The Impact of Digital Economy on the Cost of Carbon Emission Reduction—A Theoretical and Empirical Study Based on a Carbon Market Framework

Abstract

A central sustainability question is how the digital economy helps societies decarbonize at lower cost. We develop a carbon-market-consistent framework to show how digitalization can strengthen market governance, reduce regional carbon-abatement costs, and accelerate green transformation. Using data for 30 Chinese provinces from 2011–2022, we estimate panel fixed-effects models and conduct numerical simulations to test the digital economy’s dynamic, inverted-U-shaped effect on abatement costs, accounting for internal and external drivers. The digital development shifts the abatement–cost curve downward and leftward by speeding the transition from internal mitigation costs to external trading costs, enabling regions to reach the cost-reduction stage earlier and at lower overall cost. Mechanism evidence indicates two channels: externally, digitalization enhances carbon-market sophistication (liquidity, price discovery, and compliance efficiency); internally, it promotes technological progress and energy-efficiency improvements that raise emission-reduction productivity. In the short run, emissions trading provides external incentives that buffer production-cost pressures from digital-capital investment; in the long run, digital growth accelerates the energy transition and structurally increases abatement efficiency. Heterogeneity analysis shows a more pronounced inverted-U in central and western provinces, while eastern provinces have largely entered a sustained cost-decline phase. By lowering the social cost of achieving emissions targets, the digital economy directly supports sustainable development and China’s green, low-carbon transition.

1. Introduction

Carbon emissions trading (ETS) is widely regarded as a crucial tool for achieving emission reduction targets due to its institutional flexibility and cost-effectiveness. Carbon markets attract participants through quota allocation and price signals, thereby distributing reduction costs across regions [1,2]. However, such external incentives can easily lead to carbon leakage. Environmental regulations alone struggle to facilitate energy transitions in high-energy-consumption areas, potentially increasing compliance pressures and suppressing market activity. To advance sustainable green and low-carbon transformation, carbon trading must share costs in the short term while fostering long-term internal incentives for corporate emissions reduction. This requires technological progress and structural upgrades to drive sustained cost reductions and efficiency gains.

The digital economy is emerging as a new engine for overcoming technological bottlenecks, advancing industry, and accelerating the green transition [3,4]. Internally, it enables process optimization and innovation, raises energy efficiency, and supports electrification, renewable integration, energy storage, and demand response, strengthening system resilience and energy security. Externally, cloud computing and big data improve carbon market transparency and price discovery, reduce transaction costs, and align economic activity with environmental goals, supporting sustainable and just transitions. In its early stages, however, the digital economy may temporarily lift regional emissions and internal abatement costs because of infrastructure and energy use. Despite its importance, there is no consensus on how digitalization affects regional emission reduction costs. Existing research either emphasizes the reduction of internal costs through digitalization [5,6,7] or highlights the reduction of external costs via carbon markets [1,2,8,9], often treating these effects in isolation and failing to adequately recognize synergistic effects and dynamic processes: first, whether dynamic nonlinearities and inflection points exist; second, the mechanisms and relative weights of key drivers; third, whether carbon trading can buffer short-run cost pressures during the initial wave of digital investment without merely shifting emissions across space. Neglecting these issues risks biased judgments and policy misalignment, making a unified framework that integrates internal and external drivers essential for comprehensive assessment.

This paper makes three contributions. Theoretically, it embeds digital factors in a unified allowance supply–demand framework, linking external price incentives with firms’ internal productivity improvements. Empirically, using provincial data for 2011–2022, it identifies an inverted-U relationship between the digital economy and abatement costs: carbon trading buffers cost pressures in the short term, while digitalization drives reductions over the long term. Methodologically, it adopts an integrated econometric–simulation approach, using fixed effects and mediation analysis for identification and a structured numerical model to separate internal and external costs and evaluate policy scenarios. Unlike prior studies that treat carbon trading and digitalization as independent levers, this paper models their interaction in a single framework and explicitly tests dynamic nonlinearity and short-term buffering. The result is a clearer account of the mechanisms and the evolution of regional abatement costs. The remainder of this paper is structured as follows. Section 2 reviews the relevant literature and outlines the theoretical framework. Section 3 details the research methods and data sources. Section 4 presents the main empirical results, including robustness checks and numerical simulations. Section 5 offers further discussion, covering mechanism analysis, heterogeneity analysis, and additional robustness considerations. Finally, Section 6 summarizes the main conclusions and discusses the policy implications.

2. Literature Review and Research Hypothesis

2.1. Literature Review

Despite rising interest, there is no consensus on how Dig affects CR along the energy transition. From the internal-incentive perspective, studies link Dig to carbon emissions, carbon efficiency, and marginal abatement costs, arguing that digitalization lowers CR by optimizing industrial structure, accelerating technological innovation, and improving energy efficiency and factor substitutability [5,6,7]. Nevertheless, much of this work downplays the external role of emissions trading systems (ETS). In practice, ETSs set caps and intensity constraints that strengthen green transformation in high-emission regions while creating price signals and trading gains for lower-emission regions—stimulating market activity and easing local abatement pressures [10,11,12]. However, ETS on its own often reorders costs without reshaping energy use or industrial processes; it can heighten compliance challenges or invite “greenwashing,” especially in energy-intensive sectors where firms prefer allowance purchases to investments in electrification, process innovation, or efficiency retrofits [8,9,13,14,15]. As a result, observed CR declines may reflect transaction-cost savings rather than genuine, energy-efficiency-driven emission cuts. Crucially, robust quota accounting; monitoring, reporting, and verification (MRV); and oversight depend on digital infrastructures (cloud, IoT, big data) that reduce external transaction costs, while industrial digitalization (real-time monitoring, digital twins, predictive control) boosts energy efficiency and lowers internal abatement costs. Although some studies note these benefits [3,4], most treat them in isolation, overlooking the synergy between internal efficiency gains and external market functioning—an integration this paper explicitly examines [16].

In summary, much of the literature treats ETS and Dig as parallel, single-channel instruments for abatement, analyzing each in isolation. Studies that focus only on Dig’s internal drivers can overstate its mitigation potential by ignoring that firms often rely on ETS to meet compliance under regulatory pressure; conversely, ETS-only analyses may overestimate the long-run power of market signals to deliver green transformation while downplaying the role of digitalization in building firms’ own abatement capacity. A fuller account of the dynamics and evolution of CR requires a unified framework that couples digital enablement with ETS incentives along the energy-transition pathway. In practice, industrial digitalization lowers internal costs by raising energy efficiency—via real-time monitoring, predictive control, intelligent scheduling, and support for electrification and fuel switching—while digital infrastructures for carbon accounting, registries, and MRV improve market transparency and quota management, refining carbon-price adjustment and cutting external transaction costs [3]. These dual effects accelerate the rebalancing of abatement from internal reductions toward market trading and compress total costs, making Dig a key driver of coordinated CR reduction and green transformation. Early-stage digital growth entails additional capital outlays and energy use (e.g., data centers and networks) that can raise short-term production costs. Whether enhanced ETS design and market depth can offset these pressures through more substantial external incentives remains an open question. Against this backdrop, this paper takes the Dig–CR relationship as a point of departure, explicitly incorporates carbon trading, and systematically examines how internal (technology and energy-efficiency gains) and external (market sophistication and price discovery) channels interact—within a carbon-allowance supply–demand equilibrium—to reduce CR over the course of the energy transition.

2.2. Theoretical Analysis Framework and Research Hypotheses

2.2.1. Theoretical Model

Referring to existing studies [17,18], this paper constructs a carbon abatement cost function incorporating a carbon trading mechanism (see Appendix A.1 for derivation):

$${CR}_t={\displaystyle \frac{P_t^2{E}_t^2}{4a_t{Y}_t}}$$

(1)

In this framework, $P_t$ denotes the carbon trading price, $E_t$ represents regional carbon emissions, $a_t$ is the marginal cost of carbon abatement, and $Y_t$ is the total regional output. As discussed above, the influence of Dig on CR largely hinges on its ability to stimulate both internal and external incentives for emission reduction. For internal drivers, this study highlights $E_t$ as a key element in Equation (1). The central question is whether digitalization can drive technological progress in emission reduction, resulting in a sustained decrease in per-unit carbon emissions, and thus lower the compliance costs that businesses face under environmental regulations. For external drivers, the $P_t$ becomes crucial. Here, we focus on whether digital elements can invigorate carbon market activity, reduce information asymmetry, and enhance carbon price discovery and adjustment mechanisms. These improvements can help address market failures and ultimately lower transaction-related abatement costs across society. To better capture the dual role of digitalization, this study further analyzes the mechanisms underlying $E_t$, $P_t$, and ${CR}_t$, with explicit integration of digital economy elements. Drawing on the Green Solow Model [19,20], we decompose and examine how digitalization shapes the evolution of each key component. Specifically, the decomposition method for carbon emissions is as follows:

$$E_t={\Omega }_t{Y}_t-{\Omega }_t\tau \left(Y_t,Y_t^{Ƴ}\right)={\Omega }_t{Y}_t\rho \left(\theta \right)={\Omega }_t{K}_t^{\alpha }{D}_t^{\beta }{\left(A_t{L}_t\right)}^{1-\alpha -\beta }\rho \left(\theta \right)$$

