Impact of tax revenue on economic growth in Rwanda from 2007-2017

4.4 UNIT ROOT TEST (TEST FOR STATIONARITY)

Unit Root Test is done to ascertain whether the variables used in the model are normally distributed (stationary) or non-stationary (i.e. have a unit root). This is done using the Augmented Dicker-Fuller (ADF) Test as shown in Table 4.

Table 3: Augmented Dicker-Fuller tests for Unit Root at levels

Variable	AugmentedD ickey-Fuller test statistic	MacKinnon( 1996) one sided pvalues	1% level Critical Value	5% level Critical Value	10%level CriticalV alue	Stationarity
LNGDP	-2.02191	-3.60099	-2.935	-2.60584	0.2767	Non-stationary
LDT	-2.75693	-3.60559	-2.93694	-2.60686	0.0737	Non-stationary
LTGS	-1.74149	-3.62102	-2.94343	-2.61026	0.4027	Non-stationary
LTITT	-1.27281	-3.59246	-2.9314	-2.60394	0.6336	Non-stationary

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Source: Author's Computation

All variables have unit roots (i.e. non-stationary) at 5% and 10% levels of significance (as shown in Table 4) and are therefore are subjected to 1^st differencing to meet the condition that there should be no unit roots at 5 % and 10% levels of significance. .

Table 5: Augmented Dicker-Fuller tests for Unit Root after 1^st differencing

Variable	Augmented Dickey- Fuller test statistic	MacKinnon (1996) one sided pvalues	1% level Critical Value	5% level Critical Value	10% level Critical Value	Stationarity
LNGDP	-5.42252	0.0001***	-3.60099	-2.935	-2.60584	Stationary
LDT	-8.88959	0.0000***	-3.60559	-2.93694	-2.60686	Stationary
LTGS	-5.42252	0.0000***	-3.60099	-2.935	-2.60584	Stationary
LTITT	-8.0143	0.0000***	-3.59662	-2.93316	-2.60487	Stationary
***p<0.01

Source: Author's Computation

After subjecting all the non-stationary variables to 1^st differencing, they all become stationary at 5% and 10% levels of significance (as shown in Table 5). They are therefore integrated of order 1 meaning they are stationary at the 1^st difference. The null hypothesis that the variables

have unit roots at first difference is thus rejected and conclusion made that the variables have no unit roots at 1^st difference.

4.5 COINTEGRATION TESTS

Cointegration tests facilitate to establish if there is a long-term relationship between the

variables. Subject to proof of cointegration, that will be an indication that the variables share a certain type of behavior in terms of their long-term fluctuations. However before testing for cointegration, the lag length to incorporate in the model will be selected empirically. This will ensure that the model avoids spurious rejection or acceptance of estimated results and to have standard normal error terms that do not suffer from non-stationary, autocorrelation or heteroscedasticity, the results are reported in Section 4.4.1.

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4.6 LAG LENGTH SELECTION CRITERIA

The selection of optimal lag length is used in the estimation of vector autoregressive (VAR)

model. This is important to avoid spurious rejection or acceptance of estimated results. Table 3: Lag length criteria

VAR Lag Order Selection Criteria

Endogenous variables: LGDP LDT LTGS

LTITT

Exogenous variables: C

Date: 11/02/19 Time: 13:20

Sample: 2007Q1 2017Q4

Included observations: 41

Lag	LogL	LR	FPE	AIC	SC	HQ
0	100.9893	NA	1.04e-07	-4.731184	-4.564006	-4.670307
1	227.5260	222.2108*	4.74e-10*	-10.12322*	-9.287330*	-9.818834*
2	241.8056	22.29014	5.28e-10	-10.03930	-8.534698	-9.491405
3	251.0213	12.58728	7.82e-10	-9.708356	-7.535045	-8.916956

* indicates lag order selected by the criterion

LR: sequential modified LR test statistic (each test at 5%

level)

FPE: Final prediction error

AIC: Akaike information criterion

SC: Schwarz information criterion

HQ: Hannan-Quinn information criterion

Table 5 Lag length criteria revealed that researcher should use a maximum of 1 lag in order to

permit adjustment in the model and accomplish well behaved residuals. Table 5 confirms the lag lengths selected by different information criteria such AIC, SIC, Hannan-Quinn Information Criterion (HQI), FPE and the Likelihood Ratio Test (LR) selected three lags, therefore the information criteria approach produced agreeing results to adopt three lags. therefore, the Johansen Cointegration Test is conducted using one lags for the Vector Auto Regression.