Impact of Pay Gap on Innovation Performance: The Moderating Role of Top Management Team Diversity

Abstract

The pursuit of innovation and the motivation of personnel have long been crucial considerations for sustainable development of organizations. However, an insufficiently addressed issue lies in the optimization of managerial and employee motivation through compensation structures. Drawing on tournament theory and social comparison theory, this research investigates the influence of both the top management team (TMT) pay gap and the TMT-employee pay gap on firms’ innovation performance. Leveraging an empirical analysis of a longitudinal dataset comprising 2517 firms with 12,052 observations spanning from 2004 to 2020, this study reveals an inverted U-shaped relationship between the TMT team pay gap and firm innovation performance. Additionally, this effect is found to be significantly mitigated in firms characterized by highly homogeneous management teams. Furthermore, our investigation indicates that a wider pay gap between executives and employees positively correlates with improved firm innovation performance. The findings from this study contribute novel theoretical explanations and empirical evidence, offering valuable insights into the nuanced ways in which pay gaps impact innovation performance within distinct organizational contexts. A better system of incentives within organizations directly promotes the development of technological innovation, contributing to social progress, human harmony, and sustainable development.

1. Introduction

Innovation represents a multifaceted effort, encompassing both immense value and substantial risk for businesses. This endeavor demands significant human resource investment and the creativity of the workforce [1,2]. Essential to the success of innovation in companies are strategic planning, a strong advocacy for innovation, and the unwavering commitment of innovators [3,4]. The configuration of a company’s compensation scheme is pivotal in inspiring employees at all levels, from managers to rank-and-file staff [5,6]. A pronounced pay gap can profoundly affect motivation, potentially diminishing both organizational productivity and creativity [1]. Despite the extensive research underscoring the crucial role of technological innovation for a firm’s competitive edge and sustainability over time [3,7,8], as well as the importance of compensation in fostering innovation and creativity [1], there has been relatively limited exploration into how pay structures specifically influence a firm’s innovative pursuits [9].

The debate continues regarding the impact of pay disparity on a firm’s innovation outcomes. Although many studies have investigated the influence of pay gaps on performance-driven incentives [5], some scholars suggest that pay structures impact not only strategic decisions in management and innovation processes but also the motivation of employees to innovate, thereby influencing overall innovation performance [4,9]. Shen and Zhang argue, based on tournament theory, that a wider pay gap within top management teams (TMTs) can enhance innovation efficiency [9]. In contrast, Xu claimed that social comparison theory indicates a negative impact on innovation when the pay gap between executives and employees is significant [4]. These conflicting findings may arise from two main issues: (1) the absence of a definitive and coherent theoretical framework explaining how pay gaps affect innovation performance and (2) differences in the scope of the pay gap being studied, with some research focusing on TMT pay disparities and others on the gap between TMT and employees [4,9]. Since firm innovation results from the combined efforts of executives and employees [3], it is crucial to investigate the distinct effects of TMT pay gaps and TMT-employee pay gaps on innovation performance.

The divergent results in existing literature reflect two primary theories: tournament theory and behavioral theories like social comparison theory [4,10]. Innovation activities within firms are strategic and complex, involving significant risks and rewards, and necessitate collaborative efforts [3]. Tournament theory likens the highest salary to a competitive prize that motivates employees. An increasing pay gap is thought to incentivize employees to strive for higher performance, pursue promotions, take risks, and ultimately drive innovation within the firm [9,11]. Consequently, firms may use a broader pay gap to encourage their workforce [12]. Conversely, social comparison theory proposes that smaller pay gaps foster better company performance because employees compare their pay with that of their peers and prefer equitable treatment. A widening pay gap could lead to perceptions of unfairness, thereby undermining teamwork [4,13,14]. Despite the research, the combined effect of these theories on a pay gap’s impact on innovation performance within firms remains unresolved, hindering the development of consistent theoretical and empirical conclusions.

Innovation within firms requires collaborative effort from both managers and employees to achieve positive outcomes [1,4]. Nevertheless, prior research has often neglected the different roles of compensation structures in motivating innovation performance among managers and employees. Within organizations, horizontal and vertical pay comparisons are common as employees and managers evaluate their compensation relative to others [4]. Given that innovation is a critical strategic decision for companies, offering potential competitive advantages and increased benefits but also involving substantial costs [9], the level and structure of compensation can significantly influence the motivations and management processes related to innovation. This, in turn, affects the decisions and commitments of top managers in the innovation process [15]. Additionally, employees’ creative input is crucial for implementing innovation, which is inherently uncertain [2]. Thus, effectively incentivizing employees through compensation to enhance innovation performance is essential [4]. This study proposes that both tournament theory and social comparison theory play significant roles and interactively affect firm innovation performance, examining how pay gaps within TMTs and between TMTs and employees influence this performance.

