Study of the Spatio-Temporal Effects of Digital Economic Development on Hydropower Resource Mismatch

Abstract

Optimizing the allocation of hydropower resources is essential for aligning high-quality economic growth with China’s carbon neutrality goals. Due to constraints such as market segmentation and government regulation, the resource allocation function of the Chinese market has not been effectively utilized, which leads to hydropower resources being allocated inefficiently. In the digital age, it is valuable to investigate whether digital economic development can rectify the misallocation of hydropower resources and whether the corrective effects exhibit temporal dynamics and spatial heterogeneity. Accordingly, this study employs panel data collected from 30 provincial-level administrative regions in China from 2000 to 2023, employing the production function method combined with a counterfactual analysis framework for quantifying the degree of hydropower resource mismatch. Additionally, panel vector autoregression models and panel threshold regression utilized for discussing spatio-temporal effects of digital economic development on hydropower resource mismatch. Empirical results demonstrate that digital economic development significantly curbs hydropower resource misallocation, albeit with a discernible time lag. When the digital economy experiences a positive impulse shock, its impact on the hydropower resources mismatch emerges in the first lag period, peaks in the second lag period, and then stabilizes. Secondly, the corrective impact of digital economic development on hydropower resources mismatch is contingent upon the level of regional industrialization, which is more pronounced in regions with higher levels of industrialization. In conclusion, this paper offers evidence-based policy recommendations to facilitate the localized implementation of digital economy policies and enhance the efficiency of hydropower resources allocation.

1. Introduction

Global carbon dioxide emissions have exhibited a persistent upward trend over the past decade. In response, the Chinese government has actively committed to carbon reduction, pledging to attaining carbon peak neutrality goals [1]. As the world’s largest energy producer and consumer, China’s substantial energy consumption has resulted in significant environmental challenges [2]. To address these issues, the government has vigorously promoted energy transition, achieving notable progress. According to the “China Power Industry Annual Development Report 2025,” the nation’s total power generation in 2024 reached 1008.69 billion kilowatt–hours, with hydropower contributing 142.57 billion kilowatt–hours, marking a year-on-year growth of 10.9%, accounting for 14.1% of total generation.

Nevertheless, resource allocation inefficiencies persist owing to incomplete market-oriented reforms in the energy sector. Factor prices often deviate from their marginal products, impairing the market’s self-correcting mechanism for achieving optimal resource allocation. This leads to efficiency losses and energy misallocation [3] which, in the case of hydropower, not only constrains improvements in energy utilization efficiency but also impedes the achievement of China’s dual carbon objectives. Against this backdrop, digital economy has risen as a pivotal catalyst for low-carbon development, playing an increasingly important role in supporting carbon emission reduction targets.

The existing literature has explored how digital economic development influences various forms of factor misallocation, including capital [4], labor [5], urban–rural factors [6], innovation resources [7], and financial mismatches [8]. Research within energy-related studies primarily branches into two directions: one involves examining the role of the digital economy in overall energy consumption and efficiency, and the other involves investigating causes and spatial attributes of energy misallocation. For instance, studies such as those by Wang and Shao (2023) [9] and Mohsin et al. (2021) [10] suggest that digital economy development can significantly reduce energy consumption. Dzwigol et al. (2021) [11], however, found that, while Internet development increases energy consumption, it negatively affects the structure and intensity of energy use. Xie and Ma (2024) [12] identified a curvilinear association between energy consumption and digital economy. Additional scholars, including Zhang et al. (2024) [13], Cao et al. (2021) [14], Awan et al. (2021) [15], and Tomazzoli et al. (2022) [16], conclude that Internet technology markedly enhances energy efficiency. In contrast, Kwilinski (2024) [17] revealed a nonlinear relationship where digital economic development initially boosts and later inhibits total factor energy efficiency.

Concurrently, research on energy mismatch underscores that distortions in capital and intermediate product markets, government intervention, and energy policy intensity are key drivers of misallocation [18,19]. Yu et al. (2024) [20] and Afshan et al. (2022) [21] demonstrated that distortions in energy structure significantly inhibit improvements in carbon emission efficiency, environmental efficiency, and energy efficiency. Cheng et al. (2024) [22] emphasized that insufficient technological innovation leads to more severe energy mismatch in western provinces compared to eastern and central regions. Thus, energy factor misallocation has become a critical issue in resource allocation research [23].

Despite these contributions, several research gaps remain. Few studies have specifically examined whether digital economic development can mitigate misallocation in hydropower resources. Moreover, existing work has insufficiently explored the temporal dynamics and spatial heterogeneity in how the digital economy influences energy factors, both theoretically and empirically.

To address these gaps, this paper utilizes panel data from 30 provincial-level regions in China from 2000 to 2023 (excluding Tibet, Hong Kong, Macao, and Taiwan due to data availability) to analyze both linear and nonlinear relationships, as well as time-lag effects, between digital economy development and hydropower resource misallocation. Drawing on the empirical evidence, we formulate targeted policy interventions aimed at guiding future digital economy development and optimizing hydropower resource allocation in China.

