Do Debt Relief and Fiscal Rules Improve Public Debt Sustainability? The Experience of sub-Sahara African Countries

The sub-Sahara African (SSA) region accounts for 33 of the 39 Highly Indebted Poor Countries (HIPCs) with many of these countries facing challenges in public debt management. This paper examines issues that are key to improving the debt situation in the region. Specifically, the study investigates two key questions namely whether the adoption of fiscal rules and debt relief improve public debt sustainability. What factors reduce the public debt of SSA countries? Interestingly, the findings reveal that while debt relief improves debt sustainability, the imposition of fiscal rules threatens the debt sustainability of the region. Further, higher economic growth and increasing government balance are instrumental to reducing public debt. These findings have far-reaching policy implications for public debt management in developing countries.


Introduction
Arguably the most topical issue in fiscal policy discussions in developing countries is the issue of public debt sustainability.These discussions revolve around determining the sustainability or otherwise of public debt; the extent to which countries can accumulate debt; ways of reducing public debt; and ways that public debt sustainability could be achieved.The case of sub-Saharan Africa (hereafter SSA) is not an exception considering the accumulated level of public debt in the region.
There are several definitions of the concept of public debt sustainability (Debrun et al., 2019;Hakura, 2020;IMF, 2002;Wyplosz, 2007); however, the common denominator in these definitions is public debt sustainability broadly deals with ensuring the accumulated debt can be continuously serviced without much hindrance and without being a huge burden on public finances.In other words, it is associated with the satisfaction of the inter-temporal budget constraint (IBC) which states that the present value of debt should equate to the sum of future government surpluses measured in present value (Kaur et al., 2018;Trehan & Walsh, 1991) There are several approaches employed to examine the sustainability of public debt.While some are quite simple because they entail comparing debt ratios against predetermined threshold values or even examining the difference between indicators/ variables; other approaches can be more complex involving econometric estimation of models and sensitivity analysis.The most applied framework for debt sustainability analysis by policymakers is the joint World Bank-IMF public debt sustainability analysis (DSA) framework.One of the key components of this approach is examining the sensitivity of public debt to changes in some variables.Considering that the changes in these variables are based on a prediction of the future, the DSA is valid to the extent of the correctness of these predictions.Despite this weakness, it remains the dominant tool used for public debt policy decisions in SSA.This study employs other approaches to determining the debt sustainability of SSA countries.
Although the debt ratio of SSA is relatively smaller than that of advanced countries -103.78% in 2019 (IMF, 2022), as shown in Figures 1 and 2, the public debt of most of the SSA countries has grown in the past decade.While most of the countries had debt ratios of less than 40% of GDP in the year 2009; as of 2019, most of the countries had debt ratios way above 40% of GDP.Further, the revenue-to-GDP ratio of SSA countries has fallen from an average of 20.55% in 2009 to about 16.68% in 2019 (World Bank, 2021).With an increasing public debt accumulation in the face of falling revenue coupled with decelerating growth (3.3% in 2022 from 4.1% in 2021 (World Bank, 2022), the sustainability of public debt of SSA countries is of interest to economists and policymakers.
Because of the debt burden of many SSA countries, the Highly Indebted Poor Countries (HIPC) debt relief initiative was launched by the IMF/World Bank in the year 1997.The essence of this initiative is to ensure that no country faces a debt burden it could not manage (IMF, 2021).
To deepen the achievement of the MDGs by the debtor countries, the HIPC initiative was replaced by the Multilateral Debt Relief Initiative (MDRI) with the African Development Bank joining the IMF and World Bank as the third debt relief-granting party.The debt relief initiatives were meant to reduce the debt burden of the countries and free up resources that could be directed toward poverty reduction and development (Ferry & Raffinot, 2019).
According to the IMF (2019), the HIPC initiative has granted debt relief amounting to about $76.2 billion, while the MDRI has granted debt relief to the tune of about $43.3 billion as of 2017.It is important to note that of the 39 HIPC countries, 33 are in sub-Saharan Africa.
Besides, even countries such as Nigeria that aren't part of the HIPC countries received substantial debt relief from the Paris Club of Creditors in 2006.
Over the debt relief initiative period, data from the AFDB (2019) shows that as of 1996, the average debt-to-GDP ratio of SSA countries was about 44.78%, this value fell to about 23.06% in 2008 after reaching a peak of about 58.99% in 2001.Public debt accumulation post-2008 (after the global economic crises) began to rise, reaching about 34.62% in 2019.This implies that debt relief could help countries to manage their debt profile; consequently, this study empirically examines the effect of debt relief on the public debt sustainability of SSA countries.The findings will be useful for both policy decisions and the campaigns for debt relief.This is aimed at restricting the level of public debt, deficits, and public expenditure (Koptis & Symansky, 1998;Tanner, 2004), although it is mostly directed towards the first two in SSA.
The imposition of fiscal rules is rooted in neoclassical economic thought with the oldest rule being the balanced budget rule.Friedman (1948) advocated the need to balance the budget over the cycle.This is a more flexible approach compared to the preceding approaches which advocated for balancing the budget in the short term (Burger & Marinkov, 2012).On the other hand, Lerner (1943) advocated the need for balancing the economy instead of balancing the budget, arguing that "the budget will balance itself".This highlights the Keynesian position of no fiscal rule imposition.Although the imposition of fiscal rules is expected to improve the "soundness" of public finance, it could achieve the opposite if it is too restrictive and constrains government intervention at a time of need.Considering that at present many of the SSA countries have adopted the balanced budget rule and/or debt rule, examining the effect of fiscal rules imposition on the sustainability of public debt is beneficial to policy decisions.
The quest to achieve debt sustainability or reduce the level of debt could push countries to adopt restrictive fiscal policies such as fiscal consolidation efforts that could turn out to be counterproductive.The rationale for such policy measures is the argument that fiscal consolidation leads to an increase in the primary balance of government thereby reducing the need to acquire more debt while providing resources that could be directed toward reducing public debt (Estevão & Samake, 2013;Mwaba, 2006).As studies such as Chick &Pettifor (2011) andMcCausland &Theoddosiou (2016) have shown, that fiscal consolidation does not lead to a reduction in debt; and it could potentially lead to an increase in public debt i via its suppressive effect on economic activities and by extension government revenues thereby rendering it counterproductive (Nganga et al., 2019).Given the foregoing, this study identifies the determinants of public debt that could influence a reduction of public debt without hurting growth and welfare.
A review of the extant empirical literature on public debt in SSA (Ncube & Brixiova, 2015;Nya & Onyimadu, 2019;Ogbeifun & Shobande, 2020;Omotor, 2021a;Omotosho et al., 2016;Osinubi et al., 2010;Prizzon & Mustapha, 2014;Were & Mollel, 2020) shows that most of the studies employed the indicators or cointegration approach to debt sustainability analysis; few studies employed the fiscal reaction function approach.In addition, none of the studies accounted for the endogeneity problem that could arise when estimating the fiscal reaction function.Further, to the best of the authors' knowledge, none of the studies examined the effect of debt relief and the adoption of fiscal rules on the public debt sustainability of SSA countries.
In addition, none of the studies examined the role of debt relief and the adoption of fiscal rules on public debt accumulation in SSA.Thus, this study fills these gaps in the literature by investigating the following questions: do fiscal rules adoption and debt relief improve public debt sustainability?What factors influence a reduction of public debt?In what ways do debt relief and the imposition of fiscal rules influence public debt accumulation?
The remaining parts of this paper are organised as follows: Section 2 provides the framework for debt sustainability analysis while section 3 discusses the materials and methods.The estimation results and discussion of findings are presented in section 4 while section 5 concludes the paper.

