Regional Differences and Convergence of Technical Efficiency in China’s Marine Economy under Carbon Emission Constraints

Abstract

With the continuous development of China’s marine economy and the increasing pollution in marine-related industries, how to implement a sustainable development strategy in the marine economy has become an important issue. Under the stochastic frontier analysis framework, this paper measures the technical efficiency of the marine economy in 11 coastal provinces in China under carbon emission constraints from 2006 to 2016 and analyzes regional differences and the dynamic evolution of technical efficiency and its influencing factors. Panel unit root test is applied to analyze the stochastic convergence of technical efficiency of the inter-regional marine economy. The result shows that: in the reference period, the technical efficiency of the marine economy is on the rise. Guangdong and Shanghai are in the lead. Technical level and industrial structure have a positive impact on technical efficiency, while the structure of property rights, FDI, energy prices, and energy structure have a negative effect on it. On the whole, the changes in the technical efficiency of coastal provinces present a process from concentration to differentiation. There is a stochastic convergence between the Pan-Pearl River Delta and the Yangtze River Delta. Raising the technological level, promoting low-carbon production in the marine industry, and strengthening inter-regional cooperation have a certain effect on the improvement of the technical efficiency of the marine economy.

1. Introduction

As terrestrial resources gradually become fewer, more and more regions are turning their perspective to marine resources. The ocean area occupies 71% of the earth’s surface area, which contains abundant resources. Therefore, it will play an indispensable role in future economic development [1]. China has more than 32,000 km of coastline, and she shares maritime boundaries with Japan, South Korea, North Korea, Malaysia, the Philippines, Brunei, Indonesia, and Vietnam. The favorable geographical location and marine conditions have enabled China’s marine economy to develop rapidly. In 2019, the contribution rate of marine-related industries to GDP reached 9%, and the contribution rate of coastal areas’ GDP reached 17.1% [2]. Research shows that investment in the marine industry will promote increased demand for the production of other sectors, especially for the production of downstream sectors [3].

However, nowadays, as climate change and global warming have caused a lot of attention, to achieve the temperature control targets of the Paris Agreement, many countries have put forward their carbon emissions targets. Research shows that China’s total carbon emissions account for about 30% of the world, and China has become the highest carbon emission country in the world [4]. In 2020, China proposes to achieve the peak of carbon emissions around 2030 and achieve carbon neutrality around 2060. To achieve this goal, all industries should improve efficiency and keep developing while actively reducing carbon emissions. In the growth of the marine economy, marine-related industries, especially the secondary marine industry, such as the offshore oil and gas industry, marine chemical industry, ocean power industry, marine shipbuilding industry, and ocean engineering construction industry have different levels of carbon emissions, which have an important impact on the marine environment. In addition, the pollution problem of marine transportation industry cannot be ignored. In 2019, China’s coastal shipping industry emitted about 45 million tons of carbon dioxide, accounting for about 4.5% of the total carbon dioxide emissions of China’s transportation industry. If no additional policies are adopted, the total carbon dioxide emissions of China’s coastal shipping industry will exceed 162 million tons in 2060.

This paper aims to measure the technical efficiency of China’s marine economy under the constraints of carbon emissions scientifically, analyze regional differences accurately and analyze the factors that affect it, which are of great significance for further improving the technical efficiency of the marine economy and promoting the construction of environmental protection. This research brings two major contributions. Firstly, this paper discusses the regional differences and dynamic evolution of technical efficiency by kernel density estimation procedure. These findings can present the development tendencies of China’s coastal regions. Secondly, this paper uses stochastic frontier analysis to discuss the technical efficiency of the marine economy. Different from many previous papers, which mainly use DEA models, this paper introduces carbon emission constraints into the SFA model.

In this paper, Section 2 reviews the works of literature on sustainable development and the efficiency of the marine economy. Section 3 describes the research design and methodology. Section 4 presents the empirical results and Section 5 summarizes the conclusions and recommendations.

2. Literature Review

2.1. Sustainable Development of the Marine Economy

Coastal regions are economically important because of abundant resources and development potential nowadays. As a result, due to the significant stress caused by the rapid development of the marine economy, many problems such as the extensive development mode and marine environmental pollution have restricted the long-term sustainable development of the marine economy [5]. On the one hand, many marine-related companies only consider quantity while ignoring quality in their development, resulting in a waste of marine resources. On the other hand, economic development and increasing industrialization have brought marine environmental pollution, which in turn has restricted the development of the marine economy [6,7,8] and does not meet the requirements of a low-carbon economy and environmental protection at the same time.

With the emphasis on sustainable development, the number of related research begins to increase. Combing the relevant research about sustainability, it can be found that the research content mainly focuses on the following aspects: (1) the mechanism of factors affecting sustainable marine economic development, such as environmental regulation and technological innovation [9,10]; (2) conservation strategy and development path to sustainable development [11,12]; (3) evaluating local low-carbon economy from the perspective of regions or cities [13,14,15,16] and various sectors, such as the industrial sector and transport, etc. [17,18,19]. Thus, there are a lot of relevant achievements in the sustainable development of the marine economy, which provide an important research basis for this paper.

2.2. Efficiency of Marine Economy

There is not much research on the efficiency of the marine economy or marine-related industries at present. In most research, the efficiency of the marine economy is defined as the ratio of inputs to outputs within the production process of the marine economy. As a result, the efficiency of the marine economy can reflect the quality of marine economic development. Some research shows that the efficiency of China’s marine economy without considering undesirable output is higher than that considering it [20]. Although the total output of China’s marine economy is relatively high, the efficiency is low after considering the undesired output, and there is still a certain gap before reaching high-quality development [21]. According to the research, the coastal area’s marine economy efficiency was quite low, mainly concentrated between 0.4 and 0.6. However, the efficiency has shown an upward trend [22], which indicates that efficiency has great potential to rise in China. As a result, to achieve the goal of carbon emission reduction and sustainable development, there is a significant meaning to discussing the efficiency of the marine economy and putting forward corresponding improvement suggestions for existing problems.