Moreover, we contend that the primary effects of pay gaps are moderated by TMT tenure diversity. Prior research has largely focused on a pay gap’s impact under a uniform mechanism [4,9], yet different TMT characteristics may lead to varied interpretations and perceptions of compensation. Tenure diversity introduces informational differences among team members, influencing their attitudes towards pay gaps [16,17]. Therefore, this study also explores the moderating effect of TMT tenure diversity.

Therefore, our research question is how the TMT pay gap and the TMT-employee pay gap affect firms’ innovation performance, and how TMT tenure diversity moderates the effect of the TMT pay gap on innovation performance. By conducting an empirical analysis of a longitudinal dataset covering 2517 innovative firms and 12,052 observations from 2014 to 2020, this research addresses key gaps in existing literature in three main ways. First, by integrating both tournament theory and social comparison theory, we provide novel theoretical explanations and empirical evidence to clarify how pay gaps influence innovation performance. Previous studies have produced inconsistent findings regarding the impact of pay gaps on innovation [4,9]. By examining the mechanisms of tournament theory and social comparison theory within the context of TMT pay gaps and TMT-employee pay gaps, we offer insights to reconcile conflicting theoretical perspectives and pay gap scenarios. Second, our research extends prior work on factors influencing firms’ innovation performance. While Manso highlights the role of compensation in motivating employees during innovation processes [3], and various studies have explored different compensation types’ effects on innovation [1], we emphasize the significant yet distinct effects of TMT pay gaps and TMT-employee pay gaps as alternative pay structures on innovation performance. Third, we examine the boundary conditions affecting the innovation performance impact of pay gaps through intra-team characteristics. Compensation is a critical innovation incentive, and our study shows that team heterogeneity influences dynamics and communication, affecting the role of pay gaps in driving innovation performance.

2. Theoretical Background and Hypothesis

2.1. Theoretical Perspectives on Compensation and Innovation

Innovation serves as a crucial engine for ongoing business growth [7]. Despite its importance, the high rates of failure and the unpredictability of returns often discourage firms from embracing innovative efforts, making the encouragement and promotion of innovation a formidable challenge [3]. As an endeavor heavily reliant on human capital and driven by creative input, innovation demands the engagement, inspiration, and cooperation of both managers and employees within the organization [3].

Corporate innovation is not just a strategic activity but is also directed and influenced by the decisions and leadership of the executive team [1,9]. The degree to which a company undertakes innovative projects, the level of investment in these projects, and the extent of control and support they receive during their development are all significantly shaped by the subjective initiatives of the firm’s executive team. Conversely, the employees are the ones who carry out these innovative ideas, and their drive and motivation have a direct impact on the execution of innovation [4]. Due to the inherent unpredictability and fluctuating input–output relationship of innovation, accurately assessing outcomes in real-time can be challenging. Thus, the initiative and motivation of employees are vital sources for fueling innovation [4].

The structure of compensation, being a direct influencer of employee motivation, is pivotal in determining innovative performance. This influence is viewed through the frameworks of two theoretical lenses: tournament theory and social comparison theory.

2.2. Tournament Incentives and Social Comparison Effects

Tournament theory provides insight into the effects of pay disparities by examining them through the lens of game theory and principal-agent dynamics [12,18,19]. Unlike traditional economic theories that tie compensation to marginal output, tournament theory establishes a competitive hierarchy where rewards are highly disproportionate, leading to a winner-takes-all outcome [20]. By employing this competition-based model, firms can lower monitoring costs, which can be high when evaluating the contributions of managers [21]. Within this framework, a larger pay gap can serve as an incentive, motivating managers to strive for higher performance levels and encouraging employees to seek promotional opportunities by aiming for higher management positions [22,23]. In the realm of corporate innovation, a wider pay gap represents a substantial reward, spurring managers to engage in riskier and potentially high-value projects [9]. Similarly, employees, motivated by the prospect of higher rewards, may strive to innovate, enhancing their chances for career advancement within the company [3].

On the other hand, behavioral theories, particularly social comparison theory, highlight the adverse effects of significant pay gaps. Such disparities can evoke feelings of inequity among employees who receive lower compensation [13,24,25]. Within an executive team, where roles are often diverse and complementary, a substantial pay gap can foster resentment among lower-paid managers, leading to disengagement and decreased collaboration, thereby diminishing organizational commitment [26,27]. The negative implications of perceived unfairness often do not correlate with actual contributions, as fairness expectations override differences in input [28]. In the context of innovation, managers might be hesitant to invest in initiatives with uncertain returns if they perceive the compensation structure as unfair. Furthermore, innovation typically requires collaboration across various functional areas, and perceived inequity can undermine teamwork, leading to less effective innovation outcomes [4,26]. Social comparison theory also suggests that fairness issues are more pronounced within groups of similar status, such as within the executive team or within specific departments, rather than across different hierarchical levels [29]. Therefore, the negative impact of perceived unfairness is more likely to arise within the executive team rather than between executives and lower-level employees.