(2)

where $\rho \left(\theta \right)=1-\tau (1,\theta )$ is the abatement function and $\theta ={\displaystyle \frac{Y_t^{Ƴ}}{Y_t}}$ is the ratio of emission reduction outputs to total outputs. Following Brock and Taylor [19], $\tau (1,\theta )$ represents the conversion rate of emission reduction inputs, comprehensively reflecting the effectiveness of existing emission reduction technologies, the availability and complementarity of clean inputs, as well as the organization’s absorption and execution capabilities. A higher value indicates greater emission reductions per unit of input. Since low-cost opportunities are typically prioritized, $\tau (1,\theta )$ generally increases as $\theta$ (the proportion of emissions-related outputs) rises. However, the marginal improvement diminishes, reflecting the characteristic progression of emissions reduction from easier to more challenging measures. Assume that the abatement function satisfies the following conditions $\rho \left(0\right)=1$ and ${\rho }^{\prime }\left(\theta \right)<0, {\rho }^{″}\left(\theta \right)>0$. Then it represents that the abatement inputs benefit pollution-reduction efforts, and its marginal effect decreases as the degree of reduction deepens. Under certain conditions, it can be considered $\rho \left(\theta \right)={\left(1-\theta \right)}^{\xi },\xi >1$. In addition, according to Brock and Taylor, the rate of technological progress in abatement is assumed to be $-g_{\Omega }$, i.e., $-g_{\Omega }={\displaystyle \frac{\dot{{\Omega }_t}}{{\Omega }_t}}$, as the change in the amount of pollution per unit of output. Under the balanced growth path, assuming that the Inada condition is satisfied for the $Y_t$ production function, with θ fixed, then the balanced growth path $g_y=g_k=g_d=g_c=g>0$ exists. Since $k_t$ and $d_t$ converge to a constant $k^{*},d^{*}$, then the growth rate of carbon emissions along the balanced growth path, $g_E$, depends on the growth rate of population, n, the growth rate of technological progress in production, g, and the growth rate of technological progress in abatement, $g_{\Omega }$, with $g_E=n+g-g_{\Omega }$. This implies that to achieve an increase in per capita consumption and an improvement in environmental quality within the constraints of environmental resources, conditions need to be met such that $g_{\Omega }>n+g, g_E<0$. Assuming that the Inada condition is satisfied for the Y production function, with θ fixed and $\rho \left(\theta \right)$ fixed, it can be found that $a_{i1}=a_{i2}=a$ will be a constant according to the marginal carbon abatement cost a. Therefore, based on the $P_t$ reported in Appendix A.1, the analysis can be further detailed as follows:

$$\begin{array}{c}{P}_t\hfill \\ ={\displaystyle \frac{{\sum }_{i1}^{I1}\left(E_{t,i1}-A_{t,i1}-F_{t,i1}\right)+{\sum }_{i2}^{I2}\left(E_{t,i1}-A_{t,i2}-F_{t,i2}\right)}{{\sum }_{i1=1}^{I1}\frac{E_{t,i1}^2}{2a_i{Y}_{t,i1}}+{\sum }_{i2=1}^{I2}\frac{E_{t,i2}^2}{2a_i{Y}_{t,i2}}}}\hfill \end{array}$$

$$\begin{gathered} \hspace{0.33em}={\displaystyle \frac{\rho \left(\theta \right){\sum }_{i1}^{I1}{\Omega }_t{Y}_{t,i1}+\rho \left(\theta \right){\sum }_{i2}^{I2}{\Omega }_t{Y}_{t,i2}-u_t}{{\sum }_{i1=1}^{I1}\frac{{\Omega }_t^2{Y}_{t,i1}\rho {\left(\theta \right)}^2}{2a}+{\sum }_{i2=1}^{I2}\frac{Y_{t,i2}\rho {\left(\theta \right)}^2}{2a}}} \\ ={\displaystyle \frac{2a}{{\Omega }_t\rho \left(\theta \right)}}-{\displaystyle \frac{2au}{{\Omega }_t^2\rho {\left(\theta \right)}^{2}Y}}\hspace{1em}, u_t=\sum _{i1}^{I1}(A_{t,i1}+F_{t,i1})+\sum _{i2}^{I2}(A_{t,i2}+F_{t,i2}) \end{gathered}$$

(3)

Here, u represents the total quota, which can be further divided into mandatory carbon emission limits ($A_{t,i}$) and forest carbon sinks ($F_{t,i}$); the latter are used to offset emissions within the voluntary carbon market. Including $F_{t,i}$ as offsets serves two key purposes: first, it acknowledges that forest carbon sinks, as an important part of the voluntary market, should be factored into carbon trading to help stimulate market activity and address short-term quota shortages; second, it allows for a more comprehensive assessment of how digital factors influence CR when forest carbon sinks are included in robustness analyses.

It is important to note that the effectiveness of emission reductions in the carbon market depends on the stringency of the total cap and the strength of regulatory enforcement. If the cap is set too loosely, quota trading may increase in the short term without producing a meaningful decline in overall emissions [1]. This outcome reflects a policy design issue rather than a flaw in the market mechanism itself. Provided that regulatory authorities gradually tighten the total quota in line with emission reduction targets, the carbon market should, over time, lead to substantial reductions in total emissions. Therefore, this study further examines long-term CR under two scenarios: one where the total quota remains constant, and another where the quota changes dynamically over time (t).

When $u_t$ is a constant:

$p_{a,t}={\displaystyle \frac{2a}{{\Omega }_t\rho \left(\theta \right)}}$ refers to the portion of the carbon trading price that represents the total regional carbon emissions, and $p_{b,t}={\displaystyle \frac{2a{u}_t}{{\Omega }_t^2\rho {\left(\theta \right)}^2{Y}_t}}$ represents the equilibrium price determined by taking into account the inclusion of carbon emission allowances and forestry carbon sinks so that CR under the forestry carbon trading framework is:

$$CR(t)={\displaystyle \frac{{\left(p_{a,t}-p_{b,t}\right)}^2{\Omega }_t^2{Y}_t\rho {\left(\theta \right)}^2}{4a}}\hspace{0.33em}={\displaystyle \frac{\left(p_{a,t}^2+p_{b,t}^2-2p_{a,t}{p}_{b,t}\right){\Omega }_t^2{K}_t^{\alpha }{D}_t^{\beta }{\left(A_t{L}_t\right)}^{1-\alpha -\beta }\rho \left(\theta \right)\rho {\left(\theta \right)}^2}{4a}}$$

(4)

Order

$$\partial {\displaystyle \frac{p_{a,t}^2}{\partial t}}\hspace{1em}=2p_{a,t}^2{g}_{\Omega },\partial {\displaystyle \frac{p_{b,t}^2}{\partial t}}\hspace{1em}=2p_{b,t}^2\left(2g_{\Omega }-n-g-\alpha {\displaystyle \frac{\dot{k_t}}{k_t}}-\beta {\displaystyle \frac{\dot{d_t}}{d_t}}\right),\partial {\displaystyle \frac{p_a{p}_b}{\partial t}}=p_a{p}_b\left(3g_{\Omega }-n-g-\alpha {\displaystyle \frac{\dot{k_t}}{k_t}}-\beta {\displaystyle \frac{\dot{d_t}}{d_t}}\right),$$

Therefore, the CR of digital elements is included, as shown below:

$${\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}=-\underset{\mathrm{Environmental} \mathrm{Regulation}}{g_{\Omega }}+\underset{\mathrm{Internal} \mathrm{Motivation}}{g_E}+\alpha {\displaystyle \frac{\dot{k_t}}{k_t}}+\beta {\displaystyle \frac{\dot{d_t}}{d_t}}$$

(5)

From Equation (5), if regulatory authorities do not adjust carbon emission limits in line with emission reduction targets—meaning that u remains unchanged—the expected relationship between carbon prices and abatement costs may be diminished or even offset. As a result, carbon prices will no longer function effectively as an external driver for reducing CR. Furthermore, under the conditions described above, both $g_{\Omega }$ and $g_E$ can be considered constants, so ${\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}$ is a binary function on $k\left(t\right)$ and $d\left(t\right)$ when the economy reaches the steady state, $\dot{k}\left(t\right)=0, \dot{d}\left(t\right)=0{\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}=-g_{\Omega }+g_E<0$, where $g_E<0$ and $g_{\Omega }>0$. At this time, the carbon abatement cost is on a downward trend, as shown in Figure 1. Only when the condition ${\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}>0$ holds does the cost of carbon emissions reduction increase; conversely, only when the condition ${\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}<0$ is met does the cost decrease. As a result, the ratio of data capital stock to $CR\left(t\right)$ per unit of effective labor exhibits an inverted U-shaped trend—rising initially and then declining. Notably, even if the carbon trading price mechanism does not function as intended, technological progress ($-g_{\Omega }$) driven by environmental regulation continues to exert downward pressure on CR.

When $u$ is affected by time t:

According to the definition of $u_t$, regulatory authorities are expected to continuously tighten the total emissions quota in line with emission reduction targets, causing $u_t$ to decline over time. As the ETS matures, inter-regional quota transfers will likely become more frequent. For example, technologically advanced enterprises or regions with surplus quotas may sell them to areas facing greater emissions reduction challenges, without affecting the overall market cap. Thus, the initial total quota and the ongoing tightening mechanism are key to ultimately “locking in” society’s emissions ceiling.

