Note: In the table, the test statistics are shown from the model including constant term and from the model including constant
term and trend. * denotes the rejection of null hypothesis at %1 significance level and ** denotes the rejection of null
hypothesis at %5 significance level. That means the null hypothesis about the series are stationary (do not have unit root) is
rejected. The numbers in parenthesis near estimated coefficients are the optimal lag numbers determined by the selection of
Newey-West Bandwidth. Bartlett kernel spectral estimation method is used. Test statistics are compared with the critical
values of Kwiatkowski, Phillips, Schmidt, Shin (1992, Table1)
According to ADF test, all of the three variables are not stationary at their level values. We cannot reject the null
hypothesis of the series has a unit root. But when we take the first difference of these series they become stationary.
In other words, real T (Income tax revenue), real TI (Taxable Income) and the real GNP (Y) are in the form of I(1)
at the %1 level of statistical significance level.
Table 3 shows the results of the KPSS test. Here the null hypothesis says that the series is stationary. For real T and
real TI and real GNP, the null hypothesis of stationarity is rejected at %5 level in the model with constant term. In
the model with constant and trend, we can conclude that real T is not stationary at %5 level and real TI and real Y
are not stationary at %1 level. That means they are not stationary at the level values. When we take the first
differences we cannot reject the null hypothesis of stationarity at %1 level. So these three variables become
stationary at their first differences. In short, these variables are I(1) at the %5 level.
So the results of the KPSS and ADF unit root tests confirm each other. To apply the Johansen Procedure all
variables must be in the form of I(1). So this condition is satisfied.
There are three cointegration test specifications for the Johansen method. First model includes intercept but no
trend in cointegration equation and no intercept in VAR. Second model includes intercept and no trend in
cointegration equation and trend in VAR. Third model includes intercept and trend in cointegration equation and no
trend in VAR. Model selection is done according to the suggestion of Johansen (1992). In the trace test, we start
with model 1, go on with model 2 and finally model 3, where the trace test statistics is compared with critical
values. According to this criterion, the first model is the most appropriate model for our equations.
Table 4 shows the result of cointegration analysis between the variables of real income tax revenue and the real
taxable income [equation (2)]. Optimal lag selection is done by estimating the VAR system and choosing the lag
number which yields the smallest value of Schwarz Information Criteria. The optimal lag number at this model is 2.
After selecting the optimal lag number, we run the Johansen tests and both trace test and maximum eigenvalue test
indicate that there is one cointegrating vector in the system.
Johansen test also allows finding the cointegrating coefficients. These coefficients can be interpreted as long run
elasticity since the variables are in logharitmic form. Standard errors are in parenthesis and the coefficient of real
taxable income is statistically significant at %5 level.
The normalized cointegrating vector for equation 2 is as follows:
LnRealT = -1,0996 + 0,959262 LnReal TI
(1,004) (0,08937)