Co-CEOs and Asymmetric Cost Behavior

This study investigates the effect of co-CEO structure on asymmetric cost behavior. A firm’s cost behavior reflects managers’ decision making about resources, which can be influenced by various factors. One of them relates to a manager’s decision to inefficiently reallocate their company’s resources when sales decline in pursuit of their incentives for empire-building and disincentives for downsizing. These inefficient resource allocations may result in asymmetric cost behavior, and ultimately be harmful to a firm’s sustainability. We consider the co-CEO structure as an alternative corporate governance mechanism that prevents managers from making inappropriate decisions. By doing so, we investigate whether the degree of cost stickiness differs between co-CEO and single-CEO structures, and whether the former complements external governance mechanisms, particularly foreign ownership, in mitigating cost stickiness. We analyze data from Korean listed companies for 2000–2013, and find that the cost stickiness is lower in the co-CEO structure than in the single-CEO structure. Thus, the co-CEO structure works as an alternative corporate governance mechanism to control the agency problem by inducing mutual monitoring among co-CEOs. Furthermore, the reduction in cost stickiness is greater for firms with higher foreign ownership, indicating that the co-CEO structure complements external governance mechanisms.


Introduction
Recently, General Motors (GM), a car manufacturing company, announced that it would lay off more than 14,000 workers in North America.GM mentioned that in competitive and rapidly changing market conditions, reduction in labor costs and more investment in research and Development (R&D) projects are necessary for long-term success.As such, decisions of cost structure are significantly important to corporate sustainability.
While there are many factors which affect the corporate decision of the cost structure, we focus on the co-CEO structure.In a co-CEO structure, two or more CEOs sit on corporations' top position and make corporate decisions together while corporate decisions are made by only one CEO in solo-CEO firms [1].There exists a dynamic exchange of lateral influence between multiple CEOs, which increases the likelihood of co-CEO firms' making different decisions than that of solo-CEO firms [2].There are many cases of the co-CEO structure.For example, Oracle appointed two nonfounder CEOs in 2014 after Larry Ellison, the founder of Oracle, stepped down as a CEO.Considering the co-CEO structure as a corporate governance mechanism that controls managers' pursuit of private interests, we investigate whether the cost behavior in a co-CEO structure differs from that in a single-CEO structure.
Cost stickiness or asymmetric cost behavior refers to a phenomenon whereby costs rise more rapidly when there is a rise in sales than they decline for an equivalent drop in sales [3].Previous studies have explained cost stickiness from various perspectives, including resource adjustment costs, managerial expectations, and resource levels in the previous period.Recent research has suggested that the agency problem-the managerial pursuit of private benefits at the expense of the firm-is one of the factors leading to cost stickiness [4].
The empire-building incentive, one of the representative incentives of management, refers to managers' tendency to grow the firm to a size that is greater than the optimal one [5,6], with the aim of increasing their private benefits.A larger firm size is beneficial for CEOs in various ways; greater monetary compensation, the additional perquisites [7,8], higher prestige and greater media coverage [9,10].Therefore, managers have incentives to grow the size of the firm and disincentives to downsize the firm.Even if the sales decrease, managers are unlikely to adjust resources in proportion to the decrease, such as employees and assets [4].This can lead to sticky cost behavior.Hence, strong corporate governance can mitigate managers' empire-building behavior and reduce the degree of cost stickiness [4].
In the unitary leadership structure, where the decision-making authority is concentrated in a single CEO, it may be difficult to control the proprietor's pursuit of private interests.It is important to distribute the concentrated authority among more than one executive [11,12].On the other hand, in a co-CEO structure, where two or more CEOs operate together, managerial power is not concentrated in a single CEO.Mutual monitoring by co-CEOs makes it difficult for a single CEO to make managerial decisions [13].In other words, a co-CEO structure can serve as an alternative governance mechanism to control the manager's pursuit of private interests.Therefore, our first question is: does the co-CEO structure reduce cost stickiness more than the single CEO structure?
In addition to the first research question, we examine whether the co-CEO structure complement or substitute other governance mechanisms.One, supporting the substitutive role of various governance mechanism, suggests that when an external governance mechanism does not work well for monitoring their agents' actions, firms can rely on a process of mutual monitoring among multiple executives [14].However, the possibility of collusion between multiple CEOs may make agency problems severe.A strong external governance mechanism may reduce the possibility of collusion and increase mutual monitoring, which leads the co-CEO structure in a way more beneficial to the firm.This is in line with the literature stating that the effectiveness of various control mechanisms is complementary [15].Hence, the impact of the co-CEO structure on the reduction of the cost stickiness may be more pronounced under the effective other external control system or under the ineffective other external control system.Thus, our second research question is: does the impact of co-CEOs on cost stickiness differ when considering foreign ownership as the external monitoring mechanism?
To address these questions, we use the extended model of Anderson et al. [3], and analyze financial and governance data for Korean listed companies during 2000-2013.Our results suggest that the degree of cost stickiness is reduced in the co-CEO structure.Moreover, the higher the foreign ownership, the greater the reduction in the degree of cost stickiness.These results provide strong support to our argument that the co-CEO structure works as a governance mechanism for mitigating potential agency problems and complements other corporate governance mechanisms.
This study contributes to the extant literature in several ways.First, we study the role of the co-CEO structure as a corporate governance mechanism using the concept of cost stickiness.Contrary to prior studies mainly focusing on the performance implication of co-CEO, we identify the co-CEO structure as a governance mechanism to reduce the influence of a solo dominating CEO.Second, we examine whether the co-CEO structure complements other corporate governance mechanisms.Previous studies have discussed whether the various governance mechanisms complement each other and whether the complementary effect differs for each governance mechanism.We further document that the reduction in the degree of cost stickiness is more in firms with high foreign ownership, suggesting that co-CEOs' mutual monitoring complements other governance mechanisms.
The remainder of the paper is organized as follows.Section 2 presents a review of the previous literature and develops the study hypotheses.Section 3 introduces the empirical model and measures used in the analyses.Section 4 reports the results and Section 5 concludes the study.