According to the contingency proposition of effect of pay structure [30], we argue that the innovation performance effects of pay gap are different due to different comparators. The effect of tournament incentives is based on prospective promotions or awards, while social comparison effects happen between comparable personnel at the present time [26,28,31]. TMTs and employees have different functions and powers in organization, which can affect the potential rewards and present inequities perceived by executives and employees when assessing the pay structure. Specifically, considering pay gap within TMT, pay incentives and comparisons occur among similar people. When larger pay gaps reflect the organization’s tendency to reward individual contributions, creating incentives for executives to innovate [32,33]; however, there is also the potential for perceptions of unfairness as the similarity of the positions causes executives to compare themselves to each other [34]. When considering the pay gap between executives and employees, a large pay gap can provide employees with the lure of potential rewards and incentives to innovate for the high pay that may exist in the future; at the same time, it is not a zero-sum game between executives and employees, and the pay gap is caused by a large difference in current positions [26,31]. Taking the differences of positions and the inequality of status into consideration, it is difficult to take substantive measures for employees, although they may wonder if there are fairness issues. In this case, if employees do not try to innovate, they will harm their own profitability. Thus, we argue that the innovation performance effect of pay gap within TMT is driven by the tension of tournament incentives and social comparison effects; while the innovation performance effect of pay gaps between TMTs and employees is dominated by the tournament incentives effect. Our research model is shown in Figure 1.

2.3. Pay Gaps and Innovation Performance in TMT

Within an organization, the top management team (TMT) must balance both competitive and cooperative dynamics. On one side, TMT members work together to achieve organizational goals, but on the other, they compete for limited resources and opportunities, such as promotions or client accounts. The pay gap within TMT creates incentives for attracting high-level talent conducive to innovative activities but can also be detrimental to innovative collaboration, knowledge networking, and self-giving innovation [34,35].

A pay gap within TMTs benefits innovation performance by providing tournament incentives, reflected in the attraction of more creative talent and the drive for members of the executive team to acquire new knowledge in order to enhance their value. On the one hand, a greater pay gap highlights the organization’s recognition and preference for individual contribution, with more innovative people likely to be rewarded more [31]. Such incentives can motivate the executive team to introduce more novel knowledge and update the organization’s innovation knowledge, as well as facilitating the formation of a larger pool of knowledge resources in the organization [36]. Knowledge acquisition and creation facilitate organizational output of high-quality R&D [37]. On the other hand, the competitive model suggests that TMT members are driven to utilize the innovative knowledge and enhance their performance and innovation capabilities under competitive pressure to succeed in a resource-scarce environment [38]. Research has shown that healthy competition can stimulate enterprise innovation and creativity, contributing to long-term success [16]. According to tournament theory, encouraging competition among TMT members through pay disparities can enhance individual performance and drive competitiveness, particularly in organizations with resource- and benefit-oriented compensation structures [39]. A significant pay gap within the TMT signifies a competition-driven salary system, which may motivate executives to exceed expectations to secure a higher reward. This drive for the “championship prize” can spur executives to increase their innovative efforts and creativity [40], thereby enhancing the company’s innovation performance.

Conversely, a cooperative approach emphasizes collective achievement, where team-oriented behaviors such as information-sharing and mutual support are crucial for generating innovative ideas [39]. A smaller pay gap within the TMT reflects a cooperation-based compensation system, which may foster collaboration but provide less individual motivation due to smaller rewards. Large pay gaps are not conducive to knowledge sharing and knowledge networking [31,41]. Thus, while a larger pay gap can enhance firm innovation performance by driving competition and motivation, it also poses challenges. A competition-focused reward system might struggle to clearly distinguish individual from group contributions, leading to perceptions of unfairness among lower-paid executives [42]. For R&D activities, it is very difficult to accurately assess and measure the contribution of each individual, so individual performance in innovation activities is relatively ambiguous [31]. This perceived inequity can decrease the effectiveness and creativity of those team members [43]. Moreover, social categorization theory suggests that in a competition-driven system, members may withhold knowledge, resulting in redundant investments and misaligned goals [44]. The competition for higher rewards can foster envy and passive attitudes among peers, potentially leading to unethical behavior [42]. Given the risks and uncertainties inherent in innovation, TMT members might deprioritize innovation under such conditions, negatively affecting the firm’s innovation outcomes.

