Optimization Strategy of Digital Economy to Promote the Efficiency of Rural-Urban Integration Based on Big Data Analysis

The CCR model [30] is divided into two perspectives to analyze and assess the effectiveness of decision-making units from the input and output perspectives. The input-based model takes the input surface as the starting point and utilizes the linear programming method to measure the relative efficiency of each decision-making unit to obtain the effective production frontier, and the distance between each decision-making unit and the effective production frontier is used as the basis for determining whether the decision-making unit is DEA effective. If the efficiency value is equal to 1, the decision unit is said to be DEA effective; if the efficiency value is <1, the decision unit is non-DEA effective. The input-based CCR-DEA model is as follows: 1Maxθ=∑r=1suryr0(∑i=1mvixio)−1$$Max\theta = \sum\limits_{r = 1}^s {{u_r}} {y_{r0}}{(\sum\limits_{i = 1}^m {{v_i}} {x_{io}})^{ - 1}}$$ 2s.t.{ ∑r=1suryri−∑i=1mvixij≤0,j=1,2,...,n ur,vi≥ε,r=1,2,...,s;i=1,2,...,m$$s.t.\left\{ {\begin{array}{*{20}{l}} {\sum\limits_{r = 1}^s {{u_r}} {y_{ri}} - \sum\limits_{i = 1}^m {{v_i}} {x_{ij}} \le 0,\:j = 1,2,...,n} \\ {{u_r},{v_i} \ge \varepsilon ,r = 1,2,...,s;i = 1,2,...,m} \end{array}} \right.$$

where ε is a non-Archimedean infinitesimal variable, θ is the performance level index for evaluating the target inputs and outputs, x_ij is the ith input quantity for the jth decision unit (i = 1, ….m); y_ij is the rth output quantity for the jth decision unit (r = 1, …., s); v_i is the weights for the ith input (i = 1, ….m); u_r is the weights for the rth output (r = 1, …., s); If the result is θ = 1, the decision unit is DEA valid; if the result is θ < 1, the decision unit is non-DEA valid.

The above equation is a fractional planning model (the objective function is fractional), so that: 3ur=tur,vi=tvi,t=(∑i=1mvixij)−1$${u_r} = t{u_r},{v_i} = t{v_i},t = {\left( {\sum\limits_{i = 1}^m {{v_i}} {x_{ij}}} \right)^{ - 1}}$$

After Charnes-Cooper transformation into a linear programming model, Eq. (4) is the dual form of CCR-DEA: 4Maxθ=∑r=1suryr0$$Max\theta = \sum\limits_{r = 1}^s {{u_r}} {y_{r0}}$$ 5s.t.{ ∑r=1suryri−∑i=1mvixij≤0,ur≥ε,∑i=1mvixi0=1,vi≥ε r=1,2,...,s;i=1,2,...,m;j=1,2,...,n$$s.t.\left\{ {\begin{array}{*{20}{l}} {\sum\limits_{r = 1}^s {{u_r}} {y_{ri}} - \sum\limits_{i = 1}^m {{v_i}} {x_{ij}} \le 0,{u_r} \ge \varepsilon ,\sum\limits_{i = 1}^m {{v_i}} {x_{i0}} = 1,{v_i} \ge \varepsilon } \\ {r = 1,2,...,s;i = 1,2,...,m;j = 1,2,...,n} \end{array}} \right.$$

The envelope model of CCR-DEA is: 6Minθ=θ0−ε(∑r=1ssr++∑i=1msi−)$$Min\theta = \theta 0 - \varepsilon \left( {\sum\limits_{r = 1}^s {{s_r}^ + } + \sum\limits_{i = 1}^m {{s_i}^ - } } \right)$$ 7s.t.{ ∑j=1nλjxij+si−=θ0xi0,∑j=1nλjxij−sr+=yr0 λj,si−,sr+≥0,i=1,2,...,m r=1,2,...,s;j=1,2,...,n$$s.t.\left\{ {\begin{array}{*{20}{l}} {\sum\limits_{j = 1}^n {{\lambda_j}} {x_{ij}} + s_i^ - = \theta 0{x_{i0}},\sum\limits_{j = 1}^n {{\lambda_j}} {x_{ij}} - s_r^ + = {y_{r0}}} \\ {{\lambda_j},s_i^ - ,s_r^ + \ge 0,i = 1,2,...,m} \\ {r = 1,2,...,s;j = 1,2,...,n} \end{array}} \right.$$