Debt Sustainability Analysis Framework
In examining the sustainability of public debt, the starting point is the public debt dynamics equation.This identity equation provides the framework for understanding how countries accumulate public debt.It shows the present-period debt to be a function of previously accumulated debt, interest payments on accumulated debt, and the primary balance of government.In a general form, the debt dynamics equation is specified as: Bt denotes the stock of public debt at period t; Wt is the primary balance (could be in surplus or deficit); Bt-1 denotes the past period stock of public debt; rt is the interest rate on debt.
Equation (1) implies that a change in the stock of public debt is influenced by interest payment on existing debt and the primary balance.
To illustrate the theory behind the Intertemporal Budget Constraint (IBC) condition of debt sustainability, consider the model where the debt dynamics identity in (1) is presented in continuous time as in Greiner et al. (2007): Where S(t) is the government primary surplus.To get the stock of public debt at time t, equation (2) is solved, this takes the form of: Where B(0) is the stock of public debt at time t = 0.
Equation (3) could be solved further by multiplying both sides with  − .(5) By collecting like terms and making B(0) the subject of the formula, the equation becomes: If a government does not borrow more to finance interest on existing debt and amortise maturing debt, it does not run a Ponzi scheme (Nguyen, 2013;Renjith & Shanmugam, 2018).This is depicted as limiting the first term on the right-hand side of equation ( 6) to zero that is: Where E refers to expectations.If the condition of no Ponzi scheme as illustrated in equation ( 7) holds, it follows that: Equation ( 8) illustrates that the present value of public debt equates to the sum of discounted future primary surpluses of the government.This implies the satisfaction of the IBC, therefore, public debt is adjudged to be sustainable.The model assumes the interest rate of government bonds to be the same as the discount rate.For simplicity, it is also assumed to be fixed (see Bohn, 2007).
Further theoretical development on debt sustainability analysis was made by Bohn (Bohn, 1995(Bohn, , 1998) ) who criticised the use of the interest rate as the discount factor of government spending and revenues.He argued that the discount factor "depends on the distributions of the variables across different possible states of nature" (Greiner et al., 2007).And a debt policy seen to be sustainable in one state of nature might not be sustainable in another state (Bohn, 2007).As an alternative, Bohn built a stochastic version of the IBC where no explicit discount factor is specified.Based on this, he constructed an alternative debt sustainability framework where the primary surplus ratio variable is a positive function of the public debt ratio.If this is the case, public debt is sustainable because a rise in the stock of debt is accompanied by the corrective measure of running primary surpluses thereby satisfying the intertemporal budget constraint (Beqiraj et al., 2018;Bohn, 1998;Otonne et al., 2019).Further, this illustrates the mean-reverting behaviour of the public debt ratio because running primary surpluses leads to a decline in the debt ratio, returning it to its mean, further implying a satisfaction of the IBC (Greiner & Fincke, 2015;Renjith & Shanmugam, 2018).The theoretical argument of Bohn is represented by the so-called fiscal reaction function where the primary surplus is modelled as a positive function of public debt.
Using a stochastic framework, Bohn created an alternative approach to debt sustainability analysis via the feedback relationship captured by the fiscal reaction function.The equation of the fiscal reaction function is specified as: Where s is the primary surplus to GDP ratio, b is the debt to GDP ratio, Z denotes other nondebt determinants of primary surplus, and ε is the error term.Equation ( 9) can be written in a composite form as: Where: From the fiscal reaction function specified in equation ( 9), Bohn argues that the positive feedback of public debt (b) to primary surplus (s) that is captured by  > 0 is consistent with his stochastic version of IBC and illustrates the sustainability of public debt (see Beqiraj et al., 2018;Bohn, 1998;Greiner & Fincke, 2015;Mahdavi, 2014).This is because the positive response implies that the debt ratio is mean-reverting (Bohn, 1998).Therefore  > 0 signifies the sustainability of public debt.