In existing research, to measure efficiency, there are usually two methods. The first is using a single factor indicator, such as energy intensity [23] and resource intensity [24], but this method fails to consider other inputs (capital or labor) and the mutual substitution between inputs [25]. Another way considers multiple inputs to calculate the efficiency, adopting Data Envelopment Analysis and its derivative method [21,26,27] and Stochastic Frontier Analysis [28], etc. Compared with DEA, SFA has the following advantages: (1) SFA uses the maximum likelihood method to estimate each parameter and then applies the conditional expectation to calculate the technical efficiency of each decision unit [29]. It makes full use of each sample information, so the calculation result is relatively stable. It is not affected by individual abnormal points; DEA mainly constructs frontiers through technically valid samples. Therefore, the information from these samples ultimately determines the shape of the frontier surface. If there are abnormal points, it will have a greater impact on the results. Since there is a large gap in basic data between the provinces, it is reasonable to use SFA [30]. (2) SFA considers the influence of random factors on output and divides actual output into three parts: production function, random factor, and technical inefficiency. However, DEA ignores the influence of random factors on output and attributes the difference between actual and optimal output entirely to technical inefficiencies. Thus, technical efficiency measured by the SFA method is often higher than that measured by DEA [31]. (3) For the analysis of influencing variables, SFA only needs to express the technical inefficiency term as the linear form of each influencing factor and then complete the estimation of each influencing factor in the original model, which can avoid the drawbacks of assumptions contradictory caused by two-phases DEA [32]. Therefore, this paper adopts the SFA method to study the technical efficiency and its influencing factors of the marine low-carbon economy in coastal areas of China.

In addition, this paper also analyzes the convergence and divergence between regions based on the calculation of technical efficiency. The current research on convergence and divergence of efficiency is mainly concentrated in the industrial and agricultural fields [33,34]. Studying whether there is a tendency for the marine economy to converge between regions can provide better suggestions for the further development of China’s marine economy.

3. Research Design

3.1. Model of Measurement of Marine Technical Efficiency and Influencing Factors

3.1.1. Basic Model

Farrell (1957) pioneered the concept of frontier production function when he was studying the issue of production effectiveness [35]. Under the premise of the best combination of the given input factors, the optimal output can be calculated, which is called the production frontier. The ratio of actual output to optimal output is called technical efficiency, and the ratio of the difference between the optimal output and actual output to the optimal output is called technical inefficiency. Correspondingly, the technical efficiency of the marine economy in a province refers to the ratio of actual output to optimal output under a given input factor, which reflects the marine-related industries’ abilities of the effective use existing resources in this province.

This paper adopts the stochastic frontier analysis method to analyze the panel data of 11 coastal provinces from 2006 to 2016. For panel data, before the 1990s, SFA can only measure technical efficiency. Then the BC model proposed by Battese and Coelli (1995) reflects the technical inefficiency and influencing factors in the same model, which develops the stochastic frontier analysis [36]. This technology enables simultaneous estimation of technical efficiency and influencing factors. In this paper, the Battese and Coelli model is used to measure the technical efficiency η of different coastal provinces. The model is as follows:

$$Y_{it}=f\left(X_{it};\beta \right)\exp \left(v_{it}-u_{it}\right),i=1,2,\cdots ,T$$

(1)

$${\eta }_{it}=\frac{E\left(Y_{it}|u_{it}\right)}{E\left(Y_{it}|u_{it}=0\right)}=\frac{f\left(X_{it};\beta \right)\exp \left(v_{it}-u_{it}\right)}{f\left(X_{it};\beta \right)\exp \left(v_{it}\right)}=\exp \left(-u_{it}\right)$$

(2)

Equation (1), $Y_{it}$ denotes the output of unit i in period t. $f\left(X_{it};\beta \right)$ denotes the production frontier function. $X_{it}$ denotes the input vector of production unit i in period t. β denotes the coefficient vector to be estimated, and the error term is constituted by $v_{it}$ and $u_{it}$ which are independent of each other. $v_{it}$ represents a random disturbance term, $v_{it}~i.i.dN\left(0,{\sigma }_v^2\right)$ indicates technical inefficiency, and $u_{it}~N^{+}\left(u_{it},{\sigma }_u^2\right)$. In Equation (2), if $u_{it}=0$, then ${\eta }_{it}=1$. It means that the production unit i is on the production frontier in period t and no technical inefficiency exists. If $u_{it}>0$, then ${\eta }_{it}<1$. It indicates that the production unit i is below the frontier and technical inefficiency exists.

In the BC model, the mean of technical inefficiency is assumed to be a function of each influencing factor. Let ${\mu }_{it}$ be the mean of $u_{it}$, using Equations (3) and (4) to indicate:

$${\mu }_{it}={\xi }_0+z_{it}\xi$$

(3)

$$u_{it}={\mu }_{it}+w_{it}$$

(4)

$${\sigma }^2={\sigma }_u^2+{\sigma }_v^2$$

(5)

$$\gamma =\frac{{\sigma }_u^2}{{\sigma }_u^2+{\sigma }_v^2}$$

(6)