When θ₀ = 1, and s0−=s0+=0$$s_0^ - = s_0^ + = 0$$, the decision unit is DEA valid; when θ₀ = 1, and s0−≠0$$s_0^ - \ne 0$$ or s0+≠0$$s_0^ + \ne 0$$, the decision unit is DEA valid; and when θ₀ < 1, the decision unit is DEA invalid.

Based on the value of ∑j=1nλj$$\sum\limits_{j = 1}^n {{\lambda_j}}$$, the decision unit’s returns to scale are determined;

When ∑j=1nλj=1$$\sum\limits_{j = 1}^n {{\lambda_j}} = 1$$, the decision unit size reward is unchanged, indicating that the decision unit reaches the optimal size;

When ∑j=1nλj>1$$\sum\limits_{j = 1}^n {{\lambda_j}} > 1$$, the payoff of scale of the decision unit is increasing, indicating that the decision unit can increase its output by increasing its inputs;

When ∑j=1nλj<1$$\sum\limits_{j = 1}^n {{\lambda_j}} < 1$$, the payoff of scale of the decision unit decreases, indicating that the decision unit does not need to increase inputs.

The BCC-DEA model was proposed by previous authors in based on the assumption of variable returns to scale of production [31]. The BCC model is based on the assumption of variable returns to scale (VRS), which means that diminishing returns to scale (DRS) implies that the sum of output factors increased is less than the sum of input factors increased by the same units; increasing returns to scale (IRS) implies that the sum of output factors increased is greater than the sum of input factors increased by the same units. In the BCC model, the combined technical efficiency in the CCR model can be decomposed into technical efficiency and scale efficiency.

The BCC-DEA dyadic model is: 8Maxθ=∑r=1suryr0+u0$$Max\theta = \sum\limits_{r = 1}^s {{u_r}} {y_{r0}} + {u_0}$$ 9s.t.{ ∑r=1suryrj−∑imvixij+u0≤0,∑i=1mvixi0=1 ur,vi≥ε,r=1,2,...,s;i=1,2,...,m;u0$$s.t.\left\{ {\begin{array}{*{20}{l}} {\sum\limits_{r = 1}^s {{u_r}} {y_{rj}} - \sum\limits_i^m {{v_i}} {x_{ij}} + {u_0} \le 0,\sum\limits_{i = 1}^m {{v_i}} {x_i}0 = 1} \\ {{u_r},{v_i} \ge \varepsilon ,r = 1,2,...,s;i = 1,2,...,m;{u_0}} \end{array}} \right.$$

The BCC-DEA envelope model is: 10Minθ=θ0−ε(∑r=1ssr++∑i=1msi−)$$Min\theta = {\theta_0} - \varepsilon \left( {\sum\limits_{r = 1}^s {s_r^ + } + \sum\limits_{i = 1}^m {s_i^ - } } \right)$$ 11s.t.{ ∑j=1nλjxij+si−=θ0xi0,∑j=1nλjyrj−sr+=yr0 ∑j=1nλj=1,λj,si−,sr+≥0 i=1,2,...,m;r=1,2,...,s;j=1,2,...,n$$s.t.\left\{ {\begin{array}{*{20}{l}} {\sum\limits_{j = 1}^n {{\lambda_j}} {x_{ij}} + s_i^ - = \theta 0{x_{i0}},\sum\limits_{j = 1}^n {{\lambda_j}} {y_{rj}} - s_r^ + = {y_{r0}}} \\ {\sum\limits_{j = 1}^n {{\lambda_j}} = 1,{\lambda_j},s_i^ - ,s_r^ + \ge 0} \\ {i = 1,2,...,m;r = 1,2,...,s;j = 1,2,...,n} \end{array}} \right.$$

