1 Introduction

The issue of inequality in economic analysis has long remained controversial. Although there is an abundance of theoretical and empirical studies which look into the matter of inequality, economic doctrines and especially the dominant ones seem to treat with caution the question of the distribution of wealth within societies. For the neoclassical school, it seems more useful to focus on the optimal allocation of scarce resources as a focus on economics and to give up the debate on the quality of distribution and the analysis of inequalities to other disciplines which deal with power relations and institutions such as sociology (Miller, 1996). David Ricardo (1817) was the exception by suggesting the theory of distribution which makes the repartition of wealth the central object of the economy. According to this economist, the crucial problem of the economy lies in understanding the reparation of wealth between different social classes: workers who provide labor and receive a wage, landowners who own the land and are remunerated by rent, and capitalists who control productive capital in return for a profit (Braquet & Biasutti, 2016). Otherwise, orthodox theories have traditionally remained strongly attached to ‘the marginal productivity theory’ which stipulates that economic agents are paid equal to their efforts provided in the production process (Stiglitz, 2015).

Nevertheless, the dramatic change in the general trend of inequality and its magnitude, shown by the rapid rise of inequality in the majority of countries and regions from the 1980s onwards and by the outbreak of the Arab Spring Revolutions in 2011 as protest movements over poor economic and social conditions, has allowed the inequality debate to become an important issue in our times and to come to the surface. In this context, according to (Allègre, 2015) several theoretical studies have been proposed to explain the link between inequality and growth such as: (Aghion et al., 1999; Alesina & Perotti, 1996; Banerjee & Newman, 1993; Galor & Zang, 1997; Galor & Zeira, 1993; Kaldor, 1957).

Indeed, the multiplicity of theoretical works coincides with a plurality of empirical works that remain ambiguous (Allègre, 2015). In fact, since the appearance of the famous empirical work of Kuznets (1955) that points out the need to look into the characteristics of the size of income distribution to analyze changes in income over time, economists have not been able to settle the debate on the nature of the relationship between income inequality and economic growth.

In this context, Barro (2000) mentions that the main theoretical contribution examining the relationship between the evolution of inequality and growth was the Kuznets curve. This curve is based on the hypothesis that the level of inequality tends to increase at the beginning of the growth process but ends up degenerating as long as the country develops. The explanation for this non-linear relationship is based on the mobility of people between different sectors of the economy that is due to structural changes in the economic system. Indeed, the idea of Kuznets (1955) seems to be in harmony with the doctrine of Rostow (Piketty, 2013), since any society necessarily passes through universal phases of growth, first from a subsistence agricultural society characterised by low productivity to a mass consumer society dominated by the tertiary sector. This development process interacts dynamically with the level of income distribution and has a significant impact on the evolution of economic disparities. In this context, traditional societies based on the agricultural sector attracting a large volume of labour are generally characterised by a very low level of inequality as this primary sector absorbs the majority of workers in rural areas with low wages and negligible differences. However, the industrial revolution spurred technical progress which affected economic structures. Historically, economic activity has evolved into a new system based on industrialisation and mechanisation of production in which the worker plays a crucial role in its functioning and sustainability. This industrial sector is characterised by relatively higher productivity than its predecessor, which generates higher wage levels compared to the wages of agricultural workers. This major change, at the start of the growth period, leads to migratory flows to urban areas of people who wish to improve their living conditions and increase their income. This labour mobility contributes considerably to the growing economic inequalities that characterised the beginning of the development process since these small relocation movements have enabled more people to earn higher incomes than those paid in the agricultural sector, but as the economy progresses and technical progress improves, production activity is more concentrated in heavy industries which accommodate more workers. This development is accompanied by the promotion of equal opportunities such as access to mass education and the establishment of income redistribution mechanisms, which are key factors contributing to the reduction of inequalities within industrial countries (Braquet & Biasutti, 2016).

However, according to Alvarez Pereira et al. (2016), the Kuznets hypothesis has been extensively reviewed especially the factors that explain the curve results. Indeed, as indicated by the authors, there is empirical and theoretical evidence explaining that traditional factors such as the transition from an agrarian to an industrial economy seems unable to explain the diversity of the curve shape across countries. For that matter, Lyubimov (2017) points that many empirical studies have rejected the Kuznets hypothesis and proved the idea of conditional Kuznets relationship. On that basis, several works focus on the limits of Kuznets’s assumption by highlighting other theoretical factors that influence the relationship between income inequality and growth. In this context, Acemoglu and Robinson (2002) mention the role of institutions and democracy in determining the shape of the Kuznets curve. In their work, the authors indicate that democracy improves the quality of institutions that contributes significantly to the promotion of equal opportunities, encourages income redistribution and thus reduces income inequality. Therefore, the countries that adopt a democratic regime are characterised by a high level of development and low inequality. Contrariwise, autocratic regimes achieve a high level of inequality and a low level of output. Indeed, democracy is a rational choice that helps societies to avoid political instability and conflicts that inhibit development (Svolik, 2019). Piketty (2013) criticises also the Kuznets hypothesis and suggests an ‘uninverted-U’ relationship. The author points that the dynamics of income inequality depend on two strands of historical factors. On one hand, the factors which decrease inequality such as wars, natural disasters, the introduction of income tax, and in another hand the factors which stimulate inequality, notably the rate of capital accumulation, which largely exceeds the growth rates achieved. In the same vein, Milanović (2016) argues that the movement of inequality is due to several political, demographic and economic factors such as wars, epidemics and technological innovations. Moreover, the author explains that the increase in inequality during the last 30 years is driven by the second wave of technological innovation which is similar to the first industrial revolution. For this reason, the researcher has suggested extending the Kuznets curve to a new form called ‘Kuznets waves’. Indeed, the author believes that the ‘Kuznets cycles’ can explain the dynamics of inequalities in the modern era.