In the extant empirical literature, different approaches have been employed to examine the sustainability of public debt.The evolution of empirical debt sustainability analysis is traced to the work of Domar (1944) who sees the difference between the interest rate on debt and the economic growth rate as an indicator of sustainability.For him, public debt is sustainable if the economic growth rate (  ) exceeds the interest rate on debt (  ) i.e (  −   ) < 0. Similar to the position of Domar, Buiter et al. (1985) noted that the debt ratio is well-behaved if the real economic growth rate exceeds the growth rate of interest.It should, however, be noted that the sustainability condition of Domar (1944) is more applicable on a year-to-year basis, therefore, it is less useful in ascertaining debt sustainability over a time horizon.Empirical studies that employed the indicator approach to debt sustainability analysis include Chandia et al. (2019), Ley (2009), Ejaz andJavid (2011), andKaur et al. (2018).
As an alternative to the indicator approach of debt sustainability analysis (DSA), Hamilton and Flavin (1986) pioneered the econometric method of analysing debt sustainability.The approach of Hamilton and Flavin is based on the satisfaction of the intertemporal budget constraint.
Under this approach, the intertemporal budget constraint is satisfied if public debt and budget balance follow a stationary process (Liliane, 2015).If this holds, public debt is said to be sustainable because it exhibits a mean-reverting behaviour.Studies that employed the stationarity approach to debt sustainability of Hamilton and Flavin include Cuestas and Regis (2018); Nya (2019), Osinubi et al. (2010).Further to the approach of Hamilton and Flavin, Trehan and Walsh (1991) noted that if public debt and the government's primary balance are cointegrated, then public debt is sustainable.This is the cointegration approach to debt sustainability analysis (Fincke and Greiner, 2015;Beqiraj, Fedeli and Forte, 2018).The cointegration among the variables signifies the satisfaction of the intertemporal budget constraint thereby depicting the sustainability of public debt.The studies that employed the cointegration approach to DSA include Artis and Marcelino (1998), and Ogbeifun and Shobande (2020).Bohn (1998Bohn ( , 2007) ) argued that since the debt ratio is influenced by shocks to economic growth, government expenditure, interest rate, inflation, etc., using mean-reversion as a measure of sustainability is inadequate.As an alternative, Bohn propounded the fiscal reaction function approach of DSA.Under this approach, a positive response of the primary balance ratio to the public debt ratio signifies that public debt is sustainable; however, in situations where the response is negative, public debt is adjudged to be un-sustainable (Kaur and Mukherjee, 2012;Ghosh et al., 2013;Otonne, Emmanuel and Asogwa, 2019).
Another approach to debt sustainability analysis is the World Bank/IMF DSA.The IMF/ World Bank DSA is two folds The first involves the determination of threshold values based on the Country Policy and Institutional Assessment (CPIA).Under this, the debt threshold for countries with high CPIA scores is a 70% debt-to-GDP ratio; 55% for countries with intermediate CPIA scores; while countries with low CPIA ratings have a debt-to-GDP threshold level of 35% (IMF, 2017b).Under this approach, the debt ratios of countries are compared with these predetermined threshold values, a country with a debt ratio above the predetermined threshold ratio is termed as having unsustainable public debt.Wyplosz (2007) criticised this approach of DSA arguing that since debt distress also depends on other macroeconomic and political considerations and not on the debt level only, ascribing a common debt threshold level to countries might be too restrictive or lax when the peculiar features of a country are taken into account.Apart from the debt-to-GDP ratio, other indicators employed include the external debt-to-export ratios, debt service-to-export ratio, and debt service-torevenue ratio.Apart from the IMF and World Bank research, other studies that employed this approach includes Omotor (2021b), Nya and Onyimadu (2019), and Osinubi et al. (2010).
The second DSA approach of the World Bank/ IMF involves sensitivity analysis and stress tests.Under this approach, the projected path of public debt is estimated following shocks to macroeconomic variables such as economic growth rate, interest rate, exchange rate, and current account balance among others.The simulation analysis depicts the behaviour of public debt over a five-year horizon when these variables are altered with some probabilities of occurrence.Based on this, the public debt of a country is determined to be sustainable or otherwise.The criticism meted out against this approach is that since the sustainability of debt is associated with future guesses about certain macroeconomic variables, the validity of the analysis is premised upon the accuracy of the guesses made (Wyplosz, 2007).This raises reliability issues about the approach.Aside from the research by the IMF/ World Bank, other studies that employed this approach include Ncube and Brixiova (2015).

