Research on urban innovation efficiency of Guangdong-Hong Kong-Macao Greater Bay Area based on DEA-Malmquist model.

In order to scientifically evaluate the allocation efficiency of science and technology innovation system and build a good science and technology financial environment, this paper constructs an evaluation index system based on the panel data of 11 cities in Guangdong-Hong Kong-Macao Greater Bay Area from 2010 to 2019. By using the Three-stage DEA model and Malmquist model, this paper makes a static and dynamic analysis on the efficiency of scientific and technological innovation, calculates the efficiency of scientific and technological innovation, and reveals its internal reasons. The results show that: the productivity of scientific and technological innovation in Guangdong-Hong Kong-Macao Greater Bay Area has been steadily improved; technological progress is the key factor to promote the productivity of scientific and technological innovation; there are differences in the efficiency of scientific and technological innovation in the same city, and the efficiency of scale has inhibited the efficiency of scientific and technological innovation to a certain extent.

Introduction

With the advent of the era of knowledge economy, modern manufacturing means are increasingly advanced, and production efficiency is constantly improving. Innovation has become an important means for a country and region to enhance its comprehensive competitive strength. Since the twentieth century, the United States, Japan, South Korea and Europe have involved great reputation to systematic and industrial innovation, and achieved remarkable results (Hanna, 2020; Sun et al., 2020). After the reform and opening up in 1978, China also began to attach reputation to systematic and technical innovation, and in the twenty-first century, it continued to increase investment in knowledge and technology. China's total GDP in 2020 is 101.60 trillion yuan, and the per capita GDP is 74,200 yuan, equivalent to 11,400 US dollars per capita. In 2020, the per capita GDP of the United States will be US $63,000, Japan will be US $40,200, Britain will be US $42,500, Germany will be US $48,300 and South Korea will be US $32,000. By contrast, there is still a big gap between China and these countries. From the current high-speed economic growth stage to the high-quality economic growth stage, China is no longer in the pursuit of high-quality economic growth. Novel coronavirus pneumonia is affecting the world downtown pressure on the economy. Transportation, logistics, trade and tourism are all affected. Under the background of economic pressure increasing, how to change the mode of economic growth has been a tough time to tackle. Economic development needs a new engine, needs to change the past extensive growth mode, and needs to enhance the role of scientific and technological innovation in driving economic development. Total factor productivity (TFP) compares total outputs to total inputs used in the output's production. The indicator gauges TFP growth because both output and inputs are reported in terms of volume indices. Over a certain time period, the change in production and input volumes is measured.

Although Chinese enterprises pay more attention to scientific and technological innovation and their ability of scientific and technological innovation is constantly improving, there are still some problems such as low efficiency of scientific and technological innovation and lack of coordination. In 2019, the outline of growth plan for Guangdong-Hong Kong-Macao Greater Bay Area allotted by the State Council clearly proposes to build Guangdong, Hong Kong and Macao Bay area into an international science and technology innovation center with global influence. The Greater Bay Area plan for Guangdong, Hong Kong, and Macao has gone through a lengthy process. Financial sectors and port sets, such as the Superior Pearl River Economic Zone, were common in the early days. Later, the projected Hong Kong Cove Area was China's first wished-for Inlet Area, followed by the notion of Lingdingyang Bay Area, or Central Pearl River Estuary Bay Area. The “Pearl River Delta Inner-city Municipal Corresponding Progress Plan” was the official document that first introduced the Bay Area idea in 2005. How to improve the competence of scientific and technical modernization has become a hot and difficult issue in the erection of the bay area. Based on this, this paper uses DEA-Malmquist index model to evaluate the scientific and technical modernization ability of Guangdong-Hong Kong-Macao Superior Cove Area, and explores the scientific and technical novelty efficiency and its influencing factors. The Malmquist Measure (MI) is a bilateral index that can be used to compare two economies' manufacturing technology. It's called for Professor Sten Malmquist, who came up with the concept. The Malmquist Productivity Index is another name for it.

