Reduced Opportunities for Cartel Collusion and CEO Equity Incentives: Evidence From the Passage of Foreign Leniency Laws

Abstract

This paper examines whether reduced opportunities for collusion in product markets affect CEO compensation design. Using the staggered passage of leniency laws in foreign countries that exogenously strengthen anti-cartel enforcement against United States (US) firms, we find that firms significantly reduce the convexity of CEOs’ option-based pay, captured by CEO portfolio vega, following the passage of foreign leniency laws. This effect is stronger for firms operating in more concentrated industries and those with recent collusion convictions, and is weaker for firms with greater investment opportunities. Further analyses suggest that our findings are unlikely to be driven by identified alternative explanations and show that firms actively adjust CEOs’ risk-taking incentives by decreasing CEO vega from annual option grants and decreasing both the number and value of CEOs’ option grants following the passage of foreign leniency laws. Overall, our findings align with foreign leniency laws increasing firms’ downside risks, which discourages them from offering risk-taking incentives to the managers.

Introduction

A growing body of research highlights the significant impact of product market competition on executive compensation design (Bakke et al., 2022; Lie & Yang, 2023). Competitive pressures faced by firms are often linked to their strategic and widespread use of cartels, which can impose substantial costs on consumers, both in the US and globally (Bourveau et al., 2020; Dasgupta & Žaldokas, 2019; Dong et al., 2019; González et al., 2019). This has driven many countries to adopt policies aimed at destabilizing existing cartels and deterring the formation of new ones, with leniency laws being the cornerstone of anti-cartel enforcement efforts (Miller, 2009). Leniency laws offer full or partial immunity to firms that were involved in cartels but co-operated with prosecutors by providing information about the cartel (e.g., Chen & Rey, 2013; Miller, 2009). Prior research suggests that, as more countries with which US firms trade enact leniency laws, relevant authorities collaborate more effectively to prosecute cartel members, which, in turn, increases US firms’ exposure to anti-cartel enforcement and raises their expected costs of participating in cartels (Bourveau et al., 2020). In this study, we exploit the staggered passage of leniency laws in foreign countries to examine whether and how heightened anti-cartel enforcement threats affect managerial risk pay incentives, as captured by CEO portfolio vega.

While the impact of leniency laws on collusive behavior seems clear, ex ante, it is unclear how foreign leniency laws affect CEO risk pay incentives. On the one hand, identification of illegal cartels can impose significant legal costs on firms (Connor, 2020). Strengthening anti-cartel enforcement may elevate the likelihood of cartel detection and conviction, leading to potentially significant costs, including litigation fees and financial penalties. This heightened downside risk from cartel-related liability costs can diminish shareholders’ willingness to fund new projects, as they may fear that future penalties could reduce the available cash flows generated by these investments, even if the projects are unrelated to the source of the legal risk (Gormley et al., 2013; Gormley & Matsa, 2011). More generally, we argue that increases in downside risk tend to lower shareholders’ overall appetite for risk, prompting boards to reduce managerial incentives for risk-taking (e.g., Gormley et al., 2013; Hirshleifer & Suh, 1992; Smith & Watts, 1992). On the other hand, because managers have non-diversifiable financial and human capital exposures to their firms, they may face greater career concerns under heightened competition following the passage of a foreign leniency law. These concerns encompass potential financial losses, reputational damage, and diminished career prospects (Connor & Helmers, 2007; González et al., 2019), prompting managers to adopt a more risk-averse approach in their decision-making processes. Consequently, boards may opt to provide additional risk incentives to align the risk preferences between shareholders and managers (Armstrong & Vashishtha, 2012; Coles et al., 2006; Guay, 1999; Low, 2009; Smith & Stulz, 1985).

To investigate our research question, we follow Bourveau et al. (2020) and use the passage of leniency laws in foreign countries with which a US firm’s industry trades to capture the exogenous increase in anti-cartel enforcement at the industry level. Specifically, we compute the weighted average of the passage of such laws in foreign countries, where weights are determined by the proportion of a US industry’s sales imported from that particular country. ¹ Varying over time and cross-sectionally by industry, this treatment measure allows us to compare the changes in manager’s pay convexity for US firms in industries that trade relatively more with the countries adopting a leniency law with those in industries that trade less with those countries, in a given year. Our use of the passage of foreign leniency laws to examine the sensitivity of CEO risk-taking incentives to anti-cartel enforcement is appealing for at least three reasons. First, the passage of foreign leniency laws is plausibly exogenous to individual US domestic firms, given that the passage of a foreign law depends almost entirely on political decisions made outside of the US (Bourveau et al., 2020). Second, leniency laws are adopted by foreign countries in different years, which alleviates concerns about potential confounding effects of US macroeconomic conditions. Third, different industries vary in their exposure to specific foreign countries, which mitigates industry-level confounding effects.

We follow prior studies on managerial compensation (e.g., Cohen et al., 2013; Core & Guay, 2002; Gormley et al., 2013; Guay, 1999; Low, 2009) to measure CEO compensation risk-taking incentives by CEO portfolio vega—the sensitivity of the CEO’s wealth to a firm’s stock return volatility. Consistent with increased downside risks reducing shareholders’ willingness in investing in risky projects, we find that CEO portfolio vega significantly declines following the passage of foreign leniency laws. Specifically, a 1% increase in firms’ exposure to the passage of foreign leniency laws is associated with a 12% decrease in CEO portfolio vega. With the mean inflation-adjusted value of vega in our sample standing at $0.063 million, this effect translates to an average decrease of $7497 in the value of the CEO equity portfolio. These results suggest that firms adjust CEO risk-taking incentives downwards in response to stronger anti-cartel enforcement. ²

In additional analyses, we explore settings in which we expect the relation between the passage of foreign leniency laws and CEO portfolio vega to vary. First, given that prior studies suggest that collusion is easier for firms in concentrated industries (Huck et al., 2004), we expect firms in concentrated industries to be more exposed to the foreign leniency laws and therefore experience a larger reduction in CEO pay convexity. Consistent with our expectation, we find that the effect of foreign leniency laws is stronger for firms in more concentrated industries. Second, because cartels are known to proliferate in particular industries (Levenstein & Suslow, 2006), we posit and find that the effect of foreign leniency laws is stronger for firms in industries that were recently detected in a cartel case. Third, prior studies suggest that firms with substantial investment opportunities have strong incentives to provide additional risk-taking incentives to CEOs (e.g., Core & Guay, 1999; Smith & Watts, 1992). We thus expect that the reduction in CEO pay convexity is weaker for firms with substantial investment opportunities. Consistent with this expectation, we find that the effect of the passage of foreign leniency laws on CEO portfolio vega is weaker for firms with higher investment opportunities.

Next, we consider alternative explanations for our findings. First, we acknowledge and validate the impact of foreign anti-cartel collusion laws on competition. We find that foreign leniency laws are associated with an increase in import penetration, advertising and R&D expenditures and a decline in profit margin. These results align with the proposition that foreign leniency laws lead to stronger product market competition. Next, prior studies suggest that competition in product markets may affect executive pay (Bakke et al., 2022; Lie & Yang, 2023). It is therefore possible that our observed impact of foreign leniency laws on vega is mainly driven by heightened competition rather than downside risk associated with future cartel-related liabilities. While cartels primarily involve strategies adopted by firms, which may stem from either high or low competition in the industry, ³ we address this concern empirically by showing that our results are robust to controlling for various competition measures in our regression analysis. Third, to address the concern that the effect of foreign leniency laws on managerial risk preference might be driving the observed relationship between foreign leniency laws and vega, we conduct tests based on managers’ risk aversion. We posit that, if this explanation is correct, we should observe a stronger decrease in vega for less risk averse managers. However, we do not find evidence to support this proposition.

