Does it pay to ‘Be Like Mike’? Aspiratonal peer firms and relative performance evaluation

Abstract

We examine the manner and extent to which firms evaluate performance relative to aspirational peer firms. Guided by the predictions of an agency model, we find that CEO compensation increases in the correlation between own and aspirational peer firm performances. In addition, we define and test conditions where aggregate peer performance, which has been the primary focus of prior relative performance evaluation studies of competitive peers, is expected to have an association with CEO compensation. These conditions are supported by our empirical results. Finally, we document that our results are more pronounced when the firm-peer relationship is one-way and the peer firm is in a different industry and therefore is more aspirational.

Appendices

Appendix A: Theoretical foundations and derivations

The analysis of the multi-agent problem in this paper fundamentally follows the approach of Holmström and Milgrom (1987, Sections 2 and 3) augmented to allow for multiple agents using the standard Nash-approach of Holmström (1982). In the single-agent analysis in Holmström and Milgrom (1987), the agent has full control over all distributional properties of all available performance measures. The key implication of the agent’s extensive control is that the principal’s options are limited to a single, unique contract for any set of actions he or she can incentivize (their Theorem 3). This simplifies their analysis greatly because once the principal decides on a set of actions to implement, there is only one contract that will do the job, so the principal does not have to find the optimal contract from among an otherwise large set of incentive compatible contracts.

This simplifying uniqueness feature of Holmström and Milgrom (1987) does not, however, obtain in the multi-agent RPE setting of Hemmer (2017). The simple reason for this is that the addition of agents that control only their own performance measures “weakens” each agent’s span of control relative to the single-agent case in Holmström and Milgrom (1987). This, in turn, strengthens the principal by giving him more contracting options to choose from for implementing a given set of actions. As a result, the optimal RPE contract must be found through standard optimization techniques. This is important because that reintroduces the likelihood ratios absent in the single-agent setting of Holmström and Milgrom (1987) as the key determinants of the properties of the optimal RPE contract. This also makes clear that producing predictions for the multi-agent RPE case by extrapolating from the single-agent, multiple performance measure setting is not as straightforward as it may seem. Indeed, as shown by Hemmer (2017), the optimal RPE contract obtained from the multi-agent case differs fundamentally from the unique multi-measure contract obtained from analyzing the single agent case.

Importantly, however, while the uniqueness result of Holmström and Milgrom (1987) does not carry over to the multi-agent RPE setting, their key stationarity results do. Specifically, for the multi-period version of the model, an optimal solution for the principal is to implement the same set of actions using the same reward structure in every subperiod (their Theorem 4). Moreover, the optimal contract can be written on measures of aggregate performance rather than on the entire history of the performance evolution (their Theorem 5). It turns out that the optimal dynamic RPE contract can also be obtained by solving for the optimal stationary RPE contract in any one subperiod and letting the number of subperiods grow large, just as in the single agent case.

Following this strategy, we provide a detailed derivation of the main results underlying our empirical predictions by applying the above-mentioned stationarity and aggregation results. For further details we refer the diligent reader to Hemmer (2017).

Define

$$ \begin{array}{@{}rcl@{}} \begin{array}{llll} \beta_{\Omega} &\equiv& \frac{m(s_{\theta}^{++}-s_{\theta}^{--}+s_{\theta}^{+-}-s_{\theta}^{-+})}{2}, \\\\ \beta_{\rho} &\equiv& \frac{m(s_{\theta}^{++}+s_{\theta}^{--}-s_{\theta}^{+-}-s_{\theta}^{-+})}{4}, \\\\ \beta_{\Pi} &\equiv& \frac{m(s_{\theta}^{++}-s_{\theta}^{--}-s_{\theta}^{+-}+s_{\theta}^{-+})}{2}, \\\\ \beta_{0} &\equiv& ms^{--}-\beta_{\rho}. \end{array} ~~~~~~~~~ \begin{array}{rllll} {\Omega} &\equiv& A^{++}+A^{+-}, \\\\ \rho &\equiv& A^{++}+A^{--}-A^{+-}-A^{-+}, \\\\ {\Pi} &\equiv& A^{++}+A^{-+}, \\\\ ~ &~& \end{array} \end{array} $$