When a variable returns to scale relationship between inputs and outputs is assumed, the BCC (ratio) model is the DEA model utilised in Frontier Analyst. BCC stands for Banker, Charnes, and Cooper, who initially suggested it in a Management Science publication. In data envelopment analysis (DEA), cross-efficiency evaluation is a valuable tool for assessing the performance of decision-making units (DMUs). Some existing cross-efficiency assessment models, in particular, can be considered special examples of the PCE model when the parameters are adjusted appropriately.

Literature review

Proposal of related concepts

The concept of urban–rural mixed zone was first put forward in academic circles. Until 2006, when British urban planners studied the urban boundaries of Europe, North America and Asia, they put forward the concept of urban agglomeration (Satu & Vesa, 2006). The uneven distribution of resource elements among countries or regions makes it possible for regional cooperation. In order to achieve better regional cooperation among countries, regions and cities, in addition to the inherent complementarity of economic advantages and disadvantages, they also need to establish a cooperation platform through policies to reach a consensus on Cooperation (Taylor, 2010). Vesa integrates regional innovation capability into the framework of national innovation capability, and believes that regional innovation capability can continuously tap the internal relationship between technology and business application (Vesa, 2006). Innovation efficiency and innovation ability are two concepts closely related but different. By definition, regional innovation efficiency refers to the phased efficiency of regional innovation activities from factor input to innovation output, that is, the productivity of a new technology or idea transformed into new products, new processes or new equipment through research and development (Salih & Inci, 2019). Something process-oriented, systematic, and clearly set on generating something new and distinct from what has come before is what innovation entails. Innovative appears to be a more subtle concept, more of a point of view than a finished product. Incremental innovation is the process of improving something that already exists. Finding an altogether new way of doing something is what radical innovation is all about.

Application of model method

Data envelopment analysis (DEA) and stochastic frontier analysis (SFA) are two mainstream methods to measure regional innovation efficiency. DEA model is more relaxed for the setting of production frontier. SFA model defines specific production function and considers the influence of random disturbance and non efficiency term (Kiesling et al., 2002). Each of the two methods has its own advantages and has become an important tool for empirical research (Kleine, 2004). With the development of econometrics and the deepening of research, based on these two methods, a variety of analysis tools are derived to measure the regional innovation efficiency, which not only make up for the limitations of traditional DEA model and SFA model, but also more in line with the actual situation of regional innovation activities. Some scholars propose to apply DEA cross efficiency model to the evaluation of regional technological innovation efficiency (Petruzzelli, 2011; Yang & Li, 2018). DEA Malmquist directory technique is widely used to analyze the dynamic changes of regional innovation efficiency (Peter et al., 2017). A robust shared input DEA model is used to estimate regional innovation efficiency in a global way (Hahn et al., 2017; Ludwig & Macnaghten, 2020). Three stage DEA model is a comprehensive application of DEA model and SFA model on the premise of considering environmental factors, which is widely used in the current research of regional innovation efficiency (Arranz et al., 2020). The field of measuring competence in socioeconomic and technical + cononic processes is vast and well-studied. In this paper, we distinguish between technological efficacy, economic efficiency, and community efficacy. Specific technical efficacy measurements are well-defined and verified, but overall pointers for the technical efficacy of products like automobiles, washing machines, and television sets are difficult to come by.

In directive to scientifically evaluate the efficiency of methodical and technical innovation in Guangdong-Hong Kong-Macao Superior Bay Area, this paper uses the Three-stage DEA model to quantity the productivity of technical and industrial innovation statically, and analyzes the dynamic changes and reasons of the productivity of scientific and scientific innovation by combining with Malmquist index method.

Study design

In instruction to scientifically evaluate the efficiency of methodical and technical innovation in Guangdong-Hong Kong-Macao Better Cove Area, this paper uses the Three-stage DEA prototypical to portion the proficiency of scientific and technological innovation statically, and analyzes the dynamic changes and reasons of the efficacy of scientific and high-tech invention by combining with Malmquist index method.

Three stage DEA

The first stage DEA model was put forward by Charnes and other scholars, and applied to the efficiency evaluation of decision-making units. It is considered that the variable value changes between 0 and 1, where 1 means that the decision-making unit has the best efficiency value and 0 means the worst efficiency value (Charnes & Cooper, 1978). Later, Banker and others put forward the BCC model, which has a wider application scope. The technical efficiency is divided into pure technical efficiency and scale efficiency, and can be expressed as technical efficiency = pure technical efficiency × scale efficiency. In this paper, the input of urban innovation research is controllable, but the output is uncontrollable, so BCC model is chosen to calculate (Banker et al., 1984).

