Economic Growth and Extreme Poverty in Sub-Saharan African Countries: Non-Linearity and Governance Threshold Effect

Abstract

Over the last few decades, many economies in sub-Saharan Africa have experienced much faster economic growth than other parts of the world. However, many of these economies have not experienced significant poverty reduction. Several factors such as the quality of governance may limit the expected effects of economic growth on poverty. This paper examines the triangular relationship between extreme poverty, governance quality, and economic growth for the sub-Saharan African countries over the period 2010–2019. Compared to the work carried out until now, the novelty of this research lies in using the Panel Threshold Regression (PTR) and Panel Smooth Transition Regression (PSTR) models to determine the optimal level of governance index, which once attained, will make extreme poverty decrease with economic growth and governance quality. We found that the nexus between these three variables is nonlinear. Besides, results show that there exists a statistically negative relationship between governance and extreme poverty above the threshold level of 0.314 for the Global Governance Index (GGI) and 66.9 for the Ibrahim Index of African Governance (IIAG), above which governance quality decreases extreme poverty. The results showed that the economic growth would begin to reduce extreme poverty once governance reaches a threshold level of 0.367 for GGI and 63.2 for IIAG. Better performance of governance also appears to improve economic growth and reduces poverty.

Introduction

The extreme poverty is defined as living on less than $1.90 a day (in 2011 prices, equivalent to $2.15 in 2022) (World Bank, 2022). The World Bank in its biennial Poverty and Shared Prosperity Report mentions that extreme poverty was increased in 2020 for the first time in over 20 years as the disruption of the COVID-19 pandemic compounds the forces of conflict and climate change, which were already slowing poverty reduction progress. Extreme poverty affected between 9.1% and 9.4% of the world’s population in 2020. According to this report, the COVID-19 pandemic pushed more than an additional 88 million people into extreme poverty in 2020, with the total rising to as many as 150 million at the end of 2021, depending on the severity of the economic contraction. Had the pandemic not convulsed the globe, the poverty rate was expected to drop to 7.9% between 2020 and 2021. Globally, the extreme poor are concentrated in sub-Saharan Africa and South Asia. According to the Poverty and Shared Prosperity report 2020, COVID-19 can add around 27–40 million new poor in the Sub-Saharan Africa region. The World Bank has set an ambitious target to eradicate extreme poverty globally by 2030.

Economic growth is considered to be one of the main drivers of poverty reduction and improving the quality of life in developing countries (Kouadio & Gakpa, 2022). According to Department for International Development (DFID), “the extent to which growth reduces poverty depends on the degree to which the poor participate in the growth process and share in its proceeds. Thus, both the pace and pattern of growth matter for reducing poverty” (DFID, 2008). The causes of poverty cannot be narrowed down to one single source. However, poor governance, which is one of the main causes of poverty in sub-Saharan African countries, involves various mal practices by the state and its workers. Good governance is essential to combating poverty. Governance is about politics or the way in which citizens and governments relate to each other. Good governance requires state capability, responsiveness, and accountability. It means making politics work for the poor.

The problem of poverty, the redistribution of wealth, and poor governance in sub-Saharan African countries is at the heart of economic debates and is the subject of several empirical studies. Since the mid-1990s, Africa has experienced rapid growth at an average rate of 5%. This acceleration in Africa’s growth rate has not been accompanied by a significant drop in poverty compared to other regions of the world. The region has continued to experience high levels of poverty (Kouadio & Gakpa, 2022). Many economists believe that poor governance undermines the structural transformation of African economies, constitutes an obstacle to the development of economic activities and it is expensive. In essence, governance quality is a crucial determinant of the poverty level. Improving the quality of governance in sub-Saharan African countries is key to ensuring equitable growth and reducing poverty. Good governance reforms, especially when backed up by support for pro-poor spending as a means of improving government accountability, can have a direct effect on redistribution. Since poverty reduction is arithmetically a function of growth and improvements in distribution, this effect of good governance could have a significant effect on poverty reduction (Khan, 2009).

This paper questions the growth-poverty-governance trilemma by presenting empirical discoveries which fill a lacuna in the literature. Thus, we examine the non-linear association between governance quality and extreme poverty. The main objective of this paper is to determine the optimal level of governance quality,1 which once attained, will make the poverty rate decrease with economic growth in Sub-Saharan African countries. In this regard, we are questioning about the threshold value of the governance index above which economic growth and governance quality begin to reduce the extreme poverty.

The contribution of the current research study to the empirical literature of growth-poverty-governance is its focus on Sub-Saharan African countries together with the determination of their specific threshold of governance quality and which countries have reached or exceeded this threshold. Conclusions reveal, inter alia, that though growth exerts poverty-reducing tendencies the interaction with poor governance may limit the expected effects of economic growth on poverty. These are important contributions to the growth-poverty-governance literature, which provides the justification for engaging in this study. To the best of our acknowledge, the nonlinear relationship between the quality of governance and extreme poverty for the sub-Saharan African countries has not been previously studied. Thus, to fill this gap, we propose to investigate the potential threshold effects in the relationship between quality of governance, economic growth and extreme poverty. Different from previous studies, we use the panel threshold regression (PTR) models and panel smooth transition regression (PSTR).

The remainder of this paper is organized as follows. The section “Literature Review” assesses the previous literature regarding the impact of economic growth and governance quality on poverty. The section “Methodology” presents the data and the model specification. The section “Results and Discussion” shows the model estimation and results and the section “Conclusion”concludes.

Literature Review

The beginning of the 3rd millenium has witnessed the economic prominence of developing economies. Indeed, which recorded considerably high growth rates (Adeleye et al., 2020). The reduction in the number of people living in extreme poverty in the world, from 1.93 billion in 1991 to 659 million in 2018, is one of the most important success stories in development (World bank, 2023). However, many of these economies, particularly those of African countries, have experienced much faster economic growth than other parts of the world and have not experienced a considerable reduction in poverty, which is traceable to poor governance quality, high-income inequality and persistent economic fluctuations in the last few decades (Kouadio & Gakpa, 2022). In explaining how the significant growth experience of sub-Saharan Africa countries can contribute to improving human development and alleviating poverty, it is imperative to understand the importance of governance quality in the growth-poverty nexus in the literature (Adeleye et al., 2020).

While several empirical studies have been conducted on the nexus between quality of governance and extreme poverty, relatively little attention has been given to the potential threshold effects in this relationship. While poverty reduction remains central in the Post-2015 Agenda, its determinants remain debated in the literature, especially the role of structural conditions related to governance. The nexus between economic growth, governance quality, and poverty varies among different authors, countries, and periods (Babajić et al., 2022). Political corruption is one of the structural factors of poor governance that exacerbates national poverty on which there is a consensus (Zang et al., 2023). Ochi et al. (2023) determine the optimal level of governance index in South Asia and Sub-Saharan Africa, which once attained, will make the different levels of poverty decrease with governance quality. To attain the objective of their study, they used the dynamic panel threshold model as an econometric method and a sample of 57 countries for the period 2010–2019. It is an appropriate technique to solve their research problem and to identify, collect and analyze the data from their analysis. Their sample size was suitable because it contains the two poorest regions in the world but it is not appropriate in terms of heterogeneity. It was more appropriate to divide the sample into two homogeneous samples. Their findings revealed that the poverty headcount ratio at $1.90, $3.20, and $5.50 starts decreasing once the governance index reaches a threshold level of 0.20, 0.62, and 0.70, respectively. We noted that the authors were not objective because they did not mention the results of studies that contradicted their findings. The author’s most convincing thesis is that the more a country improves its quality of governance, the more it is able to reduce the rate of total monetary poverty. The author’s arguments and conclusions are convincing because they are based on theoretical and empirical foundations, and because the work ultimately contributes to a meaningful understanding of the subject, which is the quality of governance must reach a well-determined threshold so that it can decrease the poverty rate.

Gidigbi (2023) examines the impact of selected poverty alleviation programs on poverty reduction in Nigeria, covering the period from 1981 to 2015. Two categories of social intervention programs were used, and both were found to be effective in reducing the poverty rate. For example, a percentage point increase in access and empowerment programs reduces the poverty rate by 1.33%. He concludes that the provision of credit facilities, social capital, and a pleasant business environment should be encouraged by public and private bodies in the poverty alleviation programme. Nguyen et al. (2021) examine how governance quality can affect economic growth, income inequality, and poverty in Vietnam. They found that better performance of governance appears to improve economic growth and reduces poverty. Eslamloueyan and Kahromi (2022) examine the impacts of economic sanctions, the COVID-19 pandemic, and governance quality on the poverty depth in Iran for the period 1990–2020. Their results show that good governance decrease, but sanctions and income inequality increase the poverty gap in Iran. Mulok et al. (2012) attempted to determine the empirical relationship and importance of growth for poverty reduction in Malaysia. Their results show that growth explains much, but not all, about the evolution of poverty. Economic growth is necessary but not sufficient for poverty reduction, especially if the objective is rapid and sustained poverty reduction. It is considered that the sample sizes of these studies are insufficiently large. There is no consistency between the sample size and the number of parameters used in the estimation of the models. A simple rule of thumb in statistics is a minimum of 10 observations per estimated parameter. Some experts have provided more complex rules for identifying whether a sample is of adequate size. We note that the author’s arguments are supported by recent scientific findings. Generally, the arguments and findings of the authors are persuasive and the work eventually provides a significant understanding of the subject. To prove their point, it should be noted that these authors cited only studies that found results similar to their findings.

Kouadio and Gakpa (2022) studied the role of economic growth and institutional quality on inequality and poverty reduction in West Africa. They results show that economic growth remains a necessary condition for poverty reduction and that the overall improvement in the quality of institutions contributes significantly to reducing poverty and income inequality in the long term. Masduki et al. (2022) investigate and discuss the quality of government spending and then to link its effects to poverty for underdeveloped areas in Indonesia in Java. Their results indicate that the quality of government spending can reduce poverty levels. Dossou et al. (2021) investigate the moderating effect of governance quality on the relationship between tourism and poverty reduction using a panel of 15 Latin American countries over the period 2003–2015 using fixed effect (FE) as an estimation technique. They found little evidence that output growth reduced poverty. Jindra and Vaz (2019) examine the relationship between good governance and multidimensional poverty using hierarchical models and survey data for 71 countries. Their results suggest there is a direct effect of good governance on multidimensional poverty and that good governance is associated with reduced horizontal inequalities. However, they find evidence of a beneficial effect of good governance for middle-income countries but not for low-income countries. Thus, while their results suggest that good governance can play a role in reducing multidimensional poverty, they also suggest that governance reforms alone might not yield the desired effect for all countries. To achieve their objectives and to solve their research problems, these studies use the estimation techniques that is relatively more appropriate compared to the usual panel data methods namely: the Partial Least Squares Structural Equation Model PLS-SEM (Masduki et al., 2022), the Pool Mean Group PMG method (Kouadio & Gakpa, 2022), the Panel Corrected Standard Errors PCSE model estimation (Dossou et al., 2021), and hierarchical models (Jindra & Vaz, 2019). The sample sizes are appropriate and the results were interpreted and communicated effectively. The disadvantages of these studies are that contrary data is disregarded and some relevant information is ignored to prove the authors’ points.