We test the assumed mechanism through which boards adjust CEO risk-taking incentives in response to stronger anti-cartel enforcement, and find a significantly negative relation between the passage of foreign leniency laws and the subsequent options granted to CEOs. This supports our premise that boards actively adjust CEOs’ equity incentives to optimal levels by reducing the use of stock options as incentive pay in response to the increases in downside risk. A credible concern is that our results may be driven by changes in CEOs’ option exercise behaviors rather than the boards’ actions. To address this concern, we examine whether the decreases in vega are driven by new option grants or option exercises. We find no evidence that foreign leniency laws significantly impact option exercises by the CEO, but the vega from newly granted options significantly decreases following the passage of foreign leniency laws, further supporting our argument that boards actively adjust CEOs’ equity incentives. Further, we find a reduction in firms’ stock price volatility following the passage of foreign leniency laws, consistent with the underlying assumption that the passage of foreign leniency laws reduces shareholders’ risk appetites.

We subject our findings to a battery of robustness checks. First, to alleviate the concern that measurement errors in our proxy of our treatment variable (i.e., anti-cartel enforcement) could bias our estimation, we use alternative definitions of the treatment variable and find that our main results hold when we: (1) use export data in calculating the treatment variable; (2) use a binary treatment variable, based on the year in which the firm’s most important country in terms of its industry’s import volume adopted a foreign leniency law, to implement a more standard difference-in-differences design; (3) focus on the countries that are known to have a judicial system that is relatively more efficient; (4) allow for the anticipation of leniency laws by European Union (EU) member countries when the EU passed a supranational leniency law in 2002; and (5) include or exclude influential countries (China or Japan) in calculating the treatment variable. Second, we employ a matched sample design to strengthen identification. Third, we further use the binary treatment variable in multi-period dynamic and falsification analyses. We find that the decrease in CEO portfolio vega occurs immediately after the treatment year for each industry, but not before. This suggests that there is no pre-existing trend of CEO portfolio vega for the treated firms. Our falsification analyses show that the decreases in CEO portfolio vega are unlikely to be driven by chance or a general trend. Fourth, we address the concern that the decreases in CEO portfolio vega could be driven by anticipated option expensing following the passage of Sarbanes-Oxley Act (SOX) in 2002 (Cohen et al., 2013) or the changes in accounting rules imposed by Accounting Standards Codification (ASC) 718 (previously, Statement of Financial Accounting Standards (SFAS) 123R) in 2005 that reduced the attractiveness of option-based compensation (Hayes et al., 2012). Our results hold when we exclude observations after 2002 or after 2005.

We contribute to the literature in several ways. First, we contribute to the growing literature on the link between managerial misbehavior and CEO equity incentives. Prior studies suggest that managerial misbehaviors, such as insider trading and accounting restatements, attract shareholder protests and scrutiny and can affect incentive compensation awarded to CEOs (e.g., Cheng & Farber, 2008; Denis & Xu, 2013; González et al., 2019). However, unlike managerial malfeasance by which managers profit at the expense of shareholders, cartel-related misbehaviors (e.g., price-fixing or bid-rigging) may provide significant economic benefits to shareholders (Connor & Lande, 2008). ⁴ Consequently, boards may face little shareholder pressure to act against participation in cartels (González et al., 2019). Focusing on the passage of foreign leniency laws allows us to examine how strengthened enforcement against cartel activity, which is a type of corporate misconduct that is generally to the economic benefit of the shareholders, influences managerial equity incentives.

Second, our study contributes to the executive compensation literature by providing evidence that boards evaluate a firm’s exposure to anti-cartel enforcement when determining CEO risk-taking incentives. Prior studies link the design of managerial risk-taking incentives in compensation contracts to firm-specific factors, including firm size and growth opportunities (Guay, 1999; Smith & Watts, 1992), risk tolerance in policy choices (Coles et al., 2006), and workers’ exposure to a carcinogen (Gormley et al., 2013), the regulatory events such as changes in the accounting treatment of stock-based compensation (Hayes et al., 2012), the enactment of the SOX (Cohen et al., 2013), the removal of short-selling constraints associated with Regulation SHO Pilot Program (Reg SHO) (De Angelis et al., 2017), and the introduction of credit default swap trading (Chen et al., 2019). Our research complements these prior studies by showing that opportunities for collusion in product markets can also affect risk-taking incentives in the design of executive compensation.

Third, our study investigates previously unexamined consequences of the exogenous strengthening of anti-cartel enforcement arising from the passage of foreign leniency laws. Prior studies suggest that firms respond to the passage of foreign leniency laws by engaging in more merger activity (Dong et al., 2019), relying more on new equity for capital than debt financing (Dasgupta & Žaldokas, 2019) and modifying financial disclosures (Bourveau et al., 2020). Our study extends this line of research by examining the impact of the passage of foreign leniency laws on the structure of the risk-taking incentives in CEO compensation. Our results suggest that foreign leniency laws increase firms’ downside risks, which discourages firms from providing risk-taking equity incentives to the managers.

Finally, our paper is related to the literature examining the effect of competition on executive pay. While prior studies like Lie and Yang (2023) investigate how product market competition affects the stock price sensitivity of managers’ wealth (as measured by delta), which is expected to motivate managers to increase firm value, there has been less exploration of how competition influences managerial risk-taking incentives (as measured by vega) (e.g., Armstrong & Vashishtha, 2012; Coles et al., 2006; Guay, 1999; Low, 2009; Smith & Stulz, 1985). One notable exception is Bakke et al. (2022), which uses increased import penetration as a proxy for competition and find that heightened competition is associated with lower CEO vega. While import penetration reflects competition pressures faced by firms, we show that increasing prospective anti-cartel enforcement exerts a unique and economically significant influence on vega, incremental to other dimensions of competition. In addition, the passage of foreign leniency laws allows us to exploit plausibly exogenous increases in competition on executive pay, as the passage of these laws is determined by political decisions made outside the US, mitigating endogeneity concerns that are strongly associated with domestic firm actions and import penetration. Moreover, our theoretical framework, grounded on the implications of increased downside risk and shareholder risk preferences, offers a new perspective on how competition influences managerial incentives, diverging from previous studies’ focus on managerial risk aversion (e.g., Bakke et al., 2022).

The remainder of the paper is structured as follows. The next section reviews the related literature and develops the hypothesis. We then describe the sample and the research design, followed by descriptive statistics and the results of tests of hypothesis. We then report the results of the cross-sectional tests, followed by the results of the additional tests, before concluding the paper.

Related Literature and Hypotheses

Background on Leniency Laws

Striving to protect consumers’ welfare and fight cartels more effectively in the US and worldwide, leniency laws have been gradually introduced over the past decades. These laws provide full or partial amnesty for conspirators who supply information that proves helpful to the antitrust authorities. This amnesty can extend to a firm’s directors, managers, and other employees. The first US leniency program was introduced in 1978 by the Department of Justice. However, the DOJ leniency program was seen as largely ineffective until it was revised in 1993 to provide automatic amnesty for fully cooperative applicants (Ghosal & Sokol, 2014). ⁵ Antitrust authorities in other countries noted the success of the DOJ’s revised leniency program in obtaining evidence to successfully prosecute cartel members, destabilizing existing cartels and deterring cartel formation (Miller, 2009). Leniency laws were then gradually adopted as part of anti-cartel enforcement reform across developed and developing economies (Hammond, 2005); the timing of the passages of foreign leniency laws is tabulated in Appendix A.

By granting full or partial amnesty to cartel participants who cooperate with authorities in investigating and prosecuting other cartel participants, leniency laws are expected to increase the costs of engaging in collusive activities and the benefits of breaking up cartels. Prior studies suggest that leniency laws effectively weaken existing collusive arrangements and discourage new ones (Chen & Rey, 2013). Using a difference-in-differences design, Dong et al. (2019) document that the global wave of leniency laws led to higher cartel conviction rates and lower gross margins of affected firms, implying that leniency laws significantly increase the costs of collusion. Dasgupta and Žaldokas (2019) observe that firms shift toward greater reliance on equity issuances over debt following the passage of a leniency law. Focusing on US firms, Bourveau et al. (2020) note that affected firms provide more detailed information about their customers, contracts, and products in financial disclosures after the implementation of leniency laws in foreign jurisdictions.

