The symmetric and asymmetric impacts of external debt on economic growth in Tunisia: evidence from linear and nonlinear ARDL models

Abstract

This paper aims to empirically examine the symmetric and asymmetric impact of external debt on economic growth in Tunisia between 1965 and 2019. The empirical methodology used is based on the one hand on the linear autoregressive distributed lag (ARDL) model of Pesaran et al. (Econ Soc Monogr 31:371–413. 10.1371/journal.pone.0184474, 2001), and on the other hand, on the nonlinear ARDL (NARDL) model of Shin et al. (Nucleic Acids Res 42(11):90. 10.1038/s41477-021-00976-0, 2014). The results show that the asymmetry assumption is valid for the long term. In addition, the empirical analysis shows a negative impact of positive external debt variation and a positive impact of negative external debt variation. This suggests that economic growth is more sensitive and favorable to decreases than to increases in external debt, which in turn means that maintaining debt at relatively high levels is detrimental to Tunisian economic growth.

Introduction

Government indebtedness has long been one of the major issues in economics. One of the fundamental questions that arise concerns the effects of this debt on the various macroeconomic aggregates, insofar as it allows a country to invest capital beyond its own financial capacity. From this point of view, the debt, thus, created is supposed to generate growth and foster development. However, since the outbreak of the foreign debt crisis in the early 1980s, the problem of the debt of poor countries has become a matter of concern within international bodies. Indeed, the World Bank is interested in it as part of its objective to fight extreme poverty and promote development (Catherine et al. 2002; Calderón and Zeufack 2020); the IMF, for its part, considers excessive external debt to be a major obstacle to development (Gaspar et al. 2019).

Since the Tunisian youth revolution in 2011, Tunisia has made its first steps in the democratic, economic, and social transition. Six years after the revolution to follow-up on the international investment conference "Tunisia 2020", Tunisia has still made the news. With investment agreements, the recovery of tourism and the increase of the public deficit, the Tunisian economy has been swinging between challenges to be met and a potential to be developed. Even if the current economic and financial situation in Tunisia is characterized by vulnerability, this nascent democracy still presents positive signals allowing it to start on the road to growth.

Tunisia, which has been engaged in a democratic process since the 2011 revolution, is oscillating between a difficult economic situation and a desire to achieve a sustainable democratic, economic, and social transition despite the continuous efforts of the governments that have succeeded each other since 2011 to make efforts to put Tunisia on the path to sustainable growth. Although the measures are multiplying, the improvements are still modest.

However, since 2011, the economic crisis in Tunisia has only worsened. The Covid-19 health crisis and its economic consequences are further deteriorating living conditions that have become increasingly difficult for a large part of the Tunisian population. While the country is once again facing strong social protests, the repayment of its foreign debt continues to confiscate resources needed for its economic reconstruction. Tunisia is also forced to accept the conditions imposed by its creditors, which further reduces its room for maneuvre in meeting the country's social and economic challenges. In a word, the country is trapped in a spiral of debt.

First, an economic diagnostic error: in 2012, the government that emerged from the October 2011 legislative elections considered that Tunisia was undergoing a demand shock, while the country was actually undergoing a supply shock, to follow-up on the various social movements linked to the revolution, requiring immediate action in favor of businesses, such as a momentary postponement of their payments to maintain their competitiveness. The other element was the massive borrowing, mainly external, to which the state resorted to cope, among other things, with an explosion of its wage bill resulting from the various salary increases as well as aberrant recruitments made in the civil service; all this was against a background of sluggish growth and a drastic decline in the national savings rate, which fell from 23% of GDP in 2011 to 2% in 2020. These figures are to be compared with the soaring external debt, whose share of GDP has increased from 37% in 2010 to 86% in 2018, according to the IMF (2019), and should peak at 90% of GDP by 2021, according to Fitch Ratings. For Tunisia, the only way forward is, therefore, a new agreement with the IMF, which would avoid the situation of a "debt wall". However, we must be aware that the institution will certainly attach draconian conditions to its intervention for the country. The economist Michel Aglietta states that "there is no legitimate currency except when backed by sovereignty"; for the case of Tunisia, from 2021, this reflection takes on a vital meaning.

Thus, if the link between debt and growth is a fact, the impact is uncertain when considering the case of developing countries like Tunisia. This is why it is necessary to ask whether external debt has handicapped Tunisia's economic growth?

To answer such a question, the objective is to know the nature of the effect of external debt on the economic growth in Tunisia between 1965 and 2019. To achieve this objective, the rest of this paper will be articulated in three sections, namely: a literature review on the theoretical foundations that relate the concept of external debt and economic growth is presented in the second section. In the third section, we present the different approaches that we will use to evaluate the link between debt and economic growth for the period under study. Finally, we will apply these methods to the case of Tunisia and we will determine an optimal sustainable external debt threshold that favors the sustainability of the fiscal policy, the stability of economic and financial balances, and the growth of the country.

Theoretical overview

Several theoretical and empirical approaches have been developed to explain how economic policies can influence external debt and economic growth. Four main theories will be discussed in this section. These are the Keynesian-inspired theories known as traditional theories, classical/neoclassical theories, the theories of the public choice school, and the theory of the debt overhang or Laffer curve theory.

Theoretical evidences

Economic theories suggest that debt, within reasonable limits, can help developing countries sustain growth. According to the traditional Keynesian theory of economic development, increasing the deficit (otherwise debt) promotes growth (Demikha et al. 2021; Oberholzer 2021). In the case of under-activity, an increase in spending through taxes and debt induces an equivalent increase in full employment growth (Balanced Budget Multiplier).

The public choice school analyzes the role of public institutions in economic life. According to its proponents (Buchanan and Tullock 1962, close to the neoclassicals), public debt is nothing but the result of the electoralism of public leaders, but also of civil servants and other bureaucrats.

The traditional doctrine stems from the founding ideas of Keynes (1936). Indeed, for Keynes and his followers, fiscal policy and public spending policy are necessary to revive an economy. Thus, for them, the impact of public debt on economic activity depends only on the state of the economy. They argue that at full employment or when the demand for money leads to an increase in the interest rate, the public deficit is not desirable. However, stimulating aggregate demand in a recession leads to multiplier and gas pedal effects: a more than proportional increase in investment, which in turn leads to an increase in output. Consequently, the impact of increased public debt on growth is considered positive.

Keynesian and endogenous growth theories developed from the end of the 1970s onwards, notably by Romer (1986), Barro (1990) and Aghion and Aghion (2004), have reaffirmed the role and advantage of state interventionism by emphasizing the importance of returns to scale, research or innovation, and knowledge (or human capital), as factors that can impact on growth. However, the need to finance these additional expenditures results in a budget deficit, which accumulates over a long period of time and generates public debt. The early literature, following Demikha et al. (2021), Oberholzer (2021), Mohamed (2018), and Spilioti and Vamvoukas (2015), argued for a positive link between economic growth and external debt.

For the classics and neoclassics, the public deficit is harmful to the economy, and financing it by borrowing leads either to a crowding-out effect or to the risk of Ricardian equivalence.

Monetarists have put forward the theory of interest rate crowding-out, claiming that an increase in government spending causes a decline in private investment and consumption in favor of the public sector through an increase in the interest rate (Ijirshar et al. 2016).

