Abstract
High-tech small- and medium-sized enterprises (SMEs) need to innovate and invest in research and development (R&D) activities to remain competitive. However, due to their liability of smallness, the returns from R&D in terms of financial performance may not be as expected in such firms. Combining the resource management perspective with managerial ability research, we elaborate upon how managerial ability influences the effect of R&D on the financial performance of high-tech SMEs. We also investigate how this moderation is affected by the external environment in which high-tech SMEs operate. Using a moderated moderating model and the panel data of 256 Chinese high-tech SMEs from 2007 to 2019, we find that managerial ability strengthens the impact of R&D on the financial performance of high-tech SMEs. This moderating effect is more pronounced during the economic downturn and in regions with better digital economy development. Our findings provide important implications for high-tech SMEs on their R&D strategies and human capital management as well as the government.
Keywords
Introduction
High-tech small- and medium-sized enterprises (SMEs) 1 are considered to be the principal drivers of technological change, industry regeneration and economic growth. To survive and remain competitive, they have to innovate (Arslan et al., 2021; Guo et al., 2020). 2 Yet, as they suffer from the liability of smallness, they lack financial capital and multidisciplinary technological bases that can prevent them from translating innovation into financial performance (Ortega-Argilés et al., 2009; Parida et al., 2012). As such, how to effectively transform limited resources devoted to innovation into positive financial outcomes is important. However, prior studies have mainly explored the antecedents of the innovation performance of high-tech SMEs (Ghazinoory and Hashemi, 2021; Marvel et al., 2020; Parida et al., 2012) rarely examining their financial returns from innovation. Meanwhile, research exploring the contingencies that affect the innovation–performance relationship primarily focuses on generic firms, SMEs, or high-tech firms (Bardhan et al., 2013; Boeing et al., 2016; Wiklund and Shepherd, 2003), with little consideration of high-tech SMEs. This paucity is surprising since the development of high-tech SMEs will be threatened if they cannot generate positive financial returns from their innovation activities (Rosenbusch et al., 2011). Many such firms are indeed, confronted with this issue, that is, excelling in innovation but having poor financial performance and then, high failure rates. Thus, it is necessary to investigate what factors drive the effect of innovation on the financial performance of high-tech SMEs.
In this study, we focus on the relationship between one specific and crucial innovation activity, that is, research and development (R&D), 3 and the financial performance of high-tech SMEs, exploring the contingency factor of this link from the perspective of manager characteristics. Research shows that managers play a vital role in high-tech SMEs due to limited hierarchies and greater managerial discretion (Finkelstein and Hambrick, 1990; Kammerlander et al., 2015). Among various characteristics, managerial ability has received increasing attention in recent years (Baik et al., 2011; Demerjian et al., 2012; Yuan et al., 2017). Extant studies have shown that managerial ability helps reduce corporate failure, improve investment efficiency and facilitate opportunity evaluation and exploitation (Gan, 2018; Koester et al., 2017; Wang et al., 2017). These features may enable talented managers to help high-tech SMEs address the potential negative aspects of R&D such as high failure rates, inappropriate targeting and inefficient implementation. Yet, there is a lack of systematic exploration of the moderating effect of managerial ability on the financial returns of high-tech SMEs from R&D. To the best of our knowledge, only two studies that mainly focus on the relationship between managerial ability and corporate innovation (innovative inputs and outputs) have unpacked the effect of managerial ability on the innovation–performance nexus in their post hoc analyses. One is the study by Chen et al. (2015) who find that the market reacts more positively to patents generated by highly capable managers. The other is the study of Mishra (2021) who shows no significant moderating effect of managerial ability on the effect of R&D intensity on competitive advantage. While these studies are insightful, they do not focus on high-tech SMEs, lack detailed theoretical analysis and have mixed findings. In light of this, we still have a limited understanding of whether and how managerial ability conditions the effect of R&D on high-tech SME financial performance. Monetising R&D activities requires intelligence pertaining to the market, competitors, technology and environment so that these activities can be steered in a direction that is financially rewarding for these firms. Managerial ability plays a critical role in the above and hence, substantiates the need to conduct a more comprehensive examination of its moderating role in the relationship between R&D and high-tech SME’s financial performance.
Combining the resource management perspective with managerial ability research (Holcomb et al., 2009; Sirmon et al., 2007), we theorise how managerial ability moderates the R&D–performance nexus. The key tenet of the resource management perspective is that the value created by valuable, rare, inimitable and non-substitutable (VRIN) resources depends on not only the firm’s possession of these resources but also their management (Sirmon and Hitt, 2009; Sirmon et al., 2007). 4 Thus, the effect of R&D on financial performance will be higher if these R&D resources are effectively managed. Research on managerial ability suggests that greater managerial ability improves the resource management process (Koester et al., 2017; Wang et al., 2017). 5 Holcomb et al. (2009) also highlight that the extent of performance advantage that a firm enjoys depends on the managerial ability to create value from the resources the firm controls. Integrating these insights, given the critical role of managerial ability in resource management, it has a positive moderating effect on the relationship between R&D and financial performance. Specifically, we argue that managerial ability increases the financial returns of high-tech SMEs from R&D in two ways: targeting R&D resources more appropriately and utilising R&D resources more efficiently.
In addition, we explore how the impact of managerial ability on the R&D–performance nexus is conditioned by environmental factors. The resource management perspective also highlights the role of the external environment in which firms operate (Sirmon and Hitt, 2009; Sirmon et al., 2007). Only firms that effectively and efficiently manage resources within their given environmental context can maximise the value generated from VRIN resources (Sirmon et al., 2007). Via this lens, we investigate how environmental factors affect the moderating effect of managerial ability. Specifically, we focus on two vital environmental factors in the economic dimension: economic downturn and digital economy development. Economic downturn increases reliance on highly capable managers to target and utilise R&D resources (Andreou et al., 2013; Bianchi and Mohliver, 2016) thus, amplifying the moderation of managerial ability. The digital economy development promotes information transmission, financing and enterprise digital transformation; this enables highly capable managers to better manage R&D resources and realise greater financial returns (Li et al., 2022a, 2022b).