Considering that BCC model can comprehensively analyze the comprehensive technical efficiency, pure technical efficiency and scale efficiency of publishing listed companies, and that the characteristics of the production possibility set and the requirements for input-output indexes are in line with the actual situation of the publishing listed companies, this paper chooses the BCC model in the DEA method as the calculation model.

The Malmquist Productivity Index (MPI) is used to measure the dynamics of total factor productivity in the context of multiple-input multiple-output (MIMO) efficiency measurement, which can be further decomposed into changes in efficiency and technology. Applying the Malmquist index model [32-33] method requires the use of the same time period data and technological time change during the study period, setting the production technology corresponding to periods s and t to be T^s and T^t, respectively, and at the same level of technology, the ratio of the distance function of period s to that of period t is the definition of the Malmquist index. Taking T^s as a reference, the corresponding Malmquist index is calculated as: 12Ms(s,t)=Ds(xt,tt)Ds(xs,ys)$$Ms(s,t) = \frac{{{D_s}({x_t},{t_t})}}{{{D_s}({x_s},{y_s})}}$$

If the decision cell is technologically efficient (i.e., D_s(x_s, y_s) = 1) in period S, then equation (12) becomes Ms(s, t) = D_s(x_t, t_t), which indicates that the value of the distance to output at a fixed level of technology in period s is the producer’s change in productivity from period s to period t. If the producer reaches a technologically efficient state in period t, it is Ms(s, t) = D_t(x_t, t_t).

However, the production technology of enterprises in different periods is different, so the measured Malmquist productivity index has a bias, the average method can be used to eliminate the time factor caused by the measurement of the bias, the specific formula is as follows: 13M(s,t)=[ Ms(s,t)⋅Mt(s,t)]12$$M(s,t) = {\left[ {\begin{array}{*{20}{c}} {{M_s}(s,t) \cdot {M_t}(s,t)} \end{array}} \right]^{\frac{1}{2}}}$$

At the same time, the Malmquist productivity index can also be obtained by calculating the values of the D_S(x_s, y_s), D_s(x_t, y_t), D_t(x_t, y_t), D_t(x_s, y_s) four distance functions with the help of the method of multiple distance functions.

To summarize, when the decision-making unit is in a technically effective state, the calculation of Malmquist productivity index is very simple, but if the decision-making unit is technically ineffective, then the technical efficiency and the progress of the production technology may be the cause of the change of the Malmquist productivity index, and even sometimes the effect of the two together. In this case, the Malmquist productivity index needs to be decomposed in order to further determine the factors at play, decomposing the productivity index into two aspects: changes in efficiency and changes in technological progress, with the following formula: 14M(s,t)=[ Ds(xt,yt)Ds(xs,ys)⋅Dt(xt,yt)Dt(xs,ys)]12$$M(s,t) = {\left[ {\begin{array}{*{20}{c}} {\frac{{{D_s}({x_t},{y_t})}}{{{D_s}({x_s},{y_s})}} \cdot \frac{{{D_t}({x_t},{y_t})}}{{{D_t}({x_s},{y_s})}}} \end{array}} \right]^{\frac{1}{2}}}$$

Since D(x, y) is bounded and Ds(x_x, y_x) ≤ 1 and D_i(x_i, y_i) ≤ 1 always hold, it shows that it is difficult for the decision unit to keep the technology effective at all times in the production process, and in the case of ineffective technology, the formula can be modified as: 15M(s,t)=Dt(xt,tt)Ds(xs,ys)[Ds(xt,yt)Dt(xt,yt)⋅Ds(xs,ys)Dt(xs,ys)]12$$M(s,t) = \frac{{{D_t}({x_t},{t_t})}}{{{D_s}({x_s},{y_s})}}{\left[ {\frac{{{D_s}({x_t},{y_t})}}{{{D_t}({x_t},{y_t})}} \cdot \frac{{{D_s}({x_s},{y_s})}}{{{D_t}({x_s},{y_s})}}} \right]^{\frac{1}{2}}}$$