In this context, this study assumes the following relationship between regional carbon emissions ($E_t$) and the total quota ($u_t$): $u_t=\left(1-{\upsilon }_t\right)E_t$, u represents the carbon emissions that must be offset by the regulatory cap ($A_t$) and forest carbon sinks ($F_t$), and ${\upsilon }_t$ is the proportion of emissions not offset. With the advancement of digitalization, information transparency in carbon trading has improved. According to information asymmetry theory, greater transparency enhances the bargaining power of market participants and helps optimize allocation of the emissions cap ($A_t$) [3]. Additionally, Qiu et al. note that rapid Dig development enables precise monitoring of forestry production processes [21]. The digitization of forest rights—an important digital element—expands the area and absorption capacity of forest carbon sinks, increasing the value of $F_t$. This improves the overall efficiency of carbon abatement $\left(1-{\upsilon }_t\right)$ and increases the quantity of offset quotas ($u_t$). As a result, ${\upsilon }_t$ satisfies the conditions $0<{\upsilon }_t<1$ and $-g_{\upsilon }={\displaystyle \frac{\dot{{\upsilon }_t}}{{\upsilon }_t}}<0$, where $g_{\upsilon }$ represents the growth rate of carbon market sophistication. More specifically, the combination of improved transparency in quota allocation and higher value of forest carbon sinks drives the maturity of the carbon market, boosting both the volume of quota transactions and the number of emissions that can be offset. Nevertheless, as stated by condition $0<{\upsilon }_t<1$, the total volume of quotas will always remain below the carbon emissions ceiling due to ongoing regulatory constraints. Therefore, by substituting these relationships into Equation (3), we obtain $P_t={\displaystyle \frac{2a{\upsilon }_t}{{\Omega }_t\rho \left(\theta \right)}}$, and by substituting into Equation (1), we can analyze the change in CR under the carbon trading framework as follows:

$$\begin{gathered} {\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}=\underset{\mathrm{External} \mathrm{Motivation}}{2\left(g_{\Omega }-g_{\upsilon }\right)}-\underset{\mathrm{Environmental} \mathrm{Regulation}}{g_{\Omega }}+\underset{\mathrm{Internal} \mathrm{Motivation}}{g_E}+\alpha {\displaystyle \frac{\dot{k_t}}{k_t}}+\beta {\displaystyle \frac{\dot{d_t}}{d_t}} \\ =n+g-2g_v+\alpha {\displaystyle \frac{\dot{k_t}}{k_t}}+\beta {\displaystyle \frac{\dot{d_t}}{d_t}} \end{gathered}$$

(6)

As shown in Equations (5) and (6), when external incentives are present, the key factor in CR through carbon pricing is the difference between the growth rate of emission reduction technology ($g_{\Omega }$) and that of carbon market maturity ($g_{\upsilon }$). In the early stages of carbon market development, $g_{\Omega }$ is typically much lower than $g_{\upsilon }$, as firms tend to rely on carbon trading to meet emission limits—even when regulatory authorities impose stricter constraints.

Moreover, for sustained growth, ongoing technological progress is essential for supporting increases in per capita consumption. Thus, to ensure continuous improvement in ecological and environmental quality, the growth rate of technological progress needed to satisfy both mandatory emission limits ($A_t$) and forest carbon sinks ($F_t$) must exceed the growth rate of total output (i.e., $2g_v>n+g$). Otherwise, ${\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}>0$ will persist over time. Therefore, the following assumptions are made:

H1. 

There is an inverted U-shaped relationship between Dig and CR under a carbon trading framework that includes a compliance mechanism for forestry carbon sink offsets.

2.2.2. The Digital Economy Reduces Carbon Reduction Costs Through External Forces

As shown in Equation (6), changes in the equilibrium carbon price are determined by the difference between the growth rate of emission reduction technology ($g_{\Omega }$) and the growth rate of carbon market maturity ($g_{\upsilon }$). When $g_{\Omega }>g_{\upsilon }$, the carbon price ($P_t$) rises; conversely, when $g_{\Omega }<g_{\upsilon }$, the carbon price decreases. In the early stages, abatement technologies and energy-efficiency retrofits are still immature and costly, and digital/process upgrades raise unit costs—especially under carbon-intensive power mixes where electrification benefits have yet to materialize. Consequently, firms in high-emitting regions typically meet quota obligations through external mechanisms—purchasing allowances in the carbon market—rather than undertaking internal technological upgrades or industrial restructuring (e.g., electrification, fuel switching, high-efficiency systems), which require larger capital outlays and longer lead times.

Against this backdrop, Dig can materially deepen the sophistication of emissions trading systems (ETS)—i.e., strengthen external drivers—thereby easing allowance prices and lowering overall CR. On the information layer, upgraded digital infrastructure (IoT sensors, big-data MRV, blockchain, and AI analytics) enables real-time collection, transmission, and sharing of emissions data, reducing information asymmetry and transaction frictions while sharpening price discovery. These clearer price signals guide firms toward energy-efficiency retrofits, electrification of processes, and renewable integration, aligning market incentives with the energy transition. On the participation layer, digital trading platforms expand access—especially for low-carbon and quota-surplus firms—boosting liquidity, improving risk management and compliance, and offering high-emission enterprises lower-cost, flexible compliance options as they phase in internal upgrades. Through these mechanisms, Dig strengthens external incentives, accelerates the conversion of higher internal abatement costs into lower external transaction costs, and compresses CR in the near term, while crowding in longer-term investment in efficiency and clean energy. Based on these insights, this paper proposes the following hypothesis:

H2. 

Dig can reduce CR by increasing the growth rate of carbon market sophistication and reducing the price of carbon trading.

2.2.3. Dig Contributes to the Cost of Carbon Reduction by Influencing Technological Progress

To address the issue of technological progress being treated as an exogenous variable, this paper draws on Romer’s “Learning by Doing” model [22], expresses technological progress in terms of cumulative total investment (physical capital and data capital), and constructs a green Solow model that takes physical capital into account, so that technological progress can be expressed as follows.

$$A_t=K_t^{\phi }{D}_t^{\eta }$$

(7)

In order to simplify the analysis, the physical capital depreciation and data capital depreciation factors are ignored here, and the derivation is then divided by $\dot{D_t}$ so that ${\displaystyle \frac{\dot{A_t}}{\dot{D_t}}}=\phi K_t^{\phi -1}{\displaystyle \frac{\gamma }{1-\gamma }}{D}_t^{\eta }+K_t^{\phi }{D}_t^{\eta -1}\eta$ can be deduced, and taking into account that the progress of the production technology may lead to the progress of the emission reduction technology, this paper assumes that there is a correlation between the two [20], i.e., $g_{\Omega }=\phi g$, and therefore the growth rate of technological progress is:

$$g={\displaystyle \frac{\dot{A_t}}{A_t}}=\phi {\displaystyle \frac{\dot{K_t}}{K_t}}+\eta {\displaystyle \frac{\dot{D_t}}{D_t}}$$

(8)

At steady state, i.e., ${\displaystyle \frac{\dot{k_t}}{k_t}}=0,{\displaystyle \frac{\dot{d_t}}{d_t}}=0$, the growth rates of total output, total consumption, total physical capital stock, and total data capital stock are $g_Y=g_C=g_K=g_D={\displaystyle \frac{n}{1-\phi -\eta }}$, combined with the following conclusions based on Equation (5):

$$\begin{array}{c}{\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}=-2g_{\Omega }+{\displaystyle \frac{\phi n+\eta n}{1-\phi -\eta }}+n=-2\phi {\displaystyle \frac{\dot{A_t}}{A_t}}+{\displaystyle \frac{\phi n+\eta n}{1-\phi -\eta }}+n\hfill \\ =\left(-2\phi \right){\displaystyle \frac{\dot{A_t}}{A_t}}+{\displaystyle \frac{\dot{A_t}}{A_t}}+n=\left(1-2\phi \right){\displaystyle \frac{\dot{A_t}}{A_t}}+n=g-2g_{\Omega }+n\hfill \end{array}$$

(9)

From Equation (9) it follows that ${\displaystyle \frac{\partial }{g_{\Omega }}}\left({\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}\right)=-2<0$, indicating that a faster rate of emission-reduction technological progress lowers the growth rate of CR. The relevant threshold is ${\displaystyle \frac{g+n}{2}}$: when $g_{\Omega }>{\displaystyle \frac{g+n}{2}}$, ${\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}<0$ and $CR\left(t\right)$ declines over time; when $g_{\Omega }<{\displaystyle \frac{g+n}{2}}$, ${\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}>0$, and $CR\left(t\right)$ rises. Moreover, because $g_{\Omega }=\phi g={\displaystyle \frac{\phi n}{1-\phi -\eta }}$ and ${\displaystyle \frac{\partial g_{\Omega }}{\partial \eta }}={\displaystyle \frac{\phi n}{{\left(1-\phi -\eta \right)}^2}}>0$, a larger $\eta$ (stronger technological spillovers from new data capital) monotonically raises $g_{\Omega }$. Accordingly, analyses of how Dig affects CR through technological progress should focus on the position of $g_{\Omega }$ relative to the ${\displaystyle \frac{g+n}{2}}$ threshold.