To empirically test our hypotheses, we construct a moderated moderating model (see Figure 1). Using the panel data of 256 Chinese high-tech firms listed on the SME board from 2007 to 2019, we find general support for all hypotheses. Our primary contributions can be summarised as follows. First, we add to the previous literature on the innovation of high-tech SMEs by identifying managerial ability as an important contingency factor in the relationship between R&D and performance. In so doing, we also extend the managerial ability research that primarily regards managerial ability as the antecedent of business operations and strategies (Yuan et al., 2017; Yung and Chen, 2017). We show that managerial ability does not necessarily affect firm performance, but positively interacts with R&D to enhance the financial performance of high-tech SMEs. We further add to the resource management perspective by empirically testing and extending the effects of environmental factors on managing resources in value-creation activities. Specifically, we show that the role of managerial ability in enhancing high-tech SME returns from R&D is accentuated by economic downturns and digital economy development.

Research model.
Theoretical background
Innovation in high-tech SMEs and their financial returns
High-tech SMEs have two typical characteristics. First, they share the attributes of all SMEs, suffering from the liability of smallness. Specifically, they are resource-constrained (Didonet et al., 2019; Guo et al., 2020; Subramanian et al., 2019), which makes it challenging to deal with the added costs of strategic activities, such as innovation, or to absorb failures through slack resources (Rosenbusch et al., 2011). Second, since they are in the high-tech sectors where the span of the product life cycle is shorter, uncertainties are higher, and competition is greater (Gu et al., 2016; Irwin et al., 2019; Qian and Li, 2003), high-tech SMEs have to be innovation oriented to develop their competitive advantage (Arslan et al., 2021; Guo et al., 2020). Due to these paradoxical features, innovation in high-tech SMEs has been a salient research focus and a key concern of practitioners. In the context of innovation in high-tech SMEs, two issues are important. 6 The first is what drives their innovation performance; increasing innovative output, for example, patents and new product introductions, is of great significance for these firms. Concerning this issue, extant studies have undertaken many analyses of the antecedents of the innovation performance of high-tech SMEs, including subsidies and funding, managerial characteristics and absorptive capacity (Alegre et al., 2011; Chandrashekar and Bala Subrahmanya, 2017; Ghazinoory and Hashemi, 2021; Gu et al., 2016; Lin et al., 2014; Marvel et al., 2020; Parida et al., 2012).
The second issue concerns what determines the overall benefits or values high-tech SMEs obtain from their innovation activities, that is, the financial returns from innovation. This considers the extent to which investments in innovation can be transformed into the ultimate goal of firms, that is, increased firm performance. This conversion is particularly critical for high-tech SMEs since they are often resource-constrained. If such firms devote a significant proportion of their limited resources to innovation but are unable to generate a positive return, their survival and development will be threatened (Rosenbusch et al., 2011). Indeed, transforming innovation into financial performance is very challenging for high-tech SMEs given their liability of smallness (Li et al., 2012b; Ortega-Argilés et al., 2009; Parida et al., 2012). As such, even though high-tech SMEs may be successful in terms of innovation, this might not be translated into better financial performance. There are many illustrative examples, such as the Pebble technology corporation and the LeEco technology company. These firms excelled in innovation but struggled financially and eventually, failed. Teece (1986) also suggests that profiting from innovation is not straightforward and it is not the innovator who succeeds financially. Thus, it is imperative to investigate what factors influence the impact of innovation on the financial performance of high-tech SMEs.
This topic, however, is largely understudied in extant research. Most prior studies explore the factors conditioning the effect of innovation on firm performance in the context of general firms (irrespective of firm size and industry) (Boeing et al., 2016; Gu, 2016; Ruiqi et al., 2017; Wan et al., 2022) or SMEs (Rosenbusch et al., 2011; Wiklund and Shepherd, 2003) or high-tech firms (Bardhan et al., 2013; Le et al., 2006). Such studies have shown the contingency effects of many factors, such as corporate governance (Boeing et al., 2016; Le et al., 2006), firm strategy (Bardhan et al., 2013; Yiu et al., 2020) and external environment (Boeing et al., 2016; Steenkamp and Fang, 2011). While these studies are insightful, their findings may not be generalisable to high-tech SMEs due to their distinctive features. High-tech SMEs are innovation-oriented but encounter more challenges in translating R&D into financial performance, such as lack of resource support, poorly structured approaches for rent appropriation and lower technological bases for exploitation and exploration (Parida et al., 2012; Paulo et al., 2012). Thus, more pertinent and nuanced investigations on what factors affect the financial returns from R&D to high-tech SMEs should be conducted. Our study attempts to offer some insights from the perspective of managerial ability.
While there are many types of innovation, this study focuses on R&D for two reasons. First, the intensity of R&D is one of the key factors in differentiating between high-tech and generic SMEs; R&D is considered particularly important for the former (Paulo et al., 2012; Stam and Wennberg, 2009). R&D not only helps high-tech SMEs build their internal technological knowledge base to generate product or process innovation but also improves their abilities to understand and absorb external knowledge (Deeds, 2001; Ortega-Argilés et al., 2009; Stam and Wennberg, 2009). Thus, R&D is vital for high-tech SMEs to develop sustained competitive advantage and promote their long-term survival, growth and performance. Second, since the main factor affecting high-tech returns from innovation in our study is managerial ability, R&D constitutes an appropriate research context. R&D activities and their financial outcomes in terms of firm performance are more likely to be controlled by the firm and its managers, compared with other types of innovation, especially external innovation. 7 For example, when collaborating with large firms to innovate, small firms often face high risks and their innovation rents are likely to be appropriated due to their weak bargaining power (Alvarez and Barney, 2001; Rosenbusch et al., 2011; Yang et al., 2014). Consequently, we focus on the relationship between R&D and the financial performance of high-tech SMEs.