Cost Asymmetry and the Agency Problem
Cost stickiness refers to the phenomenon whereby the decrease in costs responding to a drop in sales is less than the increase in costs for a rise in sales.Following the seminal paper on sticky costs [3], numerous studies have explained cost stickiness from various perspectives.Previous studies conducted before Chen et al. [4] explain sticky cost behavior from an economic perspective.For example, it has been argued that costs are incurred because of managers' deliberate decision to adjust the resources committed to an activity [3].Changing the level of resources is costly because it entails adjustment costs, such as severance payments for dismissed employees or search and training costs for new hires.Despite the adjustment costs, managers are willing to increase resources when sales increase.However, they are also willing to retain unused resources when sales decrease because they consider the long-term adjustment costs or the intangible costs not measured in accounting.Managers' optimistic expectations regarding future sales also play a key role in sticky cost behavior.From this perspective, cost stickiness can be interpreted as a result of efficient decision making [3].
However, it has been argued that managers' personal, agency-related incentives can lead to sticky cost behavior [4].Managers' private incentive to empire building is one of the representative agency problems [5,6].They are motivated to maximize resources to increase the size of the firm because the larger the size of a company, the greater their benefits.First, monetary compensation increases with a firm size [7,8].There are also the nonmonetary benefits that managers can obtain.The large size of a firm implies that a large amount of resources can be controlled by the manager, which increases their prestige [6,16].The larger the company, the higher the company's exposure to the press; this increases executives' reputation [9,10].A superior reputation increases the probability of being hired by other firms, after their retirement from the company, as a manager, an outside director or a member of a government committee [17].In order to take advantages of these benefits, executives increase the size of the company through mergers and acquisitions that may harm firm value [18,19].
Overall, even if sales decrease, managers are less likely to reduce their resources, such as employees and assets, in order to increase their benefits, resulting in cost stickiness [4].Some studies find greater cost stickiness in companies that are subject to tax investigation or accounting enforcement actions than those that are not [20].Furthermore, research finds that the degree of sticky cost behavior increases in firms with embezzlement, implying that cost stickiness is closely associated with agency problem [21].In this context, cost stickiness derived from agency problem may be detrimental to firms' long-term value, and more, ultimately to their sustainability.