Noting that A⁺⁺ + A⁺⁻ + A⁻⁺ + A⁻⁻ = 1, straightforward algebra reconciles Eq. 7 to Eq. 6:

$$ \begin{array}{@{}rcl@{}} \begin{array}{rll} \beta_{0}+\beta_{\Omega}{\Omega} +\beta_{\Pi}{\Pi} +\beta_{\rho}\rho &=& ms_{\theta}^{--} -m\frac{s_{\theta}^{++}+s_{\theta}^{--}-s_{\theta}^{+-}-s_{\theta}^{-+}}{4} \\&& +m\frac{s_{\theta}^{++}-s_{\theta}^{--}+s_{\theta}^{+-}-s_{\theta}^{-+}}{2}(A^{++}+A^{+-}) \\&& +m\frac{s_{\theta}^{++}-s_{\theta}^{--}-s_{\theta}^{+-}+s_{\theta}^{-+}}{2}(A^{++}+A^{-+}) \\&& +m\frac{s_{\theta}^{++}+s_{\theta}^{--}-s_{\theta}^{+-}-s_{\theta}^{-+}}{4}(A^{++}+A^{--}-A^{+-}-A^{-+}) \\\\ &=& m(A^{++}s_{\theta}^{++}+A^{+-}s_{\theta}^{+-}+A^{-+}s_{\theta}^{-+}+A^{--}s_{\theta}^{--}). \end{array} \end{array} $$

Expanding the expectations in Eq. 5 and utilizing the agent’s negative exponential utility function, the principal’s contract design problem for each subperiod can be written

$$ \begin{array}{@{}rcl@{}} &&\min_{s_{\theta}^{ij}} \quad p^{*}a\gamma s_{\theta}^{++} +p^{*}(1-a\gamma )s_{\theta}^{+-} +(1-p^{*})\gamma s_{\theta}^{--} +(1-p^{*})(1-\gamma )s_{\theta}^{-+} \\\\ &&\text{s.t.} \quad p^{*}a\gamma u(s_{\theta}^{++})+p^{*}(1-a\gamma )u(s_{\theta}^{+-})+(1-p^{*})\gamma u(s_{\theta}^{--})+(1-p^{*})(1-\gamma )u(s_{\theta}^{-+}) \\ &&\qquad\geq u(\theta w+\theta c(p^{*})) \\\\ && \qquad\theta c^{\prime}(p^{*}) \left( p^{*}a\gamma u(s_{\theta}^{++})+p^{*}(1-a\gamma )u(s_{\theta}^{+-}) +(1-p^{*})\gamma u(s_{\theta}^{--})+(1-p^{*})(1-\gamma )u(s_{\theta}^{-+})\right) \\&& +\left.\left( \frac{dpa\gamma }{dp}u(s_{\theta}^{++}) +\frac{dp(1-a\gamma )}{dp}u(s_{\theta}^{+-}) +\frac{d(1-p)\gamma }{dp}u(s_{\theta}^{--}) +\frac{d(1-p)(1-\gamma )}{dp}u(s_{\theta}^{-+})\right)\right|_{p=p^{*}} =0. \end{array} $$

Let λ_𝜃 and μ_𝜃 denote the Lagrange multipliers on the individual rationality and incentive compatibility constraints. Then the first order conditions with respect to $s_{\theta }^{ij}$ are given by

$$ \begin{array}{@{}rcl@{}} \frac{\partial\mathcal{L}}{\partial s_{\theta}^{++}} &=& 0 = -p^{*}a\gamma +\lambda_{\theta}p^{*}a\gamma u^{\prime}(s_{\theta}^{++}) \\&& +\mu_{\theta}\left[\theta c^{\prime}(p^{*})p^{*}a\gamma u^{\prime}(s_{\theta}^{++}) +\left.\frac{dpa\gamma }{dp}\right|_{p=p^{*}}u^{\prime}(s_{\theta}^{++}) \right]\\ \frac{\partial\mathcal{L}}{\partial s_{\theta}^{+-}} &=& 0 = -p^{*}(1-a\gamma ) +\lambda_{\theta}p^{*}(1-a\gamma )u^{\prime}(s_{\theta}^{+-}) \\&& +\mu_{\theta}\left[\theta c^{\prime}(p^{*})p^{*}(1-a\gamma )u^{\prime}(s_{\theta}^{+-}) +\left.\frac{dp(1-a\gamma )}{dp}\right|_{p=p^{*}}u^{\prime}(s_{\theta}^{+-}) \right] \end{array} $$