Resource management perspective and managerial ability
The resource management perspective adapts from the resource-based view (RBV). The key tenet of RBV is that VRIN resources drive the development of competitive advantage and enhance firm performance (Barney, 1991). In light of this, RBV has offered an important theoretical lens for many resource–performance relationships, such as the positive effect of R&D on firm performance (Ehie and Olibe, 2010; Qian et al., 2017). However, this theory has been criticised for its inability to uncover the process of resource management within firms (Kraaijenbrink et al., 2010). The resource management perspective thus emerges, extending the traditional RBV arguments. A resource management perspective highlights the role of resource management in value creation (Sirmon et al., 2007). Specifically, the possession of VRIN resources is not a sufficient condition for value creation; instead, the value of these resources for creating competitiveness and enhancing firm performance is fully realised only when they are managed effectively and efficiently (Sirmon and Hitt, 2003; Sirmon et al., 2007, 2011). Resource management is considered the comprehensive process of structuring the firm’s resource portfolio, bundling the resources to build capabilities and leveraging these capabilities to create and maintain value for customers and owners (Sirmon et al., 2007). Firms must accumulate, combine and exploit resources to realise value creation (D’Oria et al., 2021; Sirmon et al., 2007). In a similar logic, the financial performance of VRIN R&D resources in high-tech SMEs should depend on the process of resource management. As managers are the key decision-makers in firms, their characteristics will have an influence on corporate behaviours and strategies (Hambrick and Mason, 1984). This is especially true for high-tech SMEs (Kammerlander et al., 2015; Wallace et al., 2010). These firms have fewer levels of management; this enables managers to have direct and frequent contact with other employees and guide the firm more personally (Kammerlander et al., 2015). Many managers in high-tech SMEs also have greater managerial discretion and thus, greater effects upon firm performance (Finkelstein and Hambrick, 1990). 8 As such, the role of managers is salient in high-tech SMEs. It is thus, necessary to examine the impact of managerial characteristics on the financial returns of high-tech SMEs from their R&D investments. Among various managerial attributes (e.g., age, gender and psychological attributes), managerial ability has received increasing attention. Research shows that managerial ability leads to more innovation (Chen et al., 2015), greater corporate investment efficiency (Gan, 2018), better corporate decisions (Guan et al., 2018) and better firm performance (Demerjian et al., 2012). Due to the integration of various skills, for example, technical and human skills, managerial ability also enhances the economic performance of a firm’s resource portfolio (Wang et al., 2017). Indeed, research suggests that resource expertise is one key source of managerial ability (Holcomb et al., 2009). Resource expertise accumulates through experience with resource management processes and indicates manager capabilities to structure a firm’s resource portfolio, bundle resources and leverage them to exploit specific opportunities (Holcomb et al., 2009; Sirmon et al., 2007). Kraaijenbrink et al. (2010) also associate the processes of resource management with managerial capabilities, suggesting that to create sustained competitive advantage, a firm needs both resources and managerial capabilities to recognise and exploit productive opportunities. As such, due to its important role in resource management, managerial ability may influence the effect of R&D on the financial performance of high-tech SMEs.
Hypotheses development
Effect of managerial ability on the impact of R&D on the financial performance of high-tech SMEs
Integrating the insights from the resource management perspective and managerial ability research (Holcomb et al., 2009; Kraaijenbrink et al., 2010; Sirmon et al., 2007, 2011), we anticipate that managerial ability has an important role in assuring the financial returns that high-tech SMEs gain from R&D investments. The positive moderating effect of managerial ability on the relationship between R&D and financial performance manifests in two ways. First, higher levels of managerial ability help to target R&D resources appropriately and so, better management of R&D resources and converting them into financial performance. With R&D investment, managers have to decide the specific allocation of resources, for example, the direction of R&D and the choice of R&D projects. More able managers are knowledgeable about the business and industry trends (Wang et al., 2017). This enables them to address R&D target-setting difficulties such as external technology monitoring and trend forecasting (Lamb et al., 2012) thus, finding the best-fit R&D orientation. In addition, more able managers have better career prospects, fewer career concerns and longer horizons (Yuan et al., 2017). These managers can target the most appropriate R&D activities without paying too much attention to short-term potential losses from R&D. Furthermore, higher-ability managers have a better understanding of stakeholders – particularly the taste and demand of customers (Demerjian et al., 2013). When considering these in the selection and commercialisation of high-tech SME R&D activities, talented managers enhance the success rate of R&D and thus, value creation. Indeed, Sirmon and Hitt (2009) posit that the ‘fit’ between resource investments and deployment decisions (indicating in which market segments a firm will utilise its resource investments) is vital for firm performance. As such, R&D will exert a greater impact on the financial performance of high-tech SMEs when they have highly capable managers.
Second, high managerial ability helps to utilise R&D resources more efficiently, thereby better managing R&D resources and transforming them into performance. More capable managers have superior business, technical and human skills (Coff, 1999; Holcomb et al., 2009; Wang et al., 2017). This enables them to efficiently deal with various difficulties, such as the management of project portfolios, challenging integration of knowledge and complex coordination among multiple sectors, in the process of deploying R&D resources. Moreover, research suggests that R&D-intensive firms are often exposed to the threats associated with the rapid emergence and decline of new technologies (Yiu et al., 2020). Managers with higher abilities are more sensitive to the operating environment (Baik et al., 2011; Goldfarb and Xiao, 2011), which enables them to make timely adjustments in the allocation and utilisation of R&D resources to better react to rapid technological changes. Furthermore, more capable managers play an important role in creating an internal environment to stimulate the potential of R&D employees (Chen et al., 2015). That is, managers with greater abilities are more adept at designing and putting in place effective employee schemes that allow research staff to maximise their creative potential in R&D activities. As such, greater managerial ability enables high-tech SMEs to realise more benefits from their R&D investments. Consequently, we suggest:
Moderating effects of environmental factors
The resource management perspective also posits that the processes of resource management are influenced by the external environment, that is, value is created only when VRIN resources are managed appropriately within the firm’s environmental context (Sirmon and Hitt, 2009; Sirmon et al., 2007). In other words, firms that achieve better alignment between their internal resource management activities and their external environment have superior performance. Aligned with this perspective, we argue that the extent to which managerial ability affects the impact of R&D on the financial performance of high-tech SMEs is determined by environmental factors. This study particularly focuses on the economic dimension of the external environment as the economic environment has direct, instant and profound effects on organisations. Specifically, we consider the moderating effects of two important economic factors on the role of managerial ability: economic downturn and digital economy development. Prior research has shown the great effects of these factors on enterprises and their managers’ behaviours (Bianchi and Mohliver, 2016; Luo et al., 2022; Steenkamp and Fang, 2011; Zou and Deng, 2022).