Niaz Asadullah and Savoia (2018) assess whether the adoption of Millennium Development Goals (MDGs) and state capacity facilitated the reduction in income poverty during 1990–2013 for 89 developing economies. Their results show that headcount and gap measures decreased faster after 2000, suggesting MDGs adoption was instrumental to poverty reduction and that MDGs adoption does not seem to explain substantial variation in poverty reduction performance across countries. They find that countries with higher administrative capacity saw faster poverty reduction and were more likely to achieve the MDG target. Their findings provide empirical justification for the inclusion of good governance and effective institutions in the SDG. Kwon and Kim (2014) examine the policy logic that «good governance» leads to poverty reduction, which has been adopted by international agencies in pursuit of the Millennium Development Goals MDGs. This causal relationship is examined through an empirical panel-data estimation using Worldwide Governance Indicators and the poverty headcount ratio in 98 countries. The empirical evidence does not support the hypothesis that good governance leads to poverty reduction. They find that good governance alleviates poverty only in middle-income countries, not in the least developed ones. Their findings point to the necessity to devise policies that address poverty directly, rather than through indirect instruments, and highlight the urgent need to address structural inequality in developing countries. These two previous studies used relatively large samples, linear models and classical econometric techniques, but they are enough to address the issues in both studies. They used relatively large samples and they mentioned well-founded justifications to defend their findings. Their results are confirmed after performing a series of robustness checks. The authors’ most compelling thesis is that for developing countries, the variation in poverty reduction performance is indeed explained by the challenge of poor governance at the national level.

Perera and Lee (2013) analyzed the effects of economic growth and institutional quality on poverty and income inequality in nine developing countries of Asia for the period 1985–2009. Their results confirm that growth and improvement in the level of institutional quality lead to poverty reduction. They found that the improvements in government stability and law reduce poverty and the improvements in corruption, democratic accountability, and bureaucratic quality increase poverty. Khan (2009) confirms that while improvements in distribution are important, the long-run reduction of poverty can only be assured by sustainable growth. Tebaldi and Mohan (2010) study eight alternative measures of institutions and the instrumental variable method to examine the impacts of institutions on poverty. The estimates show that an economy with a robust system to control corruption, an effective government, and a stable political system will create the conditions to promote economic growth, minimize income distribution conflicts, and reduce poverty. The results revealed that corruption, ineffective governments, and political instability will not only hurt income levels through market inefficiencies, but also escalate poverty incidence via increased income inequality. The results also imply that the quality of the regulatory system, rule of law, voice and accountability, and expropriation risk is inversely related to poverty but their effect on poverty is via average income rather than income distribution. The authors have not ignored some relevant information to prove their points. The System Generalized Method of Moments (GMM) estimation method is used to analyze the data and solve the research question. They refer to the results of studies that contradict and those that are similar with their findings. The main persuasive thesis of these analyses is that an economy with a robust system of governance will create the conditions to promote economic growth, minimize income distribution conflicts, and reduce poverty.

Grindle (2004) asserts that the good governance agenda is unrealistically long and growing longer over time. He considers that among the multitude of governance reforms that “must bedone” to encourage development and reduce poverty, there is little guidance about what’s essential and what’s not, what should come first and what should follow, what can be achieved in the short term and what can only be achieved over the longer term, what is feasible and what is not. He concludes that if more attention is given to sorting out these questions, «good enough governance» may become a more realistic goal for many countries faced with the goal of reducing poverty. Growth effectiveness in reducing poverty, generally depends for each country on its initial level of development and the initial level of income inequalities. Indeed, authors (Epaulard, 2003; Grindle, 2004; Khan, 2007, 2009; Sachs et al., 2004) seem to suggest that the relationship between the quality of governance and poverty might depend on the countries’ stage of development. In other words, good governance or the implementation of government reforms might be of no use if a country’s general resources are too low to effectively translate government capabilities into positive outcomes in terms of poverty levels.

The aim of this research is to investigate the non-linear association between the economic growth, governance quality, and extreme poverty. The triangular relationship between economic growth, governance quality, and the extreme poverty rate for sub-Saharan African countries has not been studied before. Thus, to fill this gap, we suggest to study the potential threshold effects in the relationship between these three variables. Unlike previous investigations, we employ the PTR and PSTR models.

Methodology

Data descriptions

The empirical analysis is based on annual data of 490 observations for 49 Sub-Saharan African countries. The period of the study spans from 2010 to 2019. The choice of our variables was suggested by previous studies such as Soava et al. (2020); Wan et al. (2021); Fowowe and Shuaibu (2014); Eichsteller et al. (2021); Ravallion and Chen (1997); Dollar and Kraay (2002); Kaufmann et al. (2010); and Globerman and Shapiro (2003). The variables must correspond exactly to the problem and refer to the objective of the study. The methodology used so far to obtain governance indicators has been strongly criticized. That is why in this study the quality of governance is specified using two different governance measurements, namely governance quality is represented by the global governance index (GGI) and the Ibrahim Index of African Governance (IIAG).

GGI represents the level of authority exercised in a country (Kaufmann et al., 2005) and is measured by the average of the first component (estimate) of six indicators developed by Kaufmann et al. (2010). These measures are in contrast with those suggested by Globerman and Shapiro (2003) who aggregated the indicators. If this is applied for the selected countries, it might be found that the aggregate would exceed the range (− 2.5 to 2.5) used by Kauffman et al. (2005) as a measuring yardstick. The Mo Ibrahim Foundation defines governance as the provision of political, social and economic public goods and services that every citizen has the right to expect from their government, and that a government has the responsibility to deliver to its citizens. The IIAG assesses progress under four main conceptual categories: safety and rule of law, participation and human rights, sustainable economic opportunity, and human development. These four pillars are populated with data that cover governance elements ranging from infrastructure to freedom of expression and sanitation to property rights. The measures of GGI and IIAG of sub-Saharan African countries are reported in Table 1.

Table 1.

Measures of governance quality by country: the average of the study period 2010–2019

Countries	GGI	IIAG	Countries	GGI	IIAG
Angola	−0.993086	36.2	Liberia	−0.75816687	48.35
Benin	−0.30698198	58.32	Madagascar	−1.64141304	43.51
Botswana	0.647892	66.29	Malawi	−0.75365345	52.76
Burkina Faso	−0.42439653	54.93	Mali	−0.41067578	48.45
Burundi	−1.26422	39.31	Mauritania	−0.77817842	39.6
Cabo Verde	0.5178092	72.89	Mauritius	0.802980093	78.06
Cameroon	−0.9821931	44.55	Mozambique	−0.81846860	49.44
Central African Republic	−1.49393562	30.28	Namibia	0.316855872	64.12
Chad	−1.32888707	32.12	Niger	−0.68694335	48.11
Comoros	−0.87374417	45.77	Nigeria	−1.093163105	47.06
Congo. Dem. Rep	−1.60489152	37.51	Rwanda	−0.10622797	59.53
Congo. Rep	−1.07093651	37.51	Sao Tome and Principe	−0.303237647	58.85
Cote d'Ivoire	−0.75764237	50.16	Senegal	−0.155579769	62.1
Djibouti	−0.77886359	40.13	Seychelles	0.281543915	67.12
Equatorial Guinea	−1.31910497	28.75	Sierra Leone	−0.661372807	48.44
Eritrea	−1.53802399	26.35	Somalia	−2.183382633	16.39
Eswatini	−0.60461588	42.72	South Africa	0.203934173	66.47
Ethiopia	−0.9056807	42.77	South Sudan	−1.5927128	23.68
Gabon	−0.62581767	48.35	Sudan	−1.5927128	30.56
Gambia. The	−0.55997338	48.95	Tanzania	−0.45653212	53.02
Ghana	0.0548482	64.53	Togo	−0.810398653	48.57
Guinea	−1.03072039	42.11	Uganda	−0.58975776	51.56
Guinea−Bissau	−1.15763517	39.21	Zambia	−0.301217742	53.46
Kenya	−0.60997953	57.28	Zimbabwe	−1.2857059	42.9
Lesotho	−0.20301238	53.5

Source: authors calculations using data from the World Bank dataset

All variables are collected from the World Bank database (World Development Indicators WDI and Worldwide Governance Indicators WGI) and Mo Ibrahim Foundation. The endogenous variable used in this study is the extreme poverty rate.

It is widely accepted that poverty is a multidimensional phenomenon and that, therefore, the explanatory variables of poverty can be multiple. In sub-Saharan African countries, the poverty rate varies considerably as shown in Table 3. It is difficult to specify and delimit the variables that can reduce poverty. Thus, the explanatory variables are selected in accordance with robustness results highlighted in influential past studies and the state of development of sub-Saharan African countries.

Table 3.

Descriptive statistics

Variable	Obs	Mean	Std. Dev	Min	Max
EP	490	39.21592	22.29465	0.2	82.6
IIAG	490	47.80816	12.89757	13.5	79.5
GGI	490	−0.6958097	0.6458495	−2.31388	0.8539197
GDP	490	1.3014	5.612629	−47.59058	18.06597
UR	490	7.782796	6.578071	0.32	28.18
GI	490	43.4031	8.666985	4.9	65.9
FDI	490	5.005726	9.687814	−11.6248	103.3374
DI	490	22.88461	9.382864	2.458936	79.46179
AVA	490	20.34491	13.45406	1.053502	60.28355
Ln NODAR	490	19.54098	2.978748	0.0244089	22.38781

We introduced the variable agriculture, forestry, and fishing, value-added, due to the fact that according to the World Bank (2023) in sub-Saharan African countries more than 70% of people living in extreme poverty work in agriculture. These variables include economic growth, foreign direct investment, domestic investment, governance Index, unemployment rate, inequality, the added value of agriculture and official development assistance. To capture inequality, we use the Gini coefficient based on net inequality, which is calculated by taking into account taxes and transfers. The definitions, Mesures and sources of the variables are presented in Table 2.