Equation (3), $z_{it}$ denotes the q-dimensional row vector consisting of the q factors that affect the technical inefficiency, and ξ denotes the q-dimensional column vector consisting of the coefficients of these influencing factors. If the coefficient of an influencing factor is positive, it represents this factor will have a negative effect on η; that is, it will reduce technical efficiency and increase technical inefficiency. ${\xi }_0$ is the constant term to be estimated. In Equation (4), $w_{it}$ denotes an unobservable random variable and obeys a truncated normal distribution with 0 mean and ${\sigma }^2$ variance. In Equations (5) and (6), ${\sigma }^2$ and $\gamma$ are the parameters to be estimated, and $\gamma$ is between 0–1 to test the proportion of technical inefficiency in the compound error term. If $\gamma >0$, the gap between the optimal output and the actual output may be the impact of both technical inefficiency and uncontrollable pure stochastic factors. After estimating the parameters ${\xi }_0$, $\xi$, ${\sigma }^2$ and $\gamma$, $u_{it}$ can be calculated to furtherly estimate the technical efficiency. That is:

$${\eta }_{it}=\exp \left(-u_{it}\right)=\exp \left(-{\xi }_0-z_{it}\xi -w_{it}\right)$$

(7)

3.1.2. Variable Design

(1)

Input-output variables

Since Equations (1) and (2) both contain production frontier functions, choosing reasonable input-output variables is significant to measure technical efficiency scientifically. Referring to the existing literature and based on the research objectives of this paper, the following input-output variables are selected:

①

Output variable

Gross ocean product (Gop): Gross ocean product in the coastal provinces reflects the economic output of the marine economy in each province. To reduce the impact of price on the gross ocean product, this paper takes 2005 as the base period to calculate the actual value of the gross ocean product of each province. The GOP data is from China Marine Statistical Yearbook.

②

Input variables

• Carbon dioxide emission (CO₂): The paper adopts a single-output SFA model, so carbon dioxide emission is analyzed as an input variable. Since carbon dioxide emission is not published by each province directly, the carbon dioxide emission data used in each province are derived from the China Emission Accounts and Datasets (CEADs) [37,38,39] which are compiled by several research institutes. Because most scholars have shown that GDP has an obvious positive correlation with carbon emissions, the carbon dioxide emissions of marine industries in each province can be calculated by multiplying the proportion of gross marine product to the gross domestic product by carbon dioxide emissions in the province.
• Labor input (L): It reflects the changes in the number of employees in the process of marine economic development in each province. This paper selects “sea-related employment” as the labor input variable. Data comes from China Marine Statistical Yearbook.
• Capital input (K): Due to the lack of capital input of the marine economy in related provinces in the existing statistical data, it selects the fixed investment in the marine economy of each province as capital input. It is calculated by total investment in fixed assets and the proportion of gross ocean product in the gross domestic product in each province. It also selects 2005 as the base year. The data on total investment in fixed assets comes from China Statistical Yearbook.

(2)

Influencing factors variables

①

Industrial structure (Is): Marine-related industries can be divided into the first, second, and third industries. Among them, the marine secondary industry mainly consists of manufacturing and mining sectors, with more carbon emissions than other industries. Therefore, it adopts the proportion of gross ocean product in the secondary industry to gross ocean product as an indicator to measure the industrial structure. It assumes that this indicator has a negative impact on η in each province. GOP in the secondary industry comes from China Marine Statistical Yearbook.

②

Structure of property rights (Prs): In the context of economic restructuring, many state-owned and private enterprises coexist in China’s marine-related industries. Studies have shown that the efficiency of state-owned enterprises is lower than that of private enterprises [40,41]. Therefore, the variable adopted is the proportion of the number of people employed by state-owned enterprises to the total employment in the province at the end of the year. These indicators are from the China Statistical Yearbook and the Statistical Yearbook of each province. It assumes that this proportion has a negative impact on η.

③

Foreign direct investment (FDI): Foreign direct investment has brought about the intensification of the connection between the domestic market and the international market. The increase in Sino-foreign joint ventures, Sino-foreign cooperative operations, and wholly foreign-owned enterprises can increase competition among enterprises, and promote the upgrading of industrial structure and improvement of technological level. As a result, this paper examines the influence of foreign direct investment on the technical efficiency of China’s marine low-carbon economy, assuming that foreign direct investment has a positive impact on η. Data comes from China Statistical Yearbook.

④

Energy structure (Es): Carbon emissions from different energy sources used in the production process are also very different. If the use of carbon-containing energy accounts for a relatively large proportion, the carbon emission will be relatively high. Therefore, it chooses the proportion that coal consumption accounts for total energy consumption as a proxy variable of energy structure. The data on different energy consumption is from China Energy Statistics Yearbook. It assumes that it has a significant negative impact on η.

⑤

Energy price (Ep): In general, high energy prices will increase producers’ costs. Therefore, to reduce costs, producers will heighten energy efficiency as much as possible. It selects purchasing price indicator for raw materials, fuels, and power of producers in each province as a proxy variable for energy price, which comes from China Statistical Yearbook, and the indicator is converted in the base period of 2005. It assumes that this variable has a positive impact on η.

⑥

Technique level (Tec): Under normal circumstances, the research results of scientific research institutions can greatly promote the improvement of the technical level of related industries [42]. The number of scientific papers published by marine scientific research institutions can indicate the status of marine scientific research institutions engaged in research and development within a period. A large number of published scientific papers indicates that the R&D achievements are rich, which can promote the improvement of the technical level of the marine economy and improve efficiency. In this paper, the number of scientific and technological papers of marine scientific research institutions in each province is selected as the proxy variable of technical level, assuming that the variable has a positive impact on η. Data comes from China Marine Statistical Yearbook. Special definition of each variable can be found in

Table 1. Definitions of variables.