CEO Equity Incentives

Prior studies suggest that firms structure CEO compensation as a convex function of firm performance to incentivize CEOs to make optimal risk-taking decisions (e.g., Coles et al., 2006; Guay, 1999; Knopf et al., 2002). Specifically, Guay (1999) finds that a firm’s stock-return volatility is positively associated with the convexity in the relation between CEO wealth and stock price, suggesting that convex incentive schemes influence CEOs’ investing and financing decisions. Knopf et al. (2002) find that firms tend to hedge less when the sensitivity of the manager’s option portfolio to stock return volatility increases. Similarly, Coles et al. (2006) find that higher CEO pay convexity is followed by more investment in research and development (R&D), less investment in property, plant, and equipment (PPE), and higher leverage.

Recent research on CEO equity incentives highlights that firms promptly adjust managerial risk-incentive compensation in response to changes in their operating environments. For example, Gormley et al. (2013) show that firms adjust the CEO risk incentive pay downwards following an unanticipated increase in business risks. Balsam et al. (2018) show that firms tend to reduce risk-taking incentives in executive compensation when debt covenant violations strengthen creditor influence, while Chen et al. (2019) find that risk-taking incentives in managerial compensation increase when firms are referenced by credit default swaps trading that reduces creditor monitoring. De Angelis et al. (2017) find that firms significantly increase the convexity of CEO compensation payoffs after the removal of short-sale constraints during Reg SHO, and Cohen et al. (2013) find that firms adjust incentive compensation awarded to their CEOs after SOX regulated firms’ governance structures and increased litigation risks. More related to our context, Bakke et al. (2022) find that heightened competition caused by foreign competitor entry into the US market is associated with a decline in vega. Different from Bakke et al. (2022), we examine how foreign leniency laws, which are expected to increase the cost of collusion for US firms, relate to managerial risk incentives. This represents a distinct and previously unexplored dimension of competition effects on executive compensation.

The Link Between Anti-cartel Enforcement and CEO Equity Incentives

Ex ante, it is not obvious how foreign leniency laws affect CEO equity incentives. On the one hand, the passage of foreign leniency laws raises the costs of collusion, thereby reducing the attractiveness of risky projects for firms (Cohen et al., 2013; Gormley et al., 2013; Gormley & Matsa, 2011). In response, boards may adjust CEO incentive pay downwards to deter investments in projects that carry a higher likelihood of illegal cartel activity. On the other hand, these laws also increase potential personal costs for CEOs, which may make them more cautious about pursuing risky investments due to career concerns (Connor & Helmers, 2007; González et al., 2019). Consequently, boards might choose to increase risk incentives to better align managers’ risk preferences with those of shareholders.

Hypothesis:

CEO pay convexity is not associated with the passage of foreign leniency laws.

Research Design

Sample

We collect data from multiple sources, which affects the construction of our sample. The dates for the passage of leniency laws are sourced from Dasgupta and Žaldokas (2019), which compiled this information from the Cartel Regulation 2013, published by Getting the Deal Through. The import data used to construct foreign leniency law exposures are only available for manufacturing industries, so our initial sample is comprised of 14,176 manufacturing firm-years from 1994 to 2012 that are covered by ExecuComp, which focuses on US publicly traded firms listed in the Standard & Poor’s 1500 Index. We require sample firms to have sufficient data from ExecuComp to identify CEOs, and to calculate CEO pay incentives and other compensation-related control variables, which reduces the sample to 13,051. We obtain necessary financial data from Compustat and stock trading data from CRSP. Missing data for control variables reduces the sample to 8,002 firm-year observations for 836 unique firms. The sample selection is summarized in Panel A of Table 1. We obtain the Consumer Price Index for All Urban Consumers (CPI-U) from the Bureau of Labor Statistics and the risk-free rate based on Treasury securities from the Federal Reserve.

Table 1.

Sample Selection, Descriptive Statistics, and Correlation Matrix.

Panel A: Sample selection
All firm-years for manufacturing firms covered by ExecuComp (1994–2012)	14,176
Less cases without ExecuComp data needed to calculate CEO pay incentives and compensation-related control variables	(1125)
Less cases without sufficient data needed for other control variables	(5049)
Total	8002

Panel B: Descriptive statistics
Variable	Mean	S.D.	Min	P25	Median	P75	Max
LnVega	0.057	0.085	0.000	0.008	0.025	0.067	0.469
Vega (in 000)	63.237	102.266	0.000	8.168	25.048	69.548	597.608
LnVegaNew	0.018	0.032	0.000	0.001	0.006	0.019	0.178
VegaNew (in 000)	18.596	34.050	0.000	0.611	5.688	19.211	196.200
LnDelta	0.195	0.262	0.000	0.037	0.095	0.238	1.452
Delta (in 000)	269.048	488.677	0.000	37.437	99.264	268.220	3271.932
ForeignLeniency	0.085	0.088	0.000	0.010	0.059	0.137	0.319
HHI	0.188	0.148	0.057	0.091	0.124	0.258	0.845
ImportPenetration	0.311	0.217	0.000	0.145	0.265	0.478	0.951
Size	6.079	4.851	0.061	1.465	5.065	9.457	16.947
Size (in millions)	4203.663	9845.232	37.111	325.392	894.143	2981.740	68,000.000
MB	6.965	1.616	3.507	5.791	6.798	8.004	11.067
Leverage	3.633	3.636	0.496	1.668	2.564	4.041	24.540
R&D	0.149	0.144	0.000	0.005	0.124	0.249	0.564
CAPEX	0.069	0.078	0.001	0.017	0.043	0.096	0.469
CashFlow	0.049	0.040	0.002	0.022	0.038	0.063	0.225
StockReturn	0.118	0.121	−0.417	0.070	0.128	0.184	0.389
ROA	0.181	0.607	−0.770	−0.167	0.097	0.360	3.240
ForeignSale	0.048	0.136	−0.567	0.013	0.064	0.112	0.383
LnCashCompensation	0.407	0.248	0.037	0.229	0.342	0.518	1.282
Chg_CashCompensation	0.002	0.271	−1.147	−0.046	0.006	0.082	0.931

Panel C: Correlation matrix of key variables
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)
(1) LnVega	1.000
(2) ForeignLeniency	−0.010	1.000
(3) HHI	−0.018	−0.022	1.000
(4) ImportPenetration	−0.055	0.507	−0.138	1.000
(5) Size	0.047	0.331	−0.602	0.381	1.000
(6) MB	0.589	0.023	0.177	−0.109	−0.173	1.000
(7) Leverage	0.235	−0.154	−0.074	−0.109	0.046	0.071	1.000
(8) R&D	0.073	−0.104	0.175	−0.187	−0.248	0.324	0.090	1.000
(9) CAPEX	−0.047	0.037	−0.291	0.123	0.410	−0.347	0.159	−0.267	1.000
(10) CashFlow	−0.033	−0.199	−0.047	−0.010	0.005	−0.016	0.083	−0.050	0.011	1.000
(11) StockReturn	0.190	−0.071	0.067	−0.055	−0.139	0.306	0.166	0.010	−0.455	0.183	1.000
(12) ROA	−0.013	−0.062	−0.026	0.005	0.031	−0.056	0.324	−0.060	0.007	0.015	0.085	1.000
(13) ForeignSale	0.151	−0.048	0.035	−0.024	−0.094	0.197	0.148	−0.112	−0.436	0.150	0.667	0.207	1.000
(14) LnCashCompensation	0.528	−0.189	0.128	−0.145	−0.199	0.653	0.147	0.169	−0.202	0.067	0.246	−0.056	0.162	1.000
(15) Chg_CashCompensation	0.002	−0.069	−0.008	−0.016	−0.001	−0.038	0.060	−0.012	0.001	−0.003	0.030	0.167	0.056	−0.293	1.000

Panel A reports descriptive statistics of the key variables. Panel B reports the correlation among variables used for the main regression. Correlations with absolute values >0.02 are significant at p < .01. The sample size for both panels is 8002. All variables are defined in Appendix B.

