Tournament Incentives and Firm Innovation

Tournament Incentives and Firm Innovation Abstract This study analyzes how promotion-based tournament incentives for non-CEO senior executives affect corporate innovation. We measure tournament incentives using the pay gap between a CEO and the next layer of senior executives. We find that tournament incentives are positively related to innovative efficiency, as measured by the number of patents and patent citations generated per million dollars of R&D expense. Our main finding holds in an instrumental-variable analysis and regressions using alternative innovation measures, including patent generality and originality indices and stock market reactions to patent grants. Consistent with prior theories, the positive effect of tournament incentives is found to be particularly pronounced during the period prior to CEO turnovers. 1. Introduction Technological innovation has been recognized as the engine for economic growth since Schumpeter (1942) and Solow (1957). With the arrival of a knowledge-based and innovation-driven economy, corporate innovation has an increasing influence on a firm’s long-run competitive advantage and even the survival of firms (Chaney and Devinney, 1992; Porter, 1992; Ettlie, 1998; Eisdorfer and Hsu, 2011). Therefore, a fast-growing body of literature has attempted to understand the factors driving corporate innovative activities and their success from both theoretical and empirical perspectives (e.g., Acharya and Subramanian, 2009; Aghion, Van Reenen, and Zingales, 2009; Lerner, Sorensen, and Stromberg, 2011; He and Tian, 2013). As a recent development, both academicians and commentators have called for a more thorough empirical investigation into the relation between executive compensation and corporate innovation (e.g., Manso, 2011; Ederer and Manso, 2013). To date, relatively less attention has been devoted to understanding how to structure executive compensation if shareholders want to effectively motivate executives to be innovative. Notable exceptions include several studies examining how option-based compensation (Lerner and Wulf, 2007), equity grants with longer vesting periods (Baranchuk, Kieschnick, and Moussawi, 2014; Edmans, Fang, and Lewellen, 2015), and incentives set by the duration of CEO contracts (Gonzalez-Uribe and Groen-Xu, 2015) influence firm innovation. Although these studies shed light on the effect of performance-based compensation on innovation, none of them empirically examine how promotion-based compensation incentives influence firm innovation performance.1 The present study aims to fill this gap in the literature. Although the majority of executive compensation studies examine performance-based incentives, one stream of research focuses on intra-organizational promotion-based incentives (also known as tournament incentives). In a corporate rank-order tournament, non-CEO senior executives compete with each other for the top position. These executives are evaluated relative to their peers (i.e., relative performance evaluation), and among them the best relative performer will be promoted to be the next CEO. Promotion to the CEO position is associated with higher pay and therefore provides senior executives with strong incentives to expend greater effort to enhance both their own chances of promotion as well as the company’s performance (Lazear and Rosen, 1981; Prendergast, 1999). In addition to inducing greater effort, the option-like payoff structure of a tournament also influences risk-taking behaviors of tournament participants.2 Theoretical studies (e.g., Hvide, 2002; Hvide and Kristiansen, 2003; Yumoto, 2003; Gaba, Tsetline, and Winkler, 2004) show that contestants in a tournament have strong motives to increase the probability of winning by taking greater risk. The evidence on how tournament incentives influence managerial risk-taking and innovative activities, however, remains surprisingly scant in the corporate finance literature.3 In a recent theoretical study that primarily explains the prevalence of overconfident CEOs, Goel and Thakor (2008) predict that in order to increase the chances of winning, all senior executives would undertake investments that are riskier than the ones they would otherwise have undertaken in the absence of tournament incentives. Consistent with this argument, Kini and Williams (2012) find that greater prizes in CEO-promotion tournaments indeed lead to riskier corporate policies, including greater R&D investments, higher financial leverage, and less diversified business operations. Although the result of Kini and Williams (2012) suggests that higher tournament incentives induce senior executives to undertake greater risky investments (e.g., R&D), it does not address the question of whether such risk is pursued at the expense of efficiency. We conjecture that tournament incentives could affect innovative efficiency in conflicting ways. On the one hand, James and Isaac (2000) argue that tournament incentives in the mutual fund industry may lead to excessive risk-taking behaviors by fund managers and even the formation of stock market bubbles.4Gilpatric (2009) and others theoretically demonstrate that winner-take-all tournament contests, such as CEO-promotion tournaments, can generate incentives for contestants to engage in excessive risk-taking behaviors. For example, in sports contests where only one winner gets the top prize, the contestants are more likely to pursue aggressive risk-seeking strategies, as they typically have nothing to lose but could achieve a better outcome by taking excessive risks.5 Taken together, it is a valid concern that high tournament incentives might actually lead to excessively risky and inefficient innovative activities and, as a consequence, have a destructive impact on corporate innovation efficiency. On the other hand, tournament incentive could be positively related to innovative efficiency because classical studies on tournament incentives (e.g., Lazear and Rosen, 1981; Nalebuff and Stiglitz, 1983) suggest that VPs in a tournament with a larger promotion prize work harder to identify and maneuver high-quality innovation projects. In addition, Kempf, Ruenzi, and Thiele (2009)—a study examining the mutual fund industry—argues that “if a manager takes on too high a risk (perhaps because of tournament incentives), then there is also a higher risk of poor performance,” which leads to a greater probability of losing one’s job and facing a career setback. Such a concern for employment risks could also incentivize corporate managers to consider more about the productivity of their risk-taking behaviors, leading to a positive relation between tournament incentives and corporate innovative efficiency. In sum, it remains an empirical question whether greater R&D investments induced by larger tournament incentives are efficient. To fill this void and to complement the previous work of Kini and Williams (2012), we investigate how tournament incentives for non-CEO executives influence the efficiency of corporate innovative activities. We construct the measures of corporate innovative efficiency based on the innovation output data in the National Bureau of Economic Research (NBER) Patent Citations database. We measure tournament incentive as the pay gap between a CEO and the next layer of senior executives. Using a large sample of US public firms over the period 1993–2003,6 we find that tournament incentives are positively related to corporate innovative efficiency, as measured by the number of patents and the patent citations generated per million US dollars of R&D investment. This main finding is robust in regressions with additional controls and in regressions using alternative innovation measures that capture the fundamental importance and economic value of the patents, such as the generality and originality indices (Hall, Jaffe, and Trajtenberg, 2001) and stock market reactions to patent grants (Kogan et al., 2017). Our main finding also holds in an instrumental-variable analysis, in which we treat the pay gap measure as an endogenous variable. We use the industry median value of the pay gap measure as the instrument, because prior studies find that an individual firm is likely to be a “compensation-taker”. That is, a firm likely adjusts its executive pay when peer firms change executive compensation (DiPrete, Eirich, and Pittinsky, 2010). Consistent with this view, the instrument is highly significant in the first-stage regression. The F-statistic of excluded instrument also suggests that this instrument is not weak. However, we acknowledge that the instrumental-variable analysis has a limitation and thus these results should be interpreted with caution. Specifically, although it is likely that the industry-level pay gap (i.e., the instrument) is associated with the firm-level innovative efficiency only through its influence on an individual firm’s pay gap, this exclusion restriction could be violated and poses a threat to the identification if there is an omitted-variable problem. We therefore also perform regression analysis based on a propensity-score matched sample to partially address this endogeneity issue and find that our main results hold. If tournament incentives are indeed positively related to innovative efficiency, such a positive relation should be most pronounced when a succession contest is likely to occur, such as during the period prior to CEO turnovers. We find evidence in support of this conjecture. In addition, with the assumption that ex-ante expectations of VPs are on average correct, the effect of tournament incentives should be weaker in ex-post outsider-CEO turnover cases (i.e., an outsider is later appointed as a new CEO), ceteris paribus. Consistent with this argument, we find that the positive effect of tournament incentives prior to CEO turnovers is particularly pronounced when an insider (i.e., one of the VPs) is eventually appointed as the new CEO. In a similar vein, we also find that the tournament incentive effect is stronger when VPs expect a higher probability of CEO turnover in the foreseeable future (i.e., when the incumbent CEO is approaching retirement or is underperforming). Additionally, our subsample tests suggest that not every company benefits equally from providing executives with a high CEO-VP pay gap. Specifically, tournament incentives seem to have less beneficial effects on innovative efficiency for family firms, firms with weak corporate governance, and firms in non-innovative industries. This paper contributes to the prior literature in several ways. First, a fast-growing literature has found significant relations between innovation and some firm-level variables, including corporate governance (Atanassov, 2013; Chemmanur and Tian, 2013; Balsmeier, Fleming, and Manso, 2017), institutional ownership (Aghion, Van Reenen, and Zingales, 2009), leveraged buyouts (Lerner, Sorensen, and Stromberg, 2011), venture capital (Tian, 2012; Chemmanur, Loutskina, and Tian, 2014), stock market liquidity (Fang, Tian, and Tice, 2013), financial constraint (Almeida, Hsu, and Li, 2013), firm boundaries (Seru, 2014), the decision to go public (Bernstein, 2015), and CEO contract horizon (Gonzalez-Uribe and Groen-Xu, 2015). Our study is the first one showing that tournament incentive is also a factor influencing the efficiency of corporate innovative activities and thus adds to this fast-expanding literature. Second, our research is related to a stream of studies that examine how promotion-based incentives affect firm performance. The traditional tournament theory (Lazear and Rosen, 1981; Malcomson, 1984) implies that setting CEO pay at a level higher than that of non-CEO executives encourages competition and can lead to better firm performance. Nevertheless, prior studies (e.g., Main, O’Reilly, and Wade, 1993; Bloom, 1999; Eriksson, 1999; Conyon, Peck, and Sadler, 2001; Henderson and Fredrickson, 2001; Chen, Huang, and Wei, 2013; Coles, Li, and Wang, 2014; Connelly et al., 2014; Masulis and Zhang, 2014) present mixed evidence on this prediction. Given the inconclusive evidence, we explore the effect of tournament incentives on a more proximal performance indicator—firm innovation. Our results lend support to the tournament theory that a rank-order tournament provides non-CEO executives with strong incentives to achieve better firm performance. Through the lens of firm innovation performance, this study adds fresh evidence to the executive compensation literature by showing that promotion-based incentives enhance firm performance. Third, this study also has a policy implication. A growing sentiment following the recent financial crisis is that CEOs are overpaid and that their large compensation dilutes shareholder value. For example, recent evidence shows that non-CEO executives earn only approximately 40% of a CEO’s compensation (Conyon, 2006) and that CEO pay has risen faster than that of non-CEO executives and other employees (Useem, 2003; Mishel and Davis, 2014). To shed light on the pay disparity, the US Securities and Exchange Commission (SEC) recently adopted a rule that requires a public company to disclose the CEO–Worker pay ratio (Securities and Exchange Commission [SEC], 2015). Prior studies have attributed high CEO compensation and large pay disparity to increased CEO power (Bebchuk, Fried, and Walker, 2002), CEO entrenchment (Vo and Canil, 2016), and the practice of indexing compensation to peer-group benchmarks (Bizjak, Lemmon, and Naveen, 2008). This paper provides an additional explanation for the prevalence of high pay dispersion in corporate America by showing that high pay gap may be beneficial, because it incites tournament and motivates managers to make valuable contributions to firm innovation.7 The rest of the paper is organized as follows. Section 2 introduces the data sources and variable definitions. Sections 3 and 4 present the empirical results. Section 5 concludes. 2. Data and Variables This section introduces variable definitions, describes data sources and sample selection procedure, and presents descriptive statistics. 2.1 Tournament Incentives and CEO Performance-Based Incentives We obtain executive compensation data from the Compustat Execucomp database. Following Kini and Williams (2012), we measure tournament incentives as the pay gap between a CEO and the next layer of senior executives (i.e., VPs). Specifically, the variable (Pay Gap) is defined as the difference between the total compensation of the CEO (i.e., Execucomp data item TDC1) and that of the median VP in the firm. We construct this Pay Gap measure based on all VPs’ compensation and use it as the main tournament-incentive measure for the following reasons. First, this variable captures the potential increase in a VP’s salary if she wins the tournament and has been used as a popular proxy for tournament incentives (see, e.g., Main, O’Reilly, and Wade, 1993; Kale, Reis, and Venkateswaran, 2009; Kini and Williams, 2012). Second, although some firms have a specific VP responsible for R&D projects (i.e., chief technology officer, hereafter CTO), it is quite often that multiple VPs are involved in corporate innovation processes (De Meyer and Mizushima, 1989; Smith-Doerr, Manev, and Rizova, 2004).8 Third, even if some VPs are not directly involved in R&D decisions (e.g., VP of sales), they may have an indirect impact on corporate innovation activities. Prior studies show that peer pressure could induce agents to take greater risks (Nieken and Sliwka, 2010). If a VP of sales takes greater risks (e.g., implementing an aggressive marketing strategy) to gain advantage in a CEO-promotion contest, then VPs who are involved in R&D decisions may undertake riskier R&D projects as well due to peer influence. Therefore, we follow Kini and Williams (2012) to include all VPs in the Pay Gap measure construction. To control for the effects of CEOs’ performance-based incentives, we estimate the delta and vega of CEO compensation portfolios (CEO Delta and CEO Vega) by following Core and Guay (2002). CEO Delta measures the dollar change (in millions) in a CEO’s compensation portfolio if the stock price increases by 1%. CEO Vega measures the dollar change (in millions) in a CEO’s compensation portfolio if the stock return volatility increases by 1%. We also apply the same methods to compute delta and vega for VPs in a firm and use a firm’s median values of VPs’ delta and vega (i.e., VP Delta and VP Vega) as additional controls. Following Kini and Williams (2012), we adjust these executive compensation variables for inflation. 2.2 Firm Innovation Performance Measures Firm innovations are officially introduced to the public in the form of approved patents. Extant studies (Griliches, 1990; Hirshleifer, Hsu, and Li, 2013) argue that patent-related data can be used to construct direct measures of firms’ innovation performance. We obtain patent-related data from the 2006 edition of the NBER Patent Citations database. The database provides detailed information on all US patents granted by the US Patent and Trademark Office (USPTO) from January 1976 to December 2006, such as patent assignee names, the number of patents, the number of citations received by each patent, a patent’s application year as well as its grant year, etc. Patents are included in the database only if they are eventually granted by the USPTO before the end of 2006. The database covers over 3.2 million patent grants and 23.6 million patent citations from 1976 to 2006. Following prior studies (e.g., Almeida, Hsu, and Li, 2013), we use patent data recorded by the application year as a measure of innovation output. Specifically, firm i’s innovation output in year t can be measured as the number of patents applied for by firm i in year t that are eventually granted (denoted as Pati,t). Hall, Jaffe, and Trajtenberg (2001) point out that since the NBER dataset ends in 2006 and there is on average a 2-year period between patent application date and patent granting date, patents applied for in 2004 and 2005 may not be included in the dataset. Therefore, we limit our sample period to the pre-2003 period. Since patents that continuously generate citations are considered as innovations with higher quality (Trajtenberg, 1990), our second measure of innovation output is the total number of citations received by the patents (applied for by firm i in year t) from the application year until the last-coverage year of the NBER Patent Citations database. As discussed, the NBER Patent Citations database ends its coverage in 2006, therefore the patents granted in a year close to 2006 have less time to accumulate citations. To mitigate such a truncation bias, we follow Hall, Jaffe, and Trajtenberg (2005) and adjust the citation counts of each patent by multiplying them with a weighting index provided by the NBER Patent Citations database.9 In this study, we use the adjusted total number of citations eventually received by the patents applied for by firm i in year t as an additional measure of innovation output (denoted as Citei,t). Although patent grants and citation counts are good measures of innovation output, our goal is to measure the efficiency of R&D investment, which should capture the worthiness of financial resources spent on R&D activities. For example, a firm that has a large innovation output might still suffer from an overinvestment problem if the innovation output is not large enough to justify an even greater amount of R&D investment. Following Hirshleifer, Hsu, and Li (2013) and Almeida, Hsu, and Li (2013), we define innovative efficiency as the innovation output generated per million dollars of R&D expense (denoted by RD). Since it takes time for R&D investments to generate innovations that are ready for patent applications, we construct the innovative efficiency measures by combining a firm’s R&D expense in year t + 1 with its patenting in the subsequent 3 years. Specifically, we create 2 types of innovative efficiency measures: Pati,t + n/RDi,t + 1 is the aggregate number of patents that were applied for by firm i in year t + n (where n = 1, 2, or 3), scaled by the inflation-adjusted R&D expense in year t + 1 (in million dollars); Citei,t + n/RDi,t + 1 is the aggregate adjusted number of citations received by the patents applied for by firm i in year t + n (where n = 1, 2, or 3), scaled by the inflation-adjusted R&D expense in year t + 1 (in million dollars).10 2.3 Other Variables We also calculate the following variables for our regression analysis. CEO Tenure is the number of years that the current CEO has worked as a CEO in the firm, which is obtained from the Execucomp database. CEO Age is the age of a CEO in a specific year. For those observations with missing values of CEO Age in the Execucomp database, we manually collect this data by searching the CEO profiles online. CEO Tenure and CEO Age are added as controls, because they could be negatively related to the remaining years in CEOs’ contract terms (Xu, 2013) and could also be related to CEO power. Using data from Compustat database and Thomson Reuters Ownership database, we compute the following firm characteristic variables: Sale is the annual sales of a firm; Tobin’s q is the ratio of the market value of assets to the book value of assets; Sale Growth is the average of the sales growth rates over the past 3 years; Capex/Asset is the ratio of capital expenditure to total assets; PPE/EMP is the ratio of inflation-adjusted net property, plant, and equipment to the number of employees; Inst Own is the percentage of total shares outstanding held by institutional investors averaged over four quarters in a specific year; Leverage is the ratio of total debt to total assets; Cash Flow is the ratio of operating cash flow to total assets; Cash Flow Volatility is the standard deviation of Cash Flow in the past 3 years. 2.4 Sample Construction and Descriptive Statistics Our initial sample consists of all firms in the Compustat Execucomp database from 1993 to 2003. We exclude utility firms (SIC code 4900–4999) and financial firms (SIC code 6000–6999) due to their regulatory nature. We remove financial firms also because more than 90% of them have zero patents. We then eliminate observations without sufficient data in any of the following databases: Execucomp database, NBER Patent Citations database, Compustat Fundamentals Annual database, and Thomson Reuters Ownership (13f) database. To obtain meaningful estimates of the pay gap variable, we require that a firm must have at least three senior executives (VPs) with compensation data available in the Execucomp database for a given year. Following Kini and Williams (2012), we also drop the firm-year observations when there is a negative pay gap between a CEO and the median VP, and eliminate former CEOs who remain as an executive from the list of VPs when computing Pay Gap. Finally, we drop observations with missing information in some manually collected variables (e.g., CEO Age and Inside CEO). Our final study sample consists of 5,170 firm-year observations in the period 1993–2003. Panel A of Table I presents the breakdown of the sample size in the sample construction procedure. Table I. Sample selection and summary statistics Panel A describes the sample selection procedure. We start with firm-year observations from non-financial and non-utility firms in the Compustat Execucomp database from 1993 to 2003. We then eliminate observations that do not have necessary data available in the Compustat Execucomp database, the NBER Patent Citations database, the Compustat Fundamentals Annual database, the Thomson Reuters Ownership (13f) database, and the CRSP database. After applying several additional filters, the final study sample consists of 5,170 firm-year observations. Panel B presents the summary statistics for the sample. Panel A. Sample selection All firm-year observations from non-financial and non-utility firms in Execucomp from 1993 to 2003 15,871 After merging with Compustat, CRSP, and Thomson Reuters Ownership databases 15,789 After merging with NBER Patent Citations database 5,702 Requiring at least three VPs reported in Execucomp and a non-negative CEO–VP pay gap 5,372 Requiring non-missing information for manually collected variables, e.g., CEO Age and Inside CEO 5,170 Panel A. Sample selection All firm-year observations from non-financial and non-utility firms in Execucomp from 1993 to 2003 15,871 After merging with Compustat, CRSP, and Thomson Reuters Ownership databases 15,789 After merging with NBER Patent Citations database 5,702 Requiring at least three VPs reported in Execucomp and a non-negative CEO–VP pay gap 5,372 Requiring non-missing information for manually collected variables, e.g., CEO Age and Inside CEO 5,170 Panel B. Summary statistics Variable Mean SD Q1 Median Q3 Patt+1 43.388 108.101 1.000 6.000 30.000 Citet+1 637.351 1919.400 0.000 47.191 328.863 Patt+1/RDt+1 0.234 0.279 0.016 0.133 0.343 Citet+1/RDt+1 2.976 4.794 0.000 0.913 3.755 Pay Gapt (in million $) 1.084 1.100 0.375 0.752 1.417 CEO Deltat (in million $) 0.893 2.458 0.111 0.268 0.723 VP Deltat (in million $) 0.126 0.239 0.021 0.049 0.121 CEO Vegat (in million $) 0.154 0.275 0.023 0.062 0.163 VP Vegat (in million $) 0.035 0.058 0.007 0.015 0.038 CEO Aget 55.935 14.674 51.000 56.000 61.000 CEO Tenuret 6.628 7.470 1.000 4.000 9.000 Salet (in million $) 5196.9 10499.4 429.6 1315.1 4623.5 Tobin’s qt 2.511 2.126 1.367 1.827 2.820 Sale Growtht 0.166 0.277 0.024 0.096 0.218 (Capex/Assets)t 0.057 0.042 0.029 0.047 0.073 (PPE/EMP)t 99.531 139.286 36.939 58.989 106.366 Inst Ownt 0.601 0.189 0.487 0.627 0.738 Leveraget 0.195 0.171 0.038 0.186 0.300 Cash Flowt 0.095 0.118 0.057 0.102 0.149 Cash Flow Volatilityt 0.046 0.042 0.018 0.034 0.060 Panel B. Summary statistics Variable Mean SD Q1 Median Q3 Patt+1 43.388 108.101 1.000 6.000 30.000 Citet+1 637.351 1919.400 0.000 47.191 328.863 Patt+1/RDt+1 0.234 0.279 0.016 0.133 0.343 Citet+1/RDt+1 2.976 4.794 0.000 0.913 3.755 Pay Gapt (in million $) 1.084 1.100 0.375 0.752 1.417 CEO Deltat (in million $) 0.893 2.458 0.111 0.268 0.723 VP Deltat (in million $) 0.126 0.239 0.021 0.049 0.121 CEO Vegat (in million $) 0.154 