Model Specification
In this section, the empirical models of the study are specified and discussed.

Debt Sustainability Analysis Specification
The study begins by presenting the baseline model which is the fiscal reaction function adopted from Bohn (1995).The model is specified in a panel model setting: Where b is the primary balance as a ratio of GDP, d is the ratio of public debt to GDP, and YVAR is the business cycle variable.A way to measure the effect of the business cycle is the deviation of national output from the potential output, however, due to the absence of data on potential GDP for the countries included in the study, the proxy for potential GDP used in the literature is the Hodrick-Prescott filter trend of national output (Taylor, 2000;Hodrick, 2020).
Therefore, yvar is measured as the deviation of national output from its trend (Kaur, Mukherjee and Ekka, 2018;Renjith and Shanmugam, 2018;Ogbeifun and Shobande, 2020).The parameter of interest here is β1 which captures the reaction of primary balance to public debt accumulation.A positive value of β1 signifies a sustainable public debt because primary balance is a positive function of debt.
To avoid running into the problem of omitted variable bias, the model of Bohn is augmented to include other determinants of primary balance based on the dynamics of sub-Saharan African economies.As discussed in the introduction, part of the contributions of this study is examining the role of debt relief and fiscal rules in influencing the debt sustainability of SSA countries; therefore, the study specifies a model that captures the effect of debt relief and fiscal rules on the sustainability of public debt.Consequently, the augmented empirical model of fiscal reaction function takes the form of: Where inf is inflation, sav is private savings ratio, pol denotes political stability, fr is fiscal rules, and rel refers to debt relief.
Following Baig and Abiad (2005), inflation is included as a determinant of primary balance.This is premised upon the argument that monetary financing by the government via creating more money could increase inflation, this helps to lower real spending and in turn improve the fiscal position of the government (Patinkin, 1993).Therefore, β3 is expected to be positively signed.As noted by Zeng (2014), the level of private savings affects the primary balance via the financing channel.For countries with constrained market access, the level of savings shows the availability of financial resources the government could potentially borrow.A higher level of private savings provides the government with greater room for borrowing to finance its deficits, thereby potentially leading to lower primary balance levels.Therefore, β4 is expected to be negatively signed.The model also controlled for political stability in specifying the primary balance model (Kumar et al., 2007).The reason is government fiscal policy decisions are largely political, therefore, the political climate of a nation influences the fiscal position of the government.When the political atmosphere is unstable, conflicts are likely to emerge necessitating more spending and by extension deficits.Therefore, an increase in political stability could potentially improve the government's primary balance; hence β5 is expected to be positively signed.

