Industry tournament incentives and corporate innovation

2.1 Data sources

We collect CEO compensation data from ExecuComp over 1992–2005.10 We control for firm characteristics using accounting data from Compustat, stock return data from the Center for Research in Security Prices, and institutional ownership data from Thomson Reuters 13F database. Firm-year observations must have nonmissing CEO industry pay gap and main control variables to be included in the sample. We merge CEO compensation data and firm characteristics data with patent-related data from the NBER patent database. Following the innovation literature, we set the patent-based innovation output to zero for firm-year observations that are not present in the NBER patent database. Firms that operate in Fama-French 30 industries without any filed patent in the sample period are excluded from the sample.11 The final sample, excluding financial and utility firms, consists of 11,354 firm-year observations associated with 1734 unique firms and 2816 unique CEOs from 1992 to 2005.12

2.2 Variable measurement

2.2.1 Measures of innovation

Existing literature has developed two proxies to capture firm innovation: R&D expenditures and patenting activity. Between the two measures, patenting activity is considered a better proxy, as it measures innovation output and captures how effectively a firm has utilized its innovation inputs, both observable and unobservable. In contrast, R&D expenditures are only one particular observable input and fail to capture the quality of innovation. Therefore, following existing innovation literature, we use a firm's patenting activity to measure innovation.13

We construct output-oriented measures of innovation using the latest version of the NBER patent database which contains patent and citation information from 1976 to 2006. Figure 1 shows a timeline for the measurements of patent and citation. Our first measure of innovation reflects the quantity of a firm's innovation output and is calculated as the number of patent applications filed by a firm in a given year that are eventually granted. Hall et al. (2001) recommend using application year because the actual timing of the patented innovation is closer to the application year than to the subsequent grant year.14 There is, on average, a 2-year lag between patent application and patent grant. This, in turn, leads to a truncation bias in patent counts toward the end of the sample period. As suggested by Hall et al. (2001), we include year fixed effects in our regressions to address this truncation issue. Further, we follow Hall et al. (2005) and Fang et al. (2014) to estimate the application-grant lag distribution and compute the truncation-adjusted patent count as raw patent count divided by the cumulative application-grant lag distribution. Additionally, following Atanassov (2013), we construct another adjusted measure of patent count by scaling the number of patents for each firm-year by the average number of patents of all firms in the NBER patent database for that year.

Our second measure of innovation is the number of citations per patent, which reflects the importance and quality of a firm's innovation output. It is calculated as the total number of citations ultimately received on the firm's patents applied for (and eventually granted), scaled by the number of patents applied for (and eventually granted) during the year.15 As illustrated in Figure 1, citations are counted starting from the patent grant year until the end of the sample period. Therefore, this measure also suffers from a truncation bias because patents tend to receive citations over a long period after the patents are granted. We follow the recommendations of Hall et al. (2001) and adjust the citation count of each patent in three different ways. For the first adjustment, we multiply each patent's citation count by the weighting index from Hall et al. (2001, 2005) that is created by econometrically estimating the distribution of the citation lag.16 For the second adjustment, we scale each patent's citation count by the average citation count of all patents in the same year. For the third adjustment, we scale each patent's citation count by the average citation count of all patents in the same year and technology class. For each type of adjustment, we then sum up the adjusted citation count across all patents applied for during each firm-year and compute the corresponding average number of adjusted citations per patent for each firm-year.

Our third measure of innovation is the impact of innovation which is defined as the total number of citations ultimately received by the patents applied for (and eventually granted) during a given year. The citation count of each patent is adjusted in three different ways, as explained above. The impact of innovation measure takes into account both the numbers of patents and the number of citations per patent.