From a sustainable-development perspective, the influence of digitalization on carbon abatement costs operates through two distinct pathways, governed by the relative position of the emission-reduction technology growth rate $g_{\Omega }$ against the threshold ${\displaystyle \frac{g+n}{2}}$, First, the emission-reduction technology pathway: when digitalization advances such that $g_{\Omega }>{\displaystyle \frac{g+n}{2}}$, we have ${\displaystyle \frac{\dot{C}R\left(t\right)}{CR\left(t\right)}}>0$, and $CR\left(t\right)$ declines over time. This outcome indicates that digital infrastructure, data assets, and intelligent applications reduce the marginal cost of abatement by accelerating green process innovation, upgrading pollution-control equipment, and optimizing production workflows. The result is a virtuous cycle of “economic growth → tighter emission constraints → cost reduction,” consistent with the Sustainable Development Goals—particularly Affordable and Clean Energy, Industry, Innovation and Infrastructure, and Climate Action—and supportive of a relative decoupling between growth and emissions. Second, the production-technology pathway: given the persistent presence of general technological progress $\mathrm{g}$, if $g_{\Omega }<{\displaystyle \frac{g+n}{2}}$ and the energy mix has not yet undergone substantive decarbonization, efficiency gains alone may be accompanied by scale effects and continued reliance on high-carbon energy. These forces can offset potential improvements in $CR\left(t\right)$ yielding a limited net effect of digitalization—or even a short-run increase—in abatement costs. The policy implication is clear: to convert digitalization into a genuine “decarbonization dividend,” governments and firms must jointly promote the R&D and diffusion of dedicated abatement technologies while accelerating the green transformation of the energy mix (e.g., expanding clean electricity shares, mobilizing green investment, and improving access to green finance). Such coordinated action enables systemic innovation to surpass the critical threshold $g_{\Omega }>{\displaystyle \frac{g+n}{2}}$, thereby delivering sustained, low-cost emission reductions alongside high-quality economic growth. Accordingly, we posit that

H3a. 

At the emission reduction technology level, Dig lowers CR.

H3b. 

At the production technology level, Dig has limited impact on carbon reduction costs.

In summary, the theoretical framework of how the digital economy influences carbon emission reduction costs through internal and external drivers is illustrated in Figure 2.

3. Research Methodology and Data Sources

3.1. Measurement Model

To verify the relationship between CR and Dig development derived from the theoretical model analysis, this paper will utilize the balanced panel data of 30 provinces (cities) in China for empirical analysis. This paper sets the following benchmark regression model:

$$\mathit{ln}C{R}_{i,t}={\beta }_0+{\beta }_1\mathit{ln}Di{g}_{i,t}+{\beta }_2{\left(\mathit{ln}Di{g}_{i,t}\right)}^2+\sum Controls+u_i+v_j+{\epsilon }_{it}$$

(10)

where $C{R}_{i,t}$ is CR calculated under the forestry carbon trading framework, $Di{g}_{i,t}$ is the level of digital economic development, and the following table i, t denotes the variable’s value in year t for province i, respectively. $Controls$ denotes the form of aggregation of various control variables, $u_i$ is the province fixed effect, $v_j$ is the year fixed effect, and ${\epsilon }_{it}$ is the random disturbance term.

3.2. Measurement of Variables and Descriptive Statistics

3.2.1. Implicit Variable

CR: This study measures regional carbon abatement costs (${CR}_{t,i}={\displaystyle \frac{P_t^2{E}_t^2}{4a_t{Y}_t}}$) based on the carbon emission rights supply–demand equilibrium framework [17,18]. To further test the robustness of the results, we construct an alternative indicator, $CR\_F_{t,i}$, which incorporates forest carbon sinks ($F_{t,i}$) into the calculation of abatement costs; this is addressed in the robustness analysis. Specifically, the role of forest carbon sinks is reflected by including $F_{t,i}$ in the calculation of the carbon price ($P_t$). The calculation methods for other variables involved in the analysis are described as follows:

$$P_t={\displaystyle \frac{{\sum }_{i1}^{I1}\left(E_{t,i1}-A_{t,i1}-F_{t,i1}\right)+{\sum }_{i2}^{I2}\left(E_{t,i1}-A_{t,i2}-F_{t,i2}\right)}{{\sum }_{i1=1}^{I1}\frac{E_{t,i1}^2}{2a_{t,i}{Y}_{t,i1}}+{\sum }_{i2=1}^{I2}\frac{E_{t,i2}^2}{2a_{t,i}{Y}_{t,i2}}}},a_{t,i}=1.57-0.17\times \sqrt{{\displaystyle \frac{E_{t,i}}{Y_{t,i}}}-\underset{i}{min}{\displaystyle \frac{E_{t,i}}{Y_{t,i}}}}$$

(11)

Carbon emissions: In this paper, the baseline methodology introduced in the 2006 IPCC Guidelines for National Greenhouse Gas Inventories is used to calculate the carbon emissions in the industrial sector by referring to the studies of Zuo et al. and Wang et al. [23,24], and the formulas are as follows:

$$E_{t,j}={\sum }_{j=1}^8\left(E{I}_{t,j}\times NC{V}_{t,j}\times CE{F}_{t,j}\times {\displaystyle \frac{44}{12}}\right)$$

(12)

$E{I}_j$ denotes the consumption of the energy source in j, $NC{V}_{t,j}$ denotes the standard coal conversion factor of the energy source in j, and $CE{F}_{t,j}$ denotes the carbon emission factor of the energy source in j.

Carbon Emission Allowance $A$: Based on the research of Xia et al., using the carbon emission intensity data of the past years [25], this paper obtained the initial carbon emission allowance of each province in China from 2011 to 2022. Then, based on the studies of Han et al. [26], the initial carbon emission quotas were redistributed through the ZSG-DEA method for carbon emission reduction responsibility. Among them, the specific calculation method of the initial carbon emission quota is as follows:

$$A_{t,i}=GD{P}_{i,2010}\times {\left[1+\left(5.00\sim 6.00\right)\%\right]}^{t-2010}\times I_{i,2010}\times {\left(1-q\right)}^{t-2010}$$

(13)

$q=1-\sqrt[20]{{\displaystyle \frac{I_{2005}\times \left(1-\beta \right)}{I_{2010}}}}$ is the average annual carbon intensity change rate between 2011 and 2022.

The quantity of emission reduction compliance $F_{t,i}$: New carbon sinks are additional removals of carbon dioxide from the atmosphere, in line with the principle of “additionality” in the carbon offset mechanism [27], and new forestry sinks ($\Delta C_{i,(t_2-t_1)}$) are used as a measurement indicator. The formula is as follows:

$$\begin{array}{c}{F}_{t,i}=\Delta C_{\left(t_2-t_1\right),i}=C_{t_2,i}-C_{t_1,i}\hfill \\ \hfill =\sum S_{t_2,i}\times C_{t_2,i}+\Phi \times \sum S_{t_2,i}\times C_{t_2,i}+{\rm Z}\times \sum S_{t_2,i}\times C_{t_2,i}\\ \hfill -\sum S_{t_1,i}\times C_{t_1,i}+\Phi \times \sum S_{t_1,i}\times C_{t_1,i}+{\rm Z}\times \sum S_{t_1,i}\times C_{t_1,i}\end{array}$$

(14)

$$c_{ti}=v_{ti}\times \delta \times \rho \times r$$

(15)

$\Delta C_{(t_2-t_1),i}$ is the incremental sink of forestry in the province i during $(t_2-t_1)$ (million tons). Based on the principle of conservatism and referencing the study by Li et al., we set $(t_2-t_1)$ to 1 year and limited the accounting scope to three carbon pools: aboveground, belowground, and forest soil biomass [27]. Here, $s_{ti}$ denotes the forest per unit area of province i in year t, while $v_{ti}$ denotes the forest stock per unit area of province i in year t. For details on other parameters, refer to

Table 1. Forest Carbon Stock Measurement Parameters.

Parameter	Symbol	Value
Carbon Conversion Coefficient of Understory Plants	$\Phi$	0.195
Forest Carbon Conversion Coefficient	${\rm Z}$	1.244
Biomass expansion factor	δ	1.9
Bulk density	ρ	0.5
Carbon content	r	0.5

.

3.2.2. Core Explanatory Variables

Dig: Based on the essence of the digital economy and referencing the “2019 China Digital Economy Development Index” released by the China Center for Information Industry Development, this paper constructs a comprehensive evaluation index system for the digital economy across three dimensions—digital infrastructure, digital industrialization, and industrial digitalization—drawing on existing literature [28,29]. The digital infrastructure dimension emphasizes network capacity and interconnectivity levels, hence selecting indicators such as the number of domain names, IPv4 addresses, and internet access ports. The digital industrialization dimension aims to characterize the scale and platformization of core digital industries, employing indicators such as the number of IT enterprises, software business revenue, and the scale of digital finance [29]. The industrial digitalization dimension measures corporate network application levels and e-commerce penetration through indicators including the number of websites owned by enterprises, e-commerce transaction volume, and the proportion of enterprises engaging in e-commerce activities (specific definitions are provided in Appendix B). Weight allocation employs the entropy weighting method for objective weighting: standardized indicators undergo inter-provincial variance analysis to calculate information entropy values. Greater variance indicates higher information content, thus warranting higher weights. Final scores across the three dimensions are integrated using the equal-weight averaging method to maintain structural consistency.

