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  • Big Fish in a Small Pond: CEO Compensation,Corporate Governance, and Equilibrium Matching

    Zhan Li

    September, 2016


    We model a firm-CEO matching market in a cash flow diversion environment where mon-

    itoring CEOs is costly. In such market, positive assortative matching between firm size and

    CEO talent fails under negative economic shock; CEO compensation increases in CEO talent

    irrespective of how CEOs match with firms; corporate governance is affected by aggregate

    market characteristics such as CEO talent scarcity and equilibrium matching pattern. Our

    model explains why CEO turnover is driven by exogenous economic shock, and suggests a

    robustness rule for empirical applications based on PAM, as well as other empirical and policy


    Keywords: CEO Compensation, Corporate Governance, Equilibrium Matching PatternJEL Classification: G34, J33, D82

    This paper is based on my Ph.D. thesis. I am extremely grateful for the guidance and support from my thesisadvisor Hector Chade. I am grateful for comments and help from Natalia Kovrijnykh and Galina Vereshchagina.I thank suggestions and comments from Alejandro Manelli, Tom Bates, Ilona Babenko, Yuri Tserlukevich, AndreiKovrijnykh, Manish Pandey, Stefan Dodds, Soham Baksi, Wenbiao Cai and other seminar participants at ArizonaState University, University of Winnipeg, and Greater China Area Finance Conference. All errors are mine . Addressfor correspondence: Zhan Li, Faculty of Business and Economics, University of Winnipeg, Office: 4BC09, Phone:204.786.9833, Email: Website:


  • 1 Introduction

    CEO labor market plays an increasingly central role in allocating CEOs to firms. Understand-ing economic forces that affect such allocation process is thus important. Extant literature showsthat when there is complementarity between CEO talent and firm size (marginal product of CEOtalent is higher in a larger firm), competitive market allocates CEOs into firms according to posi-tive assortative matching (PAM): the largest firm matches with the most talented CEO, the secondlargest firm matches with the second most talented CEO, so on and so forth. Based on PAM,previous literature has obtained novel empirical results on CEO turnover, CEO compensation, andcorporate governance.

    However, PAM, which serves as the foundation for the above research, merits a further exami-nation. Understandably, we can not expect PAM holds in the CEO labor market because it requiresa perfect monotonic relationship between firm size and CEO talent, which is apparently too strong.This paper considers a more general case: we ask to what extent can PAM hold and what can weknow about CEO turnover, compensation, and corporate governance when it fails.

    To this end, we examine equilibrium matching pattern by embedding a cash flow diversionmodel into a two-sided matching market. In such market, firms have different size and CEOs havedifferent talent. There are two stages in our model. In the first stage, firms match with CEOssimultaneously by anticipating the second stage payoffs resulting from optimal contract. In thesecond stage, a matched pair of firm and CEO generate cash flow by a stochastic complementarytechnology: it is a product of firm size and CEO talent with some probability and zero otherwise.The distribution of the cash flow is exogenously given, known to all firms and CEOs, and affectedby an aggregate observable economic shock: the probability of zero cash flow is higher under anegative economic shock and lower under a positive economic shock. The realization of the cashflow is only known to the CEO, who submits a report to the firm. The CEO thus can divert thefirms cash flow by falsifying a report. The firm sets CEO compensation and pays a cost to auditthe CEOs report to prevent her from diverting cash flow.

    We show that despite of the complementarity between firm size and CEO talent, PAM failswhen negative economic shock is large or marginal cost of monitoring is high, and it fails firstamong small firms and low-talent CEOs. This generates three implications: first, PAM betweenfirm size and CEO talent is not a taken-as-granted result under complementary technology; second,since PAM is more likely to fail among smaller firms and their CEOs, it is more robust to use a


  • sample of large firms when PAM is assumed in empirical applications; third, PAM is also morerobust with recent data if marginal cost of monitoring is lower due to advancement in auditingtechnology.