Measuring Anti-Cartel Enforcement

Following Bourveau et al. (2020), we create the variable ForeignLeniency to capture increases in anti-cartel enforcement at the industry level. This is based on a US firm’s exposure to the passage of leniency laws in countries from which the US firm’s industry obtains a significant fraction of its imports. Specifically, ForeignLeniency is defined as the weighted average of the passage of laws in all other countries, excluding the US, thus: ForeignLeniency _jt = ${\displaystyle \sum }_k{w}_{kj}{L}_{kt}$ , where k, j, and t denote the foreign country, three-digit SIC industry, and year, respectively, and $w_{kj}$ is the share of three-digit SIC industry j’s sales imported from country k out of all industry j’s sales in 1990. ⁶ Consistent with Bourveau et al. (2020), to avoid spurious correlation due to changes in industry structure or industry classification the weights are based on data from 1990. $L_{kt}$ equals 1 if country k has passed a leniency law by year t, and 0 otherwise. Our sample encompasses 88 industries with SIC codes ranging from 201 to 399. Our measure of exposure to foreign leniency laws is at industry level and increases over time as countries from which US firms’ industries obtain imports enact leniency laws. We show how our measure of firms’ exposures to the passage of foreign leniency laws evolves over time for top 10 and bottom 10 industries in Figure 1. We observe the largest impact is for the pulp mill products industry (SIC 261) and the least impact is on the guided missiles and space vehicles industry (SIC 376).

Figure 1.

Trends in Foreign Leniency Exposure for Top 10 and Bottom 10 Industries.

Measuring CEO Pay Convexity

Consistent with prior research (e.g., Cohen et al., 2013; Core & Guay, 2002; Gormley et al., 2013; Guay, 1999; Low, 2009), we proxy for CEO pay convexity using vega, which is the change in the dollar value of the CEO’s wealth for a 0.01 change in the annualized standard deviation of a firm’s stock return. We calculate vega based on the Black–Scholes (1973) option valuation model, as modified by Merton (1973) to account for dividend payouts. Consistent with Guay (1999) and Coles et al. (2013), we use the vega of the CEO’s options portfolio to measure the total vega of the equity portfolio (Vega). Consistent with prior studies (e.g., Gormley et al., 2013), we adjust the dollar value of vega by inflation using the annual average CPI-U.

Model

To test our hypothesis, we use ForeignLeniency to identify the impact of the passage of foreign leniency laws on CEO pay convexity, and estimate the following model:

$\begin{array}{ll}\begin{array}{l}{\mathrm{Ln}Vega}_{it}=\end{array}& \begin{array}{l}{\beta }_0+{\beta }_1{ForeignLeniency}_{jt}+{\beta }_2{HHI}_{it}+{\beta }_3{ImportPenetration}_{it}\\ +{\beta }_4{ForeignSale}_{it}+{\beta }_5{Size}_{it}+{\beta }_6{MB}_{it}+{\beta }_7{Leverage}_{it}+{\beta }_8{R\&D}_{it}\\ +{\beta }_9{CAPEX}_{it}+{\beta }_{10}{CashFlow}_{it}+{\beta }_{11}{StockReturn}_{it}+{\beta }_{12}{ROA}_{it}\end{array}\\ & +{\beta }_{13}{\mathrm{Ln}CashCompensation}_{it-1}+{\beta }_{14}{Chg\_CashCompensation}_{it}\\ & +Firm\hspace{0.17em}Fixed\hspace{0.17em}Effects+Year\hspace{0.17em}Fixed\hspace{0.17em}Effects+{\epsilon }_{it}\end{array}$

(1)

where i, j, and t denote firm, three-digit SIC industry, and year, respectively. LnVega is the natural logarithm of 1 plus Vega (the CEO portfolio vega, adjusted for inflation, as defined above). A negative (positive) and significant coefficient for ForeignLeniency (as defined above) indicates that CEO pay convexity decreases (increases) following the passage of foreign leniency laws.

We include firm-level control variables known to affect CEO portfolio vega. Unless stated otherwise, variables are for year t. Size is the natural logarithm of a firm’s total assets. MB is a firm’s market value of equity divided by its book value of equity, and proxies for growth opportunities (Smith & Watts, 1992). Leverage is total debt divided by total assets, which has been found to affect managerial risk-taking incentives (e.g., Coles et al., 2006). R&D is research and development expenditure divided by total assets. CAPEX is net capital expenditure divided by total assets. R&D and CAPEX control for variations in investment opportunities. Following Gormley et al. (2013), CashFlow is operating income adjusted for depreciation and accruals, divided by total assets, and controls for firms’ cash constraints because firms prefer equity-based pay to cash compensation if they face cash constraints (Core & Guay, 1999; Dechow et al., 1996). StockReturn is a firm’s stock return for the last 12-month fiscal period. ROA is income before extraordinary items scaled by lagged total assets. StockReturn and ROA are used to control for the effect of firm performance on CEO compensation and wealth (Core & Guay, 1999). LnCashCompensation is the natural logarithm of cash compensation for year t-1, where cash compensation is the sum of salary and bonus, adjusted for inflation using the annual average CPI-U, consistent with Gormley et al. (2013). Chg_CashCompensation is the changes in cash compensation adjusted for inflation using the annual average CPI-U from year t-1 to year t. CEOs with high cash compensation tend to be wealthier and better diversified, making them less risk-averse (Berger et al., 1997; Guay, 1999). We include three industry level controls for the potential effect of trade policy changes. HHI is industry concentration, as proxied by the Herfindahl–Hirschman Index at the three-digit SIC industry. ImportPenetration is the value of imports scaled by the sum of imports and the shipment value minus the value of exports. ForeignSale is foreign sales divided by total sales at the three-digit SIC industry-level. Firm and year fixed effects are included to control for time-invariant firm characteristics and economy-wide shocks that vary over time. The definitions and data sources for all variables are summarized in Appendix B.

Main Tests

Descriptive Statistics

Summary statistics of the variables used in our main regression analysis are reported in Table 1 Panel B. To control for outliers, continuous variables are winsorized at the bottom and top 1%. The mean value of Vega is $63,237, which indicates an average increase of $63,237 in the dollar value of CEO wealth for a 0.01 increase in the annualized standard deviation of a firm’s stock price. The mean value of ForeignLeniency is 0.085, similar to the mean of 0.070 reported in Bourveau et al. (2020). Overall, the descriptive statistics of the variables are consistent with those reported in previous studies (e.g., Bettis et al., 2018; Bourveau et al., 2020; Coles et al., 2006; Gormley et al., 2013). The correlations among the variables are reported in Table 1 Panel C. ForeignLeniency has a mildly negative relation to CEO portfolio vega.

Test of Hypothesis

The results of our main analysis using the multivariate regression in equation (1) are reported in Table 2. Column 1 reports the result with only the variable of interest ForeignLeniency and dependent variable, omitting all of the controls in the regression. Column 2 reports the result with all the controls in the regression. In both columns, the coefficient for ForeignLeniency is negative and significant (p < .01), consistent with our hypothesis that CEO portfolio vega decreases following the passage of foreign leniency laws (in all regressions, standard errors are clustered at the industry-year level).

Table 2.

Foreign Leniency Law Exposure and CEO Portfolio Vega.

	LnVega
	(1)	(2)
ForeignLeniency	−0.132***	−0.112***
	(−5.156)	(−4.586)
HHI		0.011
		(0.879)
ImportPenetration		−0.023**
		(−2.054)
ForeignSale		0.000
		(0.410)
Size		0.026***
		(13.410)
MB		0.001***
		(2.957)
Leverage		−0.031***
		(−4.061)
R&D		0.068***
		(3.701)
CAPEX		−0.004
		(−0.213)
CashFlow		−0.016**
		(−2.040)
StockReturn		−0.003***
		(−2.734)
ROA		0.038***
		(5.754)
LnCashCompensation		0.082***
		(9.069)
Chg_CashCompensation		0.029***
		(6.069)
Firm FE	YES	YES
Year FE	YES	YES
Adjusted R2	0.623	0.660
Observations	8002	8002

This table reports the regression results of the impact of a firm’s exposure to the passage of foreign leniency on the CEO’s portfolio vega. t-statistics, reported in parentheses, are based on standard errors clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively. All variables are defined in Appendix B.