Furthermore, empirical studies that examine the effect of inequality on growth reveal large differences in terms of estimation techniques, data quality and results (Neves & Silva, 2014). Some empirical analyses confirm a positive effect of inequality on economic (Bleaney & Nishiyama, 2004; Chang et al., 2018; Chen, 2020; Forbes, 2000; Li & Zou, 1998) whereas others present a negative relationship (Alesina & Perotti, 1996; Deininger & Squire, 1998; Herzer & Vollmer, 2012; Islam & McGillivray, 2020; Sarkar, 2011; Seo et al., 2020; Woo, 2011; Younsi & Bechtini, 2020). However, according to Ncube et al. (2014), many studies find no significant relationship between income inequality and growth (Castelló & Doménech, 2002; Gnangoin et al., 2019; Lee & Roemer, 1998). Other studies suggest that the sign of the impact of inequality on economic growth relies on the level of development (Barro, 2000; Bengoa & Sanchez-Robles, 2006; Breunig & Majeed, 2020; Hailemariam & Dzhumashev, 2020; Soava et al., 2020). Moreover, Halter et al. (2014) focused on the role of ‘the time dimension’. In other words, the authors show that inequality increases growth in the short run and reduces it in the long run. Likewise, Aiyar and Ebeke (2020) highlight the crucial role of inequality of opportunity which deepens the negative effect of income inequality on growth. Unlike the previous cross-country studies which employ a parametric method, Banerjee and Duflo (2003) use a non-parametric approach and argue that any change in inequality level, whether upward or downward in one period, leads to a decrease in economic growth in the next period.

Although empirical works are abundant, especially those based on the panel and cross-sectional data, there are some works that explore the relationship between inequality and growth by using the Time series approach (Andrade et al., 2014).

In this context, Ameur and Seffih (2021) examine the effect of income inequality on economic performance in Algeria between 1980 and 2015 by employing the ARDL cointegration test. The empirical findings show that inequality decreases growth. Furthermore, Getaye (2021) re-examines the inequality-growth nexus for Ethiopia over the period 1980–2014 by implementing the Engle-Granger cointegration test. the results indicate that inequality inhibits growth.

Concerning Tunisia, some studies have been carried out on the relationship between inequality and economic growth. For instance, Abida and Sghaier (2005) use panel cointegration techniques for 3 countries of North Africa (Tunisia, Morocco, and Egypt) for the period 1970–2004 to assess the relationship between inequality and economic performance. Their empirical results highlight that income inequality inhibits economic growth. Moreover, in their effort to test the causality between income inequality and economic growth for 9 countries of the MENA region over the period 1960–2011, Sbaouelgi and Boulila (2013) apply the Johansen cointegration test and the Granger causality tests. Their results argue that the variables tend to move together in the long-run for 5 countries. Besides, they find that income inequality influences positively the economic growth in 4 countries including Tunisia. By using a graphical approach and an econometric analysis, Nasfi-Fkili and El Weriemmi (2014) study the the inequality-growth nexus in Tunisia from 1984–2011. The main empirical findings suggest that economic growth increases income inequality. Another notable result is that income inequality enhances economic growth and that this effect becomes negative after the openness of the economy. i examine the effect of inequality on economic growth and poverty by employing the Pooled Ordinary Least Squares (Pooled OLS) method for MENA region including Tunisia over the period 1985–2009. Their empirical findings point out that income inequality increases poverty and inhibits economic growth in MENA countries. In another study on Tunisia, Mbazia (2017) investigates the inequality-growth nexus by using the Dynamic Ordinary Least Squares (DOLS) over the period 1975–2015. The author points out that income inequality influences positively economic growth. Belloumi and Khemili (2018) explore the causal relationship between poverty, inequality and economic growth for Tunisia over the period 1970–2013 by implementing an ARDL bounds test and Toda and Yamamoto causality test. The ARDL bounds test for cointegration shows that the three variables tend to move together in the long-run. More precisely, there is a positive correlation between inequality and poverty in the long–run. Further, the causality test reveals a feedback effect between inequality and economic growth.

