Financial development and income inequality: a nonlinear econometric analysis of 21 African countries, 1990-2019

Figures & data

Table 1. Results of the linearity test

	Transition Variable $\mathbf{F}{\mathbf{D}}_{\mathbf{i}\mathbf{t}-1}$				Results of the $H_0$	Selecting Order $m$
		$m=1$	$m=2$	$m=3$	$m=1$	m = 1;$H_{01}^{\ast }$	m = 2;$H_{02}^{\ast }$	m = 3;$H_{03}^{\ast }$
$L{M}_F$	Fs	70.45	22.05	13.40	74.02	4.35	8.34	8.50
	pv	4.896e-17	10.016e-10	8.994e-05	5.798e-34	0.76	3.304e-05	1.226e-03
$L{M}_{\chi }$	Fs	15.70	6.73	9.14	19.55	9.20	51.60	48.01
	pv	2.998e-8	4.882e-02	9.893e-07	2.768e-07	0.56	2.398e-02	3.533e-08
WB	pv	-	-	-	0.00	-	-	-
WCB	pv	-	-	-	0.00	-	-	-

Note: The dependent variable is the income inequality. All variables (Gini, FD, EQUIUNC, UNMPUNC, HPIUNC, GGFCE, OPEN, GE, ECO, and INFL) were included as candidates for identifying the appropriate transition variable using the LM-type test. The p-v are the p-values, and the Fs denotes the F-statistic.

Source: Author’s calculation based on World Development Indicators, 2021) data.

Table 2. Results of the linearity test

	Model I:Baseline	Model I:Baseline	Model III: Robustness	Model IV: Robustness
	Parameter Constancy test
$L{M}_F$	6.384 (3.238e-09)	4.940 (2.857e-19)	2.121 (4.993e-04)	8.005(3.220–10)
$L{M}_{\chi }$	82.44 (4.973e-13)	90.29 (4.973e-20)	61.30 (2.443e-15)	99.50(1.191e-15)
	No Remaining Nonlinearity
$WB$	1(p-value)	1(p-value)	1(p-value)	1(p-value)
$WCB$	1(p-value)	1(p-value)	1(p-value)	1(p-value)
	Results of the Estimated Threshold model
$\mathrm{c}$	21.90*** (2.40)	10.30** (3.20)	20.13** (3.90)	13.88***(1.66)
$\left(\gamma \right)$	12.00*** (0.07)	9.87*** (1.57)	15.03***(2.00)	11.90***(1.76)

Note: The dependent variable is the income inequality. All variables (Gini. DF, EQUIUNC, UNMPUNC, HPIUNC, GGFCE, OPEN, GE, ECO, and INFL) were included as candidates for identifying the appropriate transition variable using the LM-type test. The p-v are the p-values, and the Fs denotes the F-statistic.

Source: Author’s calculation based on World Development Indicators, 2021) data

Figure 1. The mean private credit, which is a claim against the private sector by financial intermediaries and the estimated threshold. Note: The value of private credit is expressed as a percentage. Source: Author’s calculation based on WDI (2022) data.

Table 3. Panel smooth transition regression model estimation

Variables	Model I: Finance-Inequality: Unconventional Policy Regime (2000–2019)			Model II: Financial-Inequality: Conventional Policy Regime (1990–1999)
	PSTR		GMM	PSTR		GMM
	LR ${\mathit{\beta }}_{0\mathit{j}}\times 100$	HR $\left({\mathit{\beta }}_{0\mathit{j}}+{\mathit{\beta }}_{1\mathit{j}}\right)\times 100$		LR ${\mathit{\beta }}_{0\mathit{j}}\times 100$	HR $\left({\mathit{\beta }}_{0\mathit{j}}+{\mathit{\beta }}_{1\mathit{j}}\right)\times 100$
$F{D}_{t-1}$	−5.11**(1.06)	2.50**(0.90)	−2.90**(0.89)	2.02***(0.29)	−1.40**(0.66)	1.98***(0.09)
$\mathrm{F}{{\mathrm{D}}^2}_{t-1}$			1.87**(0.32)			−1.91**(0.50)
$EQUIUNC{t}_{-1}$	2.00**(0.67)	3.09**(1.30)	0.90***(0.09)
$UNMPUN{C}_{t-1}$	3.70**(1.01)	−1.09**(0.09)	2.54**(0.42)
$HPIUN{C}_{t-1}$	1.11**(0.38)	4.09**(0.80)	2.10**(1.016)
$G{E}_{t-1}$	−2.89**(0.86)	3.10**(0.98)	3.26**(1.23)	−0.79***(0.09)	2.04**(1.00)	−2.45***(0.27)
$GGFC{E}_{t-1}$	1.21**(0.90)	3.09**(1.89)	1.90**(0.77)	0.88***(0.05)	2.06**(0.79)	1.76**(0.55)
$OPE{N}_{t-1}$	−3.88**(1.04)	−1.09***(0.02)	−2.90**(1.09)	−1.20***(0.09)	−3.60**(1.09)	−1.67**(0.80)
$EC{O}_{t-1}$	−2.09***(0.03)	1.99***(0.08)	−3.98**(0.94)	−3.43**(1.30)	2.11***(0.20)	2.06**(1.00)
$INF{L}_{t-1}$	−0.11(0.98)	0.29**(0.10)	−1.34**(0.34)	−1.33***(0.16)	0.08***(0.01)	−1.02***(0.10)
$\mathrm{D}\mathrm{u}\mathrm{m}$	Yes	No	No	Yes	No	No
Transition Parameters
$c$	21.90*** (2.40)			10.30** (3.20)
$\gamma$	12.00*** (0.07)			9.87*** (1.57)
ESD	0.02464			0.09873
AR(1): p-v			0.003			0.015
AR(2): p-v			0.140			0.179
# of obs.	420		357	210		210
# of countries	21