Therefore, the value of technical efficiency change from period s to period t based on input orientation can be calculated by Di(xi,yi)Ds(xs,ys)$$\frac{{{D_i}({x_i},{y_i})}}{{{D_s}({x_s},{y_s})}}$$, while the value of technical change solved between two periods at x and x_t can be measured by [Ds(xt,yt)Dt(xt,yt)⋅Ds(xs,ys)Dt(xs,ys)]$$\left[ {\frac{{{D_s}({x_t},{y_t})}}{{{D_t}({x_t},{y_t})}} \cdot \frac{{{D_s}({x_s},{y_s})}}{{{D_t}({x_s},{y_s})}}} \right]$$.

Based on the above equation the expression equations for the change in technical efficiency and technical progress can be written as the following two equations respectively: 16Dt(xt,yt)Ds(xs,ys)=yt/ycys/ya$$\frac{{{D_t}({x_t},{y_t})}}{{{D_s}({x_s},{y_s})}} = \frac{{yt/yc}}{{ys/ya}}$$ 17[Ds(xt,yt)Dt(xt,yt)⋅Ds(xs,ys)Dt(xs,ys)]12=[yt/ybyt/yc⋅ys/yays/yb]12$${\left[ {\frac{{{D_s}({x_t},{y_t})}}{{{D_t}({x_t},{y_t})}} \cdot \frac{{{D_s}({x_s},{y_s})}}{{{D_t}({x_s},{y_s})}}} \right]^{\frac{1}{2}}} = {\left[ {\frac{{yt/yb}}{{yt/yc}} \cdot \frac{{ys/ya}}{{ys/yb}}} \right]^{\frac{1}{2}}}$$

In this paper, the input indicators are decomposed into 3 dimensional indicators from economic integration, social integration and spatial integration. According to the requirements of urban-rural integration development policies in past years, the output indicators are decomposed into 3 dimensional indicators from digital infrastructure, industrial digitization and digital industrialization, and the urban-rural integration input-output indicator system is shown in Table 1.

This paper takes the digital economy in Guangdong Province to promote the integrated development of urban and rural areas as an example for the research of this paper’s content. The data come from the Guangdong Statistical Yearbook, China Economic and Social Big Data Platform and Wind Database. Considering the accessibility and validity of the data, a sample of 20 prefectural-level cities in Guangdong Province (except Shenzhen) is selected as the DEA decision-making unit in 2022-2023, to measure the change in the efficiency of inclusive finance to support urban-rural integrated development.

Organize the panel data of 20 prefecture-level cities in Guangdong Province from 2017 to 2023, process them with deap2.1 software, and choose to calculate the Malmquist indexes of the 20 decision-making units in the model of input orientation and variable returns to scale, and this paper lists the average Malmquist indexes of Guangdong Province cities from 2017 to 2023 and the decomposition results are shown in Table 2.

tfpch is the total factor productivity index, indicating the overall efficiency change of inclusive finance to support urban-rural integrated development; techchch is the technological progress index, indicating the technological development of inclusive finance to support urban-rural integrated development; effech is the technological efficiency index, indicating the factor allocation of inclusive finance or the utilization rate of financial resources under the consideration of scale efficiency; pech is the pure technological efficiency pech is the pure technical efficiency index, which indicates the factor allocation of inclusive finance without considering scale efficiency; and sech is the scale efficiency index, which indicates the change in output resulting from the input of financial resources.