Variables	Units	Hyp.	Sym.	Proxy Variables
Output	10,000 RMB	-	Gop	Gross ocean product, 2005 as the basic year
Carbon dioxide emissions	10,000 tons	-	CO2	Carbon dioxide emission in the marine economy
Labor input	10,000 people	-	L	Sea-related employment
Capital input	10,000 RMB	-	K	Fixed investment in the marine economy, 2005 as the basic year
Industrial structure	-	negative	Is	The output value of the marine secondary industry/GOP
Structure of property rights	-	negative	Prs	People employed by state-owned enterprises/Total employment
Foreign direct investment	100,000,000 USD	positive	Fdi	Foreign direct investment
Energy structure	-	negative	Es	Coal consumption/Total energy consumption
Energy price	-	positive	Ep	Purchasing price indicator for raw materials, fuels, and power of producers, 2005 as the basic year
Technique level	papers	positive	Tec	Number of scientific papers published by marine scientific research institutions

.

3.1.3. Econometric Model

Based on the design of variables, the interaction among input variables will have an impact on the results. A more flexible form of the beyond logarithmic Cobb-Douglas production function has been chosen as a production frontier function. The Translog function allows alternative elasticity changing with factor ratio (and time) [43], which overcomes the drawback of the CD function with its elasticity of 1. Then Equations (1) and (3) can be changed to the following Equations (8) and (9):

$$\begin{array}{l}lnGo{p}_{it}={\beta }_0+{\beta }_{1}ln{CO}_{2it}+{\beta }_{2}ln{L}_{it}+{\beta }_{3}ln{K}_{it}+{\beta }_4{[ln{CO}_{2it}]}^2+{\beta }_5{[ln{L}_{it}]}^2\\ +{\beta }_6{[ln{K}_{it}]}^2+{\beta }_7[ln{CO}_{2it}\ast ln{L}_{it}]+{\beta }_8[ln{CO}_{2it}\ast ln{K}_{it}]+{\beta }_9[ln{K}_{it}\ast ln{L}_{it}]+v_{it}\\ -u_{it}\end{array}$$

(8)

$${\mu }_{it}={\xi }_0+{\xi }_{1}I{s}_{it}+{\xi }_{2}Pr{s}_{it}+{\xi }_{3}Fd{i}_{it}+{\xi }_{4}E{s}_{it}+{\xi }_{5}E{p}_{it}+{\xi }_{6}Te{c}_{it}$$

(9)

In Equation (8), $Go{p}_{it}$ represents the gross ocean product of province i in period t. $C{O}_2{}_{it}$, $L_{it}$, $K_{it}$ represent the input of province i in period t. $I{s}_{it}$, $Pr{s}_{it}$, $Fd{i}_{it}$, $E{s}_{it}$, $E{p}_{it}$, $Te{c}_{it}$ represent influencing factor variables. The remaining parameters to be estimated and the error term are consistent with the definition in the previous section. The following analysis will be based on Equations (8) and (9), and technical efficiency η of each province will be calculated according to Equation (7).

3.2. Kernel Density Estimation

Kernel density estimation is a nonparametric estimation method for studying the characteristics of data distribution from the data itself. Kernel density distribution curve variables can describe the distribution of random variables. This method can better reflect the absolute difference and evolution law of the technical efficiency of marine economy. Kernel density estimation assumes that the density function of a random variable $\eta *$ is $f(\eta *)$, and the estimation formula of probability density is listed as follows:

$$f(\eta *)=\frac{1}{Nh}{\displaystyle \sum _{i=1}^{N}K(\frac{{\eta }_{{}_i}^{*}-\stackrel{-}{{\eta }^{*}}}{h}})$$

(10)

In Formula(10), $N$ denotes the number of observations; $h$ represents the bandwidth; $K(\cdot )$ is the kernel function; $\eta *$ represents the independent and identically distributed observations; $\stackrel{-}{\eta }*$ is the mean value. According to the characteristics of the data, this paper will select the gaussian kernel function of a random variable with normal distribution to estimate the time evolution process of technical efficiency of marine economy. Then, we can obtain the evolution law of the technical efficiency on the time axis by analyzing the kernel density curve’s shape, position, and peak.

3.3. Stochastic Convergence of Technical Efficiency

Unlike traditional convergence, stochastic convergence emphasizes the process of the output gap changing with time in a dynamic and long-term process [44]. Evans and Krass (1996) pointed out that pairing was used to test stochastic convergence [45]. In the context of panel data, it is based on a common mean value, such as Formula (11):

$$\underset{k\to \infty }{\lim }{E}_t\left(Y_{i,t+k}-{\overline{Y}}_{t+k}\right)={\phi }_i-\frac{1}{N}{\displaystyle \sum _{i=1}^N{\phi }_i}$$

(11)

Therefore, the stochastic convergence test can be converted into testing whether the panel data $\left(Y_{i,t+k}-{\overline{Y}}_{t+k}\right)$ obeys the stochastic process. Therefore, the stochastic convergence analysis of the technical efficiency is to test the smoothness of the panel data $\left({\eta }_{i,t+k}-{\overline{\eta }}_{t+k}\right)$. Due to non-observed factors in factors that affect the technical efficiency of each province, it will lead the panel data $\left({\eta }_{i,t+k}-{\overline{\eta }}_{t+k}\right)$ to heterogeneous panel data. Referring to the existing research on stochastic convergence analysis and panel unit root test [44,46], Im, Pesaran, and Shin W-stat, ADF-Fisher Chi-square, and PP-Fisher Chi-square test models can be used to test whether there is a heterogeneous panel unit root. Through EViews 9.0, it adopts the above three methods to perform unit root tests of the panel data. If two or more methods of the above three methods which are used can pass the significance test at a certain level of significance, then it considers that the panel data reject the original hypothesis, which means that there is a stochastic convergence and the common development trend exists.

3.4. Sample Selection and Data Sources

The provinces of Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Guangxi, and Hainan are selected as research objects and these eleven provinces are divided into three major regions: the Bohai Rim, the Yangtze River Delta, and the Pan-Pearl River Delta. Shandong, Liaoning, Hebei, and Tianjin provinces belong to the Bohai Rim region; Jiangsu, Shanghai, and Zhejiang are in the Yangtze River Delta region; Guangdong, Guangxi, Hainan, and Fujian are in the Pan-Pearl River Delta region. Statistical data range from 2006 to 2016, which comes from the “China Ocean Statistical Yearbook”, “China Energy Statistical Yearbook”(2007–2017), and “provincial statistical yearbook”(2007–2017). Descriptive statistics of the variables are shown in

Table 2. Descriptive statistics of the variables.

