Before specifying the actual model for loans in Gambia, it is important to test the nature of existing relationships between variables. We will just use the simple exposure of two variables X and Y respectively.
In the proposed approach of Granger (1969) i.e. X cause Y, or X explains Y, if X helps in the prediction of Y. The procedure requires quantifying the current level of variable Y can be explained by its historical values or lags with respect to previous years ??and then see if adding variables such as explained variance increases. Analysis of causality between two variables i.e. in our study it is used to find out the causality between the increase in loans and capital reserve ratio we first test whether LNRESV is due to LNLOANS in Granger, is estimated by the regression equation:
, (U)
Where k is fixed so that errors and relative to this equation, the null hypothesis that alternative are:
, X does not cause Y,
.
The same process is then repeated for if LNLOANS causes LNRESV and again the same hypothesis will be taken and the rejection and acceptance of the null hypothesis will depend on the F - value of the statistics.
Null Hypothesis:
Obs
F-Statistic
Prob.
LNRATES does not Granger Cause LNLOANS
41
0.41081
0.7463
LNLOANS does not Granger Cause LNRATES
0.66865
0.5772
LNRESV does not Granger Cause LNLOANS
41
1.13894
0.3473
LNLOANS does not Granger Cause LNRESV
0.44219
0.7243
LNCAP does not Granger Cause LNLOANS
41
2.35296
0.0894
LNLOANS does not Granger Cause LNCAP
0.04995
0.9850
Note: See Appendix for complete table
The result of the analysis shows that there exists no causality between loans and treasury bills rates i.e. they are both not causing each other as the f - statistic is insignificant and the significance value is higher than 0.05, therefore our null hypothesis will be accepted. The same relation is found between the loans and reserve ratio that is they are also not causing each other or we can say that no causality exists between them because of insignificant f - value and in this case, our null hypothesis cannot be rejected. However, the relation between the capital and loans have unidirectional causality under 90% confidence interval i.e. the hypothesis of LNCAP causes LNLOANS will be rejected and now we can conclude statistically that LNCAP causes LNLOANS but the opposite is not true statistically i.e. the causality is not bidirectional. Similarly, the complete table is appendix and the results of other causality can be found using the same technique.
Detecting Heteroskedasticity
Heteroscedasticity means that the variance of the observation is not constant over time i.e. it has different scattering for different periods, which makes the returns differ very different from the average over various time periods which makes our results biased and unreliable.
The graphical illustration of it might look like consistent or shows a particular trend if Heteroskedasticity is present. The problem of Heteroskedasticity could be solved by replacing the non - constant errors into variables. There are other methods to check this problem and what we have used in our analysis is the White Heteroskedasticity test along with its cross term to get more appropriate results.