Because the dependent variable is log-transformed, the coefficient for ForeignLeniency of 0.112 in column 2 implies that a 1% increase in ForeignLeniency is followed by a 12% decrease in CEOs’ portfolio vega, when holding other factors constant. With the mean inflation-adjusted value of vega in our sample standing at $63,237, the effect of ForeignLeniency translates to an average decrease of $7525 (0.119 × $63,237) in the value of the CEO equity portfolio. The coefficients for the control variables are generally consistent with those of prior studies (e.g., Coles et al., 2006; Croci & Petmezas, 2015; Guay, 1999). LnVega is positively related to firm size, market-to-book ratio, R&D, ROA, and cash compensation; and negatively related to leverage, cash flow, and stock return.

These results suggest that stronger anti-cartel enforcement associated with the passage of foreign leniency laws increase firms’ downside risks, which discourages them from offering risk-taking equity incentives to the managers, resulting in decreases CEOs’ portfolio vega.

Cross-Sectional Tests

This section explores whether and how the effect for ForeignLeniency differs systematically across firms, in circumstances where firms may differ in their exposure to foreign leniency laws or their impact on the firms’ opportunities.

High versus Low Market Concentration

Prior studies suggest that industry concentration is one of the most important determinants of participating in a cartel (Huck et al., 2004; Motta, 2004). These studies suggest that firms in concentrated industries with symmetric players find it easier to collude. Therefore, we expect firms in concentrated industries to experience greater reductions in CEO pay convexity following the passage of foreign leniency laws. We test this prediction using the three-digit SIC industry HHI to identify when firms face relatively high or low market concentration. We omit firms if the HHI score is in the middle tercile of the sample and set HighMarketConcentration equals 1 (0) if the firm’s HHI is in the upper (lower) tercile. We re-estimate the main model and interact HighMarketConcentration with ForeignLeniency, as reported in column 1 of Table 3. The coefficients for ForeignLeniency and the interaction are both significantly negative. These results are consistent with our prediction that the effect of the foreign leniency laws on CEOs’ portfolio vega is stronger for firms in more concentrated industries, in which collusion was expected to be higher prior to the passage of the leniency law.

Table 3.

Foreign Leniency Law Exposure and CEO Portfolio Vega: Cross-Sectional Tests.

	LnVega
	(1)	(2)	(3)
ForeignLeniency	−0.098***	−0.148***	−0.097***
	(−2.605)	(−5.151)	(−3.471)
ForeignLeniency × HighMarketConcentration	−0.066*
	(−1.857)
ForeignLeniency × HighInvestmentOpportunity		0.139***
		(5.343)
ForeignLeniency × WithRecentConviction			−0.022*
			(−1.651)
Controls	YES	YES	YES
Firm FE	YES	YES	YES
Year FE	YES	YES	YES
Adjusted R2	0.652	0.662	0.660
Observations	5272	5290	8002

This table reports the regression results of the impact, on a CEO’s portfolio vega, of the firm’s exposure to the passage of foreign leniency moderated by high market concentration, high investment opportunity, and recent cartel convictions in the focal firm’s industry. t-statistics, reported in parentheses, are based on standard errors clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively. All variables are defined in Appendix B.

High versus Low Investment Opportunities

We next test whether firms’ investment opportunities moderate the effect of foreign leniency laws on CEO pay convexity. Prior studies suggest that firms with more substantial investment opportunities are more likely to structure CEO compensation to incentivize managerial risk-taking (e.g., Core & Guay, 1999; Smith & Watts, 1992). Therefore, we expect that the reduction in CEO pay convexity is weaker for firms with high investment opportunities. To test this prediction, we measure a firm’s investment opportunity as the market-to-book ratio for equity, averaged over the two-year window. We then exclude firm-year observations in the middle tercile of market-to-book ratio for equity, and set HighInvestmentOpportunity equal to 1 (0) if it is in the upper (lower) tercile of the sample. We re-estimate the main model and interact HighInvestmentOpportunity with ForeignLeniency, as reported in column 2 of Table 3. The coefficient for ForeignLeniency is significantly negative and the coefficient on the interaction is significantly positive. These results are consistent with our prediction that the effect of the foreign leniency laws on CEOs’ portfolio vega is lower for firms with more investment opportunities, for which incentivizing risk-taking is more likely to continue to be a preferred strategy.

Recent Cartel Conviction

We posit that foreign leniency laws are more salient to firms operating in markets that are more likely to be targeted for anti-cartel enforcement, and so we predict that firms operating in industries with recent convictions in cartel cases will experience greater decreases in vega. To test this prediction, we follow Bourveau et al. (2020) and use the cartel detections reported in Connor (2014) to construct the variable WithRecentConviction, which equals 1 (0) if a firm is (not) in an industry that had a cartel case in the last three years. We re-estimate the main model and interact WithRecentConviction with ForeignLeniency, as reported in column 3 of Table 3. The coefficients for ForeignLeniency and the interaction are both significantly negative, consistent with our prediction that the effect of foreign leniency laws is stronger for firms in industries with a recently detected in a cartel case.

Additional Tests

Alternative Explanations

Competition

Frist, we verify the effect of anti-cartel laws on competition. Ample academic research and practical evidence suggests that leniency laws are widely regarded as one of the most significant and effective mechanisms for promoting competition (Dasgupta & Žaldokas, 2019; Miller, 2009). By destabilizing existing cartels and deterring the formation of new ones, these laws strip firms of the shield provided by collusive practices, compelling them to enhance efficiency and engage in competitive behavior. Consistent with this notion, prior studies find that these leniency laws are associated with a decline in the profit margins, equity returns, and product prices of the affected US firms (Bourveau et al., 2020). We analyze the effect of leniency laws on competition at both the industry and firm levels. At the industry-level, we use import penetration (ImportPenetration) as a proxy for competition, where an increase in import penetration heightens competition in domestic product markets (Bakke et al., 2022; Lie & Yang, 2023). At the firm level, we employ the advertising and R&D to sales ratio (NonPrice) as well as the profit margin (AdjProfitMargin) to measure competition (Bourveau et al., 2020; Chen et al., 2015; Gaspar & Massa, 2006; Peress, 2010). As reported in Table 4, we find that the passage of foreign leniency laws is associated with increased industry import penetration, higher ratios of advertising and R&D expenditure, and reduced profit margins at the firm level. These results align with the proposition that foreign leniency laws intensify product market competition.

Table 4.

Foreign Leniency Exposure and Competition.

	Industry-level competition		Firm-level competition
	ImportPenetration		NonPrice	AdjProfitMargin
	(1)	(2)	(3)	(4)
ForeignLeniency	0.253***	0.151***	0.001*	−0.115**
	(3.546)	(6.025)	(1.742)	(−2.077)
Firm-level controls	No	YES	YES	YES
Industry FE	YES	No	No	No
Firm FE	No	YES	YES	YES
Year FE	YES	YES	YES	YES
Adjusted R2	0.834	0.978	0.905	0.547
Observations	1325	7199	6913	6446

This table reports the regression results for the impact of a firm’s exposure to the passage of foreign leniency laws on both industry-level and firm-level competition. In columns 1 and 2, the dependent variable is industry-level ImportPenetration. In column 1 (2) the unit of analysis is industry-year (firm-year). In column 3, the dependent variable NonPrice is advertising + R&D expenditure divided by sales. In column 4 the dependent variable AdjProfitMargin is EBITDA + advertising + R&D expenditure, divided by sales. t-statistics, reported in parentheses, are based on standard errors clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively. All variables are defined in Appendix B.