2. Theoretical Analysis and Hypothesis

China’s present energy mix is unable to meet the upgrading demands of the consumer end, leading to hydropower resource mismatch, which has become a constraint on high-quality development. The advancement of digital economy can drive digital transformation of the hydropower market, thereby injecting new momentum into the efficient allocation of hydropower resources.

Overall, digital economic development can mitigate hydropower resource misallocation through specific mechanisms that enhance market efficiency and operational precision. The core economic channels include (1) real-time information discovery and price signal enhancement; (2) predictive optimization of asset utilization; and (3) reduction in cross-regional arbitrage costs.

In terms of production and market operation, the digital economy fundamentally alters decision-making paradigms. Firstly, IoT sensors and smart meters deployed in dams, grids, and consumption terminals generate massive real-time data on water inflow, reservoir levels, turbine efficiency, and electricity load. Big data analytics processes this information to create highly accurate, short-term forecasts of both supply and demand. This drastically reduces the information asymmetry between producers, grid dispatchers, and consumers. Grid operators can now make economic dispatch decisions based on near-perfect information, allocating hydropower to maximize its utilization during peak demand hours, thereby displacing more expensive and often more polluting fossil fuel generators [24].

Secondly, digital twin technology creates virtual replicas of hydropower plants, allowing operators to run simulations and optimize scheduling and maintenance plans without risking physical assets or output. AI algorithms can calculate the most economically efficient time to generate power based on real-time electricity market prices, a concept known as arbitrage. This enables plant managers to decide whether to release water to generate high-value electricity now or to store it for future, potentially more profitable opportunities. This enhances the price responsiveness of hydropower generation, a critical step in correcting misallocation driven by non-price administrative directives [25].

Thirdly, blockchain-based platforms facilitate P2P energy trading and verify green energy origins, fostering a transparent market mechanism. This creates a transparent and trustworthy market mechanism for hydropower, allowing producers to capture a premium for their renewable output and giving consumers a verifiable choice to support green energy. This market differentiation more accurately reflects the social and environmental value of hydropower, guiding investment and consumption decisions towards a more efficient equilibrium.

In terms of lifestyle, from a behavioral economics perspective, the digital economy provides “nudges” that help strengthen residents’ awareness of lowering energy use and cutting emissions, encouraging them to adopt a low-carbon and environmentally friendly lifestyle. Benefiting from the advances in digital economy, people’s access to knowledge has become more diverse and simplified [26], making them more likely to pay attention to issues including resource waste and global warming. Energy conservation and ecological protection policies have been promoted more deeply and effectively through the internet, thereby gradually enhancing people’s awareness of energy conservation in their daily lives. Simultaneously, the accelerated growth of online voice and video conferencing has enabled people to achieve the goal of remote working through digital technology without leaving their homes. In addition, the number of people who shop online and use electronic payment methods has increased significantly, which has reduced the need for transportation and thereby reduced unnecessary resource consumption [27]. In summary, digital technologies inject critical economic signals and operational flexibility into the hydropower sector. This enhances the role of the market’s “invisible hand” in the hydropower sector, leading to optimized resource allocation and reduced mismatch. This study therefore proposes Hypothesis 1.

Hypothesis 1: 

Digital economic development helps reduce the level of mismatch in hydropower resources.

The path dependence theory lays a crucial theoretical groundwork for hypothesizing the time-dynamic nature of the effects stemming from digital economy on hydropower misallocation [28]. This theory posits that past technological and institutional choices create self-reinforcing mechanisms, leading to inertia that locks systems into established development trajectories [29]. In China’s hydropower sector, this lock-in is evident in three key areas, creating significant barriers to rapid digital integration: (1) Technological and Infrastructural Lock-in. The massive sunk costs in existing mega-project infrastructure (e.g., Three Gorges and Xiluodu) create a powerful economic disincentive for radical technological change. These systems, designed around pre-digital control paradigms, exhibit high asset specificity, meaning their value is tied to the existing technological setup. Retrofitting them with integrated digital systems incurs significant switching costs and poses risks to the reliability of critical national infrastructure, leading to a preference for incremental over disruptive innovation. (2) Institutional Inertia. The sector’s governance is characterized by centralized planning and vertical management under state-owned utilities, with operational rules and market mechanisms designed for the traditional model, often clashing with the decentralized, agile nature of digital technologies. (3) Organizational Rigidity. Operational culture and expertise are deeply rooted in conventional power engineering, creating a human capital mismatch and risk aversion towards data-driven approaches.

This combination of infrastructural, institutional, and behavioral inertia means that the effect of digital economic development on optimizing resource distribution follows a complex adoption curve rather than an immediate adjustment. The diffusion of innovation typically follows an S-shaped pattern where early experimentation and piloting gradually build toward critical mass. This process involves not only technical integration but also the slow evolution of supportive governance mechanisms and skill sets. Therefore, we anticipate a discernible time lag between the impetus of digital economic development and its peak effect on mitigating hydropower mismatch. The initial phase may show limited impact as the sector undergoes necessary learning and adaptation, followed by an accelerating effect as digital solutions become more integrated. This temporal pattern aligns with both path dependence theory and innovation diffusion models. Accordingly, Hypothesis 2 is formally proposed.

