Keywords

1 Introduction

The county government has long been the basis of administration management and state governance in China. It faces to the grass-roots and serves them directly. Thus, the efficiency of its operation can greatly influence the overall quality of people’s life and production. Nowadays, as an effective way of improving administrative efficiency and transparency, the e-government has been praised highly by many countries. And China has also launched the Government Online Project since 1999. In fact, the construction of e-government within the county level is a very important part of China’s e-government development, as well as the terminal node to the provincial level e-government, and governments should pay great attention to e-government construction at county level for constructing mature e-government system structure [7]. To promote the healthy and sustainable development of a county e-government, an evaluation of its efficiency which may help improve its service quality is strongly required.

Evaluation systems like the Global E-government Evaluation from the UN [11], the “eEurope” Strategic Assessment System from the EU [3] and the Overall e-government Maturity Assessment from the Accenture company [1] are international representatives. While in China, it also has assessment models like the CCW Research [12], the China Software Testing Center [4], the CCID Consulting [5] and the CCTC [2].

According to the actual situation, the E-government efficiency evaluation index system was constructed from different perspectives and the corresponding analysis methods are used to evaluate the efficiency of the E-government. Extraordinary representatives: Luo and Shi [10] introduced genetic algorithm optimized to BP neural network weights and thresholds after reducing the established evaluation index system by rough set, and established e-government website evaluation model based on genetic neural network algorithm; Rorissa, Demissie and Pardo [13] used benchmarking to assess the strengths and limitations of six frameworks for computing e-government indexes; Luna et al. [9] used data envelopment analysis (DEA) to show how efficient are Mexico state governments in their use of certain inputs to produce high quality e-government portals; Zdjelar [17] measured efficiency of Croatian regional government implementation by Balanced Scorecard Method; Song and Guan [14] utilized a super efficiency slack-based measure (SBM) model to evaluate the e-government performance of environmental protection administrations in the 16 cities of Anhui Province; Kao [8] evaluated the e-government of 21 European countries based on the concept of Pareto optimality and developed a compromise programming model to rank these nations; Wu and Guo [15] used method of DEA to evaluate e-government performances of 31 provincial government websites in China and concluded that most of these provincial government websites operated at an inefficient level and in a bad manner.

To sum up, the achievements of researches on the e-government’s efficiency provide a useful reference to the study. However, the evaluation of Chinese e-government’s efficiency has not yet had a uniform index system. Most researches are focusing on the overall efficiency of the provincial research objects and few investigate the input-output efficiency of e-government from the perspective of e-government at county level. Therefore, this paper attempts to use principal component analysis to build the evaluation index system of county level e-government’s efficiency, and adopt the DEA model to evaluate the efficiency of e-government in 147 counties (including county level cities) of Sichuan Province to provide decision-making reference for the promotion of county level e-government’s efficiency.

The remainder of this paper is organized as follows. In the first half of Sect. 2, we briefly discuss the principle of principal component analysis and the practical application value of it. In the second half of Sect. 2, we narrate the construction of CCR model and BCC model of DEA which will be used for e-government efficiency evaluation. The process of e-government efficiency evaluation is presented in Sect. 3 which includes the samples selection, data collection, the establishment of evaluation index system and the model solution. On the basis of the solution, the analysis of the current situation in Sichuan Province and the suggestions for the ineffective county level government are given in Sect. 4. Finally, we conclude with a summary of this paper and prospect about evaluation of e-government in Sect. 5.

2 The Method of E-Government Efficiency Evaluation

2.1 Principal Component Analysis

On the premise of the least information loss, principal component analysis is a statistical procedure that uses the thought of dimension reduction to convert a set of multiple indexes with possible correlation into a few linearly uncorrelated comprehensive indexes.