Of the above, we have noticed that previous studies regarding Tunisia ignore part of the complex reality by imposing a linear relationship between inequality and economic growth. In other words, they do not investigate the possibility of a nonlinear relation between inequality and economic growth. Thereby, they fail to let policymakers make the optimal decision on resources allocation and implement the corrective measures. Indeed, recent theoretical and empirical studies point out that the effect of inequality on economic growth depends on several factors as the threshold level of inequality. Therefore, the confirmation of a nonlinear relationship between inequality and economic growth, in this paper, fills a gap in the literature concerning Tunisia and helps policymakers to avoid the ideological influences of liberal and social doctrines of politicians who may take advantage of some empirical findings to impose their convictions. Especially, the main factor of the socio-political unrest leading to the fall of the former political regime in 2011 can be summed up as the persistence of economic disparities between an elite that holds power, wealth, and a majority deprived of ‘social rise’ (Gherib, 2020). Furthermore, by using several inequality indicators, our analysis gives attention to ‘the location of inequality’(Barro, 2000), which was also a neglected aspect in the existing surveys concerning Tunisia, and studies how the situation of specific income groups (top and bottom income groups) could affect the inequality-growth nexus. In doing so, firstly, we use the Threshold regression model developed by Hansen (2000) to examine the possibility of a nonlinear relation between per capita income and inequality for observations above and below a threshold value of income inequality over the period 1980–2019. Secondly, we test the Kuznets hypothesis by allowing the possibility of a threshold level of development (economic growth) that determines the nature of the Kuznets relationship. To do this, we also use the Threshold regression model developed by Hansen (2000).

The remainder of this paper is organised as follows: Sect. 2 presents the data and the empirical methodology, Sect. 3 describes the main results and Sect. 4 presents the conclusion and provides useful policy implications.

2 Data and Methodology

2.1 Data

In order to achieve the empirical investigation, we use time-series data of Tunisia for GDP per capita (GDP) as a proxy for economic growth, the Gini index (GINI), the income share of the bottom 40% of the population (BTFOR), the income share of the bottom 50% (BTFIV) and the income share of the top 1% (TOPON) as alternative proxies for income inequality (INE) from 1980 to 2019. These measures measure different aspects of inequality. Indeed, the Gini index measures the inequality of income distribution within an entire population. In this case, an increase in the Gini index (GINI) reflects a worsening of income inequality while a decrease indicates a reduction in income inequality. The other indicators measure income distribution for specific groups in the population. Indeed, the rise in the income share of the lowest 40% (BTFOR) and the income share of the lowest 50% (BTFIV) reflects a better equal income distribution and vice versa. On the other side, the increase the income shares of the highest 1% (TOPON) reflects a worse unequal income distribution and vice versa. Further to the variables of interest, we use the education enrollment (EDU), the population growth rate (POP), the broad money to GDP ratio (FD), the total of imports and exports to GDP ratio (OPEN), net inflows to GDP ratio (FI) and the inflation rate (INF) as control variables. These data are available in the World Development Indicators (WDI) and the World Inequality Database (WID).

Indeed, despite the moderate decline in income inequality, the Gini index decreased from 0.60 in 1980 to 0.50 in 2019. The general perception of society remains in favor of the persistence and sustainability of inequality (Boughzala et al., 2020). This perception can be understood by taking into consideration the dominance of specific groups on the national income. In 2019, the top 10% group capture 40% of the national income, a share that is twice as large as that of the Bottom 50% group (17.93%). Meanwhile, the top 1% income share (10.73%) is roughly equivalent to the Bottom 40% income share (12. 23%). In effect, the structure of inequality in Tunisia relies on several demographic, economic, and political factors. Tunisia is a dynamic economy that has undergone several profound changes that have taken place and influenced the distribution of income. On the level of demography, Tunisia has known a notable demographic transition in the last 39 years, a population growth rate that peaked at over 2.5% in the 1980s, fell considerably in the late 1990s to less than 1%. The demographic transition correlated with the reduction of family size and the improvement of the income share of the bottom groups (Boughzala et al., 2020). In this context, the income share of the lowest 40% of the population increased from 8.39% in 1980 to 9.28% in 2000. Likewise, the income share of the lowest 50% of the population rose from 12.77% to 13.95% in the same period. Another notable fact is the acceleration of urbanisation. The urbanisation rate rose from 37,51 in 1960 to 50,56% in 1980. In 2019, 69.25% of Tunisians resided in urban areas. Regarding economic factors, since independence in 1956, the public authorities have chosen to adopt a centralised development strategy that tends to improve economic growth by meeting the basic needs of the citizens in terms of education, health and social protection. The State has played a crucial role in both the economic and social fields. On the one hand, it directed the investment choices of economic agents towards priority sectors such as the low-tech industry and tourism. On the other hand, it has targeted human development by investing in education and health. However, the economic crisis of 1986 forced policymakers to revise their policy choices by adopting a new decentralised development strategy that promoted economic growth through market mechanisms and economic openness. This change is consistent with the increase in the income share of the top income group. For example, between 1990 and 2000, the income shares of the highest 1% of the population rose from 14,25% to 15,85%. On the political level, the revolution in 2010 constitutes a major political event. Indeed, the absence of individual freedoms and the deterioration of economic and social conditions generated socio-political unrest. The political instability stimulated a decrease in investments by increasing transaction costs and threatening property rights. This situation correlated with the decline in the share of income of the top group. For instance, the income share of the highest 1% decreased from 10,77% to 10,74 in the same period.

