The SI-based performance equation includes the same control variables as the ROA-based equation with ROE instead of liquidity ratio. ROE is measured as net income weighted by book value of total assets. The ratio is corporate accounting-based performance measure. We assume that such accounting measure may influence market-based indicator through shareholders' perception of a company. The higher corporate efficiency the better positions on stock exchange a company can hold. Moreover, sales growth and financial leverage might also affect company reputation in the market. For example, positive sales growth enhances firm investment appeal. We also employ year dummy in order to take into account significant events occurred in a given year and that could potentially effect market sentiment. Formula 6 demonstrates SI-based performance equation. Thus, we have two different performance equations, which describe compensation influence on corporate results:

,(4)

, (5)

where: ;

- company number;

- CEO number;

- year.

Detailed description of the variables is presented in Appendix 1.

At the second stage, verification of Hypothesis 2 is suggested. As with the compensation equation, we will estimate both performance equation from Formulas 5 and 6 with the OLS method. Again, intending to consider effect of different remuneration types on different performance indicators we will run eight regressions.

The confirmation of Hypotheses 1 and 2 results in derivation of Hypotheses 3. Looking back, the last hypothesis states that treating both CEO compensation and firm performance as endogenous, executive pay for performance enhances company results. Since both variables in consideration are endogenously determined, estimators may be biased and inconsistent due to the correlation between variables and the regression residuals. So-called simultaneity problem occurs, which could be resolved by treating the compensation equation and the performance equation as a system of equations.

Thus, we evaluate compensation and performance equation jointly by implementing 2SLS method of regression analysis (Holthausen et al, 1995; Huang and Chen, 2010; Sheikh, 2013). The 2SLS method is an extensional OLS method that is used when regression residuals are correlated with independent variables. Thus, we will again run eight regressions with different performance and compensation measures.

Data for the current study has been collected by International Laboratory of Intangible-driven Economy (IDlab) in 2014-2016 with author's participation. The database includes information on approximately 1500 major European companies with market capitalization more than 170 thousand EUR and total asset size greater than 4 000 thousand EUR for the period from 2008 to 2013. The base includes companies from seven European countries: Great Britain, Germany, France, Switzerland, Italy, Spain and the Netherlands. In addition, these companies are belong to 19 industries according to NACE Rev.2 classification. The uniqueness of database is that it contains not only financial performance measures, but also information about CEOs.

An important step in preliminary data analysis is the analysis of descriptive statistics, which are presented in Table 1. After outlier exclusion and appropriate calculations, we have the sample of 330 companies for the 5-year-period from 2009 to 2013. We missed the year of 2008 because of the sales growth calculation. The number of observations is 1338.

Along with the presented descriptive statistics of studied variables, sample test for homogeneity was carried out through the variation coefficients calculation. In our sample, all variables are heterogeneous as the ratio of standard deviation to mean (coefficient of variation) is more that 30% for all parameters. Unfortunately, it is impossible to make the sample completely homogeneous through outlier removal due to insufficient volume of observations. However, we can normalize Total Assets that have high standard deviation by taking it in natural logarithm (Size). As the result, Size is homogeneous, since coefficient of variation is 25%, and nearly normally distributed having skewness and kurtosis that equal to 0.81 and 3.34, respectively. Furthermore, only one indicator is close to be normally distributed. This is Sharpe Index (SI) for which mean is approximate to median. This is a good sign since Sharpe Ratio works better when it is normally distributed.

Table 1 Variable descriptive statistics

According to the obtained statistics, in our sample, a CEO on average receives approximately 1.2 million EUR per year. The maximum CEO pay level has exceeded 7 million EUR, while the minimum level is close to 20 thousand EUR. A half of total compensation approximately consist of salary. The minimum values of zero for bonus and benefits suggests that some broads of directors did not charge their CEOs additional cash payment for some years. Due to the fact that all compensation measures are not normally distributed, the average value is closer to the minimum (median is closer to minimum) that can be explained by the prevalence of lower-paid CEOs in comparison with maximum.