Table 2.

Variable description

Variables	Symbol	Definition and measure	Source
Global Governance Index	GGI	Global Governance Index: measured as the average of six indicators: control of corruption, government effectiveness, political stability and absence of violence/terrorism, regulatory quality, rule of law, voice and accountability (Kaufmann, et al., 2005, 2010) (-2.5 = bad governance to 2.5 = good governance).	World Bank (WGI)
Ibrahim Index of African Governance	IIAG	The Ibrahim Index of African Governance (on a scale of 0–100) ($<50$:bad governance; $\ge 50$ good governance)	MoIbrahim Foundation
Extreme Poverty	EP	The World Bank defines “extreme poverty” as living on less than $1.90 per person per day. Extreme poverty is the poverty headcount ratio at $1.90 a day (2011 PPP) (% of population)	World Bank (WDI)
Unemploymen Rate	UR	The unemployment rate is the percent of the labor force (the labor force is the sum of the employed and unemployed) that is jobless The unemployment rate is calculated as: (Unemployed ÷ Labor Force) × 100.	World Bank (WDI)
Income inequality	GI	Income inequality is how unevenly income is distributed throughout a population. The less equal the distribution, the higher income inequality is. Income inequality is measured by Gini index (World Bank estimate): (on a scale of 0–100) (0 = inequality to 100 = equality)	World Bank (WDI)
Economic Growth	GDP	The annual GDP per capita growth rate (%) is calculated as the percentage change in the GDP per capita between two consecutive years.	World Bank (WDI)
Foreign Direct Investment	FDI	FDI net inflows are the value of inward direct investment made by non-resident investors in the reporting economy, including reinvested earnings and intra-company loans, net of repatriation of capital and repayment of loans. We used The net FDI inflow as a share of GDP (%)	World Bank (WDI)
Domestic Investment	DI	Domestic Investment is measured Gross capital formation (GCF) in % of GDP. Gross capital formation (formerly gross domestic investment) consists of outlays on additions to the fixed assets of the economy plus net changes in the level of inventories.	World Bank (WDI)
Neperian logarithm of Official Development Assistance	LnNODAR	Net official development assistance received (constant 2018 US$) is defined as government aid designed to promote the economic development and welfare of developing countries. Loans and credits for military purposes are excluded.	World Bank (WDI)
Agriculture Value Added	AVA	Agriculture, forestry, and fishing, value added (% of GDP). Value added is the net output of a sector after adding up all outputs and subtracting intermediate inputs. It is calculated without making deductions for depreciation of fabricated assets or depletion and degradation of natural resources.	World Bank (WDI)

Descriptive statistics are presented to reveal the main characteristics of the data used in this study. Table 3 synthesizes averages, standard deviations, as well as the minimal and the maximal values of dependant and explanatory variables. The data are from a balanced panel, including 490 observations spanning 2010–2019.

GGI of selected countries has an average value equal to−0.695 with minimum and maximum values of−2.313 and 0.853 respectively. It is worth mentioning that the minimum value of GGI is relative to Somalia in 2010 and the maximum value is relative to Mauritius, which recorded the highest score in 2015; that is 0.853. The difference between the average values of their GGI is not high over the sample period. With regard to IIAG, the average value for the sample is 47.8% with minimum and maximum values of 13.5% (Somalia in 2010) and 79.5% (Mauritius in 2017) respectively. Most sub-Saharan African countries are characterized by the poor quality of their institutions, which may not contribute to improving the growth of their economies and reducing the rate of extreme poverty.

With regard to GDP per capita growth rate, the average value for the sample is 1.30% with a minimum of−47.5% for South Sudan in 2012 and a maximum of 18.06% for Zimbabwe in 2010. The majority of the selected countries have GDP per capita growth values around the mean value of the entire sample. The EP registered on average a value of 39.21% with a maximum value of 82.6% relative to the Democratic Republic of the Congo in 2016 and a minimum value of 0.2% relative to Mauritius in 2017. Several sub-Saharan African countries suffer from a high rate of EP.

The FDI registered on average a value of 5.005%. The majority of selected countries suffer from low FDI, which is not expected to contribute to improving their economic growth. The DI represents on average 22.884% of the GDP of countries with a maximum value of 79.461% relative to the Republic of Congo in 2015 and a minimum value of 2.458% relative to South Sudan in 2019. The AVA and the LnNODAR registered on average a value of 20.344% and 19.540, respectively. Domestic investment and agriculture are an important component of GDP and are expected to favorably affect their socio-economic progress and reduce extreme poverty. Over the period 2010–2019, the UR and the GI are equal on average to 7.782% and 43.403% respectively, which are not expected to greatly contribute to reducing their extreme poverty. The descriptive statistics displayed in Table 3 therefore give some ideas about the characteristics of the sub-Saharan African countries which in fact have some socio-economic similarities and common development challenges.

Before proceeding to estimate the model, we should verify the existence of a multicollinearity problem in the data. Multicollinearity refers to a situation in which two or more explanatory variables in a multiple regression model are highly linearly related. A strong correlation leads to poor estimation of the coefficients.

We have perfect multicollinearity if the correlation between two independent variables is equal to 1 or−1. According to the limits traced by Kervin (1992), if the correlation coefficient is greater than 0.7 in the absolute value, we can confirm the existence of the multi-collinearity problem. Table 4 states the various correlation coefficients for the explanatory variables of economic growth. It appears, that the levels of correlation are very small and lower which justifies the absence of multicollinearity. According to the definition given in the paper for the Mo Ibrahim governance indicator IIAG, it is possible that governance implies an increase in public expenses (to offer social and economic public goods and services to every citizens). Since an increase in public expenses may induce an increase in GDP, we can suspect a certain correlation between governance and GDP growth. The correlation is relatively high between IIAG and GDP growth. So, we reinforce Table 4 with the VIF (variance inflation factor) multicollinearity test, which assesses how much the variance of an estimated regression coefficient increases if your predictors are correlated. If no factors are correlated, the VIFs will all be 1 (Dodge, 2008).

Table 4.

Correlation matrix for 49 sub-Saharan African countries (2010–2019)

Variable	IIAG	GGI	GDP	UR	GI	FDI	DI	AVA	Ln NODAR
IIAG / GGI	1.0000	1.000
GDP	−0.3203	0.0793	1.0000
UR	−0.0110	−0.0069	0.0455	1.0000
GI	−0.1038	0.1154	0.1305	−0.1315	1.0000
FDI	0.0032	−0.1223	−0.0101	0.0558	0.0172	1.0000
DI	−0.1001	−0.0471	−0.1389	0.0686	−0.0291	−0.2319	1.0000
AVA	0.1584	−0.0016	−0.0844	0.4944	0.1685	−0.0736	0.2139	1.0000
Ln NODAR	0.0395	0.0148	−0.0440	−0.1829	−0.1438	−0.0342	−0.1075	0.3159	1.0000

If the VIF is equal to 1, there is no multicollinearity among factors, but if the VIF is greater than 1, the predictors may be moderately correlated. A VIF between 5 and 10 indicates a high correlation that may be problematic. And if the VIF goes above 10, you can assume that the regression coefficients are poorly estimated due to multicollinearity. The output above in Table 5 shows that the VIF for the Publication and Years factors are about 1.26 for the model with GGI and 1.32 for the model with IIAG, which indicates some correlation, but not enough to be overly concerned about.

Table 5.

Variance Inflation Factor VIF

Variable	Model with GGI		Variable	Model with IIAG
	VIF	1/VIF		VIF	1/VIF
GGI	1.05	0.949962	IIAG	1.29	0.793753
UR	1.59	0.630503	UR	1.59	0.630700
AVA	1.19	0.840203	AVA	1.87	0.533840
DI	1.18	0.849056	DI	1.19	0.840506
GDP	1.08	0.929937	GDP	1.20	0.831434
Ln NODAR	1.12	0.890127	Ln NODAR	1.16	0.865201
FDI	1.10	0.908560	FDI	1.08	0.923532
GI	1.20	0.833955	GI	1.20	0.833643
Mean VIF	1.26		Mean VIF	1.32

Non-Linear Poverty Regression

In this section, we seek to highlight the threshold effect exerted by the quality of governance and economic growth on extreme poverty, from the estimation of threshold effects on panel data using brutal and smooth transition models. The methodology to be used must be appropriate to solve the research problem which is the following: what is the optimal level of governance quality, which once attained, will make extreme poverty decrease with economic growth in Sub-Saharan African countries? Hence, a threshold effect model appears to be the most appropriate to attain the overall objectives of the study. Most of the studies on threshold panel models refer to either the PTR (panel threshold regression) model proposed by Hansen (1999) or the PSTR (Panel Smooth Threshold Regression) model initiated by González et al. (2005). These are models that can highlight several regimes of a relationship between two or more variables. In the Hansen (1999) model, the transition from one regime to another is brutal. In the PSTR model, the transition from one regime to another is gradual (smooth) through a continuous transition function and not an indicator as in the PTR.

