2.1. Evaluation Index System
At present, the definition, classification, and scope of public service are still controversial in theory and practice (
Alt and Lassen 2006;
Heald 2003). According to different classification standards, scholars have sorted public services in different ways, such as by government functions, specific expenditure areas, content of public needs, etc. To comprehensively reflect the quality of public service, according to the standards in the “Thirteenth Five-Year Plan for Promoting the Equalization of Basic Public Services”, issued by the “State Council of the People’s Republic of China” and referred to in the literature, the scope of public services in this paper includes the areas that can ensure people’s basic livelihood, such as basic education, medical services, infrastructure, social security, scientific and technological services, employment services, cultural services, social services, and environmental protection.
The evaluation of public service quality in literature is mainly based on the following four perspectives.
First, it is directly measured by the government’s fiscal expenditure in a certain public service area. For example, per capita, fiscal expenditure on culture, education, science, and health is used to measure the quality of public services (
Zulkofli et al. 2018;
Pedrosa et al. 2020;
Sun and Andrews 2020;
Fan and Zhang 2013). This is the narrowest measurement method, which means a higher level of public services expenditure will inevitably lead to a higher quality of public services as so defined.
Second, the output of government fiscal expenditure can be used to assess the quality of public services, such as the total number of hospital beds per thousand people, the number of medical staff, and the teacher–student ratio to access the quality of public health and education services (
Wu et al. 2014). This kind of index is at the intermediate stage between government fiscal expenditure and final output. It is a carrier of public services but is not the ultimate goal of fiscal expenditure.
Third, people’s benefits from public services can be used to measure the quality of these services. For example, basic education is measured by the literacy rate and average years of education, and medical and health services are measured by average life expectancy. The ultimate goal of the government in providing public services is to improve the education level and health of the citizens by the intermediate output, thereby enhancing the welfare of the residents (
Jia and Lu 2010).
Fourth, questionnaire surveys may be issued to measure the respondents’ satisfaction with public services. Public service satisfaction reflects residents’ subjective feelings about the quality of public service and can evaluate the quality of public services (
Chen and Li 2010). However, due to the requirements for the accuracy and comprehensiveness of the questionnaire, and the influence on respondents of factors such as race, income, regional characteristics, and familiarity with public services (
Kelly 2003), it is difficult for a satisfaction survey to truly reflect the actual situation of the respondents, and cannot objectively reflect the quality of public service.
Based on the above analysis, according to the principles of comprehensiveness, objectivity, representativeness, and accessibility, this article constructs an evaluation index system containing 35 indexes from dimensions of public service output and effect to comprehensively evaluate the public services quality, as mentioned in
Table 1.
2.2. Evaluation Method
This paper used entropy weight TOPSIS to evaluate the quality of public service. This method was developed by Hwang and Yoon (
Hwang and Yoon 1981) and further improvement was made by Hwang (
Hwang et al. 1993). Hwang and Yoon proposed clustering, which is derived as an enhancement of the Wroclaw Taxonomy, which in turn is derived from the prior works of (
Senetra and Szarek-Iwaniuk 2019;
Czekanowski 1961). Many authors worldwide use the TOPSIS to evaluate, assess, and rank alternatives across diverse industries, such as Supply Chain Management and Logistics, Design Engineering and Manufacturing Systems, Business and Marketing Management, Health Safety and Environment Management, Human Resources Management, Energy Management, Chemical Engineering, Water Resources Management, and Other topics. (
Behzadian et al. 2012;
Lu and White 2014). The entropy weight TOPSIS method is a combination of the entropy method and TOPSIS method, in which the specific steps are as follows.
The first step is the positive processing of raw data.
Suppose there are m objects to be evaluated. Each evaluated object has
n evaluation indexes.
M = 12 refers to 12 provinces (cities and autonomous regions) in coastal provinces and cities of China;
n = 35 refers to 35 indexes that evaluate the quality of public service, constructing the following judgment matrix:
In Equation (1),
represents the value of a specific index,
and
. To compare various indexes from different dimensions, this research adopts the extreme value standardization method to deal with each index in a positive direction. The indexes that reflect the public service quality can be sorted as positive and negative indexes. The greater the value of the positive indexes, the higher the public service quality: the greater the value of the negative indexes, the lower the public service quality. To ensure the same direction in these indexes, this research adopts different calculation methods for the positive and negative indexes. The standardization method of the positive indexes is as follows in Equation (2).
The standardization method of the negative indexes is as follows in Equation (3).
In Equations (2) and (3), the terms and represent the maximum and minimum of a specific index, respectively. Thus, the standardized judgment matrix = can be established.
The second step is to calculate the entropy of the index.
According to the theory of information entropy, the entropy
of the
j-th index can be expressed as Equation (4).
In Equation (4) the symbol can be calculated as , and it is assumed that , when .
The third step is to define the weight of the index.
If the diversity of the
jth index in each sample is smaller, the entropy of the index is larger. Conversely, if the diversity of the index in each sample is larger, the entropy of the index is smaller. Thus, the weight
of the
jth index is defined as Equation (5).
In Equation (5) .
The fourth step is to form a norm matrix based on entropy weight.
Multiply the weight vector
of each index by the standardized judgment matrix
=
to form a weighted standardized decision matrix as Equation (6).
The fifth step is to determine the optimal solutions (
) as Equation (7) and worst solutions (
) as Equation (8).
The sixth step is to compute the distance between each evaluated object and the optimal or worst solutions.
Using the Euclidean distance formula, calculate the distance
as Equation (9) and
as Equation (10) from the standardized vector of each evaluated index to the optimal solution and the worst solution.
The seventh step is to calculate the degree of closeness of each evaluated object. Calculate the closeness degree
of each evaluated object as Equation (11).
The value of
is in-between 0 and 1. The higher the value of
, the greater the quality of public service. When
= 1, the quality of public services is the highest; when
= 0, the quality of public services is the lowest. According to the research results (
Lei et al. 2016), the closeness degree can be divided into four grades to characterize the quality of public service, as shown in
Table 2.
2.3. Evaluation Results
Using data (2010–2017) from 12 coastal provinces and cities in China, the judgment matrix for every year can be established through the evaluation index system mentioned in
Table 1. The entropy of each index was computed according to Equations (2)–(5). Similarly, the weight of every index was calculated by using Equations (6)–(10) to calculate the Euclidean distance
and
. Finally, the closeness degree
was calculated using Equation (11).
The closeness degrees
were sorted and shown in
Table 3. The public service quality in these coastal provinces and cities of China was relatively high. On average, from 2010 to 2017, except for Hainan, Hebei, and Guangxi, the closeness degree of public service quality was higher than 0.3. The closeness degree of Beijing was 0.6583, which is greater than 0.6, indicating the public service quality was good, as shown in
Table 2. The closeness degree of the other 8 provinces and cities, including Shanghai, was between 0.3 and 0.6, which suggests that the public service quality was of medium quality.