Economic downturn
An economic downturn is considered a crucial dimension of environmental uncertainty affecting the behaviours of firms and their managers (Andreou et al., 2013; Bianchi and Mohliver, 2016). In this study, we predict that the effect of managerial ability on the R&D–performance nexus is more pronounced during an economic downturn. During a crisis, high-tech SMEs have a greater reliance on highly capable managers to target appropriate R&D resources to attain financial returns. Economic downturns bring uncertainty, caution and fear, which results in high technological dynamism (Bianchi and Mohliver, 2016). In this environment, it is difficult for high-tech SMEs to predict future technological trends, assess technological opportunities accurately and select the most appropriate and fruitful R&D directions (Miocevic, 2022). However, highly capable managers are well-versed in these issues. For example, they are more confident and thus, more able to assess and invest in R&D projects with a long-term impact on firm performance without being unduly disturbed by the shocks of the downturn. As such, high-tech SMEs rely more upon able managers to steer R&D activities in a direction that is more financially rewarding during the economic downturn. By contrast, in an economic boom, the market is more prosperous and the technological trend is more predictable; this makes any R&D project that follows the market likely to yield positive returns (Bianchi and Mohliver, 2016; Steenkamp and Fang, 2011). In this case, high-tech SMEs have a low reliance on the capabilities of managers in R&D activities. Thus, an economic downturn amplifies the moderation of managerial ability.
When the economy retracts, resources shrink with detrimental effects on the SME resource base (Bianchi and Mohliver, 2016; Saridakis et al., 2022). Poor economic conditions also bring challenges for these firms to acquire resources from banks and the government (Flammer and Ioannou, 2021; Roper and Turner, 2020). As such, high-tech SMEs suffer from shortages of resources, that is, having very limited resources to invest in innovation as well as complementary activities, during an economic downturn. For survival and growth, they have to rely more on highly capable managers to enhance the effectiveness and efficiency of resource utilisation and capture more value. These managers help high-tech SMEs in many ways, such as securing more resources, dealing with various kinds of risks, challenges and complexity in deploying R&D resources, and exploiting the potential of employees to implement R&D projects that yield greater financial returns (Andreou et al., 2013). Hence, an economic downturn strengthens the moderating effect of managerial ability. Collectively, an economic downturn accentuates the role of managerial ability in enhancing the impact of R&D on the financial performance of high-tech SMEs; this leads to the following hypothesis:
Digital economy development
The digital economy refers to the digitisation of information with the Internet and a series of economic activities in the information and communication technology sector (Li et al., 2022b; Zou and Deng, 2022). In this study, we argue that the moderating effect of managerial ability on the R&D–performance nexus is stronger for high-tech SMEs in regions with better digital economy development. Previous research has shown that due to the development of the Internet, the digital economy promotes the transmission of information, information availability and information transparency (Shen et al., 2022; Wang and Cen, 2022). This plays a vital role in reducing the information disadvantage of high-tech SMEs. Specifically, the development of the digital economy enables highly able managers to obtain more valuable information on R&D, have greater information processing efficiency and have more channels to learn from their peers. Due to these factors, they can exploit more fruitful R&D opportunities and utilise R&D resources more effectively and thus, realise greater financial returns. In addition, a more developed digital economy indicates more developed digital finance which matters in helping enterprises secure the funds needed for innovation (Li et al., 2022a, 2022b). This is particularly important for high-tech SMEs as traditional financial providers tend to favour large companies (Feng et al., 2022; Wang et al., 2020). As such, in a highly developed digital economy, more able managers attain greater financial support; this allows them to effectively leverage their capabilities to manage R&D resources to further improve the financial performance of high-tech SMEs.
Furthermore, the development of the digital economy acts as data technology support and a modern information network carrier for high-tech SMEs which promotes the digital transformation of such firms (Li et al., 2022b; Razzaq and Yang, 2023). After such digital transformations, high-tech SMEs have greater digital capabilities that complement managerial abilities to realise higher financial returns from R&D. For example, with the technical help of advanced digital technologies, for example, business intelligence, big data analysis and cloud computing, highly capable managers can better evaluate potential R&D opportunities, make more rational R&D decisions and more effectively implement R&D projects. These managers also have more digitally disruptive avenues to get feedback from customers and affect market innovation. As such, they can more effectively convert R&D into financial performance for high-tech SMEs. For these reasons, digital economy development strengthens the role of managerial ability in enhancing the effect of R&D on the financial performance of high-tech SMEs; this leads to the following hypothesis:
Methods
Sample and data
We test these hypotheses in the Chinese context for two reasons. First, as the corporate standards and governance system in China are underdeveloped, a manager’s decision-making would be influential for business operations and strategies; this makes China an appropriate context to examine. China is also developing rapidly over a large land mass leading to great heterogeneity in the operating environment. This allows us to explore how the moderating effect of managerial ability varies across time and regions. Our sample consists of high-tech firms listed on the SME board of the Shenzhen Stock Exchange in China from 2007 to 2019. 9 Compared with the major boards with stricter standards and criteria for firms to be listed, the SME board tends to be populated with smaller, younger and private-owned firms (Yang et al., 2020). The main function of the board is to offer an important platform for SMEs to resolve financing problems in the entrepreneurial process (Yang et al., 2018). Thus, firms listed on the board can serve as a reliably representative research sample of Chinese SMEs. A focus on listed SMEs also allows us to obtain sufficient financial data to calculate the variables, such as Tobin’s Q, which depends on a firm’s stock price. In addition, following the high-tech industry classification from the Chinese National Bureau of Statistics, we include both high-tech manufacturing and service firms (Boeing, 2016). 10
We collected the data from the WIND, CSMAR and RESSET databases and made a cross-check to ensure validity of the data. These databases have been widely used in prior research (Boeing et al., 2016; Qian et al., 2017; Yin et al., 2023). We remove firms that do not report R&D expenses from 2007 to 2019, those marked for special treatment and those with missing financial information. Firms usually have major changes in corporate strategies, particularly their investments in R&D, when they experience merger and acquisition activities, industry change and ‘backdoor’ listing. To reduce the biases arising from these events, we also removed the firm-year observations for the years when these events occurred and treated the firm in subsequent years as a new case (Simeth and Cincera, 2016). All continuous variables are winsorised at the top and bottom 1% levels to eliminate the impact of outliers. The final sample covers 256 high-tech SMEs and 1691 firm-year observations. Table 1 shows the sample distribution of firms across industries.
Sample distribution by industry.