This rise in interest rates slows down private investment and, secondarily, consumption (more expensive credit) and can produce a snowball effect. This snowball effect is explained by the fact that the successive accumulation of deficits, when the state finances its expenditures by borrowing, can result in a mechanical increase in debt that is irreversibly growing, leading to a growing snowball. In the absence of growth, the debt continues to rise even if the state does not increase its spending, causing interest rates to rise if the demand for capital rises, and thus crowding-out the public sector.

In that context, Friedman (1957) develops another theory, known as the inflation crowding-out theory, according to which deficit financing by borrowing can only be effective if economic agents make errors in their expectations, considering that taxes will not increase. Friedman then shows that fiscal policy is effective in the short term because it creates an illusion among agents that their purchasing power has increased and that their permanent income has risen. However, they will quickly realize that this is a cyclical increase in their income, so they will quickly return to their previous level of consumption.

Thus, not anticipating additional demand, companies do not invest, which will result in an insufficient supply of products and lead to an increase in prices, which in turn provokes demands for wage increases. The rise in prices and wage costs sustains an inflationary process, a massive layoff of employees by firms and a rise in unemployment from its initial level, thereby neutralizing the effect of the stimulus (Mensah et al. 2019).

Drawing on a hypothesis of Ricardo (1817) and the work of Lucas (1972) on rational expectations, Barro (1974) developed a theory of the crowding-out effect of expectations known as the Ricardo–Barro equivalence theorem. He criticizes the use of deficits because they often result in borrowing or higher taxes. Indeed, according to the Ricardian approach to public debt, a tax cut financed by borrowing does nothing to stimulate consumer spending, because far from increasing lifetime income, it merely transfers today's taxes to tomorrow. Barro argues that economic agents are rational and will, therefore, frustrate the government's fiscal decisions. Thus, in the event of a budget deficit, since agents anticipate future tax increases necessary to finance the debt, rather than consume or invest, they save their additional income induced by the stimulus policy. In the end, the stimulus is neutralized.

In the same vein as monetarists, public choice theorists argue that on the eve of important elections, the government takes demagogic measures to win votes, which can have beneficial effects in the short term, but unfavorable effects in the long term. Indeed, they consider political life as a market where politicians (offerers), pursuing their private agendas, offer programs to their voters (demanders), and where the ballot paper represents the market price and the public expenditure invoked in these programs to seduce the voters by implementing more or less complex strategies. To satisfy the interests of their voters and to meet the demands of the various lobbies, the majority is led to conduct an expansionist policy financed by borrowing. The cost of public spending in the service of category interests is, thus, marked by the increase in public debt which is used to buy votes.

Then Tullock (1978) considers bureaucracy to be a cause of public debt. For him, the multiplication and reproduction of state structures are simply the result of their inefficiency and their leaders' taste for power.

Some theoretical studies on the relationship between external debt and economic growth have emphasized the negative effects of debt overhang, giving rise to the debt overhang theory. Krugman (1988), Sachs (1989), and Cohen (1992), in the context of sovereign debt contracts, show that high debt is harmful to economic growth when it discourages investment. This theory establishes that above a certain threshold, foreign debt discourages consumption and investment, and consequently limits economic growth. Using the Laffer curve, they show that the relationship between the nominal value and the market value of the debt takes the form of an inverted U-shaped curve, the abscissa of which corresponds to the outstanding debt and the ordinate to the expected value of the repayment. According to these authors, the increase in the nominal value of the debt goes hand in hand with the increase in the expected repayment (ascending part of the curve). On the other hand, an increase in the debt reduces these expectations (the descending part of the curve).

Empirical evidences

Since the debt crisis of the 1980s, several models have evaluated the link between external debt and economic growth to demonstrate the existence of a positive or negative impact of debt on growth and investment.

For his part, Warner (1992) used a set of independent variables in his attempt to understand the effect of the debt crisis in the years 1982–1989. According to him, the slowdown in investment of the highly indebted countries at that time was due to the relatively very high world interest rate, the decrease in export prices, and the slow world recession. All these shocks could contribute to the decline in investment.

However, Rockerbie (1994) criticized Warner's (1992) study, saying that his analysis contains several weaknesses, including the effects of the debt crisis on investment in indebted countries. Rockerbie argues that the low levels of investment are the cause of the crisis and not the other way around. In this regard, Rockerbie examined a composition of control variables that could affect investment in the long term using a sample of 13 Latin American countries over a period from 1965 to 1990. He finds only a positive effect of debt on investment in all the countries selected in his study except Mexico. According to his study, the period of the study as well as the country considered influenced the results of the empirical study to verify the effect of debt on investment.

In 1997, Desphande conducted an analysis of 13 highly indebted countries, his study covering a period from 1971 to 1991. He found a negative relationship between external debt and investment, and established the observation that when there is over-indebtedness, external debt tends to capture the effect of the explanatory variables of investment.

One of the limitations of his study is that it does not take into account control variables that may influence investment. The objective of Deshpande’s (1997) exercise is to essentially test the nature of the relationship between investment and debt, not to compose a model of investment behavior per se.

The authors of these studies take a linear approach in their analyses of the spillover of external debt on investment and economic growth. In most traditional theories, it is generally accepted that the impact of external debt on economic growth remains positive until a certain threshold is reached where its effect becomes negative. Therefore, a nonlinear approach must be employed.

Several models have estimated the link between debt and economic growth to test a nonlinear relationship of the Laffer curve type. Patillo et al. (2002) conducted a study of 93 developing countries covering the period 1969–1998. They, thus, confirm the theoretical view that excessive debt may dampen growth not only by reducing the resources that can be devoted to investment, but also by distorting their allocation (to less profitable short-term projects, for example) and by possibly discouraging the authorities from improving the economic climate. This is also consistent with recent empirical evidence that aggregate factor productivity, rather than factor accumulation, determines growth differences across countries. For the 93 countries, their main results show a negative relationship between external debt and GDP growth when debt exceeds 35–40% of GDP and 160–170 percent of exports, respectively.

In their empirical study, Clements et al. (2007) chose to work on 55 low-income countries for a period between 1970 and 1999. In this sense, they estimated a two-equation model and paid particular attention to the indirect impacts of external debt on growth and proposed to allocate a share of resources to public investment to accelerate growth and fight poverty. From this study, they conclude that through a liquidity squeeze, external debt has a crowding-out effect on the rate of investment. Thus, they deduce that an increase of 0.75–1 percentage point of GDP and growth of 2 percentage points will be produced with a decrease of 6 percentage points of the debt service/GDP ratio.

Furthermore, Mendoza et al. (2003) explained the nonlinear effect of the relationship between external debt and economic growth, and also estimated the equation that involves private investment, to distinguish public external debt from private external debt. They show the negative impact of the latter on private investment in Colombia and according to the nonlinear equation found in the estimated growth, they concluded that the critical threshold of the debt is 27.2%, and that an increase of 1 point of GDP of the debt leads to a decrease of 0.18 point in the growth rate.

Similarly, Ibi and Aganyi (2014) analyze the impact of external debt on economic growth in Nigeria. They use an econometric model in time series data with a Vector Autoregression (VAR) to test whether or not the ratio of external debt to exports, inflation, real exchange rate, and public investment can boost the growth rate of gross domestic product (GDP). Their results reveal that the causal link between external debt and economic growth is weak in the Nigerian context. Therefore, external debt could be used to predict the improvement and not the slowdown of economic growth in Nigeria.

