The panel data is also called longitudinal data - is a multi-dimension data which con- tains observation on several phenomenas which are observed over multiple periods of time. In our study we observe the financial ratios representing different compa- nies over a period of time which is measured on yearly bases. The advantages if using the panel data instead of using other types of data such as cross-section and time series data as listed by Baltagi (1995) are:
1. Panel data enable controlling for individual heterogeneity,
2. Panel data combine time series and cross-section observations, so it will in- clude more informative data, more variability, less collinearity among variables , more degrees of freedom and more efficiency.
3. Panel data are better suited to study the dynamic of change.
4. Panel data is better in detecting and measuring effects that cannot be ob- served normally in cross section or time sires data.
5. Panel data models allow us to construct and test more complicated behavioral model than purely cross-section or time series data.
6. Panel data are usually gathered at micro units, which could result in more accurate variables.
The panel data model take the following format as suggested by Gujarati and Porter (2009) :
Yit=β1i+β2X2it+β3X3it+uit i= 1, ...., N;t= 1, ...., T (4.1)
where idenotes the cross-sectional unit and t denotes the time-periods. In our model theidenotes the company and tdenotes the year. If eachihave the same number of time observations then the panel data is called balanced data. On the other hand, if the number is less or more then it is called unbalanced data. The
data in our sample is balanced data unless we mention otherwise.
4.4.1 Fixed Effects Models:
Before using the we should chose the assumption we make about the intercept, the slope coefficients, and the error termuit. In this study we use two variations of the
fixed effects. Which are namely:
1. Pooled Model: It is also called the population averaged model. The as- sumption is that all the coefficients are constant across time and firms. In this approach we disregard the time and the space dimensions which are the main features of panel data and simply pool the data to estimate a regular OLS. The formula for the OLS regression model is :
Yit=α+Xit0β+uit i= 1, ...., N;t= 1, ...., T (4.2)
Where, In the pooled model the uit which is the disturbance model can be
explained as :
uit =µi+vit (4.3)
Whereµrepresents the cross-section disturbance and thevitare the rest of
the effects.
2. Fixed effect Model: Also called the Least-Square Dummy Variable (LSDV), If we assume the slope coefficients are constant but the intercept is varies across firms. This model takes into account the individuality of the each firm by letting the intercept vary for each firm but in the same time the slope coef- ficients are constant across all the firms.
As the equation show the intercept term α does have a subscript i which would mean that the intercept for each firms can be different. This model is a special case of the Ordinary Least Square (OLS) but it includes dummy variables for each firm. These dummy variables are differential intercept dum- mies, where each dummy would take a value of 0 or 1 based on the group. As the following equation:
Yit=α1+α2D2i+α3D3i+α4D4i+β2X2it+β3X3it µit (4.5)
WhereD2i = 1 if this observation belongs to group A and 0 other wise,D3i=1
if the observation belongs to Group B and 0 otherwise.
.
4.4.2 Random Effects Models
The second approach to test panel data is using the Random Effects models. Al- though it is undemanding to apply the fixed effect, it comes with a large cost which is the loss of degrees if freedom. The main advantage of the (REM) is that it could be used with time invariant variables such as gender or dummy variables.In this model the αi is considered to be a random variable instead of fixed and the mean
value isα. The intercept for the individual firm in this model is expressed as:
αi =α+i, i= 1, ...., N (4.6)
equation 4.6 into equation 4.1 and the model would be as follow: Yit = αi+β0Xit+t+µit = αi+β0Xit+νit (4.7) where, νit =t+µit (4.8)
Gujarati and Porter (2009) suggest thatνitis the composite error term. It contains
two error components which are:
1. t is the firm specific error component. This error term cannot be detected
directly and it is known to be latent variable or (unobservable). 2. µitis the combined firm specific error and the time series error.
As the previous sections show that both the (FEM) and (REM) could be used in the case of this study. One way to decide which model is more suitable and appropriate is to use the Hausman test. The null hypothesis of the test is that the FEM and REM do not differ significantly. If the null hypothesis is accepted then we could conclude that using the REM is more appropriate. On the other hand, of the hypothesis is rejected then we can’t use the REM and the results of the FEM are more appropriate. The Hausman statistics test formula is as follow:
H = (βc−βe)0(Vc−V e)−1(βc−βe) (4.9)
where,
βcis the coefficient vector from the fixed effect estimator
βeis the coefficient vector from the random effect estimator
Ve is the covariance matrix of the random effect estimator
It is also worth mentioning that the Hausman statistics test is distributed asχ2.
4.4.3 Dynamical Models
In addition, a new direction in the research of capital structure argues that firms depart from their optimal capital structure temporarily as Drobetz and Fix (2005) findings show. Both Ozkan (2001) and de Miguel and Pindado (2001) developed a target adjustments model which will identify the optimal capital structure as well as adding a lagged variable to test the speed of adjustments.
Therefore we intend in this thesis to use the dynamic capital model which take the following form:
Levit−Levit−1 =αit(Levit∗ −Levit−1) (4.10) where,
αitis the coefficient of the adjustments speed.
Levitis the Leverage of firmiat timet.
Lev∗itis the lagged leverage of firmiat timet.
After inserting firm idiand timetwe get the following model:
Levit =αβ1 + (1−α)Levit−1+α
X
βjXijt+dt+ηi+νit (4.11)
where,
dtis the time specific effect.
ηi is the firm specific effect.
4.4.4 Tobit Model
The tobit model is developed by Tobin (1958). When the sample have only infor- mation about some of the observations and not all of them it is called a censored sample. For that reason the tobit model is also called the censored or the limited dependent regression mode. The tobit model which is also a linear panel-level random effects could be expressed as the following equation:
Yi∗ =Xitβ+i i= 1, ..., N (4.12)
The intuition for using this model as argued Wald (1999) is that the dependent variable which is the leverage ratio is censored at zero. The values of the Short term debt and Long term debt and Total debt proxies are all between 0 and 1. Furthermore, many companies have a zero debt policy thus it is expected that a percentage of the companies in our sample will have it. Using the Tobit instead of the OLS is because the using it will lead to a downwards-biased estimate of the slope coefficient and an upward biased estimate of the intercept. The tobit model is a random effects model and there is not fixed effect model. The observed variable
Yit∗ is the censored version ofYit. The model could be censored from the left or the
right or uncensored. The observation role for the mode is as follow:
Yit = Yi∗ if y∗i > L L if y∗i ≤L