We merge the patent data with the CEO compensation data and firm characteristics data. Following the innovation literature (see, e.g., Atanassov, 2013; He & Tian, 2013; Huang et al., 2020; Kogan et al., 2017; Mao & Weathers, 2019; Mao & Zhang, 2018), we set the patent count, citations-per-patent count and total citation count to zero for firm-year observations that are not present in the NBER patent database because this patent database covers the entire universe of firms that have filed patents with the USPTO. Following Kogan et al. (2017) and Custódio et al. (2019), we exclude firms that operate in FF30 industries without any filed patent in the sample period. Due to the right skewness of the innovation measures in our final sample, we winsorize these variables at the 99th percentile.

For robustness tests, we also calculate additional measures of innovation. First, following Chan et al. (2001) and Hirshleifer et al. (2013), we measure innovative efficiency as the ratio of the number of patent applications filed by a firm in year t, scaled by its R&D capital, which is defined as the 5-year cumulative R&D expenses over (t-4, t) assuming an annual depreciation rate of 20%. We alternatively use the truncation-adjusted patent count and the year-adjusted patent count in constructing the innovative efficiency measure. A higher value of this measure suggests a more efficient use of observable resource input, namely, R&D expenditures, into innovation and a higher level of innovative efficiency. Second, generality is the median of the generality scores of all patents applied for in a given year, and the generality score of an individual patent is defined as one minus the Herfindahl index of the technology class distribution of all subsequent patents that have cited this particular patent (Trajtenberg et al., 1997). A higher generality score suggests that the patent has a widespread impact. Finally, originality is the median of the originality scores of all patents applied for in a given year. The originality score of a patent is defined as one minus the Herfindahl index of the technology class distribution of all patents that have been cited by this particular patent (Trajtenberg et al., 1997). A patent that cites other patents in dispersed technology classes is influenced by prior innovations in a variety of fields and deemed to have greater originality. Following Lerner and Seru (2017), we also scale the individual patent's generality (originality) scores by the average generality (originality) scores of all patents in the same year and technology class and use the median of the scaled generality (originality) scores of all patents applied for in a given year as alternative measures of innovation.

2.3 Baseline specification

2.4 Descriptive statistics

Table 1 contains summary statistics of innovation variables (Panel A), CEO incentives (Panel B), baseline control variables (Panel C), and summary statistics for raw patent count by FF30 industry (Panel D). As explained earlier, we restrict the sample to those firm-year observations where we can calculate the industry tournament incentives and the baseline control variables.

On average, a firm in our sample has 15.42 patents (applied for and eventually granted) per year and each patent receives 1.69 citations. The patent counts adjusted for truncation and year effects are 17.70 and 0.45, respectively. The citations-per-patent counts adjusted using the weight index, for year effects, for year and technology class effects are 4.06, 0.36, and 0.38, respectively. The mean (median) values of industry pay gap, based on industry and size-based half industry, are $25.8 million ($14.8 million) and $15.3 million ($6.4 million), respectively. The internal pay gap is substantially smaller than the external tournament prize, with the mean (median) value being $2.5 million ($1.2 million). The mean (median) values of CEO delta and CEO vega are $1.3 million ($0.3 million) and $0.11 million ($0.043 million), respectively.

The average sample firm size is $3 billion in total assets. Annual sales average about $3 billion. The average Tobin's Q is 2.13. Institutional investors hold on average 61% of shares in our sample firms. Panel D shows there is substantial variation in the number of patents both within and across FF30 industries. For most industries, the raw patent count is significantly positively correlated with contemporaneous and 1-year forward sales.21

3.1 Baseline empirical results

The odd-numbered columns of Table 2 report the results of estimating Equation (1) using our first measure of industry tournament incentives, Indgap1, based on FF30 industry. To conserve space, in the main analysis we only report the results where the number of patents and citations are truncation-adjusted. Consistent with our expectation, the coefficient on our main variable of interest is positive and significant for all measures of innovation. Using the results in Column 1, a one-standard-deviation increase in the industry pay gap increases the number of truncation-adjusted patents in the following year by 2% of its mean.22 Similarly, the results in Column 3 imply that a one-standard-deviation increase in the industry pay gap increases the number of truncation-adjusted citations per patent in the following year by 4.5% of its mean.23 Thus, the effect of industry tournament incentives on motivating innovation appears to be economically significant.