0.275 0.023 0.062 0.163 VP Vegat (in million $) 0.035 0.058 0.007 0.015 0.038 CEO Aget 55.935 14.674 51.000 56.000 61.000 CEO Tenuret 6.628 7.470 1.000 4.000 9.000 Salet (in million $) 5196.9 10499.4 429.6 1315.1 4623.5 Tobin’s qt 2.511 2.126 1.367 1.827 2.820 Sale Growtht 0.166 0.277 0.024 0.096 0.218 (Capex/Assets)t 0.057 0.042 0.029 0.047 0.073 (PPE/EMP)t 99.531 139.286 36.939 58.989 106.366 Inst Ownt 0.601 0.189 0.487 0.627 0.738 Leveraget 0.195 0.171 0.038 0.186 0.300 Cash Flowt 0.095 0.118 0.057 0.102 0.149 Cash Flow Volatilityt 0.046 0.042 0.018 0.034 0.060 Table I. Sample selection and summary statistics Panel A describes the sample selection procedure. We start with firm-year observations from non-financial and non-utility firms in the Compustat Execucomp database from 1993 to 2003. We then eliminate observations that do not have necessary data available in the Compustat Execucomp database, the NBER Patent Citations database, the Compustat Fundamentals Annual database, the Thomson Reuters Ownership (13f) database, and the CRSP database. After applying several additional filters, the final study sample consists of 5,170 firm-year observations. Panel B presents the summary statistics for the sample. Panel A. Sample selection All firm-year observations from non-financial and non-utility firms in Execucomp from 1993 to 2003 15,871 After merging with Compustat, CRSP, and Thomson Reuters Ownership databases 15,789 After merging with NBER Patent Citations database 5,702 Requiring at least three VPs reported in Execucomp and a non-negative CEO–VP pay gap 5,372 Requiring non-missing information for manually collected variables, e.g., CEO Age and Inside CEO 5,170 Panel A. Sample selection All firm-year observations from non-financial and non-utility firms in Execucomp from 1993 to 2003 15,871 After merging with Compustat, CRSP, and Thomson Reuters Ownership databases 15,789 After merging with NBER Patent Citations database 5,702 Requiring at least three VPs reported in Execucomp and a non-negative CEO–VP pay gap 5,372 Requiring non-missing information for manually collected variables, e.g., CEO Age and Inside CEO 5,170 Panel B. Summary statistics Variable Mean SD Q1 Median Q3 Patt+1 43.388 108.101 1.000 6.000 30.000 Citet+1 637.351 1919.400 0.000 47.191 328.863 Patt+1/RDt+1 0.234 0.279 0.016 0.133 0.343 Citet+1/RDt+1 2.976 4.794 0.000 0.913 3.755 Pay Gapt (in million $) 1.084 1.100 0.375 0.752 1.417 CEO Deltat (in million $) 0.893 2.458 0.111 0.268 0.723 VP Deltat (in million $) 0.126 0.239 0.021 0.049 0.121 CEO Vegat (in million $) 0.154 0.275 0.023 0.062 0.163 VP Vegat (in million $) 0.035 0.058 0.007 0.015 0.038 CEO Aget 55.935 14.674 51.000 56.000 61.000 CEO Tenuret 6.628 7.470 1.000 4.000 9.000 Salet (in million $) 5196.9 10499.4 429.6 1315.1 4623.5 Tobin’s qt 2.511 2.126 1.367 1.827 2.820 Sale Growtht 0.166 0.277 0.024 0.096 0.218 (Capex/Assets)t 0.057 0.042 0.029 0.047 0.073 (PPE/EMP)t 99.531 139.286 36.939 58.989 106.366 Inst Ownt 0.601 0.189 0.487 0.627 0.738 Leveraget 0.195 0.171 0.038 0.186 0.300 Cash Flowt 0.095 0.118 0.057 0.102 0.149 Cash Flow Volatilityt 0.046 0.042 0.018 0.034 0.060 Panel B. Summary statistics Variable Mean SD Q1 Median Q3 Patt+1 43.388 108.101 1.000 6.000 30.000 Citet+1 637.351 1919.400 0.000 47.191 328.863 Patt+1/RDt+1 0.234 0.279 0.016 0.133 0.343 Citet+1/RDt+1 2.976 4.794 0.000 0.913 3.755 Pay Gapt (in million $) 1.084 1.100 0.375 0.752 1.417 CEO Deltat (in million $) 0.893 2.458 0.111 0.268 0.723 VP Deltat (in million $) 0.126 0.239 0.021 0.049 0.121 CEO Vegat (in million $) 0.154 0.275 0.023 0.062 0.163 VP Vegat (in million $) 0.035 0.058 0.007 0.015 0.038 CEO Aget 55.935 14.674 51.000 56.000 61.000 CEO Tenuret 6.628 7.470 1.000 4.000 9.000 Salet (in million $) 5196.9 10499.4 429.6 1315.1 4623.5 Tobin’s qt 2.511 2.126 1.367 1.827 2.820 Sale Growtht 0.166 0.277 0.024 0.096 0.218 (Capex/Assets)t 0.057 0.042 0.029 0.047 0.073 (PPE/EMP)t 99.531 139.286 36.939 58.989 106.366 Inst Ownt 0.601 0.189 0.487 0.627 0.738 Leveraget 0.195 0.171 0.038 0.186 0.300 Cash Flowt 0.095 0.118 0.057 0.102 0.149 Cash Flow Volatilityt 0.046 0.042 0.018 0.034 0.060 In Table I, Panel B presents descriptive statistics for the sample. The mean value of patent grants (Patt + 1) is 43 and its median value is 6. The mean value of citation counts (Citet + 1) is about 637 and its median value is around 47.11 With respect to the innovative efficiency measures, the mean values of Patt + 1/RDt + 1 and Citet + 1/RDt + 1 indicate that 1 million dollars of R&D investment, on average, generate 0.234 patents and 2.976 related patent citations. The statistics indicate that these patent and citation variables are skewed, and thus we use the logarithm transformation of these variables in our regressions to mitigate the impact of extreme values.12 The mean value of Pay Gap is $1.084 million, indicating that a CEO on average earns around 1 million dollars more than a non-CEO executive. The mean values of CEO Delta and CEO Vega are $0.893 million and $0.154 million, respectively. Panel B of Table I also presents the descriptive statistics of CEO characteristics and other firm characteristic variables. The average CEO Age is 56. The mean value of annual sales is about $5.2 billion. The average Tobin’s q is 2.511. The mean value of Capex/Asset is 0.057. Consistent with prior studies (e.g., Chung and Zhang, 2011), Panel B also shows that around 60% of the sample firms’ shares are held by institutional investors. The mean values of Cash Flow and Cash Flow Volatility are 0.095 and 0.046, respectively. 3. Tournament Incentives and Corporate Innovation This section presents the results of baseline regressions and several additional tests on the relation between tournament incentives and corporate innovative efficiency. 3.1. Baseline Regressions Kini and Williams (2012) show that greater tournament incentives induce senior executives to undertake greater R&D investments.13 However, they do not address the concern that the risk may be pursued at the expense of efficiency. It is possible that senior managers who face a high-prize tournament may over-invest in risky R&D projects (to increase their chance of winning the tournament) without adequate consideration of efficiency. This section answers the following empirical question: Are greater R&D investments induced by larger tournament incentives efficient or not? Specifically, we estimate the following baseline regression model: Ln(Pati,t+n/RDi,t+1) or Ln(Citei,t+n/RDi,t+1)=β0+β1Ln(Pay Gap)i,t+β2CEO Deltai,t+β3CEO Vegai,t+β4VP Deltai,t+β5VP Vegai,t+β6Ln(CEO Age)i,t+β7CEO Tenurei,t+β8Ln(Sale)i,t+β9Tobin’sqi,t+β10Sale Growthi,t+β11(Capex/Asset)i,t+β12Ln(PPE/EMP)i,t+β13Inst Owni,t+β14Leveragei,t+β15Cash Flowi,t+β16Cash Flow Volatilityi,t+Year Dummies+Industry Dummies+ɛi,t; (1) where Ln(Pati,t + n/RDi,t + 1) and Ln(Citei,t + n/RDi,t + 1) are the logarithm of the innovative efficiency measures as introduced in Section 2.2. Please refer to Appendix A and Section 2 for detailed information concerning other variables. Table II presents the results of the baseline model (1) based on ordinary least squares (OLS) regressions with firm-clustered, heteroskedasticity-robust standard errors.14 Table II. Tournament incentive and innovative efficiency Panel A presents the results of the baseline regressions. The dependent variables are the innovative efficiency measures. Panel B presents a modified specification of the baseline regression model, to which we add the following additional control variables: the governance index compiled by Gompers, Ishii, and Metrick (2003) with twenty-four IRRC anti-takeover provisions (G-index); a dummy variable (CEO Overconfidence) that equals one if the CEO of a firm is overconfident and zero otherwise, where we identify an overconfident CEO if this CEO holds stock options that are more than 100% in the money (Campbell et al., 2011); and Demerjian, Lev, and McVay’s (2012) managerial ability score measure (Managerial Ability). Due to the additional data requirements to compute these control variables, we have a smaller sample to conduct this robustness check. The variable definitions are provided in Appendix A. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at the firm level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Panel A: Tournament incentive and innovative efficiency Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.031* 0.039** 0.036** 0.117* 0.130** 0.118** (1.89) (2.36) (2.25) (1.80) (2.06) (1.97) CEO Deltat 0.001 0.001 0.000 0.005 0.005 −0.001 (0.74) (0.65) (0.05) (0.49) (0.54) (−0.06) CEO Vegat 0.035 0.019 0.010 0.099 0.054 0.042 (1.50) (0.88) (0.45) (1.11) (0.65) (0.57) VP Deltat −0.028 −0.015 −0.007 −0.051 −0.064 −0.036 (−1.39) (−0.76) (−0.32) (−0.59) (−0.76) (−0.41) VP Vegat −0.051 −0.011 0.020 −0.096 −0.066 −0.151 (−0.52) (−0.11) (0.18) (−0.23) (−0.16) (−0.40) Ln(CEO Age)t 0.045 0.043 0.015 −0.021 −0.030 −0.096 (1.05) (0.93) (0.32) (−0.12) (−0.17) (−0.55) CEO Tenuret 0.000 0.000 0.000 −0.001 −0.001 0.001 (−0.37) (−0.58) (−0.42) (−0.20) (−0.29) (0.18) Ln(Sale)t −0.005 −0.007 −0.006 0.027 0.026 0.025 (−1.03) (−1.42) (−1.17) (1.32) (1.31) (1.33) Tobin’s qt −0.001 −0.002 −0.004* 0.012 0.009 0.006 (−0.40) (−0.91) (−1.69) (1.19) (0.96) (0.64) Sale Growtht −0.019 −0.006 0.006 0.042 0.104* 0.115* (−1.44) (−0.40) (0.44) (0.74) (1.72) (1.89) (Capex/Assets)t 0.432*** 0.445*** 0.364*** 1.878*** 2.084*** 1.537*** (3.27) (3.24) (2.63) (3.43) (3.96) (3.06) Ln(PPE/EMP)t 0.021** 0.021** 0.019** 0.089** 0.069* 0.062* (2.24) (2.30) (2.15) (2.25) (1.84) (1.73) Inst Ownt −0.003 0.007 0.013 0.069 0.093 0.130 (−0.09) (0.22) (0.43) (0.56) (0.82) (1.23) Leveraget 0.041 0.019 −0.006 −0.036 −0.094 −0.145 (1.24) (0.63) (−0.19) (−0.29) (−0.82) (−1.32) Cash Flowt −0.024 0.021 0.054 −0.198 −0.032 0.095 (−0.59) (0.54) (1.24) (−1.24) (−0.21) (0.58) Cash Flow Volatilityt −0.208* −0.188* −0.126 −0.507 −0.415 −0.327 (−1.95) (−1.73) (−1.18) (−1.14) (−0.97) (−0.82) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.228 0.279 0.315 0.383 0.427 Panel A: Tournament incentive and innovative efficiency Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.031* 0.039** 0.036** 0.117* 0.130** 0.118** (1.89) (2.36) (2.25) (1.80) (2.06) (1.97) CEO Deltat 0.001 0.001 0.000 0.005 0.005 −0.001 (0.74) (0.65) (0.05) (0.49) (0.54) (−0.06) CEO Vegat 0.035 0.019 0.010 0.099 0.054 0.042 (1.50) (0.88) (0.45) (1.11) (0.65) (0.57) VP Deltat −0.028 −0.015 −0.007 −0.051 −0.064 −0.036 (−1.39) (−0.76) (−0.32) (−0.59) (−0.76) (−0.41) VP Vegat −0.051 −0.011 0.020 −0.096 −0.066 −0.151 (−0.52) (−0.11) (0.18) (−0.23) (−0.16) (−0.40) Ln(CEO Age)t 0.045 0.043 0.015 −0.021 −0.030 −0.096 (1.05) (0.93) (0.32) (−0.12) (−0.17) (−0.55) CEO Tenuret 0.000 0.000 0.000 −0.001 −0.001 0.001 (−0.37) (−0.58) (−0.42) (−0.20) (−0.29) (0.18) Ln(Sale)t −0.005 −0.007 −0.006 0.027 0.026 0.025 (−1.03) (−1.42) (−1.17) (1.32) (1.31) (1.33) Tobin’s qt −0.001 −0.002 −0.004* 0.012 0.009 0.006 (−0.40) (−0.91) (−1.69) (1.19) (0.96) (0.64) Sale Growtht −0.019 −0.006 0.006 0.042 0.104* 0.115* (−1.44) (−0.40) (0.44) (0.74) (1.72) (1.89) (Capex/Assets)t 0.432*** 0.445*** 0.364*** 1.878*** 2.084*** 1.537*** (3.27) (3.24) (2.63) (3.43) (3.96) (3.06) Ln(PPE/EMP)t 0.021** 0.021** 0.019** 0.089** 0.069* 0.062* (2.24) (2.30) (2.15) (2.25) (1.84) (1.73) Inst Ownt −0.003 0.007 0.013 0.069 0.093 0.130 (−0.09) (0.22) (0.43) (0.56) (0.82) (1.23) Leveraget 0.041 0.019 −0.006 −0.036 −0.094 −0.145 (1.24) (0.63) (−0.19) (−0.29) (−0.82) (−1.32) Cash Flowt −0.024 0.021 0.054 −0.198 −0.032 0.095 (−0.59) (0.54) (1.24) (−1.24) (−0.21) (0.58) Cash Flow Volatilityt −0.208* −0.188* −0.126 −0.507 −0.415 −0.327 (−1.95) (−1.73) (−1.18) (−1.14) (−0.97) (−0.82) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.228 0.279 0.315 0.383 0.427 Panel B. Additional control variables Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.034* 0.041** 0.038** 0.127* 0.145** 0.141** (1.95) (2.29) (2.17) (1.82) (2.11) (2.16) G-Indext 0.003 0.003 0.002 −0.004 −0.005 −0.004 (1.13) (0.98) (0.85) (−0.37) (−0.48) (−0.46) CEO Overconfidencet 0.009 0.017 0.011 0.088 0.072 0.062 (0.54) (0.87) (0.56) (1.06) (0.82) (0.77) Managerial Abilityt 0.036* 0.037* 0.044** 0.119 0.088 0.103 (1.65) (1.73) (2.10) (1.44) (1.11) (1.40) Other controls Yes Yes Yes Yes Yes Yes N 4,116 3,921 3,719 4,116 3,921 3,719 Adjusted R2 0.192 0.259 0.314 0.363 0.431 0.474 Panel B. Additional control variables Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.034* 0.041** 0.038** 0.127* 0.145** 0.141** (1.95) (2.29) (2.17) (1.82) (2.11) (2.16) G-Indext 0.003 0.003 0.002 −0.004 −0.005 −0.004 (1.13) (0.98) (0.85) (−0.37) (−0.48) (−0.46) CEO Overconfidencet 0.009 0.017 0.011 0.088 0.072 0.062 (0.54) (0.87) (0.56) (1.06) (0.82) (0.77) Managerial Abilityt 0.036* 0.037* 0.044** 0.119 0.088 0.103 (1.65) (1.73) (2.10) (1.44) (1.11) (1.40) Other controls Yes Yes Yes Yes Yes Yes N 4,116 3,921 3,719 4,116 3,921 3,719 Adjusted R2 0.192 0.259 0.314 0.363 0.431 0.474 Table II. Tournament incentive and innovative efficiency Panel A presents the results of the baseline regressions. The dependent variables are the innovative efficiency measures. Panel B presents a modified specification of the baseline regression model, to which we add the following additional control variables: the governance index compiled by Gompers, Ishii, and Metrick (2003) with twenty-four IRRC anti-takeover provisions (G-index); a dummy variable (CEO Overconfidence) that equals one if the CEO of a firm is overconfident and zero otherwise, where we identify an overconfident CEO if this CEO holds stock options that are more than 100% in the money (Campbell et al., 2011); and Demerjian, Lev, and McVay’s (2012) managerial ability score measure (Managerial Ability). Due to the additional data requirements to compute these control variables, we have a smaller sample to conduct this robustness check. The variable definitions are provided in Appendix A. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at the firm level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Panel A: Tournament incentive and innovative efficiency Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.031* 0.039** 0.036** 0.117* 0.130** 0.118** (1.89) (2.36) (2.25) (1.80) (2.06) (1.97) CEO Deltat 0.001 0.001 0.000 0.005 0.005 −0.001 (0.74) (0.65) (0.05) (0.49) (0.54) (−0.06) CEO Vegat 0.035 0.019 0.010 0.099 0.054 0.042 (1.50) (0.88) (0.45) (1.11) (0.65) (0.57) VP Deltat −0.028 −0.015 −0.007 −0.051 −0.064 −0.036 (−1.39) (−0.76) (−0.32) (−0.59) (−0.76) (−0.41) VP Vegat −0.051 −0.011 0.020 −0.096 −0.066 −0.151 (−0.52) (−0.11) (0.18) (−0.23) (−0.16) (−0.40) Ln(CEO Age)t 0.045 0.043 0.015 −0.021 −0.030 −0.096 (1.05) (0.93) (0.32) (−0.12) (−0.17) (−0.55) CEO Tenuret 0.000 0.000 0.000 −0.001 −0.001 0.001 (−0.37) (−0.58) (−0.42) (−0.20) (−0.29) (0.18) Ln(Sale)t −0.005 −0.007 −0.006 0.027 0.026 0.025 (−1.03) (−1.42) (−1.17) (1.32) (1.31) (1.33) Tobin’s qt −0.001 −0.002 −0.004* 0.012 0.009 0.006 (−0.40) (−0.91) (−1.69) (1.19) (0.96) (0.64) Sale Growtht −0.019 −0.006 0.006 0.042 0.104* 0.115* (−1.44) (−0.40) (0.44) (0.74) (1.72) (1.89) (Capex/Assets)t 0.432*** 0.445*** 0.364*** 1.878*** 2.084*** 1.537*** (3.27) (3.24) (2.63) (3.43) (3.96) (3.06) Ln(PPE/EMP)t 0.021** 0.021** 0.019** 0.089** 0.069* 0.062* (2.24) (2.30) (2.15) (2.25) (1.84) (1.73) Inst Ownt −0.003 0.007 0.013 0.069 0.093 0.130 (−0.09) (0.22) (0.43) (0.56) (0.82) (1.23) Leveraget 0.041 0.019 −0.006 −0.036 −0.094 −0.145 (1.24) (0.63) (−0.19) (−0.29) (−0.82) (−1.32) Cash Flowt −0.024 0.021 0.054 −0.198 −0.032 0.095 (−0.59) (0.54) (1.24) (−1.24) (−0.21) (0.58) Cash Flow Volatilityt −0.208* −0.188* −0.126 −0.507 −0.415 −0.327 (−1.95) (−1.73) (−1.18) (−1.14) (−0.97) (−0.82) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.228 0.279 0.315 0.383 0.427 Panel A: Tournament incentive and innovative efficiency Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.031* 0.039** 0.036** 0.117* 0.130** 0.118** (1.89) (2.36) (2.25) (1.80) (2.06) (1.97) CEO Deltat 0.001 0.001 0.000 0.005 0.005 −0.001 (0.74) (0.65) (0.05) (0.49) (0.54) (−0.06) CEO Vegat 0.035 0.019 0.010 0.099 0.054 0.042 (1.50) (0.88) (0.45) (1.11) (0.65) (0.57) VP Deltat −0.028 −0.015 −0.007 −0.051 −0.064 −0.036 (−1.39) (−0.76) (−0.32) (−0.59) (−0.76) (−0.41) VP Vegat −0.051 −0.011 0.020 −0.096 −0.066 −0.151 (−0.52) (−0.11) (0.18) (−0.23) (−0.16) (−0.40) Ln(CEO Age)t 0.045 0.043 0.015 −0.021 −0.030 −0.096 (1.05) (0.93) (0.32) (−0.12) (−0.17) (−0.55) CEO Tenuret 0.000 0.000 0.000 −0.001 −0.001 0.001 (−0.37) (−0.58) (−0.42) (−0.20) (−0.29) (0.18) Ln(Sale)t −0.005 −0.007 −0.006 0.027 0.026 0.025 (−1.03) (−1.42) (−1.17) (1.32) (1.31) (1.33) Tobin’s qt −0.001 −0.002 −0.004* 0.012 0.009 0.006 (−0.40) (−0.91) (−1.69) (1.19) (0.96) (0.64) Sale Growtht −0.019 −0.006 0.006 0.042 0.104* 0.115* (−1.44) (−0.40) (0.44) (0.74) (1.72) (1.89) (Capex/Assets)t 0.432*** 0.445*** 0.364*** 1.878*** 2.084*** 1.537*** (3.27) (3.24) (2.63) (3.43) (3.96) (3.06) Ln(PPE/EMP)t 0.021** 0.021** 0.019** 0.089** 0.069* 0.062* (2.24) (2.30) (2.15) (2.25) (1.84) (1.73) Inst Ownt −0.003 0.007 0.013 0.069 0.093 0.130 (−0.09) (0.22) (0.43) (0.56) (0.82) (1.23) Leveraget 0.041 0.019 −0.006 −0.036 −0.094 −0.145 (1.24) (0.63) (−0.19) (−0.29) (−0.82) (−1.32) Cash Flowt −0.024 0.021 0.054 −0.198 −0.032 0.095 (−0.59) (0.54) (1.24) (−1.24) (−0.21) (0.58) Cash Flow Volatilityt −0.208* −0.188* −0.126 −0.507 −0.415 −0.327 (−1.95) (−1.73) (−1.18) (−1.14) (−0.97) (−0.82) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.228 0.279 0.315 0.383 0.427 Panel B. Additional control variables Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.034* 0.041** 0.038** 0.127* 0.145** 0.141** (1.95) (2.29) (2.17) (1.82) (2.11) (2.16) G-Indext 0.003 0.003 0.002 −0.004 −0.005 −0.004 (1.13) (0.98) (0.85) (−0.37) (−0.48) (−0.46) CEO Overconfidencet 0.009 0.017 0.011 0.088 0.072 0.062 (0.54) (0.87) (0.56) (1.06) (0.82) (0.77) Managerial Abilityt 0.036* 0.037* 0.044** 0.119 0.088 0.103 (1.65) (1.73) (2.10) (1.44) (1.11) (1.40) Other controls Yes Yes Yes Yes Yes Yes N 4,116 3,921 3,719 4,116 3,921 3,719 Adjusted R2 0.192 0.259 0.314 0.363 0.431 0.474 Panel B. Additional control variables Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.034* 0.041** 0.038** 0.127* 0.145** 0.141** (1.95) (2.29) (2.17) (1.82) (2.11) (2.16) G-Indext 0.003 0.003 0.002 −0.004 −0.005 −0.004 (1.13) (0.98) (0.85) (−0.37) (−0.48) (−0.46) CEO Overconfidencet 0.009 0.017 0.011 0.088 0.072 0.062 (0.54) (0.87) (0.56) (1.06) (0.82) (0.77) Managerial Abilityt 0.036* 0.037* 0.044** 0.119 0.088 0.103 (1.65) (1.73) (2.10) (1.44) (1.11) (1.40) Other controls Yes Yes Yes Yes Yes Yes N 4,116 3,921 3,719 4,116 3,921 3,719 Adjusted R2 0.192 0.259 0.314 0.363 0.431 0.474 In Panel A of Table II, Columns 1–3 present the regressions of Ln(Pati,t + n/RDi,t + 1), while Columns 4–6 present the regressions of Ln(Citei,t + n/RDi,t + 1). The coefficients of Ln(Pay Gap) are all positive and consistently significant across all the regressions. Based on the coefficient of Ln(Pay Gap) in Column 1 of Table II, a 1% increase in Pay Gap raises Patt + 1/RDt + 1 by around 0.031%. It suggests that if a firm’s Pay Gap increases from the 25th percentile to the 75th percentile, then Patt + 1/RDt + 1 on average will increase by around 0.106.15 According to Hall, Jaffe, and Trajtenberg (2005), an extra patent per million dollars of R&D boosts a firm’s market value by about 2%. Since the average market value of equity in our sample is around $6,376 million, the 0.106 increase in Patt + 1/RDt + 1 translates into a $13.51 million (13.51 = 0.106×$6,376 × 2%) increase in market value. As such, the positive relation between tournament incentives and innovative efficiency is both statistically significant and economically meaningful. These results are consistent with the argument that greater tournament incentives induce managers to undertake more efficient R&D investments. They also complement prior studies on the bright side of the pay gap (e.g., Kale, Reis, and Venkateswaran, 2009) by shedding light on a new mechanism through which tournament incentives add value to companies. Panel A of Table II also presents the results on the relation between performance-based incentives and innovative efficiency. First, the effect of executive compensation delta on managerial risk-taking (e.g., innovative activities) is unclear in prior literature. On the one hand, John and John (1993) suggest that a higher delta increases the incentive of a manager to undertake risky projects and shift the risk to creditors. On the other hand, a higher delta increases the sensitivity of a manager’s wealth to firm performance, and consequently the risk-averse manager might trim down the risk exposure of the firm (Guay, 1999). Second, although Coles, Daniel, and Naveen (2006) find that CEO Vega is positively related to R&D investments, Shen and Zhang (2013) show that an excessively high vega might induce managers to overinvest in inefficient R&D projects. Therefore, a high executive compensation vega might not lead to greater innovative efficiency. Consistent with these mixed views, we find no significant relation between performance-based incentives and innovative efficiency measures. 3.2 Additional Control Variables An overconfident CEO may facilitate a centralized decision-making process, which could benefit the efficiency of corporate innovative activities (Boyd, 1995; Hirshleifer, Low, and Teoh, 2012). Nevertheless, overconfident CEOs are found to have mixed effects on investment efficiencies and firm value (Campbell et al., 2011). Additionally, anti-takeover provisions could enhance CEO power and lead to CEOs’ excess compensation (Borokhovich, Brunarski, and Parrino, 1997). Therefore, CEO overconfidence and anti-takeover provisions, as omitted variables, could confound our results. We identify an overconfident CEO if this CEO holds stock options that are more than 100% in the money (Campbell et al., 2011). CEO Overconfidence is a dummy variable that equals one if the CEO of a firm is overconfident and zero otherwise. We add CEO Overconfidence, Gompers, Ishii, and Metrick’s (2003) G-index, and Demerjian, Lev, and McVay’s (2012) managerial ability score (Managerial Ability) to the baseline model (1). For brevity, we only report the coefficients on Ln(Pay Gap) and these additional controls in Panel B of Table II. Sample attrition in these regressions is due to the additional data requirements for computing these additional controls. The coefficients on Managerial Ability are all positive, although they are only significant in the regressions of patent-based innovative efficiency measures. More importantly, the coefficients on Ln(Pay Gap) remain significantly positive. To the extent that these variables can isolate the effects of CEO power and the related factors, the finding suggests that tournament incentives have an incremental and positive effect on innovative efficiency.16 3.3 Alternative Measures of Firm Innovation We also conduct tests to examine whether our main finding is robust to alternative measures of firm innovation performance. Patents that cite other patents in dispersed technology classes are often believed to have greater “originality”; patents that are cited by patents in a dispersed array of technology classes are viewed as having greater “generality” (Hall, Jaffe, and Trajtenberg, 2001). The generality and originality indices devised by Hall, Jaffe, and Trajtenberg (2001) can capture the fundamental importance of the patents. We follow Lerner and Seru (2014) to scale the generality (originality) index by the average generality (originality) index of all patents granted in the same year and in the same technology class. We compute the firm-year level scaled generality index (Scaled General) by summing up the scaled generality index across all patents that were applied for by a firm during a year and were eventually granted. The scaled originality index (Scaled Origin) is computed in a similar way, except it refers to citations made. Panel A of Table III presents the modified baseline model (1) which uses these indices as alternative dependent variables. We find that the coefficients on the pay gap measure remain significantly positive. Table III. Alternative firm innovation measures Panel A presents the regressions using the generality and originality indices, and Panel B presents the regressions examining the relation between tournament incentives and stock market reactions to patent issuance. The generality index (General) for patent i is defined as 1−∑jnisij2, where sij denotes the percentage of citations received by patent i that belong to technological class j, and ni is the total number of technological classes. A high generality index indicates that a patent receives citations from a wide range of technological fields. The scaled generality index (Scaled General) for a patent is defined as the generality index of this patent scaled by the average generality index taken across all patents granted in the same year and technology class. We compute the firm-year level scaled generality index by summing up the scaled generality index across all patents that were applied for by a firm during a year and were eventually granted. The scaled originality index (Scaled Origin) is computed in a similar way, except it refers to citations made. A high originality index for a patent indicates that technologies from a wide range of fields are used to develop this particular patent. We estimate a modified version of the baseline regression model (1) in which the scaled generality index or scaled originality index is used as the dependent variable. We also add the R&D-to-asset ratio to control for the variation in corporate innovation input. Panel B presents the regressions of stock market reactions to patent grants. Following Kogan et al. (2017), we compute stock returns based on 3-day window (0, +2) and 5-day window (−1, +3) around patent issuance date, where day 0 is the patent issuance date. To obtain firm-year observations, we compute the average of the returns across all patents that were applied for by a firm during a year and were eventually granted. RET(0, +2) and RET(−1, +3) denote stock raw returns around patent issuance date based on 3-day window and 5-day window, respectively. CAR(0, +2) and CAR(−1, +3) denote market-adjusted abnormal returns around patent issuance dates, where CRSP value-weighted index returns are used as the benchmark. We then merge the data of stock returns around patent issuance dates with our main sample of firm-year observations and follow Chan, Martin, and Kensinger (1990) to estimate the following model: RETi,t+1(0,+2),CARi,t+1(0,+2),RETi,t+1(−1,+3),orCARi,t+1(−1,+3)=β0+β1Ln(Pay Gap)i,t+β2CEO Deltai,t+β3CEO Vegai,t+β4VP Deltai,t+β5VP Vegai,t+β6Ln(CEO Age)i,t+β7CEO Tenurei,t+β8MVEi,t+β9BMi,t+β10(RD/A)i,t+β11Conci,t+β12Leveragei,t+Year Dummies+Industry Dummies+ɛi,t, where RETi,t+1 and CARi,t+1 are the average stock raw returns and market-adjusted returns around the patent issuance dates for firm i in year t+1, respectively. MVE is the market value of equity for firm year i in year t, BM is the book-to-market ratio, RD/A is the R&D intensity measured as the R&D expense scaled by assets, Conc is industry concentration measured as the Herfindahl index computed as ∑isi2 in a given year, where si is firm i’s sales divided by the aggregate sales across all firms in the same three-digit SIC code industry that firm i belongs to. Other variables are defined in Section 2 and Appendix A. For brevity, both Panel A and Panel B only report the estimated coefficients on the pay gap measure. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at firm level. ***, **, and * denote significance at 1%, 5%, and 10% levels, respectively. Dependent variable = Dependent variable = Ln(Scaled Generalt+1) Ln(Scaled Generalt+2) Ln(Scaled Generalt+3) Ln(Scaled Origint+1) Ln(Scaled Origint+2) Ln(Scaled Origint+3) Panel A. Generality and originality indices Ln(Pay Gap)t 0.280** 0.238* 0.263* 0.246** 0.292** 0.350** (2.26) (1.70) (1.74) (2.06) (2.21) (2.54) Other controls Yes Yes Yes Yes Yes Yes N 3,262 2,744 2,272 4,022 3,470 2,945 Adjusted R2 0.542 0.544 0.542 0.537 0.541 0.541 Dependent variable = Dependent variable = Ln(Scaled Generalt+1) Ln(Scaled Generalt+2) Ln(Scaled Generalt+3) Ln(Scaled Origint+1) Ln(Scaled Origint+2) Ln(Scaled Origint+3) Panel A. Generality and originality indices Ln(Pay Gap)t 0.280** 0.238* 0.263* 0.246** 0.292** 0.350** (2.26) (1.70) (1.74) (2.06) (2.21) (2.54) Other controls Yes Yes Yes Yes Yes Yes N 3,262 2,744 2,272 4,022 3,470 2,945 Adjusted R2 0.542 0.544 0.542 0.537 0.541 0.541 Panel B. Stock market reaction to patent issuance RETt+1(0, +2) CARt+1(0, +2) RETt+1(−1, +3) CARt+1(−1, +3) Ln(Pay Gap)t 0.0020* 0.0021** 0.0031** 0.0029** (1.96) (2.12) (2.27) (2.47) Other controls Yes Yes Yes Yes N 4,151 4,151 4,151 4,151 Adjusted R2 0.025 0.027 0.034 0.039 Panel B. Stock market reaction to patent issuance RETt+1(0, +2) CARt+1(0, +2) RETt+1(−1, +3) CARt+1(−1, +3) Ln(Pay Gap)t 0.0020* 0.0021** 0.0031** 0.0029** (1.96) (2.12) (2.27) (2.47) Other controls Yes Yes Yes Yes N 4,151 4,151 4,151 4,151 Adjusted R2 0.025 0.027 0.034 0.039 Table III. Alternative firm innovation measures Panel A presents the regressions using the generality and originality indices, and Panel B presents the regressions examining the relation between tournament incentives and stock market reactions to patent issuance. The generality index (General) for patent i is defined as 1−∑jnisij2, where sij denotes the percentage of citations received by patent i that belong to technological class j, and ni is the total number of technological classes. A high generality index indicates that a patent receives citations from a wide range of technological fields. The scaled generality index (Scaled General) for a patent is defined as the generality index of this patent scaled by the average generality index taken across all patents granted in the same year and technology class. We compute the firm-year level scaled generality index by summing up the scaled generality index across all patents that were applied for by a firm during a year and were eventually granted. The scaled originality index (Scaled Origin) is computed in a similar way, except it refers to citations made. A high originality index for a patent indicates that technologies from a wide range of fields are used to develop this particular patent. We estimate a modified version of the baseline regression model (1) in which the scaled generality index or scaled originality index is used as the dependent variable. We also add the R&D-to-asset ratio to control for the variation in corporate innovation input. Panel B presents the regressions of stock market reactions to patent grants. Following Kogan et al. (2017), we compute stock returns based on 3-day window (0, +2) and 5-day window (−1, +3) around patent issuance date, where day 0 is the patent issuance date. To obtain firm-year observations, we compute the average of the returns across all patents that were applied for by a firm during a year and were eventually granted. RET(0, +2) and RET(−1, +3) denote stock raw returns around patent issuance date based on 3-day window and 5-day window, respectively. CAR(0, +2) and CAR(−1, +3) denote market-adjusted abnormal returns around patent issuance dates, where CRSP value-weighted index returns are used as the benchmark. We then merge the data of stock returns around patent issuance dates with our main sample of firm-year observations and follow Chan, Martin, and Kensinger (1990) to estimate the following model: RETi,t+1(0,+2),CARi,t+1(0,+2),RETi,t+1(−1,+3),orCARi,t+1(−1,+3)=β0+β1Ln(Pay Gap)i,t+β2CEO Deltai,t+β3CEO Vegai,t+β4VP Deltai,t+β5VP Vegai,t+β6Ln(CEO Age)i,t+β7CEO Tenurei,t+β8MVEi,t+β9BMi,t+β10(RD/A)i,t+β11Conci,t+β12Leveragei,t+Year Dummies+Industry Dummies+ɛi,t, where RETi,t+1 and CARi,t+1 are the average stock raw returns and market-adjusted returns around the patent issuance dates for firm i in year t+1, respectively. MVE is the market value of equity for firm year i in year t, BM is the book-to-market ratio, RD/A is the R&D intensity measured as the R&D expense scaled by assets, Conc is industry concentration measured as the Herfindahl index computed as ∑isi2 in a given year, where si is firm i’s sales divided by the aggregate sales across all firms in the same three-digit SIC code industry that firm i belongs to. Other variables are defined in Section 2 and Appendix A. For brevity, both Panel A and Panel B only report the estimated coefficients on the pay gap measure. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at firm level. ***, **, and * denote significance at 1%, 5%, and 10% levels, respectively. Dependent variable = Dependent variable = Ln(Scaled Generalt+1) Ln(Scaled Generalt+2) Ln(Scaled Generalt+3) Ln(Scaled Origint+1) Ln(Scaled Origint+2) Ln(Scaled Origint+3) Panel A. Generality and originality indices Ln(Pay Gap)t 0.280** 0.238* 0.263* 0.246** 0.292** 0.350** (2.26) (1.70) (1.74) (2.06) (2.21) (2.54) Other controls Yes Yes Yes Yes Yes Yes N 3,262 2,744 2,272 4,022 3,470 2,945 Adjusted R2 0.542 0.544 0.542 0.537 0.541 0.541 Dependent variable = Dependent variable = Ln(Scaled Generalt+1) Ln(Scaled Generalt+2) Ln(Scaled Generalt+3) Ln(Scaled Origint+1) Ln(Scaled Origint+2) Ln(Scaled Origint+3) Panel A. Generality and originality indices Ln(Pay Gap)t 0.280** 0.238* 0.263* 0.246** 0.292** 0.350** (2.26) (1.70) (1.74) (2.06) (2.21) (2.54) Other controls Yes Yes Yes Yes Yes Yes N 3,262 2,744 2,272 4,022 3,470 2,945 Adjusted R2 0.542 0.544 0.542 0.537 0.541 0.541 Panel B. Stock market reaction to patent issuance RETt+1(0, +2) CARt+1(0, +2) RETt+1(−1, +3) CARt+1(−1, +3) Ln(Pay Gap)t 0.0020* 0.0021** 0.0031** 0.0029** (1.96) (2.12) (2.27) (2.47) Other controls Yes Yes Yes Yes N 4,151 4,151 4,151 4,151 Adjusted R2 0.025 0.027 0.034 0.039 Panel B. Stock market reaction to patent issuance RETt+1(0, +2) CARt+1(0, +2) RETt+1(−1, +3) CARt+1(−1, +3) Ln(Pay Gap)t 0.0020* 0.0021** 0.0031** 0.0029** (1.96) (2.12) (2.27) (2.47) Other controls Yes Yes Yes Yes N 4,151 4,151 4,151 4,151 Adjusted R2 0.025 0.027 0.034 0.039 Although most studies (e.g., Hall, Jaffe, and Trajtenberg, 2005) find a positive relation between the private value and the scientific value of innovation (measured by patent-based metrics), we acknowledge that increases in innovative efficiency do not necessarily lead to greater shareholder value. Kogan et al. (2017) propose that economic value of each innovation can be estimated based on stock market reaction to patent grants. To investigate whether tournament incentive is positively related to economic value of firm innovation, we obtain the patent issuance-date data from Noah Stoffman’s website.17 Following Kogan et al. (2017), we compute the stock raw returns (RET) and market-adjusted returns (CAR) based on both 3-day window (0, +2) and 5-day window (−1, +3) around the patent issuance date, which is defined as day 0. Then, we compute the firm-year average of the stock returns across all patents that were applied for by a firm during a year, and merge these firm-year level return data with our main test sample to regress these return measures on the pay gap measure and other control variables. We present the detailed model specification and the regression results in Table III. We find that the coefficients on Ln(Pay Gap) are significantly positive across all the regressions in Panel B of Table III. The coefficient in Column 4 suggests that if a firm’s Pay Gap increases from the 25th percentile to the 75th percentile, the abnormal returns around the patent issuance dates on average will increase by around 0.39%.18 Such an increase translates into a $24.6 million (= $6,376 × 0.39%) increase in shareholder value, given that the average market value of equity in our sample is around $6,376 million. Overall, these results suggest that tournament incentives are positively related to corporate innovations with greater economic value to shareholders, providing direct evidence that tournament incentives induced by large pay gap increase firm value and shareholder wealth. In untabulated tests, we also find that our main findings are robust to alternative measures of tournament incentives, for example, CEO pay ratio (Burns, Minnick, and Starks, 2017). Additionally, an ancillary test shows that the pay gap between executives and lower-ranking employees is also significantly and positively related to innovative efficiency. Please refer to the Online Appendix of this paper for the results and detailed discussions. 3.4 Tournament Incentive Effect Prior to CEO Turnovers The tournament theory argues that employees are motivated by promotion opportunity and the associated higher pay to exert greater effort and take greater risks to increase their chances of being promoted (Lazear and Rosen, 1981; Hvide, 2002). So far, our results are in support of this theory. If the tournament theory is indeed the driving force behind this positive relation between CEO–VP pay gap and innovative efficiency, such a positive relation should be particularly pronounced when a succession contest is likely to occur, such as prior to CEO turnovers. For a specific firm in year t, we create a dummy variable (Bef_TOt) that equals one if a CEO turnover takes place during year t + 1 to year t + 5, and zero otherwise. About 49.3% of firm-year observations (out of the total 5,170 observations) are about to experience a CEO turnover within the next 5 years. We expand the baseline model (1) by adding Bef_TOt and its interaction term with Ln(Pay Gap).19 For brevity, Panel A of Table IV only reports the coefficients on the pay gap measure and the interaction variables. Consistent with our conjecture, the coefficients of the interaction term, Ln(Pay Gap)×Bef_TO, are all significantly positive. Table IV. Tournament incentive effect prior to CEO turnover This table presents the regression of innovative efficiency on tournament incentives. The dependent variables are the innovative efficiency measures. For a specific firm in year t, the indicator variable Bef_TOt equals one if there is a CEO turnover taking place during the period from year t+1 to year t+5, and zero otherwise. We expand the baseline regression model (1) by adding this dummy variable (Bef_TOt) and its interaction term with Ln(Pay Gap). Panel A presents the results of these regressions. In addition, we manually collect information to identify whether a new CEO is an insider or an outsider. Based on the hand-collected information, we create two dummy variables, Bef_Insider_TOt and Bef_Outsider_TOt. Bef_Insider_TOt equals one if an insider-CEO will be appointed during the period from year t+1 to year t+5, and zero otherwise; Bef_Outsider_TOt equals one if an outsider-CEO will be appointed during the period from year t+1 to year t+5, and zero otherwise. We modify the baseline regression model (1) by adding these two dummy variables (i.e., Bef_Inside_CEOt and Bef_Outside_CEOt) and their interaction terms with Ln(Pay Gap) and report the regression results in Panel B. In addition, we collect data to identify the potentially expected CEO turnover events based on these two criteria. In a given year t, a firm is classified as being prior to an “expected” CEO turnover if a CEO turnover takes place in the next 5 years and one of the following two conditions holds: (1) the incumbent CEO is more than 60 years old when she/he steps down, or (2) if the firm’s average industry-adjusted ROA across the past 3 years (years t to t−2) is below the sample median. Other firm-years that are about to experience CEO turnovers during the future 5 years are defined as those observations prior to “less-expected” CEO turnover events. We create two dummy variables to indicate the expected CEO turnovers and the less-expected CEO turnovers. For a specific firm in year t, Bef_Expected_TO equals one if the CEO turnover taking place during the period from years t+1 to t+5 is classified as an expected turnover, and zero otherwise; Bef_LessExpected_TO equals one if the CEO turnover taking place during the period from years t+1 to t+5 is classified as a less-expected turnover, and zero otherwise. We modify the baseline regression model (1) by adding these two dummies and their interaction terms with Ln(Pay Gap), and report the results in Panel C. For brevity, we only report the coefficients of the pay gap measure and its interaction terms. The definitions of other variables are provided in Appendix A. All regressions control for the two-digit SIC code industry effect, and year effect. t-Statistics are based on robust standard errors clustered at the firm level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Panel A. Tournament effect before CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.005 0.014 0.015 0.032 0.065 0.058 (0.27) (0.69) (0.69) (0.38) (0.86) (0.79) Ln(Pay Gap)t×Bef_TOt 0.048** 0.043** 0.037* 0.161** 0.127* 0.104 (2.44) (2.17) (1.82) (2.01) (1.89) (1.58) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.229 0.280 0.317 0.383 0.428 Panel A. Tournament effect before CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.005 0.014 0.015 0.032 0.065 0.058 (0.27) (0.69) (0.69) (0.38) (0.86) (0.79) Ln(Pay Gap)t×Bef_TOt 0.048** 0.043** 0.037* 0.161** 0.127* 0.104 (2.44) (2.17) (1.82) (2.01) (1.89) (1.58) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.229 0.280 0.317 0.383 0.428 Panel B. Tournament effect before insider-CEO turnover and outsider-CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.007 0.017 0.015 0.039 0.065 0.075* (0.37) (0.82) (0.72) (0.49) (1.43) (1.68) Ln(Pay Gap)t× Bef_Insider_TOt 0.053** 0.043** 0.040* 0.181** 0.134** 0.082 (2.37) (1.98) (1.84) (2.00) (2.34) (1.51) Ln(Pay Gap)t× Bef_Outsider_TOt 0.030 0.031 0.031 0.084 0.076 0.046 (1.17) (1.13) (1.10) (0.79) (1.10) (0.70) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.230 0.281 0.318 0.385 0.428 Panel B. Tournament effect before insider-CEO turnover and outsider-CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.007 0.017 0.015 0.039 0.065 0.075* (0.37) (0.82) (0.72) (0.49) (1.43) (1.68) Ln(Pay Gap)t× Bef_Insider_TOt 0.053** 0.043** 0.040* 0.181** 0.134** 0.082 (2.37) (1.98) (1.84) (2.00) (2.34) (1.51) Ln(Pay Gap)t× Bef_Outsider_TOt 0.030 0.031 0.031 0.084 0.076 0.046 (1.17) (1.13) (1.10) (0.79) (1.10) (0.70) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.230 0.281 0.318 0.385 0.428 Panel C. Tournament effect before expected and less-expected CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.008 0.015 0.015 0.032 0.056 0.073 (0.47) (0.70) (0.70) (0.39) (0.68) (0.87) Ln(Pay Gap)t× Bef_LessExpected_TOt 0.035** 0.031 0.020 0.110 0.071 0.014 (2.07) (1.32) (0.84) (1.12) (0.73) (0.14) Ln(Pay Gap)t× Bef_Expected_TOt 0.046*** 0.050** 0.045** 0.188** 0.169** 0.118 (2.81) (2.37) (2.19) (2.25) (2.03) (1.46) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.230 0.280 0.317 0.384 0.428 Panel C. Tournament effect before expected and less-expected CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.008 0.015 0.015 0.032 0.056 0.073 (0.47) (0.70) (0.70) (0.39) (0.68) (0.87) Ln(Pay Gap)t× Bef_LessExpected_TOt 0.035** 0.031 0.020 0.110 0.071 0.014 (2.07) (1.32) (0.84) (1.12) (0.73) (0.14) Ln(Pay Gap)t× Bef_Expected_TOt 0.046*** 0.050** 0.045** 0.188** 0.169** 0.118 (2.81) (2.37) (2.19) (2.25) (2.03) (1.46) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.230 0.280 0.317 0.384 0.428 Table IV. Tournament incentive effect prior to CEO turnover This table presents the regression of innovative efficiency on tournament incentives. The dependent variables are the innovative efficiency measures. For a specific firm in year t, the indicator variable Bef_TOt equals one if there is a CEO turnover taking place during the period from year t+1 to year t+5, and zero otherwise. We expand the baseline regression model (1) by adding this dummy variable (Bef_TOt) and its interaction term with Ln(Pay Gap). Panel A presents the results of these regressions. In addition, we manually collect information to identify whether a new CEO is an insider or an outsider. Based on the hand-collected information, we create two dummy variables, Bef_Insider_TOt and Bef_Outsider_TOt. Bef_Insider_TOt equals one if an insider-CEO will be appointed during the period from year t+1 to year t+5, and zero otherwise; Bef_Outsider_TOt equals one if an outsider-CEO will be appointed during the period from year t+1 to year t+5, and zero otherwise. We modify the baseline regression model (1) by adding these two dummy variables (i.e., Bef_Inside_CEOt and Bef_Outside_CEOt) and their interaction terms with Ln(Pay Gap) and report the regression results in Panel B. In addition, we collect data to identify the potentially expected CEO turnover events based on these two criteria. In a given year t, a firm is classified as being prior to an “expected” CEO turnover if a CEO turnover takes place in the next 5 years and one of the following two conditions holds: (1) the incumbent CEO is more than 60 years old when she/he steps down, or (2) if the firm’s average industry-adjusted ROA across the past 3 years (years t to t−2) is below the sample median. Other firm-years that are about to experience CEO turnovers during the future 5 years are defined as those observations prior to “less-expected” CEO turnover events. We create two dummy variables to indicate the expected CEO turnovers and the less-expected CEO turnovers. For a specific firm in year t, Bef_Expected_TO equals one if the CEO turnover taking place during the period from years t+1 to t+5 is classified as an expected turnover, and zero otherwise; Bef_LessExpected_TO equals one if the CEO turnover taking place during the period from years t+1 to t+5 is classified as a less-expected turnover, and zero otherwise. We modify the baseline regression model (1) by adding these two dummies and their interaction terms with Ln(Pay Gap), and report the results in Panel C. For brevity, we only report the coefficients of the pay gap measure and its interaction terms. The definitions of other variables are provided in Appendix A. All regressions control for the two-digit SIC code industry effect, and year effect. t-Statistics are based on robust standard errors clustered at the firm level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Panel A. Tournament effect before CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.005 0.014 0.015 0.032 0.065 0.058 (0.27) (0.69) (0.69) (0.38) (0.86) (0.79) Ln(Pay Gap)t×Bef_TOt 0.048** 0.043** 0.037* 0.161** 0.127* 0.104 (2.44) (2.17) (1.82) (2.01) (1.89) (1.58) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.229 0.280 0.317 0.383 0.428 Panel A. Tournament effect before CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.005 0.014 0.015 0.032 0.065 0.058 (0.27) (0.69) (0.69) (0.38) (0.86) (0.79) Ln(Pay Gap)t×Bef_TOt 0.048** 0.043** 0.037* 0.161** 0.127* 0.104 (2.44) (2.17) (1.82) (2.01) (1.89) (1.58) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.229 0.280 0.317 0.383 0.428 Panel B. Tournament effect before insider-CEO turnover and outsider-CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.007 0.017 0.015 0.039 0.065 0.075* (0.37) (0.82) (0.72) (0.49) (1.43) (1.68) Ln(Pay Gap)t× Bef_Insider_TOt 0.053** 0.043** 0.040* 0.181** 0.134** 0.082 (2.37) (1.98) (1.84) (2.00) (2.34) (1.51) Ln(Pay Gap)t× Bef_Outsider_TOt 0.030 0.031 0.031 0.084 0.076 0.046 (1.17) (1.13) (1.10) (0.79) (1.10) (0.70) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.230 0.281 0.318 0.385 0.428 Panel B. Tournament effect before insider-CEO turnover and outsider-CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.007 0.017 0.015 0.039 0.065 0.075* (0.37) (0.82) (0.72) (0.49) (1.43) (1.68) Ln(Pay Gap)t× Bef_Insider_TOt 0.053** 0.043** 0.040* 0.181** 0.134** 0.082 (2.37) (1.98) (1.84) (2.00) (2.34) (1.51) Ln(Pay Gap)t× Bef_Outsider_TOt 0.030 0.031 0.031 0.084 0.076 0.046 (1.17) (1.13) (1.10) (0.79) (1.10) (0.70) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.230 0.281 0.318 0.385 0.428 Panel C. Tournament effect before expected and less-expected CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.008 0.015 0.015 0.032 0.056 0.073 (0.47) (0.70) (0.70) (0.39) (0.68) (0.87) Ln(Pay Gap)t× Bef_LessExpected_TOt 0.035** 0.031 0.020 0.110 0.071 0.014 (2.07) (1.32) (0.84) (1.12) (0.73) (0.14) Ln(Pay Gap)t× Bef_Expected_TOt 0.046*** 0.050** 0.045** 0.188** 0.169** 0.118 (2.81) (2.37) (2.19) (2.25) (2.03) (1.46) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.230 0.280 0.317 0.384 0.428 Panel C. Tournament effect before expected and less-expected CEO turnover Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.008 0.015 0.015 0.032 0.056 0.073 (0.47) (0.70) (0.70) (0.39) (0.68) (0.87) Ln(Pay Gap)t× Bef_LessExpected_TOt 0.035** 0.031 0.020 0.110 0.071 0.014 (2.07) (1.32) (0.84) (1.12) (0.73) (0.14) Ln(Pay Gap)t× Bef_Expected_TOt 0.046*** 0.050** 0.045** 0.188** 0.169** 0.118 (2.81) (2.37) (2.19) (2.25) (2.03) (1.46) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.170 0.230 0.280 0.317 0.384 0.428 This finding suggests that the positive relation between tournament incentives and innovative efficiency is more pronounced prior to CEO turnovers, when a succession contest is likely to occur. Our tests are different from some recent studies on managerial myopia. Edmans, Fang, and Lewellen (2015) find that corporate R&D investment is negatively associated with the stock-price sensitivity of stocks and options that vest over the upcoming year, suggesting that managerial myopia stifles long-term investment. Xu (2013) and Gonzalez-Uribe and Groen-Xu (2015) find that CEO contract horizon, an inverse measure of managerial myopia, is positively related to R&Ds and innovation quality. Different from these studies, our study investigates the interaction effect of CEO succession contest on the positive relation between tournament incentives and firm innovation, and shows that such a positive relation is weaker when a CEO turnover will not take place in the near future (i.e., when a succession contest is less likely to occur). We also conduct two additional analyses on how the positive relation between tournament incentives and innovative efficiency varies when senior managers expect different levels of promotion probability. After a CEO turnover, the newly appointed CEO could be an insider (e.g., one of the VPs) or an outsider (e.g., an executive from another company). One would expect, with the assumption that ex-ante expectations of VPs are on average correct, that the effect of tournament incentives should be weaker in ex-post outsider-CEO turnover cases, ceteris paribus. In other words, if VPs expect that the board and/or major shareholders are likely to appoint an outsider-CEO and they have a low chance of getting a promotion, then the CEO–VP pay gap would only provide weak incentives to VPs. Consequently, we expect to observe a less significant effect of tournament incentives on innovative efficiency in this case. We hand-collect information to identify whether a newly appointed CEO is an insider (Inside CEO = 1) or an outsider. Then, we create two dummy variables: for a specific firm in year t, Bef_Insider_TO equals one if an insider-CEO will be appointed during year t + 1 to year t + 5, and zero otherwise; Bef_Outsider_TO equals one if an outsider-CEO will be appointed during year t + 1 to year t + 5, and zero otherwise. We add these two dummy variables and their interaction terms with Ln(Pay Gap) to the baseline model (1). Panel B of Table IV presents the regression results. Consistent with our conjecture, five out of the six coefficients on Ln(Pay Gap)×Bef_Insider_TO are significantly positive, while the coefficients on Ln(Pay Gap)×Bef_Outsider_TO are all positive but statistically insignificant. The results suggest that the stronger effect of Pay Gap on innovative efficiency during the period prior to CEO turnovers is especially pronounced when an insider-CEO is likely to be appointed. CEO-promotion tournaments would only take place when VPs expect the current CEO will step down. The positive relation between tournament incentives and innovative efficiency should be more significant when VPs expect a CEO turnover to occur in the foreseeable future. We conjecture that VPs would predict a relatively higher probability of CEO replacement in the following two scenarios: when the incumbent CEO is approaching retirement, and when the firm experiences below-average performance. Specifically, a firm in year t is classified as being prior to an “expected” CEO turnover if a CEO turnover takes place in the next 5 years and one of the following two conditions holds: (1) the incumbent CEO is older than 60 when she/he steps down, or (2) if the firm’s average industry-adjusted ROA in the past 3 years (years t to t−2) is below the sample median.20 Other firm-years that are about to experience CEO turnovers during the next 5 years are defined as those observations prior to “less-expected” CEO turnover.21 For a specific firm in year t, Bef_Expected_TO is a dummy variable that equals one if the CEO turnover taking place during the period from years t + 1 to t + 5 is classified as an expected turnover, and zero otherwise; Bef_LessExpected_TO equals one if the CEO turnover taking place during the period from years t + 1 to t + 5 is classified as a less-expected turnover, and zero otherwise. We modify the baseline regression model (1) by adding these two dummies and their interaction terms with Ln(Pay Gap). Panel C of Table IV shows that the coefficients on the interaction term, Ln(Pay Gap)×Bef_Expected_TO, are significantly positive in almost all the regressions. In contrast, the coefficients on the interaction term, Ln(Pay Gap)×Bef_LessExpected_TO, are all positive but only significant in one regression. Overall, we find that the positive relation between CEO-VP pay gap and innovative efficiency is particularly strong when VPs expect a CEO turnover will take place in a foreseeable future and when they expect a higher probability of being promoted. These tests provide fresh evidence to support the tournament theory. 