With respect to positive average and median Sharpe Index, shares of considered companies are efficient on average. The highest value for SI is more than 2, while the lowest is less than -2. This is the only one value, which is close to the normal distribution, since the median is almost identical to the mean, and calculated skewness and kurtosis are 0.14 and 3.3, respectively. Concerning ROA, it varies in the range from -29% to 36%. Although mean and median are close having skewness that is 0.09, the distribution of ROA cannot be called normal as kurtosis is 7.8 that is larger than 3.

In the sample, variance of ROE is greater than of ROA as it changes from -62% to 193%. The average return on equity is 13.6%. On average, all cash and liquid assets of the company cover short-term liabilities once. It is surprising that the median is less than 1, that is, many companies do not cover their debts a bit. The average sales growth is 5% with the highest value of 122% and the lowest -100%. The average size of companies in the sample is about 7 million EUR.

As for non-financial data, CEOs that have been sampled worked for their companies approximately 10 years. The maximum is 47-year-experience in the firm. The oldest company has the age of 167 years and the youngest does not exceed 12 months. Generally, we deal with 40-year-old firms. Across selected companies 20% of CEO have an MBA degree.

After data collection and preliminary analysis as well as methodology determination, we can move to the regression construction and evaluation that will be realized in the following sections. For estimation purposes, we will use statistical package Eviews.

4. Empirical results

In the previous section, we have defined a set of variables that will be used for hypotheses verification as well as methods and data with the help of which an empirical analysis will be conducted. However, before including chosen indicators into regression models, it is necessary to carry out the correlation analysis, which, in turn, reveals two potential problems. First, a correlation matrix allows us to understand whether any association between dependent and independent variables exists. Second, when dealing with financial indicators the risk of multicollinearity occurs that is a high correlation between independent variables, which can considerably distorts regression estimates.

Table 2 presents correlation coefficients for the regression variables. Concerning the main endogenous variables, as anticipated, ROA is positively correlated with all compensation types from 7% for Benefits to 17% for Bonus, what can be confirmed by significant at 1%-level coefficients. The result suggests that in companies, which have higher assets efficiency, CEOs earn more. However, SI has positive correlation only with Bonus for only 6%, since correlation coefficients with other remuneration measures are insignificant.

Considering the compensation equation (Formula 4), we can conclude that multicollinearity problem is absent, since there is no high correlation between independent variables even between Size and performance measures. Moreover, almost all indicators included in the equation are significantly correlated with compensation components. In both performance equations (Formula 5 and 6) only Size and some compensation measures are relatively high correlated. In addition, most of independent variables in these equations are significantly correlated with performance variables. Since the correlation analysis cannot completely explain the relationship between CEO remuneration and corporate performance, we turn to regression analysis.

Table 2 Correlation matrix

Note: *Significant at 10%, **significant at 5%, ***significant at 1% level. We use Spearman rank-order correlation method for Tenure, MBA, Firm Age and ordinary correlation method for all other variables.

Firm performance influence on CEO pay

The first hypothesis states that in order to stimulate executives for better performance CEO compensation is designed to be performance-sensitive. In order to confirm the hypothesis, we have investigated the firm performance influence on CEO pay. The results from OLS estimation of the compensation equation (Formula 4) are presented in Table 3. We examine total compensation together with each remuneration component. In addition, we distinguish market- and accounting-based performance.

For the hypothesis verification purposes, we need paying attention to variable estimates of ROA and SI. On a large scale, firm performance, either market- or accounting-based, positively influences CEO compensation, what confirm Hypothesis 1. ROA is positive and significant for all compensation types. Among three remuneration components, it has the most effect on Bonus. We obtained the similar findings for SI with only one difference: it is insignificant as an explanatory variable for Salary (Spec. (3)). The result can be explained by the nature of base salary, which is generally fixed. Actually, firms do not link base salary to particular performance indicator. However, at the same time, the amount of CEO salary can grow with higher company profitability that may be caused by higher net income. In other words, if companies earn more, they can afford to charge their CEOs greater amount of salary. Thus, ROA may have particular influence on CEO pay, while Sharpe Index may not.