The even-numbered columns of Table 2 report the results of estimating Equation (1) with our second measure of industry tournament incentives, Indgap2, based on FF30 size-based half industry. The industry pay gap again enters positively and significantly in all regressions. Using the results reported in Columns 2 and 4, we find that a one-standard-deviation increase in this size-based half industry pay gap increases the number of truncation-adjusted patents and the number of truncation-adjusted citations per patent in the following year by 1.2% and 3.3% of the corresponding mean, respectively.

Among the control variables, the internal pay gap is positive but falls short of being significant. The coefficient on CEO overconfidence is positive and significant in the patent (INNOV_QUANTITY) and total citation (INNOV_IMPACT) regressions, consistent with the findings of Hirshleifer et al. (2012). On the other hand, Managerial ability and the CEO pay slice enter insignificantly in all regressions. Larger firms tend to produce more patents. Tobin's Q is positively associated with future innovation output. Like Atanassov (2013) and Sapra et al. (2014), we find evidence of an inverted U-shape relationship between innovation and industry concentration, measured by the Herfindahl index of sales based on FF30 classification.24

3.2 Alternative measures of innovation

We report the results for alternative measures of innovation in Table 3 using Indgap1. Similar to Table 2, Columns 1–5 of Table 3 (Panel A) show evidence of a robust positive relationship between the industry tournament incentives and the quantity, quality, and impact of firm-level innovation output.25 The relationship between the external pay gap and innovative efficiency shown in Columns 6 and 7 is also positive. In Panel B, the alternative dependent variables are the unadjusted and scaled generality and originality. We find that the coefficient on the industry pay gap remains significantly positive.

In both panels, the results for the control variables are similar to those reported in Table 2. The internal pay gap, CEO overconfidence, and Tobin's Q are generally positively associated with future innovation output. There is robust evidence of an inverted U-shape relationship between the alternative innovation measures and industry concentration. In sum, these tests demonstrate that our main findings are robust to alternative measures of innovation output.

3.3 High-technology firms

High-technology firms need to produce a steady stream of innovations in order to survive in hyper-competitive technology markets (D'Aveni, 1994). If industry tournaments are to motivate innovation, we expect the incentive effect of industry tournaments to be more pronounced in high-technology firms, where innovation is a key source of competitive advantage not only for the firm but also for the aspirant CEO seeking to win the tournament.

We use the Massachusetts High Technology Council definition of a high-technology firm which has been employed by several earlier studies to identify high-technology firms (Balkin & Gomez-Mejia, 1987; Koberg et al., 1994; Balkin et al., 2000). Specifically, we create a dummy variable, Hi-Tech, which takes a value of 1 if the firm's average annual R&D spending as a percentage of annual sales during the sample period 1992–2005 is at or above the 5% benchmark and 0 otherwise.26 Our variable of interest is the interaction term between the industry pay gap and Hi-Tech. We expect this interaction term to enter positively in the extended regression, where Hi-Tech itself is subsumed by the CEO-firm fixed effects.

Table 4 (Panel A) reports the result of this analysis. We also report the F-test of the linear combination between Indgap1 and the interaction term, which captures the total effect of the industry pay gap for high-technology firms. This total effect is statistically significant in all regressions except one.

In Panel B, we follow Brown et al. (2009) to identify high-technology firms. Excluding aerospace which has very few firms and whose R&D is funded mostly by the U.S. government, by far the largest three-digit high-tech industries are drugs standard industry classification code (SIC 283), office and computing equipment (SIC 357), communications equipment (SIC 366), electronic components (SIC 367), scientific instruments (SIC 382), medical instruments (SIC 384), and software (SIC 737). Accordingly, the alternative industry-based Hi-Tech takes a value of 1 for firms in these seven three-digit SIC industries, and 0 otherwise. The interaction term between the industry pay gap and the alternative industry-based Hi-Tech has the expected sign and is significant in all regressions except one.