3.5 Subsample Analysis So far, our findings indicate a significantly positive relation between tournament incentives and innovative efficiency. This subsection aims to examine whether the strength of such a positive relation varies across firms with different characteristics. Firms in innovative industries must produce a steady stream of innovations to survive and prosper in hyper-competitive technology markets (D’Aveni, 1994). To become qualified CEOs for firms in these innovative industries, senior managers must demonstrate their ability and ambition in identifying and maneuvering high-quality innovation projects during a CEO-promotion tournament.22 Thus, we expect that the positive relation between tournament incentives and innovative efficiency is more pronounced for firms in these industries. We follow Hirshleifer, Low, and Teoh (2012) to define a two-digit SIC code industry as an innovative one if the average adjusted citation count per patent of this industry during a year is above the median value of this variable across all industries during the same year.23 We create a dummy variable, High_Innov, that equals one if a firm is in an innovative industry and zero otherwise. We then add the High_Innov dummy and the interaction variable Ln(Pay Gap) × High_Innov to the baseline model (1). Panel A of Table V shows that the coefficients on Ln(Pay Gap) × High_Innov are all positive and significant, suggesting that the positive effect of tournament incentives on innovative efficiency is stronger within industries where technological advance is the key for firms to survive and remain competitive. Table V. Subsample analyses This table presents the differential effects of tournament incentives across subsamples. We define a two-digit SIC-code industry as an innovative one if the average-adjusted citation count per patent for this industry during a year is above the median value of this variable across all industries during the same year. We create a dummy variable, High_Innov, that is equal to one if a firm is in an innovative industry and zero otherwise. To conduct the subsample analysis, we modify the baseline model (1) by adding the High_Innov dummy variable and the interaction variable Ln(Pay Gap) × High_Innov to the baseline regression model (1). We report the results in Panel A. We also obtain family firm data from Anderson and Reeb (2004) and divide the sample into two subsamples: family firms and non-family firms. We then create a dummy variable, Family Firm, that equals one for a family firm, and zero otherwise. Then, we expand the baseline model (1) by adding the Family Firm dummy variable and the interaction variable Ln(Pay Gap) × Family Firm. We report the results in Panel B. We obtain board of director data from the IRRC Director Database and compute the percentage of insider directors in a board, where insider directors are defined as those who are executives of the focal firms or directors who are affiliated with the executives of the firm or have other contractual relations with the firm. We divide the sample into two subsamples: firms with above-median percentage of insider directors (i.e., badly governed firms) versus firms with below-median percentage of insider directors. To indicate these two subsamples, we create a dummy variable, High_Insider, that equals one if a firm’s percentage of insider directors is above the sample median, and zero otherwise. Then, we expand the baseline model (1) by adding the High_Insider dummy variable and the interaction variable Ln(Pay Gap) × High_Insider. We report the results in Panel C. For brevity, we only report the coefficient on the key independent variables, number of observations, and R-square in this table. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at the firm level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Panel A. Firms in innovative industries versus firms in non-innovative industries Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.015 0.020 0.011 0.041 0.055 0.034 (0.94) (1.32) (0.79) (0.72) (1.05) (0.70) Ln(Pay Gap)t×High_Innovt 0.033* 0.038** 0.049** 0.147* 0.146* 0.163** (1.81) (2.02) (2.44) (1.95) (1.86) (2.07) High_Innovt −0.008 −0.006 −0.010 0.049 0.068 0.043 (−0.49) (−0.36) (−0.63) (0.79) (1.07) (0.68) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.229 0.282 0.318 0.386 0.431 Panel A. Firms in innovative industries versus firms in non-innovative industries Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.015 0.020 0.011 0.041 0.055 0.034 (0.94) (1.32) (0.79) (0.72) (1.05) (0.70) Ln(Pay Gap)t×High_Innovt 0.033* 0.038** 0.049** 0.147* 0.146* 0.163** (1.81) (2.02) (2.44) (1.95) (1.86) (2.07) High_Innovt −0.008 −0.006 −0.010 0.049 0.068 0.043 (−0.49) (−0.36) (−0.63) (0.79) (1.07) (0.68) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.229 0.282 0.318 0.386 0.431 Panel B. Family firms versus non-family firms Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.092*** 0.112*** 0.102*** 0.323*** 0.342*** 0.361*** (3.83) (4.50) (3.99) (3.25) (3.24) (3.34) Ln(Pay Gap)t × Family Firmt −0.114** −0.101* −0.078 −0.470** −0.379* −0.350 (−2.23) (−1.86) (−1.41) (−2.12) (−1.73) (−1.47) Family Firmt 0.094** 0.089** 0.083* 0.293* 0.256 0.276 (2.21) (1.99) (1.84) (1.69) (1.45) (1.44) Other controls Yes Yes Yes Yes Yes Yes N 1,005 970 935 1,005 970 935 Adjusted R2 0.158 0.167 0.168 0.237 0.272 0.302 Panel B. Family firms versus non-family firms Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.092*** 0.112*** 0.102*** 0.323*** 0.342*** 0.361*** (3.83) (4.50) (3.99) (3.25) (3.24) (3.34) Ln(Pay Gap)t × Family Firmt −0.114** −0.101* −0.078 −0.470** −0.379* −0.350 (−2.23) (−1.86) (−1.41) (−2.12) (−1.73) (−1.47) Family Firmt 0.094** 0.089** 0.083* 0.293* 0.256 0.276 (2.21) (1.99) (1.84) (1.69) (1.45) (1.44) Other controls Yes Yes Yes Yes Yes Yes N 1,005 970 935 1,005 970 935 Adjusted R2 0.158 0.167 0.168 0.237 0.272 0.302 Panel C. Subsample analysis based on the percentage of insider directors Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.049** 0.043*** 0.036*** 0.152*** 0.138*** 0.127*** (2.30) (3.02) (3.13) (3.05) (2.84) (3.15) Ln(Pay Gap)t× High_Insidert −0.043* −0.020 −0.014 −0.131** −0.085 −0.082* (−1.84) (−1.16) (−1.38) (−2.35) (−1.48) (−1.81) High_Insidert 0.019 0.004 0.006 0.063 0.026 0.041 (1.11) (0.41) (0.56) (1.41) (0.63) (0.15) Other controls Yes Yes Yes Yes Yes Yes N 3,248 3,085 2,918 3,248 3,085 2,918 Adjusted R2 0.193 0.263 0.331 0.364 0.414 0.449 Panel C. Subsample analysis based on the percentage of insider directors Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.049** 0.043*** 0.036*** 0.152*** 0.138*** 0.127*** (2.30) (3.02) (3.13) (3.05) (2.84) (3.15) Ln(Pay Gap)t× High_Insidert −0.043* −0.020 −0.014 −0.131** −0.085 −0.082* (−1.84) (−1.16) (−1.38) (−2.35) (−1.48) (−1.81) High_Insidert 0.019 0.004 0.006 0.063 0.026 0.041 (1.11) (0.41) (0.56) (1.41) (0.63) (0.15) Other controls Yes Yes Yes Yes Yes Yes N 3,248 3,085 2,918 3,248 3,085 2,918 Adjusted R2 0.193 0.263 0.331 0.364 0.414 0.449 Table V. Subsample analyses This table presents the differential effects of tournament incentives across subsamples. We define a two-digit SIC-code industry as an innovative one if the average-adjusted citation count per patent for this industry during a year is above the median value of this variable across all industries during the same year. We create a dummy variable, High_Innov, that is equal to one if a firm is in an innovative industry and zero otherwise. To conduct the subsample analysis, we modify the baseline model (1) by adding the High_Innov dummy variable and the interaction variable Ln(Pay Gap) × High_Innov to the baseline regression model (1). We report the results in Panel A. We also obtain family firm data from Anderson and Reeb (2004) and divide the sample into two subsamples: family firms and non-family firms. We then create a dummy variable, Family Firm, that equals one for a family firm, and zero otherwise. Then, we expand the baseline model (1) by adding the Family Firm dummy variable and the interaction variable Ln(Pay Gap) × Family Firm. We report the results in Panel B. We obtain board of director data from the IRRC Director Database and compute the percentage of insider directors in a board, where insider directors are defined as those who are executives of the focal firms or directors who are affiliated with the executives of the firm or have other contractual relations with the firm. We divide the sample into two subsamples: firms with above-median percentage of insider directors (i.e., badly governed firms) versus firms with below-median percentage of insider directors. To indicate these two subsamples, we create a dummy variable, High_Insider, that equals one if a firm’s percentage of insider directors is above the sample median, and zero otherwise. Then, we expand the baseline model (1) by adding the High_Insider dummy variable and the interaction variable Ln(Pay Gap) × High_Insider. We report the results in Panel C. For brevity, we only report the coefficient on the key independent variables, number of observations, and R-square in this table. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at the firm level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Panel A. Firms in innovative industries versus firms in non-innovative industries Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.015 0.020 0.011 0.041 0.055 0.034 (0.94) (1.32) (0.79) (0.72) (1.05) (0.70) Ln(Pay Gap)t×High_Innovt 0.033* 0.038** 0.049** 0.147* 0.146* 0.163** (1.81) (2.02) (2.44) (1.95) (1.86) (2.07) High_Innovt −0.008 −0.006 −0.010 0.049 0.068 0.043 (−0.49) (−0.36) (−0.63) (0.79) (1.07) (0.68) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.229 0.282 0.318 0.386 0.431 Panel A. Firms in innovative industries versus firms in non-innovative industries Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.015 0.020 0.011 0.041 0.055 0.034 (0.94) (1.32) (0.79) (0.72) (1.05) (0.70) Ln(Pay Gap)t×High_Innovt 0.033* 0.038** 0.049** 0.147* 0.146* 0.163** (1.81) (2.02) (2.44) (1.95) (1.86) (2.07) High_Innovt −0.008 −0.006 −0.010 0.049 0.068 0.043 (−0.49) (−0.36) (−0.63) (0.79) (1.07) (0.68) Other controls Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.229 0.282 0.318 0.386 0.431 Panel B. Family firms versus non-family firms Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.092*** 0.112*** 0.102*** 0.323*** 0.342*** 0.361*** (3.83) (4.50) (3.99) (3.25) (3.24) (3.34) Ln(Pay Gap)t × Family Firmt −0.114** −0.101* −0.078 −0.470** −0.379* −0.350 (−2.23) (−1.86) (−1.41) (−2.12) (−1.73) (−1.47) Family Firmt 0.094** 0.089** 0.083* 0.293* 0.256 0.276 (2.21) (1.99) (1.84) (1.69) (1.45) (1.44) Other controls Yes Yes Yes Yes Yes Yes N 1,005 970 935 1,005 970 935 Adjusted R2 0.158 0.167 0.168 0.237 0.272 0.302 Panel B. Family firms versus non-family firms Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.092*** 0.112*** 0.102*** 0.323*** 0.342*** 0.361*** (3.83) (4.50) (3.99) (3.25) (3.24) (3.34) Ln(Pay Gap)t × Family Firmt −0.114** −0.101* −0.078 −0.470** −0.379* −0.350 (−2.23) (−1.86) (−1.41) (−2.12) (−1.73) (−1.47) Family Firmt 0.094** 0.089** 0.083* 0.293* 0.256 0.276 (2.21) (1.99) (1.84) (1.69) (1.45) (1.44) Other controls Yes Yes Yes Yes Yes Yes N 1,005 970 935 1,005 970 935 Adjusted R2 0.158 0.167 0.168 0.237 0.272 0.302 Panel C. Subsample analysis based on the percentage of insider directors Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.049** 0.043*** 0.036*** 0.152*** 0.138*** 0.127*** (2.30) (3.02) (3.13) (3.05) (2.84) (3.15) Ln(Pay Gap)t× High_Insidert −0.043* −0.020 −0.014 −0.131** −0.085 −0.082* (−1.84) (−1.16) (−1.38) (−2.35) (−1.48) (−1.81) High_Insidert 0.019 0.004 0.006 0.063 0.026 0.041 (1.11) (0.41) (0.56) (1.41) (0.63) (0.15) Other controls Yes Yes Yes Yes Yes Yes N 3,248 3,085 2,918 3,248 3,085 2,918 Adjusted R2 0.193 0.263 0.331 0.364 0.414 0.449 Panel C. Subsample analysis based on the percentage of insider directors Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.049** 0.043*** 0.036*** 0.152*** 0.138*** 0.127*** (2.30) (3.02) (3.13) (3.05) (2.84) (3.15) Ln(Pay Gap)t× High_Insidert −0.043* −0.020 −0.014 −0.131** −0.085 −0.082* (−1.84) (−1.16) (−1.38) (−2.35) (−1.48) (−1.81) High_Insidert 0.019 0.004 0.006 0.063 0.026 0.041 (1.11) (0.41) (0.56) (1.41) (0.63) (0.15) Other controls Yes Yes Yes Yes Yes Yes N 3,248 3,085 2,918 3,248 3,085 2,918 Adjusted R2 0.193 0.263 0.331 0.364 0.414 0.449 We also examine whether the relation between tournament incentives and innovative efficiency varies across family firms and non-family firms. Prior studies suggest that family firms might not have a succession contest, because one family member (e.g., the first male child of a family-member CEO) is often viewed as a natural successor (Bennedsen et al., 2007). In family firms, VPs expect a low probability of being promoted to be the next CEO, and the CEO-VP pay disparity should only give rise to weak tournament incentives. Using Anderson and Reeb’s (2004) family firm data, we create an indicator variable, Family Firm, that equals one for a family firm and zero otherwise.24 We expand the baseline model (1) by adding the Family Firm dummy and the interaction variable Ln(Pay Gap) × Family Firm. Panel B of Table V reports that the coefficients on Ln(Pay Gap) × Family Firm are negative in all six models and four of them are statistically significant, suggesting that the positive relation between Pay Gap and innovative efficiency is indeed weaker in family firms. Lastly, we investigate how corporate governance quality influences the positive relation between tournament incentives and innovative efficiency. As discussed, prior studies (e.g., Gilpatric, 2009) suggest that tournament incentives could induce managers to undertake risky but inefficient projects. To the extent that corporate governance can constrain opportunistic behaviors of managers, we expect that if a firm is poorly governed, then the aforementioned negative effect of tournament incentives would dominate and lead to a weaker or even muted relation between tournament incentives and innovative efficiency. We define ill-governed firms as those with a high percentage of insider directors. Using data from the Investor Responsibility Research Center (IRRC) Director database, we create a dummy variable, High_Insider, that equals one if a firm’s percentage of insider directors is above the sample median (i.e., ill-governed firms), and zero otherwise. We expand the baseline model (1) by adding the High_Insider dummy variable and the interaction variable Ln(Pay Gap) × High_Insider. Panel C of Table V shows that the coefficients on Ln(Pay Gap) remain significantly positive, while three out of the six coefficients on Ln(Pay Gap) × High_Inside are significantly negative. The findings suggest that the positive relation between tournament incentives and innovative efficiency is weaker in ill-governed firms, implying that corporate governance plays a role in curbing the detrimental effect of tournament incentives. Table VI. Instrumental-variable regressions This table presents the results of the instrumental-variable regression. We treat the pay gap measure as the endogenous variable. We use the industry median value of Ln(Pay Gap) as the instrument, where the industries are classified based on the three-digit SIC codes. When we compute the industry median values of the pay gap measure for a firm (i.e., Industry Ln(Pay Gap)), we exclude this specific firm from the computation and obtain the median values based on other firms in this industry. Column 1 presents the first-stage regressions, and Columns 2–7 present the second-stage regressions. This table also reports F-statistic of excluded instruments and Kleibergen–Paap Wald statistics. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at the industry level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. The first-stage regression The second-stage regressions Dependent variable Ln(Pay Gap)t Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.214*** 0.229*** 0.224** 0.527* 0.630** 0.652** (Instrumented) (2.62) (2.58) (2.56) (1.74) (2.06) (2.26) Industry Ln(Pay Gap)t 0.414*** (8.55) Ln(CEO Age)t 0.003* −0.001 −0.001 −0.001 −0.001 −0.002 −0.001 (1.93) (−0.74) (−0.86) (−0.80) (−0.39) (−0.59) (−0.30) CEO Tenuret 0.159** 0.005 0.001 −0.025 −0.116 −0.138 −0.206 (2.31) (0.13) (0.02) (−0.58) (−0.79) (−0.94) (−1.41) Ln(Sale)t 0.151*** −0.033** −0.037** −0.035** −0.033 −0.053 −0.063 (29.54) (−2.23) (−2.30) (−2.30) (−0.54) (−0.91) (−1.23) Tobin’s qt 0.015*** −0.004 −0.004 −0.007*** 0.007 0.002 −0.004 (3.30) (−1.20) (−1.51) (−2.66) (0.53) (0.19) (−0.43) Sale Growtht −0.079** −0.007 0.007 0.020 0.073 0.136* 0.151** (−2.31) (−0.32) (0.35) (1.00) (1.09) (1.84) (2.30) (Capex/Assets)t −0.364*** 0.492*** 0.504*** 0.416*** 2.000*** 2.241*** 1.697*** (−3.23) (4.23) (4.04) (3.89) (3.83) (3.91) (3.48) Ln(PPE/EMP)t 0.000 0.022* 0.023** 0.022** 0.092* 0.072 0.066 (0.00) (1.95) (2.15) (2.09) (1.78) (1.64) (1.58) Inst Ownt 0.095** −0.019 −0.009 −0.003 0.027 0.052 0.092 (2.18) (−0.62) (−0.30) (−0.09) (0.21) (0.41) (0.75) Leveraget −0.068 0.048 0.023 −0.002 −0.025 −0.083 −0.129 (−1.18) (1.31) (0.58) (−0.05) (−0.16) (−0.51) (−0.78) Cash Flowt −0.253** 0.015 0.062 0.096 −0.113 0.075 0.217 (−2.76) (0.41) (1.22) (1.48) (−0.88) (0.47) (1.16) Cash Flow Volatilityt 0.346** −0.251** −0.230* −0.167 −0.607 −0.524 −0.443 (2.77) (−2.36) (−1.82) (−1.38) (−1.31) (−1.05) (−1.08) Industry Effect Yes Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes Yes N 5,170 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.443 0.169 0.231 0.284 0.315 0.384 0.429 F-statistic of excluded instruments 73.161*** Kleibergen–Paap Wald F-statistic 73.161*** 73.714*** 80.641*** 73.161*** 73.714*** 80.641*** (10% Critical value of Stock–Yogo IV size test = 16.38) The first-stage regression The second-stage regressions Dependent variable Ln(Pay Gap)t Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.214*** 0.229*** 0.224** 0.527* 0.630** 0.652** (Instrumented) (2.62) (2.58) (2.56) (1.74) (2.06) (2.26) Industry Ln(Pay Gap)t 0.414*** (8.55) Ln(CEO Age)t 0.003* −0.001 −0.001 −0.001 −0.001 −0.002 −0.001 (1.93) (−0.74) (−0.86) (−0.80) (−0.39) (−0.59) (−0.30) CEO Tenuret 0.159** 0.005 0.001 −0.025 −0.116 −0.138 −0.206 (2.31) (0.13) (0.02) (−0.58) (−0.79) (−0.94) (−1.41) Ln(Sale)t 0.151*** −0.033** −0.037** −0.035** −0.033 −0.053 −0.063 (29.54) (−2.23) (−2.30) (−2.30) (−0.54) (−0.91) (−1.23) Tobin’s qt 0.015*** −0.004 −0.004 −0.007*** 0.007 0.002 −0.004 (3.30) (−1.20) (−1.51) (−2.66) (0.53) (0.19) (−0.43) Sale Growtht −0.079** −0.007 0.007 0.020 0.073 0.136* 0.151** (−2.31) (−0.32) (0.35) (1.00) (1.09) (1.84) (2.30) (Capex/Assets)t −0.364*** 0.492*** 0.504*** 0.416*** 2.000*** 2.241*** 1.697*** (−3.23) (4.23) (4.04) (3.89) (3.83) (3.91) (3.48) Ln(PPE/EMP)t 0.000 0.022* 0.023** 0.022** 0.092* 0.072 0.066 (0.00) (1.95) (2.15) (2.09) (1.78) (1.64) (1.58) Inst Ownt 0.095** −0.019 −0.009 −0.003 0.027 0.052 0.092 (2.18) (−0.62) (−0.30) (−0.09) (0.21) (0.41) (0.75) Leveraget −0.068 0.048 0.023 −0.002 −0.025 −0.083 −0.129 (−1.18) (1.31) (0.58) (−0.05) (−0.16) (−0.51) (−0.78) Cash Flowt −0.253** 0.015 0.062 0.096 −0.113 0.075 0.217 (−2.76) (0.41) (1.22) (1.48) (−0.88) (0.47) (1.16) Cash Flow Volatilityt 0.346** −0.251** −0.230* −0.167 −0.607 −0.524 −0.443 (2.77) (−2.36) (−1.82) (−1.38) (−1.31) (−1.05) (−1.08) Industry Effect Yes Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes Yes N 5,170 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.443 0.169 0.231 0.284 0.315 0.384 0.429 F-statistic of excluded instruments 73.161*** Kleibergen–Paap Wald F-statistic 73.161*** 73.714*** 80.641*** 73.161*** 73.714*** 80.641*** (10% Critical value of Stock–Yogo IV size test = 16.38) Table VI. Instrumental-variable regressions This table presents the results of the instrumental-variable regression. We treat the pay gap measure as the endogenous variable. We use the industry median value of Ln(Pay Gap) as the instrument, where the industries are classified based on the three-digit SIC codes. When we compute the industry median values of the pay gap measure for a firm (i.e., Industry Ln(Pay Gap)), we exclude this specific firm from the computation and obtain the median values based on other firms in this industry. Column 1 presents the first-stage regressions, and Columns 2–7 present the second-stage regressions. This table also reports F-statistic of excluded instruments and Kleibergen–Paap Wald statistics. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at the industry level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. The first-stage regression The second-stage regressions Dependent variable Ln(Pay Gap)t Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.214*** 0.229*** 0.224** 0.527* 0.630** 0.652** (Instrumented) (2.62) (2.58) (2.56) (1.74) (2.06) (2.26) Industry Ln(Pay Gap)t 0.414*** (8.55) Ln(CEO Age)t 0.003* −0.001 −0.001 −0.001 −0.001 −0.002 −0.001 (1.93) (−0.74) (−0.86) (−0.80) (−0.39) (−0.59) (−0.30) CEO Tenuret 0.159** 0.005 0.001 −0.025 −0.116 −0.138 −0.206 (2.31) (0.13) (0.02) (−0.58) (−0.79) (−0.94) (−1.41) Ln(Sale)t 0.151*** −0.033** −0.037** −0.035** −0.033 −0.053 −0.063 (29.54) (−2.23) (−2.30) (−2.30) (−0.54) (−0.91) (−1.23) Tobin’s qt 0.015*** −0.004 −0.004 −0.007*** 0.007 0.002 −0.004 (3.30) (−1.20) (−1.51) (−2.66) (0.53) (0.19) (−0.43) Sale Growtht −0.079** −0.007 0.007 0.020 0.073 0.136* 0.151** (−2.31) (−0.32) (0.35) (1.00) (1.09) (1.84) (2.30) (Capex/Assets)t −0.364*** 0.492*** 0.504*** 0.416*** 2.000*** 2.241*** 1.697*** (−3.23) (4.23) (4.04) (3.89) (3.83) (3.91) (3.48) Ln(PPE/EMP)t 0.000 0.022* 0.023** 0.022** 0.092* 0.072 0.066 (0.00) (1.95) (2.15) (2.09) (1.78) (1.64) (1.58) Inst Ownt 0.095** −0.019 −0.009 −0.003 0.027 0.052 0.092 (2.18) (−0.62) (−0.30) (−0.09) (0.21) (0.41) (0.75) Leveraget −0.068 0.048 0.023 −0.002 −0.025 −0.083 −0.129 (−1.18) (1.31) (0.58) (−0.05) (−0.16) (−0.51) (−0.78) Cash Flowt −0.253** 0.015 0.062 0.096 −0.113 0.075 0.217 (−2.76) (0.41) (1.22) (1.48) (−0.88) (0.47) (1.16) Cash Flow Volatilityt 0.346** −0.251** −0.230* −0.167 −0.607 −0.524 −0.443 (2.77) (−2.36) (−1.82) (−1.38) (−1.31) (−1.05) (−1.08) Industry Effect Yes Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes Yes N 5,170 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.443 0.169 0.231 0.284 0.315 0.384 0.429 F-statistic of excluded instruments 73.161*** Kleibergen–Paap Wald F-statistic 73.161*** 73.714*** 80.641*** 73.161*** 73.714*** 80.641*** (10% Critical value of Stock–Yogo IV size test = 16.38) The first-stage regression The second-stage regressions Dependent variable Ln(Pay Gap)t Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.214*** 0.229*** 0.224** 0.527* 0.630** 0.652** (Instrumented) (2.62) (2.58) (2.56) (1.74) (2.06) (2.26) Industry Ln(Pay Gap)t 0.414*** (8.55) Ln(CEO Age)t 0.003* −0.001 −0.001 −0.001 −0.001 −0.002 −0.001 (1.93) (−0.74) (−0.86) (−0.80) (−0.39) (−0.59) (−0.30) CEO Tenuret 0.159** 0.005 0.001 −0.025 −0.116 −0.138 −0.206 (2.31) (0.13) (0.02) (−0.58) (−0.79) (−0.94) (−1.41) Ln(Sale)t 0.151*** −0.033** −0.037** −0.035** −0.033 −0.053 −0.063 (29.54) (−2.23) (−2.30) (−2.30) (−0.54) (−0.91) (−1.23) Tobin’s qt 0.015*** −0.004 −0.004 −0.007*** 0.007 0.002 −0.004 (3.30) (−1.20) (−1.51) (−2.66) (0.53) (0.19) (−0.43) Sale Growtht −0.079** −0.007 0.007 0.020 0.073 0.136* 0.151** (−2.31) (−0.32) (0.35) (1.00) (1.09) (1.84) (2.30) (Capex/Assets)t −0.364*** 0.492*** 0.504*** 0.416*** 2.000*** 2.241*** 1.697*** (−3.23) (4.23) (4.04) (3.89) (3.83) (3.91) (3.48) Ln(PPE/EMP)t 0.000 0.022* 0.023** 0.022** 0.092* 0.072 0.066 (0.00) (1.95) (2.15) (2.09) (1.78) (1.64) (1.58) Inst Ownt 0.095** −0.019 −0.009 −0.003 0.027 0.052 0.092 (2.18) (−0.62) (−0.30) (−0.09) (0.21) (0.41) (0.75) Leveraget −0.068 0.048 0.023 −0.002 −0.025 −0.083 −0.129 (−1.18) (1.31) (0.58) (−0.05) (−0.16) (−0.51) (−0.78) Cash Flowt −0.253** 0.015 0.062 0.096 −0.113 0.075 0.217 (−2.76) (0.41) (1.22) (1.48) (−0.88) (0.47) (1.16) Cash Flow Volatilityt 0.346** −0.251** −0.230* −0.167 −0.607 −0.524 −0.443 (2.77) (−2.36) (−1.82) (−1.38) (−1.31) (−1.05) (−1.08) Industry Effect Yes Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes Yes N 5,170 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.443 0.169 0.231 0.284 0.315 0.384 0.429 F-statistic of excluded instruments 73.161*** Kleibergen–Paap Wald F-statistic 73.161*** 73.714*** 80.641*** 73.161*** 73.714*** 80.641*** (10% Critical value of Stock–Yogo IV size test = 16.38) Taken together, the subsample tests in Table V suggest that not every company should provide executives with high CEO-VP pay gap as a means to incentivize firm innovation. Specifically, tournament incentives appear to have less beneficial effects on innovation for family firms, ill-governed firms, and firms in non-innovative industries. 