Dependent variable
Following prior studies (Bonini et al., 2022; David et al., 2008; Yiu et al., 2020), we use Tobin’s Q as our dependent variable to measure the financial performance of high-tech SMEs. Since Tobin’s Q is forward-looking, risk-adjusted and less susceptible to changes in accounting practices (Wies et al., 2019), it well suits our research context wherein R&D investments are expected to influence future performance and returns (Yiu et al., 2020). Specifically, we calculate Tobin’s Q as the ratio of the sum of the market value of equity and debts to the book value of assets. The market value of equity is the number of outstanding shares multiplied by the stock price at the end of the fiscal year and the market value of debt is the sum of long-term debts and current liabilities.
Independent variable
We employ the stock method to measure our independent variable because R&D has carryover effects and this stock measure can capture the accumulation of R&D efforts and knowledge (Martin et al., 2018; Simeth and Cincera, 2016). 11 Specifically, R&D stock is calculated based on Hall et al. (2007)’s declining balance formula. That is, R&D stock in year t is the sum of R&D expenditure in that year and the depreciated R&D stock in year t − 1. To calculate the first value of R&D stock in our sample period, R&D expense is assumed to have been growing at a constant annual rate before the observed history. The calculations are as follows:
Here, δ = 15% denotes the depreciation rate and g = 8% denotes the growth rate. To control for the impact of firm size, we divide R&D stock by total assets (this ratio is denoted as ‘R&D’ for short). R&D is also standardised with respect to the industry average and standard deviation to purge the industry effects (Bardhan et al., 2013).
In addition, as firms are not required to disclose their R&D expenditure, many values of R&D are missing. Following previous studies (Hall et al., 2007; Sandner and Block, 2011), we set the missing values as zero and include a dummy variable (no R&D, coded as 1 if firms do not report R&D expenditure) to control for such replacement. 12 For robustness, we also drop observations with missing R&D expenses and re-run the regression. The results are qualitatively the same.
Moderating variables
Managerial ability
We follow the approach of Demerjian et al. (2012) to measure managerial ability. This method captures the ability of managers to transform firms’ internal resources into revenues efficiently compared with industry peers. Prior measures, for example, industry-adjusted returns on assets (ROA), CEO award, CEO media citation and CEO tenure, are criticised for having much noise that cannot be attributed solely to the manager (Chen et al., 2015; Demerjian et al., 2012; Rajgopal et al., 2006). Since our study focuses on the role of managerial ability in R&D resource management, the measure developed by Demerjian et al. (2012) is considered most appropriate for our study.
Demerjian et al. (2012) use a two-stage process to estimate managerial ability. Following this method, in the first stage, we use the data envelope analysis to evaluate firm efficiency within industries based on the following inputs: (1) the cost of goods sold (COGS), (2) selling and administrative expenses (SAE), (3) net property, plant and equipment (PPE), (4) net operating leases (OL), (5) purchased goodwill (GW) and (6) other intangible assets. The first two inputs are measured at year
Here, one thing worth noting is that while Demerjian et al. (2012) consider a firm’s net R&D expense as the input, we do not include it since our main research focus is to explore whether managerial ability affects the financial returns of high-tech SMEs from R&D. If we consider R&D as an input, our constructed managerial ability measure would be naturally correlated with the impact of R&D on firm performance positively, which may make our analysis invalid.
In the second stage, we regress the firm efficiency on a set of key firm-specific characteristics to isolate manager-specific effects. The firm-specific efficiency drivers include firm size, firm age, market share, cash availability, operational complexity and foreign operations. As firm efficiency ranges from 0 to 1, we use the Tobit regression by industry and include year-fixed effects. The residual from this regression captures the efficiency attributed to the managers, that is, managerial ability.
To corroborate this managerial ability measure, Demerjian et al. (2012) have performed many validity tests, including the tests of manager fixed effects, turnover announcement returns and post-turnover performance. They also prove that the efficiency-based managerial ability measure indeed outperforms existing measures. In addition, using the data of all publicly traded nonfinancial Chinese firms from 2007 to 2012, Wang et al. (2017) ensure that this measure of managerial ability can be used in a Chinese setting. They observe that the managerial ability measure estimated using Chinese data has a similar distribution as that estimated using the American data and the announcement returns to CEO turnovers are negatively associated with managerial ability. To further check for the validity of this managerial ability measure in our study, we conducted three tests. First, we regress the firm efficiency estimated in the first stage on the CEO fixed effect and obtain the fitted value of the CEO fixed effect, which is considered the lower bound of the manager-specific component of firm efficiency (Demerjian et al., 2012). We then calculate the correlation between this fitted value and our managerial ability measure. The correlation is about 0.7, supporting the notion that the residual obtained in the second stage is largely attributable to the manager. Second, we consider several alternative measures of managerial ability, such as industry-adjusted ROA, CEO award, CEO media citation and CEO tenure (Milbourn, 2003; Rajgopal et al., 2006). 13 Unreported results show that our managerial ability measure is significantly correlated with these measures. Third, we construct the interaction terms of managerial ability and R&D using these alternative measures for robustness checks. These interactive effects are still found to be significantly positive. In sum, evidence in prior studies and our tests indicate the validity of the efficiency-based measure of managerial ability.
Considering that using the residual from the second stage to proxy for managerial ability is likely to suffer from random measurement errors, which may distort statistical inferences, we use its decile rank transformation by year and industry as our final measure of managerial ability (Andreou et al., 2017; Bonsall et al., 2017; Demerjian et al., 2013). Specifically, we assign a value of 0.1 to the decile with the 10% lowest value, a value of 1 to the decile with the 10% highest value, and in-between deciles are assigned values from 0.2 to 0.9. This ranked measure also makes managerial ability comparable across time and industries and reduces the effects of outliers. Results are similar using a continuous measure.
Economic downturn
We use a dummy variable to indicate whether firms are during the economic downturn. One representative economic downturn in our sample is the 2008 global financial crisis, which lasted from 1 August 2007 to 31 August 2009 (Balakrishnan et al., 2016). Thus, the dummy variable is coded as 1 if the year is 2007, 2008 and 2009, and 0 if otherwise.
Digital economy development
Following prior studies (Zhao et al., 2020; Zou and Deng, 2022), we construct the measure of digital economy development from two aspects: Internet development and digital financial development at the provincial level. Internet development is measured by the proportion of computer service and software workers in urban units, mobile phone users per hundred people, Internet broadband access users per hundred people and telecom revenue per person. These data are collected from the National Bureau of Statistics in China. In addition, digital financial development is measured by the digital financial inclusion index, which is jointly compiled by the digital finance research centre of Peking University and Ant Financial Group. Since these items may be correlated with each other, we perform a principal component analysis and construct a composite measure to proxy for digital economy development based on the first component.