In Panel C, we construct an alternative industry-level high-technology intensiveness following Hsu et al. (2014). We first calculate each firm's high-technology intensiveness as the time series median of its annual gross growth in R&D expenses during the sample period 1992–2005. For each FF30 industry, the industry high-technology intensiveness is calculated as the cross-sectional median of all firms’ high-technology intensiveness in that industry. The interaction term between the industry pay gap and this alternative Hi-Tech has the expected sign and is significant in all regressions except one.27

Taken together, the evidence in Table 4 suggests that the incentive effect of industry tournaments is stronger where innovation represents a core component of firms’ business strategy to achieve sustained competitiveness and success. At the same time, it should also be noted that the coefficient on Indgap1, which by itself captures the incentive effect for non-high-technology firms, is significant in a number of patents, citations-per-patent, and total citations regressions, indicating that the incentive effect of the external pay gap is not likely to be limited to high-technology firms only.

3.4 Endogeneity

To further address the endogeneity concerns, we resort to a quasi-natural experiment based on exogenous changes to the enforceability of noncompetition employment agreements. These agreements represent covenants in employment contracts designed to reduce the possibility that managers will accept employment offers from rival firms. However, the deterrence ability depends on the enforceability of these agreements (Garmaise, 2011). Changes in the enforceability of these noncompetition agreements affect the ability of CEOs to join rival firms and capture the tournament prize and therefore represent an exogenous shock to the industry tournament incentives. Greater enforcement of noncompetition agreements makes industry tournament incentives less effective, thereby reducing their impact on firm innovation output.

We obtain changes in state laws governing the enforcement of noncompetition agreements for our sample period 1992–2005 from Garmaise (2011) and Huang et al. (2019). Specifically, the enforceability of noncompetition agreements increased in Florida in 1996 and Louisiana in 2003; and it decreased in Texas in 1994 and Louisiana in 2001. Following the empirical approach described in Garmaise (2011), we construct a variable named ΔEnforce that takes the value of +1 for firms headquartered in Florida in 1997–2005; takes the value of −1 for firms headquartered in Texas in 1995–2005 and for firms headquartered in Louisiana in 2002–2003; is set equal to 0 otherwise. In our sample, ΔEnforce has a mean (median) of −0.0622 (0) and a standard deviation of 0.3387.

We add ΔEnforce and the interaction term between the industry pay gap and ΔEnforce to our baseline regression. This extended specification represents a difference-in-differences analysis. The variable of interest is the interaction term, the coefficient on which is predicted to be negative, consistent with the expectation of a lower impact of industry tournament incentives on firm innovation output when the enforceability of noncompetition agreements increases.

Panels A and B of Table 5 report the results of this analysis. As predicted, the coefficient on the interaction term is significantly negative in all the regressions except one. We also report the F-test of the linear combination of the industry pay gap minus the interaction term, which captures the total effect of the industry pay gap when the enforceability of noncompetition agreements decreases. The total effect is significant in all regressions.28 The coefficient on ΔEnforce itself is either insignificant or positive. The positive direct effect of ΔEnforce is not surprising given that innovation activities require a long-term managerial commitment while an increase in the enforceability of noncompetition employment agreements reduces the ability of executives to move to rival firms, hence, to a certain extent, reinforcing their commitment to their current firms. Overall, the result of this difference-in-differences analysis suggests that the positive relationship between industry tournament incentives and firm innovation is not likely to be spurious.

In another attempt to address the endogeneity concerns, we employ an instrumental variable approach. Our instrument for the industry pay gap is drawn from Coles et al. (2018) and represents the sum of total compensation of all other CEOs in the same industry (or the same size-based half industry), except the highest-paid CEO. This modified measure of the industry ability to pay is meant to capture the contemporaneous correlation of pay in an industry and varies across firms in the industry by construction. The correlation between Indgap1 (Indgap2) and the corresponding instrument, both in log forms, is 0.6282 (0.6267) and significant at the 1% level. Further, the inclusion of an extensive set of control variables in both regression stages should increase the likelihood that the instrument meets the exclusion condition.