Balancing these perspectives, we argue that neither extremely large nor very small pay gaps among TMT members are optimal for enhancing firm innovation performance. Excessive pay disparities can foster unethical behavior and reduce cooperation, while very small gaps might fail to sufficiently motivate individual performance. An intermediate level of pay disparity could strike the right balance, promoting competitiveness without undermining fairness and cooperation. Therefore, we hypothesize

Hypothesis 1. 

There is an inverted U-shaped relationship between the pay gap within the TMT and firm innovation performance. Either too high or too low of a TMT pay gap is not conducive to the improvement of firm innovation performance; a moderate pay gap is the optimal salary structure.

2.4. TMT-Employee Pay Gap and Firm Innovation Performance

Research specifically focusing on the impact of the pay gap between TMT members and regular employees on firm innovation performance is sparse. Cowherd and Levine found that employees often regard higher-level staff as role models, inspiring them to achieve higher goals through positive behaviors such as innovation [13]. Thus, a wider pay gap between TMT and employees can provide significant incentives for positive behavior, encouraging employees to pursue the company’s innovation objectives.

Specifically, when there is a large pay gap between employees and the executive team, employees have a stronger incentive to contribute to innovation performance by acquiring new knowledge and exploiting organizational knowledge [33]. Large performance gaps offer potential rewards for employees, suggesting that employees can be promoted to higher pay. Employees need to innovate to achieve their signature outcomes and enhance their personal competencies, so employees are more motivated to proactively acquire new knowledge [31]. At the same time, employees strive to leverage knowledge and turn it into innovations in order to lead to better projects to enrich their CVs. Thus, a larger TMT-employee pay gap can potentially enhance firm innovation performance [45]. In this study, the comparison between ordinary employees and higher-level staff occurs within the broader organizational context, aligning more closely with tournament theory.

Social comparisons are difficult to make between different levels of an organizational structure, as there is often unequal status and different types of work at different levels. Regular employees typically do not compare their salaries with those of top-level executives, so a large pay gap between TMTs and employees is less likely to induce feelings of envy or unfairness [46]. Unlike the TMT pay gap, which can generate internal tension, the hierarchical pay gap naturally aligns with the organizational structure and is less likely to cause the negative outcomes predicted by social comparison theory [42]. For instance, employees recognize that TMT members hold greater responsibility and make more substantial contributions to the company, justifying their higher compensation. The social comparison theory’s effects are more pronounced within homogeneous groups, such as the executive team [47]. In addition, while employees may have a sense of unfairness due to the large pay gap with the executive team, it is difficult to take substantive action, because the executive team can punish employees for inefficiencies and poor output [37].

Therefore, the influence of the TMT–employee pay gap is best explained by tournament theory. Based on these observations, we propose

Hypothesis 2. 

The larger the pay gap between TMT members and employees, the more likely it is to contribute to the improvement of firm innovation performance.

2.5. TMT Tenure Diversity, Pay Gap, and Innovation Performance

TMT tenure diversity reflects the range of experiences and knowledge within the team, stemming from differences in the lengths of team members’ service [17]. This diversity includes variations in demographic (unrelated to job roles) and functional (related to job roles) aspects [48,49]. For example, a TMT with high tenure diversity would have members from various tenure categories [17]. Tenure differences contribute to a broad spectrum of knowledge and cognitive perspectives within the team. These differences, referred to as diversity, form the basis for theories on information-processing in teams [50]. In our analysis, we consider TMT tenure diversity as encompassing both demographic and functional distinctions.

When the TMT pay gap is small to moderate, greater tenure diversity explains part of the pay gap and weakens the role of tournament incentives. There are often differences in pay in organizations due to tenure, e.g., the more senior the manager, the higher the pay [50]. In such cases, managers may attribute the pay gap to differences in tenure rather than to rewards for extra effort. Higher-paid managers have less incentive to pursue tournament rewards, while relatively lower-paid managers may underestimate the rewards of tournaments and reduce their efforts. Moreover, distinct sub-teams may form within the TMT, leading to intergroup discrimination and negative interpersonal dynamics [17]. In scenarios where the pay gap is significant, competition for the “championship prize” may still drive innovation, but the benefits of such competition are dampened by the increased communication costs associated with high tenure diversity.

Conversely, when the pay gap is moderate to large, increased tenure diversity highlights attitudinal and perceptual differences, resulting in social categorization issues. Clear divisions may form between newer and more tenured employees, reducing communication and comparison across groups [17]. In such cases, even with a large pay gap, the sense of injustice and its impact on team cohesion may be lessened due to limited interaction with lower-paid subgroups within the executive team [51]. Consequently, the adverse effects on innovation performance are mitigated. Therefore, we propose

Hypothesis 3. 

TMT tenure diversity negatively moderates the relationship between the TMT pay gap and firm innovation performance, such that the inverted U-shaped relationship is flattened when TMT tenure diversity is higher.