The Role of Fiscal Rules and Debt Relief
Considering that a key objective of the study is investigating the impact of fiscal rules and debt relief on debt sustainability, both variables are included in the empirical model.Fiscal rules are a set of legal instruments put in place by governments to impose long-lasting constraints on fiscal policy.According to the IMF (2017a), "Fiscal rules typically aim at correcting distorted incentives and containing pressures to overspend, particularly in good times, to ensure fiscal responsibility and debt sustainability".However, they could have a potential negative impact on fiscal outcomes if they become too restrictive.There are 4 fiscal rules: expenditure rule, revenue rule, balanced budget rule, and debt rule.Most of the SSA countries that adopted fiscal rules have balanced budget and/or debt rules in operation iii .Lerner (1943) in his principle of functional finance argued against the application of discretionary fiscal rules by authorities stating that the focus should rather be on balancing the economy and not on trying to balance the budget.This is because the imposition of restrictions to balance the budget or limit borrowing could hurt economic activities, especially in periods when economic stimulation is needed (Beqiraj et al., 2018;Ghosh et al., 2013).Restrictive fiscal rules could lead to fiscal consolidation thereby starving the economy of the stimulus needed for growth; as a result, revenues fall eventually leading to poorer primary balances.Conversely, the proponents of fiscal rules argue in favour of rules aimed at constraining deficits, debt, and expenditure to achieve fiscal sustainability (see Burger & Marinkov, 2012;Tanner, 2004).Going by the foregoing, the sign of β4 in equation ( 11) could be positive or negative.
Finally, considering that many of the sub-Saharan African countries received one form of debt relief or the other (recall that of the 39 HIPC countries, 33 are in Africa), the study included debt relief as one of the determinants of the fiscal position of SSA countries.Debt relief is expected to create the fiscal space for countries to achieve higher economic growth because resources that would have been used to service the debt could be channelled toward other productive use by the government (Battaile et al., 2015).The increase in economic growth leads to more revenue and hence the better fiscal position of countries.However, there is a potential negative effect of debt relief on the fiscal position.Debt relief packages in some instances come with the condition that a portion of the debt and accrued interest need to be paid within a certain period.This could lead to the government channelling huge resources that would have been invested in the economy towards paying the agreed sum.This diversion of resources could pose a negative effect on the economy and by extension the fiscal position of governments.Besides, conditions attached to debt relief could include privatising the public domain, restricting where investment should take place, austerity measures, cutting the size of government etc.Some of these measures could potentially negatively affect the economy if implemented suddenly and improperly.Therefore, β5 could be positively or negatively signed.

Determinants of Public Debt Specification
This study argues that considering the nature of debt sustainability analysis (DSA), it might be insufficient to depend on it alone for policy decisions.This is because a debt considered sustainable today might become unsustainable tomorrow if the fundamentals of the economy change.Moreover, debt sustainability analysis is not an end, identifying ways of reducing public debt to achieve debt sustainability will be of interest to policymakers.Given this, the study explored the factors that could be instrumental in reducing the stock of public debt.In the model examining the determinants of public debt, the study includes variables relating to the dynamics of African economies such as debt relief and fiscal rules.Doing this will aid in the understanding of whether the debt relief received by African nations helps to reduce public debt.This also assists in finding out if the imposition of fiscal rules improves the public debt position or worsens it.The theoretical underpinning of the determinants of the public debt model is given by the debt identity equation specified in equation (1).To present an estimable form of the equation in an empirical form, the variables in equation ( 1) are expressed as a ratio of GDP.By taking into account other determinants of public debt in the context of SSA, the empirical model is specified as: The real GDP growth rate (gdp) and primary balance ratio (b) are included as explanatory variables due to the theoretical underpinning given by the debt dynamics identity equation.
Exchange rate (exr) is included as a determinant of public debt similar to Chandia et al. (2019).
Considering that SSA's public debt is predominantly external and denominated in foreign currency, exchange rate dynamics affect the value of public debt in local currency terms.For instance, when the local currency depreciates, it means that the public debt has increased in value in local currency terms, and so also is its servicing cost.This necessitates the generation of more revenue in local currency terms to service the debt.Therefore, a change in the exchange rate affects the accumulation of public debt and its servicing.The flip side of the argument is exchange rate depreciation increases the competitiveness of the economy thereby leading to more exports and by extension export revenues to service the debt.Therefore,  6 could be positively or negatively signed.
An increase in inflation (inf) erodes the real value of public debt thereby reducing the debt burden on the government, therefore  4 is expected to be negatively signed.Interest payment (int) could exert a negative or positive effect on debt.In Scenarios where more debt is not needed to pay interest on existing debt, interest payment could reduce public debt; however, in situations where more borrowing (at a higher interest rate) is needed to pay interest on debt, the stock of public debt rises.Therefore, the coefficient of  7 could be positively or negatively signed.The model also controls for the effect of political stability (pol) in determining public debt.Increased political stability could reduce the need for borrowing; therefore, public debt is likely to be negatively affected.Besides, an increase in political stability provides a friendly climate for investment and stimulation of economic activities; this translates into higher government revenue that could be directed towards debt reduction.Consequently, the coefficient of  8 is expected to be negatively signed.

