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:

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.