On their part, Abdelhafidh (2014, 2020) examined the impact of external debt on economic growth in Tunisia. His empirical methodology employs the staggered lag autoregressive approach and shows that over the period 1970–2010, the impact of debt on growth has been negative in both the long and short runs. His results suggest that a reduction in Tunisia's external debt would be favorable to the country’s economic growth. In a similar vein, a majority of studies have found a negative interaction linking external debt and economic growth [see for example, Barik and Sahu (2022), Yasar (2021), Wang et al. (2021), Makun (2021), Qureshi and Liaqat (2020)].

However, Idlemounden and Raffinot (2005) argue that external debt is a burden on an economy. They argue that debt service payments tend to crowd-out public spending, leading to a decline in overall investment, and the future burden of debt, as described by the stock of debt, will affect the incentives of private economic agents through an increase in tax pressure. According to these authors, this effect will only manifest itself once a certain level is reached; thus justifying the partial cancelation of the debt when this threshold is exceeded.

In this context, Tanimoune et al. (2005) have shown, again in the context of the non-linearity of the effects of public debt on growth, that in the WAEMU, in the presence of a debt ratio lower than 83% of GDP, the State exerts a Keynesian influence on economic activity and, beyond that, a non-Keynesian or even anti-Keynesian influence. Their estimates lead to a clearly negative debt/growth ratio. The study also highlights the nonlinear nature of the relationship.

A large body of work shows that the negative correlation between debt and growth is particularly strong when debt is close to 100 percent of GDP (Reinhart and Rogof 2010; Checherita-Westphal and Rother 2012; Baum et al. 2013; Reinhart et al. 2012). In this sense, Reinhart and Rogof (2010) demonstrate, using histograms, the existence of an inverted "U" relationship between growth rates and debt, with the relationship only becoming negative once a 90% debt level is crossed. This study has, however, been heavily criticized by Irons and Bivens (2010), who argue, among other things, that for the United States, there is very little data on debt levels above 90%, so these are outliers from which no generally valid conclusion can be drawn.

Similarly, Checherita-Westphal and Rother (2012) also look at the relationship between debt and economic growth. They review 12 Eurozone countries over the period 1970–2011 and find an inverted U-shaped relationship between economic growth and government debt, with a cutoff value between 70 and 80%. However, Minea and Villieu (2012) show that the negative correlation between debt and growth disappears when they use the IMF database (Abbas and Christensen 2010). Furthermore, their PSTR model finds that the correlation between debt and growth becomes positive when debt exceeds 115 percent of GDP. Kourtellos et al. (2012) also question the existence of a debt threshold and show that thresholds depend on democracy rather than the level of debt itself.

Applying the dynamic threshold panel methodology over the period 1965–2019, Checherita-Westphal and Rother (2012) suggest that the impact of debt on growth remains positive and statistically significant in the short run. However, they confirm that this impact disappears and loses significance when the debt-to-GDP ratio exceeds the 67% threshold. For debt ratios above 95%, additional debt has a negative impact on economic activity.

Recently, Gharyeni and Yasmine (2016) conducted an empirical study on a sample composed of middle-income countries to determine their optimal debt threshold from 1980 to 2011 based on a cylindrical panel of 17 countries. The main results indicate an optimal debt threshold of 40 percent of GDP. Regarding the relationship between external public debt and economic growth, it is worth noting that, in recent years, some form of consensus seems to be emerging among economists (Panizza and Presbitero 2013).

More recently, Qureshi and Liaqat (2020) found that public external debt has a nonlinear effect on economic growth based on a survey of 123 countries over the period of 1990–2015 using the PVAR model. They did not discover evidence for a universal threshold for external debt and determined that the primary ways external debt affects growth are through savings and investment.

According to Zaghdoudi (2020) and Beyene and Kotosz (2021), the effect of public debt on economic growth changes, shifting from a positive to a negative direction. To summarize, it is evident from the literature review that the empirical evidence on the specific character of the relationship linking external debt and economic growth is rather incomplete.

This brief overview shows that both theoretically and empirically, the links between external debt and economic growth are mixed and ambiguous. This ambiguity has justified the fact that the majority of studies focus on the negative effects of debt overhang.

Empirical methodology

After the brief overview of the theoretical and empirical literatures, we will now turn to the appropriate empirical specification of the model to address our problem. Indeed, we will start with the presentation of the model and the variables followed by the main estimation techniques adopted in this paper.

Model and variables

To assess the direct impact of external debt on economic growth, we have chosen the approach of working on time series data for Tunisia during the period 1965 to 2019. With reference to Gharyeni and Yasmine (2016), Abdelhafidh (2020), and Makun (2021), we will estimate the following economic model:

$$GDP\_Growt{h}_t={\beta }_0+{\beta }_{1}External\_Deb{t}_t+{\mu }_t,$$ 1

where "GDP_Growth" is the GDP growth rate, "External_Debt" is the external debt rate, and "u" is an error term assumed to verify the Gauss–Markov assumptions.

In fact, the rate of change, or growth rate, is an economic indicator used to measure the growth of a country's economy for 2 consecutive years. It is calculated in relation to the evolution of the gross domestic product (GDP), which represents the sum of wealth produced by all companies in a country over a given period. Calculating the growth rates of different states allows us to compare them to each other.

In economics, external debt refers to all debts owed by a country, including governments, companies, and individuals to foreign lenders. It is important to distinguish between gross external debt (what a country borrows from abroad) and net external debt (the difference between what a country borrows from abroad and what it lends abroad). What is more significant is the net external debt. Too high a level of external debt is a major country risk factor: in the event of fluctuations in the national currency, the amounts of interest and principal of external debt, if denominated in foreign currency, can quickly lead to an economic crisis or even to default (Smith 2020).

Estimation techniques

The ARDL model is the most widely used model for estimating variables in a time series data context. It is a method that is independent from the order of integration of the different variables, unlike Johansen's (1991) method, which is the classic way of determining long-term relationships where it requires that all variables be integrated of order one.

On the one hand, the ARDL model provides the precise way to deal with long-run relationships by focusing on the dynamics of a simple equation where the long-run relationship and the short-run dynamics are jointly estimated. On the other hand, the ARDL model allows researchers to deal with variables that are possibly of different order of integration, namely I(0) and I(1), and not simply I(1). Indeed, the ARDL model cannot emphasize this obligation.

Note that the ARDL model estimates (p + 1)^k regressions, where p is the optimal number of lags and k is the number of variables in the equation. For the optimal number of lags, we will choose a maximum duration of two periods since the VAR model used in the Granger causality test approves the use of four lags. Indeed, the optimal number of lags selected is the one that respects the criteria of no serial correlation. This ARDL method takes into consideration the inclusion of the lag value of exogenous variables in the co-integration relationship to eliminate the problem of serial correlation of residuals and endogeneity.

More precisely, in the ARDL approach by Pesaran et al. (2001), all variables are considered as endogenous variables. Hence, the general formula of this model is the following:

$$y_t={\alpha }_0+{\alpha }_{1}t+\sum _{j=1}^p{\lambda }_j{y}_{t-j}+\sum _{m=0}^q{\delta }_k^{{}^{\prime }}{x}_{t-m}+{\mu }_t,$$ 2

where x represents the set of regressors which are assumed to be uncorrelated with the residual u. We often find an equivalent specification as:

$$\mathrm{\Delta }{y}_t={\alpha }_0+{\alpha }_{1}t+\varphi y_{t-1}+{\beta }^{{}^{\prime }}{x}_t+\sum _{j=1}^{p-1}{\lambda }_j^{\ast }\mathrm{\Delta }{y}_{t-j}+\sum _{m=0}^{q-1}{\delta }_m^{{\ast }^{\prime }}{x}_{t-m}+{\mu }_t.$$ 3

At the beginning, we briefly present a discussion of the ARDL co-integration approach by implementing the two steps to make this approach effective to the co-integration procedure. At this time, it is important to test the existence of a long period relationship between the variables in the system. Therefore, the null hypothesis of having no integration or no long-run relationship between the variables $H_0:\varphi ={\beta }_i=0$ is tested against the alternative hypothesis $H_1:\varphi \ne ;{\beta }_i\ne 0$.

