*3.2. Variables*

We operationalize our variables, following the research procedures adopted in prior studies. We employ Tobin's Q, defined as market value to book value, as our explained variable (Kim et al. 2015). Compliance with board best practice is our explanatory variable. Due to the essential role of corporate governance, we focus on compliance with recommendation on the supervisory board (Seidl et al. 2013; Huu Nguyen et al. 2020). Specifically, we include information on the presence of independent directors on the board, chairman status, the formation of an audit committee and other committees within the supervisory board, and publication of the compliance statement included in the annual report and its size (length). In order to test for the relationship between conformity to best practices and company value, we introduce three compliance variables: formal compliance (FORMALCOMPL), minimum compliance (MINCOMPL), and substantive compliance (SUBSTCOMPL). FORMALCOMPL is constructed as an arithmetic sum of compliance with the best practice on the presence of two independent directors and the formation of an audit committee and remuneration committee on the supervisory board. MINCOMPL is defined as the minimum level of compliance and is the arithmetic sum of compliance with the best practice on the presence of two independent directors and the formation of audit committee on the supervisory board. SUBSTCOMPL refers to substantive, pragmatic compliance and is the arithmetic sum of compliance with the best practice on the presence of two independent directors with the information of board directors who are independent, the presence of an independent board chairman, and the formation of a separate audit committee and remuneration committee on the supervisory board. SUBSTCOMPL is a measure which depicts compliance in substance, rather than its declarative character. Formally, the amendments of the Accounting Act imposed the obligation to form an audit committee within the supervisory board. According to the act, in the case of supervisory board with the minimum legal size of 5 directors, the whole board can function as the committee. We include additional variables which depict (1) whether a company reports the existence of an audit committee within the board, (2) whether the whole board performs the function of the audit committee, and (3) whether a separate committee within the board is formed.

Finally, we use control variables on ownership structure, company size, and financial performance. We operationalize the variables on ownership structure, following prior studies (Thomsen and Pedersen 2000; Krivogorsky and Burton 2012). Specifically, we use ownership variables on concentration (the largest shareholder), in addition to the shareholders' stakes by selected types (financial, foreign, CEO, and government), to control for the impact of ownership on firm value. In both cases, we measure the potential effect of ownership concentration and shareholder identity, using the variable of the size of the stake owned (Krivogorsky and Burton 2012; Florackis et al. 2015). Finally, we use standard control variables covering the company size (assets and debt) and performance (ROA). The list of variables used in the analysis is provided in Table 2.




**Table 2.** *Cont.*

Note: The value of return of assets (ROA) variable is the value of the return of assets measure of a company, adjusted by the year of observation and the sector it operates in (Vintila et al. 2014). This measure is calculated with the use of the median value of ROA for each sector and year, as follows: *ADJ ROAit* = *sign*(*ROAit* − *median ROASE*,*t*)· *ROAit* <sup>−</sup> *median ROASE*,*<sup>t</sup>* , *<sup>i</sup>* <sup>=</sup> 1, ... , 155; *<sup>t</sup>* <sup>=</sup> 2006, ... , 2015, where *<sup>i</sup>*—number of the company, *SE* ∈ {Industry, Services, Construction, Financial}.

#### *3.3. Descriptive Statistics*

We transform some variables (as shown in Table 2) into square root or natural logarithm measures for the purpose of constructing econometric models which allow for economic interpretation. Below we report the process of variables transformation, presenting natural values of our variables (Tables 3–8). Table 3 reveals the distribution of our explained variable, Tobin's Q.


**Table 3.** Distribution of Tobin's Q—number of companies and untransformed variables.

As reported in Table 3, the distributions of Q are one-modal, yet since 2008, they reveal strong positive asymmetry, which means that, over the analyzed period, there are more years characterized with a low value of Q than a high one. A more balanced distribution of Q is revealed in the first year of the analyzed period, while since 2008, we depict the effects of the financial crisis peaking in 2011. Due to the asymmetric distribution, we analyze the median value of Q, as shown in Table 4.


**Table 4.** Mean value of Tobin's Q by sector and year, and untransformed variables.

Table 4 reveals variations of Q in the specified sectors of operation. The maximum values of Q were noted in the initial years of the analyzed period, with a strong drop in 2008 and some recovery in 2010–2011, followed by a subsequent decline. The recovery of the median Q value in 2013 is mostly evident for industrial companies. Stagnation is observed for service and construction sectors until the end of the analyzed period. A similar trend is noted for companies operating in the financial sector, yet the values of Tobin's Q remain at the higher level. The differences between the median and arithmetic mean confirm the expectation of the positive asymmetry of Q.