The basic principles of principal component analysis are as follows:

We assume that there are p objects that each object is described by n indexes. In this way, we can constitute a data matrix:

(1)

\({X_1},{X_2}, \cdots ,{X_n}\) are defined as original variable indexes and \({F_1},{F_2}, \cdots ,{F_m}(m \le n)\) are defined as new variable indexes. By using the n vectors \({X_1},{X_2}, \cdots ,{X_n}\) of data matrix to make a linear combination, then we can get:

(2)

Coefficient \({a_{ij}}\) meets:

  • \({F_i}\) is linearly independent with \({F_j}(i \ne j;i,j = 1,2, \cdots ,n)\);

  • \({F_1}\) has the greatest variance of the linear combination of \({X_1},{X_2}, \cdots ,{X_n}\) mentioned above. \({F_2}\) has the greatest variance of the linear combination of \({X_1},{X_2}, \cdots ,{X_n}\) which are independent with \({F_1}\). The rest could be deduced in this way. \({F_m}\) has the greatest variance of the linear combination of \({X_1},{X_2}, \cdots ,{X_n}\) which are independent with \({F_1},{F_2}, \cdots ,{F_{m\mathrm{{ - }}1}}(m \le n)\).

New variable indexes \({F_1},{F_2}, \cdots ,{F_m}(m \le n)\) are called the first, second, \(\cdots \), \(m^{th}\) principal component respectively.

2.2 Data Envelopment Analysis

Based on the relative efficiency concept, the data envelopment analysis is a non-parametric statistical method employing convex analysis and linear programming as tools to calculate the relative efficiency between the same type of multi-input and multi-output decision making units. The relative efficiency is used to evaluate whether the decision-making unit is effective.

(1) CCR Mode

Assume that there are n decision-making units (hereinafter referred to as DMU), each DMU has n inputs and m outputs. The input vector of \(DM{U_j}\) is \({X_j} = {({x_{1j}},{x_{2j}}, \cdots ,{x_{mj}})^T} \ge 0,{X_j} \in {R^ + }\) while output vector is \({Y_j} = {({y_{1j}},{y_{2j}}, \cdots ,{y_{sj}})^T} \ge 0,{Y_j} \in {R^ + }\) Building a model with a non-Archimedes infinitely small to evaluate the relative efficiency of the \(\text {DMU}_j\):

$$\begin{aligned} \begin{array}{l} \min \left[ {{} {} {} \theta - \varepsilon (e_1^T{s^ - } + e_2^T{s^ + })} \right] \\ s.t.{} {} {} {} {} \left\{ \begin{array}{l} \sum \limits _{j = 1}^n {{\lambda _j}{x_j} + {s^ - } = \theta {x_0}} \\ \sum \limits _{j = 1}^n {{\lambda _j}{y_j} - {s^ + } = {y_0}} \\ {\lambda _j} \ge 0,j = 1,2, \cdots ,n\\ {s^ + } \ge 0,{s^ - } \ge 0 \end{array} \right. \end{array} \end{aligned}$$
(3)

\(\varepsilon \) is non-Archimedes infinitely small. \(s^-\) is the slack variable while \({s^+}\) is the remaining variable. Assuming that Eq. (3) has the best solution \({\theta _0},{\lambda _0},s_0^ - ,s_0^ + \) for \(\text {DMU}_{j0}\). If \({\theta _0} < 1\), \(\text {DMU}_{j0}\) will be non-DEA effective. If \({\theta _0} = 1\) and \(s_0^ - \) or \(s_0^ + \ne 0\), \(\text {DMU}_{j0}\) will be weakly DEA effective. If \({\theta _0} = 1\) and \(\text {DMU}_{j0}\) will be DEA effective.

(2) BCC Model

BCC model is the extension of fixed scale benefit data envelopment analysis. Adding the convexity condition \(\sum _{j = 1}^n {{\lambda _j} = 1} \) to the linear programming under fixed scale benefit model (CCR model) is the BCC model:

$$\begin{aligned} \begin{array}{l} \min \left[ {{} {} {} \theta - \varepsilon (e_1^T{s^ - } + e_2^T{s^ + })} \right] \\ s.t.{} {} {} {} {} \left\{ \begin{array}{l} \sum \limits _{j = 1}^n {{\lambda _j}{x_j} + {s^ - } = \theta {x_0}} \\ \sum \limits _{j = 1}^n {{\lambda _j}{y_j} - {s^ + } = {y_0}} \\ \sum \limits _{j = 1}^n {{\lambda _j} = 1} \\ {\lambda _j} \ge 0,j = 1,2, \cdots ,n\\ {s^ + } \ge 0,{s^ - } \ge 0. \end{array} \right. \end{array} \end{aligned}$$
(4)