DMU means that Decision Making Units. A decision-making unit (DMU) is a group of people who work together in an organisation to make product and service purchases. It's also known as an organization's 'purchasing centre.' The nonparametric method of data envelopment analysis (DEA) is used to estimate production frontiers in operations research and economics. It's a method of calculating the productive efficiency of decision-making units based on actual data. Initiators understand the importance of resolving a certain problem and begin looking for a solution. Gatekeepers are experts in a particular topic or product, and they manage information and access to other DMU members. In formula (1), is the pure technical efficiency coefficient of DMUj. When , the comprehensive efficiency of DMUj is efficient, and when and are equal to 0 at the same time, it means strongly efficient; When , and if or one of them is equal to 0, it means weakly efficient. When , it indicates that the comprehensive efficiency of DMU is invalid, and the closer to 1, the more effective it is.

The second stage of DEA model was put forward by Aigner and other scholars in 1985. It is a regression method based on SFA stochastic frontier production function, which can accurately judge the technical efficiency (Tariq et al., 2020). In SFA regression method, the error term is composed of random error term and invalid rate term. The invalid rate item adjusted by SFA actually reflects the invalid part of management technology (Zachary, 2011). To resolve the input slack caused by uncontrollable factors in the external environment, the regression equation of SFA is constructed based on input orientation, and the input of each decision-making unit is adjusted:

In the formula (2), ; . is the adjusted input value, is the initial input value. means to analyze the DMU under the same external environment, means to adjust the DMU to the unified random state, so as to form the unified external environment and random state of the DMU. is an estimated value, which needs to be estimated in advance.

It needs to be estimated in advance in the calculation process. Using fride's empirical formula, we can get the following conclusions:

In Formula (3), ; . is not clearly defined. In order to facilitate the follow-up operation, referring to the definition given by scholar Roaden, we get the following results:

The third stage of DEA model is to re measure the adjusted innovation input as the new initial input . Compared with the DEA model in the first stage, the efficiency of DMU calculated in the third stage is more in line with the objective reality because the interference of environmental variables and inefficiency items has been reduced to the greatest extent. This model of variable returns to scale is more suitable for regional innovation efficiency analysis. In this paper, as a huge space innovation system, Guangdong, Hong Kong and Macao Bay District has the production technology factors and policy dividends iterating with each other, and the whole innovation system is greatly affected by random variables. Therefore, the DEA model in the third stage is more in line with the reality of innovation efficiency analysis.

Malmquist model

Using Malmquist index method can dynamically reflect the regional innovation efficiency (Schwartz et al., 2016). Referring to the results of fare in 1994, using his total factor productivity index (TFP) and decomposing it, the following formula is obtained:

When the result is more than 1, tfp increases; when the result is less than 1, tfp decreases; when the result is equal to 1, tfp remains unchanged (Elvekrok et al., 2018).

The total feature production productivity is the total efficiency of scientific and technological innovation:

Among them, the index of technological efficiency change (Effch), technology progress index (Tech), pure technology efficiency index (pech) and scale efficiency index (sech).

Index selection

Through literature review, we can find that when we measure the regional innovation efficiency, we use two indicators of innovation input and innovation output to analyze, supplemented by environmental variables to judge. This paper mainly refers to the research conclusions of Based on the selection of input index, output index and environmental variable index, the index system of urban modernization proficiency in Guangdong-Hong Kong-Macao Greater Cove Area is shown in Table 1. The input and output indexes of nine cities in Guangdong Province can be directly or indirectly calculated through Guangdong statistical yearbook and Guangdong science and Technology Yearbook. Relevant data of Hong Kong and Macao can be obtained from Hong Kong Statistical Yearbook, Macao statistical yearbook, website of Hong Kong Census and Statistics Department and website of Macao census and Statistics Bureau. Some missing individual year data are supplemented by means of mean interpolation in adjacent years, or replaced by data with similar interpretation.

