3.1.1. Evaluation Index System Establishment
Step 1 is to establish an evaluation index system. This paper sorts and summarizes the common indicators via an extensive literature review. Then, it establishes a construction industry productivity evaluation index system with the help of the value-added method and Delphi method in order to increase the credibility and rationality of the evaluation results [
39]. Conducting research on the evaluation of production efficiency is systematic and long-term work. Previous studies have shown that the choice of input–output indicators is a key factor in the evaluation results. However, research on the evaluation of production efficiency in the construction industry is directly based on experience. Liu et al. (2013) combined factor analysis with correlation analysis to identify the factors, making the selection of indicators more scientific [
39]. However, there are still certain shortcomings in this process; that is, the factor identification by factor loadings may filter out some indicators with small weights but not large values. Furthermore, this phenomenon may cause bias in the model calculation. The quantitative research method can be used to reduce the index, but it is contrary to the DEA model principle. Therefore, it is not enough to rely solely on complex measurement models for the construction of input–output evaluation indicators. Empirical research should also be based on the connotation of an empirical basis, the use of measurement methods to strengthen the purpose of evaluation, and relying on empirical analysis to determine the evaluation. Accordingly, this study used the value-added method to quantitatively identify the key indicators and then combined these with the fuzzy Delphi method to further ensure the comprehensiveness of the evaluation system. The indicators of the two models were used together to determine the final input–output indicator system.
- (1)
Principle of indicator selection
The value-added method is an important research aspect of value management. It is based on whether all inputs in the balance sheet generate value or destroy value as an input or output. However, industrial research is different from research on enterprises. No balance sheet can be referenced, and input–output indicators are not as clearly defined as they are in the types of costs for enterprises. The input and output index systems constructed by existing construction-related research are often intersected or repeated. Therefore, this study only learns from such analytical ideas and uses factor analysis models to screen the critical indicators. The fuzzy Delphi method combines fuzzy theory and the Delphi method [
40,
41]. Thus, it evaluates objects or schemes with fuzzy numbers. Combined with expert scoring, the triangle fuzzy numbers are constructed by using the maximum, minimum, and geometric means. The median of each indicator expert’s scoring geometric mean is selected as the threshold of the index, and the score is converted into objective data [
42]. In this way, the credibility and reasonableness of the evaluation results are ensured.
- (2)
Input and output indicator selection
According to the literature review,
Table 1 summarizes the existing input–output variables for the evaluation of the production efficiency of the construction industry. Among them, the input indicators mainly include the number of employees, the number of construction enterprises’ technical equipment rate, the power equipment rate, and the total assets of the construction industry. Meanwhile, the output indicators mainly include the construction area, the project completion area, the construction industry’s added value, the engineering settlement profit, the total construction output value, and the total profit. Due to the technical and power equipment rate, the interprovincial data were difficult to obtain. In terms of the construction area, the total construction industry output value can be replaced by the area of construction completion and total profit. In addition, the profit of project settlement refers to the profit achieved by the settled projects, the level of which is closely related to the schedule arrangement and resource allocation efficiency, and is a more comprehensive and intuitive reflection of production efficiency. In summary, the study selected six indicators as independent variables: number of enterprises (Enterprise), number of employees (Employees), total assets of the construction industry (Assets), added value of the construction industry (Added), area of completed projects (Completed), and total profit of the construction industry (Profit). This study considered the profit of project settlement as a dependent variable for regression analysis. Based on the absolute value of the regression coefficient size, the key factors that affect the added value of the profit of the construction industry were found. The model also investigated the influence of each variable on the change in the added value of the profit of the construction industry through its direction. As shown in the regression results in
Table 2, the value added of the construction industry, the number of construction industry enterprises, and the total assets of the construction industry are the main factors affecting the value added of the profit of construction settlements.