2.2 Methodology

In this section, we introduce the methodological approach used to investigate the link between income inequality and growth. In particular, a threshold regression model (Hansen, 2000) can examine the nonlinearity in the relationship. Indeed, the threshold regression model was specifically designed to capture the nonlinear relationship between income inequality and economic growth. In this study, we employ this framework to estimate a threshold value that split the relation between income inequality and growth into two regimes.

After conducting the KPSS test (Kwiatkowski et al., 1992) and the ADF-GLS test (Elliott et al., 1996) to verify the stationarity of the series. We start to build our model by considering the following variables \(\left\{ {{\text{y}}_{{\text{t}}} {\text{,x}}_{{\text{t}}} {\text{,z}}_{{\text{t}}} } \right\}\), where \({\text{y}}_{{\text{t}}}\) represents the dependent variable,\({\text{ x}}_{{\text{t}}}\) is a vector of exogenous variables, \({\text{z}}_{{\text{t}}}\) is the threshold variable.

Since the threshold variable divides the relation into two regimes, we can write the model as:

$$y_{t} = x_{t}^{T} \delta_{1}^{1} + \varepsilon_{t} , z_{t} \le \gamma$$
(1)
$$y_{t} = x_{t}^{T} \delta_{1}^{2} + \varepsilon_{t} , z_{t} > \gamma$$
(2)

With \(\gamma\) indicates the threshold value.

When we introduce an indicator function \({\text{I (z}}_{{\text{t }}} \le {\gamma )}\), the model can be presented as:

$$y_{t} = { }x_{t}^{T} \delta_{1}^{1} I\left( {z_{t} \le \gamma } \right) + { }x_{t}^{T} \delta_{1}^{2} I\left( {z_{t} > \gamma { }} \right) + \varepsilon_{t}$$
(3)

In order to obtain the threshold value and estimate the parameters of the equation, we rely on Hansen (2000) by using the endogenous threshold determination algorithm. This procedure seeks to determine a specific threshold level which minimises the sum of the squares of the residuals. Moreover, to test if the threshold effect is statistically significant and to show that the relationship is better presented by a regression threshold (TR) relative to a linear specification, we apply a linearity test developed by Hansen (1996) of the null hypothesis:\({{~\delta }}_{{\text{1}}}^{{\text{1}}} {{ = ~\delta }}_{{\text{1}}}^{{\text{2}}} {\text{~}}\) against the alternative one:\({{ \delta }}_{{1}}^{{1}} \ne {{ \delta }}_{{1}}^{{2}}\). In fact, the linearity test faces a major problem lies in the impossibility of identifying the threshold value under the null assumption (Savvides & Stengos, 2000). To solve this problem Hansen (1996) proposed a Lagrange Multiplier (LM) bootstrap method that computes p-values and constructs confidence intervals to test the null hypothesis of a linear model against the alternative one of threshold regression. This suggests that if the p-value for the LM test is less than 5%, the alternative hypothesis indicating the threshold regression is accepted.

we undertake the empirical analysis by estimating the threshold effect of income disparity on economic performance. In other words, we examine the nonlinear effects of income inequality on economic growth above and below the threshold value. The TR adopted model is as follows:

$$LGDP_{t} = { }\beta_{0}^{1} + { }\beta_{1}^{1} LINE_{t} + { }\mu^{1} { }V_{t} + \varepsilon_{t} ,{ }LINE_{t} \le { }\gamma$$
(4)
$$LGDP_{t} = { }\beta_{0}^{2} + \beta_{1}^{2} LINE_{t} + { }\mu^{2} { }V_{t} + \varepsilon_{t} ,{ }LINE_{t} > { }\gamma$$
(5)

With \(\gamma\) denotes the threshold value.

When we introduce an indicator function \({\text{I~(LINE}}_{{\text{t}}} \le {{~\gamma )}}\), the model can be presented as:

$$LGDP_{t} = \beta_{0}^{1} + \beta_{1}^{1} LINE_{t} + \mu^{1} V_{t} I\left( {LINE_{t} \le \gamma } \right) + \beta_{0}^{2} + \beta_{1}^{2} LINE_{t} + \mu^{2} V_{t} I\left( {LINE_{t} > \gamma } \right) + \varepsilon_{t}$$
(6)

where the dependant variable \({\text{LGDP}}_{{\text{t}}}\) is the logarithmic transformation of GDP per capita, the threshold variable \({\text{LINE}}_{{\text{t}}}\) is the logarithmic transformation of income inequality indicators, these inequality indicators are: the Gini index (LGINI), the income share of the bottom 40% of the population (LBTFOR), the income share of the bottom 50% (LBTFIV), the income share of the top 1% (LTOPON),\({\text{ V}}_{{\text{t}}}\) represents a vector of controls variables that includes the education enrollment as a proxy to human capital (LEDU), the population growth rate (LPOP), the financial development measured by the broad money to GDP ratio (LFD), \({\text{I(}}{.)}\) denotes the indicator function, t = time period = 1, 2... T, and \({\upvarepsilon }_{{\text{t}}}\) is the random error.

