Welfare implication of determinants affecting aggregate consumption expenditures in Rwanda

3.1.2. Expected signs

The expected sign of the slope coefficients in model are: f30>0, f31>0, f32><0, f33<0, f34<0

f30>0: The intercept (stands for the autonomous consumption) is positively related to the explained variable GCE and to all explanatory variables.

f31>: This means that explanatory variable GDP is positively related to the explained variable GCE.

f32><: This means that the explanatory variable INT is positively or negatively related to the explained variable GCE.

f33<: Means that the explanatory variable INF is negatively related to the explained variable GCE.

f34><: Means that the explanatory variable EXCH is negatively or positively related to the explained variable GCE.

3.1.3 Test and analysis of the data

It is clear that most macroeconomic time series data are not stationary and are not linear. To make sure that there are all linear, all variables are transformed into logarithm. In order to avoid obtaining misleading statistical inferences, the researcher performed the stationarity test of all variables used in the model.

3.2. Data processing

In this study, we used annual time series data for the period 1995 to2015. Normally, most time series are non-stationary series in the model and might lead to spurious regressions. The first or the second difference terms of the most variables will usually be stationary.

3.2.1. Unit root tests

3.2.1.a. Why testing stationarity?

When economic time series are stationary, the application of Ordinary Least Squares (OLS) estimation is statistically acceptable; and when they are not stationary, the assumptions upon which OLS

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Estimation are violated, rendering its application inappropriate. In this case we use the co-integration test. To test stationary of all-time series of our model, the E-views 7 software enabled us to use the test of the Augmented Dickey Fuller (ADF) and Phillips Peron (PP) tests. By applying the strategy of these tests incorporated in E-views software. Prior to carrying out a model, it is necessary to examine the time series properties of the variables included in it. This allows one to determine whether or not the regression is spurious. For this purpose, stationarity of data set is checked by using the simple appropriate tests above mentioned. The results of the stationarity obtained arise as follows in the table:

39

SERIES

	EQUATION	ADF				PP			CONCLUSION
		lag	T-test	T-cri	Prob	T-test	T-cri	Prob
LNGCE	Intercept	0	-1.109913	-3.020686	0.690	-1.067673	-3.020686	0.707	LNGCE is not stationary at level
	Trend& Intercept	0	-1.480747	-3.658446	0.801	-11.710319	-3.658446	0.708
	None	0	5.932190	-1.959071	1.000	5.932190	-1.959071	1.000
LNGDP	Intercept	1	-0.479496	-3.029970	0.875	-0.887935	-3.020686	0.770	LNGDP is not stationary at level
	Trend& Intercept	3	-3.350081*	-3.710782	0.091	-1.654032	-3.658446	0.733
	None	1	1.967458**	-1.960171	0.984	6.832295** *	-1.969071	1.000
INT	Intercept	0	-0.240037	-3.020686	0.918	-0.059694	-3.020686	0.941	INT is not stationary at level
	Trend& Intercept	1	-3.157576	-3.673616	0.122	-3.639768*	-3.658446	0.051
	None	0	1.012776	-1.959071	0.911	1.231349	-1.959071	0.938
INF	Intercept	0	-2.822727*	-3.020686	0.072	-2.743902*	-3.020686	0.084	INF is not stationary at level
	Trend& Intercept	0	-2.747607	-3.658446	0.230	-2.680366	-3.658446	0.253
	None	0	-1.522258	-1.959071	0.117	-1.442881	-1.959071	0.134
LNEXCH	Intercept	0	-2.120302	-3.020686	0.239	-3.120302	-3.020686	0.239	LNEXCH is not stationary at level
	Trend& Intercept	3	-2.405621	-3.710482	0.363	-1.700882	-3.658446	0.712
	None	1	1.745474*	-1.960171	0.975	2.823701	-1.959071	0.997

Source: World Bank indicators1995-2015 and author's computation Table 2: Stationarity at Level