Estimation Strategy
To achieve the study objectives, several techniques are employed for data analysis.The study examines the debt sustainability of SSA countries by estimating the fiscal reaction function.In doing this, the study suspects the possibility of endogeneity in the model due to a reverse causality between public debt and primary balance.The reverse causality from primary balance to public debt could come about because a fall in the primary balance could necessitate the need for more government borrowing to finance shortfalls, therefore, public debt could rise.
To cater to the potential endogeneity problem, the Two Stage Least Square (2 SLS) estimator is used to estimate the model.
In estimating the determinants of the public debt model, the study also suspects the potential for endogeneity problems due to reverse causality from public debt to economic growth and primary balance.While economic growth is assumed to reduce public debt, the study cannot completely rule out the possibility of a feedback effect of public debt on economic growth.An increase in public debt that comes about due to borrowing to finance public investment could stimulate economic growth.To cater to the potential endogeneity problem, the panel GMM estimator is used.The GMM estimator is employed for two reasons, the first is that the setup of the panel GMM model is such that the lag of the dependent variable (in this case public debt ratio) is included in the model making the model dynamic in nature, this aligns with the theoretical setup of the debt dynamics identity equation.Therefore, it is empirically appealing to employ the panel GMM model to estimate the model.Secondly, the panel GMM model can easily cater to more than one endogenous variable just like in this model.

Data and Variables Description
This section describes the variables and presents the sources and scope of data.The definition of variables is presented in Table 1.The data covers the period 2000 -2019.The reason for the choice of this period is the availability of data on most of the study variables and the need to capture the dynamics of public debt during and after the HIPC initiative v .The sample covers 37 SSA countries also selected based on data availability.The data on debt, savings, interest payment, exchange rate, and debt relief were converted to their logarithmic forms.
As a pre-estimation test, the study checked for possible multicollinearity in the models by using the correlation matrix and the Variance Inflation Factor (VIF).The result (not presented here for brevity, but available on request) indicates less likelihood for multicollinearity problems in the models because there is no significant strong correlation between the study variables, and the VIF values are low.A VIF value close to 10 signifies high multicollinearity (Bala et al., 2021;Lin, 2008).

Results and Discussion
In this section, the results obtained from the estimated models are presented and discussed.

Fiscal Reaction Function Approach
To examine the debt sustainability of SSA countries, the fiscal reaction function for the region is estimated using the Two Stage Least Squares Estimator (2 SLS) estimator.This is done to cater to potential endogeneity problem in the model.The lag of the endogenous variable is used as an instrument.In addition, a formal test of endogeneity in the form of the Wu-Hausman test is employed to confirm the endogenous relationship between public debt and primary balance.
The result of the estimated fiscal reaction function is presented in Table 2. From the result presented in Table 2, public debt has a significant positive effect on the primary balance, indicating that primary balance is an increasing function of public debt accumulation.This finding signifies that on average, the public debt of SSA countries is sustainable.The sustainability of the public debt of SSA countries in light of the fiscal reaction function implies that public debt accumulation is accompanied by adjustment efforts aimed at improving the primary balance.Moreover, the positive response of the primary balance to public debt implies the satisfaction of the inter-temporal budget constraint.Further implied by the finding is that public debt accumulation produces a beneficial effect on the fiscal space of government.This is because when accumulated public debt is directed towards productive use such as public investment, it could be instrumental in stimulating economic activities, government revenues, and by extension a higher primary balance.This finding aligns with Belguith and Gabsi (2019), Burger et al. (2012), Liliane (2015), Nganga et al. (2019); Renjith and Shanmugham (2020).
Among the other explanatory variables in the model, savings, inflation, and political stability are found to positively influence primary balance.The positive effect of private savings on the primary balance could mean that an increase in savings is accompanied by higher interest earnings, thereby leading to higher government revenue from taxes on the interest receipts and by extension higher primary balance.Another rationale for this finding could be that an increase in savings could be seen by the fiscal authorities as a signal of buoyancy of the economy, thereby reducing the need for more government intervention spending.The reduction in spending could potentially improve the primary balance.The significant positive effect of inflation on the primary balance implies that inflation erodes the spending of the government in real terms thereby improving the government's primary balance.The significant positive effect of political stability could be interpreted to mean the lesser the instability, the lesser the need for government to spend on interventions needed to bring about political stability; therefore, the primary balance improves.Moreover, political stability is crucial for attracting investment because investors are interested in predictable business environments (Kamar & Bakardzhieva, 2015).The increase in investment is associated with higher productivity and by extension government revenues that could potentially improve the primary balance.The significance of the Wu-Hausman test statistics confirms public debt as being endogenously related to primary balance, hence the appropriateness of using the 2 SLS estimator for analysis.