3 The Process of E-Government Efficiency Evaluation

3.1 Samples, Indexes and Data Collection

The decision-making units in DEA should have the same type of characteristics. In order to evaluate the relative effectiveness of e-government at the county level in Sichuan Province, this paper selects the 147 districts and counties (including county level cities) in Sichuan Province as the objects of the research.

In accordance with the requirements of the DEA method, we need to establish an index system of input and output based on the comprehensive consideration of region informatization level, economic development, cultural and educational level and other factors. There are nine categories of input indexes in this paper which specifically include fixed telephone subscribers, the number of mobile phone users, the value of the tertiary industry income, GDP, total fiscal revenue, governmental investment in science and education, the proportion of urban population, the number of students in colleges and universities, the number of colleges and universities. These index data are mainly obtained from “Sichuan Province Statistical Yearbook” (2014) [16] and “The Statistics Bulletin of the National Economy and Social Development” (2013) issued by the various districts and counties (including county level cities).

To select proper output indicators, we referenced the objective indexes derived from CCID consulting assessment of government website performance and The United Nations for the global objective of e-government assessment. This study revolves around the authoritative evaluation results to screen the indexes. The five main evaluation indexes consist of government information publicity, work services, public participation, the website management, application of new technology. Output index data are mainly obtained from “The total Report of the Sichuan Government Website Performance Evaluation” (2013) [6].

3.2 Principal Component Analysis

The principal component analysis of 9 input indexes and 5 output indexes data were conducted by SPSS software (Tables 1 and 2).

Table 1. The result of PCA of the input indexes
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Table 2. The result of PCA of the output indexes
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According to extracts of the principal component to calculate the principal component load, the formula is:

$$\begin{aligned} {l_{ij}} = p({z_i},{x_j}) = \sqrt{{\lambda _i}} {a_{ij}}(i = 1,2, \cdots ,k,k{}\text { as main composition},~~j = 1,2, \cdots ,147) \end{aligned}$$
(5)

Then we can get the principal component index data of inputs and outputs.

Table 3. The results of e-government input and output efficiency evaluation (1)
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On account of that the result of the principal component analysis is negative number, and DEA model requires that the data is not negative, so the results of the principal component calculated by poor transformation normalized to [1, 10] interval. The range transform formula is:

$$\begin{aligned} {n_{\text {new}}} = 1 + 9 \times [(n - {n_{\min }})/({n_{\max }} - {n_{\min }})], \end{aligned}$$
(6)

where \({n_{\max }}\) and \({n_{\min }}\) represent the maximum and minimum values of the column data respectively (Tables 3 and 4).

3.3 The Solution of the DEA Model

According to the principal component analysis method, the main components of input and output index data are obtained. After that, we use the DEAP 2.1 to solve 147 counties’ (including districts’ and cities’) input-output efficiency of e-government with CCR and BCC model, and we obtain the comprehensive efficiency, pure technical efficiency and scale efficiency of all counties’ (including districts’ and cities’) e-government. All results are shown in Table 5.

Table 4. The results of e-government input and output efficiency evaluation (2)
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Table 5. The results of e-government input and output efficiency evaluation (3)
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4 Analysis of the Result

