Research status and trend of PPP in the US and China: visual knowledge mapping analysis

ABSTRACT Public-private-partnership (PPP) model has been widely used in public services and infrastructure projects, and many relevant studies on PPP have emerged. Based on CiteSpace and VOS viewer, this study aims to comprehensively analyze the research status and development trend of the PPP model in China and US. Firstly, the essential statistical characteristics of authors, institutions, and publications are given based on the relevant data collection in Web of Science core collection database. Secondly, the research hotspots and evolution trends of PPP by scholars in China and US are discussed by carrying out keywords co-occurrence analysis and cluster analysis. Finally, from the literature analysis and keyword co-occurrence network over time, the research directions, such as payment risks for the government during the operation period, early termination mechanism and system compensation mechanism, government supervision, and related information, are summarized and forecast, to provide theoretical guidance for the future research on PPP.


Introduction
The Public-Private Partnership (PPP) model has become an important way to supply public goods and purchase public services.It has brought not only significant changes and innovations to the development of the field (Cheng et al. 2020) but also brought great benefits to economic and social development (Shioji 2001).With the advantages of reducing the financial burden, improving the supply efficiency of infrastructure or public services, sharing risks, and promoting the transformation of the role of the government, and related issues, the PPP model is widely used in infrastructure projects, which significantly improves the economic value of infrastructure and public service outputs while promoting their development simultaneously.The PPP has been widely used in developed and developing countries (Cheng et al. 2020;Song et al. 2019).However, there are still great differences in various regulations and industrial applications of PPP among countries due to their varying pace of development (Cheng et al. 2020).
There is still no unified definition for the PPP model (Khanom 2010).According to the federal transportation administration, a PPP is a contractual relationship between the public and the private sectors based on a contract.The contract generally refers to the repair, construction, operation, maintenance, and management of facilities or systems, where the public sector usually owns facilities or systems.In contrast, the private sector is given the right to decide how to complete the projects or tasks (FHWA 2015;Lee and Miller 2021).PPP in China refers to the long-term cooperative relationship between the public and private sectors to provide public goods or services.The narrow sense of PPP emphasizes the complementary advantages, risk-sharing, and benefit-sharing between the public and private sectors.PPP can be understood as a long-term contractual relationship between the public and private sectors based on infrastructure and public utilities, in a broad or narrow sense, in which the public sector is the regulator, collaborator, and purchaser.The private sector is responsible for infrastructure investment, financing, design, construction, operation, and maintenance.The investment income of the private sector is obtained as "user payment" or "government payment," or "feasibility gap subsidy" (Finance 2014;Cheng et al. 2020).
Moreover, the development of PPP has gone through the stages of germination, exploration, promotion, and accelerated development, and has obtained rich research results in each stage (Song et al. 2022).In particular, the globalization of PPP has further profoundly influenced the development and growth of such projects (Siemiatycki 2013).Under the current open market economic environment, PPP projects in developed countries, represented by the United States, also have distinctive international characteristics.The United States, as an economic power, has always paid attention to introducing various forms of financing from the private sector as a process of economic development.The country has formed a unique PPP management system and development model reflecting the actual situation, such as multimodal PPPs, the world bank database, and so on (Lee and Miller 2021;Pantangi et al. 2022;Kaminsky 2022).On the other hand, some developing countries represented by China are constantly summarizing the uniqueness and successful experiences of the PPP model while actively participating in international cooperation (Ke et al. 2010;Xiong and Han 2021;Song et al. 2022).However, different development paths exist between developed and developing countries due to differences in social and economic systems and market environment.Therefore, the following questions are worth further consideration.
(1) What are the differences in development status and evolution trends between China and USA for the PPP model?(2) What is the mechanism of the differences?(3) What could be the conceptual framework and future research directions for PPP?
To answer the above questions, this study has been structured into six sections.Following a bit of background and introduction in Section 1, the research methodology is described in Section 2. This study collected all relevant pieces of literature published since 1991.01 in China and the US.Cite Space and VOS viewer were used to describe the research status and development trends, and then analyze the differences between China and the US.Section 4 includes a descriptive analysis of general trends in publications, academic "PPP" of different stakeholders, and major source journals.Section 5 analyses the research frontier and the topics of trend.Lastly, directions for future research on PPP and the conclusion of this study appear in Sections 5 and 6, respectively.