$$ \begin{array}{@{}rcl@{}} \frac{\partial\mathcal{L}}{\partial s_{\theta}^{--}} &=& 0 = -(1-p^{*})\gamma +\lambda_{\theta}(1-p^{*})\gamma u^{\prime}(s_{\theta}^{--}) \\&& +\mu_{\theta}\left[\theta c^{\prime}(p^{*})(1-p^{*})\gamma u^{\prime}(s_{\theta}^{--}) +\left.\frac{d(1-p)\gamma }{dp}\right|_{p=p^{*}}u^{\prime}(s_{\theta}^{--}) \right] \\ \frac{\partial\mathcal{L}}{\partial s_{\theta}^{-+}} &=& 0 = -(1-p^{*})(1-\gamma ) +\lambda_{\theta}(1-p^{*})(1-\gamma )u^{\prime}(s_{\theta}^{-+}) \\&& +\mu_{\theta}\left[\theta c^{\prime}(p^{*})(1-p^{*})(1-\gamma )u^{\prime}(s_{\theta}^{-+}) +\left.\frac{d(1-p)(1-\gamma )}{dp}\right|_{p=p^{*}}u^{\prime}(s_{\theta}^{-+}) \right]. \end{array} $$

Substituting $u^{\prime }(s)=-u(s)$ and dividing through by $\Pr (\omega ^{i},\pi ^{j})$ yields:

$$ \begin{array}{@{}rcl@{}} \begin{array}{lllll} \frac{1}{-u(s_{\theta}^{++})} &=& \lambda_{\theta} + \mu_{\theta}\left( \theta c^{\prime}(p^{*})+\frac{\left.\frac{dpa\gamma }{dp}\right|_{p=p^{*}}}{p^{*}a\gamma }\right) &\equiv& \lambda_{\theta}+\mu_{\theta}L^{++} \\\\ \frac{1}{-u(s_{\theta}^{+-})} &=& \lambda_{\theta} + \mu_{\theta}\left( \theta c^{\prime}(p^{*})+\frac{\left.\frac{dp(1-a\gamma )}{dp}\right|_{p=p^{*}}}{p^{*}(1-a\gamma )}\right) &\equiv& \lambda_{\theta}+\mu_{\theta}L^{+-} \\\\ \frac{1}{-u(s_{\theta}^{--})} &=& \lambda_{\theta} + \mu_{\theta}\left( \theta c^{\prime}(p^{*})+\frac{\left.\frac{d(1-p)\gamma }{dp}\right|_{p=p^{*}}}{(1-p^{*})\gamma }\right) &\equiv& \lambda_{\theta}+\mu_{\theta}L^{--} \\\\ \frac{1}{-u(s_{\theta}^{-+})} &=& \lambda_{\theta} + \mu_{\theta}\left( \theta c^{\prime}(p^{*})+\frac{\left.\frac{d(1-p)(1-\gamma )}{dp}\right|_{p=p^{*}}}{(1-p^{*})(1-\gamma )}\right) &\equiv& \lambda_{\theta}+\mu_{\theta}L^{-+}. \end{array} \end{array} $$

Using properties of the negative exponential utility function and performing a first-order Taylor series expansion allows each wage differential to be expressed as follows.

$$ \begin{array}{@{}rcl@{}} \begin{array}{lll} s_{\theta}^{ij}-s_{\theta}^{--} &=& \ln\left( \lambda_{\theta}+\mu_{\theta}L^{ij}\right) -\ln\left( \lambda_{\theta}+\mu_{\theta}L^{--}\right) \\\\ &=& \ln\left( 1+\frac{\mu_{\theta}(L^{ij}-L^{--})}{\lambda_{\theta}+\mu_{\theta}L^{--}}\right) \\\\ &\approx& \left( \ln(1)+\frac{1/1}{1!}\left( 1+\frac{\mu_{\theta}(L^{ij}-L^{--})}{\lambda_{\theta}+\mu_{\theta}L^{--}}-1\right)\right) \\\\ &=& \frac{\mu_{\theta}(L^{ij}-L^{--})}{\lambda_{\theta}+\mu_{\theta}L^{--}}. \end{array} \end{array} $$

