Countries selection
The rationale for the selection and inclusion of countries for this study is based according to the GDP per capita. According to the World Development Indicators (2020) of the World Bank, the annual SubSaharan African countries GDP per capita range from $274 to $11425. At the lower point of this range lie countries like the Central African Republic, Chad, Niger, Somalia and Democratic Republic of Congo among others. The middle point of the range has countries such as Angola, Kenya, Nigeria, Eswatini and Sao Tome and Principe among others. The upper point in the range include countries such as Botswana, Seychelles, Mauritius, South Africa, and Gabon among others. Three countries are selected from the lower, middle, and upper points of this range based on the availability of data. The lower point GDP per capita countries included are Burundi, Niger and the Central African Republic. The middle point countries included are Angola, Nigeria, and Kenya. The upper point countries by GDP per capita are Botswana, Seychelles and Mauritius.
Data
The dataset for this study is made up of three variables:
Gini coefficient
this is the dependent variable that measures income inequality. It is the ratio of the area between the diagonal and the Lorenz curve and the area of a triangle below the diagonal. The Gini coefficient lies between 0 and 1. The closer to zero the Gini is, the more equally distributed the income and the farther away from zero the Gini is, the more unequal the distribution. The Gini coefficient is derived from the Standardized World Income Inequality Database, Solt (2020).
Corruption perception index (CPI)
this is an indicator of the prevalence of corruption across the countries. It is measured by an index of 0 to 100, with 0 signifying highly corrupt and 100 not corrupt. A rise in the CPI means a decline in corruption and a fall in CPI implies a rise in corruption. This data is derived from the Transparency International (2020) database.
Unemployment
This is measured as the total percentage of the labour force that is not engaged in any work. It includes persons without work but who are able and willing to work. The data is obtained from the World Development Indicators (2020) of the World Bank.
All the data for each country are presented as annual time series from 2000 to 2020.
Table 1 presents the descriptive statistics for the Gini coefficient, corruption perception index and unemployment rate for each of the countries.
Within this period of study, Burundi has the lowest mean Gini coefficient, meaning that it has the most equally distributed income even though a low GDP per capita country. Ironically, it has one of the highest corruption perception indexes, with a low rate of unemployment. However, within the same group as Burundi, the mean Gini coefficient for CAR and Niger is higher than Burundi also with a high perception of corruption and low unemployment. The standard deviation for Nigeria’s Gini coefficient is the highest, meaning that income inequality in Nigeria is highly volatile.
The countries at the middle of the GDP per capita range all have inequality higher than the countries at the lower range except for Nigeria. The perception of corruption between countries at the lower point of the range and countries at the middle is not substantially different. Unemployment is higher in the middle GDP per capita countries. The perception towards corruption in Seychelles is extremely volatile as indicated by the standard deviation
Countries at the highest point of the range have the lowest inequality except for Botswana. The corruption perception for these countries is very low compared with the lower and middle groups. In contrast, unemployment was higher than the other groups. Unemployment is highly volatile in Angola, Nigeria and Botswana as shown by their standard deviations.
Table 1 Descriptive statistics for Gini coefficient, CPI and unemployment
Countries

Mean

Minimum

Maximum

Standard Dev.

Burundi
CAR
Niger
Angola
Kenya
Nigeria
Botswana

0.388
0.544
0.391
0.551
0.606
0.533
0.586

Gini Coefficient
0.383
0.542
0.379
0.525
0.600
0.475
0.585

0.395
0.546
0.398
0.592
0.619
0.589
0.589

0.003
0.001
0.007
0.026
0.004
0.496
0.001

Mauritius
Seychelles
Burundi
CAR
Niger
Angola
Kenya
Nigeria
Botswana
Mauritius
Seychelles
Burundi
CAR
Niger
Angola
Kenya
Nigeria
Botswana
Mauritius
Seychelles

0.381
0.392
19.619
20.857
26.238
19.905
23.523
22.333
59.809
50.190
50.762
1.164
4.317
1.280
5.711
2.794
4.849
18.211
7.758
3.296

0.377
0.381
CPI
16
13
12
15
19
10
54
41
36
Unemployment
0.800
4.040
0.320
3.612
2.599
3.539
15.880
6.360
1.720

0.386
0.402
25
26
35
27
31
28
65
57
66
1.890
4.490
3.100
9.430
2.980
9.010
23.800
9.520
5.140