We report the results of the instrumental variable (IV) regressions in Table 6. The industry pay gap is Indgap1 in Panel A and Indgap2 in Panel B. The first-stage regression results are shown in Column 1 of each panel. Consistent with our expectation, the coefficient on each instrument is positive and significant at the 1% level. The first-stage F-statistic is 770.129 for Indgap1 and 972.939 for Indgap2, strongly indicating that our instrument satisfies the relevance condition. Likewise, the Kleibergen–Paap LM test rejects the null hypothesis of under-identification, and the Kleibergen–Paap Wald test rejects the null hypothesis of weak instruments. These results further suggest that our instrument is robust. Turning to the second-stage regressions reported in Columns 2–4 of each panel, we observe that the instrumented industry pay gap enters positively and significantly in all regressions. The results are therefore consistent with our expectation of a positive relationship between industry tournament incentives and firm-level innovation performance. However, since our models are exactly identified in Table 6, we cannot assess the validity of the assumption that the suggested instrument is uncorrelated with the residuals in the second stage.

3.5 Firm unsystematic risk and the riskiness of investment policy

Coles et al.’s (2020) model of industry tournament incentives predicts that the tournament prize provides aspirant CEOs with the incentive to take higher risk. Increasing firm risk through corporate policies can generate uncertain but potentially extreme performance that increases the likelihood of the aspirant winning the tournament. Coles et al. (2018) find evidence consistent with the model's implication, that is, industry tournament incentives have a positive effect on firm risk measured by the variance of daily stock returns over the next year.

In the context of our study, the heightened risk-taking incentive provided by the industry tournament prize, in turn, supplies a plausible explanation for the positive and significant relationship between industry tournament incentives and subsequent firm innovation. Innovation projects arguably fit well into the category of riskier investment projects as they involve the exploration of untested new approaches. Furthermore, the nature of innovation projects implies an increase in a firm's unsystematic risk as the firm explores new, uncharted territory. For this reason, we expect to find a positive relationship between the industry pay gap and the firm's unsystematic risk.

Our measure of firms’ unsystematic risk—idiosyncratic risk—is constructed after controlling for market fluctuations. Following Cassell et al. (2012), we use daily stock return data 36 months prior to the beginning of fiscal year t+1 to estimate the parameters of the market model for constructing expected daily stock returns in fiscal year t+1. The daily residual stock returns are then obtained as the difference between the daily realized stock returns and expected returns. Idiosyncratic risk is estimated as the natural logarithm of the annualized variance of daily residual returns in year t+1.

Following prior literature (Cassell et al., 2012; Coles et al., 2006, 2018), we control for CEO delta and vega arising from the compensation scheme, internal tournament incentives, CEO age and tenure, firm size, firm age, Tobin's Q, sales growth, leverage, surplus cash, stock return, as well as industry stock return volatility and the number of CEOs in the industry. All independent variables are lagged by 1 year relative to the risk measure. We also include CEO-firm fixed effects and year fixed effects in the regressions. The OLS and IV results are reported in Columns 1–2 and Columns 4–5 of Table 7 , Panels A and B, respectively. Columns 1 and 4 of each panel reproduce the empirical findings of Coles et al. (2018) that industry tournament incentives encourage higher risk-taking, as reflected in higher future total risk, calculated as the natural logarithm of the annualized variance of daily stock returns in fiscal year t+1. More importantly, consistent with our expectation concerning the nature of innovation projects, in Columns 2 and 5 of each panel, we also find a significantly positive relationship between the industry pay gap and future idiosyncratic risk. As such, the change in total risk can be explained, at least partly, by the change in Idiosyncratic Risk.

