amount in 2020 being 654.26 CNY higher than that in 2016 (a 5.32-fold increase). This finding suggests that industrial and commercial users continue to bear a portion of the electricity price costs for residential users, which alleviates residential electricity expenditure pressure to a certain extent but increases the financial burden on industrial and commercial users.

The electricity price cross-subsidy values presented in Table 1 were calculated using the spread method. Notably, the minimum annual cross-subsidy value over the five consecutive years was negative; this phenomenon can be attributed to two key factors: first, conventional power generation units incur higher start-up and shutdown costs in power systems with a high penetration of renewable energy, and second, these units are only eligible to receive subsidies if they generate electricity. Consequently, such units tend to adopt negative electricity prices for electricity sales during certain periods to accelerate electricity consumption. Samples with negative electricity price cross-subsidies accounted for 0.15% of the total sample (878 households), representing a negligible proportion.

To further analyze residential electricity consumption and electricity price cross-subsidies across different income levels over the five-year period, users were categorized into three tiers based on annual electricity consumption in accordance with Hebei Province’s TEP policy. The residential electricity consumption, average cross-subsidy amount, and changes in subsidy intensity for each user tier from 2016 to 2020 were calculated separately, with the results summarized in

Table 2. Cross-subsidies of electricity consumption and electricity price under ladder electricity price from 2016 to 2020.

	Year	2016	2017	2018	2019	2020	Average
First-tier users (0-2060)	Number of users	88,274	74,446	65,656	62,582	59,028	69,997
	Average electricity price (CNY/kWh)	0.519	0.515	0.508	0.503	0.5	0.509
	Average electricity consumption (kWh)	1099.223	1153.377	1172.969	1175.871	1157.53	1151.794
	First-tier average electricity price cross-subsidy (CNY)	0.918	5.825	14.38	19.759	22.635	12.703
	Cross-subsidy level (%)	0.19	0.96	2.31	3.27	3.85	2.12
Second-tier users (2160-3372)	Number of users	19,037	24,296	24,612	23,929	23,297	23,034
	Average electricity price (CNY/kWh)	0.531	0.518	0.508	0.502	0.498	0.511
	Average electricity consumption (kWh)	2639.268	2675.694	2675.111	2684.143	2690.656	2672.974
	Second-tier average electricity price cross-subsidy (CNY)	100.446	138.913	164.662	183.404	194.174	156.319
	Cross-subsidy level (%)	6.84	9.12	10.88	11.93	12.63	10.28
Third-tier users (3372-)	Number of users	10,620	19,469	27,910	31,616	35,513	25,025
	Average electricity price (CNY/kWh)	0.585	0.541	0.501	0.489	0.483	0.519
	Average electricity consumption (kWh)	5251.086	5531.519	6472.296	6813.067	7038.125	6221.218
	Third-tier average electricity price cross-subsidy (CNY)	1177.644	1501.199	2100.419	2293.972	2413.918	1897.430
	Cross-subsidy level (%)	28.66	34.02	38.90	40.37	41.10	36.61

.

From a horizontal perspective, the data in Table 2 indicate that, with the exception of a relative decrease in electricity consumption among tier-1 residential users in 2020, the average electricity consumption of users across all tiers in Hebei Province exhibited an overall upward trend. Meanwhile, the number of users in the tier-1 electricity consumption bracket declined year-on-year, whereas the number of users in the tier-3 bracket increased annually. This phenomenon mainly arises from steady growth in residential income driven by regional economic development. Improved living standards drive up the use of household appliances and increase demand for heating and cooling, further elevating total household electricity consumption. Consequently, a substantial proportion of first-tier users exceed the consumption limit and gradually move into the second and third tiers. This trend can be attributed to rises in residents’ annual income levels and the influence of growing demand for material living standards, among other factors. In 2020, the number of users in the tier-1 bracket decreased by 5.68% year-on-year to fewer than 60,000 households; this constituted the direct cause of the reduction in electricity consumption, in addition to the impacts of economic growth, policy adjustments, and social norms [2]. The average electricity prices for tiers 1 to 3 all decreased, yet the average cross-subsidy amount and cross-subsidy intensity increased year-on-year, which suggests that the issue of cross-subsidization for residential electricity consumption is exacerbating.