Variables	Maximum	Minimum	Mean	Standard Deviation
Gop	62,713,393.23	3,007,000.00	22,908,260.97	15,729,348.43
CO2	21,411.22	427.22	5448.86	4288.09
L	868.50	81.50	305.04	210.13
K	88,204,902.50	1,239,446.77	18,860,537.44	15,516,497.74
Is	0.68	0.19	0.44	0.10
Prs	0.75	0.16	0.40	0.16
Fdi	357.60	4.47	117.56	88.95
Es	0.80	0.26	0.54	0.14
Ep	143.67	95.62	116.28	10.79
Tec	3072.00	11.00	724.94	638.80

. Table 2 shows that the gross ocean product, CO₂ emissions, fixed assets investment, foreign direct investment, and technique level are quite different among the provinces, while the difference between the ratio-type variables is smaller.

4. Empirical Results

4.1. Stability Test and Cointegration Test

In order to improve the reliability of the regression results, it is necessary to test the stability of the data. This paper mainly uses Fisher-ADF test to test the stability of panel data. In this paper, we first take the logarithm of the non-structural data, and then test the stability of the logarithmic data and structural data. Eviews11.0 software is used for ADF test. The results show that the horizontal sequence is mostly non-stationary, while the first-order difference sequence is stationary at the level of 1%, as shown in

Table 3. Fisher-ADF test results.

Variables	Original Value		First-Order Difference
	T-Statistic	p-Value	T-Statistic	p-Value
lnGop	16.6852	0.7805	56.1110	0.0001
lnCO2	30.7089	0.1022	77.4750	0.0000
lnL	110.440	0.0000	175.527	0.0000
lnK	8.76834	0.9945	78.0923	0.0000
[lnCO2]2	29.5350	0.1302	77.0286	0.0000
[lnL]2	108.457	0.0000	173.605	0.0000
[lnK]2	7.68797	0.9979	80.4224	0.0000
[lnCO2] × [lnL]	31.5872	0.0847	44.2881	0.0033
[lnCO2] × [lnK]	26.6369	0.2253	79.8509	0.0000
[lnL] × [lnK]	17.1298	0.7562	59.2864	0.0000
Is	13.6180	0.9145	57.2918	0.0001
Prs	6.11158	0.9997	43.2067	0.0045
Fdi	30.7492	0.1014	78.8859	0.0000
Es	17.3342	0.7447	56.2237	0.0001
Ep	30.9632	0.0969	46.8718	0.0015
Tec	26.9372	0.2136	77.1782	0.0000

.

The cointegration theory was put forward by Engle and Granger in 1987. That is, although two or more series are non-stationary, their linear combination may offset the influence of the trend term and make the combination stable. At this time, these series are said to be cointegrated, and there is a long-term stable relationship between them. According to the cointegration theory, if there is same-order stationarity between variables, then there may be cointegration relationship between them, which is the prerequisite for meeting the cointegration test. In this paper, Eviews 11.0 software is also used to test the cointegration relationship of each variable in Equation (8), and the Kao Residual Cointegration Test method is mainly selected. The test results show that ADF T-Statistics is −6.828470 and p-value is 0.0000. It can be seen that the T-value is significantly at the level of 1%. The original assumption that there is no cointegration relationship is rejected, that is, the variables in the model have a long-term stable cointegration relationship, and the regression estimation can be based on the logarithmic panel data.

4.2. Stochastic Convergence of Technical Efficiency

Based on the logarithmic panel data on the marine economy in nine coastal provinces from 2006 to 2016, Frontier 4.1 software is used to analyze the technical efficiency of the marine economy and its influencing factors. Calculation results are shown in

Table 4. Estimation results of the main function and efficiency influence function.

Var.	Par.	Statistical Magnitude		Var.	Par.	Statistical Magnitude
		Estimated Value	T Statistics			Estimated Value	T Statistics
Cons	β0	−21.169 ***	−11.117	Cons	ξ0	0.210	1.272
lnCO2	β1	0.744	1.629	Is	ξ1	−1.318 ***	−8.155
lnL	β2	−0.753	−1.151	Prs	ξ2	0.783 ***	3.885
lnK	β3	4.315 ***	16.294	Fdi	ξ3	0.0002	−1.707
[lnCO2]2	β4	0.424 ***	8.214	Es	ξ4	0.871 ***	3.938
[lnL]2	β5	0.028	0.999	Ep	ξ5	0.006 ***	3.933
[lnK]2	β6	−0.236 ***	−17.328	Tec	ξ6	−0.001 ***	−8.892
[lnCO2] × [lnL]	β7	−1.236 ***	−8.093	σ2	-	0.021 ***	7.880
[lnCO2] × [lnK]	β8	−0.043	−0.775	γ	-	0.988 ***	77.947
[lnL] × [lnK]	β9	0.682 ***	8.523	-	-	-	-

Note: *** indicates rejecting the original hypothesis that the value of each parameter is zero at the 1% significance levels.

and

Table 5. Technical efficiency of marine economy in each year.