When these steps have been completed, we will be ready to reexamine the Kuznets hypothesis and to see whether the relationship between income inequality and growth depends on the level of economic development (per capita income). To do this, we follow Savvides and Stengos (2000) by employing a threshold regression model. This method remains a useful framework that identifies endogenously the existence of an income threshold value which determines the nature of Kuznets relationship (inverted-U or uninverted-U) below and above the threshold level.

In order to examine the Kuznets hypothesis, we adopt the threshold regression TR as follows:

$$LINE_{t} = \alpha_{0}^{1} + \alpha_{1}^{1} LGDP_{t} + \alpha_{2}^{1} LGDP_{t}^{2} + \pi^{1} W_{t} + \varepsilon_{t} , LGDP_{t} \le \gamma$$
(7)
$$LINE_{t} = \alpha_{0}^{2} + \alpha_{1}^{2} LGDP_{t} + \alpha_{2}^{2} LGDP_{t}^{2} + \pi^{2} W_{t} + \varepsilon_{t} , LGDP_{t} > \gamma$$
(8)

With \({ }\gamma\) is the threshold value.

When we introduce an indicator function \({\text{I (LGDP}}_{{\text{t}}} \le {\gamma )}\), the model can be presented as:

$$LINE_{t} = \alpha_{0}^{1} + \alpha_{1}^{1} LGDP_{t} + \alpha_{2}^{1} LGDP_{t}^{2} + \pi^{1} W_{t } I\left( {LGDP_{t} \le \gamma } \right) + \alpha_{0}^{2} + \alpha_{1}^{2} LGDP_{t} + \alpha_{2}^{2} LGDP_{t}^{2} + \pi^{2} W_{t } I\left( {LGDP_{t} > \gamma } \right) + \varepsilon_{t}$$
(9)

where the dependent variable \({\text{LINE}}_{{\text{t }}}\) is the logarithmic transformation of income inequality indicators, the threshold variable \({\text{ LGDP}}_{{\text{t}}}\) is the logarithmic transformation of GDP per capita,\({\text{ W}}_{{\text{t}}}\) represents a vector of controls variables that includes the trade openness defined as the total of imports and exports to GDP ratio (LOPEN), the foreign direct investment measured by the net inflows to GDP ratio (LFI) and the inflation rate (LINF), \({\text{I(}}{.)}\) denotes the indicator function, t = time period = 1, 2... T, and \(\varepsilon_{t}\) is the random error.

To examine the Kuznets hypothesis, we include the squared value of \({\text{LGDP}}_{{\text{t}}}\) which helps to measure parabolic phenomena in the model (inverted U). Indeed, if the estimated coefficient of the economic growth is positive and the squared value of economic growth has a negative effect, the Kuznets hypothesis holds. In other words, an inverted-U relationship between per capita income and income inequality is accepted (Table 1).

Table 1 Descriptive statistics of logarithmic level series
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Once the last steps have been done, we verify the stability of the models by using the CUSUM and CUSUM of squares tests (Brown et al., 1975). Finally, we check the causality direction between inequality and economic growth by employing the Granger causality test (1969).

3 Results and Discussion

First, we test the stationarity of the series under consideration. Table 2 reports KPSS and ADF-GLS unit root tests outputs. The results mention the acceptance of the null hypothesis of stationarity for the KPSS test whereas the rejection of the null hypothesis that denotes the presence of unit root for the ADF-GLS test. Therefore, we confirm that the variables are level stationary.

Table 2 Unit root tests
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Once the first step has been done, we undertake the part which aims to analyse the relationship between per-capita income (GDP) and income inequality (INE) by testing the possibility of multiple regimes using income inequality indicators as the threshold variables. In doing so, we use the first vector of controls variables that includes the education enrollment (LEDU), the population growth rate (LPOP), the financial development (LFD) as suitable determinants of economic growth.

At this point, we test the null hypothesis of linearity developed by Hansen (1996) as represented in Eq. (6). Table 3 reports the results of the Lagrange Multiplier specification against the alternative of threshold regression (TR) by applying a linearity test (LM) test. The statistical significance of this test is evaluated by the p-value which is calculated by the bootstrap method with 1000 replications and 15% trimming percentage. The p-value is less than 5% for all inequality indicators, as a result, we can reject the null hypothesis: \({\upbeta }_{{1}}^{{1}}\,=\, {\upbeta}_{{1}}^{{2}}\) of no threshold model and confirm the presence of a threshold level of income inequality that splits the sample into two regimes.