The positive influence of accounting-based performance measures on CEO compensation have been justified by Griner (1996), Huang and Chen (2010) and Cambini et al (2015). Whereas, the positive impact of market-based measure on annual bonus have been confirmed by Dee et al (2005) and Banker et al (2013).

The effect of Size is significant and carries an expected positive sign within the all specifications. The estimates for Tenure are statistically significant only for Total Pay and Benefits having U-shaped influence on it. MBA is positively and significantly related to Total Pay and Benefits. Firm Age has U-shaped and significant influence on Salary and Bonus.

Table 3 OLS parameter estimates on Compensation

Note: *Significant at 10%, **significant at 5%, ***significant at 1% level. The estimates are robust as each specification is corrected by White diagonal standard errors and covariance. Standard deviations are in parentheses.

Stated briefly, the results confirm Hypothesis 1 that CEO compensation is tied to firm performance. Specifically, compensation committees trying to stimulate executives for pursuing shareholders' goals link their remuneration to corporate results. The further question is how efficient this incentive instrument may be.

CEO pay influence on firm performance

The second hypothesis proposes that CEO compensation serves as an incentive and, as the result, enhances company performance. To test the hypothesis we have separately analyzed the influence of accounting- and market-based performance measures on CEO remuneration. Again, total pay along with each compensation component is individually examined.

The results of OLS estimation for ROA are presented in Table 4. The positive estimates of all compensation types confirm Hypothesis 2. Specifically, firms, where CEOs earn more, have better in-company results. Moreover, Salary has the most influence on ROA. It can be explained that companies with well-paid executives are more efficient. Huang and Chen (2010) have also found that CEO compensation is positively related to a corporate accounting measure.

Table 4 OLS parameter estimates on ROA

Note: *Significant at 10%, **significant at 5%, ***significant at 1% level. The estimates are robust as each specification is corrected by White diagonal standard errors and covariance. Standard deviations are in parentheses.

The estimates for control variables Liquidity Ratio and Sales Growth are positive and significant within the all specifications, while Leverage has negative influence on ROA, meaning that companies invest borrowed funds at the margin inefficiently. Moreover, estimated coefficients for Size are negative and significant in Spec. (1)-(3), suggesting that smaller companies can outperform larger in terms of return on assets.

Along with ROA, we have tried to verify Hypothesis 2 through understanding the influence of CEO pay on market efficiency. Table 5 reports the findings of OLS estimation of SI-based performance equation. Total Pay and Bonus are positive and significant, meaning that companies, which pay their CEOs more, have better market performance. However, the influence of Total Pay on SI seems to come from Bonus component, since other compensation types are insignificant. In addition, the significance level for Total Pay is less than for Bonus. Thus, we can confirm Hypothesis 2 only for such remuneration type as annual bonus. Nevertheless, Huang and Chen (2010) revealed that CEO compensation as well as its components is not related to corporate stock return. Our results may differ from prior findings due to the use of different market-based performance measures. We analyzed not just market return, but market efficiency. The performance measure Sharpe Index shows the stock return gained over risk-free rate per unit of total risk.

The coefficients for such control variables as ROE and Sales Growth are statistically significant with a positive sign, suggesting that superior internal corporate results may enhances market efficiency. The reason is that strong financial outcomes may improve company reputation in the market. Size is statistically significant only in Spec. (1)-(2) and (4) having a negative sign. Leverage is insignificant within the all specifications.

Table 5 OLS parameter estimates on Sharpe Index

Note: *Significant at 10%, **significant at 5%, ***significant at 1% level. The estimates are robust as each specification is corrected by White diagonal standard errors and covariance. Standard deviations are in parentheses.

Mutual influence of CEO pay and firm performance

The OLS estimation of the compensation and performance equations independently has resulted in conformation of Hypothesis 1 and Hypothesis 2, respectively. In particular, we found that CEO compensation is performance-sensitive and, at the same time, it can influence corporate results. Since both remuneration and corporate performance can be endogenous, the OLS estimates may be biased and inconsistent. Thus, we have estimated the compensation and performance equations simultaneously. As usual, we consider total pay and its components individually.