3.2.3. Mechanism Variables

Degree of carbon market perfection: Given the limited availability of direct data on the level of carbon market development, this study utilizes numerical simulation methods to examine whether Dig can lower CR by enhancing carbon market maturity. Specifically, different scenario parameters (i.e., $g_v$ in Equation (6) set at 0.04, 0.05, and 0.06 are used to simulate dynamic changes in carbon trading prices). This approach allows us to assess the impact of digitalization on carbon prices and abatement costs via improvements in market sophistication. It should be noted that this component constitutes a sensitivity analysis, testing the model’s response to varying levels of carbon market perfection. By analyzing market sophistication as a mechanism variable, we aim to reveal its role and transmission effects more deeply in the pathway through which Dig affects CR.

Emission Reduction Technological Progress and Production Technological Progress: Based on the role of technological progress in production and environmental protection, and with reference to the literature of Liu et al., Addis et al., and Zhou et al. [30,31,32], this paper adopts the number of green patents granted per 10,000 people (GP) and the efficiency value of the green global super-efficiency SBM model (ERTP) as the metrics of emission reduction technological progress. The GML index (PTP), which is calculated based on the green global super-efficiency SBM model to remove non-expected outputs, is used as its production technology progress.

3.2.4. Control Variable

Given the many determinants of CR, we include the following covariates as controls to mitigate omitted-variable bias: (1) Industrial structure (lnIS). Upgrading the industrial structure reshapes energy use and emissions intensity. A larger service-sector share is typically associated with lower energy intensity and a reduced compliance burden, thereby lowering CR [33]. (2) Financial development (lnFDL). A well-functioning financial system eases financing constraints for green investment (e.g., equipment upgrades, process controls), lowers the cost of capital, and accelerates clean-technology adoption, thus reducing CR [34]. (3) Urbanization (lnUL). Urban agglomeration facilitates the diffusion of cleaner production practices and spreads fixed governance costs over a larger base, yielding long-run reductions in CR; however, greater demand density may temporarily raise energy consumption in the short run [35]. (4) Employment (lnHCL). A larger labor force strengthens implementation capacity and absorptive capability, reducing the marginal labor cost of carbon governance [36]. (5) Human capital (lnLFL). Higher levels of human capital enhance the absorption of green technologies, the diffusion of innovation, and process optimization, thereby lowering marginal abatement costs. (6) Technology-market development (lnTMDL). More developed technology markets reduce search, matching, and verification frictions, mitigate performance uncertainty, and accelerate the diffusion and learning of both abatement and general-purpose technologies; this hastens green process substitution and equipment upgrading, thereby lowering CR [14]. (7) Information level (lnIL). lnIL captures the intensity of information acquisition and use at the user/organizational end (demand-side). By promoting knowledge diffusion, process control, and compliance, it reduces governance frictions and implementation costs, thus lowering CR. Importantly, lnIL is conceptually distinct from Dig, which reflects supply-side digital capacity (“digital infrastructure → industrial digitization → digital industrialization”). Modeling lnIL separately limits construct overlap and endogeneity with Dig, enabling a cleaner identification of Dig’s marginal effect on CR [37]. The specific variable measurements are shown in

Table 2. Descriptive statistics of the sample.

Variable	Measurement Method	Mean	Standard	Min	Max
Ln (Carbon abatement costs)	lnCR	6.834	1.433	2.900	10.646
Ln (the digital economy)	lnDig	−2.210	0.733	−4.226	−0.340
Ln (the digital economy)2	(lnDig)2	5.419	3.329	0.115	17.862
Ln (Industrial structure)	lnIS	0.014	0.421	−0.704	1.667
Ln (Financial development level)	lnFDL	1.189	0.289	0.517	2.029
Ln (Urbanization level)	lnUL	−0.528	0.196	−1.049	−0.110
Ln (Level of human capital)	lnHCL	−3.901	0.277	−4.822	−3.132
Ln (Labor force level)	lnLFL	2.023	0.106	1.713	2.182
Ln (Level of technology market development)	lnTMDL	−4.928	1.389	−8.592	−1.656
Ln (Informatization level)	lnIL	−3.093	0.729	−4.223	0.921
Number of green patents authorized per 10,000 people	GP	0.925	1.217	0.029	8.681
Emission Reduction Technology Progress	ERTP	0.187	0.126	0	1.058
Production Technology Progress	PTP	1.337	0.303	0.924	2.454

.

3.3. Data Sources

Limited to data availability, this paper selects the panel data of 30 Chinese provinces and municipalities (excluding Tibet, Hong Kong, Macao, and Taiwan) from 2011 to 2022 for empirical research. Regarding the calculation of forestry sinks, this paper is based on the research line of Li et al. to estimate the cumulative carbon stock of forests in each province from 2011 to 2022 by using the data of forest area and forest stock in 30 provinces(municipalities) from 2010 to 2018 [27]. The data were obtained from the 2009–2017 China Forestry Statistical Yearbook and the 2018 China Forestry and Grassland Statistical Yearbook. Control and mediating variables were obtained from the China Statistical Yearbook (2011–2022). Green-patent counts were extracted from the China National Intellectual Property Administration (CNIPA) database using IPC positions listed in the World Intellectual Property Organization’s International Patent Classification (IPC) Green Inventory, and then aggregated at the provincial level. Provincial energy-consumption data were sourced from the China Energy Statistical Yearbook and the EPS Global Database. The descriptive statistical results of this paper about each variable are detailed in Table 2.

3.4. Characteristic Fact

As illustrated in Figure 3, the relationship between Dig and both $\mathit{ln}CR$ and $\mathit{ln}CR\_F$ is depicted. The results indicate a clear inverted U-shaped relationship between Dig and CR. Moreover, when forest carbon sinks are included, the peak of the inverted U-shaped curve for abatement costs shifts progressively downward, suggesting that forest carbon sinks contribute to further reducing the overall cost of carbon emission reduction.

4. Empirical Findings

4.1. Baseline Results

To empirically verify the inverted U-shaped relationship between Dig and CR, this study introduced first-order and second-order terms of Dig into the estimation model, as presented in Model 1 (

Table 3. Empirical findings.

	(1) lnCR	(2) lnCR	(3) lnCR
lnDig	−1.645 ***	−2.286 ***	−2.231 ***
	(0.553)	(0.256)	(0.264)
(lnDig)2	−0.461 ***	−0.247 ***	−0.271 ***
	(0.122)	(0.027)	(0.032)
_cons	5.371 ***	0.492	3.336
	(0.607)	(0.570)	(3.501)
Time FE	NO	YES	YES
Provinces FE	NO	YES	YES
Controls	NO	NO	YES
N	360	360	360
R 2	0.062	0.981	0.982

Note: *** represent the significance levels of 1%, and the standard errors are in parentheses.

). The results demonstrate that the coefficients for both lndg and (lndg)² are significantly negative (β = −2.231, p < 0.01; β = −0.271, p < 0.01), confirming the presence of an inverted U-shaped relationship. Importantly, this relationship remains robust after incorporating panel fixed effects and controlling for relevant covariates. In other words, the impact of Dig development on CR initially rises and then declines.

This pattern aligns with two dynamics along the energy transition. First, at low levels of digitalization, an immature ETS offers weak external incentives (limited liquidity, shallow price discovery), so digital tools cannot translate nascent efficiency gains into lower CR. Second, early digital build-out—data centers, networks, and sensors—raises energy demand on carbon-intensive grids, while incomplete industrial digitalization and abatement know-how keep production costs high. Once digitalization surpasses the estimated turning point (−b/2a ≈ 4.116), however, concurrent improvements in energy efficiency and abatement technology, together with deeper carbon-market functioning (stronger MRV transparency, better price discovery, and regional burden-sharing through trading), jointly and materially reduce CR; ongoing grid decarbonization and electrification further reinforce this decline.

4.2. Robustness Check

The study also uses the instrumental variable method for robustness testing to avoid model estimation bias due to endogeneity. The selection criteria are to be highly correlated with Dig’s existence and to be exogenous variables, i.e., unaffected by the economic system. Building upon the work of Yang et al. and Su and Li, this study develops two instrumental variables: “fixed telephone lines per 10,000 people in 1984 × national internet users in the previous year” and “fixed telephone lines per 100 people in 1984 × national information technology service revenue in the previous year” [38,39]. These instruments are plausibly exogenous for two reasons: first, the 1984 fixed-telephone density is a historical infrastructure measure that predates the modern digital economy and—apart from operating through digital development—has no direct effect on contemporary abatement costs; second, the lagged national-level variables vary only over time and are unlikely to capture region-specific shocks, making a direct link to the error term outside the Dig channel implausible.

Table 4. Robustness estimation results of the instrumental variables approach.

	Instrumental Variable		Instrumental Variable
	First	Second	First	Second
	lnDig	lnCR	lnDig	lnCR
Instrumental variable	0.035 ***
	(0.006)
Instrumental variable1			0.037 ***
			(0.006)
lnDig		−5.933 ***		−5.460 ***
		(1.148)		(1.010)
(lnDig)2	−0.100 ***	−0.651 ***		−0.602 ***
	(0.004)	(0.120)		(0.106)
_cons	−4.383 ***	−15.50 **	−4.386 ***	−13.10 **
	(0.678)	(7.158)	(0.671)	(6.476)
Time FE	YES	YES	YES	YES
Province FE	YES	YES	YES	YES
Controls	YES	YES	YES	YES
Kleibergen-Paap rk LM		31.08 (0.000)		36.41 (0.000)
Cragg-Donald Wald F		29.29 (16.38)		34.89 (16.38)
N	360	360	360	360
R2	0.992	0.971	0.992	0.973

Note: *** and ** represent the significance levels of 1% and 5%, respectively, and the standard errors are in parentheses.

reports the IV-2SLS estimation results. The stage-1 F-statistics for the weak instrument tests are 29.29 and 34.89, respectively, both of which significantly exceed the Stock–Yogo critical value of 16.38, thereby eliminating concerns about weak instruments. After addressing endogeneity, the findings remain robust: the linear term of lnDig is significantly positive, while the quadratic term (lnDig)² is significantly negative, confirming an inverted U-shaped relationship. This suggests that the effect of the digital economy on carbon emission reduction costs initially rises, then falls, following a non-linear trajectory.