Table 3 LM Test for income inequality threshold effect (dependent variable: per-capita income (LGDP))
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After verifying the nonlinearity of the model, we can estimate the model with the threshold effect for all inequality measures. The main independent variable in these models is the economic growth (GDP). Tables 4, 5, 6 and 7 report the results of the threshold model which considers inequality as a threshold variable that splits the sample into two regimes. The outcomes shown in these tables reveal that income inequality indicators (INE) have significant threshold effects on per-capita income. These results join (Banerjee & Duflo, 2003; Hailemariam & Dzhumashev, 2020; Nasfi Fkili & El Weriemmi, 2014) who argue that the relationship between inequality and growth is better presented by a nonlinear model. Indeed, for the Gini index and the income share of the top 1% (TOPON), below the threshold, inequality has an insignificant effect on economic growth, while above the threshold, inequality reduces the growth. In contrast, the estimated coefficients of the income share of the bottom 40% of the population (BTFOR) and the income share of the bottom 50% (BTFIV) are positive and statistically significant below the threshold value but they become insignificant above the threshold level. Another notable result that the education (EDU) improves economic growth particularly when the income distribution increases more equally. The effect of the population growth rate (POP) on economic growth is insignificant when the income distribution rises evenly while it becomes negative and significant when the income distribution increases unequally. The financial development (FD) inhibits economic growth in the context of unequal income distribution and does not lead to the financial inclusion of the bottom groups. Thereby, these results confirm the idea of Voitchovsky (2005) which highlights that the impact of income disparity on economic performance depends on inequality indicators used. Indeed, our results indicate that income rising at a faster speed when inequality is below the threshold level than when it is above the threshold level. Furthermore, they show that a better income distribution supports economic growth because when income increases more equally in the bottom 40–50% income groups, the impact of inequality on economic growth is positive. On the contrary, the findings mention that an unequal income disparity (more income captured by top 1% income group and increasing in the GINI index) reduces economic growth.

Table 4 Gini index threshold effect (dependent variable: per-capita income (LGDP))
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Table 5 Income share of the bottom 40% threshold effect (dependent variable: per-capita income (LGDP))
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Table 6 Income share of the bottom 50% threshold effect (dependent variable: per-capita income (LGDP))
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Table 7 Income share of the top 1% threshold effect (dependent variable: per-capita income (LGDP))
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In reality, a low level of income inequality associated with income redistribution towards the bottom income groups and can be tolerated and accepted by individuals. Moreover, it can be an incitement to work, innovate, and be more productive, thus enhancing growth (Allègre, 2015). However, if inequality exceeds a threshold level as well as the top income group captures more income than the bottoms income groups and then monopolises the fruit of growth, it becomes unacceptable and generates socio-political unrest. Indeed, the political instability, which characterises Tunisia after the 2010 revolution, reduces the investments by increasing the costs of transactions through the threatening of property rights, hence the decrease of growth (Alesina & Perotti, 1996). Besides, the high level of inequality damages ‘social trust’, with an increase in violence and crime (Rothstein & Uslaner, 2005). Poor people left to their own devices will feel lost, marginalised, humiliated, hopeless, and without support. This kind of social exclusion stimulates the will to steal, rape, and assault others as a form of revenge and self-expression (Elshout et al., 2017). In this context, Hsieh and Pugh (1993) study the relationship between economic conditions and crime and conclude that poverty and income inequality have a positive effect on the evolution of violent crime. Moreover, Daly et al. (2001) affirm that income inequality causes an increase in homicides. Also, Elgar and Aitken (2011) show that a high level of inequality leads to an increase in homicides. Besides, Anser et al. (2020) find that the rise of income inequality stimulates crimes. This psychological desire for violence and the physical effort to carry it out constitute a loss of energy and resources for the whole economy in terms of productivity (Barro, 2000). Indeed, the health damage caused by acts of violence requires an increase in health expenditure to care for the victims. This expenditure has a very high opportunity cost and is very harmful to growth.

The objective of the second part is to test the Kuznets hypothesis by allowing the possibility of a threshold level of development (economic growth) that determines the nature of Kuznets relationship. In doing this, we use the second set of controls variables that includes the trade openness (LOPEN), the foreign direct investment (LFI) and the inflation rate (LINF). This different set of controls variables takes into consideration the context of economic liberalisation and openness that influenced remarkably the dynamics of inequality in Tunisia (Nasfi Fkili & El Weriemmi, 2014) during the period of study.

We undertake the empirical analysis by testing the null hypothesis of linear model against the threshold model (Hansen, 1996) as indicated in Eq. (9). Table 8 reports the results of the Lagrange Multiplier (LM) test. The p-value is less than 5% for all inequality measures. Therefore, we reject the null hypothesis:\({ }\alpha_{1}^{1} = \alpha_{1}^{2} ;\alpha_{2}^{1} = \alpha_{2}^{2}\) of no threshold effect and confirm the presence of a threshold level of economic growth (GDP).