Table 6 The results with standard deviations are presented in Appendix 2 presents 2SLS regression results concerning relationship between CEO compensation and accounting-based company performance ROA. Considering compensation equations, the findings closely resemble those presented in Table 3 and obtained with OLS. Firstly, we get approximately the same estimates for control variables. The difference is that Firm Age has become significant in explanation of Benefits. Secondly, here we revealed that ROA is an insignificant indicator of Salary and Benefits. These results are consistent with some realities. For example, a compensation report of Siemens AG documents that base salary and benefits are non-performance-based components, while bonus is a variable component and depends on «an equal one-third weighting of target achievement of the target parameters return on capital employed, earnings per share and individual targets» (Siemens, 2015). Moreover, Banker et al (2013) also found that accounting measure return on equity has positive and significant influence on annual bonus.

Examining performance equations, the findings have changed from those in Table 4. First, as for control variables, in some specifications Size and Leverage is statistically insignificant. Second, here we get Salary as an insignificant factor of ROA. In this case, CEO salary being non-performance-based does not have impact on company efficiency, since it does not stimulate executives for better performance.

Table 6 2SLS parameter estimates on Compensation and ROA

Note: *Significant at 10%, **significant at 5%, ***significant at 1% level.

Nevertheless, on this stage we cannot make a conclusion about the third hypotheses confirmation, since we need to analyze the relationship between compensation and market-based performance. The findings of 2SLS regression estimation that examine the relationship are presented in Table 7 The results with standard deviations are presented in Appendix 3. Considering compensation equations, we again make a comparison with Table 3. There are some differences across control variables, but Tenure, Firm Age and Size are still significant factors of CEO compensation within the all specifications. In addition, now SI has positive and significant influence on all remuneration types. The results are, to a certain extent, surprising, since usually companies tie cash compensation to accounting measures and equity-based remuneration to market ones. Nevertheless, we got the similar results as Banker et al (2013).

Turning to SI-based performance equations, there is no stark contrast with OLS estimates from Table 5. As before, ROE and Sales Growth have statistically significant and positive impact on market efficiency SI. Here Size is almost an unimportant factor since insignificant within most specifications. The main finding is that none of all remuneration components as well as total compensation do not influence SI. The results coincide with that of Huang and Chen (2010).

To sum up, according to obtained results, Hypothesis 3 can be entirely confirmed when performance is measured by ROA and CEO compensation is determined as bonus or total cash compensation. Furthermore, the simultaneous estimation of compensation and SI-based performance equations provides support for Hypothesis 1.

Table 7 2SLS parameter estimates on Compensation and Sharpe Index

Note: *Significant at 10%, **significant at 5%, ***significant at 1% level. Standard deviations are in parentheses.

Conclusion

The ownership structure of contemporary corporations is such that the occurrence of agency relationship is actually inevitable. Since the capital of joint-stock company is assigned to a number of owners, as a rule, a third party agent is attracted for operational control over investors' assets. Transferring rights of investment and financial decisions from shareholders (principals) to executives (agents) can accomplished by the risk of the agency conflict, which is studied in the framework of the agency theory.

The interest conflict between a principal and an agent occurs when their goals and risk perceptions do not coincide. One of the ways to level the conflict in the relationship «principal-agent» is to design a reward system, that is, to pay for performance. However, it is not all as easy as it sounds. Subsequently, the following questions arise: how to evaluate executive performance and, as the result, how much remuneration to charge. What is more, it is necessary to assess the efficiency of chosen incentive contract. In other words, whether charged compensation aligns managers' and shareholders' interests. These questions have inspired many scholars to conduct an empirical analysis.

Indeed, the topic of the relationship between CEO compensation and firm performance have been hotly discussed in theoretical and practical studies for several decades. However, researchers still have not agreed on the existence and type of the relationship. The use of different performance and compensation measures, data and research methods has caused significant differentiation across empirical results. Moreover, previously scholars usually address the question of CEO compensation influence on firm performance or vice versa and do not examine the interrelation. In this case, the current paper have been focused on examination of the relationship between CEO compensation and firm performance. Stated differently, during the research we have tried to answer the following questions simultaneously: is CEO remuneration performance-sensitive and does this pay level influence corporate results.