1)

The direct mechanism of digital economy affecting urban-rural integration

By empowering the intelligent upgrading of transportation infrastructure, the digital economy can gradually dissolve the boundaries and spatial barriers between urban and rural development under the dualistic pattern, which is conducive to accelerating the free flow of urban and rural factors and the formation of a unified market. The integration of urban and rural economies is mainly reflected in the mutual penetration and integration of industries. The development of digital economy is not only conducive to injecting “digital vitality” into the development of modern agriculture, but also conducive to promoting the intelligent transformation and upgrading of traditional industries and services, and even giving rise to a number of new forms and modes of business, so as to realize the mutual intermingling of the three major industries in urban and rural areas and to promote each other. Through the reorganization and aggregation of factors, the digital economy can realize online medical care and distance education, guide the sinking of urban high-quality public resources into rural areas, improve the uneven allocation of public resources between urban and rural areas, eliminate the blind spots and difficulties in urban-rural integration and governance, and improve the level of urban-rural governance integration.

Hypothesis 1: Digital economy can promote urban-rural integrated development in 3 aspects: spatial integration, economic integration and social integration.

1)

Sample selection and data sources

The sample of the study is 20 municipal panel data of Guangdong Province from 2017 to 2023, which forms 2,850 sample observations.

In Equation 1, Y_i is the status of urban-rural integration development; X is the level of digital economy development; C_it denotes the set of control variables; λ_i, λ_t denotes city fixed effects and year fixed effects, respectively, and ε_i denotes the random disturbance term. The estimated coefficient α₁ of X_i reflects the effect of digital economy affecting urban-rural integration development, which is the focus of this paper.

In order to explore whether factor allocation efficiency plays a significant mediating role between the digital economy and urban-rural integration development, this paper refers to the ideas of Wen Zhonglin et al. for testing, and the specific model is set as follows: 19Mii=θ0+θ1Xii+Xiiβ+λi+λi+εii$${M_{ii}} = {\theta_0} + {\theta_1}{X_{ii}} + {X_{ii}}\beta + {\lambda_i} + {\lambda_i} + {\varepsilon_{ii}}$$ 20Yi=ω0+ω1Xi+ω2Mi+Ciβ+λi+λi+εi$${Y_i} = {\omega_0} + {\omega_1}{X_i} + {\omega_2}{M_i} + {C_i}\beta + {\lambda_i} + {\lambda_i} + {\varepsilon_i}$$

M_i is the mediating variable. α_i is the total effect of the impact of the digital economy on urban-rural integration and development, ω₁ represents the direct effect, and the mediating effect is calculated as θ₁ω₂ = α₁ − ω₁. 3)

Mediating variables

Factor allocation efficiency is reflected by the degree of factor market distortion. The factor market distortion index is negatively treated to further obtain the corresponding factor allocation efficiency.

The variable regression results are shown in Table 6. Model 1 refers to testing the direct impact of the digital economy on urban-rural integration development; Model 2 refers to examining the impact of factor allocation efficiency on urban-rural integration development; Model 3 refers to the introduction of factor allocation efficiency on the basis of Model 1. The results show that, based on controlling a series of variables, the digital economy has a significant positive impact on urban-rural integration development, at the 1% significance level, which indicates that the higher the level of digital economy development, the more favorable it is to urban-rural integration development. Factor allocation efficiency has a significant positive effect on urban-rural integration development at the 1% significance level, which means that the higher the regional factor allocation efficiency is the more favorable to urban-rural integration development. At the 1% significance level, the digital economy positively acts on urban-rural integration development, with an estimated coefficient of 0.05792. At the 1% significance level, the digital economy still positively acts on urban-rural integration development, with an estimated coefficient of 0.05206, which is decreased relative to model 1, which effectively verifies that the digital economy does act on urban-rural integration development by affecting the factor allocation efficiency of the Transmission mechanism.