From a vertical perspective, the average cross-subsidy for tier-3 users was substantially higher than that for tier-1 and tier-2 users, with differences of 1884.73 CNY and 1741.04 CNY, respectively. This indicates that users in the third electricity consumption bracket obtain excessively high subsidy gains, and electricity price subsidies cannot effectively target low-income groups, thereby revealing the inherent irrationality of the existing subsidy mechanism. This conclusion is consistent with the research findings of Lin et al. [11]. The average cross-subsidy intensity for high-income residents was 26.33% and 34.49% higher than that for middle-income and low-income residents, respectively. This indicates that the current TEP subsidy policy lacks specificity; low-income households only receive a minimal share of subsidies, resulting in inequity and a failure to achieve the goal of equalizing access to basic electricity public services. Thus, it can be preliminarily concluded that the existing tiered electricity tariff policy exhibits a significant subsidy “leakage effect”, and it is imperative to optimize the current policy to reduce the net loss of social welfare.

Additionally, the increase in average user electricity consumption observed in Table 1 can be explained by changes in the number of users across different tiers presented in Table 2. Specifically, tier-1 users may move up to tier-2 in the subsequent year due to increased electricity consumption, and similarly, tier-2 users may transition to tier-3 in the following year for the same reason. As living standards and incomes improve, the proportion of low electricity-consuming “low-income households” in the total population has decreased, while the proportion of high electricity-consuming “high-income households” has increased, leading to a year-on-year rise in average user electricity consumption, as presented in Table 1. Concurrently, the increase in cross-subsidy intensity further indicates an expansion in the scale of subsidies: cross-subsidy intensity for tier-3 users rose from 28.66% in 2016 to 41.10% in 2020, a change that is substantially larger than that for tier-1 and tier-2 users. This means subsidies are disproportionately directed toward “high-income groups” rather than “low-income groups”, which demonstrates that the income redistribution effect of the existing TEP subsidy policy is becoming increasingly imbalanced.

Subsequently, the five-year sample data were grouped using K-Means clustering according to electricity consumption levels. The Gini coefficient of electricity price cross-subsidies and its corresponding decomposition results are reported in

Table 3. Gini coefficients and decomposition results of cross-subsidy of electricity.

Year		2016	2017	2018	2019	2020	Average
Overall Gini coefficient (G_T)		0.484	0.448	0.391	0.441	0.499	0.449
Difference contribution within groups (G_W)		0.025	0.015	0.014	0.020	0.018	0.018
Differential contribution between groups (G_nb)		0.459	0.433	0.377	0.421	0.481	0.431
Ultra-high-density contribution rate (G_t)		0.022	0.016	0.089	0.061	0.053	0.048
Contribution rate of differences within groups (%)		3.352	3.098	2.331	4.121	2.561	3.093
Contribution rate of differences between groups (%)		93.450	96.631	96.140	81.977	91.372	91.914
Contribution rate of ultra-high-density contribution Rate (%)		3.199	1.092	1.530	13.901	6.067	5.158
Gini coefficients within groups	Group 1	0.354	0.375	0.374	0.429	0.429	0.392
	Group 2	0.158	0.291	0.425	0.261	0.405	0.312
	Group 3	0.036	0.261	0.110	0.161	0.153	0.145
	Group 4	0.069	0.113	0.172	0.092	0.068	0.156
	Group 5	0.181	0.123	0.086	0.130	0.076	0.114
	Group 6	0.228	0.069	0.185	0.130	0.013	0.149
	Group 7	0.299	0.206	0.295	0.189	0.198	0.237
	Group 8	0.318	0.245	0.385	0.324	0.266	0.308
	Group 9	0.387	0.293	0.400	0.442	0.323	0.388
	Group 10	0.418	0.461	0.472	0.497	0.535	0.472

. The Gini coefficient ranges from 0 to 1: a value closer to 0 indicates a more equitable income redistribution effect of the electricity price cross-subsidy policy, whereas a value closer to 1 signifies greater inequity. Internationally, 0.4 is widely recognized as the warning threshold for income distribution disparities.