Panel Threshold Regression Model (PTR)

This study is based on the assumption that economic growth will impact extreme poverty in a nonlinear way for the optimal level of governance. We follow econometric techniques developed by Hansen (1999) to test for the existence of threshold effects in the growth-governance-poverty relationship. To attain the goal of this paper, the triangular relationship between extreme poverty, governance quality and economic growth for the sub-Saharan African countries is estimated through a PTR model proposed by Hansen (1999). The aim of the PTR model is to incorporate a certain threshold value as an unknown variable in the regression model, construct a piecewise function, and empirically test and estimate the corresponding threshold value and the effect of the threshold (Wang & Wang, 2021). The structural equation of the one-threshold model {$y_{\mathit{it}}$,$q_{\mathit{it}}$, $z_{\mathit{it}}$; $1\le \mathrm{i}\le \mathrm{N}$ and $1\le \mathrm{t}\le \mathrm{T}$} is:

$$y_{\mathit{it}}={\mu }_i+{\alpha }_i{x}_{\mathit{it}}+{\beta }_1^{\prime }{z}_{\mathit{it}}I\left(q_{\mathit{it}},\le ,\gamma \right)+{\beta }_2^{\prime }{z}_{\mathit{it}}I\left(q_{\mathit{it}},>,\gamma \right){+\epsilon }_{\mathit{it}}$$ 1

where i denotes the different countries in the analysis; t represents the year; $y_{\mathit{it}}$ denotes the dependent variable EP for country i in year t; $z_{\mathit{it}}$ denote explained variable (the annual gross domestic product GDP per capita growth rate);$x_{\mathit{it}}$ is a set of control variables such as the UR, the GI, the FDI, the DI, the NODAR and the AVA; ${\alpha }_i$ is the corresponding coefficient; ${\mu }_i$ is an unpredictable factor, reflecting the individual effects of the country; ${\epsilon }_{\mathit{it}}$ is the error term, which is assumed to be ${\epsilon }_{\mathit{it}}$∼ (0,${\mathrm{\sigma }}^2$).; $q_{\mathit{it}}$ is the threshold variables (GGI and IIAG); $\gamma$ is the threshold value; ${\beta }_1\mathrm{and}{\beta }_2$ denote the extents of impact of $z_{\mathit{it}}$ on $y_{\mathit{it}}$ for the cases of $q_{\mathit{it}}\le \gamma$ and$q_{\mathit{it}}>\gamma$, respectively. $I\left(.\right)$ are the indicator functions takes the value of 0 or 1 (Wang & Shao, 2019).

The indicator function, which equals 0 when $q_{\mathit{it}}$ is below the threshold parameter and 1 in the other case, generates an abrupt transition mechanism between two extreme regimes. The transition from one regime to another requires comparing the situation of a transition factor $q_{\mathit{it}}$ with respect to the value of a threshold $\gamma$. In another form, Eq. (1) equals to:

$$y_{\mathit{it}}=\left\{\begin{array}{c}{\mu }_i+{\beta }_1^{\prime }{z}_{\mathit{it}}{+{\alpha }_i{x}_{\mathit{it}}+\epsilon }_{\mathit{it}}{\mathrm{if}q}_{\mathit{it}}\le \gamma \\ {\mu }_i+{\beta }_2^{\prime }{z}_{\mathit{it}}{+{\alpha }_i{x}_{\mathit{it}}+\epsilon }_{\mathit{it}}{\mathrm{if}q}_{\mathit{it}}>\gamma \end{array}\right)$$ 2

Therefore, the formula of the single threshold regression model can be organized as follows (Lobont et al. (2022):

$${\mathit{EP}}_{\mathit{it}}=\left\{\begin{array}{c}{\mu }_i+{\beta }_1^{\prime }{\mathit{GDP}}_{\mathit{it}}{+{\alpha }_i{x}_{\mathit{it}}+\epsilon }_{\mathit{it}}{\mathrm{if}governance}_{\mathit{it}}\le \gamma \\ {\mu }_i+{\beta }_2^{\prime }{\mathit{GDP}}_{\mathit{it}}{+{\alpha }_i{x}_{\mathit{it}}+\epsilon }_{\mathit{it}}{\mathrm{if}governance}_{\mathit{it}}>\gamma \end{array}\right)$$ 3

$${\alpha }_{\mathrm{i}}={\alpha }_1,{\alpha }_2,{\alpha }_3,{\alpha }_4,{\alpha }_5{,\alpha }_6{\mathrm{x}}_{\mathrm{it}}={\mathrm{UR}}_{\mathrm{it}},{\mathrm{GI}}_{\mathrm{it}},{\mathrm{FDI}}_{\mathrm{it}},{\mathrm{DI}}_{\mathrm{it}},{\mathrm{NODAR}}_{\mathrm{it}},{\mathrm{AVA}}_{\mathrm{it}}$$

$${\mathrm{EP}}_{\mathrm{it}},{\mathrm{GDP}}_{\mathrm{it}},{\mathrm{x}}_{\mathrm{it}},{\mathrm{governance}}_{\mathrm{it}}({\mathrm{GGI}}_{\mathrm{it}}\mathrm{and}{\mathrm{IIAG}}_{\mathrm{it}}):1\le \mathrm{i}\le \mathrm{N}\mathrm{and}1\le \mathrm{t}\le \mathrm{T}\}$$

${\alpha }_1,{\alpha }_2,{\alpha }_3,{\alpha }_4,{\alpha }_5{,\alpha }_6$ are the estimated coefficients corresponding to the control variables${\mathrm{UR}}_{\mathrm{it}},{\mathrm{GI}}_{\mathrm{it}},{\mathrm{FDI}}_{\mathrm{it}},{\mathrm{DI}}_{\mathrm{it}},{\mathrm{NODAR}}_{\mathrm{it}},{\mathrm{AVA}}_{\mathrm{it}}$.

Panel Smooth Transition Regression Model (PSTR)

To detect the potential non-linear relationship between governance quality and extreme poverty, we apply the PSTR model with fixed individual effects developed by González et al. (2005) and further improved by Fouquau et al. (2009), who extended Hansen’s PTR model (1999). We estimate a PSTR model describing the governance quality with threshold of one or two extreme regimes and a single transition function to illustrate the relationship between governance quality and extreme poverty. The theoretical form of the PSTR model is presented as follows:

$$y_{\mathit{it}}={\mu }_i+{\alpha }_0^{\prime }{x}_{\mathit{it}}+{\alpha }_1^{\prime }{x}_{\mathit{it}}g\left(q_{\mathit{it}},,,\gamma ,,,c\right)+{\epsilon }_{\mathit{it}}$$ 4

where i and t denote respectively cross-section and time dimensions of the panel. ${\mathrm{y}}_{\mathrm{it}}$ represents the dependent variable, $x_{\mathit{it}}$ represents the independent variables (the vector of explanatory and control variables), ${\mathrm{\mu }}_{\mathrm{i}}$ indicates the fixed country effects and ${\mathrm{\epsilon }}_{\mathrm{it}}$ is the classical error terms. $q_{\mathit{it}}$ is a transition variable, γ is the transition parameter, c is the threshold parameter, and ${\alpha }_0^{\prime }$ and ${\alpha }_1^{\prime }$ are the regression coefficients. $g\left(q_{\mathit{it}},,,\gamma ,,,c\right)$ is the transition function.

This transition function of the PSTR model is a continuous function and is normalized to be bounded between 0 and 1. ${\alpha }_0^{\prime }$ and ${\alpha }_1^{\prime }$ indicate respectively the parameter vectors of linear and non-linear models. It allows the system to transit from one regime to another. In order for this function of transition to be operational, Granger and Teräsvirta (1993), Teräsvirta (1994), Jansen and Teräsvirta (1996) and González et al. (2005) proposed the following logistic transition function of order m:

$$g\left(q_{\mathit{it}},,,\gamma ,,,c\right)={\left(1,+,e,x,p,\left(-,\gamma ,{\prod }_{j=1}^m,\left(q_{\mathit{it}},-,c_j\right)\right)\right)}^{-1},$$ 5

With $\mathrm{c}={(\mathrm{c}}_1,\cdots {\mathrm{c}}_{\mathrm{j}},\cdots {\mathrm{c}}_{\mathrm{m}})$ is a vector of threshold parameters with ${\mathrm{c}}_1<{\mathrm{c}}_2<\cdots <{\mathrm{c}}_{\mathrm{m}}$ and $\gamma >0$, m is the number of threshold parameters. The slope parameter γ denotes the smoothness of the transition from one regime to the other. The parameter γ makes it possible to characterize the slope of the transition function. when $\gamma \to +\infty$, the function of transition $g\left(q_{\mathit{it}},,,\gamma ,,,c\right)$ tends to an indicator function $g\left(q_{\mathit{it}},,,c_j\right)$ which takes 1 if ${\mathrm{q}}_{\mathrm{it}}>{\mathrm{c}}_{\mathrm{j}}$. However, When $\gamma \to 0$, the transition function approaches a constant and the PSTR model becomes a homogenous linear panel with fixed effects. Ibarra and Trupkin (2011) showed that if $\gamma$ is very high, the PSTR model can be confused with a two-regime model (or one threshold). Given this function of transition $g\left(q_{\mathit{it}},,,\gamma ,,,c\right)$, Eq. (4) can be written as follows:

$$y_{\mathit{it}}={\mu }_i+{\alpha }_0^{\prime }{x}_{\mathit{it}}+\sum _{j=1}^m{\alpha }_j^{\prime }{x}_{\mathit{it}}g\left(q_{\mathit{ij}}^j,,,{\gamma }_j,,,c_j\right)+{\epsilon }_{\mathit{it}}$$ 6

where ${\mathrm{c}}_{\mathrm{j}}=\left({\mathrm{c}}_1,,,.,.,,,{\mathrm{c}}_{\mathrm{m}}\right){}^{\prime }$ which is an $\mathrm{m}$-dimensional vector of parameters that includes the threshold parameters; the slope parameter $\mathrm{\gamma }$ determines the smoothness of the transition. Two transition variables are considered $:GGI$ and$\mathrm{IIAG}$. They are normalized to be bounded between−2.5 and 2.5 for $\mathrm{GGI}$ and 0 and 100 for$\mathrm{IIAG}$, and these extreme values are associated with regression coefficients ${\alpha }_0$ and (${\alpha }_0+{\alpha }_1$). For$\mathrm{m}=1$, the model has the two extreme regimes separating low and high values of the $\mathrm{governance}\mathrm{index}$ with a single monotonic transition of the coefficients from ${\alpha }_0$ to (${\alpha }_0+{\alpha }_1$) as the $\mathrm{governance}\mathrm{index}$ increases.

The PSTR model which can be written as follows:

$${\mathit{EP}}_{\mathit{it}}={\mu }_i+{\alpha }_0^{\prime }{x}_{\mathit{it}}+{\alpha }_1^{\prime }{x}_{\mathit{it}}g\left({\mathit{governance}}_{\mathit{it}},,,\gamma ,,,c\right)+{\epsilon }_{\mathit{it}}$$ 7

where i refers to country (i = 1,.., 49) and t represents time period in years (t = 2010,.., 2019).${\mu }_i$,${\epsilon }_{\mathit{it}}$, ${\alpha }_0^{\prime }$ and ${\alpha }_1$ keep the same definitions mentioned above. EP is extreme poverty which represents the dependent variable. $g\left({\mathit{governance}}_{\mathit{it}},,,\gamma ,,,c\right)$ represents the function of transition. $x_{\mathit{it}}=x_{it,}^1,..,x_{\mathit{it}}^8$ is a vector of eight independent variables divided as follows:

• One variable of transition which is the governance which is measured by GGI and IIAG

• Five explanatory variables which are, the FDI, the DI, the annual GDP per capita growth rate GDP, the UR and the GI.

