Analysing the nexus between income inequality and economic growth in Ethiopia: using the non linear auto regressive distributed lag model

Figures & data

Table 1. Variable description.

Variable	Abbreviation	Source	Variable measurement
Broad Money supply	M2	WB	Money supply
Gini index	Gini	WB	Income inequality
Real Gross Domestic Product	RGDP	WB	Economic growth
Secondary school enrolment	SSE	CSA	Human capital
Urban Population	Urb pop	CSA	Urbanization

N. B: CSA is to mean central statistical authority of Ethiopia.

Table 2. Summary statistics of variables.

Variable	Obs	Mean	Std. Dev	Min	Max	Skewedness	Kurtosis
Gini	30	36.29992	5.320044	24.23543	46.53789	0.7978	0.8285
Rgdp	30	440088.4	401834.3	125406	1624644	0.0004	0.0263
Unemp	30	2.701224	.5263152	2.075	3.714	0.2940	0.0028
Urbpop	30	1.29e + 07	5234613	6043927	2.38e + 07	0.1584	0.2774
M2	30	1.28e + 08	1.93e + 08	1810897	6.79e + 08	0.0005	0.0550

Figure 1. Trends of real GDP.

Figure 2. Trends of Gini index.

Figure 3. Relationships between Gini index and economic growth.

Table 3. The correlation matrix.

	Gini index	M2	Urban pop	RGDP	SSE
Gini index	1.0000
M2	−0.3644	1.0000
Urban pop	−0.5912	0.9111	1.0000
RGDP	−0.3763	0.9864	0.9206	1.0000
SSE	−0.0829	0.2782	0.4119	0.3303	1.0000

From the correlation matrix presented in Table 3, the Gini index is negatively correlated with all explanatory variables and highly correlated with urbanization as measured by a proxy variable of urban population growth rate and less correlated with education level as measured by secondary school enrolment. Beyond this, all explanatory independent variables are positively correlated each other and, the highest correlation exists between GDP and money supply (M2), while the lowest correlation exists between money supply and secondary school enrolment.

Table 4. Unit roots test for stationary.

Variables	Test statistics at level	Test statistics at difference	Dickey-Fuller Critical values			Stationary at
			1%	5%	10%
Gini	−3.818	–	−3.723	−2.989	−2.625	Level
Rgdp	3.253	−4.253	−3.730	−2.992	−2.626	1st difference
SSE	−0.585	−4.267	−3.736	−2.994	−2.628	1st difference
Urbpop	0.313	3.898	−3.736	2.994	2.628	1st difference
M2	−0.018	−6.029	−3.730	−2.992	−2.626	1st difference

Dickey-Fuller result obtained from stata using dfuller command.

Table 5. Bound tests for non-linear co-integration.

Null Hypothesis H0: no long run relationship Decision: reject H0 if p value < 5%	F-statistics	Prob > F	Lower bound	Upper bound	Conclusion
	3.80	0.0149	4.428	6.250	Co-integrated

N.B: rejecting the null hypothesis (with p < 5%) means there is true long run relationship even with asymmetry. A Narayan (2005) F-critical value for a small sample size was used and the null hypothesis was rejected because the statistics were not between the upper and lower bounds.

Table 6. Long run estimation of non-linear ARDL model.

Variables	Coefficients	St. error	t-value	p-value	CI
Const.	458.3808	129.8674	3.53	0.005	172.5446 744.2169
Gini	−.4623082	.1932623	−2.39	0.036	−.8876758 −.0369407
Rgdp^+	.0001986	.0000899	2.21	0.049	6.39e-07 .0003965
Rgdp^-	.0194041	.0056107	3.46	0.005	.0070551 .0317532
SSE^+	.7928663	3.046033	0.26	0.799	−5.911406 7.497139
SSE^-	−4.627437	2.191162	−2.11	0.058	−9.450151 .1952775
M2	−1.08e-07	2.99e-07	0.36	0.725	−7.66e − 07 5.50e − 07
Urbanpop	| −.0000213	.0000187	0.281	−1.13	−.0000625 .00002
R-squared = 0.8468 F (16, 11) = 3.80 Prob > F = 0.0149	Portmanteau test up to lag 12 (chi2) 21.28 0.0464 Breusch/Pagan heteroskedasticity test (chi2) .9706 0.3245 Ramsey RESET test (F) .1836 0.9046 Jarque-Bera test on normality (chi2) .02665 0.9868

Variables with p-value less than 5% are statistically significant.

Table 7. Long run and short run asymmetry test.

Exogenous variables (with non-linear relationships)	Long run asymmetry		Short run asymmetry
	F-statistics	P > F	F-statistics	P > F
RGDP	2.984	0.012	13.85	0.003
SSE	6.906	0.023	2.286	0.159

The long-run analysis we conducted considers the asymmetric relationship between the increasing and decreasing parts of real gross domestic product and secondary school enrollment. The asymmetric test with the null hypothesis of no asymmetry (H₀:${{\theta }_i}^{+}={{\theta }_i}^{-}$) is rejected by considering the probability value given in Table 6.

Figure 4. The dynamic cumulative effect of RGDP and Secondary School enrolment on Gini index.

Table 8. Error correction model non-linear ARDL estimation.

Variables	Coefficients	Std.errors	t-values	p > t	CI
$\Delta$ Gini	−.0551321	.2090794	−0.26	0.797	−.5153128 .4050485
$\Delta$ Rgdp^+	.0000703	.0000798	0.88	0.397	−.0001053 .0002458
$\Delta$ Rgdp^−	.0229956	.0055263	4.16	0.002	.0108322 .035159
$\Delta$ SSE^+	1.562755	2.247469	0.70	0.501	−3.38389 6.5094
$\Delta$ SSE^−	−1.455496 -	2.249865	−0.65	0.531	6.407415 3.496424
Const.	458.3808	129.8674	3.53	0.005	172.5446 744.2169

N.B: $\Delta$ is to mean the first deference of time series variables to consider short run relationships.

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Data availability statement

The data used for this finding are on the hands of the principal researcher and I can provide it to editors when needed.