Second, we address the concern that our main results could be driven merely by competition. Existing studies have documented that product market competition can affect executive pay. For example, Bakke et al. (2022) use increased import penetration resulting from tariff cuts to capture competition and find heightened competition leads to lower vega. Lie and Yang (2023) employ Chinese import penetration as a competition measure and find that competition is linked to lower delta. While import penetration reflects competition pressures faced by firms, cartels focus on the strategies adopted by firms that can be motivated by either high or low competition within the industry, which should capture a distinct effect not examined by prior studies. Nevertheless, to address this concern, we follow Bakke et al. (2022) to construct TariffCut, which equals 1 for years following a tariff cut shock, and 0 otherwise; and we follow Lie and Yang (2023) to construct ChineseImport as the total value of imports from China divided by the sum of total value of imports and domestic production (shipments minus exports) for each three-digit SIC industry in a year. We control for TariffCut and ChineseImport in our regression analysis. As shown in Table 5, the results are substantively unchanged after controlling for these competition measures, suggesting that leniency law has a distinct effect on compensation vega, independent of other factors.

Table 5.

Foreign Leniency Exposure and CEOs’ Portfolio Vega: Chinese Import Penetration and Tariff Cuts.

	LnVega
	(1)
ForeignLeniency	−0.096***
	(−4.174)
ChinaImport	−0.009
	(−1.463)
TariffCut	−0.020*
	(−1.663)
Controls	YES
Firm FE	YES
Year FE	YES
Adjusted R2	0.660
Observations	8002

This table reports the regression results of the impact of a firm’s exposure to the passage of foreign leniency laws on the CEO’s portfolio vega, controlling for import penetration from China and US tariff cuts. t-statistics, reported in parentheses, are based on standard errors clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively. All variables are defined in Appendix B.

Managerial Risk Preference

Bakke et al. (2022) propose that amidst heightened competition spurred by foreign entry, less risk-averse managers may voluntarily take on more risk under high competition, resulting in a less need to provide risk incentive pay. If our results are driven by this explanation, we should observe a stronger decrease in vega for less risk-averse managers. To investigate this, we perform an additional cross-sectional test based on managers’ risk aversion. Specifically, we follow Bakke et al. (2022) to use CEOs’ aircraft pilot certification as a proxy for managers’ risk aversion as literature has shown that individuals with pilot licenses are likely to be less risk-averse. We search for each CEO name in our sample in the Federal Aviation Administration’s (FAA’s) Airmen Certification database. If a given name does not produce a match in the FAA’s database, then this observation is identified as a non-pilot and vice versa. We construct an indicator variable PilotCEO, which equals 1 if the CEO holds a pilot license, and 0 otherwise. As shown in Table 6, the interaction of ForeignLeniency and PilotCEO is not significant, suggesting our observed decreases in vega is unlikely driven by this explanation.

Table 6.

Foreign Leniency Law Exposure and CEO Portfolio Vega, Moderated by Managerial Risk Preferences.

	LnVega
	(1)
ForeignLeniency	−0.109***
	(−4.415)
ForeignLeniency × PilotCEO	−0.004
	(−0.164)
Controls	YES
Firm FE	YES
Year FE	YES
Adjusted R2	0.660
Observations	8002

This table reports the regression results of the impact of a firm’s exposure to the passage of foreign leniency laws on the CEO’s portfolio vega, conditional on managerial risk preferences as proxied by holding a pilot’s license. All variables are defined in Appendix B. t-statistics are reported in parentheses. Standard errors are clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively.

Mechanism

Adjustment of CEO Compensation

Although the analyses so far establish a positive link between the passage of foreign leniency laws and subsequent CEO risk-taking incentives, the underlying mechanism through which boards adjust the incentives has not been confirmed. Prior studies suggest that option grants are used to incentivize risk-taking (Hayes et al., 2012). If firms intend to reduce convexity in response to the risk implications of stronger anti-cartel enforcement, we expect a decrease in the proportion of incentive pay in the form of options grants following the passage of foreign leniency laws. In this section, we directly examine whether option grants become a smaller component of CEO compensation after the passage of foreign leniency laws by decomposing CEOs’ yearly compensation package and separately measure: (1) the value of cash compensation (LnCash); (2) the value of equity (stock plus options) compensation (LnEquity); (3) the value of options granted to the CEOs (LnOption); (4) the proportion of options in new equity awards in terms of value (Option/Equity ($)); and (5) the proportion of options in new equity awards in terms of numbers (Option/Equity (#)). We then estimate the effect of foreign leniency laws on each of these components. The results reported in Table 7 Panel A are consistent with our expectation that boards reduce options to restructure CEO compensation incentives in response to the increased downside risk associated with foreign leniency laws. We find that ForeignLeniency does not significantly influence the cash pay component, but significantly decreases the options granted to the CEO as a proportion of equity compensation. These results are consistent with the proposition that granting fewer options is an important mechanism that boards use to restructure CEO compensation incentives in response to the increased downside risk associated with the passage of foreign leniency laws.

Table 7.

Foreign Leniency Exposure and CEO Compensation.

Panel A: The components of CEO compensation
	LnCash	LnEquity	LnOption	Options/Equity ($)	Options/Equity (#)
	(1)	(2)	(3)	(4)	(5)
ForeignLeniency	0.088	−0.754***	−0.694***	−0.494***	−0.571***
	(1.444)	(−4.985)	(−4.598)	(−4.824)	(−5.621)
Controls	YES	YES	YES	YES	YES
Firm FE	YES	YES	YES	YES	YES
Year FE	YES	YES	YES	YES	YES
Adjusted R2	0.698	0.544	0.484	0.542	0.491
Observations	8301	8092	8094	6734	6861

Panel B: CEO option exercise
	ExerciseValue	ExerciseShares
	(1)	(2)
ForeignLeniency	−0.170	−0.013
	(−0.506)	(−0.020)
Controls	YES	YES
Firm FE	YES	YES
Year FE	YES	YES
Adjusted R2	0.157	0.180
Observations	7925	7921

Panel C: CEO current vega and portfolio delta
	LnVegaNew	LnDelta
	(1)	(2)
ForeignLeniency	−0.024***	−0.230***
	(−2.955)	(−4.017)
Controls	YES	YES
Firm FE	YES	YES
Year FE	YES	YES
Adjusted R2	0.471	0.669
Observations	8002	8002

This table reports the regression results of the impact of a firm’s exposure to the passage of foreign leniency laws on different elements of the CEO’s compensation. In Panel A, the dependent variables are the value of the CEO’s cash remuneration (column 1) and equity remuneration (column 2), and the proportion of options in new equity awards in terms of value (column 3) and numbers (column 4). In Panel B, the dependent variables are the value of CEO option exercises (column 1) and the number of options exercised by the CEO (column 2) during the year. In Panel C, the dependent variables are the CEO’s vega for newly granted options (column 1) and the CEO’s portfolio delta (column 2). t-statistics, reported in parentheses, are based on standard errors clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively. All variables are defined in Appendix B.

In the main analyses, we interpret the observed decreases in CEO portfolio vega as a result of the board actively managing CEOs’ risk-taking incentives in response to the passage of foreign leniency laws. However, vega can also change for reasons that are not under the control of the board. For example, changes in CEOs’ option exercise behavior can also result in changes in vega. To test this behavior, we replace the dependent variable in equation (1) with (1) the value of options exercised divided by the CEO’s total compensation (ExerciseValue) and (2) the number of options exercised deflated by the number of outstanding shares held by the CEO (ExerciseShares). A positive effect in relation to the value or the number of options exercised would be consistent with CEOs modifying their option exercise behavior following the passage of foreign leniency laws. The results reported in Table 7 Panel B do not provide any evidence that foreign leniency laws impact option exercises by the CEO, from which we conclude that they are unlikely to be driving our main results.