• Two control variables which are net official development assistance received “NODAR” and Agriculture, forestry, and fishing, value added “AVA.”

For a higher value of governance index, the transition becomes rougher and the two transitions functions $\mathrm{g}\left({\mathrm{GGI}}_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)$ and $\mathrm{g}\left({\mathrm{IIAG}}_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)$ become the indicator functions. When tends towards infinite, the two indicator functions $\mathrm{g}\left({\mathrm{GGI}}_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)$ and $\mathrm{g}\left({\mathrm{IIAG}}_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)$ are equal to unity if event $\mathrm{governance}\mathrm{index}>c$ occurs, and indicator functions $\mathrm{g}\left({\mathrm{GGI}}_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)$ and $\mathrm{g}\left({\mathrm{IIAG}}_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)$ otherwise. When are close to 0, the two transition functions $\mathrm{g}\left({\mathrm{GGI}}_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)=1$ and $\mathrm{g}\left({\mathrm{IIAG}}_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)=1$ are constant. In that case, the PSTR converges towards the two-regime PTR of Hansen (1999). In general, for any value of $\mathrm{m}$, the two transition functions $\mathrm{g}\left({\mathrm{GGI}}_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)$ and $\mathrm{g}\left({\mathrm{IIAG}}_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)$ are constant when they are close to -2.5 and 0 respectively. In which case, the model in Eq. (1) becomes a linear panel regression model with fixed effects.

Replacing the vector $x_{\mathit{it}}$ with its eight components, we get the empirical model to be estimated which is presented as follows:

$$\begin{array}{cc}\hfill {\mathrm{EP}}_{\mathrm{it}}={\mu }_{\mathrm{i}}& +{\alpha }_0^0{\mathrm{governance}}_{\mathrm{it}}+{\alpha }_1^0{\mathrm{DI}}_{\mathrm{it}}{+\alpha }_2^0{\mathrm{FDI}}_{\mathrm{it}}\hfill \\ \hfill & +{\alpha }_3^0{\mathrm{UR}}_{\mathrm{it}}{+\alpha }_4^0{\mathrm{GI}}_{\mathrm{it}}{+\alpha }_5^0{\mathrm{AVA}}_{\mathrm{it}}{+\alpha }_6^0{\mathrm{NODAR}}_{\mathrm{it}}{+\alpha }_7^0{\mathrm{GDP}}_{\mathrm{it}}\hfill \\ \hfill & +\left[{\alpha }_0^1,{\mathrm{governance}}_{\mathrm{it}},+,{\alpha }_1^1,{\mathrm{DI}}_{\mathrm{it}},{+\alpha }_2^1,{\mathrm{FDI}}_{\mathrm{it}},{+\alpha }_3^1,{\mathrm{UR}}_{\mathrm{it}},{+\alpha }_4^1,{\mathrm{GI}}_{\mathrm{it}}\right)\hfill \\ \hfill & \left(,+,{\alpha }_5^1,{\mathrm{AVA}}_{\mathrm{it}},{+\alpha }_6^1,{\mathrm{NODAR}}_{\mathrm{it}},{+\alpha }_7^1,{\mathrm{GDP}}_{\mathrm{it}}\right]\mathrm{g}\left(q_{\mathrm{it}},,,\gamma ,,,\mathrm{c}\right)+{\epsilon }_{\mathrm{it}}\hfill \end{array}$$ 8

With governance is measured by GGI and IIAG.

The econometric approach is based on four steps. In the first one, the stationarity of each variable is examined by performing unit roots tests. In the second one, we test both the linearity against the PSTR and PTR models and the number of transition function. In the third one, we apply the non-linear least squares methods to estimate our PSTR and PTR models. Finlay, we apply Arellano and Bover (1995) and Blundell and Bond (1998) System-GMM as a robustness check of the PSTR estimates.

Results and Discussion

Empircal Tests

As noted in González et al. (2017), before estimating Eq. (7), there are three crucial tests that need to be undertaken, which are (1) testing the stationarity of each variable, (2) testing for the sequence for selecting the order m of the transition function and (3) testing for no remaining non-linearity.

Stationary tests

Before proceeding further with the estimation of the model, the first step of the estimation process consists of examining the data properties of all the series in terms of stationarity. In fact, two generations of unit root tests exist for the panel data: the first generation admits the presence of cross-sectional independence and the second generation acknowledges the existence of cross-sectional dependence. The first generation includes the panel unit root tests of Levin et al. (2002), Im et al. (2003), Breitung (2001), Fisher-type (Fisher, 1992), Harris and Tzavalis (1999) and Maddala and Wu (1999), whereas the second includes Pesaran (2007); Moon and Perron (2004), Smith et al. (2004) and Carrion-i-Silvestre et al. (2005). Nevertheless, Panel unit root tests of the first-generation may possibly lead to erroneous and incorrect results because of the presence of size distortions if significant levels of positive residual cross-section dependence exist and if it is not taken into consideration (Banerjee et al., 2005; Maddala & Wu, 1999; O'Connell, 1998). Hence, the cross-sectional dependence in a panel study is crucial to select the appropriate estimator. To explore the presence of a cross-sectional dependence, we performed the diagnostic test suggested by Pesaran (2007) for cross-sectional dependence. Results of the stationarity tests of the first and second generation are collated in Table 6.

Table 6.

Panel-data unit-root tests

Variable	First generation tests						Second generation tests
	Levin-Lin-Chu	Harris-Tzavalis	Breitung	Im-Pesaran-Shin	Fisher-type	Maddala and Wu (1999)	Panel Unit Root test (CIPS)
	Level					Lags	Lags
EP	−3.212 (0.000)***	0.402 (0.000)***	−3.099 (0.000)***	−2.415 (0.000)***	−6.766 (0.000)***	0 (0.000)***	0 (0.000)***
GGI	−6.381 (0.000)***	0.753 (0.000)***	1.941 (0.000)***	−2.005 (0.005)***	−7.661 (0.000)***	0 0.003***	0 (0.000)***
IIAG	−5.950 (0.000)***	0.809 (0.000)***	1.341 (0.000)***	−1.125 (0.000)***	−6.9925 (0.000)***	0 0.009***	0 (0.002)***
GDP	−13.801 (0.000)***	−0.018 (0.000)***	−3.906 (0.000)***	−2.304 (0.000)***	−6.443 (0.000)***	0 0.000***	0 (0.008)***
UR	−20.860 (0.000)***	0.490 (0.000)***	0.878 (0.000)	−3.327 (0.000)***	−3.0010 (0.000)***	0 0.087*	0 (0.000)***
GI	−2.524 (0.005)***	0.654 (0.0316)**	2.636 (0.000)***	−6.329 (0.000)***	−2.232 (0.012)**	0 0.000***	0 (0.000)***
FDI	−12.879 (0.000)***	0.5540 (0.0000)***	−3.232 (0.000)***	−2.631 (0.000)***	−9.210 (0.000)***	0 0.000***	0 (0.000)***
DI	−21.769 (0.000)***	0.6005 (0.0006)***	−0.215 (0.000)***	−1.928 (0.006)***	−1.72 (0.042)**	0 0.034**	0 (0.000)***
AVA	−3.606 (0.000)***	0.443 (0.000)***	1.379 (0.000)***	−2.004 (0.0044)***	−7.24 (0.000)***	0 0.008***	0 (0.001)***
Ln NODAR	−10.728 (0.000)***	0.0109 (0.0000)***	−6.208 (0.000)***	−2.517 (0.000)***	−8.316 (0.000)***	0 0.005***	0 (0.000)***

p-value in parenthesis: *p < 0.1; **p < 0.05; *** p < 0.01

Stationarity performed tests lead to the same results for all the variables. The results reject the null hypothesis of non-stationary which indicates that all the variables are stationary in level. However, the first-generation tests (LLC test, IPS test, ADF test, Fisher-PP test, Breitung test and Harris-Tzavalis and Maddala and Wu (1999)) show signs of weakness in the presence of correlation between the individuals composing the panel. New second-generation tests were, then, put in place to remedy the weakness of the first-generation tests. Among these tests, we use the Pesaran unit root test (2007).

Pesaran (2007) proposed a cross-sectional augmented version of the IPS-test of Im et al. (2003) that supposes independence across units. This is motivated by the fact that the time series is found to be simultaneously interrelated in many macroeconomic applications, considering regional or country data Christidou and Panagiotidis (2010) and Pesaran (2007) reexamined the hypothesis of cross-sectional independence and proposed a single-factor model that takes into account residuals for their heterogeneous loading actors and recommended augmenting the conventional ADF specification with the transverse averages of the lagged levels and the first differences of the individual variables. The following regression represents the cross-sectional augmented ADF $(CADF)$:

$${\mathrm{\Delta }Y}_{\mathit{it}}={\pi }_i+{\beta }_i{Y}_{i,t-1}+{\omega }_i{\overline{Y}}_{t-1}+{\phi }_i\mathrm{\Delta }{\overline{Y}}_t+{\epsilon }_{\mathit{it}}$$

where ${\overline{Y}}_t=\left(\frac{1}{N}\right){\sum }_{i=1}^N{Y}_{\mathit{it}}$, ${\mathrm{\Delta }\overline{Y}}_t=\left(\frac{1}{N}\right){\sum }_{i=1}^N{\mathrm{\Delta }Y}_{\mathit{it}}$ and ${\epsilon }_{\mathit{it}}$ is the regression error. The Pesaran (2007) panel unit root test is based on the average of the individual ADF statistics augmented in the cross-section. Pesaran (2007) constructed a modified version of the IPS-test as follows:

$$CIPS=\left(\frac{1}{N}\right)\sum _{i=1}^N{\mathit{CADF}}_i$$

where ${\mathit{CADF}}_i$ represents the cross-sectionally augmented Dickey-Fuller statistic for the i-the cross-sectional unit given by the t-ratio of ${\beta }_i$ in the $\mathit{CADF}$ equation.2 The CIPS critical values were simulated by Pesaran for different sample sizes. Due to the presence of a common factor, ${\mathit{CADF}}_i$ statistics will not be independent in cross section. As a result, a central limit theory cannot be performed to obtain the limit distribution of the $\mathit{CIPS}$ statistic, and it turns out to be non-standard even for a large N. Furthermore, in order to ensure the existence of moments for the distribution of ${\mathit{CADF}}_i$ in finished samples, Pesaran (2007) used a condensed version of $\mathit{CIPS}$ test, where, for positive constants $K_1$ and $K_2$ such that $Pr\left[-,k_1,<,{\mathit{CADF}}_i,<,k_1\right]$ is satisfactorily large. Values of ${\mathit{CADF}}_i$ smaller than -K₁ or greater that K₂ are substituted by the respective terminals. Finally, Pesaran (2007) presents the values of $K_1$ and $K_2$, which are obtained by simulations.