Research designed
This section summarizes about the relevant literature both in China and the US and further reveals the main developing trend of research in PPP in China and the US simultaneously.The research procedures and methodological framework are shown in Figure 1.

Methods
The works of literature published in a specific discipline reflect the scientific characteristics of the field to a certain extent, which means predicting the development trend of a specific discipline can be extracted and condensed from those works (Kuhn 1962).Information visualization technology can explore the dynamic structure and development law hidden in massive data to a great extent since it can make the processing and analysis of citation data no longer limited by the number of citations (Chen et al. 2012).Cite Space and VOS viewer are the most frequently used knowledge mapping tools in the field of scientific metrology (Pan, Xu, and Skare 2022).Specifically, the citation visual analysis technologies of Cite Space and VOS viewer software are comprehensively used to describe the measurement with dynamic, time-sharing, and multivariate for the literature of PPP in China and the US, respectively, which is embodied in the visual operations, such as the statistical analysis of the literature, cooccurrence of organization or author cooperation, cooccurrence and clustering, mutation of keywords.Based on the methods of co-word analysis, cluster analysis, and co-citation analysis, the visual knowledge mapping is drawn, and the primary citation nodes, knowledge turning points, and key paths in the evolution of the PPP knowledge field are identified to further explore the current development trend on PPP research field in China and the USA, respectively.

Data collection and processing
The Web of Science (WOS) database is considered an authoritative data source for publications (Singh et al. 2021).Meanwhile, the WOS core collection database is considered a convenient data source that can carry out a quantitative analysis of the PPP (Song et al. 2019).Therefore, the WOS database, including SCI, SCIE, SSCI, A&HCI, ESCI, was chosen to extract the publications in the research area of the PPP (Li et al. 2021) Out of the articles searched, the records that were not related to the topics and strategies, and duplicate articles were screened and eliminated, which resulted in a total of 478 articles from the authors of the U.S. and 615 articles from the authors of China.The selected research papers and articles were studied thoroughly to understand the trend of PPP in both countries.

General trends of publications
The development trend of PPP in China and the US could be understood by exploring the publications selected for this study.Figure 2 depicts the research on PPP in China and the US.It is observed that the research in the area of PPP rose steadily from 2010 until 2020 for both the countries where the U.S. witnessed a sharp rise between 2016 to 2020.Due to the government budget and per capita income reduction, there is a significant gap in construction and maintenance funds for public transport infrastructure.To fill in the funding gap and further stimulate economic recovery, the US promulgated the American Recovery and Reinvestment Act in 2009 to encourage the private sector to participate in infrastructure construction in terms of laws.Subsequently, the American Investment Proposal was constructed, and the strategies for expanding the infrastructure investment were further clarified through cooperation with the private sector.Since then, the PPP model in the US entered a phase of acceleration, which established a certain foundation for research on PPP in the US.On the other hand, the research on PPP in China was still at the initial stage during 2010-2014, which escalated from 2015 until 2020.Meanwhile, many relevant policies, such as guidance on innovating investment and financing mechanisms in key areas and encouraging social investment, are being issued to promote the PPP model vigorously.Many PPP projects in different 199019921994199619982000200220042006200820102012201420162018  industries are being implemented, acting as fertile soil for the research in the PPP model.