Co-CEO Structure and Cost Asymmetry
Following the studies that find the influence of agency problems on sticky cost behavior, recent research has investigated whether the mechanisms to mitigate the agency problems can reduce the extent of cost stickiness.Corporate governance refers to the system that monitors and controls executives to ensure that they work for the benefit of shareholders, rather than fulfill their private interests [22].Therefore, asymmetric cost behavior, resulting from agency problems, can be reduced under the effective control and monitoring system.Previous research on managerial incentives for building empires and unwillingness to downsize has also found that these incentives are weakened by an effective system of control.It has been found that firms with independent boards are more likely to engage in downsizing [23].Some studies suggest that overinvestment is reduced in firms with activist shareholders [24].More directly, it has been argued that cost stickiness partly reflects empire-building behavior and disincentive to downsize; further, the stickiness is mitigated by strong corporate governance [4].Furthermore, the presence of an audit committee significantly reduces the degree of cost stickiness [25].The above-mentioned evidence confirms the role of strong corporate governance mechanisms: it prevents managers from excessively increasing costs with a sales increase and encourages them to eliminate slack resources in response to a fall in sales.
In addition to boards and committees, shareholder structure, and regulatory provisions, we examine the co-CEO structure as another corporate governance mechanism.Specifically, this study examines whether the existence of co-CEOs reduces the magnitude of cost stickiness.
Previous studies mainly emphasize the performance implications of the co-CEO structure.They suggest, on one hand, that complementary skills and knowledge among multiple CEOs in a co-CEO structure enhance corporate performance, particularly when management issues are complex [26].On the other hand, they argue that coordination problems, such as role ambiguity and the corresponding weak accountability among co-CEOs, result in adverse firm performance [27].However, this study focuses more on the role of co-CEO structure as a corporate governance mechanism, contrary to prior studies.It is important to distribute the decision-making authority across two or more executives because the unitary leadership structure, wherein decision-making power is concentrated in a specific executive, is likely to cause serious agency problems [11,12].It has been argued that a co-CEO structure prevents the concentration of authority in a specific executive since mutual monitoring among multiple CEOs prevents certain executives from pursuing their own interests [13].This argument on the co-CEO structure is linked to that on the separation of CEO and board chairman.CEO duality (i.e., a structure where a CEO also sits on a seat of a board chairman) weakens the board of directors' supervisory role, leads to extreme concentration of power on executives, and results in severe agency problems.Thus, companies usually appoint outside directors to a chairman of the board to decentralize the decision-making authority and establish an effective governance structure for better monitoring.
Specifically, prior studies find that firms with co-CEOs exhibit better financial reporting quality than those with a solitary CEO [2]; co-CEOs lower audit risk and, thus, lead to a reduction in audit fee [27]; a phenomenon of more aggressive tax planning by younger CEOs is alleviated in firms with co-CEOs, since mutual monitoring prevents young CEOs from arbitrarily executing aggressive tax avoidance strategies [28].They all suggest that the mutual monitoring among multiple CEOs hinders a specific CEO from exerting his/her power for pursuing private benefit, and so work as a strong internal governance mechanism.Therefore, we also expect the degree of cost stickiness to be lower in firms with co-CEOs than in those with a solo-CEO, as mutual monitoring between co-CEOs reduces the agency problem.This discussion leads to the following hypothesis: H1.The degree of cost stickiness in firms with co-CEOs is lower than that in firms with solitary CEOs.