4. Additional Tests This section discusses the results of additional tests on the relation between tournament incentives and innovative efficiency. 4.1 Instrumental Variable Approach It is likely that board of directors take into account innovation performance when they determine managers’ compensation (Balkin, Markman, and Gomez-Mejia, 2000; Aghion et al., 2016; Frydman and Papanikolaou, 2016). This suggests a potential feedback effect (i.e., reverse causality) from corporate innovation performance to executive compensation variables, including the CEO–VP pay gap. To mitigate this endogeneity concern, our baseline model (1) examines the lead-lag relation between tournament incentives and innovative efficiency by using key independent variable (i.e., tournament incentives) with at least 1-year lag in relation to the dependent variables (i.e., the innovation measures). To further account for the endogeneity issue, we use a just-identified instrumental-variable regression model, in which we treat the Pay Gap measure as an endogenous variable and choose the industry median value of Pay Gap as the instrumental variable.25 Murphy (1999) finds that the level and structure of managerial compensation vary by industry. Other prior studies (e.g., Faulkender and Yang, 2010) find that many firms use peer firms from the same industry as the benchmark to determine executive compensation in order to offer competitive pay to attract and retain capable managers. Faulkender and Yang (2010) find that a significant percentage of peer-group firms are drawn from the same three-digit SIC industry. The preceding discussions suggest that an individual firm is likely to be a “compensation-taker”, in the sense that a firm likely adjusts its executive pay when its peer-group firms change their compensation policies (DiPrete, Eirich, and Pittinsky, 2010). Consequently, changes in executive pay of a given firm are influenced by changes in executive compensation of its industry peers across time. As such, the industry-level pay gap should be a significant and exogenous determinant of individual firm’s pay gap, and thus is a relevant instrument. We operationalize this industry-level pay gap notion by defining it as the industry median value of the pay gap variable from peer firms in the same three-digit SIC industry. When we compute the industry median value of the pay gap variable for a specific firm, we exclude this firm’s own Pay Gap from the computation. We denote this instrumental variable as Industry Ln(Pay Gap). A valid instrument can only affect the dependent variable of the second-stage regression through its effect on the endogenous variable. We believe that our instrument, the industry-level median Pay Gap measure, satisfies this exclusion restriction. As discussed, industry-level pay gap can directly influence an individual firm’s Pay Gap because of the practice of compensation benchmarking with industry peers; however, it is unlikely that the firm’s innovation efficiency is directly affected by the pay gap of other firms. This conjecture is confirmed by a thorough literature review in which we explore whether there is any prior theoretical argument or empirical evidence showing a direct linkage between industry-level pay gap and firm-level innovative performance. We find no prior studies indicating such a direct link. In the first-stage regression, we regress Ln(Pay Gap) on the instrumental variable, Industry Ln(Pay Gap), and all other control variables in the second-stage regression. In Table VI, Column 1 reports the first-stage regression results.26 Consistent with our expectation, the coefficient of the instrument, Industry Ln(Pay Gap), is significantly positive. Stock and Yogo (2005) explain that weak instruments could lead to biased instrumental-variable estimators. To mitigate this weak-instrument concern, we report F-statistic of excluded instrument in Column 1. The F-statistic exceeds 10 and rejects the null hypothesis that the instrumental variable is weak (Staiger and Stock, 1997). Columns 2–7 in Table VI report the results of the second-stage regressions as well as the Kleibergen–Paap statistics (Baum, Schaffer, and Stillman, 2007). These Kleibergen–Paap statistics are all greater than the 10% critical value derived from Stock–Yogo’s test, confirming that the instrumental variable is not weak. The coefficients of instrumented Ln(Pay Gap) in Columns 2–7 are all positive and statistically significant, indicating that the positive relation between tournament incentives and innovative efficiency is robust after further controlling for the potential endogeneity problem. We notice that the coefficients on instrumented Ln(Pay Gap) are greater than the coefficients on Ln(Pay Gap) in Panel A of Table II. This could be partly due to the fact that the instrumental-variable estimate in Table VI identifies the local average treatment effect (LATE). According to Angrist and Pischke (2008), the sample can be divided into three subgroups: the firms that always provide high pay gap (i.e., always-takers), the firms that never provide high pay gap (i.e., never-takers), and the firms in which the design of pay gap is sensitive to the instruments (i.e., compliers). Angrist and Pischke (2008) argue that the LATE identified by the instrumental-variable estimate mainly captures the causal effect on the compliers, rather than the effects on the always-takers and the never-takers. For example, the never-takers have already realized that a large pay gap is not an effective incentive mechanism for them to induce better innovation performance, therefore the instrumental-variable analysis is less likely to capture the weaker effect of instrument among the never-takers. Taken together, since the LATE identified by the instrumental-variable estimate mainly captures the stronger effect for compliers, we observe the greater coefficients on the instrumented pay gap measure in Table VI.27 As discussed, it is unlikely that the instrumental variable, industry median value of Pay Gap, is associated with innovative efficiency in any way other than through its influence on individual firm’s Pay Gap. However, this exclusion restriction could be violated if some omitted variables cause a correlation between industry median pay gap and firm-level innovative efficiency (Paul, Ni, and Bagchi, 2014). Such a possible violation of exclusion restriction poses a threat to the identification of our instrumental-variable analysis. Thus, one should interpret the results in Table VI with caution when drawing causal inference from them. To further mitigate the endogeneity concern, we conduct a propensity-score matched sample analysis in the next section. 4.2 Propensity-Score Matched Sample We conduct regression analysis on a propensity-score matched sample, in which treatment firms with high tournament incentives are matched with control firms with low tournament incentives, to control for the endogeneity issue due to systematic differences in firm characteristics across these two subgroups (Lawrence, Minutti-Meza, and Zhang, 2011). To construct the matched sample, we first estimate the following Probit regression: the dependent variable is High Pay Gap, which is coded one if a firm’s Pay Gap is above the 70th percentile in a given year, and zero if a firm’s Pay Gap is below the 30th percentile; and the independent variables include all the explanatory variables in the first-stage regression of the instrumental-variable analysis (i.e., including both instrumental and control variables of the first-stage regression in Table VI). This generates a predicted probability of being a high-pay-gap firm for each observation. Second, we match, with replacement, each treatment (a firm with high pay gap) with a matching firm (a firm with low pay gap) having the closest propensity score, using a caliper—the difference in the predicted probabilities between treatment and control observations—of 1%. This procedure results in a matched sample consisting of 1,425 matched pairs (2,850 observations). Using the matched sample, we estimate a modified version of the baseline regressions, in which the key independent variable is a dummy variable, High Pay Gap. Table VII shows that the coefficients on High Pay Gap are all positive and statistically significant. These results further mitigate the endogeneity concern and corroborate the earlier evidence. Table VII. Regressions using a propensity-score matched sample This table presents the estimates of baseline regressions using a propensity-score matched sample. To construct this matched sample, we first estimate the following Probit regression: the dependent variable (High Pay Gap) is coded one if a firm’s Pay Gap is above 70th percentile in a given year, and zero if a firm’s Pay Gap is below 30th percentile; the independent variables include all the explanatory variables in the first-stage regression of the instrumental-variable analysis. This generates a predicted probability of being a high-Pay-Gap firm for each observation. We then match, with replacement, each treatment firm (a firm with high pay gap) with a matching firm (a firm with low pay gap) having the closest propensity score, using a caliper—the difference in the predicted probabilities between treatment and control observations—of 1%. This procedure results in a matched sample consisting of 1,425 matched pairs (2,850 observations). The variable definitions are provided in Appendix A. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at the firm level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) High Pay Gapt 0.037** 0.041** 0.037** 0.187*** 0.206*** 0.178*** (2.16) (2.21) (2.07) (2.63) (2.91) (2.95) Ln(CEO Age)t 0.050 0.062 0.028 −0.180 −0.136 −0.166 (0.78) (0.95) (0.43) (−0.68) (−0.56) (−0.76) CEO Tenuret −0.001 −0.001 −0.002 −0.003 −0.003 −0.006 (−0.98) (−0.94) (−1.43) (−0.58) (−0.68) (−1.40) Ln(Sale)t −0.014** −0.015** −0.017** −0.014 −0.014 −0.031 (−2.01) (−2.08) (−2.55) (−0.48) (−0.49) (−1.29) Tobin’s qt −0.007 −0.010** −0.013*** −0.008 −0.018 −0.027** (−1.63) (−2.06) (−3.27) (−0.35) (−0.90) (−1.99) Sale Growtht −0.097** −0.027 0.015 0.009 0.174 0.191 (−2.30) (−0.64) (0.35) (0.05) (0.93) (1.16) (Capex/Assets)t 0.554** 0.571** 0.350 2.780*** 3.134*** 2.157** (2.22) (2.15) (1.36) (2.76) (3.06) (2.39) Ln(PPE/EMP)t 0.029** 0.033** 0.037*** 0.126** 0.100* 0.092* (1.98) (2.21) (2.70) (2.06) (1.71) (1.83) Inst Ownt −0.011 0.023 0.015 −0.037 0.064 0.027 (−0.22) (0.46) (0.30) (−0.20) (0.37) (0.16) Leveraget −0.023 −0.009 −0.019 −0.191 −0.173 −0.209 (−0.38) (−0.14) (−0.32) (−0.85) (−0.78) (−1.08) Cash Flowt 0.130 0.133 0.232** 0.540 0.308 0.677* (1.05) (1.33) (2.49) (1.15) (0.71) (1.93) Cash Flow Volatilityt −0.109 −0.155 −0.134 0.221 0.653 −0.207 (−0.51) (−0.74) (−0.71) (0.25) (0.75) (−0.31) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 2,850 2,748 2,598 2,850 2,748 2,598 Adjusted R2 0.253 0.332 0.382 0.459 0.502 0.548 Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) High Pay Gapt 0.037** 0.041** 0.037** 0.187*** 0.206*** 0.178*** (2.16) (2.21) (2.07) (2.63) (2.91) (2.95) Ln(CEO Age)t 0.050 0.062 0.028 −0.180 −0.136 −0.166 (0.78) (0.95) (0.43) (−0.68) (−0.56) (−0.76) CEO Tenuret −0.001 −0.001 −0.002 −0.003 −0.003 −0.006 (−0.98) (−0.94) (−1.43) (−0.58) (−0.68) (−1.40) Ln(Sale)t −0.014** −0.015** −0.017** −0.014 −0.014 −0.031 (−2.01) (−2.08) (−2.55) (−0.48) (−0.49) (−1.29) Tobin’s qt −0.007 −0.010** −0.013*** −0.008 −0.018 −0.027** (−1.63) (−2.06) (−3.27) (−0.35) (−0.90) (−1.99) Sale Growtht −0.097** −0.027 0.015 0.009 0.174 0.191 (−2.30) (−0.64) (0.35) (0.05) (0.93) (1.16) (Capex/Assets)t 0.554** 0.571** 0.350 2.780*** 3.134*** 2.157** (2.22) (2.15) (1.36) (2.76) (3.06) (2.39) Ln(PPE/EMP)t 0.029** 0.033** 0.037*** 0.126** 0.100* 0.092* (1.98) (2.21) (2.70) (2.06) (1.71) (1.83) Inst Ownt −0.011 0.023 0.015 −0.037 0.064 0.027 (−0.22) (0.46) (0.30) (−0.20) (0.37) (0.16) Leveraget −0.023 −0.009 −0.019 −0.191 −0.173 −0.209 (−0.38) (−0.14) (−0.32) (−0.85) (−0.78) (−1.08) Cash Flowt 0.130 0.133 0.232** 0.540 0.308 0.677* (1.05) (1.33) (2.49) (1.15) (0.71) (1.93) Cash Flow Volatilityt −0.109 −0.155 −0.134 0.221 0.653 −0.207 (−0.51) (−0.74) (−0.71) (0.25) (0.75) (−0.31) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 2,850 2,748 2,598 2,850 2,748 2,598 Adjusted R2 0.253 0.332 0.382 0.459 0.502 0.548 Table VII. Regressions using a propensity-score matched sample This table presents the estimates of baseline regressions using a propensity-score matched sample. To construct this matched sample, we first estimate the following Probit regression: the dependent variable (High Pay Gap) is coded one if a firm’s Pay Gap is above 70th percentile in a given year, and zero if a firm’s Pay Gap is below 30th percentile; the independent variables include all the explanatory variables in the first-stage regression of the instrumental-variable analysis. This generates a predicted probability of being a high-Pay-Gap firm for each observation. We then match, with replacement, each treatment firm (a firm with high pay gap) with a matching firm (a firm with low pay gap) having the closest propensity score, using a caliper—the difference in the predicted probabilities between treatment and control observations—of 1%. This procedure results in a matched sample consisting of 1,425 matched pairs (2,850 observations). The variable definitions are provided in Appendix A. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at the firm level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) High Pay Gapt 0.037** 0.041** 0.037** 0.187*** 0.206*** 0.178*** (2.16) (2.21) (2.07) (2.63) (2.91) (2.95) Ln(CEO Age)t 0.050 0.062 0.028 −0.180 −0.136 −0.166 (0.78) (0.95) (0.43) (−0.68) (−0.56) (−0.76) CEO Tenuret −0.001 −0.001 −0.002 −0.003 −0.003 −0.006 (−0.98) (−0.94) (−1.43) (−0.58) (−0.68) (−1.40) Ln(Sale)t −0.014** −0.015** −0.017** −0.014 −0.014 −0.031 (−2.01) (−2.08) (−2.55) (−0.48) (−0.49) (−1.29) Tobin’s qt −0.007 −0.010** −0.013*** −0.008 −0.018 −0.027** (−1.63) (−2.06) (−3.27) (−0.35) (−0.90) (−1.99) Sale Growtht −0.097** −0.027 0.015 0.009 0.174 0.191 (−2.30) (−0.64) (0.35) (0.05) (0.93) (1.16) (Capex/Assets)t 0.554** 0.571** 0.350 2.780*** 3.134*** 2.157** (2.22) (2.15) (1.36) (2.76) (3.06) (2.39) Ln(PPE/EMP)t 0.029** 0.033** 0.037*** 0.126** 0.100* 0.092* (1.98) (2.21) (2.70) (2.06) (1.71) (1.83) Inst Ownt −0.011 0.023 0.015 −0.037 0.064 0.027 (−0.22) (0.46) (0.30) (−0.20) (0.37) (0.16) Leveraget −0.023 −0.009 −0.019 −0.191 −0.173 −0.209 (−0.38) (−0.14) (−0.32) (−0.85) (−0.78) (−1.08) Cash Flowt 0.130 0.133 0.232** 0.540 0.308 0.677* (1.05) (1.33) (2.49) (1.15) (0.71) (1.93) Cash Flow Volatilityt −0.109 −0.155 −0.134 0.221 0.653 −0.207 (−0.51) (−0.74) (−0.71) (0.25) (0.75) (−0.31) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 2,850 2,748 2,598 2,850 2,748 2,598 Adjusted R2 0.253 0.332 0.382 0.459 0.502 0.548 Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) High Pay Gapt 0.037** 0.041** 0.037** 0.187*** 0.206*** 0.178*** (2.16) (2.21) (2.07) (2.63) (2.91) (2.95) Ln(CEO Age)t 0.050 0.062 0.028 −0.180 −0.136 −0.166 (0.78) (0.95) (0.43) (−0.68) (−0.56) (−0.76) CEO Tenuret −0.001 −0.001 −0.002 −0.003 −0.003 −0.006 (−0.98) (−0.94) (−1.43) (−0.58) (−0.68) (−1.40) Ln(Sale)t −0.014** −0.015** −0.017** −0.014 −0.014 −0.031 (−2.01) (−2.08) (−2.55) (−0.48) (−0.49) (−1.29) Tobin’s qt −0.007 −0.010** −0.013*** −0.008 −0.018 −0.027** (−1.63) (−2.06) (−3.27) (−0.35) (−0.90) (−1.99) Sale Growtht −0.097** −0.027 0.015 0.009 0.174 0.191 (−2.30) (−0.64) (0.35) (0.05) (0.93) (1.16) (Capex/Assets)t 0.554** 0.571** 0.350 2.780*** 3.134*** 2.157** (2.22) (2.15) (1.36) (2.76) (3.06) (2.39) Ln(PPE/EMP)t 0.029** 0.033** 0.037*** 0.126** 0.100* 0.092* (1.98) (2.21) (2.70) (2.06) (1.71) (1.83) Inst Ownt −0.011 0.023 0.015 −0.037 0.064 0.027 (−0.22) (0.46) (0.30) (−0.20) (0.37) (0.16) Leveraget −0.023 −0.009 −0.019 −0.191 −0.173 −0.209 (−0.38) (−0.14) (−0.32) (−0.85) (−0.78) (−1.08) Cash Flowt 0.130 0.133 0.232** 0.540 0.308 0.677* (1.05) (1.33) (2.49) (1.15) (0.71) (1.93) Cash Flow Volatilityt −0.109 −0.155 −0.134 0.221 0.653 −0.207 (−0.51) (−0.74) (−0.71) (0.25) (0.75) (−0.31) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 2,850 2,748 2,598 2,850 2,748 2,598 Adjusted R2 0.253 0.332 0.382 0.459 0.502 0.548 5. Summary and Concluding Remarks Kini and Williams (2012) find that rank-order tournament incentives have a positive impact on R&D investments. However, prior theoretical studies (e.g., Gilpatric, 2009) imply that senior managers in firms with excessive tournament incentives may over-invest in risky R&D projects without adequate consideration of efficiency. Therefore, it remains an open empirical question as to whether the larger R&D investments induced by greater tournament incentives are efficient. Our study goes beyond Kini and Williams (2012) to explore how tournament incentives are related to corporate innovative efficiency. Using a sample of US public firms over the period 1993–2003, we find that tournament incentives are positively related to innovative efficiency, as measured by the number of patents and patent citations generated per million dollars of R&D investments. The positive relation is robust in model specifications with additional controls for CEO characteristics (e.g., CEO overconfidence), in regressions using alternative innovation measures that capture the fundamental importance and economic value of the patents, in instrumental-variable regression analysis, and in regressions based on a propensity-score matched sample. If tournament incentives are indeed positively related to innovation, then one would expect that the positive relation should be more pronounced when a succession contest is most likely to occur, such as prior to CEO turnovers. We find empirical evidence consistent with this conjecture. We also note that tournament incentives have a more pronounced positive impact on innovative efficiency, when an insider-CEO is more likely to be appointed and when VPs expect a higher probability of CEO turnover in the foreseeable future. Additionally, our subsample tests show that tournament incentives seem to have less beneficial effects on innovative efficiency for family firms, firms with weak corporate governance, and firms in non-innovative industries. Our study contributes to the literature in three ways. First, it adds new evidence to the emerging literature on corporate innovation (e.g., Acharya and Subramanian, 2009; He and Tian, 2013) by showing that a rank-order tournament with a large prize could enhance corporate innovation performance. Second, through the lens of corporate innovation, our study examines the relation between tournament incentives and firm performance. We complement prior studies (e.g., Kale, Reis, and Venkateswaran, 2009) by identifying a specific channel (i.e., innovation) through which tournament incentives add value to companies. Third, it is well known that both CEO–VP and CEO–worker pay gaps keep rising in recent decades, and prior studies (e.g., Bebchuk, Fried, and Walker, 2002) have attributed this phenomenon to increased CEO power and rent extraction. Our study contributes by offering an additional explanation to this phenomenon. That is, as innovation becomes increasingly important to businesses in recent decades, firms might choose to significantly increase pay gaps between hierarchy levels in order to incentivize executives and other employees to achieve better innovation performance. This study has some limitations. First, the sample of this study is limited to the public firms covered by the Execucomp database. Ferreira, Manso, and Silva (2014) find that public firms and private firms have different incentives to pursue innovative projects. It would be interesting for future studies to explore how the relation between tournament incentives and firm innovation varies across private and public firms. Second, the lack of quasi-natural experiments limits our ability to fully address the endogeneity issues (e.g., omitted-variable bias). Appendix A. Variable Definitions Variables Definition Innovation output variables Pat Aggregate number of patents that were applied for by a firm during a year and were eventually granted. Cite Aggregate adjusted number of citations received by the patents applied for during a year, where the adjusted number of citations is computed by multiplying each patent’s raw citations with the weighting index in Hall, Jaffe, and Trajtenberg (2001, 2005). Innovative efficiency variables Pat/RD Aggregate number of patents that were applied for by a firm during a year and were eventually granted, scaled by the inflation-adjusted R&D expense (in million dollars). Cite/RD Aggregate adjusted number of citations received by the patents applied for during a year, scaled by the inflation-adjusted R&D expense (in million dollars). Executive compensation variables Pay Gap Difference (in million dollars) between a CEO’s total compensation and the median compensation of non-CEO senior executives. CEO Delta Dollar increase (in million dollars) in the value of a CEO’s compensation portfolio if the stock price increases by 1%. CEO Vega Dollar increase (in million dollars) in the value of a CEO’s compensation portfolio if the stock return volatility increases by 1%. VP Delta A firm’s median value of VPs’ compensation delta. VP Vega A firm’s median value of VPs’ compensation vega. Other variables CEO Age Age of the CEO in a specific year. CEO Tenure Number of years that the current CEO has worked as a CEO in the firm. Sale Annual sales of a firm (Compustat data item SALE). Tobin’s q Ratio of the market value of assets to the book value of assets, where the market value of assets is defined as the book value of assets (Compustat data item AT) minus the book value of equity (Compustat data item CEQ) plus the market value of equity (Compustat data item PRCC_F*CSHO). Sale Growth Average sales growth rates over the past 3 years. Capex/Assets Ratio of capital expenditure (Compustat data item CAPX) to total assets. PPE/EMP Ratio of inflation-adjusted net property, plant, and equipment (Compustat data item PPENT) to the number of employees (Compustat data item EMP). Inst Own Fraction of a firm’s outstanding shares owned by institutional investors. Leverage Ratio of total debt (Compustat data item DLTT+DLC) to total assets. Cash Flow Ratio of operating cash flow (Compustat data item OANCF) to total assets. Cash Flow Volatility The standard deviation of Cash Flow in the past 3 years. G-index The governance index compiled by Gompers, Ishii, and Metrick (2003) with 24 IRRC anti-takeover provisions. CEO Overconfidence A dummy variable that equals one if the CEO of a firm is classified as overconfident. We identify a CEO as being overconfident if this CEO holds stock options that are more than 100% in the money (Campbell et al., 2011). Managerial Ability The managerial ability measure of Demerjian, Lev, and McVay (2012), which captures how efficiently managers generate revenues from given economic resources based on the data envelopment analysis (DEA) approach. Variables Definition Innovation output variables Pat Aggregate number of patents that were applied for by a firm during a year and were eventually granted. Cite Aggregate adjusted number of citations received by the patents applied for during a year, where the adjusted number of citations is computed by multiplying each patent’s raw citations with the weighting index in Hall, Jaffe, and Trajtenberg (2001, 2005). Innovative efficiency variables Pat/RD Aggregate number of patents that were applied for by a firm during a year and were eventually granted, scaled by the inflation-adjusted R&D expense (in million dollars). Cite/RD Aggregate adjusted number of citations received by the patents applied for during a year, scaled by the inflation-adjusted R&D expense (in million dollars). Executive compensation variables Pay Gap Difference (in million dollars) between a CEO’s total compensation and the median compensation of non-CEO senior executives. CEO Delta Dollar increase (in million dollars) in the value of a CEO’s compensation portfolio if the stock price increases by 1%. CEO Vega Dollar increase (in million dollars) in the value of a CEO’s compensation portfolio if the stock return volatility increases by 1%. VP Delta A firm’s median value of VPs’ compensation delta. VP Vega A firm’s median value of VPs’ compensation vega. Other variables CEO Age Age of the CEO in a specific year. CEO Tenure Number of years that the current CEO has worked as a CEO in the firm. Sale Annual sales of a firm (Compustat data item SALE). Tobin’s q Ratio of the market value of assets to the book value of assets, where the market value of assets is defined as the book value of assets (Compustat data item AT) minus the book value of equity (Compustat data item CEQ) plus the market value of equity (Compustat data item PRCC_F*CSHO). Sale Growth Average sales growth rates over the past 3 years. Capex/Assets Ratio of capital expenditure (Compustat data item CAPX) to total assets. PPE/EMP Ratio of inflation-adjusted net property, plant, and equipment (Compustat data item PPENT) to the number of employees (Compustat data item EMP). Inst Own Fraction of a firm’s outstanding shares owned by institutional investors. Leverage Ratio of total debt (Compustat data item DLTT+DLC) to total assets. Cash Flow Ratio of operating cash flow (Compustat data item OANCF) to total assets. Cash Flow Volatility The standard deviation of Cash Flow in the past 3 years. G-index The governance index compiled by Gompers, Ishii, and Metrick (2003) with 24 IRRC anti-takeover provisions. CEO Overconfidence A dummy variable that equals one if the CEO of a firm is classified as overconfident. We identify a CEO as being overconfident if this CEO holds stock options that are more than 100% in the money (Campbell et al., 2011). Managerial Ability The managerial ability measure of Demerjian, Lev, and McVay (2012), which