Table 1

Changes of main pointers of urban modernization network over the years

Year	Central potential	Average size of structural hole
Input index	Personnel input	Number of scientific and technological personnel
	Capital input	Proportion of R & D expenditure in GDP
	Incubator carrier input	Number of provincial new R & D institutions
Output index	Patent output	Patent authorization
	Value output	Output value of high tech products
	Profit output	Profits of Industrial Enterprises above Designated Size
Environment variable	Economic environment	GDP
	Government environment	Financial expenditure on science and technology
	Investment environment	Total foreign investment in import and export

Empirical analysis

This part uses the panel data from 2010 to 2019 and three-stage DEA prototypical to examine the revolution productivity of Guangdong-Hong Kong-Macao Greater Bay Area in that year. Then, we use the same period, the same region data and Malmquist directory technique to portion the dynamic change of innovation efficiency of each city. From the static and dynamic point of view, comprehensive analysis of urban innovation. Panel data, also known as longitudinal data, is information collected over time that incorporates observations on several cross sections. Countries, corporations, individuals, and demographic groups are all examples of groups that can make up panel data series.

Three stage DEA analysis of urban innovation efficiency

The first stage: urban innovation efficiency measured by traditional DEA

Deap2.1 software is used to analyze the BCC model of Guangdong-Hong Kong-Macao Better Cove Area data from 2010 to 2019. We can estimate the technical productivity, untainted technical efficacy and scale efficacy of Guangdong, Hong Kong and Macao Cove area and each city every year.

Table 2 shows the technical competence, pure technical efficacy and scale efficacy of Guangdong-Hong Kong-Macao Greater Bay Area in 2010–2019. The data envelopment analysis (DEA) method is used to determine the relative efficiency of decision-making units (DMUs) doing identical tasks in a production system that uses many inputs to produce multiple outputs. In DEA, the Malmquist productivity index shows how each decision-making unit is progressing or regressing (Tables 3, 4).

Table 2

Overall characteristics of innovation efficiency in Guangdong-Hong Kong-Macao Greater Bay Area

Year	Technical efficiency	Pure technical efficiency	Scale efficiency
2010	0.923	0.933	0.989
2011	0.916	0.927	0.988
2012	0.935	0.942	0.993
2013	0.907	0.925	0.979
2014	0.918	0.926	0.991
2015	0.926	0.949	0.974
2016	0.906	0.972	0.932
2017	0.842	0.971	0.868
2018	0.861	0.977	0.881
2019	0.869	0.993	0.875
Mean	0.901	0.951	0.947

Table 3

Overall characteristics of innovation efficiency in different cities

Year	Technical efficiency	Pure technical efficiency	Scale efficiency
Guangzhou	1	1	1
Shenzhen	0.981	1	0.981
Zhuhai	0.901	0.926	0.973
Foshan	0.83	0.934	0.889
Huizhou	0.952	0.978	0.972
Dongguan	1	1	1
Zhongshan	1	1	1
Jiangmen	0.812	0.915	0.892
Zhaoqing	0.597	0.773	0.822
HongKong	0.931	1	0.931
Macao	0.899	0.94	0.957
Mean	0.9	0.951	0.947

Table 4

SFA regression results of urban innovation

Year	Personnel input slack variables	Capital investment slack variable	Incubator carrier input slack variable
Constant term	0.524*** (5.278)	0.341*** (6.142)	0.484*** (3.129)
Economic environment	−0.145*** (4.447)	−0.267** (−1.285)	0.186* (2.953)
Government environment	0.142* (2.578)	−0.053*** (4.639)	0.106*** (4.775)
Investment environment	−0.025** (−2.436)	0.119*** (3.383)	0.904*** (−4.474)
δ^2	0.067*** (3.418)	0.038** (3.372)	0.042** (4.291)
γ	0.984*** (8.041)	0.997*** (6.754)	0.969*** (6.287)
Log function value	98.423***	99.254***	96.247***

*Means significant at 10%, **means significant at 5% and ***means significant at 1%. The corresponding estimated T-test values are in brackets