The "Bounds tests" procedure is based on Fisher's "F" statistics. This statistics used for this procedure has a non-standard distribution because the variables in the system are I(0) or I(1). Thus, two sets of critical values are calculated by Pesaran et al. (2001, p. 300) for a given level of significance. One set assumes that all variables are I(0) and the other set assumes they are all I(1). If the calculated "F" statistics exceeds the upper bound of the critical values, then H₀ is rejected.

The second step is that if the long-run relationship is established then the long term and error correction model (ECM) estimates of the ARDL model can be obtained from the initial short-run equation. The estimation of an ARDL model first involves determining the number of lags to be introduced. The Akaike information criterion (AIC) and the Schwarz's Bayesian criterion (SBC) are often used. A general ECM representation of the initial short-run equation is formulated as follows:

$$\mathrm{\Delta }{y}_t={\alpha }_0+{\alpha }_{1}t+\delta E{C}_{t-1}+\sum _{i=1}^p{\lambda }_i\mathrm{\Delta }{y}_{t-i}+\sum _{k=1}^K\sum _{j=0}^{\mathit{qk}}{\delta }_j\mathrm{\Delta }{x}_{k,t-j}+{\zeta }_t$$ 4

where $\delta$ is the speed of adjustment parameter and EC are the residuals obtained from the estimation of the co-integration model of the short run Eq. 3. Since we use annual observations, we can experiment with up to “4” lags on the first difference of each of the variables, and we have calculated the F-statistics for the joint significance of the lag levels of the variables in the initial short-term equation. So, the long-term conditional model can be obtained from the solution of the initial short-term reduced form, it is written as follows:

$$y_t={\theta }_0+\sum _{k=1}^K{\theta }_k{x}_{\mathit{xt}}+{\mu }_t,$$ 5

where ${\theta }_0=-{\alpha }_0/\varphi$ and ${\theta }_0=-{\beta }_k/\varphi$.

However, the previous model does not take into account the direction of the exogenous variable in relation to the endogenous one. Therefore, the application of a more appropriate model is necessary to accurately reflect the complexity of the real world. Thus, we employ the nonlinear autoregressive distributed lag (NARDL) model developed by Shin et al. (2014). In fact, the latter worked on a NARDL model which takes into account an asymmetric long-run regression:

$$y_t={\beta }^{+}{x}_t+{\beta }^{-}{x}_t+{\mu }_t,$$ 6

and

$$\mathrm{\Delta }{x}_t={\upsilon }_t$$ 7

where $y_t$ and $x_t$ are scalar $I(1)$ variables, and $x_t$ is decomposed as $x_t=x_0+x_t^{+}+x_t^{-}$, where $x_t^{+}$ and $x_t^{-}$ are partial sum processes of positive and negative changes in $x_t$:

$$x_t^{+}=\sum _{j=1}^t\mathrm{\Delta }{x}_j^{+}=\sum _{j=1}^{t}max(\mathrm{\Delta }{x}_j,0);x_t^{-}=\sum _{j=1}^t\mathrm{\Delta }{x}_t^{-}=\sum _{j=1}^{t}min(\mathrm{\Delta }{x}_j,0)$$ 8

The above provides modeling asymmetric co-integration with partial sum decompositions. Schorderet (2003) defines a stationary linear combination of the partial sum components as follows:

$$z_t={\beta }_0^{+}{y}_t^{+}+{\beta }_0^{-}{y}_t^{-}+{\beta }_1^{+}{x}_t^{+}{\beta }_1^{-}{x}_t^{-}$$ 9

If $z_t$ is stationary, then $y_t$ and $x_t$ are “asymmetrically cointegrated”. The standard linear (symmetric) co-integration is a special case of Eq. 9, obtained only if ${\beta }_0^{+}={\beta }_0^{-}$ and ${\beta }_1^{+}={\beta }_1^{-}$. Shin et al. (2014) consider the case where the following restriction holds: ${\beta }_0^{+}={\beta }_0^{-}={\beta }_0$. In Eq. 9, this implies that ${\beta }^{+}=-{\beta }_1^{+}/{\beta }_0$ and ${\beta }^{-}=-{\beta }_1^{-}/{\beta }_0$.

So, Shin et al. (2014) use this foundation to propose the nonlinear ARDL(p,q) model:

$$y_t=\sum _{j=1}^p{\varphi }_j{y}_{t-j}+\sum _{j=0}^q\left({\varphi }_j^{{+}^{\prime }}{x}_{t-j}^{{+}^{\prime }}+{\varphi }_j^{{-}^{\prime }}{x}_{t-j}^{{-}^{\prime }}\right)+{\epsilon }_t$$ 10

where $x_t$ is a $k\times 1$ vector of multiple regressors, $x_t=x_0+x_t^{+}+x_t^{-}$, ${\varphi }_j$ is the autoregressive parameter, ${\varphi }_j^{+}$ et ${\varphi }_j^{-}$ are the asymmetric distributed lag parameters, and ${\epsilon }_t$ is an i.i.d. process with zero mean and constant variance, ${\sigma }_{\epsilon }^2$. Indeed, Shin et al. (2014) considers $x_t$ is decomposed into $x_t^{+}$ and $x_t^{-}$ around zero, distinguishing between positive and negative changes in the rate of growth of $x_t$. They follow Pesaran et al. (2001) and Bertsatos et al. (2022), and write Eq. 10 in the error correction form as:

$$\begin{array}{cc}\hfill \mathrm{\Delta }{y}_t& =\rho y_{t-1}+{\theta }^{{+}^{\prime }}{x}_{t-1}^{+}+{\theta }^{{-}^{\prime }}{x}_{t-1}^{-}+\sum _{j=1}^{p-1}{\gamma }_j\mathrm{\Delta }{y}_{t-j}+\sum _{j=0}^{q-1}\left({\varphi }_j^{{+}^{\prime }}\mathrm{\Delta }{x}_{t-j}^{+}+{\phi }_j^{{-}^{\prime }}\mathrm{\Delta }{x}_{t-j}^{-}\right)\hfill \\ \hfill & =\rho {\xi }_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\mathrm{\Delta }{y}_{t-j}+\sum _{j=1}^{q-1}\left({\phi }_j^{{+}^{\prime }}\mathrm{\Delta }{x}_{t-j}^{+}+{\phi }_j^{{-}^{\prime }}\mathrm{\Delta }{x}_{t-j}^{-}\right)\hfill \\ \hfill \end{array}$$ 11

where $\rho ={\sum }_{j=1}^p{\phi }_{j-1},{\gamma }_j=-\sum _{i=j+1}^p{\phi }_i$ for $j=1,...,p-1$, ${\phi }^{+}={\sum }_{j=0}^q{\theta }_j^{+}$, ${\phi }^{-}={\sum }_{j=0}^q{\theta }_j^{-}$, ${\phi }_0^{+}={\phi }_0^{+}$, ${\phi }_j^{+}=-{\sum }_{i=j+1}^q{\theta }_j^{+}$ for $j=1,...,q-1$, ${\phi }_0^{-}={\theta }_0^{-}$, ${\phi }_j^{-}=-{\sum }_{i=j+1}^q{\theta }_j^{-}$ for $j=1,...,p-1$ and ${\xi }_t=y_t-{\beta }^{{+}^{\prime }}{x}_t^{+}-{\beta }^{{-}^{\prime }}{x}_t^{-}$ is the nonlinear ECM, where ${\beta }^{+}=-{\theta }^{+}/\rho$ and ${\beta }^{-}=-{\theta }^{-}/\rho$ are the associated asymmetric long-run parameters.