	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	Mean	Region
Tianjin	0.5068	0.5118	0.5404	0.5511	0.5704	0.5585	0.6094	0.6489	0.7391	0.9395	0.6045	0.6164	Bohai Rim
Hebei	0.2831	0.2836	0.3007	0.3217	0.3211	0.3132	0.3257	0.3408	0.3994	0.4010	0.4304	0.3383	Bohai Rim
Liaoning	0.3147	0.3289	0.3400	0.3310	0.3431	0.3791	0.3678	0.3845	0.3816	0.3378	0.3457	0.3504	Bohai Rim
Shanghai	0.9764	0.9903	0.9557	0.8600	0.8559	0.8229	0.8170	0.7799	0.8198	0.8174	0.8634	0.8690	Yangtze River Delta
Jiangsu	0.4819	0.5264	0.5226	0.5618	0.6003	0.5993	0.6314	0.6387	0.7173	0.7601	0.7825	0.6202	Yangtze River Delta
Zhejiang	0.4350	0.4466	0.4796	0.5136	0.5169	0.5458	0.5232	0.5024	0.4714	0.4850	0.4933	0.4921	Yangtze River Delta
Fujian	0.4062	0.4104	0.4102	0.4324	0.4196	0.4362	0.3917	0.3872	0.4438	0.5117	0.5400	0.4354	Pan-Pearl River Delta
Shandong	0.6318	0.6830	0.7135	0.6882	0.7312	0.7503	0.7665	0.8149	0.8683	0.9001	0.9171	0.7696	Bohai Rim
Guangdong	0.7718	0.6836	0.8301	0.8322	0.9282	0.9798	0.9876	0.9328	0.9880	0.9806	0.9895	0.9004	Pan-Pearl River Delta
Guangxi	0.3308	0.2807	0.2724	0.2457	0.2568	0.2508	0.2657	0.2829	0.3000	0.3204	0.3366	0.2857	Pan-Pearl River Delta
Hainan	0.2704	0.2957	0.2758	0.2270	0.2104	0.2035	0.1994	0.2056	0.1893	0.1872	0.2013	0.2242	Pan-Pearl River Delta
Mean	0.4917	0.4946	0.5128	0.5059	0.5231	0.5308	0.5351	0.5381	0.5744	0.6037	0.5913	-	-
Maximum	0.9764	0.9903	0.9557	0.8600	0.9282	0.9798	0.9876	0.9328	0.9880	0.9806	0.9895	-	-
Minimum	0.2704	0.2807	0.2724	0.2270	0.2104	0.2035	0.1994	0.2056	0.1893	0.1872	0.2013	-	-

. In Table 4, the γ value is 0.988, rejecting the null hypothesis at the 1% level of significance, which indicates that the gap between the optimal output and actual output is mainly from technical inefficiency, so the use of stochastic frontier analysis is reasonable. From the estimation results, estimated values of parameters in the main function and efficiency influence function reject the null hypothesis at different levels of significance, and the data fit better.

In Table 5, except for Shanghai and Hainan, the η of marine economy in coastal provinces has shown an upward trend generally, especially in Guangdong, Shandong, Jiangsu, and Hebei. Guangdong and Shandong reach 0.9 in 2016, and Jiangsu and Hebei increased by 62.40% and 52.03%, respectively during the study period. In terms of the average value of each province and city, Guangdong and Shanghai are in the leading position. During the study period, the average η of the two provinces’ marine economy has reached more than 0.8, and the average η of Guangdong in these 11 years is 0.9004, which is the highest among the 11 coastal provinces. Since 2010, Guangdong has surpassed Shanghai to become the most technically efficient province. In recent years, Guangdong’s gross ocean product has grown rapidly, growing at a rate of more than 10% from 2006 to 2013. After 2013, the growth rate slowed down. By 2016, the GOP has reached more than 1.5 trillion RMB in Guangdong, surpassing Shanghai in both scale and growth rate. During the study period, Shanghai’s gross ocean product increased by about 6.8%. By 2016, the GOP is 746.34 billion yuan. This may be the reason why η of Guangdong’s marine economy gradually rises and exceeds that of Shanghai. Among the 11 provinces, η of Hainan and Guangxi is relatively low, which is below 0.3. The GOP of these two provinces is at a relatively low level in the coastal provinces, and the carbon dioxide emissions of the marine economy are also small. It is necessary to further strengthen the development potential of marine-related industries. From the perspective of time, the mean of η of marine economy in 11 coastal provinces increased by 0.1 in the study period, with the maximum and minimum in 2006 and 2015, respectively.

Figure 1 shows η and GOP of the marine economy in 11 coastal provinces. In general, there is a positive correlation between η and GOP of the coastal provinces. Guangdong, Shandong, and Shanghai have higher GOP, and their η is also higher. During the study period, with the development of the marine economy and the support of related policies of some provinces and cities, the technical efficiency of these provinces and cities has gradually increased, and the gap between η has gradually decreased.

Fujian’s GOP ranks high among the 11 coastal provinces, and the average value is fourth in coastal provinces. However, η of the marine economy is not high. It may be because Fujian’s marine science and technology is relatively weak compared to other provinces, and the funding of marine scientific research institutions and the number of scientific papers published are lower than those of other provinces with higher GOP. Marine science and technology have not yet produced enough stimulus for the marine low-carbon economy in Fujian Province. It is necessary to strengthen the emphasis on marine scientific research, and further promote the role of scientific and technological innovation in heightening the technical efficiency of the marine economy.