Technical efficiency reflects the production efficiency of input factors when the supervisory element is in the optimal scale. When the technical efficiency is 1, it shows that the DEA efficiency is effective. From the perspective of technical efficiency, urban modernization in Guangdong-Hong Kong-Macao Better Cove Zone has the highest technical efficiency in 2012, with an average technical efficiency of 0.935, close to the effective value of 1; in 2017, the technical efficiency is the lowest, with an average comprehensive efficiency of 0.842, which is related to the world Federal Reserve interest rate increase and brexit events in 2017, and the export-oriented economy of Guangdong Province has been greatly affected. In the 10 years from 2010 to 2019, the average value of innovation technology efficiency is 0.901, which indicates that the overall level of science and expertise novelty in Guangdong-Hong Kong-Macao Superior Bay Area is high, and there is a great room for future growth. It should be noted that there has been a zigzag downward trend since 2012, but it began to rebound after 2018. This also reflects the importance of China's timely launch of Guangdong-Hong Kong-Macao Superior Bay Area Planning in 2018. From the standpoint of pure technical efficiency, the average value reaches 0.951, which shows an increasing trend year by year, indicating that the talent accumulation and technical advantages of Guangdong-Hong Kong-Macao Superior Cove Area are constantly emerging. From the view of scale efficiency, the average value over the years is 0.947, and the scale efficiency is relatively high. Before 2016, it presents a zigzag decline, and after 2017, it begins to show an upward trend year by year.

In 2010–2019, the innovation technology efficiency of Guangzhou, Dongguan and Zhongshan is 1, which indicates that the most high-quality input and output of systematic and technological modernization development in the Guangdong-Hong Kong-Macao Superior Cove Area is within the statistical range. Guangzhou and Dongguan mainly build manufacturing and high-tech industries, and their favorable endowment conditions of innovation resources provide stable support for the high-quality development of technical and high-tech invention. Although Zhongshan City is not outstanding in the total economic volume or per capita in Guangdong-Hong Kong-Macao Superior Cove Area, it actively implements the traditional advantage industry promotion plan, and encourages enterprises to undertake major national and provincial science and technology projects and key R & D plans. Because of the low input and high output, it also achieves a better level of technical efficiency. During the study period, the average innovation technology productivity of Guangdong-Hong Kong-Macao Greater Bay Zone was 0.897. In addition to the cities with technical efficiency of 1, the comprehensive efficiency of innovation in Shenzhen, Zhuhai, Huizhou, Hong Kong and Macao was higher than this average, with the proportion of cities accounting for 72.73%. In the future, cities below the average of technical efficiency in the bay area should take active measures to improve. At the same time, these cities should effectively improve the comprehensive efficiency value, so as to improve the innovation technology efficiency level of the whole bay district.

The second stage: SFA regression analysis

By the service of Frontier 4.1 software, this paper deals with the slack variables of urban modernization investment in Guangdong-Hong Kong-Macao Superior Cove Zone, and takes the processed outcomes as explanatory variables.

The third stage: DEA efficiency analysis after input adjustment

Before excluding the impact of environmental variables, the analysis results may lead to some cities' innovation efficiency index values on the high side and some on the low side, which affects the scientificity of efficiency evaluation. Therefore, it is essential to eliminate the conservational variables without interference, peel off the impact of ineffective management and arbitrary factors, and use deap2.1 software to analyze the innovation efficiency, so as to make it in the same environment. The specific statistical analysis results are shown in Table 5.

Table 5

Overall characteristics of urban innovation efficiency after adjustment

Year	Technical efficiency	Pure technical efficiency	Scale efficiency
Guangzhou	1	1	1
Shenzhen	0.977	0.996	0.981
Zhuhai	0.921	0.935	0.985
Foshan	0.913	0.975	0.936
Huizhou	0.965	0.978	0.987
Dongguan	1	1	1
Zhongshan	0.999	0.999	1
Jiangmen	0.835	0.923	0.9052
Zhaoqing	0.645	0.784	0.823
HongKong	0.954	1	0.954
Macao	0.947	0.968	0.978
Mean 1	0.917	0.954	0.957
Mean 2	0.923	0.956	0.958

Mean 1 represents the innovation scale efficiency of 9 metropolises in Guangdong Province, mean 2 represents the innovation scale efficiency of 11 metropolises in Guangdong-Hong Kong-Macao Greater Bay Area, and mean 3 represents the annual average of scale efficiency of apiece region