As for the non-zero contemporaneous correlation between regressors and residuals in Eq. 11, Shin et al. (2014) suggest the following reduced form data generation process for $\mathrm{\Delta }{x}_t$:

$$\mathrm{\Delta }{x}_t=\sum _{j=1}^{q-1}{\mathrm{\Lambda }}_j{\mathrm{\Delta }}_{t-j}+{\upsilon }_t,$$ 12

where ${\upsilon }_t\to iid(0,\sum {}_{\upsilon })$ with $\sum {}_{\upsilon }ak\times k$ is positive definite covariance matrix. In terms of their focus on conditional modeling, they express ${\epsilon }_t$ in terms of ${\upsilon }_t$ as:

$${\epsilon }_t={\omega }^{{}^{\prime }}{\upsilon }_t+e_t={\omega }^{{}^{\prime }}\left(\mathrm{\Delta }{x}_t-\sum _{j=1}^{q-1}{\mathrm{\Lambda }}_j\mathrm{\Delta }{x}_{t-j})+e_t^{{}^{\prime }}\right),$$ 13

where $e_t$ is uncorrelated with ${\upsilon }_t$, by construction. If we substitute Eq. 13 into Eq. 11 and rearrange, we obtain a nonlinear conditional ECM:

$$\mathrm{\Delta }{y}_t=\rho {\xi }_{t-1}+\sum _j^{p-1}{\gamma }_j\mathrm{\Delta }{y}_{t-j}+\sum _{j=1}^{q-1}\left({\pi }_j^{{+}^{\prime }}{\mathrm{\Delta }}_{t-j}^{+}+{\pi }_j^{{-}^{\prime }}{\mathrm{\Delta }}_{t-j}^{-}\right)+e_t,$$ 14

where ${\pi }_0^{+}={\theta }_0^{+}+\omega$, ${\pi }_0^{-}={\theta }_0^{-}+\omega$, ${\pi }_j^{+}={\phi }_j^{+}+{\omega }^{{}^{\prime }}{\mathrm{\Lambda }}_j$, and ${\pi }_j^{-}={\phi }_j^{-}+{\omega }^{{}^{\prime }}{\mathrm{\Lambda }}_j$ for $j=1,...,q-1$.

Equation 14 corrects for weak endogeneity of non-stationary explanatory variables, and the choice of lag structure frees the model from any residual correlation. The model explains both long- and short-run asymmetries and, as it is linear in all parameters, can be estimated by ordinary least square (OLS).

Thus, before proceeding to estimate the two models ARDL and NARDL, it should be noted that we will go through the Breusch–Godfrey (LM) serial correlation test of order “1”, the ARCH test of heteroskedasticity of order 1, the Jarque–Bera (JB) test for normality of the residuals, and the Ramsey functional form (RESET) test of order “1”. The assumptions of the serial error correlation test are as follows:

$$\left\{\begin{array}{c}{H}_0:Cov\left({\epsilon }_t,{\epsilon }_s\right)=0\forall t\ne s:\text{Absence of serial correlation}\\ {\mathrm{H}}_1:Cov\left({\epsilon }_t,{\epsilon }_s\right)\ne 0\forall t\ne s:\text{Autocorrelation of errors exists}\\ \end{array}\right).$$ 15

The Jarque and Bera (1980) test evaluates the hypothesis of approximate normality of the distribution based on the values of moments “3” and “4” of the distribution skewness and kurtosis. The hypotheses of this test are as follows:

$$\left\{\begin{array}{c}{H}_0:{\epsilon }_{\text{t}}\to N\left(0,{\sigma }^2\right)\text{: Errors follow a normal distribution}\\ {\mathrm{H}}_1:\text{Errors do not follow a normal distribution}\\ \end{array}\right)$$ 16

To test these assumptions, the following formula is used:

$$\text{Jarque - Bera}=\frac{N-L}{6}(S^2+\frac{{(K-3)}^2}{4})\to {\chi }_2^2$$ 17

where N is the number of observations, L is the number of estimated parameters, S is the skewness value and K is the kurtosis value.

The Ramsey (1969) regression equation specification error test (RESET) checks for missing variables or a functional form problem in our model. The assumptions of this test are as follows:

$$\left\{\begin{array}{c}{H}_0\text{: The model is well specified}\\ H_1:\text{The model is misspecified}\\ \end{array}\right).$$ 18

Then more formally, we apply the Ljung–Box test (Ljung and Box 1978) to the residual series, which tests whether the first K autocorrelations ${\widehat{\rho }}_k^2\left({\epsilon }^2\right)$ (k = 1,…,K) of a process are collectively small. Suppose we have the first K autocorrelations (k = 1,…,K) of any ARMA(p, d, q) process. For a sufficiently large fixed K, the usual Ljung–Box statistic Q is given by:

$$Q=N\left(N+2\right)\sum _{k=1}^K\frac{{\widehat{\rho }}_k^2\left(\epsilon \right)}{N-k},$$ 19

where N is the sample size, K is the number of autocorrelations included in the statistic, and ${\widehat{\rho }}_k^2$ is the sample autocorrelation squared to the residual series {ε_t} at lag k. Under the null hypothesis of model fit, the test statistic is asymptotically distributed χ²(K–p–q). Thus, we would reject the null hypothesis at the α level if the value of Q exceeds the (1–α) quantile of the χ²(K–p–q) distribution.

McLeod and Li (1983) proposed a formal test for the ARCH effect based on the Ljung–Box test. It examines the autocorrelation function of the squares of the pre-whitened data and tests whether the first K autocorrelations for the squared residuals are collectively small. The hypotheses of the ARCH (autoregressive conditional heteroscedasticity) test are stated as follows:

$$\left\{\begin{array}{c}{H}_0:V\left({\epsilon }_t\right)={\sigma }^2\forall t:\text{Absence of heteroscedasticity}\\ H_1:V\left({\epsilon }_t\right)={\sigma }_t^2:\text{Errors are heteroscedastic}\\ \end{array}\right).$$ 20

Similar to Eq. 19, for a sufficiently large fixed K, the Ljung–Box Q-statistic of the McLeod-Li test is given by:

$$Q=N\left(N+2\right)\sum _{k=1}^K\frac{{\widehat{\rho }}_k^2\left({\epsilon }^2\right)}{N-k}$$ 21

where N is the sample size, and ${\widehat{\rho }}_k^2$ is the autocorrelation of the sample to the squared residual series at lag k. Under the null hypothesis of a linear generating mechanism for the data, namely, no ARCH effect in the data, the test statistic is asymptotically distributed χ²(K).

Estimates and interpretations

Our study focuses on the interaction between external debt and economic growth in Tunisia during the period 1965–2019. In the following, we will try to present the different variables statistically to describe the relationships between them in the next part.

