Evaluation of the Non-Linear Effects of the Public Debt on the Economic Growth of the WAEMU

The aim of this article is to analyse the nature of the relationship between public debt and economic growth in the WAEMU. A standard growth model was specified and then estimated in quadratic form from the GMM (GMM). The results show a non-linear relationship between public debt and economic growth. Thus, public debt stimulates economic growth when it does not exceed the threshold of 15% of GDP. Robustness tests show that public debt is boosting the economic conditions of countries with sound macroeconomic policies and good institutional quality.

activity. In addition, the implementation of severe measures during a recession increases its depressive effects and ultimately increases the burden of public debt.
In sum, several empirical studies have made it possible to identify the "optimal" level of public debt in order to avoid the negative effects on economic growth. The results confirm the existence of a negative and non-linear causal relationship between public debt and growth. Indeed, a low level of public debt has no impact on economic growth, while from a certain level, public debt negatively affects growth.
Previous studies have determined a critical debt threshold between 90% and 100% of GDP. However, in certain cases, several observed facts invalidate this threshold. This is the case of Japan where the debt exceeds 200% of the GDP. Therefore, there is no well-defined magic threshold from which growth declines appreciably. It is therefore, essential when analysing the critical debt threshold to take into account the economic, budgetary and institutional characteristics of each country apart.

Public Debt and Economic Growth
In the empirical literature, while some have been interested in the existence of a critical debt threshold, others have shown that a certain level of institutional quality is necessary in order to encourage investment, stimulate growth and therefore benefit from the debt relief policy. Indeed, Cordella et al. (2010) show that for developing countries the link between public debt and economic growth depends not only on the scale of debt but on the quality of policies and institutions as well. The authors have proven the existence of over-indebtedness in countries with good institutional quality, and this when the net present value of the debt rises above 20 to 25% of the GDP, but beyond a rate of 70 to 80% of GDP debt has no effect. In countries with poor institutional quality, the rates are lower than in other countries but without overlooking the importance of the debt burden. In an article on the relationship between debt relief and institutional quality, Asiedu (2003) shows that poor, heavily indebted countries have weak institutions and must reach a certain level of quality institutions to take advantage of debt relief. In addition, Dessy and Vencatachellum (2007), shows that the relief granted to 14 African countries between 1989 and 2003 positively affected the share of resources of countries that have reformed their institutions.
All in all, previous studies suggest that public debt affects the economic conditions of countries with sound macroeconomic policies and good institutional quality.

Specification of the Empirical Model
In this article, the selected empirical model follows the above-mentioned empirical literature. The basic model can take the following form: The transformation e the equation (1) can write equation (2) below: www.scholink.org/ojs/index.php/rem Research in Economics and Management Vol. 5, No. 2, 2020 Published by SCHOLINK INC.
In equation (2), represents the GDP growth rate for the country at time. −1 is the endogenous explanatory variable. It measures GDP growth for the country right now − 1.
is the public debt of the country at the moment . X is a vector of control variables, the country specific effect and γ t the temporal effect? Finally, the term error.
The non-linear approach is based on the idea of introducing the square of the variable "public debt" into the group of exogenous variables and generally takes the following form: The basic hypothesis of our work is to verify the effect of a very high debt on economic activity. The conditional convergence hypothesis implies a negative and significant value of the coefficient of the delayed value of GDP per capita. In this case, the control variables and the individual specific effect increase the level of income per capita over the long term towards which each country converges. On the contrary, a positive value of this coefficient signifies the rejection of the convergence hypothesis, defined as a catch-up process. The sample consists of eight WAEMU countries for the period 2000-2019.

Variables and Data Sources
The endogenous variable being the annual growth of GDP per capita. The explanatory variables are presented in Appendix 2. As an indicator of the performance of economic activity, we use the annual growth rate of GDP per capita. This measurement being the most appropriate allowing the verification of the conditional convergence hypothesis. This variable was explicitly used in the empirical literature (Patillo et al., 2004;Schclarek, 2004;Ferreira, 2009;Checherita & Rother, 2010;Kumar & Woo, 2010;Presbitero, 2010;Baum et al., 2013). Regarding the explanatory variables of the model, the variable of interest, gross public debt, measures the degree of debt and helps to interpret the debt situation. Indeed, the ability to pay or the solvency of an economy is linked to its wealth; public debt can therefore, be considered as an indicator of the financial situation of countries. The prevailing view is that public debt can stimulate growth in the short term, but seems harmful to growth in the long term. In addition, economic theory suggests that debt can promote economic growth, but within limits to be determined. As a result, the link between these two variables is not clear and is still tainted with imprecision. The variable of interest has been used in almost all recent studies on the importance of the relationship between public  (Table 2).   The unit root hypothesis is rejected at * 1%, ** 5%, *** 10%. LLC and IPS correspond respectively to the test results of Levin, Lin and Chu (2002) and Im, Pesaran and Shin (2003).
Source: construction of authors.