Define a technical efficiency value of 0.7–1 as a high-efficiency area, 0.4–0.7 as a medium-efficiency area, and 0–0.4 as a low-efficiency area. Figure 1 shows the technical efficiency of coastal provinces in 2006, 2011, and 2016. It can be seen that high-efficiency areas have increased from 2 in 2006 to 4 in 2016, while low-efficiency areas have decreased from 6 to 3, indicating that the difference in technical efficiency between some provinces is gradually shrinking. Shandong is the province with the most obvious increase in η. It has been increasing year by year since 2006, and it has become a high-efficiency region in 2010. Among the three main regions, except for the Yangtze River Delta region, the remaining two regions still have low-efficiency provinces and cities in 2016, and there is a big gap between the high-efficiency provinces and cities in the region. By calculating the coefficient of variation, it can be seen that among the three regions, the Pan-Pearl River Delta has the largest coefficient of variation, that is, the largest difference within the region. The gap of η between the three provinces and cities in the Yangtze River Delta is relatively small, and the coefficient of variation in the Bohai Rim region is relatively similar to that of the 11 coastal provinces and cities. The changes in the coefficient of variation in the Yangtze River Delta and the Pan-Pearl River Delta show opposite trends. As time went by, the gap within the Yangtze River Delta gradually narrows, while the gap between the four provinces and cities in the Pan-Pearl River Delta gradually increases. It is mainly due to the low η of Guangxi and Hainan provinces, especially Hainan province, which has the lowest efficiency value in the coastal provinces and the efficiency has slightly decreased during the study period. The coefficient of variation in the Bohai Rim region is about 0.4. Although it has not changed much, it is still at a relatively high level. Cooperation within the region still needs to be strengthened to improve the coordinated development of the regional marine economy. The next part will further analyze changes and differences of η in coastal provinces using kernel density estimation.

4.3. Dynamic Evolution of Technical Efficiency

Kernel density estimation can be used to describe the dynamic changes and regional differences of η in coastal provinces over the past 11 years. In Figure 2, the abscissa represents the value of η, and the ordinate represents the kernel density. The dynamic change of η of the marine low-carbon economy can reflect the government’s attention to the development of the marine economy and marine environmental management. From 2006 to 2009, η shows a significant unimodal distribution. The peak efficiency in 2006 is about 0.4, and the kernel density is greater than 1.75. The kernel density curve has shown a right-skewed shape. The area on the left is smaller than the area on the right, indicating that the technical efficiency of coastal provinces in 2006–2009 is generally low, and there is a cluster of technical efficiencies in various regions. The tail area on the right side of the curve has gradually become flat over time, indicating that the technical efficiency of some provinces and cities has improved, and the aggregation has declined. In 2010–2013, the kernel density curve did not change much and remained a unimodal distribution.

In 2013, the curve begins to show the characteristics of a ‘multimodal distribution’. In 2014–2016, the kernel density curve shows a bimodal distribution. The peak efficiencies in 2015 are 0.45 and 0.85, respectively. The density of the peak on the right is lower than that on the left, indicating that the 11 coastal provinces and cities began to differentiate gradually in the past. With the government’s support for the development of the marine economy and the strengthening of marine environmental management in some provinces, the marine economy has developed rapidly and η has improved. However, there are still fewer regions that have become highly efficient than those that have become moderately efficient.

Overall, from 2006 to 2016, the peak kernel density has reduced, the peak value of technical efficiency has increased, and the area of the tail regions on both sides has decreased gradually, which indicates that the development of the technical efficiency of coastal provinces has shown a process from concentration to differentiation. The development gap between regions has become larger, and the development speeds of various provinces are different. For example, Guangdong and Shandong have risen significantly in η and become high-efficiency regions, while the marine economic development of Guangxi and Hainan is poor, which has brought about a flattening of the kernel density curve.

4.4. Analysis of Factors Influencing Technical Efficiency of the Marine Economy

In Table 3, the estimated value of Is is −1.318, which rejects the null hypothesis at a significance level of 1%. An increase in Is will bring about an increase in η, which is inconsistent with the hypothesis. Among the provinces, Hainan province has the lowest Is of 0.217 and the corresponding η value is also the lowest. Tianjin has the highest value of 0.628, and the values of the rest provinces are all between 0.4 and 0.5, which is consistent with the estimated results. This shows that the proportion of the marine secondary industry has a positive impact on technical efficiency, which may be due to the obvious pulling effect of the marine secondary industry on marine economic development. In recent years, due to the national attention to green development, the marine secondary industry pays more attention to low-carbon production, which leads to the positive impact of industrial structure on technical efficiency.

The estimated value of Prs is 0.783, which rejects the null hypothesis at a significance level of 1%. If Prs increases by 1%, η will increase by 0.783%, which is consistent with the hypothesis. From the perspective of provinces, Guangxi and Hainan have higher average Prs, which is 0.600 and 0.591, respectively, and the corresponding average η is also lower. From the perspective of various regions, Prs in the Yangtze River Delta region is significantly lower than the other two regions, and the η value is the highest among the three regions, which is consistent with the estimated results, confirming the claim that the efficiency of state-owned enterprises is lower than that of private enterprises. Therefore, the government can actively encourage private capital to invest in marine-related industries.

The estimated value of Fdi is 0.0002, which means that the increase in Fdi will bring about a decrease in η. It does not conform to the hypothesis, and the estimated value is extremely small and insignificant. During the reference period, the average value of Fdi in each province is proportional to the average value of η. The Fdi value of the Yangtze River Delta and the Bohai Rim is greater than that of the Pan-Pearl River Delta, and the average η value of the Pan-Pearl River Delta is also the smallest. After the introduction of advanced technology, the provinces conduct in-depth research and knowledge transfer to achieve the purpose of promoting the improvement of their technical level. However, compared with the direct development of marine science and technology, the role of foreign direct investment in improving the efficiency of the marine economy is not obvious.

The estimated coefficient of Es is 0.871, rejecting the null hypothesis at the significance level of 1%, indicating that the increasing value of Es will reduce η accordingly, which is consistent with the hypothesis. The mean values of Es in Hainan and Shanghai are low, ranging from 0.3 to 0.4. The mean values of the remaining provinces are between 0.5 and 0.8. The highest Es in Shandong province is 0.771. China’s coal resources are large in total quantity and will be used for a long time. However, the increase in coal use will inevitably lead to an increase in carbon emissions, which in turn will reduce technical efficiency. Therefore, if we can further improve the energy extraction technology and energy efficiency, and increase the use of other energy sources, η will rise.