Monitoring Role of Co-CEO Structure and Cost Asymmetry
There are various monitoring mechanisms that affect business management, and these mechanisms may play a complementary or substitutive role each other.We further investigate whether the effects of the co-CEO structure on cost stickiness are more pronounced when other governance mechanisms are weak or strong.It would be desirable to encourage multiple agents to monitor each other if the external monitoring mechanism does not work well [14].In other words, if the board or regulatory clauses do not play a supervisory role on executives, companies can prevent specific agents from exerting managerial power for their own interests, through mutual monitoring among agents [14].The co-CEO structure has been identified as a mechanism to substitute external monitoring mechanisms.In a similar vein, it has been found that the lower the board independence, the higher the likelihood that co-CEOs will be elected [13].Therefore, the effect of co-CEOs in reducing the cost stickiness may become more apparent when the external monitoring mechanism is weak.
In contrast, the effectiveness of various monitoring mechanisms introduced in corporate governance can be complementary [15,29].Although a co-CEO structure can mitigate agency problems by mutual monitoring among agents, it may involve a slight risk of aggravating the agency problems because of the possible collusion between co-CEOs.If the other controlling mechanisms are strong, the possibility of collusion will be reduced, and mutual monitoring will be more active.Hence, it is also possible that the effect of co-CEOs in reducing the cost stickiness may be more pronounced under strong external monitoring mechanism.
We examine this issue, using foreign ownership ratio as the external monitoring mechanism.Foreign investors play a significant role as external supervisors in the corporate decision-making process of companies they invest in, and by doing so, they attempt to reduce the information asymmetry that exists between domestic and foreign investors [30].Consistent with this result, many previous studies have reported that foreign investors play a significant role as external monitors.Concerning the quality of financial reporting and the improvement of the corporate information environment, it has been found that the number of financial analysts increases, whereas the earnings forecast error and discretionary accruals decrease when foreign ownership increases [31].Moreover, it is expected that companies with foreign shareholding are subject to a more stringent audit because of information asymmetry [32]; similarly, such firms tend to appoint auditors from big audit firms, and the audit fee is high.Under the fair disclosure system that prohibits selective disclosures of material information to specific investors and requires companies to voluntarily disclose material information to all investors, firms with higher foreign ownership are found to provide more voluntary disclosure than firms with less foreign ownership [33].Previous studies also document that when foreign ownership is high, the entertainment expenses decreases [34] and investment efficiency increases [35].Credit rating agencies appreciate the external monitoring role of foreign investors, and so give favorable credit ratings to such firms [30].Overall, foreign investors perform well the external monitoring role.The above discussion leads to the following hypothesis: H2.The effect of co-CEOs in reducing the degree of cost stickiness differs according to the foreign ownership ratio.