Through the analysis of CCR, it appears that Wuhou District in Chengdu and Gongxian County in Yibin have achieved a full effectiveness of comprehensive efficiency \((\text {CCR}=1.000)\) among 147 counties, districts, or cities of Sichuan Province, which indicates that they have obtained a fully efficient outcome. However, two districts, Jinjiang and Chenghua in Chengdu, are in the position of a light level of non-DEA effective degree \((0.700\le \text {CCR} < 1.000)\). For those of a light level of non-effective degree, the development of electronic administration requires focusing more on the control and management of details and proper distribution of the investment, as there’s still some room for improvement. Meanwhile, most of counties (including districts and cities) are in a severe level of non-DEA effective degree \((\text {CCR} \le 0.500)\), which suggests that most counties’ e-government development in Sichuan province don’t work out. The overall development gap is huge, and most of objects have not achieved the comprehensive effectiveness. The input of the e-government construction has not acquired the desired results. On the one hand, the technical inefficiency leads to the comprehensive ineffectiveness. On the other hand, the low scale efficiency also affects the improvement of the comprehensive efficiency. Therefore, the government should make a huge effort to find out the route to suit the situation, so as to surmount the problem fundamentally. The counties and districts with the lowest CCR, Jinyang County and Butuo County in Liangshan, Rangtang County in Tibetan Qiang Autonomous Prefecture of Aba, Qingshen county in Meishan, Dawu County in Tibetan Autonomous Prefecture of Garze, Aba County in Aba Tibetan and Qiang Autonomous Prefecture, correspond to their relatively weak national economy and social development, as well as the influence of little capital invested by the government on information construction. Thus, problems should be solved and development should be sped up in the future construction of e-government.

The pure technical efficiency results obtained by the BCC model show that Jinjiang district, Wuhou District and Pixian County of Chengdu are with pure technical effective \((\text {BCC}=1.00)\). It indicates that their services systems of e-government run well, and the resources invested can develop productivity efficiently. The pure technical efficiency of 132 counties, districts or cities are lower than 0.5, and it appears that these local governments’ technical outcomes are not enough. The last 5 counties, districts or cities with the lowest BCC successively are Hongya County in Meishan, Peng’an County in Nanchong, Qingshen County in Meishan, Pengxi County in Suining, Chaotian District in Guangyuan. It indicates these governments didn’t distribute the resources legitimately, and they need more technological innovation to improve the service abilities of e-government from technology level.

From the point of view of scale efficiency, there are 9 counties or districts of Sichuan Province in full scale efficiency. They are Wuhou District, Qingbaijiang District and Shuangliu County in Chengdu, Gongxian County in Yibin, Dachuan District and Xuanhan District in Dazhou, Fucheng District in Mianyang, Lizhou District in Guangyuan and Bazhou District in Bazhong. These governments input resources in e-government are proper, and returns of scale remain unchanged. The rest 138 counties, districts or cities are not in full scale efficiency, it manifests that these governments waste some resources during the construction of e-government. In the future, the governments need to increase the investment in information technology and science and education, for speeding up the process of urbanization and informatization. What’s more, the governments should allocate resources more reasonably to improve the level of government information disclosure, services and websites management. Besides, governments should make more and more people participate in the construction of e-government in order to take better use of the resources.

5 Conclusions

Due to the wave of the informatization and popularization of the network, the construction of e-government in the human condition is getting better and better. Governments at all levels are also vigorously investing money and human resources for the construction of e-government to promote the informatization. To guide the construction of e-government, how to accurately evaluate and scientifically observe the efficiency of e-government is a hotspot and difficulty in the field of current e-government. Although there are a lot of foreign standards being references, different countries may have different national conditions. The real effective e-government construction has to be combined with the actual situation. According to the views of scholars and organizations at home and abroad, based on observation and thinking, we use different indexes and principal component analysis and DEA model to evaluate the e-government construction efficiency of all districts and counties of Sichuan Province. We hope to be able to scientifically evaluate the comprehensive efficiency of various districts and counties of Sichuan Province in the construction of e-government. On the whole, the local government’s information department should focus on improving their investment scale and technical efficiency to enhance the efficiency of e-government.

However, this paper also has some limitations. Firstly, we take both input and output into consideration which also have been rotated, extracted and standardized. Therefore, this paper couldn’t use the projection algorithm to get the improvement solutions which give the target value and scope for the non-DEA effective. Secondly, DEA focus on the relative efficiency. It means that different evaluation range may have different result. So how to choose the evaluation range is a project worth exploring. In later study, we will commence on diminishing the limitations above and optimize the solution.