Academic "PPP" of different stakeholders
To fully understand the academic contributions of the countries, mainstream institutions, and the researchers in the relevant fields of (Li et al. 2021) research, the academic "PPP" of different stakeholders are divided into macro level, meso level, and micro level, where the countries as in macro level are only set for the US and China, and the meso and micro levels being the institutions and scholars from these countries respectively (Li et al. 2021).
According to the WOS core collection database, the number of publications (NP) on PPP in the US from January 1991 through March 2022 was 478, and that in China was 615.Table 1 summarizes the top 10 institutions for the most NP in China and the U.S. The values of betweenness centrality (C) for the corresponding institutions are also included.An American scholar Leydesdorff (2007) used the betweenness centrality as a key index to measure the academic characteristics of literary journals.Professor Chen Chaomei (Chen et al. 2012), the developer of Cite Space, also used betweenness centrality to represent the importance of the scientific measurement units, such as authors and citations in the literature.Therefore, the academic influence can be evaluated by intermediary centrality.
From Table 1, in the U.S., the University System of Maryland ranks in the top with NP = 35 and C = 0.07, followed by Cornell University with NP = 20 and C = 0.09.On the other hand, in China, Hong Kong Polytechnic University is at the top with the highest NP = 102, followed by other institutions.This shows that many institutions have begun to invest a lot of scientific research in the field of PPP, and cooperative relationships among various institutions have gradually been established.
In Table 2, the top 10 authors in the field of PPP is listed sorted by their NP.Here, the h-index and AVE (Average Citation per Publication) are introduced to further evaluate their academic contributions in the field of PPP.These are important indicators to measure the scientific research level of a researcher (Li et al. 2021).Albert P.C. Chan has the highest NP (88) as well as h-index (59), while Yong Jian Ke has the highest AVE (64.93) among the listed authors.The mentioned authors in this list are considered to deliver a valuable impact in the research area.

Major source journals
Although the relevant works of literature have been published in more than 200 different journals, the research publications are mainly focused on some authorized journals, for example, Sustainability, Journal of Management in Engineering, Journal of Construction Engineering, and Management, Transportation Research Record, Journal of Cleaner Production, Engineering Construction and Architectural Management.The factors, such as NP, Co-citation frequency (Co), and Journal Impact Factor™ (Five Year) (JIF), that effectively reflect the importance of periodicals and publications, have been introduced to evaluate the journals publishing the research on PPP (Pu, Xu, and Marques 2021;Li et al. 2021).The data are represented in Table 3.
From Table 3, it is observed that there are 65 articles published in the Sustainability Journal, which shows that the scholars pay more attention

Keywords co-occurrence analysis
The trend topics mainly refer to one or more of the core topics in a scientific research field, representing the theoretical knowledge and technical application concerned by most researchers in this field.
Co-occurrence analysis is the quantitative research on the co-occurrence times of keywords that can reveal the relevance and corresponding characteristics of the research content (Kraus, Breier, and Dasí-Rodríguez 2020;Kraus et al. 2020).Specifically, the trending topics from January 1991 to March 2022 and the time every keyword first appeared are counted, which reflects the research progress of China and the US in the field of PPP.VOS viewer was used to obtaining the cooccurrence network of all keywords (Author keywords and keywordsPlus) corresponding to the research on PPP.
Here the occurrence threshold of each keyword is set to 20.The number of articles meeting the threshold is 35 out of 1968 keywords and 90 out of 2385 keywords from articles published in the US and China, respectively.Figure 3. shows the co-occurrence network for China and the US.
The occurrence times of keywords with time evolution can be better understood according to the color change of keywords in Figure 3. Specifically, the heavier the color, the earlier the keyword appears.Conversely, the lighter the color, the later the keyword appears (Pan, Xu, and Skare 2022).As seen in Figure 3., the color yellow appears later.Hence, the keywords in yellow represent the primary research hotspot in recent years.It is well understood that the research from American scholars since 2017 is mainly focused on critical success factors, performance, determinants, incomplete contracts, and governance.Those from Chinese scholars since 2019 are mainly on governance, sustainability, contracts, investment, and decisionmaking.
On the other hand, from the temporal and spatial distribution of keywords, the research on PPP in China and US are at different stages.Primarily, researchers are found to be concerned about the sustainability of PPP projects since 2019.Although some contributions to the Chinese economy are adopted from foreign PPP experience and knowledge, some problems still exist (Song, Hu, and Feng 2018).For example, the projects such as Fuzhou No. 4 Minjiang River Bridge, Quanzhou Citong Bridge, brought massive loss to society due to the mistakes in decision-making by the government.Therefore, scholars in China have been paying attention to the contents of governance, sustainability, investment, and decision-making in PPP projects.Also, it is worth mentioning that the research on low-carbon and renewable energy is not shown in the figure, with the current issues in global warming, climate degradation, and energy depletion still being on the table.This research should focus on the application and practice with the development of society.