0.003
0.008
2.376
4.292
7.930
2.931
3.473
5.544
3.076
4.643
8.596
0.242
0.133
0.849
1.949
0.104
1.935
1.917
0.934
0.849

Source: Authors computation
Model
The quantileonquantile (QQ) approach is used to study the relationship between income inequality and corruption, and income inequality and unemployment. The quantile regression first used by Koenker and Bassett (1978) is designed for modelling timechanging variables with regards to the structure of dependence. It is a blend of nonparametric estimation and quantile regression. The merits of this technique are numerous. Quantile regression is employed to show the relationship between an explanatory variable and the diverse quantiles of the explained variable. The classical linear regression permits a specific quantile of an explanatory variable to predict an explained variable. For this reason, combining these two techniques enables the modelling of quantiles of the explanatory variable and quantiles of the explained variable for both the top and bottom quantiles of a given distribution, thereby providing a robust outcome across time. The QQ provides better information than other estimation techniques such as the OLS and quantile regression. Let us start with the following nonparametric quantile regression equations.
$${Gini}_{t}={\delta }^{\theta }\left({\varphi }_{t}\right)+{u}_{t}^{\theta } \cdots \cdots \cdots \cdots \cdots \cdots \cdots \left(1\right)$$
Where \({Gini}_{t}\) represents the income inequality of a country at time \(t\). \({\varphi }_{t}\)is the explanatory variable that represents either the corruption perception index or the unemployment rate. \(\theta\) denotes the \(\theta th\)quantile of the conditional distribution of Gini coefficient as predicted by \({\varphi }_{t}\). \({u}_{t}^{\theta }\) signifies the quantile residual term. \({\delta }^{\theta }\) is an undefined factor lacking in any previous information. The QQ model enables is to examine the changing effect of corruption and unemployment across quantiles of inequality.
We use a firstorder Taylor expansion to approximate the unknown term \({\delta }^{\theta }\).
$${\delta }^{\theta }\left({\varphi }_{t}\right)\approx {\delta }^{\theta }\left({\varphi }^{\tau }\right)+{\delta }^{\theta }\left({\varphi }^{\tau }\right)\left({\varphi }^{\tau }{\varphi }_{t}\right) \left(2\right)$$
Where \({\delta }^{\theta }\left({\varphi }^{\tau }\right)\) denotes the partial derivative of \({\delta }^{\theta }\left({\varphi }_{t}\right)\) with respect to each of the explanatory variables. Equation \(\left(2\right)\) can be presented as:
$${\delta }^{\theta }\left({\varphi }_{t}\right)\approx {\delta }_{0}\left(\theta , \tau \right)+{\delta }_{1}\left(\theta , \tau \right)\left({\varphi }^{\tau }{\varphi }_{t}\right) \left(3\right)$$
Substituting equation \(\left(3\right)\) into \(\left(1\right)\) gives
$${Gini}_{t}={\delta }_{0}\left(\theta , \tau \right)+{\delta }_{1}\left(\theta , \tau \right)\left({\varphi }^{\tau }{\varphi }_{t}\right)+{u}_{t} \left(4\right)$$
We can have the estimate for the linear regression as
$${min}_{{\delta }_{0},{\delta }_{1}}{\sum }_{i}^{n}{\rho }_{\theta }\left[{Gini}_{t}{\delta }_{0}{\delta }_{1}\left({\widehat{\varphi }}_{t}{\widehat{\varphi }}^{\tau }\right)K\left(\frac{{F}_{n}\left({\widehat{\varphi }}_{t}\tau \right)}{h}\right)\right] \left(5\right)$$
Where \({\rho }_{\theta }\left(u\right)\) represent the quantile loss function which is expected as \({\rho }_{\theta }\left(u\right)=u\left(\theta I\left(u<0\right)\right)\). \(I\) is the indicator function and \(K\) is the kernel function. The quantile on quantile technique presents a detail and reliable interpretation. A three dimensional graph shows the plot of corruption shock on income inequality and unemployment shock on income inequality. The Zaxis shows the value of the estimate of the slope coefficient, \({\delta }_{1}\left(\theta , \tau \right)\) which evaluates the response of each of the \(\tau\)th quantile of corruption and unemployment shocks movement (xaxes) on the quantile of inequality \(\theta\)th in the yaxes.