3. Research Methods

3.1. Data and Sample

The data in this study come from the China Stock Market & Accounting Research Database (CSMAR), which is a widely used and well-known database for financial information of Chinese listed companies [52]. Our data are mainly divided into three parts, namely financial information, governance structures, and transaction data. The financial data of this study were obtained from the sub-database named the “Chinese Listed Company Financial Statement Database”, while the salary data of the executive team members were obtained from the “China Stock Market Transaction Database”.

It should be noted that the financial indicators of CSMAR are quarterly data. In order to match other annual data, we used the year-end value to represent the annual value for the financial data. Our research sample is Chinese listed companies. For a different sub-database, I used stock code and year as unique codes to perform the one-to-one matching. To remove the impact of price fluctuations, we adjusted the value variables using the GDP deflator. To mitigate the effect of outliers on the model estimates, we excluded observations outside the 1st and 99th percentiles of each variable. Finally, 12,052 firm-year observations were obtained, covering 2517 listed companies, and the time range was 2004–2020. The data are unbalanced panel data.

3.2. Measures

3.2.1. Dependent Variable

Innovation performance (IP): The dependent variable in this study is innovation performance; following Liu et al. [53], we measured innovation performance by the number of patents granted by the Chinese Patent Bureau. The data comes from the CSMAR and WIND databases [54]. The reasons for choosing the number of patents granted as a measure are as follows: A patent inherently signifies a unique and novel piece of knowledge, directly linking it to inventiveness, as it is granted only for ‘non-obvious’ improvements or solutions with clear utility. Second, patents offer an externally validated measure of technological novelty. Third, they confer property rights to the assignee, giving them economic significance. Consequently, patents have become a widely used measure of innovation in the literature [53].

3.2.2. Independent Variables

Pay gaps within TMT: Conceptually, the TMT consists of the chief executive officer and those individuals who belong to the dominant coalition. To measure the pay gap within TMT, we include top management members who are responsible for strategy formulation as well as those more involved in strategy implementation [55].

According to Siegel and Hambrick [55], the CEO is the only first-level executive, and their salary is the “tournament pay”. Additionally, according to tournament theory, we are measuring the disparity between the tournament pay and the executives most likely to receive it. Thus, we measure the pay gap within top management team members (TMT_SA) by the formula below [56]:

G = Ln[S − (TS − S)/2]

where S is the salary of the CEO and TS represents the number of total compensation (straight salary, bonuses not included) of the top three executives with the highest compensation. A larger value of G means a greater pay gap between executive team members.

Pay gap between TMT and employees (TE_SA): This variable represents the relative difference between the average salary of the executive team and the average compensation of employees. To measure the average salary of the executive team, we followed the measurement of Liu and Sun [57], which is defined as the average annual salary of the top three executives with the highest salary, and the average salary of employees is the total salary divided by the number of employees. Specifically, the formula is as follows:

G_te = ln(S_top/3 − S_e/N)

where S_top is the total compensation of the top three executives with the highest salary, S_e is the total salary of employees, and N is the total number of employees. The greater the value of G_te, the greater the pay gap between the executive team and the average employee.

3.3. Moderator

Tenure diversity (TD): Tenure diversity reflects the sense of distance or separation team members feel toward each other due to different organizational tenures and represents the range of knowledge sources that can influence team decisions, as team members may have different access to information based on their tenure differences [50]. We concentrated on tenure diversity because it encompasses both demographic differences (unrelated to the job) and functional differences (related to the job). Demographic differences form the basis of social categorization research, while functional differences are the focus of information processing research.

As recommended by Harrison and Klein [58], the standard deviation (SD) of the team tenure is used to measure tenure separation. A larger value of SD indicates that there is higher heterogeneity in the tenure of top managers.

3.4. Control Variables

We controlled for several variables that serve as standard controls in studies on performance.

Invisible Asset Intensity (Invisible_Asset_Intensity): Invisible Asset Intensity = Total Intangible Assets/Total Assets.

Asset Liability Ratio (Asset_Liability_Ratio): Asset Liability Ratio = Total liabilities/Total assets.

Firm_Size: Measured by the logarithm of the firm’s paid-in capital.

Total number of employees (EMP): Take the logarithm of the total number of employees in the business.

Whether the shareholding structure has changed (Change_of_Shareholder_Structure): A value of 0 indicates no change, and a value of 1 indicates a change.

Chairman concurrently (CEO_Duality): A value of 0 means that the chairman does not concurrently serve as the general manager, and a value of 1 indicates that the chairman concurrently serves as the general manager.

The ratio of independent directors (Independent_Director_Ratio): Independent Director Ratio = the number of independent directors/the total number of directors.

In addition, to control for the fluctuation of the economy over time and the influence of industry characteristics, we add time dummy variables and industry dummy variables to the model.