It can be seen from Table 5 that after stripping the external interference such as environmental factors and random factors, the overall technical productivity, untainted procedural efficacy and scale efficacy of the cities in Guangdong-Hong Kong-Macao Greater Bay Area have increased by 0.023, 0.005 and 0.011 respectively, indicating that the external interference has inhibited the improvement of innovation efficiency to some extent. In terms of technical efficiency, nine cities in the Pearl River Delta, Hong Kong and Macao increased by 0.020, 0.023 and 0.048 respectively, with Macao having the largest increase. From the perspective of cities, only Shenzhen and Zhongshan, due to the decline of technical efficiency, lead to the decline of the overall comprehensive efficiency of 0.004 and 0.001 respectively.

Malmquist index analysis

Regional dimension analysis

Based on the panel data of inner-city origination competence in Guangdong-Hong Kong-Macao Superior Bay Zone region from 2010 to 2019, this paper decomposes and calculates the total factor productivity index of 11 cities in the region, and the results are shown in Table 6.

Table 6

TFP index of regional dimension and its decomposition

Year	Effch	Tech	pech	sech	tfp
Guangzhou	1.005	1.153	1.005	1.000	1.159
Shenzhen	1.006	1.035	1.006	1.000	1.041
Zhuhai	1.003	1.104	1.000	1.003	1.107
Foshan	1.003	1.021	1.002	1.001	1.024
Huizhou	1.003	1.000	1.003	1.000	1.003
Dongguan	1.002	1.053	1.000	1.002	1.055
Zhongshan	1.000	1.015	1.000	1.000	1.015
Jiangmen	0.996	0.985	0.995	1.001	0.981
Zhaoqing	0.986	0.956	0.987	0.999	0.943
HongKong	1.000	0.999	1.000	1.000	0.999
Macao	1.007	1.024	1.002	1.005	1.031
Mean 1	1.001	1.036	1.000	1.001	1.037
Mean 2	1.001	1.030	1.000	1.001	1.031

Mean value 1 represents the mean value of 9 cities in Guangdong Province, and mean value 2 represents the mean value of 11 cities in Guangdong-Hong Kong-Macao Greater Bay Area. Effch is technical efficiency index, tech is methodological growth index, Pech is pure technical efficiency index, sech is scale efficiency index, TFP is total factor productivity index

Overall, the TFP index and technical efficiency index of Guangdong-Hong Kong-Macao Greater Bay Area are 1.031 and 1.001 respectively, which indicates that the overall innovation efficiency of the whole region has increased by 3.1% and technical efficiency by 0.1% on average, and the overall resource allocation level of the whole region is in an upward channel. And from the decomposition of innovation technical efficiency, the pure technical efficiency index is 1, which indicates that the pure technical efficiency has no change in the period of 2010–2019. The scale efficiency index is 1.001, and the scale of innovation activities in Guangdong-Hong Kong-Macao Superior Bay Zone is in the expansion stage, which plays a direct role in promoting the comprehensive efficiency.

Combining with Fig. 1, it can be found that Guangzhou and Zhuhai have TFP values greater than 1.1, which are 1.159 and 1.107 respectively, demonstrating that the general innovation competence of these two cities has a very obvious improvement during 2010–2019. The cities with TFP values between 1.000 and 1.100 were Dongguan, Shenzhen, Macao, Foshan, Zhongshan and Huizhou, which were 1.055, 1.041, 1.031, 1.024, 1.015 and 1.003 respectively. The TFP of Hong Kong, Jiangmen and Zhaoqing has regressed, which has not reached 1. The TFP of Hong Kong is 0.999, which has regressed by 0.001. The reason is that the level of technological progress has regressed by 0.001. The reason is that the previous pure technical efficiency has reached 1, so it is difficult to break through the current level of investment in science and technology, so it has entered the "winner trap". The TFP values of Jiangmen and Zhaoqing are 0.981 and 0.943 respectively, representative that the general innovation productivity has decreased by 1.9% and 5.7%. The main reason is that the pure technical efficiency of the two cities is less than 1, and there are obvious disadvantages in technical efficiency. Because of its successful applications and case studies, DEA has gotten too much attention from researchers. Using DEA in various areas includes evaluating bank branch performance, examining bank efficiency, analysing firm financial statements, measuring higher education institution efficiency, solving facility layout design (FLD) problems, and measuring the efficiency of organisational information technology investments.