The Results of the Estimates by the Generalized Moments Method
Tables 3 and 4 summarize the results of the dynamic panel estimates of the chosen model using the Generalized Moments Method (GMM) in first differences of Arellano and Bond (1991). Table 3 summarizes all the linear and non-linear (quadratic) regressions regarding the three institutional variables, the debt indicator and the control variables taken from the different specifications. Table 4 presents the different estimates after the introduction of new control variables. Finally, Table 5 summarizes the different thresholds determined.
The estimation results of the first specification of our model are presented in the following   Source: construction of authors.

Robustness Tests
We test the robustness of the results already obtained by adding other control variables, namely, the population growth rate (log_popgrowth) and the unemployment rate (log_unempl_rate). The results for this specification are presented in Table 4.  (1,000) (1,000) (1,000) (1,000) (1,000) (1,000) (1,000) (1,000) (1,000) (1,000) AR ( we observe that economic growth is negatively influenced by the rate of population growth.
As for the debt indicator, the results obtained are the same as those obtained in the previous specifications.
Public debt in its linear form has a negative impact on economic growth. Moreover, the results of the quadratic form in Table 2 shows that up to a limit value, the public debt promotes economic growth.
Exceeding this value, public debt becomes detrimental to growth, which proves the existence of a non-linear relationship between these two variables. However, it must be emphasized that the coefficients on public debt are not significant, and this, in the presence of the unemployment rate as a control variable. This can be explained by the high level of unemployment in the WAEMU area. The effect on economic growth of the public debt is absorbed by that of the unemployment rate.

Identification of the Threshold Effect
In the section, it is about determining the optimal level of public debt by the quadratic method. The derivation of equation (3) with respect to DP it gives: At the point of optimal indebtedness, DP it = 0. This makes it possible to derive the optimal threshold for public debt: The public debt variable in the basic model is expressed in logarithms, so the determination of the optimal debt threshold is done by taking the exponential: * = exp (− 1 2 2 ).  Table 3 Specification (4)'from Table 4 14.037% 15.095% 12.194% Source: author's calculation. Table 3 shows the point of debt diversion beyond which the effect of public debt becomes negative. We note that the debt threshold for the entire sample varies between 12 and 15% of GDP. Indeed, the thresholds obtained are appropriate for our case, and this, generally, by the consistency of the results with the various works dealing with the link between public debt and growth. The level of public debt of the WAEMU countries is relatively lower compared to that of the developed countries, which explains, although partially, the thresholds obtained. This seems important to us because of the absence of theoretical or empirical work that has explained the public debt-growth relationship in the region as a whole.

Conclusion
The purpose of this article was to investigate the nature of the relationship between public debt and economic growth and to decide whether there is a threshold beyond which such a relationship will change for countries of WAEMU.
The econometric results obtained reveal that, overall, public debt has an effect on economic growth.
However, two kinds of specifications were adopted. Linearly, public debt positively and significantly affects economic growth. According to a quadratic specification, public debt has a positive impact to a certain threshold beyond which its effect becomes negative. This threshold is around 12% to 15% confirming the hypothesis of non-linearity of the debt. Robustness tests consist of introducing new control variables, namely, the population growth rate and the unemployment rate. The results are, for the most part, significant and consistent with the various theoretical works.
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In addition, the threshold at which the public debt-growth relationship changes sign is around 15%.
This threshold is not surprising due to the low debt ratios of several countries of the Union relative to developed ones.
These results have implications for economic policies. Indeed, governments can stimulate economic growth by reducing the weight of their debt. In fact, public debt is a question of sustainability before being a need for liquidity. Thus, significant levels of public debt raise sustainability problems in terms of public finances as well as solvency risks, and this, through the increase in the premium risk, which in turn, leads to an increase in the cost of borrowing for countries. In addition, the accumulation of public debts generates a sharp increase in interest rates that can harm economic growth through a decline in private investment.