First, in Table 1, we present the main descriptive statistics of the two predefined variables. Consequently, we will interpret the graphs that show the evolution of the variable. Indeed, based on the statistics presented in Table 1, we will describe the main characteristics of the two variables used in this study. In addition, we add the Jarque and Berra statistic and its probability to test the normality of the series and the Ljung–Box Q test (p = 5) of autocorrelation and its probability. It is clear from the last test that all variables have a serial autocorrelation problem.

Table 1.

Descriptive statistics of variables

Statistics	GDP_Growth	External_Debt
Mean	2.627	56.762
Standard deviation	3.183	14.244
Minimum	– 3.915	26.612
P25	0.763	50.270
P50	2.621	55.937
P75	4.270	65.205
Maximum	15.183	100.999
Skewness	0.793	0.505
Kurtosis	6.144	4.218
Coefficient of variation (CV)	1.212	0.251
Jarque–Berra (JB) statistics	28.41	5.744
JB probability	0.000	0.000
Ljung–Box (LB) statistics (p lag = 5)	5.566	91.082
LB probability	0.351	0.000

LB refers to Ljung and Box (1978) where p represents the number of delays chosen for the Ljung–Box test

JB refers to Jarque and Bera (1980) normality test

“p” represents the number of lags in the Ljung–Box test

Concerning the descriptive analysis, we start with the growth rate (GDP_Growth) where the latter, according to the left-hand side of Fig. 1, is characterized by an oscillation of each value for each country around its relative mean. Overall, this variable has a global average of 2.627 with a standard deviation of 3.183, making it highly heterogeneous (CV = 1.212). These values range from − 3.915 to 15.183 with a high concentration around 2.621. Its sample distribution is asymmetrically spread to the right (skewness = 0.793) and strongly leptokurtic (kurtosis = 6.144). According to the probability of the Jarque–Bera test, we reject the null hypothesis of normality.

Fig. 1.

Trend evolution of GDP_Growth and External_Debt

According to the right-hand side of Fig. 1, the External_Debt variable is characterized by the same upward and downward trends along the study period. In total, this variable has an overall mean of 56.762 with a standard deviation of 14.244 making it more heterogeneous (CV = 0.251). All these values range from 26.612 to 100.999 with a high concentration around 55.937. In addition, the sample distribution is weakly skewed to the right (skewness = 0.505) and strongly leptokurtic (kurtosis = 4.218). Based on the probability of the Jarque–Bera test, we reject the null hypothesis of normality.

Overall, the two series reveal an autocorrelation problem and the persistence of strong heterogeneity that will influence the results of the estimations that follow. Thus, we can consider them not stable.

For a purely empirical logic, and to determine the order of the sequences used, we correct for the existence of unit root on the selected variables. In fact, this process is very important to fit the econometric model. Thus, to explain the stability of the series, various stationarity tests are used, but some classical tests [such as the Dickey and Fuller (1979) or Phillips and Perron (1988) test] do not take into account structural changes. In this respect, the systematic method of unit root testing with the presence of shocks relies in particular on the Zivot and Andrews (1992) test (ZA), which considers the null hypothesis of the existence of unit roots of the series with the presence of structural breaks. We adopt the presence of a single shock given the small sample size (T = 55).

Table 2 presents the results of Zivot and Andews (1992) test for the two transformed series in level and first difference. Indeed, we find that the GDP_Growth variable is non-stationary in level with the existence of significant breaks for the three models A, B, and C. In fact, this break is significant in 1996 for model A, in 2008 for model B, and in 1973 for model C. Applying the same ZA procedure for the External_Debt variable, Table 2 also shows that it is non-stationary in level with significant breaks in 1981, 1986, and 1995. These dates are too remarkable with the different financial and political crises that Tunisia experienced during the study period.

Table 2.

Zivot and Andrews (1992) unit root test results

Model	Designation	GDP_Growth	External_Debt
		In level
A	Date of break	1996	1995
	t-statistics	− 8.353	– 2.961
B	Date of Break	2008	1986
	t-statistics	− 7.725	-2.502
C	Date of Break	1973	1981
	t-statistics	− 9.383	-3.029

Decision		Non-stationary	Non-stationary
Model	Designation	In first difference
A	Date of break	1990	1988
	t-statistics	− 8.896	– 6.190
B	Date of break	1976	2011
	t-statistics	− 8.661	– 5.916
C	Date of break	1984	1988
	t-statistics	− 8.896	– 6.178
Decision		Stationary	Stationary

The critical values at 1% and 5%, respectively, for model A are (− 5.34) and (− 4.80), for model B (− 4.93) and (− 4.42) and for model C (− 5.57) and (− 5.08)

^*, ^** and ^*** represent significance at 10%, 5%, and 1%

Similarly, the second panel of Table 2 of the ZA test in first difference shows the rejection of the null hypothesis of unit root at 5% or at 1%. This result indicates that all the series in first difference are stationary at the 5% critical threshold with the existence of significant shocks for the three models A, B, and C. Therefore, we can consider them as integrated of order 1 (I[1]).1

Table 3 presents the short-term estimates, the recall strength of the ECM model as well as the set of validity diagnostics of the first growth model.

Table 3.

ARDL short-term estimation

ARDL model	ARDL(1,1)		Maximum number of lags	1
Endogenous: ΔGDP_Growtht	Coefficient	Standard error	t-statistic	p value
Constant	1.424	0.401	3.55	0.001
GDP_Growtht-1	– 0.201	0.087	– 2.32	0.025
External_Debtt-1	– 0.011	0.005	– 2.44	0.018
ΔGDP_Growtht-1	– 0.201	0.134	– 1.49	0.142
ΔExternal_Debtt-1	0.193	0.079	2.42	0.020
δ (ECTt-1)	– 0.781	0.089	– 8.732	0.000
R2	0.632
Adjusted R2	0.608
F-statistic (bounds test)	38.843	CV at 5% (k = 1)	8.734	0.000
Akaike		Schwarz
Durbin Watson statistic	2.009			–
LM test (lags = 5)	0.024			0.877
McLeod-Li ARCH test (lags = 1)	1.792			0.180
Jarque–Bera test	4.133			0.127
Ljung–Box test (lags = 12)	14.065			0.296
McLeod test (lags = 12)	10.333			0.587
Breusch–Pagan (BP)	2.661			0.103
Ramsey RESET test	2.192			0.103

Δ represents the first difference, LM test Lagrange multiplier test (Breusch-Godfrey serial autocorrelation), ARCH autoregressive conditional heteroscedasticity test, RESET Ramsey regression equation specification error Test, BP Breusch–Pagan test for heteroscedasticity, δ (ECT_t–1) is the error correction term that shows the speed of adjustment toward long-run equilibrium (this term must be significantly negative to ensure the existence of the long-run relationship), k represents the number of explanatory variables in the Narayan (2005) bound test. CV critical value (An additional validation taking into account the effect of the 2011 revolution has been performed and is available upon request)

The optimal growth model is verified by a 1 lag ARDL without trend [ARDL(1,1)] (i.e., unrestricted constant and no trend) model where the F-statistic of the bounds test displays a value of 38.843 considerably higher than 4.416, according to Narayan (2005). This leads us to reject the null hypothesis of no co-integration.