In addition, external environmental shocks, especially policy shocks, may also affect the CR. According to carbon emission policy documents, China’s ETS began in 2013. However, the preparatory work and key steps for ETS started in 2011, and due to the existence of the “announcement effect”, the economic behaviors of provinces and cities were already impacted by the announcement of the “Notice on Carbon Emission Trading Pilot Work” by the National Development and Reform Commission (NDRC). The economic behavior of provinces and cities was already affected when the National Development and Reform Commission (NDRC) announced the “Notice on Carbon Emission Trading Pilot Work”, and enterprises around the world also adjusted their production and investment behaviors according to the policy. Meanwhile, carbon trading pilot programs exert significant spillover effects on surrounding and non-pilot regions. Non-pilot regions also make corresponding adjustments under expected constraints. Therefore, excluding pilot regions does not alter the overall direction or magnitude of the estimates. Therefore, to eliminate the effect of the carbon trading pilot policy, the study controls for and excludes its impact in seven provinces (cities): Shanghai, Beijing, Tianjin, Chongqing, Hubei, Guangdong, and Shenzhen, respectively, and conducts robustness tests on the model.

To identify the causal effect of digital economic development on carbon abatement costs, we exploit the staggered rollout of China’s National Big Data Comprehensive Pilot Zones as an exogenous policy shock in a quasi-natural experiment [40]. Since 2015, these zones—launched in regions such as Guizhou, the Beijing–Tianjin–Hebei cluster, and the Yangtze River Delta—exhibit substantial spatial heterogeneity and policy exogeneity. We construct a treatment indicator equal to one for pilot-zone localities in post-implementation years and estimate a difference-in-differences (DID) model to identify the effect of digital policies on abatement costs. As shown in

Table 5. Model robustness test.

	Dig Policy Shock	TES Policy Shock	Remove Provinces	Substitution of Explanatory Variables	Replacement of Core Explanatory Variables
	lnCR	lnCR	lnCR	lnCR_F	lnCR
Did_Dig	−0.102 **
	(0.050)
Did_TES		−0.372 ***
		(0.082)
lnDig	−2.148 ***	−2.064 ***	−1.690 ***	−2.231 ***
	(0.265)	(0.258)	(0.350)	(0.264)
(lnDig)2	−0.261 ***	−0.244 ***	−0.233 ***	−0.271 ***
	(0.032)	(0.032)	(0.039)	(0.032)
lnDig_pca					−13.035 ***
					(1.716)
(lnDig_pca)2					−6.431 ***
					(1.623)
_cons	3.216	1.166	−3.693	3.336	1.934
	(3.484)	(3.429)	(4.030)	(3.501)	(3.781)
Time FE	YES	YES	YES	YES	YES
Province FE	YES	YES	YES	YES	YES
Controls	YES	YES	YES	YES	YES
N	360	360	288	360	360
R2	0.982	0.983	0.985	0.945	0.982

Note: *** and ** represent the significance levels of 1% and 5%, respectively, and the standard errors are in parentheses.

, after controlling for concurrent digital-economy initiatives and carbon-trading pilot programs, the inverted-U relationship between the digital economy and carbon abatement costs remains robust.

Finally, to address potential endogeneity issues arising from differences in variable measurement, which may lead to biased model estimates, we conducted a series of robustness checks by substituting the dependent and explanatory variables. We replaced lnCR with lnCR_f for the dependent variable, representing regional carbon emission reduction costs calculated under a carbon trading framework incorporating forest carbon sinks. Regarding the explanatory variables, following Zhao Tao et al. [41], we constructed an index system encompassing both internet development and digital inclusive finance development. Using principal component analysis, we assessed the macro-level development of the digital economy and replaced the core explanatory variables in the regressions. The results consistently confirm our findings’ robustness: Dig’s impact on CR maintains an inverted U-shaped relationship, reinforcing the validity of the main conclusions.

4.3. Numerical Simulation Validation

This study employs numerical simulation methods to assess whether integrating digital elements can reduce overall societal costs—and to track the evolution of both internal and external drivers. Specifically, we construct and solve steady-state equations, set relevant parameters, and simulate the relationship between Dig and CR.

4.3.1. Solving the Steady-State Equations

This study draws on the green Solow model proposed by Brock and Taylor to transform Equation (5) [19] into a time-varying carbon abatement cost $CR\left(t\right)$ and price $p\left(t\right)$, with the results shown below:

$$\begin{array}{c}CR\left(t\right)=P^2{\Omega }^2\left(0\right)A\left(0\right)L\left(0\right)EXP\left(\left(n+g-2g_{\Omega }\right)t\right)k^{\alpha }{d}^{\beta }{\rho }^2\left(\theta \right)/4a\hfill \\ p\left(t\right)={\displaystyle \frac{2a\upsilon \left(0\right)EXP\left(-g_{v}t\right)}{\Omega \left(0\right)EXP\left(-g_{\Omega }t\right)\rho \left(\theta \right)}}\hfill \end{array}$$

(16)

Prior to the numerical simulation, to ensure the model achieves a steady state, the relevant variables $k\left(t\right)$ and $d\left(t\right)$ in Equation (15) need to be appropriately treated in order to obtain its steady-state equations. Specifically, when the parameter θ is fixed, it is assumed that the economy starts from any moment t = 0 with positive values of physical capital per unit of effective labor k(0) > 0 and data capital per unit of effective labor d(0) > 0, which means that the economy possesses a certain amount of physical and data capital in the initial stage and puts them into production over time, which will eventually converge to a unique steady-state solution $\left(k^{*},d^{*}\right)$. The result is as follows:

$$\begin{array}{c}{k}^{*}={\left[{\displaystyle \frac{s\left(1-\gamma \right)\left(1-\theta \right)}{n+g+{\delta }_D}}\right]}^{{\displaystyle \frac{1}{1-\alpha -\beta }}}{\left({\displaystyle \frac{\gamma }{1-\gamma }}\times {\displaystyle \frac{n+g+{\delta }_D}{n+g+{\delta }_K}}\right)}^{{\displaystyle \frac{1-\beta }{1-\alpha -\beta }}} \\ d^{*}={\left[{\displaystyle \frac{s\gamma \left(1-\theta \right)}{n+g+{\delta }_K}}\right]}^{{\displaystyle \frac{1}{1-\alpha -\beta }}}{\left({\displaystyle \frac{1-\gamma }{\gamma }}\times {\displaystyle \frac{n+g+{\delta }_K}{n+g+{\delta }_D}}\right)}^{{\displaystyle \frac{1-\beta }{1-\alpha -\beta }}}\end{array}$$

(17)

4.3.2. Parameterization

Based on the analysis of the endogenous variable problem-solving and dynamic equations above, this study verifies the derivation results and related assumptions through a numerical simulation case. Meanwhile, to ensure that the numerical solution of the model has good convergence and stability, this paper sets the initial values of both data capital and physical capital to 0.01 during the Matlab R2021b simulation process. Other specific parameter settings are shown in

Table 6. Parameter value calibration.

Parameter	Baseline	Literature	Parameter	Baseline	Literature
n	0.0053	Zou and Yin [42]	$\beta$	0.2	Wang et al. [43]
$\gamma$	0.5	Wang et al. [43]	s	0.4719	Wang et al. [43]
g	0.02	Luo et al. [44]	a	1.57	Appendix A.1
${\delta }_K$	0.1	Liu et al. [45]	$g_v$	0.02	This paper assumes
${\delta }_D$	0.1	Liu et al. [45]	$A_0$	1	This paper assumes
$\theta$	0.05	Brock and Taylor [19]	$L_0$	1	This paper assumes
$g_{\Omega }$	0.041	Liu et al. [46]	${\Omega }_0$	1	This paper assumes
$\xi$	35	Brock and Taylor [19]	$v_0$	1	This paper assumes
$\alpha$	0.4	Zhou et al. [47]

.

Figure 4a shows that CR follows a clear inverted-U over time with or without digital elements. With digitalization, however, the peak shifts downward and leftward: the highest cost occurs earlier and at a lower level. This reflects not only faster technological progress and energy-efficiency gains (e.g., real-time optimization, predictive control, intelligent scheduling), but—crucially—the external effects of a more sophisticated carbon market that digital tools enable (better MRV transparency, liquidity, and price discovery), thereby hastening the transition toward a cleaner energy mix via electrification and renewable integration.

Figure 4b decomposes internal versus external drivers of CR(k,d) (see Appendix A.2). Introducing digital elements markedly raises the early-stage share of external transaction costs, indicating that digitalization strengthens ETS incentives and lowers market frictions. So high-emission regions can meet compliance through allowance trading while internal abatement technologies are still immature. By enhancing information flow, registry interoperability, and participation—especially from low-carbon firms with surplus quotas—digitalization converts higher internal abatement costs into relatively lower external transaction costs, optimizing the social cost structure during the early energy-transition phase.