As shown in Table 3, the overall Gini coefficient exceeded 0.4 in four of the years from 2016 to 2020 (with the exception of 2018), recording an average value of 0.449. This finding indicates a significant disparity in the extent of cross-subsidy received by users across different income groups. With respect to intra-group Gini coefficients (see Figure 1), the annual overall distribution exhibited an inverted U-shape: the Gini coefficient for the low-income group (Group 1) approached 0.4, and even surpassed this threshold in 2020; the middle-income groups (Groups 3–8) had relatively small Gini coefficients; in contrast, the high-income group (Group 10), which consumed large amounts of electricity, had a Gini coefficient exceeding 0.4 for all five years. This suggests that the disparity in cross-subsidy allocation between high- and low-income groups is more pronounced than that among middle-income groups, with a greater share of subsidies accruing to high-income households and thus reflecting inequitable distribution. Additionally, the degree of inequity increased annually, as evidenced by the year-on-year rise in Gini coefficients for both low- and high-income groups. The average between-group differential contribution (G_nb) stood at 0.43, accounting for 91% of the total variance, whereas the within-group differential contribution accounted for only 3.09%. These results confirm that disparities in the income redistribution effect of residential electricity price cross-subsidies stem primarily from inter-group differences.

4. TEP Classification Optimization Method

This study adopts the RSR method to establish the tiered electricity pricing structure. Most existing studies mainly use the coefficient of variation to measure disparities in residential electricity consumption. This single-indicator approach has limited explanatory power and dimensional coverage. Accordingly, this paper builds a multi-dimensional evaluation framework for pricing tiers. It incorporates key indicators into the calculation of tiered electricity thresholds: the overall Gini coefficient, average electricity cost, average electricity price, per capita disposable income and average cross-subsidy. Relevant data on per capita disposable income is sourced from the Hebei Provincial Statistical Yearbook. The overall Gini coefficient quantifies inequality in the distribution of residential electricity resources. It directly reveals how tiered pricing policies regulate consumption equity across different user groups and acts as a core indicator to assess the fairness of electricity allocation. Average electricity cost reflects the real expenses of power generation and supply, ensuring the pricing mechanism aligns with the sustainable operation of the power industry. Average electricity price indicates users’ financial burden from power use. It serves as a key reference for pricing scheme optimization and policy adjustment, and is closely linked to household electricity expenditure pressure. Per capita disposable income objectively reflects households’ affordability, and provides an important reference for setting pricing tiers and formulating livelihood-friendly electricity policies. Average cross-subsidy reveals benefit transfers across different electricity user groups. It effectively evaluates how the subsidy mechanism narrows consumption gaps and improves income distribution. Subsequently, the rank $R_{ij}$ of each indicator was calculated using Equations (8) and (9), followed by the computation of the rank-sum ratio (RSR) value via Equation (10). After sorting the RSR values, the estimated rank-sum ratio $\widetilde{RSR}$ was derived by querying the probit values and fitting the regression equation, with the results presented in

Table 4. Calculation process of RSR.

Year	RSR	Probit (Probit)	$\widetilde{\mathit{R}\mathit{S}\mathit{R}}$
2016	0.63	5.2533	0.669
2017	0.48	5.8416	0.484
2018	0.44	6.6449	0.349
2019	0.24	4.1584	0.232
2020	0.04	4.7467	0.096

. Ranking the RSR values further yielded the fitted regression equation $\widetilde{RSR}=-0.8623+0.2305\times P_{\mathrm{robit}}$, and the calculated regression equation exhibited a goodness of fit of 93.32%, indicating a high level of fitting accuracy.

Following the calculation of the estimated rank-sum ratio (RSR) values, the TEP structure was graded in accordance with the grading principles of the RSR method. Currently, the design of tiered pricing structures across different countries and regions typically ranges from 2 to 6 tiers. Considering constraints related to economic and social conditions, this study divided the annual tiered electricity consumption into 3 to 5 grades and conducted separate Bartlett’s tests using Stata 16 software. The test results indicated that when the data for 2016, 2017, and 2020 were divided into 5 tiers, and the data for 2018 and 2019 into 4 tiers, the final F-statistic was 9.06, the chi-square value was 0.001, and the p-value was 0.971 (greater than 0.05). This result confirmed that the variances across all categories were homogeneous (passed Bartlett’s test), demonstrating that this tiering method aligns with the optimal classification principles of the RSR method.