To better understand how foreign leniency laws change CEO compensation vega, we investigate whether the decrease in vega is driven by new option grants during the year. While portfolio vega is a comprehensive and precise measure of managers’ risk-taking incentives and captures the overall effect of aggregate holdings following a government spending shock, examining the vega of annual option grants provides more insight into whether changes in CEO portfolio vega are attributable to changes in the vega of new options granted to CEOs during the current year and whether the passage of foreign leniency laws have an immediate impact on CEOs’ pay convexity. We use LnVegaNew to measure vega estimated for newly granted options. To have a more comprehensive understanding of how anti-cartel leniency laws affect managerial compensation, we also examine changes in delta in our context of cartels. Following Coles et al. (2013), we measure LnDelta as the natural logarithm of 1 plus portfolio delta, where delta is the change in the dollar value of the CEO’s wealth for a 1% change in a firm’s stock price. The results are reported in Table 7 Panel C. Column 1 shows a decrease in vega of new option grants following the passage of foreign leniency laws, suggesting boards actively adjust CEOs’ risk-taking incentives by decreasing CEO vega from annual option grants in response to the passage of foreign leniency laws. As shown in column 2, we find delta also decreases following the passage of foreign leniency laws, which is consistent with the suggestion in Gormley et al. (2013) that decreases in desired investments also reduce the need for delta.

Firm Performance Volatility

To test our underlying assumption that the passage of foreign leniency laws reduces affected firms’ risk appetites, we examine whether the passage of foreign leniency laws leads to a decrease in the riskiness of a firm’s projects, as reflected in stock return volatility. Stock return volatility captures market perceptions of the overall riskiness of a firm, embracing risks inherent in its business strategies, management, and projects. We measure StockVolatility as the standard deviation of a firm’s monthly stock return for the year following the passage of foreign leniency laws, as measured by ForeignLeniency. As reported in Table 8, the coefficient for ForeignLeniency is negative and significant, consistent with shareholders’ risk appetites decreasing following the passage of foreign leniency laws.

Table 8.

Foreign Leniency Exposure and Firm Performance Volatility.

	StockVolatility
	(1)
ForeignLeniency	−0.092***
	(−3.226)
Controls	YES
Firm FE	YES
Year FE	YES
Adjusted R2	0.598
Observations	7546

This table reports the regression results of the impact of a firm’s exposure to the passage of foreign leniency laws on the firm’s stock return volatility. t-statistics, reported in parentheses, are based on standard errors clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively. All variables are defined in Appendix B.

Robustness Tests

Alternative Measures

As robustness checks, we re-estimate our model using four different specifications of the treatment variable based on foreign leniency laws.

First, to alleviate the concern that a firm’s industry exports are more exposed than imports to the passage of leniency laws in foreign countries, we construct the treatment variable ForeignLeniency_Export by replacing the weight in ForeignLeniency (the country share of imports in an industry) with the share of exports of each three-digit SIC industry from the US to the relevant countries.

Second, we use a binary treatment in place of the continuous measure of ForeignLeniency, which allows us to implement a more standard difference-in-differences estimation of the staggered assignment of the treatment, following Bourveau et al. (2020). For each three-digit SIC industry, we identify the treatment year as the year in which the most important country in terms of import volume adopted the foreign leniency law. ForeignLeniency_Dummy equals 1 for the industry following the treatment year and 0 otherwise.

Third, given that the enforcement of leniency laws may not be effective in some countries, we reconstruct our treatment variable to focus on the countries with more efficient judicial systems based on World Bank Worldwide Governance Indicators (WGI). The WGI reports time-varying national governance index for 212 countries annually over the period 1996–2021. ⁷ It reflects both the quality of policy formulation and implementation and the credibility of the government’s commitment to such policies. We follow Dasgupta and Žaldokas (2019) to use this country-level governance index to proxy for a country’s judicial system effectiveness. We construct ForeignLeniency_Enforcement by including only leniency laws that were passed in countries whose governance index is larger than the sample median around the world at the time of the relevant leniency law’s implementation.

Fourth, in 2002 the EU resolved that all member countries should introduce leniency laws but the passage of leniency laws in member countries was staggered over several years. In our main analysis, we use the year in which the individual country passed the law. Here, we address a possible concern about anticipation of the leniency law for EU members in 2002. We construct ForeignLeniency_EU by setting the effective year for the leniency law of an EU member country to be the later of 2002 or the year when the country joined the EU.

Fifth, we explore which country creates the biggest changes in foreign leniency in our sample. Our variable of interest is constructed based on the import volume from foreign countries in 1990, with Japan emerging as the most influential country for US industries in terms of imports. Acknowledging the substantial role of Chinese imports in influencing competition levels for US firms as highlighted in numerous existing studies (Lie & Yang, 2023), we incorporate the effects of both Japan and China in our additional analysis. Specifically, we re-construct our treatment variable by: (1) including only the anti-cartel collusion law passed in China (ForeignLeniency_China); (2) including only the anti-cartel collusion law passed in Japan (ForeignLeniency_Japan); (3) excluding the anti-cartel collusion law passed in China (ForeignLeniency_Excl_China); and (4) excluding the anti-cartel collusion law passed in Japan (ForeignLeniency_Excl_Japan).

For each of these alternate variables, we re-estimate our main test and report the results in Table 9. We find that our main results are robust to alternative measures of foreign leniency exposure. We also find that, while there is no significant effect of Chinese leniency laws on vega, leniency laws passed in Japan and other foreign countries exhibit a significantly negative effect on vega. This suggests that our results are unlikely to be driven by the leniency laws of China or Japan alone.

Table 9.

Foreign Leniency Exposure and CEOs’ Portfolio Vega: Alternative Measures.

	LnVega
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
ForeignLeniency_Export	−0.059**
	(−2.156)
ForeignLeniency_Dummy		−0.013***
		(−2.732)
ForeignLeniency_Enforcement			−0.123***
			(−4.372)
ForeignLeniency_EU				−0.099***
				(−4.240)
ForeignLeniency_China					0.119
					−0.252
ForeignLeniency_Japan						−0.140***
						(−2.980)
ForeignLeniency_Excl_China							−0.114***
							(−4.648)
ForeignLeniency_Excl _Japan								−0.163***
								(−4.804)
Controls	YES	YES	YES	YES	YES	YES	YES	YES
Firm FE	YES	YES	YES	YES	YES	YES	YES	YES
Year FE	YES	YES	YES	YES	YES	YES	YES	YES
Adjusted R2	0.659	0.659	0.66	0.66	0.658	0.659	0.66	0.66
Observations	8002	8002	8002	8002	7952	7963	8002	8002

This table reports the regression results of the impact of a firm’s exposure to the passage of foreign leniency laws on the CEO’s portfolio vega using alternative measures of foreign leniency law exposure. t-statistics, reported in parentheses, are based on standard errors clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively. All variables are defined in Appendix B.

Matched Sample

In this section, we employ a matched sample to conduct DID tests to strengthen identification. Specifically, we use a propensity score matching (PSM) method to construct a sample in which the control firms are comparable to the treated firms in terms of various firm and industry-level characteristics one-year prior to the event. We first employ a logit model with Treat as the dependent variable and all control variables in the baseline regression model as independent variables. Treat equals 1 for firms in industries experiencing the largest increase in leniency law exposure in terms of import volume in a year, and 0 otherwise. We use nearest-neighbor matching without replacement and a caliper of 0.005 to balance potential differences in covariates between treated and control groups. The resulting matched sample comprises 326 firms in each of the treatment and control groups. As reported in Panel A of Table 10, the mean comparisons of matched pairs indicate that the matching procedure successfully balances covariates. We then examine the effect of leniency laws on vega using this matched sample by creating two indicator variables. Treated equals 1 for treatment firms and 0 for the matched control firms. Because the dynamic tests suggest that the effect of foreign leniency laws persist for three years (as mentioned above), we estimate the model in which Post equals 1 in the event year and two subsequent years, and 0 in the three years preceding the event. The results are reported in Panel B of Table 10. The coefficient on Treated × Post, is negative and significant. This suggests that firms decrease CEO vega relative to control firms following the passage of foreign leniency law.