In the longer term—especially after the inverted-U inflection—the internal component of CR dominates as digitalization drives sustained energy-efficiency improvements, process innovation, and low-carbon technology adoption; ETS remains complementary but no longer primary. These results indicate that digitalization accelerates the shift from internal to external costs early on and anchors structural efficiency gains later, indirectly supporting.

Hypothesis 3.

Well-functioning carbon-market mechanisms can buffer short-run production and technology cost pressures from digital investment. In contrast, ongoing digital development underpins lasting improvements in emission-reduction efficiency. Sensitivity tests and mediation models (Figure 4; Table 6) further unpack these internal–external channels.

5. Further Analysis

To further elucidate the influence of Dig on CR and its heterogeneous effects, this section employs sensitivity analysis and mediation effect models to examine the mechanisms of carbon market sophistication (external motivation) and technological progress (internal motivation). Additionally, regional heterogeneity analyses are conducted to assess variation across different areas.

5.1. Mechanism Analysis

5.1.1. A Test of the Mediating Effect of Carbon Market Sophistication

This study employs numerical simulation to assess whether Dig can lower CR by deepening carbon-market sophistication—an external channel that complements firms’ internal energy-efficiency gains along the energy-transition path. We implement a sensitivity analysis by setting the growth rate of market sophistication $g_v$ to 0.04, 0.05, and 0.06, and observing how allowance prices and the internal–external decomposition of CR(k,d) respond as the carbon market develops. These settings reflect early-stage conditions in which policy refinement and rising digital penetration (MRV, registries, data connectivity) typically allow market depth and price discovery to accelerate faster than abatement-technology progress. Three considerations motivate this assumption: First, external, market-based compliance costs are generally lower than firms’ short-run marginal costs of internal abatement—especially before substantial grid decarbonization and process electrification—making trading economically attractive for high-emission entities. Second, under regulatory pressure, firms in carbon-intensive regions tend to purchase allowances rather than immediately undertake capital-intensive retrofits while efficiency technologies and clean-energy supply are still maturing. Third, digitalization enhances information flow and matching efficiency in ETS (lower search, verification, and settlement frictions), accelerating higher internal abatement costs into relatively lower external transaction costs. We then trace the dynamic evolution of carbon prices and CR under each gv scenario to reveal how digital elements shape price mechanisms and, over time, interact with energy-efficiency improvements and energy-system decarbonization to redirect the trajectory of abatement costs. The specific simulation results are as follows (Figure 5):

As shown in Figure 5, by holding emissions E fixed and abstracting from the internalization of technological progress, we isolate the external-market channel in a focused sensitivity test. As carbon-market sophistication rises, allowance prices fall and carbon-abatement costs decline. This pattern indicates that cost reductions stem not only from internal technology upgrades but—under early energy-transition conditions—are primarily driven by stronger market mechanisms: high-emission regions substitute expensive in-plant measures with allowance purchases, accelerating the conversion of internal abatement costs into lower external transaction costs and improving the social cost of mitigation. Digitalization catalyzes this shift by enhancing MRV transparency and data connectivity, strengthening participants’ bargaining power, and streamlining allocation, search, and settlement—thereby raising transaction efficiency and speeding entry into the cost-decline phase. At the same time, firms ramp up energy-efficiency retrofits and plan for electrification as the power system decarbonizes. These results strongly support Hypothesis 2: digital elements reduce carbon-abatement costs chiefly by optimizing carbon-price formation and trading efficiency, complementing—but analytically distinct from—the internal efficiency and technology channel.

By aligning the simulations with China’s ETS timeline, we find that digital investment steers market maturity along a clear arc—from primarily quota price discovery toward primarily price stabilization and risk management. In the early pilot phase (2013–2016, $g_v$ = 0.04), the model still shows persistent upward pressure on allowance prices, consistent with thin trading and pronounced volatility across regional pilots [48]. At this stage, digital investment delivers the greatest marginal gains: practical upgrades—digital MRV, unified registries, and better data interoperability—reduce search, verification, and settlement frictions, deepen market depth, and sharpen price discovery. In the decomposition of CR(k,d) in Figure 4b, the external market channel provides most of the cost reductions, while enterprise-side transformations lag.

In the national transition phase (2017–2021, $g_v$ = 0.05), simulated prices turn from rising to falling. Digitalization still lowers transaction frictions and supports price discovery, but its marginal contribution to maturity begins to taper as internal measures—energy-efficiency improvements and gradual electrification—start to matter alongside trading. Since the operational maturity phase beginning in 2022 ($g_v$ = 0.06), as institutional frameworks and sectoral coverage become more comprehensive, the cost-reduction slope of the external channel flattens and prices continue to ease. Digital tools increasingly focus on price stabilization, liquidity provision, and risk management, with maturity growth slowing; cost reductions are now driven mainly by internal efficiency gains [49].

5.1.2. A Test of the Mediating Effect of Technological Progress

A mediation effect model was utilized to assess whether Dig impacts CR by advancing technological progress. As shown in

Table 7. Results of the analysis of mechanisms.

	(1)	(2)	(3)	(4)	(5)	(6)
	GP	lnCR	ERTP	lnCR	PTP	lnCR
lnDig	2.383 ***	−1.924 ***	0.419 ***	−1.665 ***	0.228 ***	−2.283 ***
	(0.443)	(0.270)	(0.057)	(0.274)	(0.087)	(0.266)
(lnDig)2	0.324 ***	−0.229 ***	0.036 ***	−0.223 ***	0.023 **	−0.276 ***
	(0.054)	(0.033)	(0.007)	(0.032)	(0.011)	(0.032)
GP		−0.129***
		(0.033)
ERTP				−1.350 ***
				(0.254)
PTP						0.229
						(0.172)
_cons	−15.097 **	1.393	−0.747	2.327	9.723 ***	1.113
	(5.878)	(3.461)	(0.751)	(3.362)	(1.154)	(3.877)
Time FE	YES	YES	YES	YES	YES	YES
Province FE	YES	YES	YES	YES	YES	YES
Controls	YES	YES	YES	YES	YES	YES
N	360	360	360	360	360	360
R2	0.811	0.983	0.685	0.984	0.953	0.982

Note: *** and ** represent the significance levels of 1% and 5%, respectively, and the standard errors are in parentheses.

, Dig significantly promotes both production technology progress (PTP) and emission reduction technology progress (ERTP) (see also Table 1 and Table 3). Notably, it exerts a significant inverted U-shaped effect on CR through the pathway of emission reduction technology progress, with both first-order and second-order terms being negative. Although Dig fosters improvements in general production technology, this channel does not significantly impact CR. This suggests that, under the current stage of China’s digital economy development, any cost increases arising from production technology advancement do not notably raise overall abatement costs. Two factors may explain this finding. First, in digitally advanced regions, the digital economy has reached a stage where it catalyzes plant-level low-carbon process innovation, real-time energy management, and efficiency retrofits—supporting electrification, fuel switching, and renewable integration—thereby strengthening emission-reduction technologies and accelerating the energy transition. Second, as digitalization lifts output (and initially energy demand), high-carbon regions increasingly rely on external incentives through carbon trading to buffer near-term cost pressures, converting expensive in-house abatement into lower-cost market transactions and preventing a sharp rise in total CR. In sum, digitalization chiefly reduces CR via the internal efficiency channel—sustained improvements in energy efficiency and abatement technology—while ETS provides a complementary, short-run hedge against rising production and technology costs.

Furthermore, the digital economy affects the two technology pathways in different ways: it complements emission-reduction technological progress (ERTP) more closely, whereas its contribution to emission reductions through production technological progress (PTP) is relatively weaker. As industrial digitalization and enabling infrastructure diffuse, AI, digital twins, and energy management systems are turning continuous monitoring, predictive control, electrification, and renewable integration into routine operations. In hard-to-abate sectors such as steel, cement, non-ferrous metals, and chemicals, these data-driven interventions increasingly translate into measurable energy-efficiency gains and tangible emissions reductions, rather than mere capacity upgrades [50]. By contrast, digital upgrades to PTP often coincide with automation, quality enhancement, and output expansion; although energy intensity falls, total energy use and emissions may temporarily rise—reflecting rebound—thereby diluting PTP’s short-run mediating effect on CR [51]. This pattern aligns with broader evidence: cross-country and city-level studies show that digitalization generally improves energy efficiency, yet an inverted-U relationship with emissions frequently appears in early diffusion, so durable net reductions require deeper process optimization and green innovation [52]. From a sustainable-development perspective, prioritizing ERTP-oriented digital adoption (AI-enabled energy management, digital twins, flexible demand, and electrification-/renewables-ready operations) supports long-term efficiency gains, clean energy uptake, better air quality, and higher resource productivity, while carbon markets provide cost hedging during output expansion and complement ERTP upgrades [53].

5.2. Heterogeneity Analysis

Given the variations in resource endowments and economic development across different regions, this study differentiates between regional (economic development level) and Dig development levels to examine potential heterogeneity in the impact of Dig on CR, as reported in

Table 8. Heterogeneity analysis results.