From the results of the Pesaran test (2007) presented in Table 6, we accept the hypothesis of dependence between the individuals composing the panel (in the form of an unobserved common factor). These findings confirm the results of the first-generation unit root tests. They, too, validate the hypothesis of stationarity of these ten variables in level.

Linearity Tests

In PSTR, at the first step, the linear test is performed. This test examined whether the relationship between the variables is captured by the linear model, the standard panel model with fixed effects or by the non-linear model, the PSTR model.

The goal is to demonstrate that the relation between governance quality and economic grow this non-linear. To this point, we conduct a test of linearity against the PSTR model. The null hypothesis is $H_0:{\alpha }^1=0$ against the alternative $H_0:{\alpha }^1\ne 0$. However, this test is not standard since under the null hypothesis, the PSTR model contains nuisance unidentified parameters (Hansen, 1996). To solve this problem, as suggested by Luukkonen et al. (1988), we replace the transition function by its first-order Taylor around$\gamma =0$. The null hypothesis becomes$H_0:{\alpha }^1=0$. After rewriting, we obtain the following regression:

$${\mathrm{EP}}_{\mathrm{it}}={\mathrm{\mu }}_{\mathrm{i}}+{\alpha }_0^{\ast 0}{\mathrm{DI}}_{\mathrm{it}}{+\alpha }_1^{\ast 0}{\mathrm{FDI}}_{\mathrm{it}}+{\alpha }_2^{\ast 0}{\mathrm{UR}}_{\mathrm{it}}{+\alpha }_3^{\ast 0}{\mathrm{GI}}_{\mathrm{it}}{+\alpha }_4^{\ast 0}{\mathrm{AVA}}_{\mathrm{it}}{+\alpha }_5^{\ast 0}{\mathrm{LnNODAR}}_{\mathrm{it}}{+\alpha }_6^0{\mathrm{GDP}}_{\mathrm{it}}+\left[{\alpha }_0^{\ast 1},{\mathrm{DI}}_{\mathrm{it}},{+\alpha }_1^{\ast 1},{\mathrm{FDI}}_{\mathrm{it}},{+\alpha }_2^{\ast 1},{\mathrm{UR}}_{\mathrm{it}},{+\alpha }_3^{\ast 1},{\mathrm{GI}}_{\mathrm{it}},{+\alpha }_4^{\ast 1},{\mathrm{AVA}}_{\mathrm{it}},{+\alpha }_5^{\ast 1},{\mathrm{LnNODAR}}_{\mathrm{it}},{+\alpha }_6^{\ast 1},{\mathrm{GDP}}_{\mathrm{it}}\right]\mathrm{g}\left(q_{\mathrm{it}},,,\mathrm{\gamma },,,\mathrm{c}\right)+{\mathrm{\epsilon }}_{\mathrm{it}}$$

where the vectors of parameter ${\alpha }^{\ast 1},..,{\alpha }^{\ast m}$ are multiples of $\mathrm{\gamma }$ and ${\epsilon }_{\mathit{it}}^{\ast }$ is ${\epsilon }_{\mathit{it}}$ plus the residue of Taylors development. The null hypothesis of the linearity test becomes $H_0:{\alpha }^{\ast 1}=,..,={\alpha }^{\ast m}$= 0. The linearity is tested with standard tests. We use Wald test expressed as follows:

$${WaldLMtest=LM}_{\omega }=\frac{NT({\mathit{SSR}}_0{-SSR}_1)}{{\mathit{SSR}}_0}$$

where ${\mathit{SSR}}_0$ and ${\mathit{SSR}}_1$ are the panel sum of square residuals under $H_0$ (linear panel model with individual effects) and the panel sum of square residual under $H_1$ (PSTR model with m regimes) respectively. For small sample, González et al. (2005) suggest to use the Fisher test defined as:

$${FischerLMtest=LM}_F=\frac{NT({\mathit{SSR}}_0{-SSR}_1)/mk}{{\mathit{SSR}}_0/TN-N-mk}$$

$$Likelihoodratiotest=-2\left[L,o,g,\left({\mathit{SSR}}_1\right),-,L,o,g,({\mathit{SSR}}_0)\right]$$

With k the number of explanatory variables. ${\mathit{LM}}_F$ follows a Fisher distribution with $\mathit{mk}$ and $TN-N-mk$ degrees of freedom $\left(F,\left(m,k,,,T,N,-,N,-,m,k\right)\right).$ All these linearity tests are distributed $X^2(k)$ under the null hypothesis.

Results of linearity tests are reported in Table 7. From this table it can be noted that the hypothesis of linearity of the model is rejected at 1% significance level. Moreover, rejection of linearity is stronger for m = 2, the exponent specification (m = 2) is preferred to logistic one (m = 1). The results imply that there exists non-linear relationship between governance quality (GGI/IIAG) and EP in the sub-Saharan African countries. This implies that the non-linear association between the governance quality and EP can be analyzed by the PSTR model.

Table 7.

Linearity tests

Variables	m = 1		m = 2
	Statistic	p-value	Statistic	p-value
Transition variable ${\mathbf{G}\mathbf{G}\mathbf{I}}_{\mathbf{i}\mathbf{t}}$
Lagrange multiplier (${\mathbf{L}\mathbf{M}}_{\mathbf{W}}$)	31.1806	0.0000***	54.36125	0.0000***
Fisher Test (${\mathbf{L}\mathbf{M}}_{\mathbf{F}}$)	9.5048	0.0000***	10.0451	0.0000***
Likelihood-ratio test $\left(\mathbf{L},\mathbf{R}\right)$	31.1078	0.0000***	57.2354	0.0000***
Transition variable ${\mathbf{I}\mathbf{I}\mathbf{A}\mathbf{G}}_{\mathbf{i}\mathbf{t}}$
Lagrange multiplier (${\mathbf{L}\mathbf{M}}_{\mathbf{W}}$)	45.2387	0.0000***	73.37383	0.0000***
Fisher Test (${\mathbf{L}\mathbf{M}}_{\mathbf{F}}$)	16.3185	0.0000***	18.3278	0.0000***
Likelihood-ratio test $\left(\mathbf{L},\mathbf{R}\right)$	41.9238	0.0000***	58.0299	0.0000***

*p < 0.1; **p < 0.05; ***p < 0.01

The Number of Regimes Test

After the confirmation of non-linearity, the second step is to measure the number of regimes. To ensure this, no remaining non-linearity test is performed. The test of the number of regimes consists to verify the null hypothesis for which the PSTR model has a single transition function $\left(1,=,m\right)$ against the alternative hypothesis that the PSTR model has at least two transition functions $\left(2,=,m\right)$. The decision of the test relies on the statistics of $\mathit{LR}$ and ${\mathit{LM}}_F$. If the coefficients are statistically significant at the critical level of 1%, we reject the null hypothesis and we conclude that there exist at least two transition functions. Otherwise, we do not reject the null hypothesis and we conclude that the model has two regimes and therefore has one threshold. Results from Table 8 indicate that both hypotheses without threshold $\left(r,=,1\right)$ and with at least two thresholds $\left(r,=,2\right)$ are rejected at the 1% significance for the two tests. This means that in the context of the sub-Saharan African countries, the relationship between governance quality and extreme poverty has only one threshold or two regimes (the PSTR with one transition or two regimes).

Table 8.

Tests for no remaining non-linearity

Variables	$r=1$		$r=2$
	Statistic	P-value	Statistic	P-value
Transition variable ${\mathrm{GGI}}_{\mathrm{it}}$
Fisher Test (${\mathrm{LM}}_{\mathrm{F}}$)	44.520	0.000***	60.190	0.000***
Likelihood-ratio test $\left(\mathrm{LR}\right)$	9.459	0.000***	7. 539	0.000***
Transition variable ${\mathrm{IIAG}}_{\mathrm{it}}$
Likelihood-ratio test $\left(\mathrm{LR}\right)$	66.392	0.000***	78.972	0.000***
Likelihood-ratio test $\left(\mathrm{LR}\right)$	16.447	0.000***	12.778	0.000***

* p < 01; **p < 0.05; ***p < 0.01

PTR and PSTR Estimation Results.

When giving the evidence of non-linearity, we estimate the threshold regression by applying non-linear least squares techniques developed by Hansen (2000). The results of the PTR and PSTR estimations are reported in Table 9.

Table 9.

Regression estimates

Variables	PTR model estimation		Variables	PSTR model estimation
	GGI	IIAG		GGI		IIAG
				${\alpha }_0$ (Lower)	${\alpha }_1$ (Upper)	${\alpha }_0$ (Lower)	${\alpha }_1$ (Upper)
DI	−0.238 (1.18)	−0.291 (1.25)	DI	−0.095 (1.05)	−0.217 (0.96)	−0.116 (0.92)	−0.191 (1.37)
FDI	−0.148 (0.90)	−0.091 (0.20)	FDI	−0.120 (1.39)	−0.194 (2.70)*	−0.116 (1.52)	−0.135 (2.85)***
UR	0.046 (1.78)*	0.073 (1.91)*	UR	0.029 (1.84)*	0.003 (1.95)*	0.103 (1.67)*	0.040 (1.90)*
GI	0.170 (2.29)**	0.142 (1.83)*	GI	0.328 (4.00)***	0.218 (3.98)***	0.266 (4.38)***	0.245 (2.76)***
AVA	−0.049 (1.94)*	−0.003 (1.81)*	AVA	−0.019 (1.32)	−0.032 (1.92)*	−0.034 (1.13)	−0.067 (2.03)**
LnNODAR	−0.021 (1.86)*	−0.028 (1.95)*	NODAR	−0.014 (1.05)	−0.057 (1.75)*	−0.015 (1.32)	−0.081 (1.68)*
${\widehat{\mathrm{\beta }}}_1$	0.464 (0.29)	3.071 (0.85)	GDP	−0.008 (0.53)	−0.077 (1.95)*	−0.005 (0.44)	−0.079 (1.92)*
${\widehat{\mathrm{\beta }}}_2$	-5.147 (5.09)***	-3.422 (3.94)***
Transition parameters
Threshold	0.367	63.2	c	0.314		66.9
			Slope (γ)	0.126		0.675
			AIC	2.810		2.690
			BIC	2.772		2.728

*p< 0,1; **p< 0,05; ***p< 0,01. (t-statistic are in parenthesis)

According to Ibarra and Trupkin (2011), when γ is very high, we choose the PTR model. However, when γ is very weak, the PSTR is the most appropriate model. The results show that the estimated value of γ is very weak 0.126 for GGI and 0.675 for IIAG, which means that PSTR is more appropriate than PTR. But we notice that the thresholds of the two methods PTR and PSTR are very close and the results of the two estimations evolve in the same direction, that is why we consider the results of the two methods PTR and PSTR.