3.5. Estimation Method

The descriptive statistics and the correlations of the variables of the main variables are presented in

Table 1. Descriptive statistics and correlation matrix.

Variable	Mean	S.D	Min	Max	1	2	3	4	5	6	7	8
1. Innovation Performance	15.69	73.89	0.46	2780	1
2. TMT_SA	11.58	1.15	7.92	14.80	0.173 ***	1
3. TE_SA	12.64	0.82	9.97	14.65	0.157 ***	0.604 ***	1
4. TMT_SA2	135.5	26.33	62.70	219.10	0.098 **	0.997 ***	0.605 ***	1
5. Invisible_Asset_Intensity	0.04	0.06	−0.01	0.86	0.011	−0.030 ***	−0.089 ***	−0.032 ***	1
6. Asset_Liability_Ratio	0.46	0.33	0.00	18.84	−0.253 ***	−0.041 ***	−0.068 ***	−0.040 ***	0.022 ***	1
7. Firm_Size	19.81	1.01	17.37	26.59	−0.017	0.158 ***	0.359 ***	0.162 ***	−0.018 **	0.105 ***	1
8. EMP	7.53	1.33	1.95	13.22	0.156 **	0.086 ***	0.233 ***	0.090 ***	0.005	0.084 ***	0.574 ***	1
9. Independent_Director_Ratio	0.36	0.07	0.00	0.80	−0.038 *	0.186 ***	0.256 ***	0.177 ***	−0.009	−0.010	0.087 ***	0.014 *

Standard errors in parentheses; * p < 0.1, ** p < 0.05, *** p < 0.01.

.

According to the procedure suggested by Wooldridge [59], we conducted a model screening test. The results of Lagrange multiplier test showed that we should choose a panel model instead of pooled OLS, and the results of the Hausman test showed that a panel fixed-effects model should be used (p = 0.027 < 0.05). After determining the model, we tested the data. First, the modified Wald statistic was used to test the problem of heteroscedasticity between groups, and the test results showed that there was a problem of heteroscedasticity between groups in the data. Secondly, the data was tested according to the serial correlation test method of the panel data model proposed by Wooldridge [59], and the test results showed that the data has a first-order serial correlation problem. Therefore, we calculated Driscoll–Kraay standard errors to correct for heteroskedasticity and first-order serial correlation problems as suggested by Driscoll and Kraay [60], and the final estimated model was a panel fixed-effects model using Driscoll–Kraay standard errors.

4. Results

The descriptive statistics and correlation metrics are shown in Table 1. To test whether a potential problem of multicollinearity existed, we followed the approach recommended by Neter and computed variance inflation factors (VIFs) when all variables were included in each model [61]. The VIFs ranged from 1.01 to 2.09, with a mean of 1.35. The maximum VIF is less than 10; as noted by Neter et al., this indicates that multicollinearity is not an issue in this study [61].

The dependent and independent variables exhibit significant variability, and the correlation coefficients align with our expectations. Subsequently, we employed fixed-effects models using a hierarchical approach, with the results presented in

Table 2. Regression results.

	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
Dependent variables
TMT_SA		25.467 ***		28.467 ***	28.462 **	31.661 *
		(10.756)		(11.467)	(14.761)	(12.582)
TE_SA			2.917 **	2.616 **		2.813 **
			(0.121)	(0.101)		(0.101)
TMT_SA2				−1.339 **	−1.375 **	−1.289 *
Interaction				(0.547)	(0.475)	(0.273)
Tenure Diversity × TMT_SA					−79.46 *** (20.467)	−81.43 ** (22.752)
Tenure Diversity × TMT_SA2					3.411 ***	3.430 ***
					(0.924)	(0.985)
Moderator
Tenure_Diversity	317.5 ***	379.6 ***	415.7 **	456.7 ***	347.61 ***	401.3 **
	(130.7)	(143.2)	(123.7)	(110.3)	(127.8)	(157.7)
Control Variables
Invisible_Asset_Intensity	−5.083 ***	−5.033 ***	−5.026 ***	−5.029 ***	−5.026 ***	5.013
	(0.703)	(0.803)	(0.004)	(0.904)	(0.904)	(2.907)
Asset_Liability_Ratio	−6.512	−6.653	−6.556	−6.670	−6.523	4.602
	(6.879)	(6.872)	(6.854)	(6.854)	(6.654)	(9.458)
Firm_Size	7.323 ***	7.445 ***	6.870 ***	7.173 ***	7.181 ***	7.319 *
	(1.769)	(1.628)	(1.550)	(1.378)	(1.380)	(3.786)
EMP	3.299 **	3.041 **	3.103 *	2.944 *	2.923 *	−3.177 **
	(1.650)	(1.542)	(1.712)	(1.626)	(1.607)	(1.472)
Change_of_Shareholder_Structure	−1.577	−1.484	−1.503	−1.447	−1.421	0.895
	(1.312)	(1.279)	(1.273)	(1.254)	(1.241)	(1.592)
CEO_Duality	−0.803	−0.409	−1.039 **	−0.572	−0.540	−0.465
	(0.590)	(0.584)	(0.496)	(0.565)	(0.619)	(0.658)
Independent_Director_Ratio	13.338	15.239	14.455	15.765	15.932	−5.868
	(11.278)	(11.821)	(10.990)	(11.487)	(11.607)	(19.723)
Year dummy	Included	Included	Included	Included	Included	Included
Industry dummy	Included	Included	Included	Included	Included	Included
_cons	0.000	0.000	0.000	0.000	0.000	0.000
	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
N	12,052	12,052	12,052	12,052	12,052	12,052
r2_w	0.041	0.048	0.050	0.057	0.101	0.107
F	116.146	118.343	531.006	171.200	172.155	207.790