To further validate the rationality of the aforementioned grading approach, this study conducted a Gini coefficient test on the grading results, which consisted of four distinct steps, as detailed below:

4.1. Evaluation of Grouping Optimization via Inter-Group Gini Coefficients

The grouping optimization results were evaluated by analyzing inter-group Gini coefficients. Based on the fairness criterion for Gini coefficients (≤0.4), an inter-group Gini coefficient close to or exceeding 0.4 necessitated subdividing the graded electricity consumption and increasing the number of tiers. Taking the 2020 data as an example (

Table 5. Gini coefficient between groups in 2020.

Group 1	coef	Group 2	coef	Group 3	coef	Group 4	coef	Group 5	coef	Group 6	coef	Group 7	coef	Group 8	coef	Group 9	coef
(1&2)	0.419
(1&3)	0.343	(2&3)	0.330
(1&4)	0.323	(2&4)	0.381	(3&4)	0.138
(1&5)	0.326	(2&5)	0.383	(3&5)	0.142	(4&5)	0.072
(1&6)	0.315	(2&6)	0.387	(3&6)	0.093	(4&6)	0.059	(5&6)	0.064
(1&7)	0.436	(2&7)	0.404	(3&7)	0.348	(4&7)	0.240	(5&7)	0.239	(6&7)	0.278
(1&8)	0.557	(2&8)	0.525	(3&8)	0.515	(4&8)	0.408	(5&8)	0.405	(6&8)	0.456	(7&8)	0.250
(1&9)	0.531	(2&9)	0.503	(3&9)	0.448	(4&9)	0.358	(5&9)	0.356	(6&9)	0.384	(7&9)	0.295	(8&9)	0.274
(1&10)	0.844	(2&10)	0.831	(3&10)	0.829	(4&10)	0.782	(5&10)	0.780	(6&10)	0.804	(7&10)	0.677	(8&10)	0.449	(9&10)	0.290

):

• The inter-group Gini coefficient between Group 1 and Group 2 was 0.4188 (>0.4), indicating inequitable cross-subsidy distribution between these groups; thus, further subdivision was required. The maximum electricity consumption in Group 1 was 871 kWh, so users in Group 1 were classified into the first tier, with the annual tiered electricity consumption range set as 0–871 kWh.
• The inter-group Gini coefficient between Group 2 and Group 3 was <0.4, so no additional subdivision was needed. However, the inter-group Gini coefficient between Group 3 and Group 4 was 0.3806 (close to 0.4), signifying renewed inequity in inter-group redistribution. The maximum electricity consumption in Group 3 was 2634 kWh, so the second tier was defined as 871–2634 kWh of annual electricity consumption.
• The inter-group Gini coefficients between Group 4 and Groups 5, 6, and 7 were all <0.4 (no subdivision required), while the inter-group Gini coefficient between Group 7 and Group 8 was 0.40832 (>0.4), indicating renewed inequity in cross-subsidy distribution and necessitating subdivision. The maximum electricity consumption in Group 7 was 8167 kWh, so the third tier was set as 2634–8167 kWh of annual electricity consumption.
• The inter-group Gini coefficient between Group 8 and Group 9 was <0.4 (no subdivision required), whereas the inter-group Gini coefficient between Group 8 and Group 10 was 0.449 (>0.4). Consequently, Groups 8 and 9 were merged into the fourth tier; the maximum electricity consumption in Group 9 was 12,247 kWh, so this tier was defined as 8163–12,247 kWh of annual electricity consumption.
• The remaining Group 10 was independently classified into the fifth tier, with the annual electricity consumption range set as ≥12,247 kWh.

4.2. Recalculation and Analysis of the Overall Gini Coefficient

The overall Gini coefficient following grading via the rank-sum ratio (RSR) method was recalculated and analyzed. A recalculated value lower than the pre-regrouping overall Gini coefficient of electricity price cross-subsidies indicated that cross-subsidy distribution was relatively more equitable under this grouping approach.