The Role of Debt Relief
Another key contribution of this study is to examine the impact of debt relief and the imposition of fiscal rules on public debt sustainability in SSA.To achieve this, the fiscal reaction function model is augmented to account for these factors.The estimation result of the model that examines the role of debt relief in influencing public debt sustainability is presented in Table 3.
The result in Table 3 signifies the sustainability of public debt.Further, debt relief positively impacts the primary balance implying that debt forgiveness improves the fiscal space of SSA countries.The rationale for this finding could be that an increase in debt relief eases the burden of public debt thereby providing an avenue for government resources to be directed toward economic-stimulating activities.This by extension leads to an increase in government revenues and the primary balance.To capture the effect of debt relief on debt sustainability, the study interacts the debt relief variable with the public debt variable.The coefficient of the interaction term is positive and significant, implying that debt relief is positively associated with the sustainability of public debt via its mediating effect on the stock of public debt.As can be seen in the determinants of public debt model (presented in Table 6), the depreciating effect of debt relief on public debt contributes to greater sustainability of public debt.

The Role of Fiscal Rules
The results of the model that examines the role of fiscal rules on the public debt sustainability of SSA countries are presented in Table 4. From the results presented in Table 4, public debt maintains a significant positive effect on the primary balance, signifying the sustainability of public debt in SSA countries.To examine the effect of the adoption of fiscal rules on debt sustainability through its mediating effect on public debt, two interaction terms are used.The first is an interaction between the public debt ratio and a dummy variable for countries that imposed the balanced budget and/or debt rule.The second scenario is an interaction between the public debt ratio and a dummy variable accounting for the periods when fiscal rules are operational.Also, the direct effect of fiscal rules imposition on the primary balance is explored by regressing the primary balance on the fiscal rule variable which is a dummy for periods when fiscal rules are in place.
The direct effect of fiscal rules on the primary balance is presented in the first column of Table 4. From the result, the coefficient of the fiscal rules variable could be interpreted to mean that in comparison to periods when fiscal rules are not in place, the periods where fiscal rules are in operation are associated with a higher primary balance; however, the relationship is statistically insignificant.For this reason, it could be inferred that all things being equal, the imposition of fiscal rules does not necessarily improve government balances as argued by the proponents of fiscal rules.This could mean that although the imposition of fiscal rules is meant to control government finances, it could be too restrictive thereby not producing a beneficial effect on government finances.
In the second column of Table 4, the coefficient of the interaction term aimed at capturing the effect of fiscal rules on debt sustainability via its mediating effect on public debt is presented.
The negatively signed and significant coefficient implies that compared to countries where fiscal rules are not imposed vi , the effect of public debt on the primary balance in countries where fiscal rules are imposed is lower.This implies that the imposition of fiscal rules is associated with reduced public debt sustainability.In the last column of Table 4, the periods of fiscal rules operation are interacted with the public debt ratio.The coefficient of the interaction term is negative and statistically significant.Considering the construction of the variable, the coefficient could be interpreted to mean that compared to periods when fiscal rules are not operational, the effect of public debt on the primary balance in periods when fiscal rules are operational is lower.This also implies that the imposition of fiscal rules is associated with reduced public debt sustainability of SSA countries.The inference that could be drawn from the result of both interaction terms is that all things being equal, the imposition of fiscal rules is associated with threatening the public debt sustainability of SSA countries.This finding contradicts that of Mahdavi (2014) who found that states with fiscal stringency have a stronger positive effect of public debt on the primary balance.