Table 3. Panel Smooth Transition Regression model estimation. Note: The dependent variable is the Income inequality. The numbers in brackets denote that the standard errors in brackets are obtained by using the cluster-robust and heteroskedasticity-consistent covariance estimator, allowing for error dependency within individual countries. The (***), (**), (*) reflect the 1%, 5%, 10% levels of significance, respectively. ESD denotes the estimated standard deviation (residuals), while p-v are the p-values. For our difference GMM, we set the number of lags to 1 for yearly differences in our yearly data, and we further cut our time period for the unconventional policy regime to start from 2003–2019 in order to comply with the conditions of the GMM that $T$ should not be greater than $N$. Source: Author’s calculation based on SWIID data (Solt, 2020) and World Development Indicators, 2021) data.

Table 4. Finance-Inequality: robustness and sensitivity checks model

	Model III: Development Inequality (2003–2019)	Model IV: Development Inequality (1990–1999)
PSTR	Gini = − 3.91FDD** + 3.98 EQUIUNC** +1.87UNMPUNC*** + 2.45HPIUNC** − 4.00GE*** + 2.11GGFCE** − 3.16ECO*** − 1.40INFL*[15.03γ***, 21,13C**] + 1.88FDD***− 2.76EQUIUNC** +0.567UNMPUNC** + 3.00HPIUNC*** + 2.98GE** + 0.82GGFCE** +2.00ECO*** +0.99INFL*)	Gini = 1.99FDD** −2.71GE** + 2.04GGFCE** − 2.57ECO** + 1.00INFL*[11.90γ***, 13,88C***] − 2.22FDD** + 1.09GE** + 1.56GGFCE**+ 3.00ECO*** + 0.20INFL**
	Model V: Development Inequality (2003–2019)	Model VI: Development Inequality (1990–1999)
GMM	Gini = −2.40FDD** +1.89 $\mathrm{F}\mathrm{D}{\mathrm{D}}^2$** + 1.40 EQUIUNC** +3.00UNMPUNC** + 1.09HPIUNC*** − 2.00GE*** − 0.80GGFCE** − 2.16ECO*** + 0.10INFL**	Gini = 1.57FDD** − 0.54 $\mathrm{F}\mathrm{D}{\mathrm{D}}^2$** − 3.78GE** + 2.00GGFCE − 1.45ECO** − 0.04INFL
	AR(1): p-value (0.01) AR(2): p-value (0.554) Countries: 19	AR(1): p-value (0.019) AR(2): p-value (0.686) Countries:19

The***/**/* denote levels of significance at 1%, 5% and 10%, respectively. Source: Author’s calculation results based on SWIID data (Solt, 2020; World Development Indicators, 2021). We adopted the domestic credit to the private sector as a share of GDP to measure financial development. For our difference GMM, we set the number of lags to 1 for yearly differences in our yearly data, and we further cut our time period for the unconventional policy regime to start from 2003–2019 in order to comply with the conditions of the GMM that $T$ should not be greater than $N$. We further removed two countries that were found to have a high mean of private credit, as shown in section 4.2, figure 1.

World Development Indicators. (2021). World Bank., available at: http://data.worldbank.org/data-catalog/world-development-indicators (accessed 05 October 2022)

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Solt, F. (2020). The standardized world income-inequality database. Social Science Quarterly, 90(2), 231–242. https://doi.org/10.1111/j.1540-6237.2009.00614.x

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Data availability statement

Publicly available datasets were analysed in this study. This data can be found here: [http://data.worldbank.org/data-catalog/world-development-indicators (accessed on 2 October 2022)]. Further inquiries can be directed to the corresponding author.