Hypothesis 2: 

Although digital economic development helps to correct the mismatch of hydropower resources, the correction effect has a time lag due to the influence of path dependence theory.

The comparative advantage theory offers a robust framework for understanding the anticipated spatial heterogeneity in the mitigating influence of digital economic development on hydropower mismatch [30,31]. At its core, this theory suggests that regions can improve overall economic efficiency by specializing in activities where they hold a relative advantage, even in the absence of an absolute one, thereby maximizing output through optimal resource allocation across different localities. When applied to the digital transformation of the hydropower sector, this theory helps explain why the effectiveness of digital tools varies significantly across regions. The application of digital economy tools to optimize hydropower allocation is not a one-size-fits-all solution; its effectiveness is contingent upon a region’s inherent capacity to absorb and leverage these technologies. From an economics perspective, this capacity can be understood through the lens of endowment structures and factor proportions. Highly industrialized regions typically possess a superior endowment of complementary factors: advanced physical infrastructure (e.g., stable power grids, IoT sensor networks, and cloud computing facilities), a highly skilled workforce capable of deploying and maintaining digital systems, abundant financial capital for technological upgrades, and institutional environments conducive to innovation and risk-taking [32]. These factors collectively enhance the region’s “comparative advantage” in implementing digital solutions, as posited by the Heckscher–Ohlin theory, which emphasizes that regions export goods and services that intensively use their abundant factors. Here, industrialized regions are abundant in the capital and human capital necessary for digital adoption, thereby experiencing higher returns and more efficient resource reallocation when integrating digital technologies. Conversely, less industrialized regions face comparative disadvantages due to factor scarcity—particularly in human capital and technological infrastructure—which constrains their ability to effectively deploy and utilize digital tools. The diminishing marginal returns on digital investments in these regions further exacerbate spatial disparities. In economics terms, the initial investment in digital technology in a low-industrialization context may yield minimal gains due to insufficient absorptive capacity, high adaptation costs, and lack of technical expertise. This aligns with the concept of appropriate technology, which suggests that technologies must match local factor supplies to be effective. In regions where industrialization is low, digital solutions may not be “appropriate” without prior investments in foundational infrastructure and skills. Moreover, digital tools become more valuable as more users and systems adopt them. In highly industrialized regions, the dense concentration of firms, research institutions, and digitally literate users accelerates learning and innovation spillovers, creating a virtuous cycle of increasing returns. Meanwhile, less developed regions struggle to achieve the critical mass required for these network effects to take hold, resulting in a slower and less effective diffusion of digital technologies. Thus, the marginal benefit of digital economic development is expected to vary significantly across regions with different industrialization levels. Industrialized regions not only possess the requisite factor endowments but also exhibit stronger dynamic gains from digital integration, including innovation spillovers, economies of scale, and enhanced market linkages. Less industrialized regions, however, may suffer from a “digital divide” that limits their ability to correct resource misallocation, at least in the short to medium term. This spatial heterogeneity, deeply rooted in structural economic disparities, underscores the importance of tailoring digital economy policies to regional comparative advantages to achieve equitable and efficient outcomes in hydropower allocation. In summary, this study proposes Hypothesis 3.

Hypothesis 3: 

The extent to which digital economic development mitigates hydropower resource misallocation depends on regional industrialization levels and demonstrates significant spatial variation.

3. Variable Selection

3.1. Dependent Variable

The degree of mismatch in hydropower resources ($\tau$) is a dependent variable. Following Luo et al. (2024) [33] and employing a counterfactual analysis framework, the degree of mismatch in hydropower resources is measured using Formula (1).

$${\gamma }_i={\displaystyle \frac{1}{1+{\tau }_i}}$$

(1)

In the above equation, ${\gamma }_i$ represents the absolute deviation coefficient of hydropower prices, indicating the scenario where hydropower is comparatively undistorted. When determining the allocation of hydropower resources, the degree of relative price distortion is clearly more important than the degree of absolute price distortion. In empirical practice, relative price distortions of energy factors is employed as a proxy variable, as shown in Equation (2):

$${\gamma }_i=\raisebox{1ex}{$\left(\frac{E_i}{E}\right)$}\!\left/ \!\raisebox{-1ex}{$\left(\frac{s_i{\beta }_i}{\beta }\right)$}\right.$$

(2)

In Equation (2), $\frac{E_i}{E}$ denotes the actual share of hydropower consumption within region $i$ compared to the total national hydropower consumption. Considering data availability, $E_i$ is used as a substitute indicator based on hydropower production in regions; $s_i$ is the output share of region $i$, using regional GDP as a substitute indicator; ${\beta }_i$ represents the output elasticity of hydropower resources in region $i$; and $\beta ={\displaystyle \sum _i^n{s}_i{\beta }_i}$ represents the output-weighted contribution value of hydropower. In summary, ${\displaystyle \frac{s_i{\beta }_i}{\beta }}$ stands for the theoretically optimal share of hydropower consumption in region $i$ relative to total hydropower consumption across all regions; ${\gamma }_i$ reflects the extent of divergence between the actual hydropower usage in region $i$ and the hydropower consumption under optimal allocation. If ${\gamma }_i>1$, then the cost of using hydropower resources in region i is relatively low compared to the economy as a whole, indicating a tendency toward overuse of resources. Conversely, if ${\gamma }_i<1$, then the actual allocation of hydropower resources in the region is below the theoretical level of efficient allocation, indicating an insufficient allocation of hydropower resources.