In addition, the estimated co-integration coefficient of ECT_t-1 is -0.781. Since the error correction term is negative and significant, this implies that the results support the existence of a long-run relationship between variables. Thus, the error correction term indicates that the deviation from the long-term growth path due to a certain shock is adjusted by 78.1% each year. In other words, this coefficient associated with the force of recall allows us to conclude that the shocks on the economic growth in Tunisia are corrected to 78.1% by the effect of "feedback"; that is to say, we manage to adjust 73.9% of the imbalance between the desired and effective level of the Tunisian economic growth. Thus, we can identify an average delay equal to |1⁄0.781|= 1.28. This means that a shock to Tunisian economic growth is fully absorbed after 1 year, 3 months, and 11 days on average.

Moreover, it is of average quality since the value of the adjusted R² statistic is around 0.5 (0.632). The results of the different model checking tests, respectively, Breusch–Godfrey (LM) five-order serial autocorrelation test, the ARCH test for first-order heteroscedasticity, the Jarque–Bera (JB) residual normality test, the McLoyd test for serial autocorrelation, and the Ramsey (RESET) test for functional form validation, confirm that there is no serial autocorrelation, no heteroscedasticity, and the normal distribution of the residuals. In addition, the functional form of specification chosen is correct. Furthermore, the stability tests of the CUSUM and CUSUM squared parameters prove that the estimated coefficients are stable in mean and variance over the study period (see Fig. 2).

Fig. 2.

Evolution of CUSUM and CUSUMQ statistics

As evidenced by our observations, in the short term, there is a noticeable adverse effect of the lagged value of GDP_Growth on the changes in GDP_Growth. Additionally, we noticed the significant negative effect of the lagged value of External_Debt on the GDP_Growth variation. Based on this, we acknowledge the negative and significant impact of External_Debt on long-term economic growth.

Our long-term results, inferred from Table 4, suggest that, on the one hand, the effect of debt on Tunisia's growth was negative (− 0.056) and significant over the entire 1965–2019 period. The problems associated with the accumulation and use of foreign debt, thus, do not seem to have been specific to the latter's period. On the other hand, the negative effect was higher in the long-term compared to the short-term as reported by Caravaggio and Carnazza (2022). Incentive effects may explain this result. The increase in debt, as suggested by the debt overhang theory, may reduce the incentive to invest because economic agents anticipate an increase in future taxes to repay the debt. It is plausible that these effects diminish as initial expectations are not realized and repayment arrears are not observed. During the period under consideration, Tunisia has indeed always honored its debt service obligations. In fact, our result confirms the work of Krugman (1988), Sachs (1989), and Cohen (1992) who show that an increase in external debt is detrimental to economic growth.

Table 4.

ARDL long-term estimation

GDP_Growtht	Coefficient	Standard error	t-statistic	p value	95% confidiential interval
External_Debtt	− 0.056	0.025	− 2.200	0.033	− 0.107	− 0.004
Constant	7.085	2.003	3.540	0.001	3.054	11.115

However, and according to the theoretical lessons described above, the relationship between growth and indebtedness is mixed. For this, we will check it using the NARDL approach. In fact, the nonlinear ARDL model recently developed by Shin et al. (2014) uses positive and negative partial sum decompositions allowing the detection of the asymmetric effects in the long and the short terms. Unlike the classical co-integration models, NARDL models have some other advantages. First, they perform better for the determination of co-integration relations in small samples (Romilly et al. 2001). Second, they are applicable regardless of whether the regressors are stationary in level or at the first difference (i.e., I(0) or I(1)). Yet, they are not applicable when the regressors are I(2). As for the other advantages of NARDL, therefore, the asymmetric NARDL framework of Shin et al. (2014) fits our research problem more appropriately as it allows us not only to gauge the short- and long-run asymmetries, but also to detect hidden co-integration. For example, a positive shock of External_Debt may have a larger absolute effect in the short run whereas a negative shock has a larger absolute effect in the long term (or vice-versa).2

As a first step, we started by testing the asymmetry of external debt on growth by subdividing the External_Debt variable into two other variables: “External_Debt_pos” denotes positive changes (External_Debt_pos = External_Debt if ΔExternal_Debt > 0 and 0 otherwise) and “External_Debt_neg” denotes negative changes (External_Debt_neg = External_Debt if ΔExternal_Debt < 0 and 0 otherwise) where Δ represents the first change. Asymmetric effects results are shown in Table 5. Indeed, the results show significant effects of the two variables “External_Debt_pos” and “External_Debt_neg” at 5% and 10%, respectively, on economic growth. The former has a negative impact while the latter has a positive impact. This proves the presence of an asymmetric effect of external debt on growth rather than a purely negative effect. That is why we will justify it using the NARDL approach.

Table 5.

Asymmetric statistics

GDP_Growtht	Coefficient	Probability
External_Debt_post	− 0.084	0.018
External_Debt_negt	0.089	0.056
Constant	2.712	0.004
R2	0.127
F-statistic	F(2, 52) = 3.80**
Probability F-statistic	0.029

**denotes significance at the 5% level

Therefore, the results of the asymmetry effect, that are against the monetarists, assert the work of Abdelhafidh (2014, 2020) and Mendoza et al. (2003) concerning the existence of an inverted "U" relationship between growth rates and external debt.

Based on the above, we moved to the second step which is to estimate the short-run relationship by the NARDL approach as suggested by Shin et al. (2014). Indeed, the most representative and significant form of our relationship is a NARDL(1;1;1). Therefore, the short-run estimates of the NARDL approach, shown in Table 6, illustrate a negative and significant effect at the 5% level of the one-period lagged External_Debt_pos variable on the change in the short-term growth rate. However, we record a positive and significant effect of the variable External_Debt_neg lagged by one period on the variation of the short-term growth rate. This proves the previous results of a mixed effect of external debt on growth.

Table 6.

NARDL short-term estimation

Endogenous: ΔGDP_Growtht	Coefficient	Standard error	t-statistic	p value
GDP_Growtht-1	– 1.422	0.246	– 5.780	0.000
External_Debt_post-1	– 0.096	0.047	– 2.040	0.047
External_Debt_negt-1	0.101	0.059	1.710	0.094
ΔGDP_Growtht-1	0.128	0.147	0.870	0.391
ΔExternal_Debt_post	– 0.080	0.120	– 0.670	0.509
ΔExternal_Debt_post-1	0.038	0.134	0.280	0.777
ΔExternal_Debt_negt	– 0.669	0.221	– 3.020	0.004
ΔExternal_Debt_negt-1	– 0.109	0.225	– 0.490	0.629
Constant	2.635	1.356	1.940	0.058

Δ represents the first difference

More precisely, in general, an increase in external debt leads to a decline in the growth rate. Thus, the increase of the external debt will have a large negative effect on economic growth which hinders the positive effects of other aggregates (foreign direct investment and trade openness), (Adow et al. 2018; Zaman et al. 2018) in a rentier country such as Tunisia. While, its decrease plays a positive role in stimulating economic growth.

One must test whether the variables are cointegrated, otherwise the coefficients would be spurious in the case where the co-integration relationship is absent. To test for co-integration under a NARDL model, Shin et al. (2014) recommended using the joint null hypothesis of the level (undifferentiated) variables and comparing the critical values of the linked tests in Pesaran et al. (2001). Then if calculated "F” is greater than the critical value, then there is evidence of co-integration. Otherwise, no evidence of co-integration is found.

The next step is to estimate the long-term relationship. In fact, the lessons of Table 7 justify the previous results of the existence of a strong asymmetry. Indeed, both Student's (t_BDM) and Fisher's (F_PSS) statistics are in favor of the existence of a cointegrating relationship where these two values are higher than the critical values of Pesaran et al. (2001). In addition, the diagnostic tests show the validity of the model where the probability of the Ramsey test is greater than 5% despite the residuals not being normal.