Keywords cluster analysis
Based on the keyword frequency analysis, this section will continue to study the development mode and research trend through keyword clustering analysis.Keywords and high-frequency words are firstly extracted from the collected literature, and then the chart representing cluster analysis is drawn on the research of PPP in China and the US, which represents the major research topics.From the cluster analysis based on the Log-Likelihood Ratio (LLR) algorithm, the major research topics are #0 "management", #1 "policy", #2 "behavior", #3 "performance", #4 "risk", #5 "pricing", #6 "governance", #7 "revenue risk", #8 "operational" and #9 "dispute", as shown in Figure 4.The relevant parameters of the network are labeled in the upper left corner of Figure 4.In particular, the modularity Q of 0.58 in the clustering structure is significant(>0.3),which represents that inter-cluster connections are considerable and overwhelming (Chen, Ibekwe-Sanjuan, and Hou 2010).In addition, the mean silhouette used to evaluate the average homogeneity of these clusters is 0.8256  (>0.5), representing a rational high silhouette value and a more uniform structure (Chen, Ibekwe-Sanjuan, and Hou 2010).Cluster #0 "management" mainly refers to project management of PPP projects, which began with the construction project management and developed in the field of construction, investment, and financing management for infrastructure projects.The research team led by scholars Ke et al. (2009) from China firstly did the literature analysis and theoretical reviews on project management of PPP.This laid a theoretical foundation for the construction and research on the theoretical management system of PPP projects (Ke et al. 2009).Tang, Shen, and Cheng ( 2010) conducted a literature review on the project management of PPP in the construction engineering field to improve existing practices and provide new insights for future research on PPP (Tang, Shen, and Cheng 2010).Song, Zhang, andDong (2016, 2019) successively carried out statistics and analysis on research literature on PPP in WOS using knowledge clustering and other methods (Song, Zhang, and Dong 2016;Song et al. 2019).It reveals the research hot spots and evolution trends in the research of PPP in recent 20 years from the perspective of project management, which brings enlightenment in future research.
Cluster #1 "policy" mainly refers to the system or policy of PPP.In recent years, the problems exposed by the large-scale implementation of PPP are related to the imperfect construction of systems and policies.The expected development of PPP should include fair and standardized systems and procedures, extensive public participation (Boyer 2016).While developing countries usually face difficulties, such as lagging construction of the system and weak awareness in the market, which increases the risks of PPP failure (Qin, Luo, and Wang 2022).With the intensive release and active implementation of policies in the field of PPP, relevant research has been enriched, including regulation systems (Yuan et al. 2018), policies on diffusion, policy learning, and the role of government in the implementation process of projects.Meanwhile, the research on matching the legal system construction is also becoming more abundant (Zhang 2015).Rouhani, Oliver Gao, and Richard Geddes (2015) pointed out that previous studies on infrastructure PPP projects mostly focused on modeling without policy analysis and provided corresponding suggestions to policymakers on the payment mechanism of PPP projects (Rouhani, Oliver Gao, and Richard Geddes 2015).Osei-Kyei and Chan (2017) explored the critical success factors of PPP projects through case studies and compared the results with global experience, which provided practical and management enlightenment for the policy implementation of PPP projects (Osei-Kyei and Chan 2017).Wu et al. (2020) studied the impact of policy changes on PPP projects through a case study (Wu et al. 2020).It is of great significance to the research on identifying and preventing policy risks for PPP projects.
Cluster #2 "behavior" refers to opportunism behaviors.The research on opportunism behaviors began with the transaction cost theory, which reflected that one party to the transaction pursuing their interests does not hesitate to sacrifice other parties.It is not only manifested in deliberately avoiding and evading contractual obligations but also in behaviors of false commitment, deception, concealment, and dishonesty (Brown, Grzeskowiak, and Dev 2009;Ozkan-Tektas 2014).Due to the particularity of PPP projects, there are always the risks of private sectors taking speculative behaviors in PPP projects.Xiang, Huo, and Shen (2015) pointed out that the main reason causing losses and risks is the opportunistic behaviors of the private sector led by information asymmetry (Xiang, Huo, and Shen 2015).To curb the opportunistic behaviors of the private sector, Liu et al. (2016) analyzed the mechanism restraining the opportunistic behaviors through the principal-agent theory, which is based on the contractual relationship between public and private sectors and provides new insights for the construction of PPP contracts (Liu et al. 2016).Furthermore, from the perspective of government supervision, Liu et al. (2017) gave the selection strategies of opportunistic behaviors of public and private sectors during the operation period using evolutionary game theory.They put forward policy suggestions for government supervision (Liu et al. 2017).The existence of opportunistic behavior is not conducive to the cooperation between the public sector and the private sector and may also bring more conflicts (Feng, Hao, and Li 2021).