As can be seen from the above formula, to calculate the degree of mismatch in hydropower resources, it is necessary to first calculate the output elasticity ${\beta }_i$ of hydropower resources in each region. Referring to the research by Jiang et al. (2023) [34], the output elasticity ${\beta }_i$ is computable by applying the C-D functional form, as shown in Equation (3):

$$Y_{it}=A{K}_{it}^{{\alpha }_i}{L}_{it}^{{\eta }_i}{E}_{it}^{{\beta }_i}$$

(3)

In the above equation, $Y_{it}$ represents regional gross domestic product (GDP); $K_{it}$, $L_{it}$, and $E_{it}$ represent capital, labor, and hydropower resource inputs, respectively, with total labor, capital stock, and hydropower production used as proxy variables. Based on this, the output elasticities of the three factors can be calculated as ${\alpha }_i$, ${\eta }_i$, and ${\beta }_i$. For simplified calculations, logarithmic transformation can be applied to both sides of the equation, as shown in Equation (4).

$$Ln{Y}_{it}=LnA+{\alpha }_{i}Ln{K}_{it}+{\eta }_{i}Ln{L}_{it}+{\beta }_{i}Ln{E}_{it}$$

(4)

3.2. Explanatory Variables

Digital economy development (Dig). Referring to research by Jin et al. (2022) [35], we collect and organize the occurrence rate of terms associated with the digital economy across annual policy documents from 30 provinces, municipalities, and autonomous regions. Using Python 3.7.4, the government work reports are processed through text segmentation, and the rate at which digital economy-related terminology appears is statistically analyzed to quantify the level of government policy support. Related terminology encompasses a wide range of concepts and technologies, such as: digital economy, smart economy, information economy, knowledge economy, intelligent economy, digital information, modern information networks, information and communication technology (ICT), communication infrastructure, Internet, cloud computing, blockchain, Internet of Things (IoT), digitalization, digital villages, digital industries, e-commerce, 5G, digital infrastructure, artificial intelligence, e-commerce, big data, data-driven, industrial digitization, digital industrialization, data assetization, smart cities, cloud services, cloud technology, cloud-based, e-government, mobile payments, online, information industry, software, information infrastructure, information technology, and digital lifestyle.

This proxy variable is justified on three grounds: First, provincial government work reports constitute authoritative policy documents that articulate a region’s strategic priorities and resource allocation directives for the forthcoming fiscal year. The frequency of digitally relevant terminology serves as a direct indicator of the extent of governmental attention and policy commitment to the digital economy. Second, within China’s state-led development model, government policy functions as a critical catalyst for economic restructuring. Pronounced policy signals typically precede and induce substantial investments in digital infrastructure, human capital development, and sectoral digitization, thereby formatively influencing the actual trajectory of digital economic development. Third, this text-based metric offers an objective, reproducible, and consistent measure conducive to interregional and intertemporal comparisons. It reduces subjectivity in expert assessments and avoids methodological issues arising from partial data unavailability.

3.3. Threshold Variables

One key objective of this study is to analyze whether the corrective effect of digital economic development on the misallocation of hydropower resources is influenced by the degree of regional industrialization (LOI) and exhibits spatial heterogeneity. Accordingly, the degree of regional industrialization is used as a threshold variable. The degree of industrialization is proxied by share of industrial value-added in regional GDP.

3.4. Control Variables

(1)

Urbanization level (Urb). Referring to the research by Sun and Tong (2024) [36], it is believed that the urbanization level is a key control variable affecting the productivity in deploying hydro resources. The high concentration of population and economic activities during the urbanization process has profoundly altered the spatio-temporal patterns of regional water resource demand and electricity load. On the one hand, urban systems demand higher stability, quality, and reliability in hydropower supply, and their vulnerability becomes more evident under extreme weather conditions or emergencies, serving as a key catalyst for the intelligent and precise management of hydropower resources. On the other hand, as hubs for technological innovation and infrastructure investment, urban areas generate digital technology spillover effects and resource integration platform advantages, providing foundational conditions for applying digital technology to optimize hydropower allocation. Therefore, controlling the level of urbanization helps to isolate the impact of urban development itself on the structure and allocation pressure of hydropower demand, thereby enabling a clearer identification of the impact effects of digital economic development on hydropower resource misallocation.

(2)

Profitability of the power industry (Rev). Referring to Fan et al. (2017) [37], the profitability of the regional power industry is used as another control variable. Industry profitability serves as a key indicator of the financial sustainability and investment capacity of hydropower systems, and its level profoundly influences the feasibility and depth of digital upgrading and transformation. On the one hand, corporate profit surpluses provide the capital needed to support the construction and maintenance of expensive digital infrastructure. On the other hand, a better financial status enhances the industry’s willingness to adopt new technologies and its risk tolerance, thereby facilitating technological iteration. Conversely, regions with weak profitability may struggle to effectively apply digital technologies to optimize resource allocation due to funding constraints, and rising maintenance costs may exacerbate misallocation. Controlling for industry profitability helps distinguish between the inherent potential of digital technologies and their actual economic feasibility in application, preventing misinterpretation of poor outcomes caused by financial constraints as evidence of digital technology ineffectiveness.