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SERIES

	EQUATION	ADF				PP			CONCLUSION
		lag	T-test	T-cri	Prob	T-test	T-cri	Prob
LNGCE	Intercept	0	-3.201338**	-3.029970l	0.035	-3.147755	-3.029970	0.039	LNGCE is not stationary at first difference
	Trend& Intercept	0	-3.170959	-3.676316	0.119	-3.140534	-3.673616	0.125
	None	1	-1.883162*	-1.961409	0.058	-1.783670*	-1.96071	0.073
LNGDP	Intercept	0	-2.698763*	-3.029970	0.092	-2.621696	-3.029970	0.106	LNGDP is not stationary at first difference
	Trend& Intercept	0	-2.634522	-3.676316	0.270	-2.570212	-3.673616	0.295
	None	0	-1.500754	-1.960171	0.121	-1.460394	-1.960171	0.130
INT	Intercept	1	-4.739894***	-3.040391	0.001	-5.966575***	-3.029970	0.000	INT is stationary at first difference
	Trend& Intercept	1	-4.740442**	-3.690814	0.007	-6.311193***	-3.673616	0.000
	None	0	-3.706693***	-1.960171	0.000	-3.704162***	-1.960171	0.000
INF	Intercept	0	-4.942504***	-3.029970	0.001	-8.562930***	-3.029970	0.000	INF is stationary at first difference
	Trend& Intercept	1	-4.880297***	-3.690814	0.005	-8.930822***	-3.673616	0.000
	None	0	-5.067116***	-1.960171	0.000	-8.255686***	-1.960171	0.000
LNEXCH	Intercept	3	-1.482842	-3.065585	0.516	-3.071608**	-3.029970	0.046	LNECH is not stationary at first difference
	Trend& Intercept	3	-1.531298	-3.733200	0.774	-2.637027	-3.673616	0.269
	None	0	-2.354457**	-1.960171	0.021	-2.354457**	-1.960171	0.021

Source: World Bank indicators1995-2015 and author's computation Table 3: Stationarity at first difference

41

SERIES

	EQUATION	ADF				PP			CONCLUSION
		lag	T-test	T-cri	Prob	T-test	T-cri	Prob
LNGCE	Intercept	1	-6.094004***	-3.040391	0.000	-6.381671***	-3.040391	0.000	LNGCE is stationary at second difference
	Trend& Intercept	2	-3.708039*	-3.733200	0.042	-6.153897***	-3690814	0.000
	None	0	-6.123911***	-1.961409	0.000	-6.388171***	-1.961409	0.000
LNGDP	Intercept	0	-4.676807***	-3.040391	0.001	-4.831284***	-3.040391	0.001	LNGDP is stationary at second difference
	Trend& Intercept	1	-4.729190**	-3.710482	0.008	-4.610669**	-3.690814	0.009
	None	0	-4.709419***	-1.961409	0.000	-4.873309***	-1.961409	0.000
INT	Intercept	2	-5.474011***	-3.065585	0.000	-7.841476***	-3.040391	0.000	INT is stationary at second difference
	Trend& Intercept	2	-5.202147***	-3.733200	0.004	-9.109500***	-3.690814	0.000
	None	2	-5.738162***	-1.964418	0.000	-7.932883***	-1.961409	0.000
INF	Intercept	2	-5.472188***	-3.065585	0.000	-14.57497***	-3.040391	0.000	INF is stationary at second difference
	Trend & Intercept	2	-5.570167***	-3733200	0.002	-13.16833***	-3.690814	0.000
	None	2	-5.688618***	-1.964418	0.000	-14.48986***	-1.961409	0.000
LNEXCH	Intercept	3	-2.356842	-3.081002	0.048	-5.010709***	-3.040391	0.001	LNESCH is stationary at second difference
	Trend& Intercept	3	-2.407857	-3.759743	0.361	-4.836133**	-3.690814	0.006
	None	3	-2.402642**	-1.966270	0.020	-5.203143***	-1.961409	0.000

Source: World Bank indicators1995-2015 and author's computation Table 4: Stationarity at second difference

3.2.1.b. Interpretation of stationarity test From the above table, the so called stars:

***: Stationary at 1% level of significance **: stationary at 5% level of significance *: Stationary at 10 % level of significance

- LNGCE is not stationary at both level but it becomes stationary at second difference at 1% level of significance, when we consider all equations.

- LNGDP is not stationary at both level and first difference but it becomes stationary at second difference when we consider all equations.

- INT is not stationary at level but it becomes stationary at both first and second difference when we consider all equations.

- INF is not stationary at level but it is stationary at both first and second difference when we consider all equations using.

- LNEXCH is not stationary at level but it becomes stationary at first difference when we consider none by all equations and it is stationary at second difference when we consider all equations. Our model meets the condition for co-integration because all other series are integrated of the same order after being differentiated.