captures how efficiently managers generate revenues from given economic resources based on the data envelopment analysis (DEA) approach. Appendix A. Variable Definitions Variables Definition Innovation output variables Pat Aggregate number of patents that were applied for by a firm during a year and were eventually granted. Cite Aggregate adjusted number of citations received by the patents applied for during a year, where the adjusted number of citations is computed by multiplying each patent’s raw citations with the weighting index in Hall, Jaffe, and Trajtenberg (2001, 2005). Innovative efficiency variables Pat/RD Aggregate number of patents that were applied for by a firm during a year and were eventually granted, scaled by the inflation-adjusted R&D expense (in million dollars). Cite/RD Aggregate adjusted number of citations received by the patents applied for during a year, scaled by the inflation-adjusted R&D expense (in million dollars). Executive compensation variables Pay Gap Difference (in million dollars) between a CEO’s total compensation and the median compensation of non-CEO senior executives. CEO Delta Dollar increase (in million dollars) in the value of a CEO’s compensation portfolio if the stock price increases by 1%. CEO Vega Dollar increase (in million dollars) in the value of a CEO’s compensation portfolio if the stock return volatility increases by 1%. VP Delta A firm’s median value of VPs’ compensation delta. VP Vega A firm’s median value of VPs’ compensation vega. Other variables CEO Age Age of the CEO in a specific year. CEO Tenure Number of years that the current CEO has worked as a CEO in the firm. Sale Annual sales of a firm (Compustat data item SALE). Tobin’s q Ratio of the market value of assets to the book value of assets, where the market value of assets is defined as the book value of assets (Compustat data item AT) minus the book value of equity (Compustat data item CEQ) plus the market value of equity (Compustat data item PRCC_F*CSHO). Sale Growth Average sales growth rates over the past 3 years. Capex/Assets Ratio of capital expenditure (Compustat data item CAPX) to total assets. PPE/EMP Ratio of inflation-adjusted net property, plant, and equipment (Compustat data item PPENT) to the number of employees (Compustat data item EMP). Inst Own Fraction of a firm’s outstanding shares owned by institutional investors. Leverage Ratio of total debt (Compustat data item DLTT+DLC) to total assets. Cash Flow Ratio of operating cash flow (Compustat data item OANCF) to total assets. Cash Flow Volatility The standard deviation of Cash Flow in the past 3 years. G-index The governance index compiled by Gompers, Ishii, and Metrick (2003) with 24 IRRC anti-takeover provisions. CEO Overconfidence A dummy variable that equals one if the CEO of a firm is classified as overconfident. We identify a CEO as being overconfident if this CEO holds stock options that are more than 100% in the money (Campbell et al., 2011). Managerial Ability The managerial ability measure of Demerjian, Lev, and McVay (2012), which captures how efficiently managers generate revenues from given economic resources based on the data envelopment analysis (DEA) approach. Variables Definition Innovation output variables Pat Aggregate number of patents that were applied for by a firm during a year and were eventually granted. Cite Aggregate adjusted number of citations received by the patents applied for during a year, where the adjusted number of citations is computed by multiplying each patent’s raw citations with the weighting index in Hall, Jaffe, and Trajtenberg (2001, 2005). Innovative efficiency variables Pat/RD Aggregate number of patents that were applied for by a firm during a year and were eventually granted, scaled by the inflation-adjusted R&D expense (in million dollars). Cite/RD Aggregate adjusted number of citations received by the patents applied for during a year, scaled by the inflation-adjusted R&D expense (in million dollars). Executive compensation variables Pay Gap Difference (in million dollars) between a CEO’s total compensation and the median compensation of non-CEO senior executives. CEO Delta Dollar increase (in million dollars) in the value of a CEO’s compensation portfolio if the stock price increases by 1%. CEO Vega Dollar increase (in million dollars) in the value of a CEO’s compensation portfolio if the stock return volatility increases by 1%. VP Delta A firm’s median value of VPs’ compensation delta. VP Vega A firm’s median value of VPs’ compensation vega. Other variables CEO Age Age of the CEO in a specific year. CEO Tenure Number of years that the current CEO has worked as a CEO in the firm. Sale Annual sales of a firm (Compustat data item SALE). Tobin’s q Ratio of the market value of assets to the book value of assets, where the market value of assets is defined as the book value of assets (Compustat data item AT) minus the book value of equity (Compustat data item CEQ) plus the market value of equity (Compustat data item PRCC_F*CSHO). Sale Growth Average sales growth rates over the past 3 years. Capex/Assets Ratio of capital expenditure (Compustat data item CAPX) to total assets. PPE/EMP Ratio of inflation-adjusted net property, plant, and equipment (Compustat data item PPENT) to the number of employees (Compustat data item EMP). Inst Own Fraction of a firm’s outstanding shares owned by institutional investors. Leverage Ratio of total debt (Compustat data item DLTT+DLC) to total assets. Cash Flow Ratio of operating cash flow (Compustat data item OANCF) to total assets. Cash Flow Volatility The standard deviation of Cash Flow in the past 3 years. G-index The governance index compiled by Gompers, Ishii, and Metrick (2003) with 24 IRRC anti-takeover provisions. CEO Overconfidence A dummy variable that equals one if the CEO of a firm is classified as overconfident. We identify a CEO as being overconfident if this CEO holds stock options that are more than 100% in the money (Campbell et al., 2011). Managerial Ability The managerial ability measure of Demerjian, Lev, and McVay (2012), which captures how efficiently managers generate revenues from given economic resources based on the data envelopment analysis (DEA) approach. Supplementary Material Supplementary data are available at Review of Finance online. Footnotes * We are grateful to two anonymous reviewers and Vikrant Vig (the editor) for their constructive and valuable comments. The paper also benefitted greatly from the comments from Konan Chan, John Ettlie, Ron Hira, Chun-Keung Stan Hoi, Jiekun Huang, Richard Lord, Zhong Ma, Gustavo Manso, Zhao Rong, Sarah Shaikh (AAA discussant), Yanzhi Wang, Qiang Wu, Jing Zhao (FMA discussant), the seminar participants at National Chengchi University, National Taiwan University, Beijing Jiao Tong University, and the session participants in the 2013 American Accounting Association (AAA) Annual Meeting, 2013 Financial Management Association (FMA) Annual Meeting, 2013 FMA European Conference, the 6th NCTU International Finance Conference, and the RIT Saunders College Research Colloquium. C.H.-H.S. acknowledges the research grant from the Ministry of Science and Technology of Taiwan, and H.Z. thanks the Saunders College of Business at RIT for summer research support. The Securities and Exchange Commission, as a matter of policy, disclaims responsibility for any private publication or statement by any of its employees. The views expressed herein are those of the author and do not necessarily reflect the views of the Commission or of the author’s colleagues upon the staff of the Commission. 1 Individuals’ incentives have important effects on firm innovation (Schumpeter, 1934). The R&D management literature (Pelz and Andrews, 1976; Manners, Steger, and Zimmerer, 1997) also suggests that various employee incentives have significant impact on corporate innovative activities and their productivity. From a survey of 1,544 employees in multinational enterprises’ R&D laboratories, Manolopoulos (2006) finds that the three most influential motivators of innovation are salary, bonuses, and opportunity for hierarchical advancement. As Green and Stokey (1983, p. 349) argue, “in most organizations, one of the most important rewards is promotion.” Thus, McAllister and Vandlen (2010) and others argue that variable compensation scheme and internal promotion are two major motivators of firm innovations. Tournament incentives, the focus of our study, are related to these two motivators and thus should have a significant effect on corporate innovation. 2 For example, Gilpatric (2009) argues that both stock options and winner-take-all tournaments generate asymmetric payoffs, that is, rewarding good outcomes, but generally not penalizing poor outcomes. Thus, just like the effect of executive stock options, winner-take-all contests (e.g., CEO-promotion tournaments) should generate incentives for contestants to engage in risk-taking behaviors. 3 Researchers in other areas have provided empirical evidence that rank-order tournaments lead to risk-taking behaviors in car races (Becker and Huselid, 1992; Bothner, Kang, and Stuart, 2007), poker games (Lee, 2004), professional sports (Grund and Gürtler, 2005; Grund, Höcker, and Zimmermann, 2013; Ozbeklik and Smith, 2017), laboratory experiments (Nieken and Sliwka, 2010), etc. In the finance literature, most studies on tournament incentives focus on the risk-taking behaviors of mutual fund managers (Brown, Harlow, and Starks, 1996; Chevalier and Ellison, 1997; Busse, 2001; Qiu, 2003; Taylor, 2003; Goriaev, Nijman, and Werker, 2003; Kempf and Ruenzi, 2008; Sato, 2016). 4 The following anecdotal quotation of an employee who used to work for Fidelity Investments provides an intuitive description of the situation: “Everything, your compensation, all your incentives, were tied to your performance against other funds in your class. Obviously, in order to depart from the mean, to do better than the average, you had to do something different. You had to take risks” (Cohen, 1997). 5 This is similar to the “wasteful” risk-taking behavior in Gilpatric (2009), which reflects the circumstance that very risky projects might have a lower mean output. Similarly, some prior empirical studies on professional sports (e.g., Grund, Höcker, and Zimmermann, 2013) find that a rank-order tournament induces some contestants to engage in inefficient risk-taking behaviors that lead to poor performance. 6 The sample period is largely limited by the data availability of the NBER Patent Citations database. 7 Similarly, Kale, Reis, and Venkateswaran (2010) point out that “companies should pay careful attention to promotion incentives when structuring their top management compensation. What might appear to be excessive compensation for the CEO could have important secondary effects by motivating senior executives at the next level down” (p. 127). Thus, our study sheds further light on the bright side of “overpaying” CEOs. 8 For example, in firms with multiple divisions, Divisional VPs’ support is crucial to the success of R&D projects (Smith-Doerr, Manev, and Rizova, 2004). In addition, we include all the VPs in the pay gap measure construction, partly because the Execucomp database often does not provide enough information allowing us to classify a VP as a R&D-related VP. Thousands of executives’ titles in the Execucomp database are simply “executive vp”, “exec. v-p”, “sr. v-p”, “senior vp”, etc. Therefore, we include all VPs into the Pay Gap measure construction. As a robustness check, we use CEO-CTO Pay Gap as an alternative measure, where a CTO is identified if an executive’s title contains keywords such as “technology”, “research”, “information”, “science”, and “laboratory”. Although the number of observations in the regression on CEO-CTO Pay Gap is significantly smaller, we continue to find a significant and positive relation between the pay gap measure and innovative efficiency. 9 To mitigate the truncation bias, some other studies (Lerner, Sorensen, and Stromberg, 2011; Seru, 2014) normalize the citation measure by computing the measure based on a fixed window. However, Lerner and Seru (2014) argue that “as Hall and co-authors (2001) suggest, by undertaking such a normalization, one may be sweeping away information.” Therefore, we choose to follow Hall, Jaffe, and Trajtenberg (2005) to use the weighting index method in the main tests. In a robustness check, we follow Lerner, Sorensen, and Stromberg (2011) to define the citation count as the number of times for which a given patent has been cited in the calendar year of the patent grant and the three subsequent years. Additionally, we also follow Seru (2014) to scale citation count of a given patent by the total number of citations received by all patents in that year and in the same technological class. Then, we divide these two citation count variables by R&D expenditure to construct alternative innovative efficiency measures and then use them as the dependent variables in our regressions. Our main findings hold when we use these alternative measures. 10 In unreported robustness tests, we also examine patents applied for during years t+4 and t+5 and find qualitatively similar results. 11 As discussed in the previous section, we adjust the citation counts of each patent by multiplying them with the weighting index from Hall, Jaffe, and Trajtenberg (2001, 2005). Thus, the values of citation counts may not be integral numbers. 12 Specifically, the log variables are defined as the logarithm of one plus the corresponding patent and citation-related variables. In a robustness check, we use the original patent and citation-related variables as the dependent variables and re-estimate the regressions using both the OLS regression method and the Tobit regression method. We find the results are qualitatively unchanged. For brevity, we do not tabulate the results, but the results are available from the authors upon request. 13 We conduct a test to examine whether the main finding of Kini and Williams (2012) holds in our sample. In this untabulated test, we also find a positive and statistically significant relation between tournament incentives and R&D investments even though we include several additional controls (e.g., CEO Age, average daily stock returns, and return volatility). 14 To mitigate statistical concerns arising from cross-sectional dependence of regression residuals, we also estimate model (1) using the Fama–MacBeth method. Specifically, we drop the year dummies from the specification, estimate the revised models by year, and then test the statistical significance of the average coefficients using a t-test. The Fama–MacBeth regression results indicate the coefficients of Ln(Pay Gap) remain significantly positive, indicating that our main findings are robust to the alternate regression method. 15 According to Table I, the 25th percentile of Pay Gap is 0.375 and the 75th percentile is 1.417. Because both the dependent variable (i.e., the logarithm of one plus Patt+1/RDt+1) and the independent variable are in logarithm, it suggests that an inter-quartile increase in a firm’s Pay Gap could increase (1+ Patt+1/RDt+1) by around 8.6% (= 0.031 × (1.417 − 0.375)/0.375). Because the mean value of Patt+1/RDt+1 in our sample is 0.234, an 8.6% increase in (1+Patt+1/RDt+1) suggests an increase in Patt+1/RDt+1 by around 0.106 ( = (1 + 0.234)*8.6%). 16 In untabulated tests, we find that our main findings are robust to the inclusion of some other controls such as the general ability index of Custodio, Ferreira, and Matos (2014), market liquidity measure (Chung and Zhang, 2014), KZ-score (Kaplan and Zingales, 1997), etc. 17 We thank Noah Stoffman and his coauthors for sharing the data on the website. 18 According to Table I, the 25th percentile of Pay Gap is 0.375 and the 75th percentile is 1.417. The coefficient on Ln(Pay Gap) in Column 4 of Panel B equals 0.0029, which suggests that an increase of CAR(−1, +3) by around 0.39% [=0.0029 × (Ln(1.417)−Ln(0.375))]. 19 CEO turnover events could be associated with poor firm performance and corporate governance quality. Thus, we have already added several variables to control for the effect of firm performance (e.g., Ln(Sale), Sale Growth, Cash Flow, Cash Flow Volatility) and corporate governance (Inst Own) in the baseline model. In an untabulated robustness check, we also add more controls for corporate governance (e.g., G-index) and CEO characteristics (e.g., CEO/Chairman Dummy). Although the number of observations significantly decreases, we continue to find that the effect of tournament incentives on innovative efficiency is more pronounced during the period prior to CEO turnover. 20 We also use the change in operating performance to identify firms with performance deterioration when we identify the potentially expected CEO turnover events. We find our results are qualitatively unchanged. 21 To increase the accuracy of this classification, we also search news in the Factiva database to make sure that firms with less-expected CEO turnover did not make any announcements about CEOs’ plan to retire during the 3 years prior to the turnover events until within 6 months before the CEO turnover. We acknowledge that the aforementioned classification method of expected CEO turnover and less-expected CEO turnover may have limitations. For example, VPs might have inside information to predict a future CEO turnover. However, compared with the expected CEO turnover cases (e.g., CEO is older than 60), VPs should expect a lower probability of CEO turnover in the less-expected turnover cases, and therefore the tournament incentives should have a weaker effect. 22 As an example, when Satya Nadella (Microsoft’s Vice President of Cloud and Enterprise group) was appointed as the new Microsoft CEO in 2014, Bill Gates (the founder of the company) made a comment that “his vision for how technology will be used and experienced around the world is exactly what Microsoft needs as the company enters its next chapter of expanded product innovation and growth.” 23 We also use an alternate way to classify high-tech and low-tech firms. Specifically, we follow Brown, Fazzari, and Petersen (2009) to define those firms in seven industries (with SIC three-digit codes 283, 357, 366, 367, 382, 384, and 737) as high-tech firms, while other firms are defined as low-tech firms. We find the subsample-analysis results to be qualitatively unchanged. 24 We thank David M. Reeb for sharing the family firm data on his website. The data classify S&P 500 firms into family firms and non-family firms during 1992–1999, whereby family firms are defined as those where the family (founder and/or founder’s descendants) continues to maintain a 5% or greater ownership stake. We manually expand it to cover the post-1999 period by reading firm histories from various websites and collecting information on the presence of founding families from SEC filings. Since the family firm data only cover S&P 500 firms, our tests using the family firm data have a smaller sample size. 25 Although other compensation variables, for example, CEO Delta and CEO Vega, could also be endogenous, we do not include these variables in the instrumental-variable regression analysis for the following reasons. First, they are not our key independent variables, and these compensation control variables are not statistically significant in the baseline model. Second, the results of Hausman tests suggest that these variables can be treated as exogenous variables. However, in an untabulated robustness check, we treat Pay Gap, CEO Delta, and CEO Vega as endogenous variables and use four instrumental variables in these over-identified instrumental-variable regressions. We continue to find a significantly positive relation between the instrumented tournament incentive measure and innovative efficiency measures. 26 We have six second-stage regressions; thus, we also have six corresponding first-stage regressions. These first-stage regression results are very similar. For brevity, Column 1 of Table VI only reports the one corresponding to the second-stage regression reported in Column 2 of Table VI. 27 We thank an anonymous reviewer for sharing this insight. References Acharya V. , Subramanian K. 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For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Review of Finance Oxford University Press

Tournament Incentives and Firm Innovation

Review of Finance , Volume Advance Article (4) – Apr 12, 2017

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Oxford University Press
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© The Authors 2017. Published by Oxford University Press on behalf of the European Finance Association. All rights reserved. For Permissions, please email: journals.permissions@oup.com
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1572-3097
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Abstract

Abstract This study analyzes how promotion-based tournament incentives for non-CEO senior executives affect corporate innovation. We measure tournament incentives using the pay gap between a CEO and the next layer of senior executives. We find that tournament incentives are positively related to innovative efficiency, as measured by the number of patents and patent citations generated per million dollars of R&D expense. Our main finding holds in an instrumental-variable analysis and regressions using alternative innovation measures, including patent generality and originality indices and stock market reactions to patent grants. Consistent with prior theories, the positive effect of tournament incentives is found to be particularly pronounced during the period prior to CEO turnovers. 1. Introduction Technological innovation has been recognized as the engine for economic growth since Schumpeter (1942) and Solow (1957). With the arrival of a knowledge-based and innovation-driven economy, corporate innovation has an increasing influence on a firm’s long-run competitive advantage and even the survival of firms (Chaney and Devinney, 1992; Porter, 1992; Ettlie, 1998; Eisdorfer and Hsu, 2011). Therefore, a fast-growing body of literature has attempted to understand the factors driving corporate innovative activities and their success from both theoretical and empirical perspectives (e.g., Acharya and Subramanian, 2009; Aghion, Van Reenen, and Zingales, 2009; Lerner, Sorensen, and Stromberg, 2011; He and Tian, 2013). As a recent development, both academicians and commentators have called for a more thorough empirical investigation into the relation between executive compensation and corporate innovation (e.g., Manso, 2011; Ederer and Manso, 2013). To date, relatively less attention has been devoted to understanding how to structure executive compensation if shareholders want to effectively motivate executives to be innovative. Notable exceptions include several studies examining how option-based compensation (Lerner and Wulf, 2007), equity grants with longer vesting periods (Baranchuk, Kieschnick, and Moussawi, 2014; Edmans, Fang, and Lewellen, 2015), and incentives set by the duration of CEO contracts (Gonzalez-Uribe and Groen-Xu, 2015) influence firm innovation. Although these studies shed light on the effect of performance-based compensation on innovation, none of them empirically examine how promotion-based compensation incentives influence firm innovation performance.1 The present study aims to fill this gap in the literature. Although the majority of executive compensation studies examine performance-based incentives, one stream of research focuses on intra-organizational promotion-based incentives (also known as tournament incentives). In a corporate rank-order tournament, non-CEO senior executives compete with each other for the top position. These executives are evaluated relative to their peers (i.e., relative performance evaluation), and among them the best relative performer will be promoted to be the next CEO. Promotion to the CEO position is associated with higher pay and therefore provides senior executives with strong incentives to expend greater effort to enhance both their own chances of promotion as well as the company’s performance (Lazear and Rosen, 1981; Prendergast, 1999). In addition to inducing greater effort, the option-like payoff structure of a tournament also influences risk-taking behaviors of tournament participants.2 Theoretical studies (e.g., Hvide, 2002; Hvide and Kristiansen, 2003; Yumoto, 2003; Gaba, Tsetline, and Winkler, 2004) show that contestants in a tournament have strong motives to increase the probability of winning by taking greater risk. The evidence on how tournament incentives influence managerial risk-taking and innovative activities, however, remains surprisingly scant in the corporate finance literature.3 In a recent theoretical study that primarily explains the prevalence of overconfident CEOs, Goel and Thakor (2008) predict that in order to increase the chances of winning, all senior executives would undertake investments that are riskier than the ones they would otherwise have undertaken in the absence of tournament incentives. Consistent with this argument, Kini and Williams (2012) find that greater prizes in CEO-promotion tournaments indeed lead to riskier corporate policies, including greater R&D investments, higher financial leverage, and less diversified business operations. Although the result of Kini and Williams (2012) suggests that higher tournament incentives induce senior executives to undertake greater risky investments (e.g., R&D), it does not address the question of whether such risk is pursued at the expense of efficiency. We conjecture that tournament incentives could affect innovative efficiency in conflicting ways. On the one hand, James and Isaac (2000) argue that tournament incentives in the mutual fund industry may lead to excessive risk-taking behaviors by fund managers and even the formation of stock market bubbles.4Gilpatric (2009) and others theoretically demonstrate that winner-take-all tournament contests, such as CEO-promotion tournaments, can generate incentives for contestants to engage in excessive