3.5. Data Sources and Descriptive Statistics

The data utilized in this study were obtained from the China Urban Statistical Yearbook, the China Urban Construction Statistical Yearbook, the CSMAR database, provincial statistical yearbooks, and the National Economic and Social Development Statistical Bulletin. Missing values were addressed through interpolation and mean imputation methods. All indicators related to finance were deflated using the corresponding indices. Descriptive statistics of the variables are summarized in

Table 1. Descriptive statistics.

Variable	Observed Value	Mean	Std.	Min.	Max.
τ	696	0.431	0.133	0.037	1.914
Dig	696	0.274	0.167	0.001	1.022
LOI	696	0.398	0.131	0.031	1.000
Urb	696	0.597	0.119	0.363	0.896
Rev	696	2.326	0.660	0.318	3.645

Note: The sample is a balanced panel covering 30 provinces in China from 2000–2023, yielding 696 province-year observations.

.

4. Empirical Verification

4.1. Model Construction

This study discusses the effect on hydropower resource mismatch caused by digital economic development, so as to construct a direct effect model, as shown in Equation (5):

$${\tau }_{it}={\beta }_0+{\beta }_{1}Di{g}_{it}+{\displaystyle \sum {\beta }_{\mathrm{i}}}controls+{\mu }_i+{\delta }_i+{\epsilon }_{it}$$

(5)

In the equation, $i$ represents region; t represents time; $Controls$ represents control variables; ${\mu }_i$ refers to individual fixed effects; ${\delta }_i$ refers to time fixed effects; ${\epsilon }_{it}$ represents random disturbance terms; ${\beta }_0$ represents constant term; and ${\beta }_1$ represents the regression coefficient of digital economic development on hydropower resource mismatch.

Refer to Liu et al. (2024) [38] for the use of the PVAR model to validate the time lag effects generated by path dependency. The PVAR model captures temporal dependencies and dynamic responses in the relationship of the digital economy on the hydropower resources misallocation through the inclusion of lagged variables. It does not presume causal relationships between variables but instead analyzes how a shock to one variable transmits over time and affects another variable. The core impulse response function intuitively depicts the entire time path of this influence, thereby clearly revealing whether the impact is delayed, when it peaks, and how long it persists. Therefore, the PVAR model is used to discuss time-dynamic effects of digital economic development on the hydropower resource mismatch, as shown in Equation (6):

$$y_{it}={\alpha }_i+{\displaystyle \sum _{p=1}^p{\beta }_p{y}_{it-p}+{\mu }_{it}}$$

(6)

In the above equation, $Y_{it}$ represents the column vector containing all variables in Table 1; ${\alpha }_i$ represents the individual fixed-effects vector, reflecting heterogeneity among individuals; $P$ represents the lag order; and ${\beta }_p$ represents the coefficient matrix, used to measure the impact coefficient of the lag $P$ period.

We referred to Xu and Li (2022) [39] using the panel threshold model to validate the impact of the digital economy varies depending on regional attributes. The threshold regression can automatically identify the specific threshold value of the industrialization level and divide the sample into different regimes. Through piecewise regression, it can estimate the differential impact coefficients of digital economy on hydropower resources mismatch in regions with high versus low industrialization levels. This allows the model to precisely reveal how the effect of the digital economy changes with varying degrees of regional industrialization. Taking a single threshold as an example:

$${\tau }_{it}={\phi }_0+{\phi }_{1}Di{g}_{it}I\left(LO{I}_{it}\le \chi \right)+{\phi }_{2}Di{g}_{it}I\left(LO{I}_{it}>\chi \right)+{\phi }_{3}Controls+{\mu }_i+{\epsilon }_{it}$$

(7)

where $\chi$ denotes the threshold value to be evaluated; $I$ acts as a indicator function, defined such that it is 1 under the bracket condition and 0 in all other cases; and ${\phi }_1$, ${\phi }_2$, and ${\phi }_3$ denote the parameters to be estimated. Specifically, when the level of industrialization in the region is less than the $\gamma$ value, the estimated coefficient capturing the effect of digital economy development on the hydropower resource mismatch is ${\phi }_1$; otherwise, the regression coefficient is ${\phi }_2$. ${\phi }_3$ is the parameter estimates associated with the control variables.

4.2. Empirical Results

(1)

Impact effect analysis

Before conducting the impact effect analysis, the Hausman test must be performed to determine the applicability of fixed effects and random effects while testing the original data for stationarity. The results are shown in

Table 2. Hausman test.

Chi2(4)	Prob > Chi2	H0: Suitable for Random Effects Model
18.51	0.001	Reject the null hypothesis

and

Table 3. Stationarity test.

