R OBUSTNESS OF OUR RESULTS

We will now discuss the adjustments we have done in our research due to robustness concerns, and why we might have some issues regarding endogeneity. The results of the various tests performed in this section also explain alterations done to the model in the previous section (Section 6.2). The tests are based on the Gauss-Markov assumptions described in Appendix A3.

6.3.1 Linearity

To check for linearity, we created a scatter plot (Appendix A2) of total CEO pay and total Assets.

From the plots, we see that most of the data is placed in the bottom left corner, indicating that a log-transformation might be necessary. This also makes intuitive sense as linear-scale regressions inform on absolute changes while log-scale present the relative changes. When

discussing monetary sizes like compensation and assets, it is more expedient to talk about percentage changes and not absolute changes, as the firm sizes vary a lot in the dataset. By log transforming both Assets and CEO pay we get a much better scatter plot (Appendix A2). The summary statistics and scatterplots indicate that we should use the log of CEO pay in our analysis.

The current model shows the changes in CEO pay as a constant percentage of the independent variables instead of providing an absolute number, which is more comparable across firms regarding firm size and other firm characteristics. The model is generically written as:

𝑙𝑛 (𝑦) =𝛽_𝑜+ 𝛽₁𝑥₁+ 𝛽₂𝑥₂+. . . + 𝛽_𝑘𝑥_𝑘+ 𝑢

6.3.2 Multicollinearity

Table 14 in the appendix shows a correlation between the different variables in our models studying differences in total pay. Correlations in the two first columns are not an issue, as CEO pay in 2018 and 2017 is our dependent variables. Unsurprisingly, CEO duality correlates with ownership percentage, and the dummy for non-owner is negatively correlated with ownership percentage. Board size correlates with most of the variables, and so does non-owner. However, the correlations are not very strong, and checking VIF values confirms that multicollinearity should not be a problem in these models.

Moving on to the variables used for explaining the difference in pay sensitivity (Table 15 & 16 in the appendix), the liquidity variables between the years are very correlated. At first sight, this is an indication that liquidity is relatively constant from year to year. Though, the other performance variables are not nearly as correlated with each other. The problems of multicollinearity are confirmed when looking at the VIF-values for our models on sensitivity.

However, the issue does not appear in the actual analysis, because very large values that inflates correlation are removed as outliers. Thus, we do not have problems regarding multicollinearity in our analysis.

6.3.3 Heteroskedasticity

In order to ensure that our estimated coefficients are valid, we tested the data for heteroskedasticity. We used the White test and the Breusch-Pagan (BP) test, which both test the null hypothesis that homoskedasticity is present. The White test show little evidence of heteroskedasticity, but the BP test describes another picture. The BP test shows a clear rejection

of the null hypothesis in every model except the model with 2018 pay, indicating that heteroskedasticity is present in the other models.

When using STATA, we can correct for heteroskedasticity by using the robust command. Now STATA will produce robust standard errors, t-tests, and confidence intervals in order to make our inference valid. The effects of using heteroskedasticity robust regressions are slim. The biggest change is regarding EBIT, which goes from being significant at a 10 percent level to the 5 percent level (Table 10, Model 1). Moreover, we see a small change in the t-statistics of liquidity and board size, but these changes are so small that it does not affect our discussion.

Since the use of robust show little changes, we are not worried that our analyses are invalid, but we used the robust command in relevant cases to ensure that our test statistics are not biased.

6.3.4 Endogeneity

Problems with endogeneity occur when the error term correlates with an explanatory variable.

CEO tenure can be an example, as tenure possibly correlates with both pay and age. Endogeneity problems lead to biased OLS estimates, and problems of endogeneity should therefore be addressed (Wooldridge, 2013, p. 87). Another concern is the reason why some companies have owner CEOs and others not. To be an owner could be an endogenous choice, and there may be several things that the error term picks up that correlates with both the non-owner variable and our dependent variable. For example, if the firm is a family business, the CEO is more likely to be an owner. A family business may also be smaller than a large corporation. Thus, being a family business may be correlated to assets, the CEO being an owner, and CEO compensation.

These are all cases of unobserved heterogeneity.

Wintoki, Linck & Netter (2008) portray two other types of endogeneity. Simultaneity happens when the explanatory variables are a function of the outcome variable. In our case, this might be an issue if CEO pay is important in describing firm performance. This can generate a bias in the estimates on how performance affects pay. Wintoki et al. (2008) also argue that there is a third and frequently overlooked source of endogeneity. The performance today might affect future board structures and governance choices, which in turn will affect firm performance in the future. A similar example can be used when thinking about ownership structures. The ownership structure today affects future ownership decisions, which will affect future performance. A problem can thus arise if ownership structure, or the fact that the CEO is an owner, both affect pay and performance.

6.3.5 Dealing with outliers in the models of pay-sensitivity

The summary statistics in Table 7 indicate that there are some outliers in our variables on performance. A commonly used limit for outliers is three times the standard deviation from the mean. This suggests an upper limit between approximately 95 and 100 for ROA, based on the mean and standard deviation for all years. Therefore, we went for an upper outlier limit of 100.

A lower limit of -82 was set using the same logic.

The rule of thumb of three times the standard deviation from the mean is a bit trickier with growth in EBIT and liquidity. The reason is that the standard deviation and mean vary a lot between the years, while ROA is more consistent. Therefore, a visualization of the variables was necessary to look for outliers. After we removed the upper observation of liquidity from 2016, an observation as high as 4711, we see the following distribution of observations (Figure 5):

Figure 5 – Distribution of liquidity 2016

Liquidity above 50 seems like outliers. The same pattern is visible, looking at liquidity for 2017 and 2015. Therefore, we decided to remove liquidity observations above 50 for all the relevant years. Removing these outliers solved the problems of multicollinearity that we discussed earlier. There are no negative liquidity numbers, and we do not need to worry about negative outliers. A histogram of EBIT shows more or less the same as liquidity (Figure 6). The 2015 and 2017 numbers also gave us an indication of negative and positive outliers below -50 and over 50 as well. Therefore, the decision regarding EBIT was to remove observations above 50 and below -50. Regression results did change when we removed the largest (smallest) outliers, but further reduction below 50 did not change the results much.

0.02.04.06.08.1Density

0 50 100 150 200

Liquidity16

Figure 6 – Distribution of growth in EBIT 2016

6.3.6 Limitations in our analysis

Evidence in favor of Hypothesis 1 is present in both the descriptive statistics and the regressions.

Though, one shortcoming of the model is that we are missing data on some of the CEO characteristics. These characteristics include education, tenure, skill level, and so on. For example, how long a CEO has worked in the company and been in the position as the top executive may reflect his level of pay. Regarding the variables on female CEOs and female chairmen, the numbers of observations are quite low. The validity of the estimates is affected by this, and we cannot confidently conclude on the gender effects.

The analysis of pay-sensitivity shows inconsistent results. This is apparent because different measures show inconsistent correlation with the change in CEO pay, but also because the firms might use other performance measures when monitoring CEO performance. One possible issue is a change of CEO during the period we examined. This could lead to further inaccuracies regarding the change in pay, especially when looking at the change in compensation from 2016 to 2017. The further away from today we examine pay sensitivity, the more likely it is that a change of the top executive has occurred. We have also discussed possible endogeneity problems in Section 6.3.4. Besides, the models examining pay-sensitivity show low adjusted R-squares, indicating that the models do not explain much of the changes in pay.