    The failure of PAM under negative economic shock is easy to understand by considering thetradeoff between higher CEO productivity and more expensive monitoring at a larger firm. Whena large firm competes against a small firm for a high talent CEO, the large firm has both advantageand disadvantage in such competition. The CEO has higher marginal product at the large firmdue to complementary production technology, thus the large firm tends to outbid the small firm.However, since cash flow subject to diversion is higher at the large firm, the large firm monitors theCEO more intensively, which increases its monitoring cost, and thus tends to underbid the smallfirm. Under negative economic shock, advantage of the large firm decreases because marginalproduct from CEO talent decreases faster in the large firm, and disadvantage increases becausemonitoring cost decreases slower at the large firm. When the negative economic shock is largeenough, PAM fails and the high talent CEO matches with the small firm, i.e., big fish in a smallpond.

    The change in equilibrium matching pattern is equivalent to CEO turnover in our model. Ka-plan and Minton (2006) and Jenter and Kanaan (2015) show that CEOs are more likely to bedismissed after negative economic shock. However, if CEO turnover is determined by optimalcontract (Holmstrom, 1982; Gibbons and Murphy, 1990), observable economic shock, which isoutside of CEOs control, should be filtered out in firms decision on CEO dismissal. Our paperthus explains why economic shock can drive CEO turnover by considering how economic shockaffects firms ability in competing for CEO talent in a matching market. Eisfeldt and Kuhnen(2013) also consider CEO turnover in a matching market. Unlike our model, their paper abstractsaway agency problems and considers CEOs multidimensional types. CEO turnover in their pa-per is driven by firms demand for different types of talent under different economic conditions.Our paper thus complements Eisfeldt and Kuhnen (2013) in understanding CEO turnover in thematching market.

    The second part of our paper discusses how the failure of PAM affects CEO compensationand corporate governance. For tractability, we treat different matching patterns as exogenous,which is only made possible if we have shown that matching patterns other than PAM can occurin equilibrium. Unlike previous literature on CEO compensation and corporate governance in thefirm-CEO matching market which relies on PAM, our solution applies to any matching pattern.


  • We show that irrespective of equilibrium matching pattern, CEO compensation satisfies mono-tonicity and equal treatment. Monotonicity means CEO compensation is strictly increasing inCEO talent and equal treatment means CEOs of the same talent matching with firms of differentsize have the same compensation. This implies CEO compensation increases in firm size if andonly if CEO talent increases in firm size cross-sectionally, i.e., PAM holds.

    The above result is important for empirical research from at least two aspects. First, sinceCEO compensation increases in CEO talent, the matching pattern between CEO compensationand firm size identifies the matching pattern between CEO talent and firm size. We can thusrecover market matching pattern from compensation data despite of the difficulty in measuringCEO talent. Second, it shows Gabaix and Landier (2008)s predication that CEO compensationincreases in firm size cross-sectionally is true if and only if PAM holds. We know that PAM ismore likely to hold with a sample of large firms or more recent data. Thus Gabaix and Landier(2008)s cross-sectional prediction is more robust with a sample of large firms or more recent data.This explains why Gabaix and Landier (2008) only include top 1000 firms in total market value intheir sample. 1 It also explains why Frydman and Saks (2010) cannot replicate Gabaix and Landier(2008)s cross-sectional results for the sample period from 1936 to 1975: PAM may have failed inthat early sample period.

    Next, we show that corporate governance is affected by aggregate market characteristics such asequilibrium matching pattern and the scarcity of CEO talent. Under PAM, larger firms have weakercorporate governance than smaller firms when CEO talent is scarce enough, and under negativeassortative matching (NAM), larger firms always have stronger corporate governance than smallerfirms. 2 This result is easy to understand by noting that compensation and corporate governanceare substitutes for a firm to incentivize its CEO for truthful reporting. Under NAM, larger firmsmatch with less talented CEOs, who have lower compensation than more talented CEOs, thuslarger firms impose stronger corporate governance than smaller firms. Under PAM, larger firmsmatch with more talented CEOs, and when scarcity of CEO talent drives CEO compensation up(due to competition for CEO talent), larger firms can incentivize their CEOs with weaker corporategovernance.

    The above result holds even when it is costless to monitoring CEOs. This implies that the

    1Gabaix and Landier (2008)s sample choice is based on statistics. They resort to extreme value theory for com-puting CEO talent, which is only applicable to large firms.

    2Negative assortative mat