Research Design
To examine the relationship between the existence of co-CEOs and asymmetric cost behavior, we first estimate the following regression model, which is based on the extended model by Anderson et al. [3].
where, for firm i and year t, ln(SG&A it /SG&A it−1 ) is the log-change in costs; ln(SALES it /SALES it−1 ) is the log-change in sales revenue; and D is a sales drop dummy that takes the value of one when sales revenue in year t are less than those in year t − 1, and zero otherwise.Coefficient β 1 measures the percentage increase in selling, general and administrative (hereafter, SG&A) costs for a 1 percent increase in sales revenue, and measures the relative importance of variable costs.Coefficient β 2 represents the incremental effect when sales decrease.In general, the costs increase when sales revenue increases, and thus, β 1 is expected to have a positive value.Because the value of D is one when sales revenue decreases, the sum of the coefficient (β 1 + β 2 ) measures the percentage decrease in costs for a 1 percent decrease in sales revenue.β 2 measures the degree of asymmetry in cost behavior.
A significantly positive coefficient β 1 and negative coefficient β 2 indicate that costs fall less after a demand decrease than they rise after an equivalent demand increase.Our main independent variable, COCEO, is a dummy variable that takes the value of one if a firm has multiple CEOs, and zero otherwise.
If the co-CEO structure reduces the degree of cost stickiness, the coefficient on the interaction term β 3 is expected to have a significant positive value.
We include several control variables that have been used in the previous literature [3,4].SUCCESSIVED and GDPGRW are signals of managerial expectations regarding future sales.SUCCESSIVED is an indicator variable that takes the value of one if sales revenue in year t − 1 is less than that in year t − 2, and zero otherwise.GDPGRW is the GDP growth rate.Managers who experience a decline in sales revenues expect lower future resource requirement.When the current sales revenue decreases, pessimistic managers are likely to adjust slack resources and reduce costs.Conversely, the higher the economic growth rate, the more likely that managers have an optimistic view of future sales.Optimistic managers expect a higher level of future resource requirement, and, thus, they tend to delay resource adjustments and retain unused resources when current sales decrease.AINT represents asset intensity, which is calculated as the log-ratio of total assets to sales; EINT stands for employee intensity, computed as the log-ratio of the number of employees to sales.These variables reflect adjustment costs associated with adjusting resources.According to previous studies, the higher the asset intensity and employee intensity, the lower the adjustment cost and expected resource adjustment.Finally, a year dummy, ΣYEAR, is included to control the year effect.
Following Chen et al. [4], we applied the mean-centering method to the continuous variables used in the interaction terms before they were included in the analysis, to control multicollinearity.Thereafter, we performed firm clustering to calculate the t-value.To examine whether the effects of co-CEOs differ depending on the external monitoring mechanisms, we divided the sample into two groups based on the median value of foreign ownership (FOREIGN) and analyzed Equation (1) for each group.If the co-CEO structure is complementary to the external monitoring mechanisms, the coefficient β 3 will be significant in the group with high foreign ownership, or its value will be higher.However, if the co-CEOs structure is a substitute for the external monitoring mechanism, β 3 will be significant only in the group with low foreign ownership, or its value will be higher.

Sample Selection
This study conducted an empirical analysis using data for listed companies in the Korean stock exchange market from 2000 to 2013.Data were collected as follows.We extract our main explanatory variable, the number of CEOs per firm, from the Total Solution (TS) 2000 database, which is provided by the Korea Listed Companies Association.We obtained financial data and foreign ownership information from the FnGuide, one of the largest providers of financial information about Korean firms.The sample selection process was performed according to the following general criteria.First, we exclude financial companies from the analysis.Financial companies have different institutional background and business structure with that of nonfinancial companies.In financial companies, resource adjustment for responding to the sales change is not the main business issue.Hence, we limit our sample to nonfinancial companies, following prior literature.We include only companies with December fiscal year-end to ensure the comparability of accounting standards.Firms with negative total assets and capital were not included in the sample because they are regarded as firms that find it difficult to perform normal business activities.In addition, we limit our sample to firm-year observations with revenue less than SG&A expenses, following prior literature of cost stickiness [4].We also eliminate observations with missing variables used in the regression model.Finally, all variables are truncated at the top and bottom 1% of their distribution to control the effect of outliers, following prior studies [4].The final sample consists of 7148 firm-year observations.In Tables 1 and 2 present the sample selection procedure and sample composition by industry, respectively.