Determinants of Public Debt
As stated earlier, part of the contributions of this paper is the identification of factors that could be used to reduce public debt without hurting the economy.In doing this, the effect of debt relief and fiscal rules on public debt accumulation is also explored.As discussed in section 3.2, the Panel GMM model is used for estimations, the result is presented in Table 5.In Table 5, the results of both one-step and two-step panel GMM models are presented.The result reveals a depressing effect of primary balance on public debt.The rationale for this finding could be that an increase in the primary balance provides the fiscal space for the government to direct resources toward debt servicing which eventually leads to a fall in the stock of public debt.Besides, an improvement in the primary balance might reduce the need for further public debt accumulation.The negative effect of primary balance on public debt conforms to the finding of Nganga et al. (2019).In addition, economic growth exerts a depressing effect on public debt.This implies that as the economy expands, government revenues also expand thereby providing the resources needed to service and amortise the debt.
Also, an increase in economic growth reduces the need for government borrowing due to higher government revenues and the buoyancy of the economy.The finding of the depressing effect of economic growth on public debt is similar to Abubakar (2020), Kraay and Nehru (2006); Pirtea et al (2012); Gargouri and Ksantini (2016); Sinha et al (2011).
An increase in interest payment depresses public debt implying that interest payment helps to defray public debt accumulation.This finding is not surprising considering that the public debt of SSA countries (especially external debt) operates under the compound interest principle.
Exchange rate depreciation weakly depresses public debt while the effect of political stability is statistically insignificant.The Sargan test probability value signifies the validity of the instruments, while the Arellano-Bond test probability value implies the absence of secondorder serial correlation.

The Role of Debt Relief and Fiscal Rules
The role of debt relief and the adoption of fiscal rules in determining public debt accumulation is presented in Table 6.Table 6 presents the result of the estimated panel GMM model where the role of debt relief and imposition of fiscal rules on debt accumulation is examined.From the coefficient of debt relief in the first column, debt relief produces a depressing effect on public debt.An increase in the debt relief received by SSA countries is instrumental in the reduction of public debt in two ways.The first is the direct cancellation of a part of the debt stock.The second way is by freeing up funds that could be channelled towards economic stimulation; this leads to higher revenues which could be used for further debt amortisation.The effect of the imposition of fiscal rules is captured in two ways.The first is the direct effect where the fiscal rules period dummy is included in the model; in the second case, the fiscal rules period dummy interacts with the primary balance.From the result presented in the second column, fiscal rule imposition insignificantly impacts public debt.This implies that there is no evidence that the imposition of fiscal rules improves the public debt position for SSA countries because compared to the period when fiscal rules are not imposed, the periods of fiscal rules imposition is not associated with significantly lower public debt.The coefficient of the interaction term in the last column is found to be positive and statistically significant.This implies that relative to periods of no fiscal rules, the primary balance leads to an increase in public debt in periods of fiscal rules adoption.This is a complete contrast to the stand-alone depressing effect of primary balance on public debt.This implies that the imposition of fiscal rules is undesirable as it dampens the deleterious effect of an increase in primary balance on the stock of public debt.It could be inferred that the restrictive nature of fiscal rules negatively affects economic activities, which translates to lower revenues, primary balance, and debt-carrying capacity of governments.The Sargan test probability value signifies the validity of the instruments, while the Arellano-Bond test probability value implies the absence of second-order serial correlation.

Conclusion and Policy Recommendations
This paper investigates the sustainability of public debt in SSA and explores the role of fiscal rules and debt relief on debt sustainability in the region.Beyond debt sustainability analysis, the study identifies the factors that could help reduce public debt in the region without having detrimental effects on the economy.The findings of the study revealed that all things being equal, the public debt of SSA countries is sustainable.Further, while debt relief improves the sustainability of public debt in SSA, the imposition of fiscal rules threatens it.In addition, the factors that are instrumental in reducing public debt are stronger economic growth, higher government primary balance, and the pursuit of more debt relief.Interestingly, the study did not find evidence in support of the argument that the imposition of fiscal rules improves the public debt position of SSA countries.Rather, the study finds that the imposition of fiscal rules is associated with an increase in public debt via its mediating effect on government primary balance.
The findings of this study have far-reaching policy implications.Firstly, the public debt of sub-Saharan African countries is sustainable; therefore, there is no need for the imposition of consolidation efforts aimed at depressing public debt to achieve debt sustainability.Also, because the debt of SSA countries is sustainable on average, the countries should not starve themselves of the opportunity to borrow, especially from domestic sources, should the need for it arises.The caveat however is the borrowed fund should be directed towards productive use such as public investment and economic stimulation.Further, SSA countries should be cautious about the imposition of restrictive fiscal rules due to its undesirable effect on debt sustainability and its association with an increasing stock of public debt.Although improving the primary balance is instrumental to reducing public debt, this must be pursued with caution because increasing the balance via fiscal consolidation (spending cuts) when the economy needs fiscal intervention could negatively affect growth and welfare, thereby rendering it counterproductive.The focus should however be on improving the primary balance through higher revenues.To improve the public debt position of SSA countries, policymakers should focus on improving economic growth, pursuing more debt relief, ensuring more political stability, and exchange rate depreciation to improve the competitiveness of the economies.

Declaration of Interest Statement:
The authors declare no competing interests.

Data Statement:
The data used are available from the corresponding author upon request.