For additional corroborating evidence, we investigate the relationship between the industry tournament incentives and R&D expenditures which represent an observable and important input to the innovation process and are thus often used as a proxy to capture firm innovation. Further, compared with other investment choices (e.g., capital expenditures), R&D expenditures arguably are riskier as their future economic benefits are highly uncertain. Therefore, R&D expenditures scaled by total assets can serve as a proxy for the riskiness of firm investment policies (Coles et al., 2006). To account for industry-specific factors that may drive investment decisions, we subtract the industry mean from the firm-level R&D expenditures. The OLS and IV results are tabulated in Columns 3 and 6 of Table 7, Panels A and B, respectively. As expected, the industry pay gap is positively and significantly related to future industry-adjusted R&D expenditures. As such, our main findings are robust to alternative proxies for firm innovation.

Overall, the results reported in Table 7 support the contention that the industry pay gap provides aspirant CEOs with greater incentives for risk-taking. The increase in firm risk is achieved, in part, through undertaking riskier investment projects. Our main findings reported earlier, in turn, suggest that among these riskier investment choices are innovation projects that increase idiosyncratic risk and result in higher innovation output.

While we are able to replicate the empirical findings of Coles et al. (2018) that the industry pay gap is positively related to future R&D expenditures in Table 7, which in and of itself serves as a robustness check that our main findings are not sensitive to alternative measures of firm innovation, it is important to note from Tables 2 and 3 that, in the presence of an extensive set of control variables, higher R&D expenditures are not necessarily associated with higher future patent and citation output, but are negatively related to innovative efficiency.29 This evidence highlights the fact that R&D expenditures are only one particular observable input to the innovation process. If other inputs, such as physical and human capital, managerial and employee effort, and creativity are not effectively employed, high R&D expenditures are less likely to result in successful innovation. This, in turn, supports the contention that, compared with R&D expenditures, measures describing a firm's patenting activity are a better proxy for capturing firm innovation.

3.6 Firm valuation and patent value

Using a specification which includes the same control variables as that of Coles et al. (2018), in Table 8 we find that 1-year forward firm valuation, measured by Tobin's Q, is positively and significantly related to the industry tournament incentives.30 This evidence is consistent with the implication of Coles et al.’s (2020) model and the empirical findings of Coles et al. (2018) that Tobin's Q increases with the external pay gap. In the context of our paper, higher innovation output arguably contributes to higher firm valuation.

Our next analysis aims to provide more direct evidence on the channels through which industry tournament incentives potentially improve firm valuation by encouraging firm innovation. For this purpose, we first calculate the total dollar value of all patents applied for (and eventually granted) in a given year where the economic value of patent j is constructed as the product of the estimate of the stock return due to the value of the patent times the market capitalization of firm i that is issued patent j on the day prior to the announcement of the patent issuance.31^,32 Since large firms tend to produce more patents, we then scale the total dollar value of all patents alternatively by the firm's total assets or its market capitalization. The construction of these measures is thus analogous to how Tobin's Q is calculated, and the measures therefore can be interpreted as capturing the contribution of innovation output to firm valuation. We then use these patent-related value measures as dependent variables in the same specification used to explain future Tobin's Q.

The results reported in Table 8 show that higher industry tournament incentives are associated with a greater economic value of patents.33 This new evidence serves to corroborate the prior findings of a positive relationship between the industry pay gap and future firm valuation, and more importantly, to illustrate how higher innovation output incentivized by the industry pay gap can contribute to higher firm valuation.34^,35

3.7 CEO future compensation

We form our hypothesis of a positive relationship between industry tournament incentives and innovation output based on the primary implications of Coles et al. (2020), that is the riskiness of firm investment policy and firm valuation increase with the size of the industry tournament prize. The aspirant CEO is motivated because he/she earns the tournament prize if unseating the highest-paid CEO. On the other hand, the potential external opportunity also puts pressure on the current firm's board to increase the aspirant CEO's compensation, and therefore the CEO need not move to extract benefits of the industry tournament.