Cluster #3 "performance" mainly refers to the performance evaluation of PPP projects.The performance evaluation is evaluated for economic, social, risk sharing, environment, technology, and other factors related to the implementation and operation of the projects should be evaluated comprehensively and objectively, which to the requirements of PPP project stakeholders such as project investors, government departments and the public and the interests of project objectives (Yuan et al. 2009(Yuan et al. , 2010;;Love et al. 2015).Improving the performance of PPP projects has always been a key goal of PPP to achieve value for money (Zhang 2005;Song et al. 2019).From Figure 4, the most highly cited article from Yuan et al. (2009) defined performance objectives and key performance indicators (KPIs) to evaluate the performance of PPP projects.Based on the perspective of stakeholders, questionnaires and interviews are further used to determine the KPI of the PPP projects (Yuan et al. 2009(Yuan et al. , 2010)).Given the fact that the traditional fixed capital structure and performance measurement methods cannot describe the dynamic evolution of project performance risk, a dynamic capital structure method is constructed to carry out performance and risk management of projects under uncertainty (Sundararajan and Tseng 2017).Wang et al. (2021) analyzed the impact of various stakeholders on the performance of PPP projects using a social network to measure the output and results during the whole life cycle of PPP projects (Wang et al. 2021).
Cluster #4 "risk" and Cluster #7 "revenue risk" can be summarized as risk management, including risk assessment, allocation, and revenue risk.However, Cluster #9 "dispute" is risk assessment and unreasonable risk sharing.Currently, the research on risk management has become one of the hot issues in PPP (Yuan et al. 2018).Taking the PPP projects in Hong Kong as an example, Shen, Platten, and Deng (2006) discussed the main risks in the implementation process of PPP projects and further studied the risk sharing between public and private sectors (Shen, Platten, and Deng 2006).Wang et al. (2000Wang et al. ( , 2004) ) put forward the relevant risk management model for PPP projects (Wang et al. 2000;Wang, Dulaimi, and Aguria 2004).Subsequently, Ke, Wang, and Chan (2013) put forward the risk sharing mechanism and studied the preference for risk sharing in China, Hong Kong, the United Kingdom, and Greece (Ke et al. 2010;Ke, Wang, and Chan 2013).The basis of financing and cooperation for infrastructure projects is the risk sharing between public and private sectors (Ke et al. 2010), and reasonable risk sharing can reduce the occurrence of a dispute during the concession period (Ke, Wang, and Chan 2010).And scholars extended the existing risk research framework and empirical research.Additionally, several risks, such as political risk, financial risk, revenue risk, and so on, have also been hot issues in the risk management of PPP projects.Unfortunately, the present risk research in the field of project management is mainly based on subjective data such as questionnaire surveys, which can make the research results rely on "participants" and the project risk factors depend on "situation".
Cluster #5 "pricing" mainly refers to pricing products or services of PPP projects.The factors affecting the price decision include the goals, cost, market demand, competitors, and other external factors of enterprises (Yuan et al. 2019(Yuan et al. , 2021)).With the increase in the number of PPP projects, the design and optimization of PPP concession pricing are of great significance in improving the management efficiency of PPP projects (Xu et al. 2012;Yuan et al. 2019;Li et al. 2022).However, due to the unique economy of public goods or services, PPP projects' products or services differ from those in the general market.The fundamental goal of PPP project pricing is to maximize social utility (Li et al. 2022).Meanwhile, the costs of the products or services, which are determined by the participation of the private sector, are still an important factor affecting the pricing of PPP projects (Yuan et al. 2021).Due to the construction, operation and maintenance, and risk transfer of PPP projects, Blanc-Brude, Goldsmith, and Välilä (2009) found that the construction cost is higher than that of the traditional procurement method by analyzing the construction contract price of traditionally procured roads and public-private partnerships (Blanc-Brude, Goldsmith, and Välilä 2009).The marketbased option pricing approach called the risk-neutral valuation method was used to determine the correct value of minimum revenue guarantee (MRG) options (Ashuri et al. 2012), which is the most frequently cited literature in clustering (Ashuri et al. 2012).Song et al. (2018)studied government guarantees in the PPP toll road projects, which suggested that the government considers the surplus of private firms, and the surplus and social welfare of service-users when making the guarantee scheme (Song et al. 2018).Feng et al. (2016) investigated optimal subsidy schemes of the public sector and optimal service prices for toll roads, which found that the subsidy from the public sector can improve service quality for a low sufficiently publicmanagement cost, and for the optimal service price and the subsidy, the private sector only obtains reservation surplus (Feng et al. 2016).
Cluster #6 "governance", that is project governance.The inherent incompleteness of contract and the inherently unstable partnership of PPP projects increases the difficulty of project management.The existing governance system based on project contract and relationship norms are difficult to deal with the complex practical problems of PPP projects effectively and falls into the dilemma of incomplete project governance mechanism and the relationship of unclear elements, resulting in the low effectiveness of management for PPP projects.Good project governance is an important factor for the success of PPP projects (Zhang et al. 2015;Xiong et al. 2019).By comparing the development of the PPP model in China and the US, Dong, Wang, and Yang (2016) discovered that the government plays a key role in the operation process of PPP projects, which is very important for the reasonable supervision of the projects (Dong, Wang, and Yang 2016).Derakhshan, Turner, and Mancini (2019) analyzed the role and relationship of stakeholders inside and outside the organization from a systematic review of the literature on project governance (Derakhshan, Turner, and Mancini 2019).It opens a new way for relevant research on stakeholders in project governance.From the research on pre-contractual relational governance in PPP projects, Mu, Wu, and Haershan (2021) discovered that ex-ante relational governance could effectively reduce various uncertainties in the implementation process of a contract.It is of great significance to sign the formal contract (Mu, Wu, and Haershan 2021).In addition, compared with general construction projects, the governance issues of PPP projects are more complex (Chen 2020).For the complex governance network system of PPP projects, different governance mechanisms and their elements are joint and influence each other instead of isolated.The strength of the relationship among all elements has become the core content of the research on project governance and project governance network system.
Cluster #8 "operational" mainly refers to the management of PPP projects during the operational period or concession period.As more and more PPP projects begin the operation period, more attention and discussions are focused on problems that occurred during the operation period.Lam and Javed (2015) pointed out that the uncertainty of incomes still is one of the main risks when performance standards and output parameters are used in the monitoring process of operation and maintenance for PPP projects (Lam and Javed 2015;Liang and Ashuri 2020).The performance of the highway pavement and the complex interactions among all relevant factors of stakeholders were simulated using the system dynamics (SD) model during the concession period of the PPP highway project, which can help either the public sector or the private investor evaluate concession decision-making through addressing pavement maintenance of the PPP highway project (Zhang et al. 2018).Osei-Kyei and Chan (2017) explored the perceptual differences in the factors contributing to the successful management of PPP projects at the operational stage among stakeholders.The research findings show that each stakeholder group considers an efficient and well-structured payment mechanism the most crucial operational management critical success factor (CSF) (Osei-Kyei and Chan 2017).Moreover, they identified the factor groupings of 19 CSFs associated with managing PPP projects at the operational stage and examined the most significant factor grouping using the fuzzy synthetic evaluation (FSE) technique (Osei-Kyei, Chan, and Ameyaw 2017).Liu et al. (2017) studied the selection strategies problem of public and private sectors during the operation and maintenance period for PPP projects and put forward relevant policy suggestions from a government supervision perspective (Liu et al. 2017).