risk-taking behaviors. For example, in sports contests where only one winner gets the top prize, the contestants are more likely to pursue aggressive risk-seeking strategies, as they typically have nothing to lose but could achieve a better outcome by taking excessive risks.5 Taken together, it is a valid concern that high tournament incentives might actually lead to excessively risky and inefficient innovative activities and, as a consequence, have a destructive impact on corporate innovation efficiency. On the other hand, tournament incentive could be positively related to innovative efficiency because classical studies on tournament incentives (e.g., Lazear and Rosen, 1981; Nalebuff and Stiglitz, 1983) suggest that VPs in a tournament with a larger promotion prize work harder to identify and maneuver high-quality innovation projects. In addition, Kempf, Ruenzi, and Thiele (2009)—a study examining the mutual fund industry—argues that “if a manager takes on too high a risk (perhaps because of tournament incentives), then there is also a higher risk of poor performance,” which leads to a greater probability of losing one’s job and facing a career setback. Such a concern for employment risks could also incentivize corporate managers to consider more about the productivity of their risk-taking behaviors, leading to a positive relation between tournament incentives and corporate innovative efficiency. In sum, it remains an empirical question whether greater R&D investments induced by larger tournament incentives are efficient. To fill this void and to complement the previous work of Kini and Williams (2012), we investigate how tournament incentives for non-CEO executives influence the efficiency of corporate innovative activities. We construct the measures of corporate innovative efficiency based on the innovation output data in the National Bureau of Economic Research (NBER) Patent Citations database. We measure tournament incentive as the pay gap between a CEO and the next layer of senior executives. Using a large sample of US public firms over the period 1993–2003,6 we find that tournament incentives are positively related to corporate innovative efficiency, as measured by the number of patents and the patent citations generated per million US dollars of R&D investment. This main finding is robust in regressions with additional controls and in regressions using alternative innovation measures that capture the fundamental importance and economic value of the patents, such as the generality and originality indices (Hall, Jaffe, and Trajtenberg, 2001) and stock market reactions to patent grants (Kogan et al., 2017). Our main finding also holds in an instrumental-variable analysis, in which we treat the pay gap measure as an endogenous variable. We use the industry median value of the pay gap measure as the instrument, because prior studies find that an individual firm is likely to be a “compensation-taker”. That is, a firm likely adjusts its executive pay when peer firms change executive compensation (DiPrete, Eirich, and Pittinsky, 2010). Consistent with this view, the instrument is highly significant in the first-stage regression. The F-statistic of excluded instrument also suggests that this instrument is not weak. However, we acknowledge that the instrumental-variable analysis has a limitation and thus these results should be interpreted with caution. Specifically, although it is likely that the industry-level pay gap (i.e., the instrument) is associated with the firm-level innovative efficiency only through its influence on an individual firm’s pay gap, this exclusion restriction could be violated and poses a threat to the identification if there is an omitted-variable problem. We therefore also perform regression analysis based on a propensity-score matched sample to partially address this endogeneity issue and find that our main results hold. If tournament incentives are indeed positively related to innovative efficiency, such a positive relation should be most pronounced when a succession contest is likely to occur, such as during the period prior to CEO turnovers. We find evidence in support of this conjecture. In addition, with the assumption that ex-ante expectations of VPs are on average correct, the effect of tournament incentives should be weaker in ex-post outsider-CEO turnover cases (i.e., an outsider is later appointed as a new CEO), ceteris paribus. Consistent with this argument, we find that the positive effect of tournament incentives prior to CEO turnovers is particularly pronounced when an insider (i.e., one of the VPs) is eventually appointed as the new CEO. In a similar vein, we also find that the tournament incentive effect is stronger when VPs expect a higher probability of CEO turnover in the foreseeable future (i.e., when the incumbent CEO is approaching retirement or is underperforming). Additionally, our subsample tests suggest that not every company benefits equally from providing executives with a high CEO-VP pay gap. Specifically, tournament incentives seem to have less beneficial effects on innovative efficiency for family firms, firms with weak corporate governance, and firms in non-innovative industries. This paper contributes to the prior literature in several ways. First, a fast-growing literature has found significant relations between innovation and some firm-level variables, including corporate governance (Atanassov, 2013; Chemmanur and Tian, 2013; Balsmeier, Fleming, and Manso, 2017), institutional ownership (Aghion, Van Reenen, and Zingales, 2009), leveraged buyouts (Lerner, Sorensen, and Stromberg, 2011), venture capital (Tian, 2012; Chemmanur, Loutskina, and Tian, 2014), stock market liquidity (Fang, Tian, and Tice, 2013), financial constraint (Almeida, Hsu, and Li, 2013), firm boundaries (Seru, 2014), the decision to go public (Bernstein, 2015), and CEO contract horizon (Gonzalez-Uribe and Groen-Xu, 2015). Our study is the first one showing that tournament incentive is also a factor influencing the efficiency of corporate innovative activities and thus adds to this fast-expanding literature. Second, our research is related to a stream of studies that examine how promotion-based incentives affect firm performance. The traditional tournament theory (Lazear and Rosen, 1981; Malcomson, 1984) implies that setting CEO pay at a level higher than that of non-CEO executives encourages competition and can lead to better firm performance. Nevertheless, prior studies (e.g., Main, O’Reilly, and Wade, 1993; Bloom, 1999; Eriksson, 1999; Conyon, Peck, and Sadler, 2001; Henderson and Fredrickson, 2001; Chen, Huang, and Wei, 2013; Coles, Li, and Wang, 2014; Connelly et al., 2014; Masulis and Zhang, 2014) present mixed evidence on this prediction. Given the inconclusive evidence, we explore the effect of tournament incentives on a more proximal performance indicator—firm innovation. Our results lend support to the tournament theory that a rank-order tournament provides non-CEO executives with strong incentives to achieve better firm performance. Through the lens of firm innovation performance, this study adds fresh evidence to the executive compensation literature by showing that promotion-based incentives enhance firm performance. Third, this study also has a policy implication. A growing sentiment following the recent financial crisis is that CEOs are overpaid and that their large compensation dilutes shareholder value. For example, recent evidence shows that non-CEO executives earn only approximately 40% of a CEO’s compensation (Conyon, 2006) and that CEO pay has risen faster than that of non-CEO executives and other employees (Useem, 2003; Mishel and Davis, 2014). To shed light on the pay disparity, the US Securities and Exchange Commission (SEC) recently adopted a rule that requires a public company to disclose the CEO–Worker pay ratio (Securities and Exchange Commission [SEC], 2015). Prior studies have attributed high CEO compensation and large pay disparity to increased CEO power (Bebchuk, Fried, and Walker, 2002), CEO entrenchment (Vo and Canil, 2016), and the practice of indexing compensation to peer-group benchmarks (Bizjak, Lemmon, and Naveen, 2008). This paper provides an additional explanation for the prevalence of high pay dispersion in corporate America by showing that high pay gap may be beneficial, because it incites tournament and motivates managers to make valuable contributions to firm innovation.7 The rest of the paper is organized as follows. Section 2 introduces the data sources and variable definitions. Sections 3 and 4 present the empirical results. Section 5 concludes. 2. Data and Variables This section introduces variable definitions, describes data sources and sample selection procedure, and presents descriptive statistics. 2.1 Tournament Incentives and CEO Performance-Based Incentives We obtain executive compensation data from the Compustat Execucomp database. Following Kini and Williams (2012), we measure tournament incentives as the pay gap between a CEO and the next layer of senior executives (i.e., VPs). Specifically, the variable (Pay Gap) is defined as the difference between the total compensation of the CEO (i.e., Execucomp data item TDC1) and that of the median VP in the firm. We construct this Pay Gap measure based on all VPs’ compensation and use it as the main tournament-incentive measure for the following reasons. First, this variable captures the potential increase in a VP’s salary if she wins the tournament and has been used as a popular proxy for tournament incentives (see, e.g., Main, O’Reilly, and Wade, 1993; Kale, Reis, and Venkateswaran, 2009; Kini and Williams, 2012). Second, although some firms have a specific VP responsible for R&D projects (i.e., chief technology officer, hereafter CTO), it is quite often that multiple VPs are involved in corporate innovation processes (De Meyer and Mizushima, 1989; Smith-Doerr, Manev, and Rizova, 2004).8 Third, even if some VPs are not directly involved in R&D decisions (e.g., VP of sales), they may have an indirect impact on corporate innovation activities. Prior studies show that peer pressure could induce agents to take greater risks (Nieken and Sliwka, 2010). If a VP of sales takes greater risks (e.g., implementing an aggressive marketing strategy) to gain advantage in a CEO-promotion contest, then VPs who are involved in R&D decisions may undertake riskier R&D projects as well due to peer influence. Therefore, we follow Kini and Williams (2012) to include all VPs in the Pay Gap measure construction. To control for the effects of CEOs’ performance-based incentives, we estimate the delta and vega of CEO compensation portfolios (CEO Delta and CEO Vega) by following Core and Guay (2002). CEO Delta measures the dollar change (in millions) in a CEO’s compensation portfolio if the stock price increases by 1%. CEO Vega measures the dollar change (in millions) in a CEO’s compensation portfolio if the stock return volatility increases by 1%. We also apply the same methods to compute delta and vega for VPs in a firm and use a firm’s median values of VPs’ delta and vega (i.e., VP Delta and VP Vega) as additional controls. Following Kini and Williams (2012), we adjust these executive compensation variables for inflation. 2.2 Firm Innovation Performance Measures Firm innovations are officially introduced to the public in the form of approved patents. Extant studies (Griliches, 1990; Hirshleifer, Hsu, and Li, 2013) argue that patent-related data can be used to construct direct measures of firms’ innovation performance. We obtain patent-related data from the 2006 edition of the NBER Patent Citations database. The database provides detailed information on all US patents granted by the US Patent and Trademark Office (USPTO) from January 1976 to December 2006, such as patent assignee names, the number of patents, the number of citations received by each patent, a patent’s application year as well as its grant year, etc. Patents are included in the database only if they are eventually granted by the USPTO before the end of 2006. The database covers over 3.2 million patent grants and 23.6 million patent citations from 1976 to 2006. Following prior studies (e.g., Almeida, Hsu, and Li, 2013), we use patent data recorded by the application year as a measure of innovation output. Specifically, firm i’s innovation output in year t can be measured as the number of patents applied for by firm i in year t that are eventually granted (denoted as Pati,t). Hall, Jaffe, and Trajtenberg (2001) point out that since the NBER dataset ends in 2006 and there is on average a 2-year period between patent application date and patent granting date, patents applied for in 2004 and 2005 may not be included in the dataset. Therefore, we limit our sample period to the pre-2003 period. Since patents that continuously generate citations are considered as innovations with higher quality (Trajtenberg, 1990), our second measure of innovation output is the total number of citations received by the patents (applied for by firm i in year t) from the application year until the last-coverage year of the NBER Patent Citations database. As discussed, the NBER Patent Citations database ends its coverage in 2006, therefore the patents granted in a year close to 2006 have less time to accumulate citations. To mitigate such a truncation bias, we follow Hall, Jaffe, and Trajtenberg (2005) and adjust the citation counts of each patent by multiplying them with a weighting index provided by the NBER Patent Citations database.9 In this study, we use the adjusted total number of citations eventually received by the patents applied for by firm i in year t as an additional measure of innovation output (denoted as Citei,t). Although patent grants and citation counts are good measures of innovation output, our goal is to measure the efficiency of R&D investment, which should capture the worthiness of financial resources spent on R&D activities. For example, a firm that has a large innovation output might still suffer from an overinvestment problem if the innovation output is not large enough to justify an even greater amount of R&D investment. Following Hirshleifer, Hsu, and Li (2013) and Almeida, Hsu, and Li (2013), we define innovative efficiency as the innovation output generated per million dollars of R&D expense (denoted by RD). Since it takes time for R&D investments to generate innovations that are ready for patent applications, we construct the innovative efficiency measures by combining a firm’s R&D expense in year t + 1 with its patenting in the subsequent 3 years. Specifically, we create 2 types of innovative efficiency measures: Pati,t + n/RDi,t + 1 is the aggregate number of patents that were applied for by firm i in year t + n (where n = 1, 2, or 3), scaled by the inflation-adjusted R&D expense in year t + 1 (in million dollars); Citei,t + n/RDi,t + 1 is the aggregate adjusted number of citations received by the patents applied for by firm i in year t + n (where n = 1, 2, or 3), scaled by the inflation-adjusted R&D expense in year t + 1 (in million dollars).10 2.3 Other Variables We also calculate the following variables for our regression analysis. CEO Tenure is the number of years that the current CEO has worked as a CEO in the firm, which is obtained from the Execucomp database. CEO Age is the age of a CEO in a specific year. For those observations with missing values of CEO Age in the Execucomp database, we manually collect this data by searching the CEO profiles online. CEO Tenure and CEO Age are added as controls, because they could be negatively related to the remaining years in CEOs’ contract terms (Xu, 2013) and could also be related to CEO power. Using data from Compustat database and Thomson Reuters Ownership database, we compute the following firm characteristic variables: Sale is the annual sales of a firm; Tobin’s q is the ratio of the market value of assets to the book value of assets; Sale Growth is the average of the sales growth rates over the past 3 years; Capex/Asset is the ratio of capital expenditure to total assets; PPE/EMP is the ratio of inflation-adjusted net property, plant, and equipment to the number of employees; Inst Own is the percentage of total shares outstanding held by institutional investors averaged over four quarters in a specific year; Leverage is the ratio of total debt to total assets; Cash Flow is the ratio of operating cash flow to total assets; Cash Flow Volatility is the standard deviation of Cash Flow in the past 3 years. 2.4 Sample Construction and Descriptive Statistics Our initial sample consists of all firms in the Compustat Execucomp database from 1993 to 2003. We exclude utility firms (SIC code 4900–4999) and financial firms (SIC code 6000–6999) due to their regulatory nature. We remove financial firms also because more than 90% of them have zero patents. We then eliminate observations without sufficient data in any of the following databases: Execucomp database, NBER Patent Citations database, Compustat Fundamentals Annual database, and Thomson Reuters Ownership (13f) database. To obtain meaningful estimates of the pay gap variable, we require that a firm must have at least three senior executives (VPs) with compensation data available in the Execucomp database for a given year. Following Kini and Williams (2012), we also drop the firm-year observations when there is a negative pay gap between a CEO and the median VP, and eliminate former CEOs who remain as an executive from the list of VPs when computing Pay Gap. Finally, we drop observations with missing information in some manually collected variables (e.g., CEO Age and Inside CEO). Our final study sample consists of 5,170 firm-year observations in the period 1993–2003. Panel A of Table I presents the breakdown of the sample size in the sample construction procedure. Table I. Sample selection and summary statistics Panel A describes the sample selection procedure. We start with firm-year observations from non-financial and non-utility firms in the Compustat Execucomp database from 1993 to 2003. We then eliminate observations that do not have necessary data available in the Compustat Execucomp database, the NBER Patent Citations database, the Compustat Fundamentals Annual database, the Thomson Reuters Ownership (13f) database, and the CRSP database. After applying several additional filters, the final study sample consists of 5,170 firm-year observations. Panel B presents the summary statistics for the sample. Panel A. Sample selection All firm-year observations from non-financial and non-utility firms in Execucomp from 1993 to 2003 15,871 After merging with Compustat, CRSP, and Thomson Reuters Ownership databases 15,789 After merging with NBER Patent Citations database 5,702 Requiring at least three VPs reported in Execucomp and a non-negative CEO–VP pay gap 5,372 Requiring non-missing information for manually collected variables, e.g., CEO Age and Inside CEO 5,170 Panel A. Sample selection All firm-year observations from non-financial and non-utility firms in Execucomp from 1993 to 2003 15,871 After merging with Compustat, CRSP, and Thomson Reuters Ownership databases 15,789 After merging with NBER Patent Citations database 5,702 Requiring at least three VPs reported in Execucomp and a non-negative CEO–VP pay gap 5,372 Requiring non-missing information for manually collected variables, e.g., CEO Age and Inside CEO 5,170 Panel B. Summary statistics Variable Mean SD Q1 Median Q3 Patt+1 43.388 108.101 1.000 6.000 30.000 Citet+1 637.351 1919.400 0.000 47.191 328.863 Patt+1/RDt+1 0.234 0.279 0.016 0.133 0.343 Citet+1/RDt+1 2.976 4.794 0.000 0.913 3.755 Pay Gapt (in million $) 1.084 1.100 0.375 0.752 1.417 CEO Deltat (in million $) 0.893 2.458 0.111 0.268 0.723 VP Deltat (in million $) 0.126 0.239 0.021 0.049 0.121 CEO Vegat (in million $) 0.154 0.275 0.023 0.062 0.163 VP Vegat (in million $) 0.035 0.058 0.007 0.015 0.038 CEO Aget 55.935 14.674 51.000 56.000 61.000 CEO Tenuret 6.628 7.470 1.000 4.000 9.000 Salet (in million $) 5196.9 10499.4 429.6 1315.1 4623.5 Tobin’s qt 2.511 2.126 1.367 1.827 2.820 Sale Growtht 0.166 0.277 0.024 0.096 0.218 (Capex/Assets)t 0.057 0.042 0.029 0.047 0.073 (PPE/EMP)t 99.531 139.286 36.939 58.989 106.366 Inst Ownt 0.601 0.189 0.487 0.627 0.738 Leveraget 0.195 0.171 0.038 0.186 0.300 Cash Flowt 0.095 0.118 0.057 0.102 0.149 Cash Flow Volatilityt 0.046 0.042 0.018 0.034 0.060 Panel B. Summary statistics Variable Mean SD Q1 Median Q3 Patt+1 43.388 108.101 1.000 6.000 30.000 Citet+1 637.351 1919.400 0.000 47.191 328.863 Patt+1/RDt+1 0.234 0.279 0.016 0.133 0.343 Citet+1/RDt+1 2.976 4.794 0.000 0.913 3.755 Pay Gapt (in million $) 1.084 1.100 0.375 0.752 1.417 CEO Deltat (in million $) 0.893 2.458 0.111 0.268 0.723 VP Deltat (in million $) 0.126 0.239 0.021 0.049 0.121 CEO Vegat (in million $) 0.154 0.275 0.023 0.062 0.163 VP Vegat (in million $) 0.035 0.058 0.007 0.015 0.038 CEO Aget 55.935 14.674 51.000 56.000 61.000 CEO Tenuret 6.628 7.470 1.000 4.000 9.000 Salet (in million $) 5196.9 10499.4 429.6 1315.1 4623.5 Tobin’s qt 2.511 2.126 1.367 1.827 2.820 Sale Growtht 0.166 0.277 0.024 0.096 0.218 (Capex/Assets)t 0.057 0.042 0.029 0.047 0.073 (PPE/EMP)t 99.531 139.286 36.939 58.989 106.366 Inst Ownt 0.601 0.189 0.487 0.627 0.738 Leveraget 0.195 0.171 0.038 0.186 0.300 Cash Flowt 0.095 0.118 0.057 0.102 0.149 Cash Flow Volatilityt 0.046 0.042 0.018 0.034 0.060 Table I. Sample selection and summary statistics Panel A describes the sample selection procedure. We start with firm-year observations from non-financial and non-utility firms in the Compustat Execucomp database from 1993 to 2003. We then eliminate observations that do not have necessary data available in the Compustat Execucomp database, the NBER Patent Citations database, the Compustat Fundamentals Annual database, the Thomson Reuters Ownership (13f) database, and the CRSP database. After applying several additional filters, the final study sample consists of 5,170 firm-year observations. Panel B presents the summary statistics for the sample. Panel A. Sample selection All firm-year observations from non-financial and non-utility firms in Execucomp from 1993 to 2003 15,871 After merging with Compustat, CRSP, and Thomson Reuters Ownership databases 15,789 After merging with NBER Patent Citations database 5,702 Requiring at least three VPs reported in Execucomp and a non-negative CEO–VP pay gap 5,372 Requiring non-missing information for manually collected variables, e.g., CEO Age and Inside CEO 5,170 Panel A. Sample selection All firm-year observations from non-financial and non-utility firms in Execucomp from 1993 to 2003 15,871 After merging with Compustat, CRSP, and Thomson Reuters Ownership databases 15,789 After merging with NBER Patent Citations database 5,702 Requiring at least three VPs reported in Execucomp and a non-negative CEO–VP pay gap 5,372 Requiring non-missing information for manually collected variables, e.g., CEO Age and Inside CEO 5,170 Panel B. Summary statistics Variable Mean SD Q1 Median Q3 Patt+1 43.388 108.101 1.000 6.000 30.000 Citet+1 637.351 1919.400 0.000 47.191 328.863 Patt+1/RDt+1 0.234 0.279 0.016 0.133 0.343 Citet+1/RDt+1 2.976 4.794 0.000 0.913 3.755 Pay Gapt (in million $) 1.084 1.100 0.375 0.752 1.417 CEO Deltat (in million $) 0.893 2.458 0.111 0.268 0.723 VP Deltat (in million $) 0.126 0.239 0.021 0.049 0.121 CEO Vegat (in million $) 0.154 0.275 0.023 0.062 0.163 VP Vegat (in million $) 0.035 0.058 0.007 0.015 0.038 CEO Aget 55.935 14.674 51.000 56.000 61.000 CEO Tenuret 6.628 7.470 1.000 4.000 9.000 Salet (in million $) 5196.9 10499.4 429.6 1315.1 4623.5 Tobin’s qt 2.511 2.126 1.367 1.827 2.820 Sale Growtht 0.166 0.277 0.024 0.096 0.218 (Capex/Assets)t 0.057 0.042 0.029 0.047 0.073 (PPE/EMP)t 99.531 139.286 36.939 58.989 106.366 Inst Ownt 0.601 0.189 0.487 0.627 0.738 Leveraget 0.195 0.171 0.038 0.186 0.300 Cash Flowt 0.095 0.118 0.057 0.102 0.149 Cash Flow Volatilityt 0.046 0.042 0.018 0.034 0.060 Panel B. Summary statistics Variable Mean SD Q1 Median Q3 Patt+1 43.388 108.101 1.000 6.000 30.000 Citet+1 637.351 1919.400 0.000 47.191 328.863 Patt+1/RDt+1 0.234 0.279 0.016 0.133 0.343 Citet+1/RDt+1 2.976 4.794 0.000 0.913 3.755 Pay Gapt (in million $) 1.084 1.100 0.375 0.752 1.417 CEO Deltat (in million $) 0.893 2.458 0.111 0.268 0.723 VP Deltat (in million $) 0.126 0.239 0.021 0.049 0.121 CEO Vegat (in million $) 0.154 0.275 0.023 0.062 0.163 VP Vegat (in million $) 0.035 0.058 0.007 0.015 0.038 CEO Aget 55.935 14.674 51.000 56.000 61.000 CEO Tenuret 6.628 7.470 1.000 4.000 9.000 Salet (in million $) 5196.9 10499.4 429.6 1315.1 4623.5 Tobin’s qt 2.511 2.126 1.367 1.827 2.820 Sale Growtht 0.166 0.277 0.024 0.096 0.218 (Capex/Assets)t 0.057 0.042 0.029 0.047 0.073 (PPE/EMP)t 99.531 139.286 36.939 58.989 106.366 Inst Ownt 0.601 0.189 0.487 0.627 0.738 Leveraget 0.195 0.171 0.038 0.186 0.300 Cash Flowt 0.095 0.118 0.057 0.102 0.149 Cash Flow Volatilityt 0.046 0.042 0.018 0.034 0.060 In Table I, Panel B presents descriptive statistics for the sample. The mean value of patent grants (Patt + 1) is 43 and its median value is 6. The mean value of citation counts (Citet + 1) is about 637 and its median value is around 47.11 With respect to the innovative efficiency measures, the mean values of Patt + 1/RDt + 1 and Citet + 1/RDt + 1 indicate that 1 million dollars of R&D investment, on average, generate 0.234 patents and 2.976 related patent citations. The statistics indicate that these patent and citation variables are skewed, and thus we use the logarithm transformation of these variables in our regressions to mitigate the impact of extreme values.12 The mean value of Pay Gap is $1.084 million, indicating that a CEO on average earns around 1 million dollars more than a non-CEO executive. The mean values of CEO Delta and CEO Vega are $0.893 million and $0.154 million, respectively. Panel B of Table I also presents the descriptive statistics of CEO characteristics and other firm characteristic variables. The average CEO Age is 56. The mean value of annual sales is about $5.2 billion. The average Tobin’s q is 2.511. The mean value of Capex/Asset is 0.057. Consistent with prior studies (e.g., Chung and Zhang, 2011), Panel B also shows that around 60% of the sample firms’ shares are held by institutional investors. The mean values of Cash Flow and Cash Flow Volatility are 0.095 and 0.046, respectively. 