In previous sections, we have documented empirical evidence that industry tournament incentives are positively related to future innovation output, economic value of patents, and firm valuation measured by Tobin's Q. In this section, we examine the implication of higher innovation output for CEO future compensation. The first analysis considers CEOs who move to other firms during our sample period, and the second analysis considers CEOs’ internal changes in total compensation.

In the first analysis, we track CEO movement over 1992–2005 in the ExecuComp database. We are able to collect the needed data for 62 instances of moving from the CEO position at one firm to the CEO position at another firm, and 31 instances of moving from the CEO position at one firm to a non-CEO executive position at another firm.36 For each instance, we collect data on total compensation and the number of patents in the final year at the old firm (year t) and total compensation in the first year at the new firm (year t+1). We then compare the change in total compensation from the final year at the old firm (year t) to the first year at the new firm (year t+1) conditional on whether the number of patents in the final year at the old firm is positive. Other things being equal, we expect higher pay increase for CEOs moving from firms with innovation output. Our analysis is limited to univariate because multivariate regression analysis, especially with fixed effects, is not feasible for the small sample size.

The result of this analysis is presented in Table 9, separately for movement from the CEO position at one firm to the CEO position at another (Panel A1) and movement from the CEO position at one firm to a non-CEO executive position at another (Panel A2). Panel A1 shows that the mean (median) change in total compensation is significantly greater for CEOs moving from firms with innovation output compared with those moving from firms with zero innovation output. For CEOs who move to a non-CEO executive position at another firm, however, the change in total compensation conditional on whether the number of patents in the final year at the old firm is positive is not statistically different (Panel A2). Though both sets of results should be interpreted with caution due to the small number of observations, the result documented in Panel A1 is more pertinent to our study. There are likely reasons for why CEOs move to a non-CEO executive position at new firms that we are unable to measure and control for in our univariate analysis.

In the second analysis that considers internal changes in CEO total compensation, we regress the CEO total compensation in year t+1 on the industry pay gap measured in year t, the innovation output measured in year t+1, the interaction between the industry pay gap and the innovation output, and a set of control variables measured in year t including CEO tenure, firm size, sales growth, and 1-year stock return. We also control for year fixed effects and CEO-firm fixed effects. This estimator relies only on within-CEO-firm variation, and therefore we are able to rule out all of the alternative explanations that are associated with time-invariant characteristics of the CEO-firm pair. The variable of interest is the interaction term between the industry pay gap and the innovation output. We expect higher industry pay gap coupled with greater innovation output to be associated with greater future compensation, that is a positive interaction term. We report the result of this analysis in Panel B of Table 9, Columns 1–3. In all regressions, while the industry pay gap and innovation output each remain insignificant, the interaction term is significantly positive, thereby supporting the interpretation that the increasing innovation by CEOs with large industry pay gaps increases their future compensation.

In Columns 4–6 (Columns 7–9), we repeat the regression analysis using the total pay increase (total pay reduction) from year t to year t+1 as the dependent variable instead. Each variable is computed as the natural logarithm of the absolute value of the change in total compensation from year t to year t+1. In effect, we partition our sample into two subsamples. For the subsample of pay-increase observations in Columns 4–6, the result is qualitatively similar to that reported in Columns 1–3 and supports a similar interpretation. Regarding the subsample of pay-reduction observations in Columns 7–9, the industry pay gap is significantly negative in all regressions, the innovation output is also significantly negative in all regressions, and the interaction term is always significantly positive. Therefore, individually, either lower industry pay gap or lower innovation output is associated with a greater reduction in total compensation, and jointly, a combination of lower industry pay gap and lower innovation output is associated with a greater reduction in total compensation.

Collectively, the results of this section suggest that innovation output matters for CEO future compensation, whether or not he/she moves to another firm. In particular, results reported in Panel B are consistent with the interpretation that the increasing innovation by CEOs with large industry pay gaps increases their future compensation.

3.8 Other robustness checks