Table 10.

Foreign Leniency Exposure and CEOs’ Portfolio Vega: DID Test.

Panel A: The mean comparisons of matched pairs
	Means
Variable	Treat	Control	t	p > |t|
HHI	0.182	0.185	−0.290	0.771
ImportPenetration	0.267	0.287	−1.170	0.243
ForeignSale	5.097	5.414	−0.950	0.344
Size	6.651	6.736	−0.670	0.501
MB	4.148	4.104	0.080	0.934
Leverage	0.166	0.173	−0.650	0.513
R&D	0.075	0.073	0.240	0.814
CAPEX	0.059	0.058	0.110	0.910
CashFlow	0.112	0.116	−0.300	0.762
StockReturn	0.318	0.261	0.970	0.333
ROA	0.051	0.059	−0.720	0.472
LnCashCompensation	0.429	0.437	−0.360	0.716
Chg_CashCompensation	0.061	0.077	−0.500	0.618

Panel B: Difference-in-difference test using PSM
	LnVega
	(1)
Treated × Post	−0.011**
	(−2.098)
Controls	YES
Firm FE	YES
Year FE	YES
Adjusted R2	0.703
Observations	3001

This table reports the regression results of DID test using matched sample. Panel A reports the mean comparisons of matched pairs. Panel B reports the difference-in-difference test, using a PSM sample, for the results for the impact of a firm’s exposure to the passage of foreign leniency laws on the CEO’s portfolio vega. t-statistics, reported in parentheses, are based on standard errors clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively. All variables are defined in Appendix B.

Falsification Test and Dynamic Test

We perform a falsification test and then further utilize the binary treatment variable ForeignLeniency_Dummy to explore the multi-period dynamics of the effect of foreign leniency laws on vega.

It is plausible that the negative effect of foreign leniency laws on CEO equity incentives is spurious or reflects a general trend. Therefore, we perform a falsification test by constructing a variable (ForeignLeniency_Falsification) that identifies a pseudo treatment year (i.e., the passage year of foreign leniency law) as four years before the actual year of passage. We then replace ForeignLeniency with ForeignLeniency_Falsification in our main model. As reported in column 1 of Table 11, the insignificant and seemingly trivial coefficient for ForeignLeniency_Falsification is suggests that the decline in CEO portfolio vega is unlikely to be driven by chance or a general trend.

Table 11.

Foreign Leniency Exposure and CEOs’ Portfolio Vega: Falsification Test and Dynamic Test.

	LnVega
	(1)	(2)
ForeignLeniency_Falsification	0.000
	(0.071)
ForeignLeniency (−3)		−0.003
		(−0.620)
ForeignLeniency (−2)		−0.004
		(−0.829)
ForeignLeniency (−1)		−0.006
		(−1.303)
ForeignLeniency (0)		−0.012*
		(−1.712)
ForeignLeniency (+1)		−0.012**
		(−1.997)
ForeignLeniency (+2)		−0.009**
		(−1.982)
ForeignLeniency (+3)		−0.006
		(−1.195)
Controls	YES	YES
Firm FE	YES	YES
Year FE	YES	YES
Adjusted R2	0.658	0.659
Observations	8002	8002

This table reports the regression results of a falsification test (column 1) and a dynamics test (column 2) for the impact of a firm’s exposure to the passage of foreign leniency laws on the CEO’s portfolio vega. The falsification test uses a pseudo treatment year as four years before the actual year of the passage of a foreign leniency law. The dynamics test uses lags (−3, +3) of ForeignLeniency_Dummy from Table 9 t-statistics, reported in parentheses, are based on standard errors clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively. All variables are defined in Appendix B.

To explore the dynamics of the leniency law effect, we decompose ForeignLeniency_Dummy into seven time-period indicator variables that simultaneously replace ForeignLeniency in the main model. ForeignLeniency (−3), ForeignLeniency (−2), and ForeignLeniency (−1), respectively, equals 1 for observations in year 3, 2, and 1 before the treatment year, and 0 otherwise. ForeignLeniency (0) equals 1 for observations in the treatment year, and 0 otherwise. ForeignLeniency (+1), ForeignLeniency (+2), and ForeignLeniency (+3), respectively, equals 1 for observations in year 1, 2, and 3 after the treatment year, and 0 otherwise. As reported in column 2 of Table 11, the coefficients for these period indicators show that CEO portfolio vega does not significantly decrease before the treatment year but begins to fall immediately in the year of treatment, and this effect continues for the subsequent 2 years.

Subsample Tests

One may be concerned that the observed decline in pay convexity for firms is driven by the changes in accounting rules introduced by ASC 718 in 2005 that reduced the attractiveness of option-based compensation. Under ASC 718, from 2006 firms could no longer expense employee option-based compensation at nominal values but must expense these options at their much higher fair values. This change in accounting treatment reduced accounting advantages associated with option-based compensation and firms significantly reduced their usage of option-based compensation from 2006, decreasing the sensitivity of CEO wealth to stock return volatility. Also, the 2007–2008 financial crisis may have affected compensation contracting or the parameters used to estimate vega. Therefore, we re-estimate equation (1) using only observations prior to 2005, as reported in column 1 of Table 12. The results are consistent with our main results, suggesting they are not driven by the implementation of ASC 718 or the financial crisis.

Table 12.

Foreign Leniency Exposure and CEOs’ Portfolio Vega: Subsample Tests.

	LnVega
	(1)	(2)
ForeignLeniency	−0.172***	−0.140**
	(−3.786)	(−2.312)
Controls	YES	YES
Firm FE	YES	YES
Year FE	YES	YES
Adjusted R2	0.686	0.637
Observations	5004	3253

This table reports the regression results for the impact of a firm’s exposure to the passage of foreign leniency laws on the CEO’s portfolio vega, after excluding observations post-ASC 718 (column 1) or post-SOX (column 2). t-statistics, reported in parentheses, are based on standard errors clustered by industry-year. ***, **, * indicate significance at p = .01, .05, and 0.10, respectively. All variables are defined in Appendix B.

We observe that option-based compensation began to decrease after the 2002 passage of SOX and before ASC 718. Prior studies suggest that there was increased pressure from shareholder activists and regulators to reform the rules governing firms’ stock option plans post-SOX (Yang et al., 2021). We further restrict our sample to pre-SOX observations, as reported in column 2 of Table 12, and the effect of ForeignLeniency remains negative and significant in the pre-SOX period.

Conclusions

In this study, we exploit the staggered passage of leniency laws in foreign countries to explore how exogenously strengthened anti-cartel enforcement affects US firms’ CEO risk-taking incentives, as captured by CEO portfolio vega. We find that firms significantly reduce CEO portfolio vega following the passage of foreign leniency laws. Further analyses reveal that the observed reduction in risk-taking incentives is stronger for firms that are in more concentrated industries, have low investment opportunities, have fewer prospects for new competitive projects, and are in industries that had recent cartel investigations. We also show our results are unlikely to be driven by other dimensions of competition, managerial risk aversion, or CEO option exercising behaviors. Despite our efforts to isolate the effect of anti-cartel enforcement on vega, we acknowledge the challenge of untangling the individual impacts of these factors and establishing causal relationships due to their interconnected and often overlapping nature.

This study extends the literature exploring the link between managerial misbehaviors and CEO compensation structure and contributes to the growing literature exploring the determinants of CEO risk-incentive compensation. Our results are consistent with foreign leniency laws increasing firms’ downside risks, which discourages their boards from offering risk-taking equity incentives to managers. In this respect, our results imply a connection between anti-cartel enforcement and executive compensation design that may have broader ethical and policy implications. The evidence that foreign leniency laws affect compensation vega also contributes to the literature examining the economic consequences of the passage of foreign leniency laws. Finally, our study advances understanding of competition’s effects on executive pay by showing that anti-cartel enforcement exerts a unique and significant influence on vega.