Variable	LLC Unit Root Test		IPS Unit Root Test
	Statistic	p-Value	Statistic	p-Value
τ	−7.713 ***	0.000	−0.724	0.235
Dig	−12.458 ***	0.000	−3.641 ***	0.001
LOI	−8.587 ***	0.000	0.859	0.805
Urb	−8.696 ***	0.000	−0.022	0.491
Rev	−6.7711 ***	0.000	1.082	0.860

Note: (1) The null hypothesis for both LLC and IPS test is that the panel contains a unit root; (2) *** indicates significance at the 1% level.

.

The results of the Hausman test reject the null hypothesis in favor of the fixed effects model over the random effects specification.

The stationarity test indicates that all variables are stationary according to the LLC unit root test but fail the IPS test. Therefore, to obtain stationary data, first-order differencing is performed on each variable. The results of stationarity test after differencing are shown in

Table 4. First-order difference stationarity test.

Variable	LLC Unit Root Test		IPS Unit Root Test
	Statistic	p-Value	Statistic	p-Value
τ	−29.771 ***	0.000	−12.571 ***	0.000
Dig	−20.067 ***	0.000	−9.704 ***	0.000
LOI	−48.189 ***	0.000	−14.357 ***	0.000
Urb	−34.836 ***	0.000	−9.321 ***	0.000
Rev	−44.227 ***	0.000	−9.164 ***	0.000

Note: *** indicates significance at the 1% level.

.

For datasets integrated at the same order, the Kao and Pedroni tests were employed to establish the presence of cointegration among the variables, thereby determining whether the raw data could be utilized directly for modeling analysis. The test results are presented in

Table 5. Kao test.

	Statistic	p-Value
Modified Dickey–Fuller t	1.604 *	0.054
Dickey–Fuller t	1.529 *	0.063
Augmented Dickey–Fuller t	2.467 ***	0.007

Note: *** indicates significance at the 1% level; * indicates significance at the 10% level.

and

Table 6. Pedroni test.

	Statistic	p-Value
Modified Phillips–Perron t	8.420 ***	0.000
Phillips–Perron t	−13.776 ***	0.000
Augmented Dickey–Fuller t	−16.598 ***	0.000

Note: Both the Kao and Pedroni tests examine the null hypothesis that no cointegration exists among the variables. *** indicates significance at the 1% level.

.

The cointegration tests refute the null hypothesis of no cointegration is rejected at the 10% significance level, confirming a long-run relationship among variables. Therefore, the original dataset can be utilized within a fixed-effects framework to assess the immediate influence of the digital economy on the hydropower resource mismatch, as shown in

Table 7. Direct impact effects.

τ	Coefficient	Standard Error	T-Statistic	p-Value	95% Confidence Interval
Dig	−0.069 ***	0.018	−3.80	0.000	[−0.105, −0.334]
Rev	−0.153 ***	0.019	−8.12	0.000	[−0.190, −0.116]
Urb	−0.782 ***	0.102	−7.70	0.000	[−0.982, −0.582]
Cons	−0.378 ***	0.064	−5.90	0.000	[−0.505, −0.252]

Note: The dependent variable is the degree of hydropower resource mismatch τ. *** indicates significance at the 1% level.

.

The estimated effect of Dig is −0.069, significant at the 1% level. Regression results confirm the validity of Hypothesis 1, i.e., the digital economy can effectively mitigate the hydropower resources mismatch. Notably, the negative and significant coefficients on Rev and Urb suggest that promoting urbanization levels and enhancing industrial profitability are also important avenues for alleviating the misallocation of hydropower resources.

(2)

Time-dynamic analysis

Furthermore, we use the PVAR model to deconstruct the above effects from a time-dynamic perspective. The AIC, BIC, and HQIC principles are used to select the lag order in the model. The corresponding results are presented in

Table 8. Optimal lag order test.

Lag	AIC	BIC	HQIC
1	−35.636 *	−31.042 *	−33.774 *
2	−34.561	−28.379	−32.049
3	46.419	54.712	49.787
4	40.598	51.875	45.146
5	42.760	58.642	48.972

Note: * indicates significance at the 10% level.

.

Combining the AIC, BIC, and HQIC test, the optimal lag order is determined to be 1. Based on Formula (5), the impulse response of digital economic development to hydropower resource mismatch is shown in Figure 1.

As illustrated in Figure 1, when digital economy receives a pulse signal of 1 unit, it can have a negative effect on hydropower resource mismatch. This negative effect appears after a lag of 1 period, reaches its maximum after a lag of 2 periods, and then tends to stabilize. This indicates that China’s hydropower industry is constrained by existing technological pathways and exhibits path dependence, preventing the advantages of digital economic development from being fully realized in a timely manner. This creates a “time lag” in technological benefits, and Hypothesis 2 is confirmed.

(3)

Spatial heterogeneity analysis

By means of panel threshold regression, the effect of digital economic development on hydropower resource mismatch across regions with differing industrialization levels can be seen. The threshold number test is shown in

Table 9. Threshold number test.

Maximum Number of Thresholds	Threshold Value	Sum of Squared Residuals	Mean Square Error	F Statistic	p-Value
Single threshold	0.256 ***	0.767	0.003	68.43	0.000

Note: *** indicates significance at the 1% level.

, and the threshold value maximum likelihood test is shown in Figure 2.