The results of the mediation effect test of factor allocation efficiency are shown in Table 7. The estimated coefficient of digital economy in model 4 is significantly positive, indicating that the total effect of digital economy on urban-rural integration development is significantly positive; the estimated coefficient of digital economy in model 5 is significantly positive, indicating that the enhancement of the development level of digital economy can significantly improve the efficiency of factor allocation; the estimated coefficients of digital economy and the mediator variable of factor allocation efficiency are both significantly positive in model 6 and the estimated coefficient of digital economy in model 6 is significantly positive and decreases compared with model 4. The estimated coefficients of digital economy in model 6 are both significantly positive, and the estimated coefficient of digital economy in model 6 decreases relative to that of model 4, indicating that factor allocation efficiency plays a mediating effect between digital economy and urban-rural integration development. The digital economy improves factor allocation efficiency by avoiding information asymmetry, reducing market transaction costs, and breaking through the geographic limitations of transactions between supply and demand sides. The high allocation efficiency of factors is conducive to the complementarity and mutual promotion of urban and rural factors of production, which is conducive to the convergence of urban and rural factor returns, thus promoting urban-rural integrated development. The above mediation effect test results prove that the hypothesis 2 of the article is valid.

Given the differences in development stages and resource endowments across regions, both the level of digital economy development and the level of urban-rural integration development are characterized by heterogeneity across regions. Therefore, the impact of digital economy on urban-rural integration development may also be characterized by regional heterogeneity. The regional heterogeneity of the impact of digital economy on urban-rural integration development is shown in Table 8. The impact of digital economy on urban-rural integration development has obvious regional heterogeneity, the digital economy in the eastern and western regions has a significant positive effect on urban-rural integration development, and the regression coefficient of the digital economy in the eastern region is larger relative to that in the western region, which indicates that the digital economy in the eastern region promotes urban-rural integration development, more than in the west. It is worth noting that the digital economy in the central region has a significant negative effect on the development of urban-rural integration, indicating that the current development of the digital economy in the central region inhibits the development of urban-rural integration in the region. The reason for the above result may be that in the eastern region, the development level of digital economy is the highest, the digital infrastructure in urban and rural areas has been arranged in a balanced way, and the ability of farmers to identify, utilize and process information is less different from that of urban residents due to the long period of learning, and the digital economy is able to strongly promote the development of urban-rural integration in this scenario. In the central region, despite the relatively high level of development of the digital economy, the problem of the urban-rural “digital divide” is more prominent, and there exists not only a first-level digital divide between urban and rural areas in terms of digital infrastructure and other aspects, but also a second-level digital divide in terms of the differences in the processing and handling of information, which is not conducive to the integrated development of urban and rural areas in the region. In the western region, the development of the digital economy is at an early stage, mainly in terms of universality, with the entire population sharing the “digital dividend”, while rural areas can also learn from the experience of applying digital technology in urban areas, with a clear latecomer’s advantage, which is able to effectively promote integrated urban-rural development, but with a lesser effect compared with that in the eastern part of the country.

Taking digital economy as the entry point and factor allocation efficiency as the mediating variable, this paper takes urban-rural integration efficiency of 20 cities in Guangdong Province during 2017-2023 as the research object to explore the internal mechanism of its digital economy to promote the efficiency of urban-rural integration and put forward optimization strategies. The main conclusions are as follows: 1)

Malmquist index decomposition shows that technological progress is the main factor affecting the average total factor productivity in Qingyuan City. In 2017-2023 the efficiency of financial inclusion in Qingyuan City to support urban-rural integration development is generally growing, with a tfpch value of 1.1018, and the support efficiency has increased by 10.18%.

Strengthening the construction of rural digital infrastructure, upgrading the level of digital access in rural areas, and narrowing rural digital disparities. Promote the in-depth integration of digital technology with rural industries, cultivate new forms of rural digital economy, and enhance the vitality of the rural economy. Improve the mechanism for the length of data elements, promote the free flow and sharing of urban and rural data resources, and enable the synergistic development of urban and rural industries. The implementation of these strategies will help give full play to the advantages of the digital economy, improve the efficiency of urban-rural integration, promote the synergistic development of urban and rural areas, and realize the goal of common prosperity.