Reason of
applying FMOLS (Fully Modified Ordinary Least Square)
- 1. This model contains different categories of several time series models and these models directly estimate the long run relationship between dependent and independent variables.
- 2. These models correct the problem of endogeneity in the time series.
- 3. In FMOLS models, we also apply cointegration equations.
- 4. All variables should be non stationary at level and stationary at first difference which means its oder of integration is always I(1).
- 5. First of all we apply cointegration test, if long run relation exist then we further precede FMOLS model.
FMOLS is very appropriate estimation
technique for panel data.
Panel data
- Large number of years
- Large
number of countries
For FMOLS model technique, we using
data on SAARC countries and GDP use as dependent variable and independent
variables are Foreign Direct Investment,
savings,
capital investment, education spending
and life expectancy.
Panel cointegration model
We can run panel cointegration
model.
I go to Quick- group
statistics – johansen cointegration test
Firstly, we select dependent
variable or target variable and independent variables then press ok
So here panel conintegration test dialog box open. In this box three types of test are presenting and out of these three tests. I shall choose only test one and test two such as pedroni (Engle Granger based) and Kao (Engle Granger based).
Pedroni test
Pedroni test has three shapes:
- Individual
intercept
- Individual
intercept and individual trend
- No
intercept or trend
We shall check all these shapes and
here we select Automatic Selection it is lag selection criteria (optimum
lag selection).
First, we proceed with shape individual
intercept- ok
Results of Pedroni test with individual
intercept
Null hypothesis: no co-integration
Trend assumption: no deterministic
trend
There are list of all dependent and
independent variables. This test contain seven statistics such as panel
v-statistic, panel rho-statistic, panel pp-statistic, panel ADF-statistic,
group rho-statistic, group pp-statistic and group ADF-statistic also here is
weighted stastic and its corresponding probability. There are two thongs first
one is within dimension and send one is between dimensions. There are 11
outcomes of prob values.
If prob value is greater than 0.05(in-significant)
then we accept null hypothesis which means that there is no co-integrating
relationship exit in these variables. If prob value is less than 0.05(significat)
then we reject null hypothesis which means that there is co-integrating
relationship exit in these variables. If majority of variables are significant
which means that majority of variables can reject the null hypothesis and can
accept the alternative hypothesis so our variables are cointegrating these
variables have long run association. Same as with results of Pedroni test of
individual intercept and individual trend, no intercept or trend. If in these
test shapes, majority of prob values is insignificant which means that there is
no cointegration or long run relationship exist in these variables and vice
versa.
In these three shapes, if majority
of prob value of two shapes is significant so in this model log ran
relationship is exist.
Kao (Engle Granger based)
The results of kao test shows pro
value is 0.054 which indicates that we reject null hypothesis of no
co-integration and accept alternative hypothesis of co-integration. There is
long run relationship exist in these variables.
FMOLS (Fully Modified Ordinary Least
Square)
When the variables are co-integrated
then we have the validity to run the long run model such as panel FMOLS Model.
Process
Go to quick – Estimate Equation then
select co-integrating regression
First select dependent variables and
then independent variables- in trend specification select none- panel
method- group- method- fully modified OLS (FMOLS) – ok
Results
Results indicate that all variables
are statistically significant except saving. Trade openness has positive impact on economic
growth. Life expectancy and FDI have positive impact on economic growth but
education, and capital investment has negative impact on economic growth.