Control variables
We include a comprehensive list of control variables. Following prior research, we include firm size, firm profitability, firm leverage and firm slack (Wan et al., 2022; Yiu et al., 2020). 14 Firm size may affect firm performance through economies of scale or scope and is measured as the logarithm of the total number of employees (Roberts and Dowling, 2002). 15 Firm profitability, measured by the return on assets, is an important control since its absence may lead to biased results (Erickson and Jacobson, 1992). Firm leverage is calculated as the ratio of total debts to total assets, given that leverage indicates a firm’s capital structure and affects firm performance (Zhang, 2015). The excessive resources a firm has are documented to influence its performance (George, 2005). We measure firm slack by the working capital to sales. We also control for analyst coverage (the logarithm of the number of financial analysts covering a firm) because analyst following may exert a significantly positive impact on firm performance (Chung and Jo, 1996). In addition, as governance structure can control manager behaviour and affect firm performance (Bhagat and Bolton, 2008; Wan et al., 2022), we include state ownership and board independence. State ownership is measured as the proportion of shares held by the government. Board independence is the proportion of independent directors on the board. Furthermore, to account for the industrial variations (Bardhan et al., 2013), we include industry Q, the median Tobin’s Q at the three-digit industry level. Three typical environmental factors, that is, environmental dynamism (Dynamism), environmental munificence (Munificence) and industry competition (Competition), are also controlled. Dynamism is calculated by regressing industry sales against time over the prior 5 years and dividing the standard errors of the regression slope coefficient by the mean value of sales in the industry; Munificence is measured by the regression slope coefficient divided by the mean value of industry sales (Dess and Beard, 1984). Competition is measured by the sum of every firm’s squared proportion of total industry sales. Finally, we include year dummies to control for the year effects.
Statistical method
We employ a fixed-effects panel model for the analyses to reduce the endogeneity arising from the omission of time-invariant variables. The results of the Hausman test also support the use of the fixed-effects model rather than the random-effects model. We also report the firm-clustered robust standard errors to eliminate the problems of heteroscedasticity and serial correlations. To reduce the potential effects of multicollinearity, variables are mean-centred before constructing the interaction terms.
Results
Results of regression analysis
Table 2 presents the descriptive statistics and correlations for the key variables. Inspection of the variance inflation factors (VIFs) shows that multicollinearity is not a concern in our study. The largest VIF is 1.78, which is much lower than the threshold of 10.
Summary statistics.
The correlation between economic downturn and digital economy development is missing because the data on digital economy development are available from 2010 to 2019, during which period, the values of economic downturn are all zero. Correlations with an absolute value greater than 0.049 are significant at p < 0.05.
Table 3 presents the results of the fixed-effects estimations. Model 1 only includes the control variables. Model 2 includes R&D and managerial ability. Results show that the coefficient on R&D is statistically significant, which is consistent with prior findings that R&D contributes to firm performance in the long run (Hall et al., 2007; Simeth and Cincera, 2016). The coefficient on managerial ability is insignificant, which is reasonable as prior studies show that managerial ability has mixed effects on firm performance (Cheung et al., 2017). Model 3 adds the interaction terms between R&D and managerial ability to examine the moderating effect of managerial ability on the nexus between R&D and the financial performance of high-tech SMEs. To explore its boundary conditions, we include the three-way interaction terms among R&D, managerial ability and economic downturn/digital economy development in Models 4–5.
Fixed-effects estimations on firm performance.
Robust standard errors are in parentheses.
p < 0.1. **p < 0.05. ***p < 0.01.
H1 argues that managerial ability enhances high-tech SMEs’ financial returns from R&D investments. The results in Model 3 of Table 3 show that the coefficient for the interaction terms between R&D and managerial ability is positive and statistically significant (b = 0.534, p < 0.05). Specifically, when managerial ability is low (one standard deviation below the mean), the effect of R&D on the financial performance of high-tech SMEs is 0.420, which rises to 0.728 in the case of high managerial ability (one standard deviation above the mean). The combined evidence supports H1.
H2 proposes that the moderating effect of managerial ability on the impact of R&D on the financial performance of high-tech SMEs is more pronounced during the economic downturn. Consistent with this hypothesis, the three-way interaction terms among R&D, managerial ability and economic downturn are positive and significant in Model 4 of Table 3 (b = 1.448, p < 0.01). Figure 2 presents a graphic representation of this interactive effect. As shown, the difference between the slopes (indicating the moderation of managerial ability) during the economic downturn (diff = 1.055, p < 0.01) is much greater than that in the prosperous time (diff = 0.220, p < 0.1). Collectively, H2 is supported.

Moderating effect of economic downturn (ED) on the impact of managerial ability (MA) on high-tech SME’s financial returns from research and development (R&D).
H3 predicts that the moderating effect of managerial ability on the R&D–performance relationship in high-tech SMEs is more pronounced in regions with better digital economy development. The results in Model 5 of Table 3 show that the three-way interaction terms between R&D, managerial ability and digital economy development are significantly positive (b = 0.318, p < 0.01). Figure 3 shows this interactive effect graphically and provides more evidence. As demonstrated, in the case of high digital economy development, the moderation of managerial ability is positive and significant (diff = 0.467, p < 0.01). However, in the case of low digital economy development, this moderating effect is negative and insignificant (diff = −0.175, p > 0.1). Hence, H3 is supported.

Moderating effect of digital economy development (DED) on the impact of managerial ability (MA) on high-tech small- and medium-sized enterprises’ financial returns from research and development (R&D).
Robustness checks
We perform a battery of robustness tests. 16 While we have used the fixed-effects model to address the endogeneity arising from the omitted time-invariant factors and set the lags between our key independent and dependent variables to mitigate reverse causality, endogeneity may be from other sources. First, there may be a concern for self-selection bias as high-ability managers may opt to serve in certain firms, such as firms with good performance. To address this issue and the resulting endogeneity, we use a propensity score matching method (Wang et al., 2017). Thus, we estimate a probit model that regresses the likelihood that a firm has high-ability managers (managerial ability greater than 0.5) on all control variables in the main model. Next, using the propensity scores obtained from this estimation, we perform a one-to-one nearest matching of high-low managerial ability firms without replacement and with a caliper distance of 0.01. 17 Using this matched sample, we still find that the interactive effect of R&D and managerial ability is significantly positive.