Estimated coefficients and associated robust standard errors (in parentheses) are reported; * p < 0.1, ** p < 0.05, *** p < 0.01.

: Model 1 is the basic model and includes only the control variables, while Models 2 through 5 add the independent and interaction variables, and Model 5 is the full model, including all control, independent, and interaction variables. In Model 4 of Table 2, we tested Hypothesis 1 by introducing both the linear and quadratic terms of Pay gap within TMT. The result indicates that innovation performance initially increases with pay gap within TMT (b = 25.467) but significantly decreases as the value of pay gap within TMT continues to grow (b = −1.339). This outcome suggests a curvilinear relationship, specifically an inverted U-shaped, between pay gap within TMT and innovation performance. Furthermore, we exam the inverted-U shape by following the three-step procedure outlined by [62]. First, the result shown in Table 2 confirms that the second-order term is significant and of the expected sign. Second, we tested whether there is a significant change in the slope of the relationship at different levels of the independent variable, using the “utest” command in Stata 14 [62]; we confirmed that when pay gap within TMT members = 7.918, the slope = 2.54 (p = 0.048), and the slope = −11.47 (p = 0.011) when pay gap within TMT members is largest. Third, by using the “utest” command in Stata 14, we tested whether the turning point lies within the data range of the pay gap within TMT. The result indicates that the turning point (10.357) falls within the observed range of “pay gap within TMT members”. Overall, the inverted U-shape is supported with p = 0.04. The effect of pay gap within TMT is shown in Figure 2. All these findings suggest that Hypothesis 1 is supported.

According to the results of Model 3, TE_SA has a significantly positive relationship with firm innovation (b = 2.97, p < 0.01); therefore, Hypothesis 2 is supported. To evaluate the moderating effect of tenure diversity, Model 3 incorporates interaction terms between both the linear and quadratic terms of the pay gap within TMT and tenure diversity. The result indicates that tenure diversity makes the inverted U-shape flatten since the second-order interaction term is significantly positive. Additionally, Figure 3 provides further evidence of the moderating effect of tenure diversity, thereby supporting Hypothesis 3.

According to the results, all hypotheses are supported. The results shows that TMT pay gaps are most conducive to organizational innovation performance when they are moderate, while larger pay gaps between TMT and employees can provide employees with greater incentives to innovate. This result suggests that within organizations, tournament incentives apply to comparisons within the same hierarchy and to pay comparisons across hierarchical levels, whereas the social comparison effect only plays an important role in same-level comparisons. Compensation structures need to be designed with both cross-tier and peer-to-peer structures in mind: Peer-to-peer needs to balance better incentives with better collaboration; while cross-tier compensation needs to be designed to provide sufficient incentives to enhance employees’ willingness to move up the ladder, and thus motivate employees to dedicate themselves to their own endeavors.

4.1. Robustness Test

To ensure the validity and reliability of our findings, we took several tests with alternative specifications of the empirical model as robustness checks. First, to avoid the potential endogeneity issue, we ran the dynamic model based on a two-step system generalized method of moments (GMM) estimator. The coefficient of quadratic terms of Pay gap within TMT is −0.001 (p = 0.02), thus the result of the GMM model also supported our a curvilinear relationship (which has an inverted U-shaped) between pay gap within TMT and innovation performance. Second, we tested the alternative measurement of innovation performance with the numbers of patents applied. Patents information was also obtained from the CSMAR database. We then ran the models again, and the results were consistent and provide consistent support for our hypothesis (the coefficient of TMT_SA2 is −1.82 with a p value of 0.031; the coefficient of TE_SA is 14.74 with a p value of 0.00; and the coefficient of tenure diversity*TMT_SA2 is 6.91 with a p value of 0.049).