4.3. Recalculation and Analysis of Intra-Group Gini Coefficients

The inter-group Gini coefficients post-grading (via the RSR method) were recalculated and analyzed. If the intra-group Gini coefficient for each tier in each year was less than 0.4, it demonstrated that intra-group cross-subsidy distribution was relatively fair, validating the rationality of grouping users within this electricity consumption range into the same tier.

4.4. Recalculation of Inter-Group Gini Coefficients

The inter-group Gini coefficients were recalculated. An inter-group Gini coefficient close to or exceeding 0.4 for each tier in each year indicated inequitable cross-subsidy distribution between groups, confirming that differentiating users based on this grading method was more reasonable.

In summary, the overall, intra-group, and inter-group Gini coefficients of electricity price cross-subsidies were recalculated for each year post-reclassification. The grading results were deemed valid if three conditions were simultaneously met: (1) a relative reduction in the overall Gini coefficient; (2) inter-group Gini coefficients ≥ 0.4; and (3) intra-group Gini coefficients < 0.4. The results are presented in

Table 6. Cross-subsidy equity calculation in TEP based on the RSR method.

Year		2016	2017	2018	2019	2020	Average
Overall Gini coefficient		0.452	0.445	0.381	0.440	0.487	0.440
Gini coefficients within subgroups	Group 1	0.368	0.278	0.298	0.315	0.270	0.318
	Group 2	0.187	0.142	0.159	0.229	0.122	0.172
	Group 3	0.205	0.158	0.073	0.105	0.026	0.116
	Group 4	0.187	0.377	0.236	0.318	0.189	0.268
	Group 5	0.288	0.210
Gini coefficients between subgroups	(1&2)	0.852	0.638	0.787	0.791	0.844	0.818
	(2&3)	0.681	0.586	0.593	0.581	0.692	0.639
	(3&4)	0.452	0.803	0.446	0.395	0.443	0.435
	(4&5)	0.703	0.449
Difference contribution within subgroups		0.083	0.029	0.072	0.083	0.083	0.081
Contribution rate of differences within groups (%)		18.051	4.18	14.835	15.356	16.972	16.531
Difference contribution between subgroups		0.357	0.653	0.418	0.614	0.403	0.437
Contribution rate of differences between groups (%)		77.793	95.8	84.696	80.001	82.829	80.874
Contribution rate of ultra-high-density contribution rate (%)		4.157	0.01	1.985	6.379	0.199	2.777

.

As shown in Table 6, the calculated average overall Gini coefficient was 0.4402, which was lower than the pre-optimization average overall Gini coefficient (0.4487). This finding indicates that the fairness of cross-subsidy redistribution was enhanced following re-grading. Intra-group Gini coefficients were all below 0.4, whereas inter-group Gini coefficients exceeded 0.4; additionally, the contribution rate of inter-group disparities was substantially higher than that of intra-group disparities. These results confirm that the overall Gini coefficient was primarily driven by inter-group differences, thereby validating the rationality of the proposed grading framework.

5. Discussion

The empirical analysis based on residential electricity consumption data from Hebei Province (2016–2020) reveals critical insights into the performance of China’s tiered residential electricity pricing (TREP) policy, particularly regarding cross-subsidy distribution and income redistribution equity. This section contextualizes these findings within existing literature, interprets the underlying mechanisms, and highlights the theoretical and practical implications of the optimized pricing framework.

5.1. Trends and Drivers of Residential Electricity Consumption and Cross-Subsidies

Consistent with the upward trajectory of residential energy demand observed in developing economies [30], our study found that both residential electricity consumption and the average scale of cross-subsidies in Hebei Province exhibited a synchronous growth trend from 2016 to 2020. This dual upward pattern not only reflects macroeconomic factors including population expansion, rising household income, and growing material demand, all of which are widely acknowledged as key drivers of electricity consumption growth [31], but is also closely associated with the structural evolution of user groups across consumption tiers. Specifically, the migration of low-tier users to higher tiers expanded the base of high-cost electricity consumers who bear the cross-subsidy burden, thereby amplifying the total cross-subsidy scale. This finding complements previous national-level studies by providing micro-level evidence of user behavior dynamics, which helps explain the persistent expansion of cross-subsidies despite incremental policy adjustments.