Main Regression Analysis
The descriptive statistics are presented in Table 3.The average COCEO is 0.39, which indicates that 39% of sample firms have multiple CEOs.Meanwhile, the average and median number of CEOs are 1.48 and 1, respectively.The SG&A cost to sales ratio is, on average, 15%, which implies that SG&A cost is an important cost item.This finding is similar to previous studies on listed companies in the Korean securities market.In the total sample, 32% of the firms experienced a decrease in sales for the current period, which implies that sales increase more than they decrease for the overall sample.Next, we examine the relationship between the co-CEO structure and other monitoring mechanisms.The average foreign ownership is 0.1, which implies that the foreign ownership of the sample is, on average, 10%.This table presents the descriptive statistics for the testing sample.Sales Revenue and SG&A costs are total sales revenue and SG&A expenses reported in the FnGuide database.Variable definitions are as follows: COCEO is a dummy variable, which takes the value of one if a firm has multiple CEOs, and zero otherwise; #CEO is the number of CEOs; ln(SG&A it /SG&A it−1 ) is the log-change in costs; ln(SALES it /SALES it−1 ) is the log-change in sales revenue; D is a sales drop dummy that takes the value of one when sales revenue in year t are less than those in year t − 1, and zero otherwise.SUCCESSIVED is an indicator variable that takes the value of one if sales revenues in year t − 1 are less than those in year t − 2, and zero otherwise and GDPGRW is the GDP growth rate.AINT is asset intensity, calculated as the log ratio-of total asset to sales; EINT is employee intensity, computed as the log-ratio of number of employees to sales; FOREIGN is the share of foreign ownership.
Table 4 provides the Pearson correlation between our main variables.First, the change in SG&A costs (ln(SG&A it /SG&A it−1 )) and the change in sales (ln(SALES it /SALES it−1 )) are significantly positive at the 10% level.These two variables have a positive correlation with co-CEO structure (COCEO).However, this is the result before controlling the effect of other variables on the cost behavior of SG&A expenses.Thus, it needs to be verified by regression analysis using Equation (1).Table 5 presents the results of Hypothesis 1 and reports the difference in cost behavior between companies with co-CEO and single-CEO structures, respectively.Model 1 is the basic model to confirm the cost asymmetry, which is the result of not controlling other major variables that affect the changes in SG&A costs.The estimated value of β 1 is 0.502 (t = 26.38)and that of β 2 is −0.134 (t = −4.62).This confirms that SG&A costs are sticky, a result consistent with that in previous literature.Model 2 is tested by controlling the key variables that affect asymmetric cost behavior.The coefficients on the economic variable interaction terms are consistent with those in previous studies.The coefficient on SUCCESSIVED is positive but not statistically significant.The significantly negative coefficient on GDPGRW suggests that the higher the economic growth rate, the more likely it is that the manager is optimistic about the future performance, despite the sales drop in the current period.They tend to retain slack resources, rather than dispose of them.We find a significantly negative coefficient on AINT, which implies that the more the assets, the higher the adjustment costs, and the more the mangers' willingness to retain unused resources.The coefficient on EINT is not significant.3. 2) To control for multicollinearity, continuous variables used in the interaction terms are demeaned.
3) The t-values presented in parentheses are values adjusted using firm clustering to control the heteroskedasticity of residuals.On the other hand, observations with Student's t residuals greater than 2 are excluded to eliminate outliers.4) "*", "**" and "***" denote significance at 1%, 5%, and 10% levels, respectively, in two-tailed tests.
Model 3 shows the results of Hypothesis 1 about firms with a co-CEO structure having lower cost stickiness than those with a single-CEO structure.We find that the coefficient on the interaction term β 3 is 0.116 (t = 3.26) and significant at the 1% level; this suggests that the degree of cost stickiness is lower in firms with co-CEOs.This result implies that co-CEOs mitigate the agency problem by preventing managers from arbitrarily making decisions that serve their own interests, because decision-making authority in a co-CEO structure is equally distributed among multiple CEOs.Therefore, we can conclude that the co-CEO structure serves as a governance mechanism to mitigate agency problems inherent in firms with a dominating solitary CEO.Additionally, Model 5 presents the result of substituting the number of CEOs (#CEO) for the dummy variable, indicating whether the firm is with co-CEOs or not.In this case, the coefficient on interaction term β 3 is 0.076 (t = 2.90) and significant at the 1% level.
To test Hypothesis 2, we partition our sample into two subsamples-representing strong and weak monitoring-by using the median value of foreign ownership as the criterion for division.Table 6 presents the results for our subsample tests based on foreign ownership (FOREIGN) as the other monitoring mechanism.We find that the effect of co-CEOs on sticky cost behavior is only significant in the subsample where foreign ownership is more than the median value.Specifically, the coefficient on the COCEO interaction term is significantly positive at the 1% level (coefficient = 0.168, t-value = 3.87).However, the coefficient is not statistically significant in the subsample with low foreign ownership.Our empirical results provide evidence that the complementarity of co-CEO structure with other monitoring mechanisms may be important in mitigating cost stickiness.While many are of the view that foreign investors serve as a monitoring mechanism to improve long-term value of firms, others point to the short-term investment behavior of foreign investors.Yang examines the effect of foreign ownership on the cost and the dividend behavior [36].He finds that the higher the share of foreign ownership, the lower the degree of cost stickiness.He suggests that when corporate sales decline, foreign investors shrink resource investment, and maintain or expand the dividends [35].Therefore, it is necessary to conduct research that considers different types of environment to improve our understanding of the role of foreign shareholders.