Next, we investigate the variability of Tobin's Q over the analyzed period and across the years under consideration, using the standard deviation and average mean, as presented in Table 5.


**Table 5.** Variability of Tobin's Q, and untransformed variables.

The between variation coefficient, which measures the variability of Tobin's Q, has risen since 2009, suggesting the variability of adaptability and capability to survive amongst listed companies. The within variation coefficient is calculated as the quotient within standard deviation, which remains stable across time, and the arithmetic mean of Tobin's Q for the given years (Table 4).

We test the variables used in the econometric analysis, employing the Shapiro–Wilk normality test (null hypothesis assumes normal distribution of variable) and the Harris–Tzavalis stationarity test for a balanced panel (null hypothesis assumes the variable has unit root). Tests are run for the untransformed variables. The results are given in Table 6.


**Table 6.** Shapiro–Wilk normality test and Harris–Tzavalis stationarity test for variables, and untransformed variables.

None of variables have normal distribution and reveal a stationary distribution over the analyzed period at every level of significance. While the absence of a normal distribution of variables may constitute challenges for econometric modeling, the stationary distribution does not hinder further analysis. Thus, using the logarithm or square root of selected variables before employing them as regressand or regressors means recognizing the non-linearity in the analyzed link between Tobin's Q and selected company attributes. It does not serve as a solution to eliminating non-stationarity of variables. Table 7 presents descriptive statistics of variables used in econometric modeling.


**Table 7.** Descriptive statistics of variables, and untransformed variables.

As shown in Table 7, variables are characterized by asymmetry and kurtosis. Only the distributions of MINCOMPL, FILASHA, INDUSTINV, and ADJ\_ROA remain moderately asymmetric, while distributions of other variables are strongly asymmetric (FORMALCOMPL, SUBSTCOMPL, and INSTINV) or extremely asymmetric (Q, CEOSHA, GOVSHA, ASSETS, and DEBT\_ON\_ASSETS). The strong asymmetry present in the majority of variables may lead to lesser explanatory power of the estimated econometric models and may limit the ability to interpret kurtosis. In addition, the minimal value of Tobin's Q is zero, which was not transformed into a logarithm. However, a value of zero is present in only eight cases from 1550 observations, making it an acceptable number.

We analyze the distribution of compliance variables, specifically formal compliance, minimum compliance, and substantive compliance, as shown in Table 8.


**Table 8.** Distribution of compliance variables (formal, minimum, and substantive).

The data presented in Table 8 are indicative of a constant improvement in compliance by the sample companies in all the measured categories over the analyzed period. For each identified variable, the number of companies which do not comply with any code provisions drops significantly—from 133 or 134 firms in 2006 to 16–27 firms in 2015. Interestingly, the highest improvement is noted for the medium value of compliance—formal compliance between 1 and 3 increases from 21 companies in 2006 to 132 companies in 2015. The growth for the high value of compliance end is marginal—formal compliance between 4 and 8 is noted in 0 companies in 2006 and increases to 7 companies in 2015.

Using a Pearson linear correlation coefficient, we report the correlation coefficients of regressand and regressors in Table 9.


**Table 9.** Correlation coefficients of variables, regressand and regressors.

Table 9 presents the correlation matrix for both untransformed and transformed variables (with the use of logarithm and square root measures). In rows with two lines, the upper line represents the value of the untransformed variable, while the bottom line shows the value of transformed variables. The column "ln\_Q" presents the coefficient of linear correlation between regressand and regressors. The correlation matrix illustrates the strength and directions of the analyzed relations between variables, similar to linear correlation. It shows the relations in which the value of a given variable increases or decreases by a stable unit in line with the value change of another variable within a given time (year).

With the non-linear relations, the Pearson linear correlation coefficient may incorrectly suggest a magnitude which may be stronger than initially anticipated. The statistical test indicates that all correlation coefficients higher than 0.04 may be viewed as statistically different from zero. As reported in Table 8, changes in ln\_Q are correlated with ROA, assets, CEO ownership and ownership concentration. A weaker link is noted for compliance measures. With low correlation coefficients, we do not identify the multicollinearity problem.