Second, the endogeneity may arise from measurement error. To address this concern, we employ the instrumental variable (IV) method which is argued to be the most common way to address various types of endogeneity (Bascle, 2008). Specifically, we use the two-stage residual inclusion (2SRI) estimation, which is similar to the linear two-stage least squares estimation but is more consistent in nonlinear contexts (Terza et al., 2008). In the first stage, we predict R&D and managerial ability using all control variables in our focal model and their IVs, respectively. The IV for R&D is the average R&D in the province where a firm is headquartered; the IVs for managerial ability is the average managerial ability and the average percentage of the population holding a college degree in the province where a firm is headquartered (Bui et al., 2018; Demerjian et al., 2020). 18 In the second stage, we include the first-stage residuals in our models to correct for endogeneity. Results still show the significantly positive moderating effect of managerial ability.
Third, endogeneity may result from the omission of time-variant variables, especially the lagged dependent variable. Firm performance tends to persist over time, that is, current performance is likely to be affected by prior performance. Thus, we include the lagged Tobin’s Q as further controls. Yet, the lagged dependent variable is naturally related to the error term, which incurs endogeneity. To address this issue, we use the two-step system GMM estimator with robust standard errors, which use the lagged and differenced values as the IVs (Roodman, 2009). 19 Results show that the interactive effect of R&D and managerial ability is significantly positive. Meanwhile, we use the diagnostic test for the omitted variable bias developed by Oster (2019). Considering the interaction term of R&D and managerial ability as the treatment effect, we calculate the bias-adjusted treatment effect under the assumptions of Rmax = 1 and δ = 1. Results show that the identified set safely excludes zero, implying that potentially omitted variables do not significantly affect our results.
We also performed several additional tests to verify the robustness of our findings. First, we use several alternative measures of managerial ability. In the main analysis, we use the ranked managerial ability measure. Here, we use the continuous measure. In addition, when calculating managerial ability, we do not include firm-fixed effects in the second stage following the study of Demerjian et al. (2012). However, this may overstate the efficiency attributable to managerial ability. To address this issue, we control the firm-fixed effects in the second stage. Given the concern that using the residuals to proxy for managerial ability may inevitably incur measurement errors and high managerial ability in a single year may reflect luck instead of true ability, we also use the 2-year average value of managerial ability and a persistent managerial ability measure (Bui et al., 2018). The latter is indicated by a dummy variable, which equals 1 if a firm’s managerial ability over the previous 3 years is all above the industry median and 0 if otherwise. Furthermore, we estimate our models using the aforementioned alternative measures of managerial ability, that is, industry-adjusted ROA, CEO award, CEO media citation and CEO tenure. Meanwhile, since we cannot deny that these measures may capture a part of the managerial ability that our efficiency residuals cannot measure, we also use a single index, which is calculated based on the principal component analysis using these measures and our efficiency-based measure (Baik et al., 2011). Using these alternative measures, we still find that managerial ability significantly enhances the effect of R&D on the financial performance of high-tech SMEs. Second, concerning the missing values of R&D expenditure, we exclude these observations from our sample rather than replacing them with zero. The results are similar. Third, we employ higher depreciation (20%) and growth rates (10%) to calculate R&D stock because R&D knowledge quickly becomes obsolete and grows. The results remain qualitatively the same. Fourth, we use the Hausman–Taylor panel data regression method to address the concerns that the fixed-effects estimators may exacerbate estimation problems as R&D tends to change slowly over time and is highly correlated with the firm-specific effect (Hall et al., 2005; Hausman and Taylor, 1981). The results are unchanged.
Discussion
High-tech SMEs have to maintain a competitive advantage through innovation. However, they suffer from the liability of smallness, which makes them resource-constrained. Due to these paradoxical features, how high-tech SMEs translate their investments in innovation into financial returns in terms of firm performance is very important. To shed light on this issue, we combine a resource management perspective with managerial ability research to explore how managerial ability influences the effect of R&D on the financial performance of high-tech SMEs. Because of its critical role in the management of R&D resources, managerial ability helps ensure high-tech SMEs enjoy the positive financial outcomes R&D can generate. Using panel data from 256 listed Chinese high-tech SMEs from 2007 to 2019, we find that managerial ability does enhance the relationship between R&D and the financial performance of high-tech SMEs. This finding helps reconcile the inconsistent results in prior studies (Chen et al., 2015; Mishra, 2021), showing that managerial ability plays a particularly important role in guaranteeing financial returns from innovation in the context of high-tech SMEs. Considering that firms and manager behaviours are affected by the external environment in which firms operate, we also investigate how the moderating effect of managerial ability depends on economic downturn and the digital economy development. We find that the enhancement effect of managerial ability is stronger during the economic downturn as high-tech SMEs rely more on high-ability managers to target and utilise R&D resources. This finding is consistent with prior arguments that managerial roles are increasingly important during the economic recession (Andreou et al., 2013; Steenkamp and Fang, 2011). In addition, we find that the enhancement effect of managerial ability is more pronounced in regions with a better digital economy development. This is because the development of digital economy promotes information transmission, financing and enterprise digital transformation, which allows highly capable managers to more effectively transform R&D into increased performance. This finding sheds new light on the economic consequences of digital economy (Wang and Cen, 2022; Zou and Deng, 2022) and has significant implications for the government.
Theoretical implications
This study offers several important theoretical contributions. First, we extend the research on innovation in high-tech SMEs. Due to innovation orientation and resource constraints, high-tech SMEs are generally concerned about two issues: what affects innovation performance (i.e., innovation outputs such as patents and new products) and what affects financial returns from innovation (i.e., whether investments in innovation result in increased firm performance) (Guo et al., 2020; Liu et al., 2020). While existing studies primarily examine the antecedents of the innovation performance of high-tech SMEs (Alegre et al., 2011; Ghazinoory and Hashemi, 2021; Gu et al., 2016; Lin et al., 2014), we extend the literature by showing how their innovation is transformed into better financial performance. This exploration is necessary since high-tech SME survival and growth will be threatened if they devote limited resources to innovation but receive few positive financial returns (Rosenbusch et al., 2011). To shed light on this, we explore whether and how managerial ability affects the effect of R&D on the financial performance of high-tech SMEs. Specifically, we find that managerial ability enhances the financial returns of high-tech SMEs from R&D that offer novel insights into the second critical yet, understudied issue of innovation in high-tech SMEs. This finding also extends the current notion that due to resource constraints, high-tech SMEs should concentrate their limited resources on strategic assets, such as R&D and brands (Li et al., 2012a). Our study indicates that these firms should also focus on the investment in managerial resources, such as recruiting capable managers as they are critical to realise financial returns from strategic assets. In so doing, we further extend the extant literature that largely relates intellectual capital to scientists and inventors and explores their effect on corporate innovation by emphasising the importance of managers in translating the potential of those scientists and inventors into something tangible for the firm (Subramanian, 2012).