Robustness Test
The analysis so far shows that there is a difference in cost behavior between firms with and without co-CEO structure.This suggests that the co-CEO structure has a significant influence on the adjustment of corporate resources.However, if firm characteristics derive the adoption of co-CEO structure, our empirical results may be attributed to factors to adopt co-CEO rather than the structure itself.Unless the adoption of co-CEO structure is not random, our empirical results are not free from potential endogeneity problems.To address this issue, we employ the propensity score matching (PSM) approach and conduct robustness tests.
Specifically, we need to ensure that the samples of single-CEO and co-CEOs have similar characteristics.To do this, we calculate the propensity of co-CEO adoption for the entire sample using the following logit model [13].We then form matched pairs of a co-CEO firm and a single-CEO firm with the smallest propensity-score difference within a distance of 1%.Our final sample includes 3478 observations.
where, for firm i and year t, MV is the natural logarithm of the market value; LEV is the leverage, calculated by dividing total liabilities with total assets; #SEG is the natural logarithm of the number of business segments; HHI is the industry Herfindahl-Hirschman index, calculated as the sum of the squared market share of all the firms in the two-digit Korean SIC industry; FCF represents the free cash flow, defined as the operating income before depreciation minus taxes, interest expenses, and dividends, scaled by lagged total assets; LARGE is the largest shareholders' holdings; OUTDIR represents board independence, calculated as the number of outside directors divided by the total number of board members; BSIZE is the natural logarithm of the number of total board members, which is the sum of outside directors and inside directors; and CHAEBOL takes the value of one if a firm belongs to the top 30 business groups in Korea, and zero otherwise.Table 7 presents the robustness test results of the matched sample.Column 1 of Table 7 shows the result of verifying Hypothesis 1 for the entire sample, and Columns 2 and 3 present the results of verifying Hypothesis 2 for the subsample with foreign ownership ratio.First in Columns 1, we find that the coefficient on the COCEO interaction term β 3 is significantly positive at the 1% level (coefficient = 0.117, t-value = 2.63), suggesting that cost stickiness is alleviated under a co-CEO structure.Next, in columns 2 and 3, the coefficient on β 3 has a statistically significant value only in firms with high foreign ownership.These indicate that reducing the cost stickiness in firms with co-CEOs cannot be attributed to the bias in selecting the co-CEO structure.We also perform a fixed-effect model and a random-effect model for robustness check, but the results remain unchanged.We do not present the tables for the sake of brevity.