The estimated value of Ep is 0.006, indicating that the increasing value of Ep will reduce η accordingly, which is consistent with the hypothesis. In coastal provinces, the average Ep of Shandong, Hebei, and Guangxi exceeds 120. In the three regions, the Ep-mean values of the Yangtze River Delta, the Pan-Pearl River Delta, and the Bohai Rim are 119.01, 114.34, and 115.01, respectively. The corresponding mean value of η is the highest in the Yangtze River Delta, which is consistent with the estimated content, indicating that the rise in energy price has not caused the relevant companies to change their energy use and the overall impact is not significant.

The estimated value of Tec is negative but small, which rejects the null hypothesis at a significance level of 1%. If Tec increases by 1%, η decreases by 0.001%, which is consistent with the hypothesis. Guangdong and Shandong have the highest average of Tec, which is 1854.6 and 1766.5, respectively, and their corresponding technical efficiency averages are also the highest. Guangxi and Hainan have the lowest number of scientific papers published, and their corresponding average technical efficiency is also the lowest. It can be explained that the development of science and technology plays a vital role in the development of a region’s marine economy. To increase the development potential of the marine economy, it is necessary to pay more attention to science and technology.

4.5. Stochastic Convergence

In

Table 6. Stochastic convergence test.

Regions	IPS W-Stat	p-Value	ADF-Fisher Chi-Square	p-Value	PP-Fisher Chi-Square	p-Value
11 coastal provinces and cities	−0.110	0.456	26.274	0.240	12.232	0.952
Three regions	−0.319	0.375	7.958	0.241	4.505	0.609
Yangtze River Delta	−1.691	0.046	13.075	0.042	13.454	0.036
Pan-Pearl River Delta	−1.440	0.075	15.507	0.050	3.464	0.902
Bohai Rim	1.249	0.894	4.833	0.775	4.597	0.800

, the IPS, ADF, and PP tests of η in the Yangtze River Delta region reject the null hypothesis of heterogeneous panel unit roots at a significance level of 5%. The ADF and IPS tests in the Pan-Pearl River Delta reject the null hypothesis at the levels of 5% and 10%, respectively. It can be considered that there is stochastic convergence within the Yangtze River Delta and the Pan-Pearl River Delta, and there is a common development trend. It can be seen from the technical efficiency of each province that the common development trend of the Yangtze River Delta is relatively obvious, and the gap between the three provinces in this region is gradually narrowing. The 11 coastal provinces and cities and three regions cannot reject the null hypothesis in the three tests, indicating that there is no common development trend among coastal provinces, which is consistent with the above analysis of the gradual differentiation of technical efficiency in coastal provinces. In the Bohai Rim, the null hypothesis cannot be rejected in the three tests, and there is no stochastic convergence. Within the Bohai Rim, except for Shandong, the technical efficiencies of the other three provinces are in the middle and lower level. In 2016, the technical efficiency of Shandong was 0.3126 higher than that of Tianjin, which ranked second in the region. There is a large gap in the region and there is no common development trend.

5. Conclusions

Based on the panel data of 11 provinces and cities from 2005 to 2016, this paper uses the SFA method to analyze the technical efficiency of the marine economy and its influencing factors under the carbon emission constraints of China’s coastal areas. On this basis, the stochastic convergence of technical efficiency is discussed. The following main research conclusions and suggestions can be obtained.

(1)

The technical efficiency of the marine low-carbon economy varies substantially in different regions of China. During the study period, the maximum and minimum annual average values of η are 0.4917 and 0.6037, respectively. The overall η of all provinces and cities is on the rise. Guangdong and Shanghai are in the lead. The technical efficiency of Guangdong has surpassed Shanghai since 2010 and reached 0.9895 in 2016. The marine economic development of Fujian does not match the η. The marine economic development is relatively good, but the η is low. The technical efficiencies of Hainan and Guangxi provinces are relatively low, both below 0.3. The coefficients of variation of the 11 coastal provinces are large. Therefore, the government needs to further increase its emphasis on marine science and technology, and strengthen cooperation within various regions and the entire coastal area to reduce regional gaps and improve coordinated development capabilities.

(2)

From 2006 to 2009, the technical efficiency of coastal provinces is generally low, and there is a cluster of η in various regions. As time passed, the 11 provinces and cities began to differentiate gradually, and the technical efficiency of some provinces increased. However, apart from the Yangtze River Delta and the Pan-Pearl River Delta, there is no common development trend in other regions and the entire 11 coastal provinces and cities. In general, the changes in η in coastal provinces have shown a process from concentration to differentiation. The development gap between regions has become larger, and the development speed of each province is different. Based on strengthening cooperation, local governments should continue to strengthen their support for marine economic development and constraints on marine environmental management.

(3)

The number of marine scientific papers published and the proportion of the output value of marine secondary industry have a positive effect on η, while the proportion of state-owned enterprise employment, foreign direct investment, producer purchase price index, and coal consumption proportion have a negative impact on η. The influence of property rights structure, industrial structure, and energy consumption structure is more obvious. As a result, the government must continue to promote low-carbon production in the marine economy, actively encourage private capital to invest in marine-related industries, and heighten the development of the marine low-carbon economy through advances in marine science and technology.

This paper discusses marine economic efficiency and its influencing factors under the constraint of carbon emissions in China’s coastal areas, which has reference significance for the selection of paths to improve marine economic efficiency. However, many marine economic indicators have no authoritative definition and processing methods at present because of the difficulty to draw a clear line between the marine economy and the land economy. Due to the lack and lag of relevant data on the marine economy, this paper has some deficiencies in the index selection and timeliness. In addition, many studies have shown that marine and environmental policies impact marine economic efficiency. Therefore, we will focus on the impact of relevant policies on marine economic efficiency in further research.