Directions for future research
Through literature measurement tools, such as Cite Space and VOS viewer, systematic reviews on the research of PPP in China and the US were carried out from different perspectives.Although the existing research has rich theoretical support, some directions still are worthy of further research and exploration.Therefore, the future research trends of PPP will be stated as follows.
(1) Research on payment risks from the government during the operation and maintenance period: Many problems arise with PPP projects being transferred to the operation period (Ming, Hu, and Zheng 2021).The operation and maintenance are the fundamental differences between PPP and traditional government projects.Although the time, source, and process of government payment, as well as the liability for breach of contract for failure to pay in time, is stipulated in advance, there is a phenomenon that payment cannot be made in time due to the financial resources of some governments and the reputation of honoring agreements, especially the impact of COVID-19 in the recent two years.Given this risk, the public and private sectors should further design the refined pricing mechanism or innovate the business model (Li et al. 2022;Yuan et al. 2021).When multiple PPP projects are implemented simultaneously, the private sector, especially large investment companies, can establish an internal capital pool taking the private sector as the main equity investment to deal with various financing or repayment risks.
(2) Design of early termination and compensation mechanism: Many problems have also been exposed with the rapid development of the PPP model (Liu et al. 2017;Song et al. 2018;2018;Zhang et al. 2020).There are many risk factors in a long period (about 10 to 30 years) for most PPP projects, which may lead to the early termination of projects once some risk factors occur.Early termination will affect the supply of public projects and bring a heavy burden to the public and private sectors (Zhang and Xiong 2015).In addition, determining the responsibility sharing and calculating the amount of compensation is the core issue in dealing with the early termination of PPP projects (Xiong, Zhang, and Chen 2016;Zhang et al. 2020;Xiong and Han 2021).However, the static compensation mechanism is not suitable for the early withdrawal from PPP projects under the current situation (Song et al. 2018;Zhang et al. 2020).
Although some general compensation models are studied in the existing research (Treasury 2007), other factors affecting the early termination of PPP projects are not considered.Therefore, it needs to be further studied for the early termination mechanism and more systematic compensation mechanism of PPP projects.
(3) Management and control of the implementation of the projects from the regulatory level: Since PPP projects are usually infrastructure projects involving the public interests, it is necessary for the government to manage and control the implementation and quality of the projects (Marques 2017; Chen 2020).At present, a range of factors, such as the imperfect supervision system, project supervision process, and public participation supervision mechanism of PPP projects, lead to opportunistic behavior in the implementation process of PPP projects (Xu et al. 2010;Li, Li, and Wang 2016;Han et al. 2020).Thus, it is a problem worth exploring for current researchers and practitioners on how to achieve a balance between supervision and efficiency, and deal with the relationships among administration, public supervision, and contract management to do an excellent job in supervision, which is neither absent nor offside (Koliba et al. 2014;Mouraviev and Kakabadse 2015).In short, some deficiencies, such as the legal basis of government supervision, supervision process, industry supervision, project performance supervision, and the consistency of institutional supervision, needed to be further studied.(4) Expand new application areas: During the past two decades, the PPP model has been increasingly applied to transportation, water, energy, and other industries (Liu, Yu, and Cheah 2014;Love et al. 2015;Song, Zhang, andDong 2016, 2018).To cope with the climate crisis, effectively reduce carbon emissions and vigorously develop green energy, countries can use the PPP model in renewable power infrastructure to reform and innovate the public service supply mechanism in the energy field and broaden investment and financing channels, which can fully mobilize the enthusiasm of the private sector to participate in the construction of energy projects, and then effectively improve the level of public services and meet the requirements of the public for safe, reliable and clean energy supply.The PPP model is also encouraged to introduce rural revitalization, agriculture, and other fields in China.It is worth further exploring whether the previous research experience can be directly applied in these new fields.(5) Emphasize Green Bonds in PPP: Green Bonds enhance the development of green infrastructure projects.Mostly, PPPs depend on financial institutions or other public/private entities to fund their projects (Ordonez, Uzsoki, and Dorji 2015).Green bonds encourage sustainability and promote projects proven to be environmentally beneficial.Hence, such an approach that involves multiple benefits to the environment and solves a project's financing gap should be encouraged and promoted.The feasibility of the green bond is worth further exploration and study.