Hemmer (2017) shows that the wage differentials converge to this Taylor series approximation as $m\to \infty$. Making this substitution into the coefficients in Eq. 7 yields

$$ \begin{array}{@{}rcl@{}} \begin{array}{lllll} \beta_{\Omega} &=& \frac{m\mu_{\theta}}{2(\lambda_{\theta}+\mu_{\theta}L^{--})} (L^{++}-L^{--}+L^{+-}-L^{-+}) \\\\ \beta_{\rho} &=& \frac{m\mu_{\theta}}{2(\lambda_{\theta}+\mu_{\theta}L^{--})} (L^{++}+L^{--}-L^{+-}-L^{-+}) \\\\ \beta_{\Pi} &=& \frac{m\mu_{\theta}}{2(\lambda_{\theta}+\mu_{\theta}L^{--})} (L^{++}-L^{--}-L^{+-}+L^{-+}). \end{array} \end{array} $$

Finally, substituting the above definitions of the likelihood ratios L^ij into these coefficients yields Eq. 8:

$$ \begin{array}{@{}rcl@{}} \begin{array}{llll} L^{++}-L^{--}+L^{+-}-L^{-+} &=& \frac{\left.\frac{dpa\gamma}{dp}\right|_{p=p^{*}}}{p^{*}a\gamma} -\frac{\left.\frac{d(1-p)\gamma}{dp}\right|_{p=p^{*}}}{(1-p^{*})\gamma} +\frac{\left.\frac{dp(1-a\gamma)}{dp}\right|_{p=p^{*}}}{p^{*}(1-a\gamma)} -\frac{\left.\frac{d(1-p)(1-\gamma)}{dp}\right|_{p=p^{*}}}{(1-p^{*})(1-\gamma)} \\\\ &=& \frac{2}{p^{*}(1-p^{*})} +\gamma_{p^{*}}\frac{1-a}{(1-\gamma)(1-a\gamma)} \\ \\ L^{++}+L^{--}-L^{+-}-L^{-+} &=& \frac{\left.\frac{dpa\gamma}{dp}\right|_{p=p^{*}}}{p^{*}a\gamma} +\frac{\left.\frac{d(1-p)\gamma}{dp}\right|_{p=p^{*}}}{(1-p^{*})\gamma} -\frac{\left.\frac{dp(1-a\gamma)}{dp}\right|_{p=p^{*}}}{p^{*}(1-a\gamma)} -\frac{\left.\frac{d(1-p)(1-\gamma)}{dp}\right|_{p=p^{*}}}{(1-p^{*})(1-\gamma)} \\ &=& \left( \frac{2}{\gamma} +\frac{a}{1-a\gamma} +\frac{1}{1-\gamma}\right)\gamma_{p^{*}} \\ \\ L^{++}-L^{--}-L^{+-}+L^{-+} &=& \frac{\left.\frac{dpa\gamma}{dp}\right|_{p=p^{*}}}{p^{*}a\gamma} -\frac{\left.\frac{d(1-p)\gamma}{dp}\right|_{p=p^{*}}}{(1-p^{*})\gamma} -\frac{\left.\frac{dp(1-a\gamma)}{dp}\right|_{p=p^{*}}}{p^{*}(1-a\gamma)} +\frac{\left.\frac{d(1-p)(1-\gamma)}{dp}\right|_{p=p^{*}}}{(1-p^{*})(1-\gamma)} \\\\ &=& \frac{a-1}{(1-a\gamma)(1-\gamma)}\gamma_{p^{*}}. \end{array} \end{array} $$

Appendix B: Variable descriptions and measurement

1.1 B.1 CEO compensation variable

C o m p _{j t} :

Change in the natural logarithm of total annual compensation for firm j’s CEO between fiscal years t and t − 1, where total annual compensation in a given fiscal year is equal to the sum of salary, bonus, total value of restricted stock granted, total value of stock options granted, long-term incentive payouts, and all other compensation (ExecuComp TDC1).

1.2 B.2 Firm-year-peer variables

${ret}_{jt,\tau }^{{3\text {-}day}}$ :

Natural logarithm of one plus firm j’s stock return for a three-day subperiod τ within fiscal year t.

${peer\rule [0pt]{5pt}{0.2pt}{}ret}_{jt,k,\tau }^{3\text {-}day}$ :

Natural logarithm of one plus the stock return for firm j’s peer k for a three-day subperiod τ within fiscal year t.

p e r f c o r r _jt,k :

Correlation coefficient between firm j’s three-day stock returns (${ret}_{{jt;t}}^{{3\text {-}day}}$) and the three-day stock return for firm j’s peer k (${peer\rule [0pt]{5pt}{0.2pt}{}ret}_{jt,k,\tau }^{{3\text {-}day}}$), which is estimated using the 84 three-day return windows within j’s fiscal year t (i.e., approximately 84 × 3 = 252 trading days total within a fiscal year).