5.2. Equity of Cross-Subsidy Distribution: Leakage Effect and Income Disparities

A striking finding of this study is the significant inequity in cross-subsidy allocation across income groups, with high-income households capturing a disproportionate share of subsidies while low-income households receive minimal support. This observation aligns with the “subsidy leakage” phenomenon identified in prior evaluations of TREP [11], wherein subsidies intended for vulnerable groups are inadvertently appropriated by higher-income groups. In Hebei Province, the poor targeting of the existing subsidy policy not only violates the fairness principle of universal public services but also undermines the equalized provision of electricity as a basic public good, which contradicts the core objective of TREP in balancing affordability and equity. The underlying driver of this leakage may lie in the static design of tier thresholds, which fails to distinguish between the basic electricity needs of low-income households and the discretionary consumption of high-income groups [3].

Further analysis of intra-group and inter-group disparities using Gini coefficients reveals a nuanced pattern of distribution inequality. The “inverted U-shaped” distribution of the intra-group Gini coefficient indicates relatively balanced subsidy allocation among middle-income groups alongside unbalanced distribution within low- and high-income groups, which further reveals the heterogeneous impact of TREP across different subgroups. This pattern suggests that middle-income households, as the largest consumer group, benefit from the current three-tier structure’s moderate thresholds, while extreme groups (low-income with low consumption, high-income with high consumption) face structural disadvantages. From an inter-group perspective, the dominance of inter-group differences in driving redistribution effect disparities underscores the failure of the existing policy to mitigate income-based consumption gaps. The widening subsidy gap between high-income high-consumption and low-income low-consumption groups over the study period further indicates that TREP, in its current form, may exacerbate rather than alleviate social inequality.

5.3. Implications for Optimizing the Tiered Pricing Framework

Our findings challenge the effectiveness of the current three-tiered pricing system in achieving equity goals, emphasizing that the number of tiers directly influences the fairness of subsidy distribution. This conclusion is consistent with the viewpoint proposed by Wang et al. [32] that increasing the number of pricing tiers is more compatible with China’s national context, as our RSR-based optimization suggests that lowering the first-tier threshold and adding a fourth tier can substantially improve distribution equity. The rationale for reducing the first-tier threshold is to better target basic electricity needs: the existing threshold may be excessively high, allowing high-income households to consume large amounts of electricity at the lowest price and, thus, occupy subsidies intended for low-income groups. Adding a fourth tier, by contrast, addresses the over-consumption of high-income households by imposing a higher price on excessive electricity use, thereby reducing their disproportionate share of cross-subsidies. This optimized structure aligns with the “align price signals with long-term low-carbon transition goals” principle advocated by international energy policy guidelines, which emphasizes that pricing systems should reflect both affordability for low-income groups and cost recovery for utilities [33].

Notably, the year-on-year migration of users to high tiers underscores the necessity of dynamic threshold adjustments. Static thresholds, as adopted in most Chinese provinces, fail to adapt to evolving consumption patterns driven by technological progress (e.g., popularization of high-power appliances) and rising living standards [4,34]. Our study’s proposal for continuous revision of tier thresholds based on empirical data fills a critical gap in existing research, which has largely focused on static optimization. Dynamic adjustment ensures that the pricing system remains responsive to structural changes in electricity demand, thereby sustaining the equity and efficiency of cross-subsidy distribution over time.

5.4. Theoretical and Practical Contributions

This study makes several key contributions to the literature on TEP. First, methodologically, it integrates inter-group and intra-group Gini coefficient analyses to comprehensively evaluate distribution equity, overcoming the limitations of single-dimensional inequality measures used in previous studies [17]. The innovative application of the RSR method to optimize tier thresholds also provides a quantitative tool for evidence-based policy design, which can be replicated in other regions with similar consumption characteristics. Second, in terms of theoretical insights, this study identifies the “dual drivers” of cross-subsidy growth (macroeconomic factors and user tier migration) and the “inverted U-shaped” intra-group inequality, enriching the understanding of TREP’s performance in middle-income regions. Practically, the optimized pricing framework offers actionable policy recommendations for local governments: lowering the first-tier threshold to ~150 kWh/month (based on RSR grading) and adding a fourth tier above 500 kWh/month can effectively reduce subsidy leakage and enhance the equalization of electricity services. These recommendations are particularly relevant for northern Chinese provinces with high winter heating demand, such as Hebei, where electricity consumption disparities across income groups are exacerbated by seasonal usage patterns.