Conclusions
With the wide application of the PPP model in developed and developing countries, a large number of high-level academic papers on PPP have been published (Song et al. 2019).Different from the existing research systematically stating the current situation and trend of PPP with a global perspective (Zhang et al. 2016(Zhang et al. , 2020;;Wang et al. 2018;Song et al. 2019), this study only focuses on the research in China and the US, which aims to accurately identify the current research status and trend of PPP projects, and is more conducive to the improvement of quality and efficiency of PPP projects in these countries.This study analyzes and summarizes the literature on PPP in China and US from different perspectives during 1991.01-2022.3.The main results of this study include: ( The limitations of this study include: (1) The techniques of literature collection and data processing should be comprehensive and mastered more deeply.The use of only one database to search the literature might confine the study, although there is the fact that collecting articles from the additional database will be time-consuming.
(2) The relevant algorithm should be further optimized during data screening for a proper literature visualization.Although the data in this study has been screened in several steps, it is still inevitable to face errors.Hence, the optimization of algorithm improving the data accuracy can be studied further.

Figure 1 .
Figure 1.The framework of the relevant research procedures and methodological.

Figure 2 .
Figure 2. The Number of Publications of PPP from 1991 to 2022 in the US and China.

Figure 4 .
Figure 4. Cluster analysis of documents in the PPP research field.

Figure 3 .
Figure 3. Visualization map of the keyword co-occurrence network related to PPP research (Occurrences of keyword≥20).

Table 1 .
The top 10 active and productive institutions in PPP research.

Table 2 .
The top 10 active and productive authors in PPP research.
(Pu, Xu, and Marques 2021)and the US carried out many PPP projects in the field of transportation during the early stage which led to the study in that field and resulted in 42 articles being published in the Transportation Research Record.After many years of development, the application of the PPP model has transformed to the construction or service of government projects(Song et al. 2022) such as public transport, education, medical treatment, environmental protection, and even prisons and police stations(Song et al. 2022).More importantly, the International Journal of project management, one of the top journals in SSCI, has a JIF of 9.222.Its citation is as high as 2097 times, while the NP is only 24, which is sufficient to illustrate this journal's importance and reference value for research in the field of PPP(Pu, Xu, and Marques 2021).Additionally, scholars from China and the US have also published articles related to PPP in journals like the Journal of Management in Engineering, and the Journal of Construction Engineering and Management with a considerable number of publications.

Table 3 .
The top 10 source journal of PPP research in the US and China.
1) The essential statistical characteristics, including authors, and institutional publications in China and US, are firstly shown, mainly focusing on annual NP, institutional NP and C, authors NP, h-index, and AVE, and NP, Co, and JIF of major journals.The analysis concluded that the research on PPP by Chinese and American scholars is positive.The results also show that the research on PPP in China has made rapid progress from 2009 to 2022.(2) The cooperation among the scientific research institutions in China and US is analyzed.Most institutions were found to be of the same type in the same country or region.Not much diversity was witnessed in the cooperation of the institutions.In other words, cooperation among significant research institutions is a rare breed that needs further improvement.(3) The existing theoretical research fields of PPP are summarized.The research on representative clustering summarized that the academic research fields of PPP mainly include project management, policy, behavior, performance, risk management, pricing project governance, and the management of the operational period or concession period.(4) Through this study, emerging trends, such as government payment risk during operation period, early termination mechanism and system compensation mechanism, regulatory level, and new field application, are put forward in combination with the practice, which provides theoretical guidance for future research on PPP.