Columns (2) and (3) of Table 9 report least squares coefficient estimates from Eq. (3) where GGI and IIAG governance indices are used as the threshold variables, respectively. When columns (4)–(6) and (5)–(7) present least squares coefficient estimates from Eq. (6) with GGI and IIAG governance indices used as the threshold variables and corresponding to lower and upper regimes, respectively.

The estimates of the coefficients in the PTR model have the same sign in both estimations. It should be noted that GDP, FDI, DI, GGI and IIAG, UR, GI, AVA, and NODAR display coefficients corresponding to our expectations.

However, there is a strong positive relationship between UR and EP. The coefficient value of GI is statistically significant and positive for regressions over the two threshold variables. Extreme poverty in sub-Saharan Africa is therefore increasing under the effect of inequality and high levels of unemployment. Added to this is an exploitation of wealth that does not benefit the majority of Africans. The structural deterioration of the labor market (precariousness and low wages in particular) weighs in particular on the standard of living of the poor. These findings consistent with the literature on poverty, which suggests that a decrease of unemployment and inequality reduction can support poverty alleviation. Also, this result is similar to the results presented by Soava et al. (2020), Kiaušienė (2015) and Danson et al. (2021), who found that, unemployment is one of the main reasons of poverty, whereas high inequality levels aggravate poverty. Certain practical solutions will make it possible to reduce unemployment considerably: Appropriate training, promotion of apprenticeship, promotion of jobs for the future, encouragement for the creation of businesses by young people. The main recommendations in favor of equality are the following:

• A better distribution of human capital, which encourages public authorities to assume a greater role in the provision of services with a view to building a more just society.

• Increased direct taxation and the efficiency of tax administration, as well as increased well-targeted social spending that reduced inequality.

Moreover, It was found that the threshold level of governance for the negative relationship in the poverty-growth nexus is about 0.367 for GGI and 63.2 for the IIAG. The regression slope estimates in the TAR model indicate the effect of economic growth in the two regimes: when GGI ≤ 0.367 and IIAG ≤ 63.2, the positive coefficients of 0.464 and 3.071 suggest that economic growth is positively related to extreme poverty. When GGI > 0.3670 and IIAG > 63.2, the negative and significant coefficient of -5.147 and -3.422 implies a negative relationship between economic growth and poverty extreme. According to Table 1, with GGI threshold values, 46 countries have a smaller value and 3 countries have a larger value and with IIAG threshold values, 42 countries have a smaller value and 7 countries have a larger value. As long as these two thresholds are not achieved, economic growth has no role to play in the nexus, and the benefit of economic growth to extreme poverty reduction will either decline or disappear. The level of GDP is still by far the most important determinant of poverty. Our result, which confirms the existence of an optimal threshold level of governance quality which, once attained, will make extreme poverty decrease with economic growth, is expected. Therefore, the level of governance quality influences the expected impacts of economic growth on the poverty rate in sub-Saharan African countries. The findings are, indeed, in line with the results presented by Ochi et al. (2023), Lin et al. (2022), Mirza et al. (2021), Adeleye et al. (2020), Wan et al. (2021), Marrero and Serven (2018) and Škare and Družeta (2016), who conclude that economic growth relieves poverty. Moreover, high inequality and bad governance dampens the positive effect of economic growth on poverty reduction. An economy with a robust system of governance will create the necessary conditions to promote economic growth, minimize income inequality, and reduce extreme poverty in sub-Saharan African countries. So we can conclude that good governance can be the solution to several problems of the African continent. For this reason, we propose the following recommendations that can help improve governance in the countries of sub-Saharan Africa:

• Ensure sound management of public resources at national and sub-national levels to achieve macroeconomic stability.

• Promote structural transformation by fostering a competitive private sector and fair conditions of competition for all businesses.

• Increase transparency, accountability and inclusion in decision-making and service delivery.

• Fight against corruption in the public and private sectors. promote respect for the rule of law and human rights.

• Consolidate peace, security and good governance.

Results show also that there is no significant impact of DI and FDI on the extreme poverty rate. Possibilities exist for investment to have no effect on poverty reduction. This result is unexpected because at the theoretical level, economic growth, which is a key factor in poverty reduction, can be stimulated by FDI through two basic processes either directly via the increase in the stock of physical capital in the host country or indirectly via productivity externalities between foreign and domestic firms through the transfer of technology and knowledge, the development of human capital, the stimulation of domestic investment and export promotion. Our findings regarding the relationship between investment and poverty reduction are similar to the Lewis model which is one of the oldest theories of development, where investment in the early stages of development, leads workers to move from agriculture to manufacturing. However, the additional production translates into profits for investors rather than into higher wages for workers, thus having little impact on poverty. This result is not consistent with the literature on poverty, which suggests that higher rates of investment are associated with a more rapid reduction in the share of the population living in extreme poverty. Our results are in opposition to those obtained by Topalli et al. (2021), Meyer (2004), such as Fowowe and Shuaibu (2014), Gohou and Soumaré (2012), Sharma and Gani (2004), who show that higher rates of investment are associated with faster poverty reduction. This result leads us to ask a new research question that emerged from our analysis: what is the optimal level of governance quality, which once attained, will make economic growth increase with FDI in sub-Saharan African countries?

Moreover, findings indicate that an increase of AVA decreases the extreme poverty rate in the sub-Saharan African countries. These results were expected. In the development community, it is now widely accepted that the establishment of productive agriculture is crucial for employment creation and poverty reduction. According to the International Fund for Agricultural Development (IFAD annual report, 2020), 70% of the poor live in rural areas, which is why growth in agriculture remains more poverty-reducing than growth elsewhere. So, the poorest benefit most from agricultural growth. Our findings are similar to the results presented by Maisonnave and Mamboundou (2022), Eichsteller et al. (2021), Etuk and Ayuk (2021), Bodenstein and Kemmerling (2015), Ravallion and Chen (1997), Demery and Squire (1995), Ravallion (2001), Dollar and Kraay (2002) and (Adams, 2004), who found that, agriculture contributes to poverty reduction. Investments in the agricultural sector, an essential factor for the reduction of poverty in the sub-Saharan Africa. To reduce poverty in rural areas, we propose that agriculture must be transformed into a profitable commercial activity. The majority of the poor depend on agriculture for their livelihoods, and therefore their productivity and incomes need to be improved. The majority are smallholders who cannot afford to engage in commercial farming. The productivity of the agricultural, livestock and fisheries sectors must be increased by developing and disseminating efficient production technologies and distribution systems to eradicate rural poverty and promote economic growth.

Furthermore, the results reveal that an increase of NODAR decreases the extreme poverty rate in the sub-Saharan African countries. NODAR is a key poverty reduction tool. Sub-Saharan Africa receives more official development assistance than any other region to promote private sector development, which plays a crucial role in the development process. Official development assistance is one of the strategies that aims to promote economic growth in in developing countries and thus contributing to poverty reduction. Our findings are similar to the results presented by Doucouliagos and Paldam (2008), Burnside and Dollar (2000), Fiodendji and Evlo (2013), Stiglitz (2002) and Sachs (2005) who found that, official development assistance contributes to economic growth and poverty reduction. Moreover, contemporary studies on aid effectiveness in the context of Sub-Saharan Africa, the analyzes of Arndt et al. (2010), Dreher and Langlotz (2020), Aboubacar et al. (2015) and Civelli et al. (2017) come to the same conclusion regarding the positive effect of aid on economic growth. In contrast to our result, which promotes aid effectiveness, Moyo (2009) and Mbah and Amassoma (2014) point out that aid has a negative effect on the growth of developing countries in that it encourages mismanagement and only benefits a certain oligarchy in developing countries at the expense of the people and subsequently does not reduce poverty. Somalia was cited as an example. Based on our empirical results, it is recommended to increase the volume of aid to sub-Saharan African countries that aspire to achieve the Sustainable Development Goals (SDGs). In addition, transparency in the management of aid in these countries should be improved. These two recommendations challenge both the donor organizations or countries and the beneficiary countries in their National Information Management Systemson on Aid, which should establish an annual evaluation of the performance of aid mechanisms and, above all, mobilize public opinion on the subject of aid effectiveness. Moreover, international aid is an external resource that combines volatility and uncertainty. This is why questions are constantly being asked about its future. Thus, future studies would benefit from analyzing the impacts that a shock to international aid would have on recipient economies such as those in sub-Saharan Africa and the adjustment mechanisms that they could formulate to withstand an external shock of such a nature.

For PSTR model, the estimated threshold for the quality of governance is 0.314 for GGI and 66.9 for IIAG and the speed of transition is quite fast γ = 0.126 and 0.675 respectively. The results show that, the impact of all explanatory variables on extreme poverty has improved once GGI and IIAG reache a threshold level of 0.314 and 66.9 respectuively. For GGI (IIAG), below the threshold of 0.314 (66.9), an increase of 1% of GDP, FDI, DI, AVA and NODAR, decreases EP by 0.8% (0.5%), 12% (11.9%,) 9.5% (11.6%), 1.9% (3.4%) and 1.4% (1.5%) respectively. When the value of GGI (IIAG) exceeds this threshold of 0,314 (66.9), an increase of 1% of GDP, FDI, DI, AVA and NODAR decreases EP by 7.7% (7.9%), 19.4 (13.5%), 21.7% (19.1%), 3,2% (6.7%) and 5.7% (8.1%). The findings revealed too that, for GGI (IIAG), below the threshold of 0.314 (66.9), an increase of 1% of UR and GI, increases EP by 2.9% (10.3%) and 32.8% (26.6%) respectively. When the value of GGI (IIAG) exceeds this threshold of 0,3146 (66.9), an increase of 1% of UR and GI increases EP by 0.3% (4%) and 21.8% (24.5%). Overall, the extreme poverty rate could be decreased with good governance. Indeed, the lower the level of governance quality is in the sub-Saharan African countries, the lower the local real GDP per capita and the higher the unemployment rate would be, which means the misgovernance could explain the high level of extreme poverty in Africa. The findings are in line with the results presented by Nunan et al. (2021), Nguyen et al. (2021), Niaz Asadullah and Savoia (2018), Jindra and Vaz (2019) and Grindle (2004), Perera and Lee (2013) who found that, the quality governance will make extreme poverty decreases with good governance and increases with bad governance.