In order to ensure the rationality of the constructed post–input–output index system, this study also uses the Delphi method to conduct the secondary screening of input–output indicators to the screening of indicators through the value-added method. The detailed processing steps are as follows: (1) Based on the preliminary indicator system obtained above (number of enterprises, number of employees, total assets of the construction industry, value added of the construction industry, area of completed projects, total profit of the construction industry, and profit of the project settlement), the questionnaire of the input–output indicator structure of the productivity of the construction industry was prepared. (2) The questionnaire for preliminary research was distributed. Then, the questionnaire was revised and improved based on the research results, and the final questionnaire was prepared. This was then distributed to relevant experts in order to obtain professional and authoritative opinions and suggestions. In this study, the research was conducted via email questionnaire, and the 12 experts included 6 master and doctoral students in the field of construction economics and management, 3 engineers working in the construction industry, and 3 professors in the construction economics and management area. A total of 12 valid questionnaires were collected in the study. (3) Based on multiple rounds of research, the index system of the input–output of productivity in the construction industry was determined through statistical analysis. Due to space limitation, the calculation process was omitted. The final Delphi method determined the input indicators as the number of enterprises in the construction industry (Enterprise) and the total assets of the construction industry (Assets) and the output indicators as the value added of the total output value of the construction industry (Added) and the area of completed projects (Completed). The results of the two models were combined, and the number of enterprises and assets in the construction industry was used as input indicators, while the value added of the total construction output value and completed area was used as output indicators. In this paper, the panel data of 31 provinces and autonomous regions from 2010 to 2020 were used as the research sample, and the data were compiled from China Construction Industry Yearbook and China Statistical Yearbook, and the missing values were completed using the gray prediction model. For the comparative analysis of regional construction industry productivity, the 31 provinces, municipalities, and autonomous regions were divided into eastern, central, and western for analysis. Eastern includes Beijing, Tianjin, Hebei, Shandong, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Guangdong, and Hainan; central includes Henan, Hubei, Hunan, Anhui, Jiangxi, Shanxi, Jilin, and Heilongjiang; and western includes Sichuan, Chongqing, Inner Mongolia, Guangxi, Yunnan, Ningxia, Shaanxi, Guizhou, Gansu, Qinghai, Tibet, and Xinjiang.
3.1.2. Evaluation Model Establishment and Data Analysis
In order to measure the productivity of the construction industry more comprehensively, this study examines the productivity of the construction industry from both static and dynamic measurement approaches. First, we integrated the scale effect, limited resources, and overall comparability parameters. Then, we chose the nonradial, nonoriented, and variable returns to scale (VRS) bootstrap-DEA model. Compared with the traditional static DEA measurement method, this model excludes the interference of the random factors and errors that are caused by omitted variables, and it can more accurately estimate the static evaluation results of the regional construction industry’s productivity covering 31 provinces, municipalities, and autonomous regions across China. Additionally, then, the study was based on the Malmquist-DEA model, which is used to calculate the dynamic production efficiency values of the construction industry. This idea can effectively reduce the errors in the evaluation results, which are often from random shocks, such as statistical errors and omitted data variables, and which decompose the construction productivity from a dynamic perspective.
- (1)
DEA
Data envelopment analysis (DEA), the most typical nonparametric method, is widely used to evaluate the efficiency of different systems. DEA uses mathematical planning models to evaluate the relative effectiveness (called DEA validity) between “departments” or “units” (called decision-making units, abbreviated as DMUs) with multiple inputs, especially multiple outputs, and to determine whether a DMU is DEA valid based on the data observed for each DMU. This method can effectively reduce the subjectivity of uncertainty in the calculation process [
43]. The conventional DEA model has certain deficiencies. On the one hand, when the observed samples are limited, the DEA estimation results are highly susceptible to random factors, and there are obvious sample sensitivities. On the other hand, the conventional DEA model estimates ignore statistical inference and random error problems; moreover, there are often small samples used. The biased problem leads to a certain deviation in the evaluation value of production efficiency. The bootstrap-DEA model proved to be effective in correcting this shortcoming [
21]. Later, more research gradually applied the bootstrap model to the DEA model [
44,
45] and proposed a mathematical variant of the bootstrap method in order to correct the DEA method. Bootstrap techniques based on repeated self-sampling can provide a more accurate measure of the estimated efficiency of traditional DEA models and its variation.