Discussion and Conclusions
This study investigated the effect of the co-CEO structure on asymmetric cost behavior.Previous studies have argued that agency problems result in sticky cost behavior [4].Managers have a tendency to grow the firm to a size that is greater than the optimal one since they benefit from the large size of the firm: greater monetary compensation and perquisites, greater reputation and higher visibility to the public.Due to their empire-building incentives and disincentives to downsize, CEOs are less likely to reduce resources for a given sales drop, which results in asymmetric cost behavior.Therefore, prior literature has examined whether the governance mechanism to monitor and control CEOs reduces the degree of asymmetric cost behavior.In this paper, we introduce the co-CEO structure as another tool to control managers' pursuit of private interests.
In the co-CEO structure, two or more CEOs manage the firm together.Thus, decision-making power is not concentrated in a specific CEO, and multiple CEOs share responsibilities for management decisions while the decision-making authority is concentrated in one CEO in the non co-CEO structure; in the unitary leadership structure [1].The mutual monitoring among multiple CEOs hinders a specific CEO from exerting his/her power for pursuing private benefit, and so work as a strong internal governance mechanism [13].Hence, we examine whether co-CEOs reduce the degree of cost stickiness and whether the co-CEO structure complements other governance mechanisms.Using foreign ownership as a proxy for other governance mechanisms, we examine the effect of the co-CEO structure on the degree of asymmetric cost behavior.
Using data for Korean listed companies from 2000 to 2013, we find that the degree of cost stickiness is reduced in a co-CEO structure but not in a single-CEO structure.Given that the sticky cost behavior is caused by CEOs' empire-building incentive for their private benefits such as higher prestige and greater exposure to the press, our empirical findings suggest that the co-CEO structure indeed works as an internal governance mechanism and mitigate CEOs' private incentive of stacking corporate resources, and therefore leads corporate cost structure in a way to improve corporate sustainability.We also find that the reduction is more pronounced if the foreign ownership is higher, suggesting that the co-CEO structure complements other corporate governance mechanisms.
This study contributes to the literature, showing that the co-CEO structure works as an alternative internal corporate governance tool for mitigating the agency problem related to sticky cost behavior.Over the past decade, business operations have been more complex and the business environment has rapidly changed.Since this circumstance increases the information asymmetry between managers and shareholders, shareholders become to face more difficulties to monitor CEOs' rent-seeking behavior solely with the traditional governance mechanism such as a board of directors.Accordingly, the necessity of an alternative internal monitoring mechanism increases.In this sense, this paper provides implication to practice, suggesting that appointing more than one CEO brings an additional governance mechanism suitable in this era.
However, the results of our study should be interpreted with the following caveats.First, we assume the cost stickiness is caused by agency problems on the basis of previous research's argument [4].However, prior studies also suggest that economic factors, such as resource adjustment costs, lead to cost stickiness.In order to address these issues, we have controlled for known economic determinants in the extant literature; however, the fundamental questions on how to interpret sticky cost behavior may still remain.Second, we assume that all co-CEOs have the same level of authority in the firm with consideration of difficulty in identifying and measuring the magnitude of difference in power among CEOs.Even if co-CEOs share the top title at their firm, there is no guarantee that actual decision-making power will be distributed evenly among them [37].

Table 2 .
Sample Composition by Industry.

Table 5 .
The relationship between co-CEO structure and cost stickiness.

Table 6 .
The relationship between co-CEO structure and cost stickiness: effect of foreign investors.Variables are defined in Table3.2) To control multicollinearity, continuous variables used in the interaction terms are demeaned.3) The t-values presented in parentheses are values adjusted using firm clustering to control the heteroskedasticity of residuals.On the other hand, observations with Student's t residuals greater than 2 are excluded to eliminate outliers.4) "*" "**" and "***" denote significance at 1%, 5%, and 10%, respectively, in two-tailed tests.

Table 7 .
The relationship between co-CEO structure and cost stickiness using propensity score matched sample.

Table 3
. 2) To control for multicollinearity, continuous variables used in the interaction terms are demeaned.3) The t-values presented in parentheses are values adjusted using firm clustering to control the heteroskedasticity of residuals.On the other hand, observations with Student's t residuals greater than 2 are excluded to eliminate outliers.4) "*', '**', '***' denote significance at levels 0.1, 0.05, and 0.01, respectively, in two-tailed tests.