Fig. 1

Regional total factor productivity index and decomposition chart

Time dimension analysis

Based on the panel data from 2010 to 2019, this paper incomes all the cities in Guangdong-Hong Kong-Macao Greater Bay Area as a whole, and analyzes the changes of TFP index and its decomposition from the time dimension. The results are shown in Table 7.

Table 7

Changes and decomposition of TFP in time dimension

Year	Effch	Tech	pech	sech	tfp
2010–2011	1.015	1.003	1.012	1.003	1.018
2011–2012	1.011	0.997	1.008	1.003	1.008
2012–2013	1.003	0.989	1.001	1.002	0.992
2013–2014	0.999	0.978	0.998	1.001	0.977
2014–2015	0.996	1.013	0.995	1.001	1.009
2015–2016	1.003	1.017	1.001	1.002	1.020
2016–2017	1.017	1.018	1.015	1.002	1.035
2017–2018	1.019	1.025	1.016	1.003	1.045
2018–2019	1.023	1.037	1.016	1.007	1.061
Mean	1.010	1.008	1.007	1.003	1.018

It can be found from Table 7 that the TFP file of metropolises in Guangdong-Hong Kong-Macao Superior Bay Zone is 1.018, with an increase rate of 1.8%, indicating that the development of technical and high-tech modernization in these cities is relatively stable. At the same time, combined with Fig. 2, it can be found that TFP index presents a certain fluctuation in the statistical interval. From the perspective of time, we can see that TFP index decreased continuously from 2010 to 2014, and it was less than 1 in 2013 and 2014. The reason is that under the influence of the US subprime mortgage crisis in 2008, Guangdong Province began to adopt the "free cage for birds" approach in 2010, actively adjusting the industrial structure, actively slowing down economic growth, and avoiding the traditional approach of factor driven and investment driven. So in the next few years, the performance of technical and high-tech invention indicators is not ideal, and the role of systematic and technical novelty has not really burst out. Since 2015, TFP index has risen year by year, and reached the maximum value of 1.061 in 2018–2019, up 6.1 percentage points. On the one hand, the practice of actively adjusting the industrial structure has achieved actual results; on the other hand, it is also related to the implementation of the policy of Guangdong-Hong Kong-Macao Greater Bay Area, which has accelerated the investment in scientific and technological innovation.

Fig. 2

Time dimension total factor productivity index and decomposition chart

Conclusion

This paper makes an empirical study on the novelty efficacy of 11 cities in Guangdong-Hong Kong-Macao Greater Bay Area.

The Three-stage DEA model is more objective than the single-stage DEA model. After removing the redundant variables, the technical efficiency, pure technical competence and scale proficiency of each city increased by 0.023, 0.005 and 0.011 respectively, indicating that external interference inhibited the improvement of innovation efficiency to some extent.

From 2010 to 2019, the efficiency of science and technology innovation in Guangdong-Hong Kong-Macao Greater Bay Area shows a fluctuating trend, but on the whole, the efficiency of science and technology innovation shows a steady improvement trend.

There are obvious differences in innovation efficiency between cities. The innovation efficiency of Guangzhou, Dongguan and Zhongshan has always been 1, which is at a very high level. Shenzhen, Zhuhai, Huizhou, Hong Kong and Macao are all above the average. The performance of Zhaoqing and Jiangmen is not ideal. Shenzhen's innovation efficiency is not as good as expected, and it is also inconsistent with its status as the first in GDP region. The main reason is that the scale of innovation investment is too large, which affects the upgrading of novelty productivity.

The improvement of innovation efficiency mainly comes from the improvement of clean practical competence. No matter from the time dimension or the regional dimension, this law is very obvious. Especially for some cities with large innovation investment and good foundation, the improvement of innovation efficiency mainly comes from the improvement of pure technical efficiency, and the impact of scale efficiency is not big.