According to Table 1, we notice that the values of the governance index of most sub-Saharan African countries are below the threshold of 0.314 for GGI (45 countries) and 66.9 for IIAG (46 countries). The poor quality of governance plays a negative role on extreme poverty reduction. Indeed, only 4 countries have a GGI above the threshold of 0.314, these countries are Mauritius, Botswana, Cabo Verde and Namibia and only 3 countries have a IIAG above the threshold of 66.9, these countries are Seychelles, Mauritius, Cabo Verde.

Robustness Checks with Generalized Method of Moments (GMM)

In order to check the robustness of our estimation, we apply the Roodman (2009) System-GMM extension of Arellano and Bover (1995) which has been established to restrict overidentification and limit the proliferation of instruments (see Love & Zicchino, 2006; Baltagi, 2008; Asongu et al., 2017; Tchamyou and Asongu (2017); Boateng et al., 2018; Tchamyou et al. (2019); Asongu and Acha-Anyi (2019) and Tchamyou (2019)). There are four principal justifications explain the choice of GMM as a robustness-checking technique for our estimation: First, the number of countries (N = 49) is higher than the number of years in each cross section (T = 10). This condition where the number of cross sections (N) is greater than the number of time series in each cross section (T) is an important criterion for the application of the GMM. Second, The outcome variable is persistent because the correlation between extreme poverty and its first lag is 0.884 for the model with GGI and 0.826 for the model with IIAG, which are higher than the rule-of-thumb threshold of 0.800 required for establishing persistence. Third, this empirical technique has the advantage of treating with endogeneity by monitoring for time-invariant omitted variables and simultaneity. Finally, The GMM approach does not eliminate cross-country variations. The estimated results from system-GMM estimates are reported in Table 10.

Table 10.

Estimation results of system-GMM

Variables	Model with GGI		Model with IIAG
	Coefficient	Prob.	Coefficient	Prob.
L.EPR	0.884	0.000***	0.826	0.000***
GGI	−0.643	0.032**
IIAG			−0. 651	0.033**
GPD	−0.747	0.000***	−0.329	0.029**
UR	0.012	0.017**	0.014	0.008***
GI	0.097	0.011**	0.110	0.002***
FDI	−0.048	0.596	−0.045	0.590
DI	−0.228	0.213	−0.284	0.202
AVA	−0.055	0.000***	-0.036	0.000***
Ln NODAR	−0.045	0.000***	-0.048	0.000***
_cons	27.099	0.000***	60.702	0.000***
AR (1)	0.351		0.332
AR (2)	0.489		0.465
Hansen OIR	0.754		0.726
Sargan OIR	0.063		0.061
DHT for instrument (a) Instruments in levels
H excluding group	0.760		0.732
Dif(null, H = exogenous)	0.784		0.711
(b) IV (years, eq (diff))
H excluding group	0.851		0.833
Dif (null, H = exogenous)	0.634		0.622
Fisher	483,062***		411,051***
Instruments	45		45
Countries	49		49
Observations	490		490

DHT difference in Hansen Test for exogeneity of Instruments’ Subsets, Dif difference, OIR over-identifying restrictions test, The significance of bold values is twofold. (1) The significance of estimated coefficients and the Wald statistics. (2) The failure to reject the null hypotheses of: (a) no autocorrelation in the AR(1) & AR(2) tests and; b) the validity of the instruments in the Sargan and Hansen OIR tests

*p < 0,1; **p < 0,05; ***p < 0,01 (P-values) are in parenthesis

Sargan p value must not be less < 5% and > 10%. H0: over-identifying restrictions are valid. For Sargan’s test, p value = 8%, we accept the Ho; that is, all instruments are valid.

Four statistical tests are employed to examine the validity of the model: “First, the null hypothesis of the second-order Arellano and Bond autocorrelation test (AR(2)) in difference for the absence of autocorrelation in the residuals should not be rejected. Second the Sargan and Hansen over-identification restrictions (OIR) tests should not be significant because their null hypotheses are the positions that instruments are valid or not correlated with the error terms. In essence, while the Sargan OIR test is not robust but not weakened by instruments, the Hansen OIR is robust but weakened by instruments. In order to restrict identification or limit the proliferation of instruments, we have ensured that instruments are lower than the number of cross sections in most specifications. Third, the Difference in the Hansen Test (DHT) for exogeneity of instruments is also employed to assess the validity of results from the Hansen OIR test. Fourth, a Fischer test for the joint validity of estimated coefficients is also provided.” (Asongu & De Moor, 2016, p.200).

From this table, it is noted that the signs of all coefficients in both equations are consistent with those of PTR and PSTR estimates. Furthermore, results show that there is no auto-correlation in our System-GMM estimation, meaning that our result is not biased.

Conclusion

Theoretical Implications

Theoretical implications relate to how our findings connect to other theories or ideas. Are our results consistent with previous studies? Did our results confirm the methods used in previous studies or invalidate them? There is considerable debate about the relative contribution of governance and growth to poverty reduction. However, research has not reached a consensus on whether governance has a significant or insignificant impact on poverty reduction. Theoretical studies on the economic impact of governance have generated very varied results.

This paper explores the relationship between governance quality, economic growth and extreme poverty for the Sub-Saharan African countries over the period 2010–2019. Results from Panel PTR and PSTR model estimates indicate that the nexus between economic growth, governance quality and extreme poverty is non-linear. For the PTR models, estimates indicate that the negative effect(s) of GDP) on EP would begin to manifest once the governance index reaches a threshold level of 0.367 for GGI and 63.2 for IIAG. However, for PSTR models the result showed that the positive effect(s) of governance would begin to manifest once the governance index reaches a threshold level of 0.314 for GGI and 66.9 For IIAG. Moreover, findings show that there exists a negative relationship between the governance index and extreme poverty rate above these threshold levels, where governance quality starts decreasing extreme poverty in sub-Saharan African countries. Our results is consistent with a large theoretical literature that examines the effects of economic growth and governance quality on poverty reduction and confirm the methods used by Wang and Shao (2019), González et al. (2005), Fouquau et al. (2009) and Ochi et al. (2023).

Results indicate also that there is a negative relationship between FDI, DI, GDP, AVA, and NODAR and EP. The poor quality of governance plays a negative role in extreme poverty reduction in sub-Saharan African countries. Eradicating extreme poverty by 2030 is the focus of Goal 1.1 of the Sustainable Development Goals. Unfortunately, forecasts indicate that this result will not be achieved, as the year 2020 saw the first increase in global extreme poverty in a generation, and the concentration of extreme poverty has shifted from Asia to sub-Saharan Africa.

Managerial Implications

Managerial Implications summarize what the results mean in terms of actions. In other words, Managerial Implications indicate what action should be taken in response. The findings from this study have several policy and managerial implications. The policy-makers in sub-Saharan Africa must implement various measures of institutional quality which aim to influence economic governance. Indeed, the debate remains about the role of good governance in poverty reduction through economic growth. However, it is already more and more accepted that economic growth alone cannot help reduce extreme poverty if that growth is not accompanied with good governance. The argument is that many people will remain poor if the income created is not well redistributed but goes to a few privileged classes. The ways in which good governance impacts poverty are mainly twofold: it contributes, on the one hand, to accelerating the pace of economic growth which is necessary for the improvement of household incomes and state revenues and allows, on the other hand, to strengthen the human capacities of the poor to facilitate their integration into the circuit of production and distribution of wealth.

In this context, the dimensions of governance that require priority development in order to strengthen the effectiveness of poverty reduction actions are, on the one hand, those relating to the promotion of a framework favorable to investments in order to accelerate the pace of economic growth and on the other hand, those relating to the establishment of a regulatory and institutional framework capable of improving the effectiveness of public policies in the field of development and in particular those oriented towards the strengthening of human capacities of the poor. For the establishment of a framework conducive to growth, the reforms should relate to the strengthening of coherence and anticipation in the actions of the State, the strengthening of the facilities for doing business, the establishment an incentive tax system, the establishment of flexible labor legislation, the fight against corruption, the renovation of the judicial system and the reform of land tenure. With regard to the reforms to be undertaken in order to strengthen the human capacities of the poor in order to facilitate their integration in the process of production and distribution of wealth, they concern, on the one hand, the elaboration and execution of pro-poor policies in the areas of education, health, housing, employment and water and electricity and, on the other hand, improving the effectiveness of development policies through better integration between these policies, the establishment of a poverty reduction pact, the strengthening of the process of decentralization and deconcentration, the moralization of public life, the strengthening of the system of control and rendering of accounts and by upgrading the system of monitoring/ Evaluation.

Limits and Ideas for Future Research

This study has some limitations and can be improved in two directions. Firstly, as we mentioned in our introduction, another emerging debate is on the table. Some people (particularly African officials and politicians) are thinking that good governance is essential only for countries with a minimum level of economic growth. This argument is sometimes used to support attempted dictatorships in the continent. Secondly, the main shortcoming of this study includes ignoring the heterogeneity among the sub-Saharan African countries.

Thus, as a future research direction, a possible extension of this investigation may be to segment the entire sample of countries into different subsamples depending on the economic communities: Common Market for Eastern and Southern Africa (COMESA), Community of Sahel-Saharan States (CEN-SAD), East African Community (EAC), Economic Community of Central African States (ECCAS), Economic Community of West African States (ECOWAS), Intergovernmental Authority on Development (IGAD) and Southern African Development Community (SADC).

Availability of Data and Materials

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Compliance with Ethical Standards

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Competing Interests

The authors declare no competing interests.