Panel Data Analysis

This study employed panel data methodology to examine the direct and indirect relationships between corporate governance mechanisms and firm value, and the indirect relationships between corporate governance mechanisms and firm value mediated by earnings attributes.

Longitudinal data or panel data refers to data on the same subjects observed over several years. Greene (2008) noted that some issues could be studied purely by cross sectional or time series data; firms’ reporting quality, particularly the quality of reported earnings can be better captured if firms are examined for longer period. This study examined a sample of 100 public firms listed on Bursa Malaysia stock exchange over six years.

Panel data suggest that the subjects under study are heterogeneous. It means that although some variables vary across subject and time, there are many other variables that may be subject-invariant or time-invariant. Subject-invariant refers to factors that influence all subjects but varies across time. Time-invariant refers to factors that are time constants as they are unique to the subjects. It is important to include these type of variables (subject or/and time-invariant) in the model equation; otherwise it would lead to bias in the resulting estimates. The panel data methodology provides a solution to control these invariant factors that are not controlled for either in cross sectional or time series studies. Moreover, a further motivation for using panel data is to solve the omitted variables problems (Wooldridge 2002).

Panel data provide a richer source of information as it accounts for multiple observations on cross sectional units. Thus, it offers more variability and is more efficient in the estimation of parameters. The informative data also provide more reliable estimates and tests a more sophisticated behavioural model with less restrictive assumptions.

For pure time series data, multicollinearity problem appears among the independent variable (X); where the current period independent variables (Xt) are highly correlated

with those of the previous period (Xt-1). Hence, for panel data, differences in the X across

cross sectional unit can be used to reduce the collinearity. This is due to the fact that the pooling of cross sectional and time series data increases variability that can be decomposed into variation between subjects and variation within subjects.

99

Individual heterogeneity is controlled in panel data. The panel data model resolves or reduces the problem of omitted variables, due to mismeasurement or no observed items that correlate with the included independent variables in the model.

Panel data allow the researcher to study the complex issues of dynamic behaviour because it can identify and estimate effects that are simply not detectable in either pure cross section or time series data. Panel data enable the researcher to identify an otherwise unidentified model which under usual circumstances may be undetectable due to measurement errors.

The simple OLS regression assumes that the sample firms were homogeneous, thus do not account for heterogeneity unlike in the panel regression technique. Jager (2008) investigated whether panel data, analysed using a simple OLS regression technique would produce a different result than if analysed using panel data techniques. The results generated from the two techniques are substantially different; implying that adopting OLS technique on panel data leads to incorrect inference.

Panel data observations cannot be assumed as independently distributed across time due to individual unique factors that remained constant over time (Baddeley & Barrowclough 2009; Wooldridge 2002). Therefore, a simple regression (also known as pooled OLS) applied in pure cross-sectional or time series analysis, which assumes homogeneity, if estimated on panel data may lead to misleading inference (Baddeley & Barrowclough 2009). In simple pooling on panel data no adjustment is made for firm specific factors, resulting in autocorrelation, because for each year under study, the firm unique factor was left in the residual. Additionally, it also results in heterogeneity bias in terms of omitted variables bias because the firm unique factor is not included in the deterministic part of the model (Baddeley & Barrowclough 2009).

Panel data regression models control the heterogeneity effect in panel data by using either a fixed effects model or random effects model. The main difference between the two methods is whether the unobserved effects (the error term) are correlated with included independent variables (Wooldridge 2002).

100

Fixed Effects Model

Each entity has its own individual attributes, which are constant across time that may or may not affect the dependent variables. Fixed effects, which investigate the relationship between dependent and independent variables within an entity, control for these unobserved unique attributes (the time-invariant factor) within the entity may affect or bias against the dependent variables. Following the assumptions underlying the use of a fixed effects method that the error term is correlated with the independent variables; this method removes the effect of unobserved time-invariant characteristics from the independent variables so that the net effect of the independent variables is assessable. Therefore, the fixed effects method is unbiased as it controls for unobserved time- invariant factors but it may be inefficient if the correlation that it assumes is really zero (Allison 2009).

The fixed effects method can be implemented either by dummy variables or through the mean deviation method. A dummy variable is implemented by creating a set of dummy variables for each entity in the data set. The coefficient of an entity’s dummy variable produced upon analysis represents an estimate of the unobserved time-invariant factors. However, Wooldridge (2002) suggested that this method is not practical for data sets with many cross sectional observations. Allison (2009) points out that this method imposes difficulty as it may be beyond the capacity of the accounting software.

The mean deviation method is an alternative to estimate fixed effects regression which is simple to perform using accounting software. The mean deviation method implies that mean values for all time-varying variables is identified for each entity. Subsequently, these entity’s specific means are subtracted from the observed value for each variable. In this method, estimate coefficients for the time-invariant independent variables are not given, since their values are constant for each entity; subtracting the entity-specific mean of time-invariant variables from the individual values yield a value of zero for all entities. Accordingly, the time-invariant independent variables are dropped out of the equation, nevertheless their effect has been controlled (Allison 2009).

Random Effects Model

The advantage of a random effects model over the fixed effects model is that time- constant independent variables are allowed and can be examined in a regression model.

101

This results from the assumption that the unobserved effect is not correlated with the independent variables, whether or not they are fixed over time.

Accordingly, a random effects model allows for time-constant independent variables and does not drop them out of the regression model. However, if it violates the assumption that fixed effects are not correlated with the disturbances reflected in the between-effects, it may produce biased results.

Panel Effect Test

Poolabilty refers to the calculation of a common slope and a common intercept across all cross-sections. The more restrictive definition of poolability is that all coefficients are the same across time and cross-sections. In the unrestrictive model, slope and intercept coefficients are allowed to vary across time and cross sections (Jager 2008).

Breush-Pagan Lagrange Multiplier (LM Test) is commonly used to test the poolability. The null hypothesis is that the variances across entities are zero or there is no significant difference across the unit and thus no pooling effect. Where the pooling effect is not observed, simple pooled OLS is merely appropriate. Otherwise, in the situation where the null hypothesis is rejected, random effect model or fixed effect model may be applicable and Hausman specification test is due to be run to determine which model is superior to the another.

Hausman Specification Test

According to Greene (2008), the assumption in the random effects model that individual effects are uncorrelated with the other regressor has little justification. Thus, it may suffer inconsistency should this correlation exist. As noted earlier, the main factor that distinguishes fixed effects from the random effects is whether the error term correlated with the included independent variables. Hence, in order to choose between the fixed effects method and random effects method of panel data regression, the Hausman

specification test is used to determine the existence of the correlation.

As may be recalled, the fixed effects model assumes that the independent variables are correlated with the error term whilst the random effects model does not. Thus, the following hypotheses are to be tested:

102

HA: Unobserved effect is correlated with explanatory variables

The null hypothesis predicts the use of random effects and the alternative as fixed effects. To test whether there is any correlation between the error term and the explanatory variables; the Hausman specification test is performed upon running the fixed effects and random effects regression models (Baltagi 2008). If the Hausman test produces a significant p-value, the null hypothesis is rejected; hence the fixed effects model is appropriate.