*3.4. Econometric Modeling*

We test our hypotheses on the links between firm value and compliance with board best practice, with the use of the following econometric model:

*Q* = *f Compliance*, *FILASHASQ*, *INSTINSQ*, *INDUSTINSQ*, *CEOSHA*, *GOVSHA*, ln \_*ASSETS*, *ADJ*\_*ROA*, *DEBT*\_*ON*\_*ASSETS*

where *Compliance* is FORMALCOMPL, MINCOMPL, and SUBSTCOMPL.

We test the formulated hypotheses with the use of panel analysis (Cameron and Trivedi 2005, 2010). Constructing the econometric models, we address three main issues. Firstly, we consider the problem of heteroskedasticity with the parallel variability of random variables between units and time period, which requires the adoption of a method for estimating parameters robust enough for standard estimates errors. We acknowledge heteroskedasticity and calculate the values of robust errors with the use of a Wald test in all models. Secondly, we run a Hausman test to determine the type of the model to be constructed. For each model, the significance level equals zero, indicating a rejection of the null hypothesis and acceptance of the alternative hypothesis to choose the fixed effects model. Thus, we decide to run fixed effects for all A–C models, meaning that the individual effects which differentiate the reactions of the companies under analysis are represented by an intercept, which remains stable over time.

Considering the heteroskedasticity of the random variable we use a dedicated version of the Hausman test (rhausman test). Next, for A–C models, we employ an F-test to determine the statistical significance of the entire set of regressors. In each of the models, we reject the null hypothesis, suggesting that there is no variable that impacts the changes in the value of the regressand in the models. We also run the Shapiro–Wilk test, which assumes a normal distribution of the random variable. This hypothesis is rejected. Finally, to test for multicollinearity of regressors, we determine the variance inflation factor (VIF) for each regressor in a given model. A VIF below 2, as is revealed in the A–C models, eliminates multicollinearity. The VIF coefficients, overall and between, are close to zero, signifying that the A–C models only explain the time changes of Tobin's Q value. These tests support the supposition that the changes of each explanatory variable have a statistically significant impact on the value of explained variable.

The results of the tests and models under discussion are reported in Table 10.


**Table 10.** Estimation results for dependent ln\_Q.


**Table 10.** *Cont.*

Notes: The symbol of L1 by the regressor name indicates the variable value lagged by 1 year. The robust standard error for each coefficient in models A, B, and C is reported in parentheses; \*\*\* *p* < 0.01, \*\* *p* < 0.05, and \* *p* < 0.1, where the *p*-value is called the observed level of significance. The significance test for the coefficients is the *t*-statistics test. Models AS, BS, and CS are models estimated for standardized variables, with standard deviations for values of non-standardized variables presented in parentheses.

As shown in Table 10, for each A–C model, a given set of regressors differs only by one variable on compliance. We use a compliance variable lagged by 1 period (year) to examine the effect on the company market valuation after the publication of the conformity declaration and the information on compliance practice. The results indicate a negative correlation between compliance with board best practice and Tobin's Q. The negative association is noted for all three measures of compliance, i.e., formal compliance (FORMALCOMPL), minimum compliance (MINCOMPL), and substantive compliance (SUBSTCOMPL). This means that from the perspective of our hypotheses we find support for H1, which assumes a negative association between compliance with best practice code and firm value. We also find support for H2, as we observe a negative and statistically significant relation between the minimum level of compliance with code provisions and Q. Finally, for H3, our results reveal a negative relation between company value and SUBSTCOMPL, which measures the most substantive scope of compliance. Hence, we find support for H3, as well.

In addition, we tested A–C models for endogeneity. Based on prior studies, we identify ln\_ASSETS as the potential endogeneity driver and we proceed as follows. We estimate fixed-effect models with the same set of regressors, using two approaches: the least-squares method (LS) and instrumental variables method (IV). In the latter model, we use the lagged value of ln\_ASSETS as the instrument. We estimate both models for 2007–2015, in order to ensure full comparability. We use a Hausman test, comparing LS model (null hypothesis) with the IV model. The rejection of the null hypothesis would suggest selection of the IV model and would indicate that the ln\_ASSETS variable may cause endogeneity problems. We find no reason to reject the null hypothesis, which implies that we should choose the LS model and that we do not note endogeneity issues. For models A–C, we do not reject the null hypothesis, so fixed effect models estimated with the use of the least squared method offer the most appropriate approach. Thus, there is no need to adopt instrumental variables, and the variable of ln\_ASSETS does not cause an endogeneity problem. As a consequence, it follows that the use of other estimation methods is not appropriate.

We address the question concerning the changes in the values of regressors that have the strongest impact on changes in the regressand. For this purpose, we estimate the equivalents for the A–C models with standardized variables. The coefficients in models with standardized variables show how the regressand changes within its own standard deviation if the regressor values change by one standard deviation. Table 10 shows the values of standardized coefficients and values of standard deviation of regressors for models AS, BS, and CS in dedicated columns. Models estimated with standardized variables reveal that the signs of the regression parameters and the values of *t*-statistics of regression parameters do not change, so the statistical significance of the relations does not change

either. Other values of the statistical verification for our models remain stable, as well. The value of ln\_Q ranges between −2.303 and 2.251, with the standard deviation equal to 0.815. It shows that ln\_ASSETS and ADJ\_ROAs have the strongest impact on a change in the regressand value, followed by CEOSHA, FILASHA, and compliance. DEBT\_ON\_ASSETS reveals the lowest impact on the change of ln\_Q.

Finally, we run an additional BC model with the measure of decomposed substantive compliance (dec\_SUBSTCOMPL). We observe that, in the A–C models, the variable for independent directors is the main explanatory component, since WSE-listed companies do not report numerous aspects included in the substantive compliance measure (e.g., independent chair, the identification of independent directors, and the formation of a separate audit committee). Thus, in the BC model for decomposed substantive compliance (dec\_SUBSTCOMPL) we exclude the variable of INDNED from compliance. As presented in Table 10, for the BC model, the decomposed substantive compliance (dec\_SUBSTCOMPL) remains statistically insignificant, while INDNED is statistically significant. While this approach offers a deeper insight into compliance practice, it has two limitations: Firstly, dec\_UBSTCOMPL and INDNED are strongly correlated; secondly, neither are more strongly correlated with the variable ln\_Q than SUBSTCOMPL. This means that introducing two variables instead of one measure, being the sum of the two variables, may increase parameter estimation error and consequently render the regressors statistically insignificant. Importantly, the decomposition of SUBSTCOMPL into INDNED and dec\_UBSTCOMPL changed neither the signs of the estimated parameters of other regressors nor the statistical characteristics of the estimated models reported with the F test, Shapiro–Wilk test, and Hausman test.