As shown in Table 9, the threshold number test indicates that a single threshold value is significant. From the threshold value maximum likelihood test in Figure 2, no double threshold effect is observed. Therefore, the level of industrialization in a region can be divided into two segments (i.e., LOI ≥ 0.256 and LOI < 0.256) to study how the digital economy influences the hydropower resource mismatch, as shown in

Table 10. Threshold regression results based on industrialization level.

τ	Coefficient	Std.	T-Statistic	p-Value	95% Confidence Interval
Dig (LOI ≥ 0.256)	−0.056 ***	0.020	−2.74	0.007	[−0.096, −0.157]
Dig (LOI < 0.256)	−0.086 ***	0.019	−4.59	0.000	[−0.122, −0.489]
Rev	0.154 ***	0.019	8.22	0.000	[0.117, 0.191]
Urb	0.820 ***	0.091	9.00	0.000	[0.640, 0.999]
Cons	−0.390 ***	0.061	−6.36	0.000	[−0.510, −0.269]

Note: (1) The dependent variable is the degree of hydropower resource mismatch τ; (2) the threshold variable is the level of industrialization (LOI). The estimated threshold value is 0.256, which splits the sample into two regimes: low industrialization and high industrialization. *** indicates significance at the 1% level.

.

According to the findings presented in Table 10, when a region’s level of industrialization is below the threshold of 0.256, the estimated coefficient for digital economy development on hydropower resource mismatch is −0.056, significant at the 1% level. When industrialization exceeds 0.256, the estimated coefficient becomes −0.086, significant at the 1% level. Specifically, regions with weak industrialization foundations limit the digital economy’s capacity to enhance the efficiency of hydropower resource allocation through mechanisms such as information sharing, technological penetration, and platform economies, whose positive effects have not yet been fully realized. As industrialization levels rise, the marginal effect of digital economic development in alleviating hydropower resource misallocation significantly increases. A stronger industrialization foundation provides a more favorable environment for the digital economy to empower resource allocation. This enables digital tools and technologies to more effectively promote the optimized utilization of hydropower resources, with their leverage effect in mitigating mismatches being significantly amplified. The above conclusions confirm the validity of Hypothesis 3.

(4)

Robustness tests

This study uses alternative indicator measures for robustness testing. Building upon the findings of He et al. (2024) [40] and Wang and Shi (2021) [41], an indicator system was constructed as a measure of digital economic development, considering data availability. Indicator weighting was conducted by means of the entropy method.

All indicators in

Table 11. Digital economy development indicator system.

First-Level Indicator	Second-Level Indicator	Third-Level Indicator	Weight
Dig	Digital Infrastructure	Broadband internet penetration rate	0.019303
		Internet broadband penetration rate	0.018685
		Mobile phone infrastructure scale	0.023538
		Long-haul fiber optic cable length	0.019692
		Number of web pages	0.125858
		Count of domain names	0.077648
	Digital Industrialization	Telecom business volume per capita	0.071201
		Popularization rate of mobile phones	0.012631
		Registered firms in ICT and software services	0.066565
		Share of workforce engaged in IT and software sectors	0.050498
		Number of patents granted	0.08112
		Patent applications received	0.071792
	Industrial Digitalization	Peking University digital financial inclusion index	0.013716
		Proportion of enterprises engaged in e-commerce activities	0.01897
		E-commerce sales	0.083743
		Websites per 100 enterprises	0.006832
		Added value of secondary and tertiary industries	0.038384
		Investment in scientific and technological innovation	0.06947
		Express delivery volume	0.130356

are positive-oriented. Broadband Internet penetration rate is calculated as the number of Internet broadband access ports divided by the number of permanent residents in the region; Internet broadband penetration rate is calculated as the number of Internet broadband access users divided by the number of permanent residents in the region; mobile phone infrastructure scale refers to the capacity of mobile phone switches; telecom business volume per capita is calculated as the total telecom business volume divided by the region’s permanent residents; popularization rate of mobile phones is calculated as the number of telephones per 100 people; share of workforce engaged in IT and software sectors is calculated as the number of employees in urban units of information transmission, software, and information technology services divided by the total number of employees in urban units; investment in scientific and technological innovation refers to the R&D funds of industrial enterprises above a designated size.

The dataset comprises information compiled from National Bureau of Statistics of China and the Wind Database, while the digital financial inclusion index comes from the institute of digital finance at Peking University.

Comparing results in Table 7 and

Table 12. Robustness test results.

τ	Coefficient	Standard Error	T-Statistic	p-Value	95% Confidence Interval
Dig	−0.637 ***	0.058	−10.94	0.000	[−0.752, −0.523]
Rev	−0.127 ***	0.016	−3.29	0.000	[−0.190, −0.116]
Urb	−0.302 ***	0.092	−3.29	0.001	[−0.159, −0.096]
Cons	−0.126 **	0.056	−2.24	0.026	[−0.238, −0.015]

Note: The dependent variable is the hydropower mismatch τ. *** indicates significance at the 1% level; ** indicates significance at the 5% level.

reveals that, during the robustness test using the alternative indicator measure, the direction of influence on hydropower resource misallocation remained unchanged for all variables. This confirms that the empirical analysis presented in this paper exhibits good robustness.