Residential electricity cross-subsidies have a natural optimization ceiling, so the overall Gini coefficient only declines moderately after tier adjustment. This marginal change is not a meaningless numerical fluctuation but reflects notable progress in structural equity. The revised tiers considerably reduce the contribution of inter-group inequality and balance subsidy allocation across user groups, reversing the long-standing issue of excessive subsidy acquisition by high-income households. With a sample covering 120,000 residential households, this adjustment also curbs the growing unfairness in subsidy distribution from 2016 to 2020, cuts social welfare losses during tariff redistribution, and delivers tangible benefits for local residents and policy implementation.

5.5. Limitations and Future Research

Despite these contributions, this study has certain limitations. First, the data is restricted to Hebei Province, and the findings may not be fully generalizable to southern provinces with distinct climate conditions (e.g., higher summer cooling demand) and economic structures. Future research should expand the sample to include cross-provincial comparisons to explore regional heterogeneity in TREP’s effects. Second, this study focuses on income redistribution equity but does not consider environmental externalities (e.g., carbon emissions) of electricity consumption, which are increasingly important in global energy policy. Integrating environmental indicators into the optimization framework could yield a more comprehensive pricing system that balances equity, efficiency, and sustainability. Third, this study lacks direct household income data. Due to privacy and data access restrictions, we cannot collect actual income information (e.g., wages, assets). Following the widely accepted paradigm, we use electricity consumption as a proxy to infer income levels and classify users into income groups based on Hebei Province’s tiered pricing standards. While this approach is common, it remains an indirect proxy. Future research should integrate household survey data to validate and refine our findings.

Furthermore, constrained by rigid power operational costs, livelihood security requirements and heterogeneous user consumption behaviors, the current tier optimization can only achieve gradual equity improvement rather than a sharp drop in the Gini coefficient. Subsequent studies may incorporate carbon emissions and electricity use efficiency indicators to further improve the rationality and comprehensive performance of tiered electricity pricing schemes.

6. Conclusions and Policy Implications

6.1. Conclusions

This study adopts micro-level household electricity consumption data covering 589,285 residential users in Hebei Province from 2016 to 2020. We apply the price-gap approach to calculate power tariff cross-subsidies and employ the Dagum Gini coefficient decomposition method together with the rank-sum ratio (RSR) method to systematically assess the income redistribution effects of the existing three-tiered electricity pricing scheme. We finally propose a four-tiered optimized pricing framework. The key empirical findings are as follows:

• The scale of cross-subsidies expands alongside residential power consumption, accompanied by growing subsidy leakage. Over the study period, the average annual residential electricity consumption in Hebei Province rose from 1561.71 kWh to 3232.88 kWh, an increase of 107.0%. The average cross-subsidy amount increased from 122.95 CNY to 777.21 CNY, a surge of 532.2%. Subsidy intensity, defined as the ratio of subsidy amount to total electricity charges, climbed from 2.12% to 41.10%. The distribution of subsidies exhibits clear reverse redistributive characteristics. Users in the third tier, with annual consumption above 3372 kWh, received an average subsidy of 1897.43 CNY. This amount is 149.4 times and 12.1 times the subsidies received by first-tier and second-tier users, respectively. The subsidy intensity of third-tier users reached 36.61%, which is 34.49 percentage points higher than that of first-tier users. These results indicate that high-income and high-consumption groups capture most of the subsidy benefits, while low-income groups gain limited welfare improvement under current policies.
• Gini coefficient analysis identifies the structural sources of unequal cross-subsidy distribution, with inter-group disparity dominating overall inequality. The five-year average overall Gini coefficient stands at 0.449, exceeding the internationally recognized fairness warning line of 0.4. Dagum decomposition results show that inter-group disparity contributes 91.91% to total inequality, while intra-group disparity accounts for only 3.09%. Uneven subsidy distribution primarily stems from structural gaps among consumption groups rather than internal allocation differences within each group. Intra-group Gini coefficients follow an inverted U-shaped trend. The intra-group Gini coefficient reaches 0.392 for low-income group 1 and 0.472 for high-income group 10, both exceeding 0.4. For middle-income groups 3 to 8, the coefficient remains below 0.3. This distribution pattern reflects the insufficient discriminatory power of the current three-tier thresholds for extreme user groups. Subsidy allocation exhibits large fluctuations within low-income groups due to mixed basic living electricity demand, while serious imbalance exists in subsidy distribution among high-income users. Middle-income residents enjoy relatively equitable subsidy benefits because of their homogeneous electricity consumption behavior.
• The optimized scheme based on the rank-sum ratio method effectively improves subsidy distribution fairness. We adjust the 2020 residential power tariff structure of Hebei Province from three tiers to five tiers, with consumption thresholds of 0–871 kWh, 871–2634 kWh, 2634–8167 kWh, 8167–12,247 kWh, and above 12,247 kWh. The average overall Gini coefficient drops from 0.449 to 0.440, a decline of 2.0%. All intra-group Gini coefficients fall below 0.4, with a minimum value of 0.026. Inter-group Gini coefficients remain above 0.4 and peak at 0.852. The contribution rate of inter-group disparity rises to 80.87%. The optimized scheme reduces the first-tier annual consumption threshold from the original 2060 kWh to 871 kWh. The proportion of first-tier users increases from 50.1% in 2020 to approximately 65%, which effectively curbs excessive subsidy acquisition by high-income user cohorts.

6.2. Policy Implications

The empirical results highlight significant structural and distributional deficiencies in the current tiered electricity pricing system. Accordingly, targeted policy reforms are necessary to mitigate subsidy leakage, reverse redistributive inequities, and achieve a fair and efficient cross-subsidy allocation. The specific recommendations are as follows.

First, restructure tiered electricity pricing and establish a dynamic threshold adjustment mechanism. The existing three-tiered structure causes severe subsidy leakage. Annual threshold revision helps narrow unreasonable subsidy appropriation. Static pricing thresholds have remained unchanged since 2012, whereas annual residential power consumption grows by 15.6% on average. Outdated threshold setting constitutes the fundamental institutional cause of subsidy leakage. Authorities shall build an annual assessment and quarterly adjustment mechanism. Price regulators cooperate with power grid enterprises to recalculate pricing thresholds via the rank-sum ratio method based on provincial power consumption data at the end of each year. Revised standards get released and implemented in the first quarter of the subsequent year. Minor adjustments apply in regular years and structural revision takes place amid power tariff reform and energy structure transformation. Dynamic threshold setting maintains consistent matching with actual residential power consumption characteristics.

Second, optimize price gaps between adjacent tiers. Pricing design follows the principle of increasing marginal cost. The first-tier tariff keeps the current basic guarantee level. Moderate and gradual price hikes apply to the second and third tiers to stabilize household electricity expenditure. A reasonable premium charge set for the fourth tier restrains excessive power consumption without imposing excessive financial burden on rational electricity use, and guarantees practical policy implementation.

Third, construct a digital governance system and closed-loop policy evaluation framework. Build a tripartite data sharing platform connecting price administrative departments, power grid enterprises and statistical institutions. Upgrade intelligent billing systems to support automatic switching of dynamic pricing thresholds. Take cross-subsidy Gini coefficient, subsidy leakage rate and low-income household subsidy coverage as core annual evaluation indicators. Policymakers conduct fine policy tuning with the rank-sum ratio method and form a complete circulation covering assessment, feedback and optimization.

Fourth, launch differentiated policy pilot projects in northern heating-intensive provinces. Carry out two to three-year pilot programs in North China and Northeast China to verify the applicability of a multi-tiered pricing structure, calibrate seasonal price fluctuation range and evaluate public affordability of adjusted price gaps. Track cross-subsidy distribution effects semiannually through Dagum Gini coefficient decomposition. Compile standardized operation guidelines and provide replicable references for nationwide tiered electricity pricing optimization.