Second, we advance the research on managerial ability. Prior studies mainly regard managerial ability as an antecedent of business practices, for example, accounting-related strategies (Baik et al., 2011), firm risk-taking (Yung and Chen, 2017) and firm performance (Cheung et al., 2017; Demerjian et al., 2012). While these studies have shown how managerial ability directly influences performance, we show a different mechanism through which managerial ability contributes to firm performance. Specifically, we find that R&D and managerial ability interact positively to enhance the financial performance of high-tech SMEs. This helps to reconcile the prior inconsistent findings on the relationship between managerial ability and firm performance (Cheung et al., 2017; Demerjian et al., 2012). Our result indicates that highly capable managers alone cannot necessarily guarantee financial performance, but they need some bandwidth to leverage their competencies, such as the investment in R&D and related resource management activities. In other words, only high-tech SMEs with sufficient R&D investment and talented managers can attain superior financial performance. In addition, we offer a more fine-grained view of the role of managerial ability by considering the contingency effects of environmental factors. In so doing, our work also responds to the call for further investigation into the boundary conditions of the impact of R&D on SME performance (Rosenbusch et al., 2011).
Finally, we add to the resource management perspective by considering and empirically testing how economic downturn and digital economy development interact with managerial ability to affect value-creation activities. This view posits that to what extent the effective management of resources determines the amount of value the firm generates and maintains over time is affected by the firm’s given environmental context, in particular, the uncertainty of the external environment (Sirmon et al., 2007). However, the related empirical analysis of this secondary moderation is relatively scant. In this study, we empirically test the role of environmental uncertainty, that is, economic downturn, and extend this framework by considering the role of another crucial environmental factor, that is, digital economy development. The digital economy has developed rapidly in recent years and assessing whether and how it influences firm and manager behaviours is of great strategic importance for governments (Jiang and Murmann, 2022; Luo et al., 2022). Using a moderated moderating model, our study shows that the positive moderating effect of managerial ability on the impact of R&D on the financial performance of high-tech SMEs is more pronounced during the economic downturn and in regions with better digital economy development. Thus, we offer critical empirical evidence for the resource management perspective as well as extend its framework on the impact of environmental factors.
Practical implications
This study also offers some practical implications. First, we have critical implications for high-tech SMEs. In general, high-tech SMEs often face a dilemma when making strategies for R&D investments. On the one hand, high-tech SMEs should invest in R&D activities to develop and maintain their competitiveness (Arslan et al., 2021; Guo et al., 2020). On the other hand, due to their liability of smallness, high-tech SME returns from R&D may be relatively low, or even negative (Rosenbusch et al., 2011), which reduces their willingness to invest in R&D activities. Confronted with this dilemma, high-tech SMEs have difficulties in deciding how to allocate resources and make R&D investment decisions. Our study shows that the general impact of R&D on the financial performance of high-tech SMEs is positive and it is strengthened by managerial ability. This finding indicates the complementary effects of investments in technical resources and managerial resources on firm performance. Thus, we suggest that to develop a competitive advantage in the long term, high-tech SMEs should not only persist with R&D activities but also pay full attention to their human resource management as highly capable managers play vital roles in the management of R&D resources. In addition, high-tech SMEs should understand that the enhancement effect of managerial ability varies across contexts. Our analysis suggests that the impact of managerial ability on the R&D–performance link in high-tech SMEs is strengthened by economic downturn and digital economy development. Thus, in these contexts, high-tech SMEs should hire more talented managers and take full advantage of their capability to improve the financial returns from R&D. This has similar implications for such firms in the recent time of COVID-19 which has created turmoil in economic conditions.
Second, we have critical implications for governments as many target investment in SMEs that are technologically capable. Motivated by this, high-tech SMEs leverage these funds and invest their valuable time into innovation-related activities. But whether high-tech SMEs can monetise these investments of resources and time into R&D warrants careful consideration. If the constraints faced by high-tech SMEs prevent them from translating their R&D into financial returns, these policies need to be revisited. Our study shows that the effect of R&D on the financial performance of high-tech SMEs is enhanced by managerial ability. Thus, when considering the sponsoring target and the policy benefits, the governmental agencies should assess the managerial ability of these firms as they are instrumental in converting R&D into financial performance. In addition, our finding of the positive interaction effect of R&D, managerial ability and digital economy development on the financial performance of high-tech SMEs has implications for local government. The innovation activities of high-tech SMEs are very important for local economic growth; these firms also contribute to local employment growth. Hence, the local government has the responsibility to help high-tech SMEs realise more financial returns from their R&D activities and promote their long-term survival and growth. Based on our findings, one potential way is to attract more high-ability managers to work in local high-tech SMEs through talent policies, and meanwhile, develop the local digital economy to offer a more favourable environment for these firms.
Limitations and future research
This study has some limitations suggesting areas for further research. First, this study only focuses on how managerial ability affects the impact of R&D on the financial performance of high-tech SMEs. However, the empirical analysis of this effect may also be interesting in other contexts. For example, multinational enterprises may provide a good context to examine the effect of managerial ability on the financial returns from R&D due to their complex operations and diverse management teams. Further research can be carried out in this direction. Second, due to data unavailability, we do not explicitly capture the heterogeneity of managerial ability. Future research may advance our understanding by further investigating how the moderating effects of various types of managerial ability (e.g., general and specialised managerial ability) on the R&D−performance nexus in high-tech SMEs differ. Meanwhile, they may tease out manager capabilities along with targeting and utilising R&D resources to see which one plays a more significant role in generating better financial performance. Finally, in addition to the economic downturn and digital economy development, the role of managerial ability in enhancing financial returns from R&D may be bounded by other environmental factors as well as firm characteristics, which provides several promising avenues for future studies.
Footnotes
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China [grant number 72071154].