4.2. Discussion

This study investigates how compensation structures impact firms’ innovation performance, utilizing both theoretical insights and empirical data. By leveraging tournament theory and behavioral theory, we examined the effects of pay disparities within executive teams and between executives and employees in Chinese firms. Our empirical analysis reveals a significant inverted U-shaped relationship between the TMT pay gap and firm innovation performance. Specifically, firm innovation thrives when the pay gap within the executive team is moderate; innovation performance declines when the gap is either too narrow or too wide. Additionally, our findings highlight that tenure diversity within the executive team moderates this effect. We also find that a larger pay gap between executives and employees positively correlates with enhanced innovation performance.

4.3. Theoretical Implications

Firstly, this study deepens the understanding of how compensation structures influence firms’ innovation performance by integrating insights from tournament theory and social comparison theory. Previous research has shown conflicting views on how pay gaps within firms impact innovation [4,9]. By combining these two theoretical perspectives, we explore their unique contributions to innovation performance in the context of intra-team pay gaps and TMT–employee pay gaps. Our results suggest that tournament theory’s principles extend beyond homogeneous groups to those with significant status differences. In contrast, behavioral theory’s emphasis on fairness is more relevant within homogeneous groups, where direct comparability exists. Our findings indicate that an optimal compensation strategy balances efficiency and fairness: a very small pay gap may fail to motivate executives adequately, while a very large pay gap may create perceptions of inequity among lower-paid executives, potentially leading to negative organizational behaviors.

Secondly, this study broadens the scope of research on firms’ innovation performance by focusing on pay structure rather than pay level. For strategic activities characterized by high value and high uncertainty, such as innovation, we find that a well-designed compensation structure can foster self-driven goals among employees, unlocking their full potential. By comparing compensation structures, organizations can set managerial and employee objectives that encourage risk-taking and self-investment, thereby enriching the literature on incentives for corporate innovation.

Moreover, this study delves into the boundary conditions affecting the pay gap’s impact on innovation performance by examining intra-team characteristics. We uncover that tenure diversity within the executive team influences the dynamics of comparability, cooperation, and goal setting. This, in turn, affects how tournament and behavioral theories operate within teams, enhancing our understanding of the theoretical mechanisms behind the pay gap’s impact on innovation.

4.4. Managerial Implications

Our findings provide valuable insights for managers tasked with designing effective compensation structures. Firstly, we demonstrate that the pay gap has a dual impact on innovation performance in the same tier. Designers of compensation structures need to balance better incentives with a better willingness to work together. On one hand, it can drive healthy competition among employees, boosting innovation performance. On the other hand, excessive pay gaps can create fairness issues, undermining innovation. Therefore, managers should aim for a moderate pay gap among executive team members to balance motivation and fairness. This approach optimizes strategic decision-making, resource allocation for innovation, and team collaboration, ultimately enhancing innovation performance.

Secondly, for cross-tier pay structure design, sufficient promotion incentives need to be built in so that employees are motivated to give themselves only if the incentives are large enough. Our study suggests that in the context of heterogeneous groups, such as between the TMT and regular employees, fairness concerns are less significant, and a larger pay gap between these groups can positively influence firm performance. Managers can leverage this by establishing significant pay differentials between hierarchical levels and creating clear promotion paths, thereby motivating employees to commit to organizational goals and engage proactively in innovation initiatives.

Thirdly, it is important for policymakers to promote sustainable innovation in firms [63] and provide both normative and supportive policies for pay design within organizations. For example, companies can be guided to balance the rewarding and collaborative effects in the design of internal remuneration systems for their executive teams. At the same time, the government can provide appropriate subsidies for important talents, so as to better motivate managers and employees to engage in innovative activities.

4.5. Limitations and Future Research Directions

While our study provides novel insights into the pay gap’s impact on innovation performance, several limitations should be acknowledged. Firstly, due to data constraints, our sample is limited to Chinese listed firms. Future research should examine whether our findings hold true in different cultural contexts, such as in India or Africa, and across various industries to enhance the generalizability of our results. Secondly, this study concludes that the negative effects of the pay gap between the TMT and employees (e.g., sense of unfairness) are relatively weak, based on the assumption that employees are motivated to innovate and will comply with managerial mandates. In some cases, employees’ sense of unfairness may be amplified or manifested in some specific behaviors, and such negative effects deserve to be studied in the future. Thirdly, our focus on two factors—TMT pay gaps and tenure diversity—leaves room for exploring other influences on pay expectations, such as industry context. A more comprehensive analysis incorporating these factors could provide deeper insights. Fourthly, innovation performance encompasses a number of dimensions, such as new products, processes, and services, and future research could further explore the relationship between pay gaps and these dimensions. Lastly, challenges in accessing detailed employee salary data led to limitations in our measurement. Future studies could benefit from more refined metrics to validate and expand upon our findings.