Table 8 LM test for economic growth threshold effect (dependent variable: inequality indicators)
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Results show that, for the indicators: The Gini index (GINI), the income share of the bottom 40% of the population (BTFOR), the income share of the bottom 50% (BTFIV) and the income share of the top 1% (TOPON), it is preferable to estimate a threshold regression in order to analyse how economic development affects the nature of Kuznets curve.

According to the results in Table 9, for the observations below the threshold value, we find that economic growth has a positive effect on income inequality. However, the estimated coefficient of the squared value of per capita income is negative. Instead, for the observations above the threshold level, the economic growth decreases income inequality, at the same time, the squared value of economic growth influences positively inequality. Hence, for the Gini index (GINI), an inverted-U Kuznets curve is accepted below the threshold value, while above the threshold value, there is evidence of an uninverted-U Kuznets relationship.

Table 9 Economic growth threshold effect (dependent variable: gini index (LGINI))
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Conversely, the results presented in Tables 10 and 11 point that for observations below the threshold level of development (GDP), the economic growth has a negative impact on income inequality, simultaneously, the squared value of economic growth boosts inequality. In contrast, for observations above the threshold level of development (GDP), economic growth enhances income inequality and the estimated coefficient of the squared value of per capita income becomes negative. Therefore, for the income share of the bottom 40% of the population (BTFOR) and the income share of the bottom 50% (BTFIV), below the threshold level, there is evidence of an uninverted-U Kuznets relationship. However, above this threshold, the Kuznets hypothesis (an Inverted-U) is verified.

Table 10 Economic growth threshold effect (dependent variable: income share of the bottom 40% (LBTFOR))
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Table 11 Economic growth threshold effect (dependent variable: income share of the bottom 50% (LBTFIV))
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Finally, the results in Tables 12 show that for observations below and above the threshold level of development (GDP), there is a negative relationship between income inequality and economic performance, but on the other hand, the squared value of economic growth has a positive impact on inequality indicators. These results indicate an uninverted-U Kuznets curve, below and above the threshold level, for the income share of the top 1% (TOPON).

Table 12 Economic growth threshold effect (dependent variable: income share of the top 1% (LTOPON))
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In this context, our results are consistent with the empirical findings of (Savvides & Stengos, 2000) which suggest that the Kuznets curve depends on a threshold level of economic growth. Also, these results support the idea of Barro (2000) which points out that the effect of economic growth on income inequality differs across the income groups. In addition, our findings provide support for theoretical works which criticise the Kuznets curve (Acemoglu & Robinson, 2002; Milanović, 2016; Piketty, 2013). In other words, these results confirm the idea which assumes that the Kuznets hypothesis (an Inverted-U) seems unable to explain the diversity of the inequality dynamics across countries, periods and income groups. Indeed, other historical, political, and demographic factors can interfere with economic growth in explaining the dynamics of inequality.

Concerning Tunisia, many elements can explain the diversity of the Kuznets curve across income groups: the change of the source of economic growth and the rational responsiveness of each income group to this change (Hermansen et al., 2016), the demographic, political, and historical factors.

Historically, Tunisia has experienced major events and profound changes which have influenced its choices concerning development strategies and changed its sources of economic growth. In general, Tunisia has adopted two major development strategies that are centralised and decentralised. Indeed, since independence in 1956, the political authorities had chosen to adopt a centralised development policy. This development strategy aimed to stimulate economic growth, in the first step, by directing the large fortunes (owned by the landowners) towards investments in the low-technology industrial and tourism sector in return for banking facilities and tax privileges, in the second step, by accumulating human capital through public investments in education and professional training sectors. Initially, this development strategy leads to migratory flows from rural to urban areas of people who give up their agricultural activities to improve their living conditions and increase their income. This labor mobility contributes to the temporary income reduction in the bottom groups during the job search period (the economic growth impacts negatively LBTFOR and LBTFIV below the threshold). The first stage of this strategy conducts as well to the income decrease in the top group. Indeed, the landowners have sacrificed their rents to obtain higher profits in return for their investments in the industrial and touristic sectors (the economic growth impacts negatively LTOPON below the threshold). However, at the final stage, the centralised development policy reduces the unemployment rate, absorbs a large part of the qualified and disqualified workers, and boosts the productivity gains for the first investors (landowners). As a result, the economic growth increases the income share of top and bottom groups (the squared value of economic growth has a positive impact on LBTFOR, LBTFIV and LTOPON below the threshold level) and decreases the income inequality (the squared value of economic growth influences negatively LGINI below the threshold level).

Nevertheless, the financial and economic crisis in the 1980s stimulated the intervention of the international monetary fund (IMF) that encouraged the Tunisian government to adopt a new decentralised development strategy based on the liberalisation of the economy, the encouragement of the private sector, and the attraction of foreign investment. These reforms had fortified by the free trade agreement with the European Union in 1995 that accelerated trade opening.

