Panel consequence, the parameter estimates will be meaningless

Panel data analysis is a frequently used approach in ethnic
diversity, socio-economic development research since it permits to study the
dynamics of the change of economy for a short time series (1990-2010). Since
panel data combines both cross-sections and time series, it can enhance the
quality of data and sort out economic effects that cannot be distinct with only
cross-sections or time series data. Moreover, using information of both
temporal (time) and country (cross-section) effect, we can substantially tackle
the problems of omitted or missing variables (Hsiao, 1986). Some models that can be used for panel data analysis
are described below.

Constant coefficient model:

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   j = 1,…N,j = 1,…T,

The basic assumption of the constant coefficient model
is that all coefficients, both the slopes

 and intercepts

, are
constant with

 as the error term. The first step here is
simply combining both the time-series and cross-section data, also known as
pooling, and then estimating parameters with ordinary least squares (OLS). A
drawback of the constant coefficient model is that it is very unlikely that
with pooled data of different developing countries, the assumption that the
relationship between

 and Y will be the same for all the countries
will hold (Sayrs, 1989). By ignoring the country and or time specific effects
that possibly exist among cross-sections and times series unit, there can be a
possibility of heterogeneity in the model specification. As a consequence, the
parameter estimates will be meaningless and inconsistent (Hsiao, 1986).  To account
for possible heterogeneity among countries, fixed effects models and random
effects models are considered to be more appropriate for handling panel data.

Fixed effects model

Model with intercept dummies:

Contrary to the constant coefficient model, the fixed
effects model assumes that the country specific intercept

 that relates to the different countries may
not be constant and it may or may not differ over time. Adding cross-section
and/or period dummy variables in the model may control for the effects of
omitted variables that are specific to the individual countries. The intercept

 represents the omitted variables for every
specific country (cross-section and time fixed effects) and induce the unobserved
heterogeneity in the model. The intercept is allowed to be correlated with the
independent variables. The ‘

‘ are the observed parts of the heterogeneity.  The error term

 contains the rest of the omitted variables.

Random effects model

                       

Where

 

 = cross country error

 = time-series error

For further improvement of the efficiency of the
estimation process which accounts for cross-section and times series
disturbances, the use of a random effects model may also be appropriate.
Contrary to fixed effects models where each country has its own intercept
through the inclusion of dummy variables, random effects model treats the
intercept as a result of a draw from some distribution. Only the mean effect
from the random cross-section and time-series effects is included in the
intercept term. This has an advantage over the fixed effects model since it
does not sacrifice the number of degrees of freedom. The random deviations
about the mean are now a component of the error term (

).
However, these errors component are not allowed to be correlated with the
independent variables.

Fixed
versus Random effects model

Now, the question is whether to treat

 as fixed or random. According to Hsiao (1986), it makes  no
difference whether fixed or random effect models are used when T (time series)
is large, but if T is finite and N is large it can make a difference in the
estimates. Since the data set of this paper only consists of 5 years for each
country, it is essential to choose the correct model to make the best use of
this small amount of information. One way to decide to use fixed effects or
random effects model is to test for misspecification of the random effects
model, where ‘

‘ is assumed to be random and uncorrelated with the
independent variables(Hsiao, 1986). For this, the following hypothesis has to be tested:

:

 and

:

.

To test this hypothesis, this paper performs a
Hausman-test which tests for correlated random effects. If ‘

‘ is uncorrelated with the independent variables and
thus the null hypothesis holds, then a random effects model should be applied.
Contrary, if the alternative hypothesis holds, a fixed effects model should be
applied. 

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