Table 7.

NARDL long-term estimation

GDP_Growtht	Positive long-term effect				Negative long-term effect
External_Debtt	Coefficient	F-statistic		p value	Coefficient	F-statistic	p value
	− 0.068	5.432		0.024	0.071	3.595	0.065
		Long-term asymmetry			Short-run asymmetry
External_Debtt		F-statistic		p value		F-statistic	p value
		5.087		0.029		2.230	0.143
Cointegration test	t_BDM				F_PSS
	− 5.781				11.522
	Statistic		p value
Jarque–Bera test	9.107		0.010
Ramsey test	1.177		0.330

The dynamic asymmetric relationship between the given variables was further enriched by plotting the stability statistics of the CUSUM and CUSUMQ coefficients (Fig. 3). These dynamic recursive statistics show the adjustments of external debt and economic growth, and their new long-run equilibrium in response to a positive or negative unit shock over the 55 years. The positive (negative dashed green line) and negative (dashed red line) change curves describe the adjustment of external debt to a positive and negative effect of economic growth. The skewness line (solid blue line) reflects the difference between the positive and negative impact variables over 55 years.

Fig. 3.

Nonlinear evolution of CUSUM and CUSUMQ statistics

The results presented above can be used for the analysis of external debt use policies and economic growth in Tunisia. Moreover, comparing the results of the previous literature with existing studies could help researchers understand whether asymmetry is important in modeling the link between these two concepts. The results show a nonlinear co-integration between the variables (GDP_Growth and External_Debt). Regarding the asymmetric and symmetric relationships between the variables, the results are quite diverse. The results in the tables show evidence of a long- and short-term asymmetric relationship between the two variables. Finally, the implementation of a policy of increasing external debt will have a very significant negative impact on economic growth in Tunisia.

These are very restrictive conditions because they exclude countries that, like Tunisia, have always honored their external obligations to maintain access to international markets. However, it is possible that this access was used to fund the accounts of former President Ben Ali and his relatives abroad instead of being used in projects with high economic growth potential (Abdelhafidh 2020).

The issue of government debt will always be a major topic in economics. Its perception varies according to the schools of thought. Indeed, while some economists defend the idea that debt can be necessary and even efficient for the development of a country, others systematically reject public borrowing and think that any public borrowing can only be harmful for economic agents. The debate about the effects of debt is now even more contentious, especially as many developed and developing countries continue to engage in government debt reform processes.

Lastly, an increasing literature maintains that the impact of external debt on economic growth is nonlinear but rather follows an inverted U-shape (see, by way of example, Reinhart and Rogoff 2010; Presbitero 2012; Tanna et al. 2018; Le et al. 2019; Beyene and Kotosz 2021) as a result of a mix of the previous two patterns. The origin of such a nonlinear impact can be found in the principles of the Laffer curve (Krugman 1988), which states that the greater the total debt, the less capacity to repay. Therefore, as the amount of borrowing increases, both economic growth and the ability to repay debt increase. Nevertheless, when total debt reaches some point (that is, the point of optimal debt where the potential for growth is maximal), then a marginal increase in external debt will result in reduced growth and a diminished capacity for debt repayment. Therefore, the main point of this approach is the hypothesis of the presence of a threshold level of external debt. Many studies have tried to identify such a critical level of debt. According to the empirical literature, the threshold is not always universal, but rather depends on the specific circumstances of each country. Beyene and Kotosz (2021) argue that external debt can have an impact on growth through total factor productivity, which is driven by the amount of outstanding external debt of countries.

Conclusion and policy implications

This paper studies the link between external debt and economic growth in Tunisia over the period 1965–2019 using the linear ARDL model by Pesaran et al. (2001) and the nonlinear ARDL (NARDL) model developed by Shin et al. (2014). Our results suggest that: (i) the effect of external debt on growth in Tunisia was negative both over the entire 1965–2019 period and over the periods before and after Ben Ali's presidency. The problems related to the accumulation and use of foreign debt, thus, do not seem to have been specific to the latter's period; (ii) the negative effect was higher in the short run compared to the long run. Incentive effects may explain this result. The increase in debt, as suggested by the debt overhang theory, may reduce the incentive to invest because economic agents anticipate an increase in future taxes to repay the debt. It is plausible that these effects diminish as initial expectations are not realized and repayment arrears are not observed. During the period under consideration, Tunisia has in fact always been able to meet its debt service obligations.

The results suggest that the external debt accumulated by Tunisia between 1965 and 2019 has reduced its growth. This is an impact obtained in the context of a country whose debt is considered moderate by the World Bank. It is, therefore, not eligible for the debt reduction mechanisms implemented by multilateral institutions in favor of certain indebted countries. These institutions consider a high debt burden and repayment difficulties as necessary but not sufficient conditions. These conditions are very restrictive because they exclude countries, like Tunisia, that have always honored their external obligations to maintain access to international markets. However, it is possible that this access was used to feed the accounts of the former president and his relatives abroad instead of being used for projects with high economic growth potential.

Although Tunisia still has challenges to meet, particularly in terms of reducing debt, unemployment and inequality, reforming the public sector and reviving the economy, the forecasts of international organizations remain optimistic. There is an international awareness that despite the challenges, Tunisia will manage to move forward on the path of growth, supported by the aid of international organizations and by the proximity of the European market.

Author contributions

All authors participated in the methodology and the writing of the different sections of the article. Professor Kamel HELALI carried out the empirical part on the basis of the available data.

Funding

This project was completed without any funding.

Availability of data and material

The data that support the findings of this study are available from the databases of the Tunisian National Institute of Statistics (INS) [http://www.ins.tn/en/statistiques] and the Central Bank of Tunisia (BCT) [https://www.bct.gov.tn/bct/siteprod/index.jsp?la=AN]. Data are, however, available from the authors upon request.

Code availability

We use Winrats 8.0 and Stata 15.0 software to run different programs. Codes are available on request.

Declarations

Conflict of interest

The authors state that the article is original and not under consideration in any other journal.

Ethical approval

Hereby, I, Kamel HELALI, consciously assure that for the manuscript titled “The symmetric and asymmetric impacts of external debt on economic growth in Tunisia: Evidence from linear and nonlinear ARDL models”, the following is fulfilled: (1) This material is the authors’ own original work, which has not been previously published elsewhere. (2) The paper is not currently being considered for publication elsewhere. (3) The paper reflects the authors’ own research and analysis in a truthful and complete manner. (4) The paper properly credits the meaningful contributions of co-authors and co-researchers. (5) The results are appropriately placed in the context of prior and existing research. (6) All sources used are properly disclosed (correct citation). Literally copying of text must be indicated as such using quotation marks and giving proper reference. (7) All authors have been personally and actively involved in substantial work leading to the paper and will take public responsibility for its content.

Consent for publication

Title of product: The symmetric and asymmetric impacts of external debt on economic growth in Tunisia: evidence from linear and nonlinear ARDL models. Main author: Rima ALOULOU, Maha KALAI, and Kamel HELALI. Affiliation: Faculty of Economics and Management of Sfax, University of Sfax, Tunisia. This is to state that I give my full permission for the publication and reproduction in all editions of the above-named product. I hereby agree to release and discharge any editors or other contributors and their agents, publishers, successors and assigns from any and all claims, demands or causes of action that I may now have or may hereafter have for libel, defamation, invasion of privacy, copyright or moral rights or violation of any other rights arising out of or relating to any use of my image or case history.