${i}_{{jt,k}}^{{{1\text {-}way}}}$ :

An indicator variable equal to one (zero) if the relationship between firm j and its peer k is (not) one-way (i.e., k does not also consider j as its peer).

${i}_{{jt,k}}^{{larger}}$ :

An indicator variable equal to one (zero) if the market value of firm j’s peer k is (not) larger than the market value of equity of firm j at the beginning of fiscal year t.

${i}_{{jt,k}}^{{diff\text {-}ind}}$ :

An indicator variable equal to one (zero) if firm j is (not) in a different two-digit SIC industry from its peer k during fiscal year t.

p e e r r e t _jt,k :

Natural logarithm of one plus the annual stock return for firm j’s peer k measured during j’s fiscal year t, such that ${\sum }^{84}_{\tau =1}{{peer\rule [0pt]{5pt}{0.2pt}{}ret}}_{jt,k,\tau }^{{3\text {-}day}}={{peer\rule [0pt]{5pt}{0.2pt}{}ret}_{jt,k}}$.

${ret}_{jt,\tau }^{+}$ :

Indicator variable equal to one if ${ret}_{jt,\tau }^{3\text {-}day}\geq 0$ and equal to zero otherwise.

${peer\rule [0pt]{5pt}{0.2pt}{}ret}_{jt,k,\tau }^{+}$ :

Indicator variable equal to one if ${{peer\rule [0pt]{5pt}{0.2pt}{}ret}}_{jt,k,\tau }^{{3-day}}\geq 0$ and equal to zero otherwise.

$\gamma _{{jt,k}}^{+}{}$ :

Conditional probability of a positive stock return for firm j’s peer k during a three-day subperiod τ, within fiscal year t given that firm j also has a positive return during τ. For a given firm j, peer firm k, and fiscal year t, $\gamma _{jt,k}^{+}$ is estimated using 252 three-day return windows during the three most recent fiscal years prior to t (i.e., t− 1, t− 2 and t− 3) as follows.

$$ \begin{array}{@{}rcl@{}} \gamma_{{jt,k}}^{+} &=& {Pr}({{peer\rule[0pt]{5pt}{0.2pt}{}ret}}_{jt,k,\tau}^{+} = 1|{{ret}}_{jt,\tau}^{+}=1)\\ &=& \frac{\sum\limits_{s=1}^{3} \sum\limits_{\tau=1}^{84} \left[{{peer\rule[0pt]{5pt}{0.2pt}{}ret}_{jt-s,k,\tau}^{+} \times {ret}_{jt-s,\tau}^{+}}\right]}{\sum\limits_{s=1}^{3} \sum\limits_{\tau=1}^{84} {{ret}_{jt-s,\tau}^{+}}} \end{array} $$

$\gamma _{jt,k}^{-}$ :

Conditional probability of a nonpositive stock return for firm j’s peer k during a three-day subperiod τ, within fiscal year t given that firm j also has a nonpositive return during τ. For a given firm j, peer firm k, and fiscal year t, $\gamma _{jt,k}^{-}$ is estimated using 252 three-day return windows during the three most recent fiscal years prior to t (i.e., t− 1, t− 2 and t− 3) as follows.

$$ \begin{array}{@{}rcl@{}} \gamma_{jt,k}^{-} &=& {Pr}\left[{{peer\rule[0pt]{5pt}{0.2pt}{}ret}}_{jt,k,\tau}^{+}=0|{{ret}_{jt,\tau}^{+}}=0\right]\\ &=& \frac{\sum\limits_{s=1}^{3} \sum\limits_{\tau=1}^{84}\left[(1-{{peer\rule[0pt]{5pt}{0.2pt}{}ret}_{jt-s,k,\tau}^{+}}) \times (1-{{ret}}_{jt-s,\tau}^{+})\right]}{\sum\limits_{s=1}^{3} \sum\limits_{\tau=1}^{84}(1-{{ret}}_{jt-s,\tau}^{+})} \end{array} $$

1.3 B.3 Firm-year performance variables

R e t _{j t} :

Natural logarithm of one plus firm j’s annual stock return in fiscal year t, such that ${\sum }^{84}_{\tau {}=1} {ret}_{jt,\tau }^{3\text {-}day} = {Ret}_{jt}$.