- (2)
Bootstrap-DEA correction measure model
The bootstrap-DEA estimation model can eliminate the influence of extreme values, random errors, and missing variables on the efficiency measurement results. Giving a statistical estimate of the efficiency can make the efficiency evaluation and analysis results more accurate. Thus, by considering that, this study designs a bootstrap-DEA model based on a variable-scale, nonradial, and nonoriented approach in order to measure the static production efficiency of a regional construction industry in China. In the evaluation result, if the efficiency value is less than 1, the decision unit does not reach the optimal production efficiency; if the efficiency value is equal to 1, it indicates that the evaluated decision unit is strong and effective. The model implementation steps are as follows:
Step 1: Calculate the original efficiency of each decision unit
DMUk (
k = 1, 2, 3, …,
n) using the traditional DEA measurement model. Extract a simple sample of size
n using the repeated sampling bootstrap method. Further,
b represents the number of iterations of the bootstrap sample. The sample collection is as follows:
Step 2: Use the kernel density estimation method to smooth the sample that is obtained by the plain Bootstrap method. Then, obtain the sample according to the smoothing bootstrap method to correct the original sample input index. This adjusted calculation is as follows:
According to the bootstrap-adjusted input data and the initial output data as a new sample, the traditional DEA method is used to recalculate the efficiency value:
Step 3: Repeat steps 1 and 2 to obtain a series of efficiency values, and then calculate the correction efficiency value deviation and correct DEA efficiency value of each decision unit
DMUk (
k = 1, 2, 3, …,
n). The expression is as follows:
In the above formula, Biask is the deviation of the correction efficiency value.
- (3)
Malmquist exponential decomposition method
The DEA-Malmquist index method effectively solves this problem and, as an extension of the DEA model, it can be used not only to measure the change in total factor productivity of DMUs over time but also to avoid the assumptions made in the calculation of Solow residuals. It can also avoid the assumptions made in the calculation of Solow residuals and can be decomposed into the product of efficiency improvements and technological progress, resulting in a more scientific dynamic analysis. Based on the variable assumption of factor size return, Banker et al. (2004) proposed a BCC model to further decompose technical efficiency into pure technical efficiency and scale efficiency [
46]. This method has been widely used [
47,
48,
49]. In the DEA-Malmquist index method, the change in TFP between two adjacent data points is measured by estimating the ratio of the distance of each data point to a common boundary of the production possibilities. The measured index is called the Malmquist-TFP index [
50], and the output-oriented Malmquist-TFP index of the
i-th DMU from base period
s to period
t can be defined:
In Equation (6), and are the distance functions at constant payoffs to scale. denotes the production point distance function for the i-th DMU in period t, using the technology in period t as a reference, and denotes the production point distance function in period s. When > 1, this indicates that the TFP has a growth from base period s to period t; when < 1, this indicates that the TFP has a negative growth from base period s to period t.
The Malmquist index obtained from the above formula can be decomposed into two categories: the efficiency change (EFF) and the technical change index (Techch), which are expressed as follows:
In the case of variable scale compensation, the technical efficiency change index (
EFFch) can be further broken down into the pure technical efficiency change (
PTEch) and the scale efficiency change (
SEch), which can be expressed as follows:
Therefore, the TFP index can be expressed by the product of the technological progress index, the scale efficiency index, and the pure technical efficiency index. Among them, the changes in research and development and the introduction of new technology are reflected by technological advances. The changes in the optimization, promotion, and application of current technologies, and the rational allocation of production factors, are reflected by pure technical efficiency, management methods, and production scale. Changes in the aforementioned are reflected by scale efficiency. TFP is a comprehensive reflection of the overall changes in these aspects [
51].