	East	Central	West	Low Dig Region	High Dig Region
	lnCR	lnCR	lnCR	lnCR	lnCR
lnDig	−0.542 **	−2.501 **	−4.810 ***	−3.283 ***	−0.894 **
	(0.273)	(1.166)	(0.379)	(0.892)	(0.382)
(lnDig)2	−0.060 *	−0.477 ***	−0.515 ***	−0.381 ***	−0.087
	(0.036)	(0.174)	(0.046)	(0.101)	(0.085)
_cons	18.755 ***	14.003 *	−21.239 ***	−24.528 ***	11.946 ***
	(3.824)	(7.404)	(6.648)	(5.528)	(4.364)
Time Fe	YES	YES	YES	YES	YES
Province FE	YES	YES	YES	YES	YES
Controls	YES	YES	YES	YES	YES
N	132	96	132	175	185
R2	0.991	0.991	0.991	0.989	0.981

Note: ***, **, and * represent the significance levels of 1%, 5% and 10%, respectively, and the standard errors are in parentheses.

. The results show that the inverted U-shaped relationship between Dig and CR is pronounced in central and western regions and in areas with lower digital economy development. In contrast, this relationship is not evident in eastern regions or areas with more advanced digital economies. Specifically, this can be viewed from two perspectives: (1) From a regional economic structure standpoint, eastern provinces possess a more concentrated production services/manufacturing ecosystem, a more mature platform economy, and a deeper pool of digital talent and complementary capabilities. These conditions compress the “learning and restructuring” phase of digital transformation, enabling enterprises to cross the inflection point earlier and enter the monotonous cost reduction phase sooner [54]. In contrast, many central and western economies remain more resource-intensive or focused on low-to-mid-tier manufacturing. In such contexts, early digitalization requires substantial supplementary investments (process reengineering, data governance, workforce retraining), temporarily elevating coordination and adjustment costs and thus producing a more pronounced inverted U-shaped curve. (2) From an energy endowment perspective, the coal-heavy, energy-intensive structures typical in parts of the Midwest temporarily raise operational and electricity costs for digital technologies, delaying the onset of net cost savings. Eastern provinces benefit from higher energy efficiency, stronger grid interconnections, cleaner energy mixes, and denser digital infrastructure—all accelerating the transition from Dig to CR [55]. In summary, regions with stronger digital ecosystems and energy efficiency (eastern regions) find it easier for Dig to reduce production costs and sustain cost reductions. Conversely, in areas with heavier industrial structures and higher energy intensity (central and western regions), enterprises first encounter greater upfront friction before realizing cost reductions, resulting in the observed inverted U-shaped pattern.

6. Conclusions and Policy Implications

6.1. Main Findings

Strengthening the role of Dig—the new engine—and improving the ETS, an important institutional arrangement for the construction of ecological civilization, are of far-reaching practical significance for promoting China’s green development and realizing a high-quality, inclusive, and sustainable economic transformation. This paper combines the regional carbon trading model with the analytical framework of the Green Solow model and explores the possibility of an inverted U-shaped relationship in which CR shows an increase and then a decrease with the development of Dig under the ETS. Based on the balanced panel data of 30 provinces (municipalities) in China from 2011 to 2022, this study conducts an empirical analysis and verifies how Dig can affect CR by influencing the ETS price through numerical simulation. The results of the study show the following:

First, the theoretical model and the empirical evidence indicate an inverted-U relationship between Dig and CR within the ETS context: costs rise initially and then fall. This result is robust to variable substitution, instrumental-variable estimation, and alternative policy-tier specifications. Mechanistically, Dig accelerates the energy transition—supporting electrification, fuel switching, and integration of renewables—and lifts energy efficiency via real-time monitoring and process optimization. In parallel, it hastens the reallocation of costs from internal abatement to external transaction channels, shifting the inverted-U curve downward and leftward, so regions enter the cost-decline phase earlier and at lower overall CR.

Second, the inverted-U is most pronounced in central and western provinces and areas with lower Dig penetration. In high-energy-consuming regions, digitalization helps overcome initial high-cost barriers by unlocking early efficiency gains and facilitating access to external ETS incentives, yielding sizable reductions in total CR as the power mix gradually decarbonizes.

Third, numerical simulations and mediation models show two operative pathways. Externally, Dig deepens carbon-market sophistication (MRV transparency, liquidity, price discovery), lowering transaction frictions; internally, it advances abatement technologies and sustained energy-efficiency improvements. In the short run, ETS incentives buffer production and technology cost pressures from digital capital; over the long run, sustained digital development becomes the dominant driver of higher abatement efficiency and rising technological standards, reinforcing progress along the energy-transition path.

6.2. Discussions

In the face of urgent decarbonization targets and mounting pressure for regional economic upgrading, governments are accelerating carbon-market development to lower firms’ abatement costs. However, amid rapid digitalization, we still know little about how the digital economy can be harnessed to optimize market mechanisms and drive down both internal (plant-level) and transaction-based abatement costs while advancing the energy transition (electrification, fuel switching, renewable integration) and energy-efficiency improvements. This study fills that gap by explicating how Dig interacts with CR, tracing how Dig enhances carbon-market performance (MRV transparency, liquidity, price discovery) and fosters green technological innovation and efficiency gains. Methodologically, we embed digital factors in a regional carbon-trading model and combine panel fixed-effects estimation with numerical simulation to quantify the dynamic impacts and mechanisms of Dig on CR—capturing both market-driven incentives and production-side efficiency effects. Our framework reflects firms’ true economic calculus during the green transition and is distinct from prior work that isolates single cost dimensions. For the first time, we introduce and test an inverted-U relationship between Dig and CR, and show how digitalization leverages external (market sophistication) and internal (technology and energy-efficiency) drivers to reduce overall regional costs. Key findings are as follows: (1) a robust inverted-U holds—Dig accelerates the shift from internal abatement costs to external transaction costs and shifts the curve downward and leftward, enabling earlier entry into the cost-reduction phase and lower total CR as energy efficiency improves; (2) Dig delivers synergistic reductions in both transaction and internal costs by deepening market sophistication and promoting abatement technologies and operational energy-efficiency, generating leapfrog benefits along the transition path; and (3) under China’s current Dig and ETS trajectories, the production costs of digital investment can be absorbed without materially raising regional CR, particularly as the power mix decarbonizes and efficiency gains compound. Unlike existing studies, we emphasize digitalization’s dual role—optimizing carbon markets and enabling corporate green transformation—and uncover pronounced regional heterogeneity, especially where digital capacity is less developed. Our analysis employs provincial-level data and model simulations, which have inherent limitations: First, measurement errors in indicators may cause misalignment in estimating the inflection point of the inverted U-curve. Second, aggregation at the provincial level obscures significant variations among enterprises. Therefore, our conclusions primarily apply to provinces with mature ETS systems and robust digital infrastructure. Extrapolation should be approached with caution in regions with weak MRV (Monitoring–Reporting–Verification) capabilities, differing electricity market transmission mechanisms, or limited digital capacity. Future work should extend the model to the enterprise level, linking transaction/registration records with corporate energy consumption and cost data to directly estimate actual corporate abatement costs and calibrate parameters accordingly.

6.3. Policy Implications

Based on the conclusions and discussions in this paper, the study draws the following policy implications:

(1)

Digitally upgrade the ETS to raise market efficiency and transparency while advancing the energy transition and broader sustainability outcomes (air quality, resource efficiency, and environmental integrity). Accelerate the informatization and intelligentization of the carbon market by integrating blockchain registries, big-data MRV, and AI-driven anomaly detection to deliver real-time, auditable emissions data and fair price discovery with strengthened safeguards against greenwashing. Build interoperable carbon-accounting systems and an intelligent trading platform with open APIs to enable cross-regional linkage, higher liquidity, and lower transaction costs that also interoperate with corporate sustainability reporting. Couple ETS data with firms’ energy-management systems (IoT, SCADA/MES, digital twins) so that verified energy-efficiency gains and electrification/fuel-switching outcomes are reflected promptly in quota allocation and compliance—thereby reducing CR and improving market functioning.

(2)

Accelerate green technological innovation and shift the energy mix toward cleaner, more efficient supply and use. Increase R&D and demonstration for renewables integration, flexible grids, industrial electrification (e.g., heat pumps, electric kilns), hydrogen for hard-to-abate heat, and high-efficiency motor/drive systems. Resolve bottlenecks in key enabling technologies through university–industry consortia; expand public finance (grants, concessional loans) and targeted incentives (tax credits, contracts for difference, green PPAs). Embed energy-efficiency standards and ISO 50001 adoption, scale retrofit programs, and support demand-response and storage. Complement these with circular-economy and life-cycle design measures (materials efficiency, waste heat/use, reuse and recycling) to curb resource and water footprints, so that higher efficiency and cleaner energy supply lower marginal abatement costs, reduce CR, and deliver growth–environment co-benefits and climate resilience.

(3)

Promote place-based digitalization to leverage complementary regional advantages and support a just energy transition. Pursue differentiated Dig pathways: the eastern region should focus on frontier R&D, advanced analytics, and scaling of low-carbon process innovations; the central and western regions should prioritize digital and power infrastructure (fiber, 5G, industrial IoT), expand the “East-to-West computing power” initiative with energy- and water-efficient green data centers co-located with renewables, and develop platforms that enable traditional industries to digitize operations and improve energy efficiency. Pair investment with worker reskilling/SME support and community co-benefits to ensure an equitable, just transition. Strengthen talent and investment attraction to western hubs, foster interregional data and carbon-market connectivity, and share best practices. Narrowing digital gaps will align external ETS incentives with internal energy-efficiency upgrades nationwide, amplifying CR reductions and accelerating green transformation while safeguarding local environmental quality and ecosystem health.