In attempt to identify the potential results, the investigation may lead to, and what hypotheses it is necessary to put forward, we have provided the literature review on the topic. The consideration of three groups of papers reveals that the results may be completely different. The association can be positive, insignificant or even negative. One more implication is that performance can be measured through either accounting- or market-based indicators.

According to the literature review on the topic and agency theory, we have put forward three hypotheses. The first states that CEO remuneration is performance-sensitive. The second is that CEO compensation enhances company results. The last proposed that CEO compensation is tied to corporate results and influences firm performance simultaneously.

Since firm performance can be determined in various ways, we employed two measurements. The first is accounting-based that is defined as ROA, while the second is Sharpe Index that represents market-based performance. In addition, we considered total compensation, which is determined as the sum of salary, bonus and benefits, along with each remuneration component.

For the purpose of hypothesis verification, we have conducted an econometric analysis of the relationship between CEO remuneration and firm performance with the use of data on European companies for the period from 2009 to 2013. Consequently, we have come to mixed results.

The OLS estimation of the compensation equation revealed that Hypothesis 1 is completely confirmed when performance is determined as ROA. Thus, companies tie CEO pay to accounting-based measures. The findings is consistent with some prior papers (Griner, 1996; Huang and Chen, 2010, Cambini et al, 2015). As for market-based performance, Sharpe Index also influences all compensation types with the exception of salary. The positive impact of stock return have revealed by Dee et al (2005) and Banker et al (2013).

From the OLS regression analysis of the performance equation, it was found that Hypothesis 2 is entirely accepted when performance is measured through ROA. We can conclude that CEO compensation enhance company accounting-based results. Considering market-based performance, only total compensation and bonus influence Sharpe Index. Our findings are partially consistent with that of Huang and Chen (2010), who found that compensation influences only accounting-based measures.

Since at the previous stages we found that both compensation and performance could be endogenous, we estimated the system of equations in order to overcome possible simultaneity problem. The results show that we can completely accept Hypotheses 3 when compensation is determined as bonus and firm performance is defined as ROA. Therefore, companies tie bonus to accounting-based measures and this incentive pay enhance corporate internal performance. Moreover, we found that compensation linked to Sharpe Index does not improve company market performance.

The results obtained within the current paper are, to some extent, consistent with real practices. Indeed, usually compensation committees determine salary and benefits as non-performance-based components of remuneration and bonus as variable one. Moreover, most companies tie cash compensation to accounting-based performance indicators and equity compensation to market-based ones. The good example is Siemens AG. From the compensation report of the company we can found that annual bonus is designed to be a function of return on capital employed (ROCE), earning per share (EPS) and some individual targets, while stock-based compensation is tied to market performance compared to main competitors (Siemens, 2015). One more example is BASF SE, where ROA is a key determinant of executive directors' compensation (BASF, 2014).

However, as a rule, companies do not link cash compensation to market-based performance measures like our results show. Company market performance is accompanied with high risk, which is not subject to CEO's actions. Nevertheless, remuneration committees of some companies are aimed to motivate executives in such a manner that delivers substantial return to shareholders (Tullow Oil, 2014). Moreover, sometimes firms do not distinguish market- and accounting-based performance, therefore, charging compensation with respect to a set of measures.

To sum up, we can conclude that companies link variable compensation such as bonus to particular accounting-based indicators. In addition, company market-based performance can also influence firm performance. Furthermore, trying to evaluate efficiency of such incentive contract, we found that compensation tied to operational results is efficient since enhances accounting-based measures. At the same time, remuneration linked to stock indicators is inefficient in market performance.

Nevertheless, the current research paper has some strong restrictions associated with the model estimation as well as the data collection. The 2SLS estimation requires equations to be correctly identified. Certainly, we cannot be completely sure that our equations are correct, but we have tried to specify them as accurately as possible. What is more, most of our variables are not normally distributed that can lower the estimation quality. In addition, in this paper, we ...