5. Discussion and Implications

5.1. Discussion

This study extends the application of path dependence theory from institutional and technological evolution to resource allocation. It empirically demonstrates that historical legacy issues within energy systems create inertia, thereby delaying the digital economy’s ability to correct the hydropower resource misallocation. Furthermore, it deepens the application of Comparative Advantage Theory by introducing a region’s level of industrialization as a threshold variable. This provides a new perspective for rationally employing digital technologies to address hydropower resource misallocations across different regions.

Empirical discussions reveal that digital economic development significantly alleviates hydropower resource misallocation, which aligns with studies such as [9,10,11,12,13,14,15,16], demonstrating digitalization’s positive role in enhancing energy efficiency. However, by introducing the critical dimension of temporal dynamics, this study uncovers a time-lag effect in how digital economic development influences the hydropower resource mismatch. This provides a detailed explanation of some scholars’ view that enhancing resource allocation efficiency remains challenging within the digital economy [42,43]. The short-term ineffectiveness of digital policies may reflect a broader phenomenon of path dependence.

Secondly, guided by the comparative advantage theory, this paper uses the level of industrialization to analyze the spatial heterogeneity in the effects of digital economic development. This finding supports conclusions drawn by Ulucak (2021) [44] and Cheng et al. (2024) [22], both of whom emphasized that gains from technological advancement are not automatically distributed evenly. Building on this, our study highlights that the level of industrialization serves as a critical threshold condition, providing a theoretical basis and empirical evidence for explaining when and where digital economy policies are most likely to successfully correct the misallocation of hydropower resources.

5.2. Policy Implications

This study offers significant theoretical, practical, and social contributions. Theoretically, it extends the path dependence theory and Comparative Advantage Theory into the domain of resource allocation, illustrating how historical technological and institutional inertia delay the benefits of digitalization and how regional factor endowments shape the effectiveness of digital economy policies. The findings advocate for differentiated policy interventions: regions with higher industrialization levels should pursue deep digital integration, while less industrialized regions should focus on strengthening foundational infrastructure and digital literacy to enhance absorptive capacity. Socially, by mitigating hydropower misallocation, this research supports China’s dual carbon goals, promotes energy conservation, reduces emissions, and facilitates the transition toward a more efficient, equitable, and sustainable energy governance model. In summary, the following policy implications are proposed:

(1)

Digital infrastructure should be expanded to enhance the foundation for digital economic development. Comprehensive coverage of digital infrastructure across the region should be promoted to ensure that local residents enjoy a better digital life. The digital economy should be used to eliminate information transmission barriers and shorten the distance of resource transmission to alleviate the problem of hydropower resource mismatch resulting from market information asymmetry. Growing number of Internet users enables faster and more convenient transmission of information and knowledge. Digital technology can promote initiatives and policies related to energy conservation and emission reduction and encourage people to adopt a green and low-carbon lifestyle.

(2)

The hydropower industry’s issue of technical path lock-in should be addressed through timely and appropriate measures. In the short term (lagging by one period), given that the potential of the digital economy remains partially untapped, efforts should focus on breaking free from existing technical path dependencies. Policy guidance can be used to encourage hydropower companies to pilot digital technology adaptation projects, thereby shortening the application adaptation period for digital technology in the hydropower sector and laying the groundwork for its future impact. In the medium to long term, as the negative effects of the digital economy peak, we should take advantage of the momentum to promote large-scale application. We should boost dedicated investment in the digital transformation of hydropower and improve the accuracy of water resource allocation.

(3)

The estimated industrialization threshold of 0.256 is not merely a statistical artifact but carries significant practical meaning. It serves as a critical quantitative benchmark that distinguishes between two distinct phases of regional economic structure. A region with an industrialization level (LOI) below 0.256 typically relies on a more traditional economic mix, potentially with a larger agricultural or nascent service sector. Its industrial base is likely less mature, with limited advanced manufacturing, weaker technological absorption capacity, and less developed supporting infrastructure. Conversely, a region with an LOI exceeding 0.256 has reached a stage of more advanced industrialization, characterized by a denser aggregation of industrial enterprises, more complex supply chains, greater capital intensity, and a more robust foundation in physical and human capital.

In policy terms, this threshold provides a clear, data-driven answer to the following question: “Which type of digital economy policy should be prioritized for optimizing hydropower allocation?” Our findings indicate that the corrective influence of the digital economy is markedly stronger in regions that have crossed this developmental threshold (LOI ≥ 0.256). For these regions, policymakers can confidently promote deep-integration digital policies, the adoption of AI-powered predictive maintenance, and the implementation of real-time data-driven resource dispatch systems. These regions possess the necessary ecosystem to effectively absorb and utilize such advanced technologies.

For regions still below the threshold (LOI < 0.256), the policy focus must be fundamentally different. In this study, the marginal returns on advanced digital applications are lower. Instead, policy should prioritize building foundational capacities by strengthening basic grid and water network infrastructure, enhancing digital literacy, promoting the intelligent transformation of traditional industries, and fostering market-oriented reforms to improve the business environment. Prematurely investing in advanced digital tools in these regions may lead to inefficient capital allocation and poor outcomes.