3. Tournament Incentives and Corporate Innovation This section presents the results of baseline regressions and several additional tests on the relation between tournament incentives and corporate innovative efficiency. 3.1. Baseline Regressions Kini and Williams (2012) show that greater tournament incentives induce senior executives to undertake greater R&D investments.13 However, they do not address the concern that the risk may be pursued at the expense of efficiency. It is possible that senior managers who face a high-prize tournament may over-invest in risky R&D projects (to increase their chance of winning the tournament) without adequate consideration of efficiency. This section answers the following empirical question: Are greater R&D investments induced by larger tournament incentives efficient or not? Specifically, we estimate the following baseline regression model: Ln(Pati,t+n/RDi,t+1) or Ln(Citei,t+n/RDi,t+1)=β0+β1Ln(Pay Gap)i,t+β2CEO Deltai,t+β3CEO Vegai,t+β4VP Deltai,t+β5VP Vegai,t+β6Ln(CEO Age)i,t+β7CEO Tenurei,t+β8Ln(Sale)i,t+β9Tobin’sqi,t+β10Sale Growthi,t+β11(Capex/Asset)i,t+β12Ln(PPE/EMP)i,t+β13Inst Owni,t+β14Leveragei,t+β15Cash Flowi,t+β16Cash Flow Volatilityi,t+Year Dummies+Industry Dummies+ɛi,t; (1) where Ln(Pati,t + n/RDi,t + 1) and Ln(Citei,t + n/RDi,t + 1) are the logarithm of the innovative efficiency measures as introduced in Section 2.2. Please refer to Appendix A and Section 2 for detailed information concerning other variables. Table II presents the results of the baseline model (1) based on ordinary least squares (OLS) regressions with firm-clustered, heteroskedasticity-robust standard errors.14 Table II. Tournament incentive and innovative efficiency Panel A presents the results of the baseline regressions. The dependent variables are the innovative efficiency measures. Panel B presents a modified specification of the baseline regression model, to which we add the following additional control variables: the governance index compiled by Gompers, Ishii, and Metrick (2003) with twenty-four IRRC anti-takeover provisions (G-index); a dummy variable (CEO Overconfidence) that equals one if the CEO of a firm is overconfident and zero otherwise, where we identify an overconfident CEO if this CEO holds stock options that are more than 100% in the money (Campbell et al., 2011); and Demerjian, Lev, and McVay’s (2012) managerial ability score measure (Managerial Ability). Due to the additional data requirements to compute these control variables, we have a smaller sample to conduct this robustness check. The variable definitions are provided in Appendix A. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at the firm level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Panel A: Tournament incentive and innovative efficiency Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.031* 0.039** 0.036** 0.117* 0.130** 0.118** (1.89) (2.36) (2.25) (1.80) (2.06) (1.97) CEO Deltat 0.001 0.001 0.000 0.005 0.005 −0.001 (0.74) (0.65) (0.05) (0.49) (0.54) (−0.06) CEO Vegat 0.035 0.019 0.010 0.099 0.054 0.042 (1.50) (0.88) (0.45) (1.11) (0.65) (0.57) VP Deltat −0.028 −0.015 −0.007 −0.051 −0.064 −0.036 (−1.39) (−0.76) (−0.32) (−0.59) (−0.76) (−0.41) VP Vegat −0.051 −0.011 0.020 −0.096 −0.066 −0.151 (−0.52) (−0.11) (0.18) (−0.23) (−0.16) (−0.40) Ln(CEO Age)t 0.045 0.043 0.015 −0.021 −0.030 −0.096 (1.05) (0.93) (0.32) (−0.12) (−0.17) (−0.55) CEO Tenuret 0.000 0.000 0.000 −0.001 −0.001 0.001 (−0.37) (−0.58) (−0.42) (−0.20) (−0.29) (0.18) Ln(Sale)t −0.005 −0.007 −0.006 0.027 0.026 0.025 (−1.03) (−1.42) (−1.17) (1.32) (1.31) (1.33) Tobin’s qt −0.001 −0.002 −0.004* 0.012 0.009 0.006 (−0.40) (−0.91) (−1.69) (1.19) (0.96) (0.64) Sale Growtht −0.019 −0.006 0.006 0.042 0.104* 0.115* (−1.44) (−0.40) (0.44) (0.74) (1.72) (1.89) (Capex/Assets)t 0.432*** 0.445*** 0.364*** 1.878*** 2.084*** 1.537*** (3.27) (3.24) (2.63) (3.43) (3.96) (3.06) Ln(PPE/EMP)t 0.021** 0.021** 0.019** 0.089** 0.069* 0.062* (2.24) (2.30) (2.15) (2.25) (1.84) (1.73) Inst Ownt −0.003 0.007 0.013 0.069 0.093 0.130 (−0.09) (0.22) (0.43) (0.56) (0.82) (1.23) Leveraget 0.041 0.019 −0.006 −0.036 −0.094 −0.145 (1.24) (0.63) (−0.19) (−0.29) (−0.82) (−1.32) Cash Flowt −0.024 0.021 0.054 −0.198 −0.032 0.095 (−0.59) (0.54) (1.24) (−1.24) (−0.21) (0.58) Cash Flow Volatilityt −0.208* −0.188* −0.126 −0.507 −0.415 −0.327 (−1.95) (−1.73) (−1.18) (−1.14) (−0.97) (−0.82) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.228 0.279 0.315 0.383 0.427 Panel A: Tournament incentive and innovative efficiency Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.031* 0.039** 0.036** 0.117* 0.130** 0.118** (1.89) (2.36) (2.25) (1.80) (2.06) (1.97) CEO Deltat 0.001 0.001 0.000 0.005 0.005 −0.001 (0.74) (0.65) (0.05) (0.49) (0.54) (−0.06) CEO Vegat 0.035 0.019 0.010 0.099 0.054 0.042 (1.50) (0.88) (0.45) (1.11) (0.65) (0.57) VP Deltat −0.028 −0.015 −0.007 −0.051 −0.064 −0.036 (−1.39) (−0.76) (−0.32) (−0.59) (−0.76) (−0.41) VP Vegat −0.051 −0.011 0.020 −0.096 −0.066 −0.151 (−0.52) (−0.11) (0.18) (−0.23) (−0.16) (−0.40) Ln(CEO Age)t 0.045 0.043 0.015 −0.021 −0.030 −0.096 (1.05) (0.93) (0.32) (−0.12) (−0.17) (−0.55) CEO Tenuret 0.000 0.000 0.000 −0.001 −0.001 0.001 (−0.37) (−0.58) (−0.42) (−0.20) (−0.29) (0.18) Ln(Sale)t −0.005 −0.007 −0.006 0.027 0.026 0.025 (−1.03) (−1.42) (−1.17) (1.32) (1.31) (1.33) Tobin’s qt −0.001 −0.002 −0.004* 0.012 0.009 0.006 (−0.40) (−0.91) (−1.69) (1.19) (0.96) (0.64) Sale Growtht −0.019 −0.006 0.006 0.042 0.104* 0.115* (−1.44) (−0.40) (0.44) (0.74) (1.72) (1.89) (Capex/Assets)t 0.432*** 0.445*** 0.364*** 1.878*** 2.084*** 1.537*** (3.27) (3.24) (2.63) (3.43) (3.96) (3.06) Ln(PPE/EMP)t 0.021** 0.021** 0.019** 0.089** 0.069* 0.062* (2.24) (2.30) (2.15) (2.25) (1.84) (1.73) Inst Ownt −0.003 0.007 0.013 0.069 0.093 0.130 (−0.09) (0.22) (0.43) (0.56) (0.82) (1.23) Leveraget 0.041 0.019 −0.006 −0.036 −0.094 −0.145 (1.24) (0.63) (−0.19) (−0.29) (−0.82) (−1.32) Cash Flowt −0.024 0.021 0.054 −0.198 −0.032 0.095 (−0.59) (0.54) (1.24) (−1.24) (−0.21) (0.58) Cash Flow Volatilityt −0.208* −0.188* −0.126 −0.507 −0.415 −0.327 (−1.95) (−1.73) (−1.18) (−1.14) (−0.97) (−0.82) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.228 0.279 0.315 0.383 0.427 Panel B. Additional control variables Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.034* 0.041** 0.038** 0.127* 0.145** 0.141** (1.95) (2.29) (2.17) (1.82) (2.11) (2.16) G-Indext 0.003 0.003 0.002 −0.004 −0.005 −0.004 (1.13) (0.98) (0.85) (−0.37) (−0.48) (−0.46) CEO Overconfidencet 0.009 0.017 0.011 0.088 0.072 0.062 (0.54) (0.87) (0.56) (1.06) (0.82) (0.77) Managerial Abilityt 0.036* 0.037* 0.044** 0.119 0.088 0.103 (1.65) (1.73) (2.10) (1.44) (1.11) (1.40) Other controls Yes Yes Yes Yes Yes Yes N 4,116 3,921 3,719 4,116 3,921 3,719 Adjusted R2 0.192 0.259 0.314 0.363 0.431 0.474 Panel B. Additional control variables Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.034* 0.041** 0.038** 0.127* 0.145** 0.141** (1.95) (2.29) (2.17) (1.82) (2.11) (2.16) G-Indext 0.003 0.003 0.002 −0.004 −0.005 −0.004 (1.13) (0.98) (0.85) (−0.37) (−0.48) (−0.46) CEO Overconfidencet 0.009 0.017 0.011 0.088 0.072 0.062 (0.54) (0.87) (0.56) (1.06) (0.82) (0.77) Managerial Abilityt 0.036* 0.037* 0.044** 0.119 0.088 0.103 (1.65) (1.73) (2.10) (1.44) (1.11) (1.40) Other controls Yes Yes Yes Yes Yes Yes N 4,116 3,921 3,719 4,116 3,921 3,719 Adjusted R2 0.192 0.259 0.314 0.363 0.431 0.474 Table II. Tournament incentive and innovative efficiency Panel A presents the results of the baseline regressions. The dependent variables are the innovative efficiency measures. Panel B presents a modified specification of the baseline regression model, to which we add the following additional control variables: the governance index compiled by Gompers, Ishii, and Metrick (2003) with twenty-four IRRC anti-takeover provisions (G-index); a dummy variable (CEO Overconfidence) that equals one if the CEO of a firm is overconfident and zero otherwise, where we identify an overconfident CEO if this CEO holds stock options that are more than 100% in the money (Campbell et al., 2011); and Demerjian, Lev, and McVay’s (2012) managerial ability score measure (Managerial Ability). Due to the additional data requirements to compute these control variables, we have a smaller sample to conduct this robustness check. The variable definitions are provided in Appendix A. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at the firm level. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. Panel A: Tournament incentive and innovative efficiency Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.031* 0.039** 0.036** 0.117* 0.130** 0.118** (1.89) (2.36) (2.25) (1.80) (2.06) (1.97) CEO Deltat 0.001 0.001 0.000 0.005 0.005 −0.001 (0.74) (0.65) (0.05) (0.49) (0.54) (−0.06) CEO Vegat 0.035 0.019 0.010 0.099 0.054 0.042 (1.50) (0.88) (0.45) (1.11) (0.65) (0.57) VP Deltat −0.028 −0.015 −0.007 −0.051 −0.064 −0.036 (−1.39) (−0.76) (−0.32) (−0.59) (−0.76) (−0.41) VP Vegat −0.051 −0.011 0.020 −0.096 −0.066 −0.151 (−0.52) (−0.11) (0.18) (−0.23) (−0.16) (−0.40) Ln(CEO Age)t 0.045 0.043 0.015 −0.021 −0.030 −0.096 (1.05) (0.93) (0.32) (−0.12) (−0.17) (−0.55) CEO Tenuret 0.000 0.000 0.000 −0.001 −0.001 0.001 (−0.37) (−0.58) (−0.42) (−0.20) (−0.29) (0.18) Ln(Sale)t −0.005 −0.007 −0.006 0.027 0.026 0.025 (−1.03) (−1.42) (−1.17) (1.32) (1.31) (1.33) Tobin’s qt −0.001 −0.002 −0.004* 0.012 0.009 0.006 (−0.40) (−0.91) (−1.69) (1.19) (0.96) (0.64) Sale Growtht −0.019 −0.006 0.006 0.042 0.104* 0.115* (−1.44) (−0.40) (0.44) (0.74) (1.72) (1.89) (Capex/Assets)t 0.432*** 0.445*** 0.364*** 1.878*** 2.084*** 1.537*** (3.27) (3.24) (2.63) (3.43) (3.96) (3.06) Ln(PPE/EMP)t 0.021** 0.021** 0.019** 0.089** 0.069* 0.062* (2.24) (2.30) (2.15) (2.25) (1.84) (1.73) Inst Ownt −0.003 0.007 0.013 0.069 0.093 0.130 (−0.09) (0.22) (0.43) (0.56) (0.82) (1.23) Leveraget 0.041 0.019 −0.006 −0.036 −0.094 −0.145 (1.24) (0.63) (−0.19) (−0.29) (−0.82) (−1.32) Cash Flowt −0.024 0.021 0.054 −0.198 −0.032 0.095 (−0.59) (0.54) (1.24) (−1.24) (−0.21) (0.58) Cash Flow Volatilityt −0.208* −0.188* −0.126 −0.507 −0.415 −0.327 (−1.95) (−1.73) (−1.18) (−1.14) (−0.97) (−0.82) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.228 0.279 0.315 0.383 0.427 Panel A: Tournament incentive and innovative efficiency Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.031* 0.039** 0.036** 0.117* 0.130** 0.118** (1.89) (2.36) (2.25) (1.80) (2.06) (1.97) CEO Deltat 0.001 0.001 0.000 0.005 0.005 −0.001 (0.74) (0.65) (0.05) (0.49) (0.54) (−0.06) CEO Vegat 0.035 0.019 0.010 0.099 0.054 0.042 (1.50) (0.88) (0.45) (1.11) (0.65) (0.57) VP Deltat −0.028 −0.015 −0.007 −0.051 −0.064 −0.036 (−1.39) (−0.76) (−0.32) (−0.59) (−0.76) (−0.41) VP Vegat −0.051 −0.011 0.020 −0.096 −0.066 −0.151 (−0.52) (−0.11) (0.18) (−0.23) (−0.16) (−0.40) Ln(CEO Age)t 0.045 0.043 0.015 −0.021 −0.030 −0.096 (1.05) (0.93) (0.32) (−0.12) (−0.17) (−0.55) CEO Tenuret 0.000 0.000 0.000 −0.001 −0.001 0.001 (−0.37) (−0.58) (−0.42) (−0.20) (−0.29) (0.18) Ln(Sale)t −0.005 −0.007 −0.006 0.027 0.026 0.025 (−1.03) (−1.42) (−1.17) (1.32) (1.31) (1.33) Tobin’s qt −0.001 −0.002 −0.004* 0.012 0.009 0.006 (−0.40) (−0.91) (−1.69) (1.19) (0.96) (0.64) Sale Growtht −0.019 −0.006 0.006 0.042 0.104* 0.115* (−1.44) (−0.40) (0.44) (0.74) (1.72) (1.89) (Capex/Assets)t 0.432*** 0.445*** 0.364*** 1.878*** 2.084*** 1.537*** (3.27) (3.24) (2.63) (3.43) (3.96) (3.06) Ln(PPE/EMP)t 0.021** 0.021** 0.019** 0.089** 0.069* 0.062* (2.24) (2.30) (2.15) (2.25) (1.84) (1.73) Inst Ownt −0.003 0.007 0.013 0.069 0.093 0.130 (−0.09) (0.22) (0.43) (0.56) (0.82) (1.23) Leveraget 0.041 0.019 −0.006 −0.036 −0.094 −0.145 (1.24) (0.63) (−0.19) (−0.29) (−0.82) (−1.32) Cash Flowt −0.024 0.021 0.054 −0.198 −0.032 0.095 (−0.59) (0.54) (1.24) (−1.24) (−0.21) (0.58) Cash Flow Volatilityt −0.208* −0.188* −0.126 −0.507 −0.415 −0.327 (−1.95) (−1.73) (−1.18) (−1.14) (−0.97) (−0.82) Industry Effect Yes Yes Yes Yes Yes Yes Year Effect Yes Yes Yes Yes Yes Yes N 5,170 4,916 4,651 5,170 4,916 4,651 Adjusted R2 0.166 0.228 0.279 0.315 0.383 0.427 Panel B. Additional control variables Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.034* 0.041** 0.038** 0.127* 0.145** 0.141** (1.95) (2.29) (2.17) (1.82) (2.11) (2.16) G-Indext 0.003 0.003 0.002 −0.004 −0.005 −0.004 (1.13) (0.98) (0.85) (−0.37) (−0.48) (−0.46) CEO Overconfidencet 0.009 0.017 0.011 0.088 0.072 0.062 (0.54) (0.87) (0.56) (1.06) (0.82) (0.77) Managerial Abilityt 0.036* 0.037* 0.044** 0.119 0.088 0.103 (1.65) (1.73) (2.10) (1.44) (1.11) (1.40) Other controls Yes Yes Yes Yes Yes Yes N 4,116 3,921 3,719 4,116 3,921 3,719 Adjusted R2 0.192 0.259 0.314 0.363 0.431 0.474 Panel B. Additional control variables Dependent variable = Dependent variable = Ln(Patt+1RDt+1) Ln(Patt+2RDt+1) Ln(Patt+3RDt+1) Ln(Citet+1RDt+1) Ln(Citet+2RDt+1) Ln(Citet+3RDt+1) Ln(Pay Gap)t 0.034* 0.041** 0.038** 0.127* 0.145** 0.141** (1.95) (2.29) (2.17) (1.82) (2.11) (2.16) G-Indext 0.003 0.003 0.002 −0.004 −0.005 −0.004 (1.13) (0.98) (0.85) (−0.37) (−0.48) (−0.46) CEO Overconfidencet 0.009 0.017 0.011 0.088 0.072 0.062 (0.54) (0.87) (0.56) (1.06) (0.82) (0.77) Managerial Abilityt 0.036* 0.037* 0.044** 0.119 0.088 0.103 (1.65) (1.73) (2.10) (1.44) (1.11) (1.40) Other controls Yes Yes Yes Yes Yes Yes N 4,116 3,921 3,719 4,116 3,921 3,719 Adjusted R2 0.192 0.259 0.314 0.363 0.431 0.474 In Panel A of Table II, Columns 1–3 present the regressions of Ln(Pati,t + n/RDi,t + 1), while Columns 4–6 present the regressions of Ln(Citei,t + n/RDi,t + 1). The coefficients of Ln(Pay Gap) are all positive and consistently significant across all the regressions. Based on the coefficient of Ln(Pay Gap) in Column 1 of Table II, a 1% increase in Pay Gap raises Patt + 1/RDt + 1 by around 0.031%. It suggests that if a firm’s Pay Gap increases from the 25th percentile to the 75th percentile, then Patt + 1/RDt + 1 on average will increase by around 0.106.15 According to Hall, Jaffe, and Trajtenberg (2005), an extra patent per million dollars of R&D boosts a firm’s market value by about 2%. Since the average market value of equity in our sample is around $6,376 million, the 0.106 increase in Patt + 1/RDt + 1 translates into a $13.51 million (13.51 = 0.106×$6,376 × 2%) increase in market value. As such, the positive relation between tournament incentives and innovative efficiency is both statistically significant and economically meaningful. These results are consistent with the argument that greater tournament incentives induce managers to undertake more efficient R&D investments. They also complement prior studies on the bright side of the pay gap (e.g., Kale, Reis, and Venkateswaran, 2009) by shedding light on a new mechanism through which tournament incentives add value to companies. Panel A of Table II also presents the results on the relation between performance-based incentives and innovative efficiency. First, the effect of executive compensation delta on managerial risk-taking (e.g., innovative activities) is unclear in prior literature. On the one hand, John and John (1993) suggest that a higher delta increases the incentive of a manager to undertake risky projects and shift the risk to creditors. On the other hand, a higher delta increases the sensitivity of a manager’s wealth to firm performance, and consequently the risk-averse manager might trim down the risk exposure of the firm (Guay, 1999). Second, although Coles, Daniel, and Naveen (2006) find that CEO Vega is positively related to R&D investments, Shen and Zhang (2013) show that an excessively high vega might induce managers to overinvest in inefficient R&D projects. Therefore, a high executive compensation vega might not lead to greater innovative efficiency. Consistent with these mixed views, we find no significant relation between performance-based incentives and innovative efficiency measures. 3.2 Additional Control Variables An overconfident CEO may facilitate a centralized decision-making process, which could benefit the efficiency of corporate innovative activities (Boyd, 1995; Hirshleifer, Low, and Teoh, 2012). Nevertheless, overconfident CEOs are found to have mixed effects on investment efficiencies and firm value (Campbell et al., 2011). Additionally, anti-takeover provisions could enhance CEO power and lead to CEOs’ excess compensation (Borokhovich, Brunarski, and Parrino, 1997). Therefore, CEO overconfidence and anti-takeover provisions, as omitted variables, could confound our results. We identify an overconfident CEO if this CEO holds stock options that are more than 100% in the money (Campbell et al., 2011). CEO Overconfidence is a dummy variable that equals one if the CEO of a firm is overconfident and zero otherwise. We add CEO Overconfidence, Gompers, Ishii, and Metrick’s (2003) G-index, and Demerjian, Lev, and McVay’s (2012) managerial ability score (Managerial Ability) to the baseline model (1). For brevity, we only report the coefficients on Ln(Pay Gap) and these additional controls in Panel B of Table II. Sample attrition in these regressions is due to the additional data requirements for computing these additional controls. The coefficients on Managerial Ability are all positive, although they are only significant in the regressions of patent-based innovative efficiency measures. More importantly, the coefficients on Ln(Pay Gap) remain significantly positive. To the extent that these variables can isolate the effects of CEO power and the related factors, the finding suggests that tournament incentives have an incremental and positive effect on innovative efficiency.16 3.3 Alternative Measures of Firm Innovation We also conduct tests to examine whether our main finding is robust to alternative measures of firm innovation performance. Patents that cite other patents in dispersed technology classes are often believed to have greater “originality”; patents that are cited by patents in a dispersed array of technology classes are viewed as having greater “generality” (Hall, Jaffe, and Trajtenberg, 2001). The generality and originality indices devised by Hall, Jaffe, and Trajtenberg (2001) can capture the fundamental importance of the patents. We follow Lerner and Seru (2014) to scale the generality (originality) index by the average generality (originality) index of all patents granted in the same year and in the same technology class. We compute the firm-year level scaled generality index (Scaled General) by summing up the scaled generality index across all patents that were applied for by a firm during a year and were eventually granted. The scaled originality index (Scaled Origin) is computed in a similar way, except it refers to citations made. Panel A of Table III presents the modified baseline model (1) which uses these indices as alternative dependent variables. We find that the coefficients on the pay gap measure remain significantly positive. Table III. Alternative firm innovation measures Panel A presents the regressions using the generality and originality indices, and Panel B presents the regressions examining the relation between tournament incentives and stock market reactions to patent issuance. The generality index (General) for patent i is defined as 1−∑jnisij2, where sij denotes the percentage of citations received by patent i that belong to technological class j, and ni is the total number of technological classes. A high generality index indicates that a patent receives citations from a wide range of technological fields. The scaled generality index (Scaled General) for a patent is defined as the generality index of this patent scaled by the average generality index taken across all patents granted in the same year and technology class. We compute the firm-year level scaled generality index by summing up the scaled generality index across all patents that were applied for by a firm during a year and were eventually granted. The scaled originality index (Scaled Origin) is computed in a similar way, except it refers to citations made. A high originality index for a patent indicates that technologies from a wide range of fields are used to develop this particular patent. We estimate a modified version of the baseline regression model (1) in which the scaled generality index or scaled originality index is used as the dependent variable. We also add the R&D-to-asset ratio to control for the variation in corporate innovation input. Panel B presents the regressions of stock market reactions to patent grants. Following Kogan et al. (2017), we compute stock returns based on 3-day window (0, +2) and 5-day window (−1, +3) around patent issuance date, where day 0 is the patent issuance date. To obtain firm-year observations, we compute the average of the returns across all patents that were applied for by a firm during a year and were eventually granted. RET(0, +2) and RET(−1, +3) denote stock raw returns around patent issuance date based on 3-day window and 5-day window, respectively. CAR(0, +2) and CAR(−1, +3) denote market-adjusted abnormal returns around patent issuance dates, where CRSP value-weighted index returns are used as the benchmark. We then merge the data of stock returns around patent issuance dates with our main sample of firm-year observations and follow Chan, Martin, and Kensinger (1990) to estimate the following model: RETi,t+1(0,+2),CARi,t+1(0,+2),RETi,t+1(−1,+3),orCARi,t+1(−1,+3)=β0+β1Ln(Pay Gap)i,t+β2CEO Deltai,t+β3CEO Vegai,t+β4VP Deltai,t+β5VP Vegai,t+β6Ln(CEO Age)i,t+β7CEO Tenurei,t+β8MVEi,t+β9BMi,t+β10(RD/A)i,t+β11Conci,t+β12Leveragei,t+Year Dummies+Industry Dummies+ɛi,t, where RETi,t+1 and CARi,t+1 are the average stock raw returns and market-adjusted returns around the patent issuance dates for firm i in year t+1, respectively. MVE is the market value of equity for firm year i in year t, BM is the book-to-market ratio, RD/A is the R&D intensity measured as the R&D expense scaled by assets, Conc is industry concentration measured as the Herfindahl index computed as ∑isi2 in a given year, where si is firm i’s sales divided by the aggregate sales across all firms in the same three-digit SIC code industry that firm i belongs to. Other variables are defined in Section 2 and Appendix A. For brevity, both Panel A and Panel B only report the estimated coefficients on the pay gap measure. All regressions control for the two-digit SIC code industry effect and year effect. t-Statistics are based on robust standard errors clustered at firm level. ***, **, and * denote significance at 1%, 5%, and 10% levels, respectively. Dependent variable = Dependent variable = Ln(Scaled Generalt+1) Ln(Scaled Generalt+2) Ln(Scaled Generalt+3) Ln(Scaled Origint+1) Ln(Scaled Origint+2) Ln(Scaled Origint+3) Panel A. Generality and originality indices Ln(Pay Gap)t 0.280** 0.238* 0.263* 0.246** 0.292** 0.350** (2.26) (1.70) (1.74) (2.06) (2.21) (2.54) Other controls Yes Yes Yes Yes Yes Yes N 3,262 2,744 2,272 4,022 3,470 2,945 Adjusted R2 0.542 0.544 0.542 0.537 0.541 0.541 Dependent variable = Dependent variable = Ln(Scaled Generalt+1) Ln(Scaled Generalt+2) Ln(Scaled Generalt+3) Ln(Scaled Origint+1) Ln(Scaled Origint+2) Ln(Scaled Origint+3) Panel A. Generality and originality indices Ln(Pay Gap)t 0.280** 0.238* 0.263* 0.246** 0.292** 0.350** (2.26) (1.70) (1.74) (2.06) (2.21) (2.54) Other controls Yes Yes Yes Yes Yes Yes N 3,262 2,744 2,272 4,022 3,470 2,945 Adjusted R2 0.542 0.544 0.542 0.537 0.541 0.541 Panel B. Stock market reaction to patent issuance RETt+1(0, +2) CARt+1(0, +2) RETt+1(−1, +3) CARt+1(−1, +3) Ln(Pay Gap)t 0.0020* 0.0021** 0.0031** 0.0029** (1.96) (2.12) (2.27) (2.47) Other controls Yes Yes Yes Yes N 4,151 4,151 4,151 4,151 Adjusted R2 0.025 0.027 0.034 0.039 Panel B. Stock market reaction to patent issuance RETt+1(0, +2) CARt+1(0, +2) RETt+1(−1, +3) CARt+1(−1, +3) Ln(Pay Gap)t 0.0020* 0.0021** 0.0031** 0.0029** (1.96) (2.12) (2.27) (2.47) Other controls Yes Yes Yes Yes N 4,151 4,151 4,151 4,151 Adjusted R2 0.025 0.027 0.034 0.039 Table III. Alternative firm innovation measures Panel A presents the regressions using the generality and originality indices, and Panel B presents the regressions examining the relation between tournament incentives and stock market reactions to patent issuance. The generality index (General) for patent i is defined as 1−∑jnisij2, where sij denotes the percentage of citations received by patent i that belong to technological class j, and ni is the total number of technological classes. A high generality index indicates that a patent receives citations from a wide range of technological fields. The scaled generality index (Scaled General) for a patent is defined as the generality index of this patent scaled by the average generality index taken across all patents granted in the same year and technology class. We compute the firm-year level scaled generality index by summing up the scaled generality index across all patents that were applied for by a firm during a year and were eventually granted. The scaled originality index (Scaled Origin) is computed in a similar way, except it refers to citations made. A high originality index for a patent indicates that technologies from a wide range of fields are used to develop this particular patent. We estimate a modified version of the baseline regression model (1) in which the scaled generality index or scaled originality index is used as the dependent variable. We also add the R&D-to-asset ratio to control for the variation in corporate innovation input. Panel B presents the regressions of stock market reactions to patent grants. Following Kogan et al. (2017), we compute stock returns based on 3-day window (0, +2) and 5-day window (−1, +3) around patent issuance date, where day 0 is the patent issuance date. To obtain firm-year observations, we compute the average of the returns across all patents that were applied for by a firm during a year and were eventually granted. RET(0, +2) and RET(−1, +3) denote stock raw returns around patent issuance date based on 3-day window and 5-day window, respectively. CAR(0, +2) and CAR(−1, +3) denote