P e r f C o r r _{j t} :

Average performance correlations between firm j and its peer firms k during fiscal year t, which is equal to ${\sum }_{k=1}^{Njt} {{perf\rule [0pt]{5pt}{0.2pt}{}corr}}_{jt,k}/{{N}}_{jt}$, where N_jt is the number of firms with nonmissing performance measures that firm j considers to be a peer in fiscal year t.

P e e r R e t _{j t} :

Average of aggregate peer performances for all of firm j’s peer firms k during fiscal year t, which is equal to ${\sum }_{k=1}^{{{N}_{jt}}}{{{peer\rule [0pt]{5pt}{0.2pt}{}ret}_{jt,k}}/{{N}_{jt}}}$, where N_jt is the number of firms with nonmissing performance measures that firm j considers to be a peer in fiscal year t.

${\Gamma }_{jt}^{+}$ (${\Gamma }_{jt}^{-}$):

Average across all of firm j’s peer firms k during fiscal year t of conditional probability of a positive (nonpositive) stock return for j’s peer k during a three-day subperiod τ within fiscal year t given that firm j also has a positive (nonpositive) return during τ, which is equal to ${\sum }_{\tau =1}^{N_{jt}}~\gamma _{jt,k}^{+}/N_{jt}$ $({\sum }_{\tau =1}^{N_{jt}}~\gamma _{jt,k}^{-}/N_{jt})$ where N_jt is the number of firms with nonmissing performance measures that firm j considers to be a peer in fiscal year t

${A}_{jt}^{+}$ :

Positive asymmetric sensitivity to peer performance represented by an indicator variable equal to one if the average conditional probability of positive returns for both firm j and its peer firms ${\Gamma }_{jt}^{+}$ is greater than the average conditional probability of non-positive returns for both firm j and its peer firms ${\Gamma }_{jt}^{-}$ and equal to zero otherwise.

1.4 B.4 Firm-year control variables

I S V _{j t} :

Idiosyncratic return volatility for firm j in fiscal year t, which is equal to the standard deviation of residuals from a time-series regression of firm j’s monthly returns on two-digit SIC industry returns estimated using the most recent 36 (minimum of 18 required) monthly returns immediately prior to the beginning of fiscal year t. Industry returns are computed as the equal-weighted portfolio return based on firms in the same two-digit SIC, excluding the monthly return of firm j.

S i z e _{j t} :

Change in the size of firm j, between the beginning of fiscal years t and t − 1, where firm size is measured by the natural logarithm of the book value of firm j’s total assets.

M T B _{j t} :

Change in the market-to-book ratio of firm j, between the beginning of fiscal years t and t − 1, where the market-to-book ratio is computed as firm j’s market value of total assets divided by the book value of total assets. Market value of assets is equal to the book value of total assets minus the book value of equity plus the market value of equity.

N _{j t} :

Number of firms with nonmissing firm-performance variables that firm j considers to be a peer in fiscal year t.

$\%{{Peers}}^{{1\text {-}way}}_{{jt}}$ :

Fraction of firm j’s peer firm relationships during fiscal year t that are one-way (i.e., peer firm does not consider j as a peer), which is computed by ${\sum }_{k=1}^{N_{jt}} i_{jt,k}^{{{1\text {-}way}}} / N_{jt}$.

$\%{{Peers}}_{jt}^{{larger}}$ :

Fraction of firm j’s peer firms that have a larger market value of equity than j at the beginning of fiscal year t, which is computed by ${\sum }_{k=1}^{N_{jt}} i_{jt,k}^{{diff\text {-}ind}} / N_{jt}$.

$\%{Peers}_{jt}^{{diff\text {-}ind}}$ :

Fraction of firm j’s peer firms that are in a different two-digit SIC industry during fiscal year t, which is computed by ${\sum }_{k=1}^{N_{jt}} i_{jt,k}^{{diff\text {-}ind}} / N_{jt}$.

O w n _{j t} :

CEO’s percentage ownership of firm j and is equal to the number of shares (excluding options) owned divided by the number of common shares outstanding at the beginning of fiscal year t.

C h a i r _{j t} :

Indicator variable equal to one (zero) if the title of firm j’s CEO in fiscal year t indicates (does not indicate) that the CEO is also the board chair.

T e n u r e _{j t} :

The natural logarithm of the tenure of firm j’s CEO at the end of fiscal year t, where tenure is defined as the number of days between the last day of fiscal year t and the day when the CEO assumed the position.