Indeed, the Tunisian economy has evolved into a new system characterised by the competition between national and foreign companies and the adoption of new technologies. In the beginning, the foreign direct investment flows stimulate jobs in both low and medium technology sectors and reduce the unemployment rate that contributes to the improving income in the bottom groups (the economic growth influences positively LBOTFR and LBOTFIV above the threshold level). On the contrary, the national firms face competition from foreign companies. This competition reduces both output and profit of national firms. Therefore, the income of top group falls initially (the economic growth influences negatively LTOPON above the threshold level). At the last stage, the national firms benefit from the transfer of high technology and tend to reduce the production cost by introducing machines and robots, and layoffs disqualified workers. These measures contribute to the improvement of productivity of national firms, but the rise of unemployment. Therefore, the economic growth enhances the income of the top group (the squared value of economic growth impacts positively LTOPON above the threshold level), reduces that of the bottom groups (the squared value of economic growth impacts negatively LBTFOR and LBTFIV above the threshold level) and thus increases the income inequality (the squared value of economic growth influences positively LGINI above the threshold level).

Concerning the results of CUSUM and CUSUM of squares tests. Figures 1 and 2 show that the statistics values of both tests are inside the confidence bands at a 5% significance level. Therefore, our models are stable.

Fig. 1
figure 1

CUSUM and CUSUM of squares tests of income inequality threshold effect models

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Fig. 2
figure 2

CUSUM and CUSUM of squares tests of economic growth threshold effect models

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In the final step, we perform the Granger causality test to check the causality between the inequality indicators and the economic growth. Table 13 contains the p-values of the F-statistic which confirm the rejection of the null hypothesis of no bidirectional causality and thus show evidence of a feedback effect between inequality indicators and economic growth. More precisely, the Gini index and the economic growth cause each other at the 10% significance level. For the bottom income groups, the findings indicate the existence of bidirectional causality between the income share of the lowest 40% of the population and economic growth at the 5% significance level. Moreover, there is evidence of feedback effect between the income share of the lowest 50% of the population and economic growth at the 10% significance level. Regarding the top income group, the income share of the highest 1% of the population causes the economic growth and vice versa at the 5% significance level. These results are in agreement with (Belloumi & Khemili, 2018; Shahbaz et al., 2015) who point out a feedback effect between income inequality indicator and economic growth and in contrast with (Cetin et al., 2021) who show evidence of unidirectional causality running from the economic growth to the income inequality.

Table 13 Granger causality test
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4 Conclusion

This paper has investigated the impact of income disparity on economic growth for Tunisia for the period 1980–2019. Our contribution lies in proving the existence of an income inequality threshold effect on economic growth and determining endogenously this threshold level by applying threshold regression developed by Hansen (2000). Besides, we test the Kuznets hypothesis by allowing the possibility of a threshold level of development (economic growth) that determines the nature of the Kuznets relationship. In doing so, we also employ the Threshold regression model developed by Hansen (2000). The findings of this study show that a significant threshold level of income inequality exists which is in agreement with (Hailemariam & Dzhumashev, 2020; Nasfi Fkili & El Weriemmi, 2014). Indeed, for the Gini index and the income share of the highest 1% of population, inequality has an insignificant effect on economic growth below the threshold value while above the threshold value, inequality reduces the economic growth. Meanwhile, for the income share of the lowest 40% of the population and the income share of the lowest 50% of the population, inequality has an insignificant effect on economic growth above the threshold value while below the threshold value, inequality promotes the economic performance. In other words, a better income distribution supports economic growth while an unequal income disparity reduces economic growth. Another notable result is that human capital plays a crucial role in enhancing economic growth particularly when the income distribution rises equally. Concerning the Kuznets hypothesis, the evidence is mixed and depends on the inequality indicators which is in line with (Barro, 2000). Indeed, our results indicate that the Kuznets relationship depends on a threshold level of economic growth which is in agreement with (Savvides & Stengos, 2000). More precisely, for the Gini index, the Kuznets curve is accepted below the threshold value, while above the threshold value, there is evidence of an uninverted-U Kuznets relationship. Conversely, for the income share of the bottom 40% of the population and the income share of the bottom 50% of the population, below the threshold level, there is evidence of an uninverted-U Kuznets relationship. However, above this threshold, the Kuznets hypothesis is verified. Concerning the income share of the top 1% of the population, below and above the threshold level, there is evidence of an uninverted-U Kuznets relationship.

Hence, given the obtained results, it is crucial and useful to recommend policymakers adjust high-income inequality levels and prevent further increases in them. Otherwise, the high level of income inequality reduces economic growth. Indeed, policymakers should further redistribute income and encourage income equalising policies towards the bottom income groups (bottom 40–50% of the population). Besides, they should invest massively in education which constitutes the main factor in promoting economic growth. Moreover, policymakers should rethink the financial system by introducing reforms that encourage the financial inclusion of the bottom income groups, for example, the creation of special funds that finance their needs at the lowest rate of interest can grantee their access to financial services at a lower cost.