Three schools of thought structure the debate on the effects of public debt. The classical and neoclassical approach, via the Ricardian equivalence theorem ([2]), postulates the neutrality, or even the harmfulness, of debt: rational agents anticipating future tax increases raise their savings by an equivalent amount, neutralizing any stimulus effect. The Keynesian approach, by contrast, defends its stabilizing role through the fiscal multiplier ([19]) and the IS-LM model ([16]), particularly in a liquidity-trap situation where the crowding-out effect is neutralized. Between these two readings, [11] propose a conditional synthesis: debt stimulates growth below a critical threshold but hinders it beyond that point—that is, its marginal impact changes sign or intensity depending on the level of indebtedness, implying the existence of at least two distinct regimes ([27]). [14] provides the most operational formalization of this: the critical threshold is defined there as the parameter c that separates observations into a low regime (debt/GDP ≤ c) and a high regime (debt/GDP > c), estimated by the grid-search method minimizing the sum of squared residuals. This non-linearity hypothesis has, since [32], given rise to an abundant empirical literature using increasingly sophisticated methods, from bracket regressions to endogenous threshold models and on to the PSTR models of [13], which allow for a gradual transition between regimes rather than an abrupt switch.

These schools of thought are not mutually exclusive: they in fact correspond to distinct transmission channels whose relative importance depends on the institutional and financial context under consideration. A first mechanism relates to public investment: when debt finances the accumulation of public and human capital, it generates positive externalities consistent with endogenous growth frameworks ([33]; [25]), but this effect remains conditional on the quality of the spending financed, which explains why it does not hold systematically. Conversely, when the state finances its deficit by issuing securities, it competes with private firms for available savings ([29]): this is the crowding-out channel, whose intensity depends directly on the depth of domestic capital markets. Beyond a certain stock level, a third mechanism takes over with a time lag: debt service (interest and principal) absorbs a growing share of public revenue, mechanically squeezing productive spending—an intuition that extends, on the fiscal side, the Debt Overhang concept of [23] and [34], formalized by [9]. For commodity-exporting economies, this mechanism is compounded by a fourth one, linked to dependence on external financing and vulnerability to price shocks: high debt particularly weakens countries whose fiscal revenues follow world price cycles. Finally, institutional quality and the quality of public spending do not determine the sign of these effects but rather their intensity: for an identical level of indebtedness, stronger institutions limit the capture of spending by special interests ([30]).

In the specific context of CEMAC, this channel-based framework takes on particular significance. Because domestic capital markets are shallow there, the crowding-out channel is expressed less through rising interest rates, as in financially developed economies, than through the rationing of bank credit: general government, the main borrower in the regional banking system, absorbs a growing share of loanable resources to the detriment of private-sector financing. This structural feature directs the analysis from the outset toward the other two channels (debt service and external vulnerability) rather than toward classic financial crowding-out. Moreover, five of the six member countries are oil producers, and their fiscal revenues and foreign exchange reserves move procyclical with world prices ([1]): high debt, combined with a negative oil shock, thus exposes these economies to a sudden liquidity constraint that forces a procyclical fiscal adjustment, as illustrated by the 2014-2016 shock. It is this interaction that seems to dominate in the CEMAC zone: the critical debt threshold would correspond less to the point at which financial crowding-out stifles private investment than to the point at which debt service becomes heavy enough that any negative oil shock forces a procyclical adjustment.

The work of [32], covering forty-four countries over 1790-2009, marked the starting point of the empirical literature by identifying a threshold of 90% of GDP beyond which median growth falls sharply. These results were nevertheless weakened by [15], who revealed coding and weighting errors in the original data, bringing average growth above 90% back to a slightly positive level. These controversies steered the literature toward more rigorous econometric methods, notably threshold (PTR) and smooth transition (PSTR) models. [6] thus estimate a threshold of 85% for eighteen OECD countries; [7] identify a threshold between 90% and 95% for the euro area; [27], using a PSTR model, identify two transition points at 90% and 115%. [10], in a systematic meta-analysis, shows that these results are highly sensitive to methodological choices and sample composition, arguing for region-specific estimates. More recent work confirms this heterogeneity: [31] estimate thresholds between 58% and 73% for eleven new EU member states; [12] find 79.4% for emerging European economies; [28] confirms a threshold between 84% and 90% for twenty-seven EU countries, highlighting the moderating role of institutional quality; [36] show that the threshold rises with the level of development, from 50.2% for lower-middle-income economies to 62.6% for the upper bracket.

For Africa, the estimated thresholds are systematically lower than those found for developed economies. [22], combining PSTR and GMM on twenty-two sub-Saharan African countries (1990-2021), estimates a threshold of 53% for the region as a whole, 49% for ECOWAS, and 45% for SADC. [30], using forty-seven African countries (2002-2022), establishes a threshold of 53.49% for external debt, with governance quality mitigating the negative effect beyond this threshold. For CEMAC specifically, [20] remain the reference study, with a threshold of 82.3% (95% CI: [62.7%; 109.2%]) over 1990-2017, joined by [8] for Cameroon (63%).

The dependent variable is the growth rate of real GDP per capita, constructed as a forward-looking four-year moving average (t to t + 3), in order to smooth out cyclical fluctuations, capture the medium-term effects of indebtedness on growth, and limit endogeneity problems linked to reverse causality between growth and public debt, following [20].

The model uses seven explanatory variables. The gross public debt/GDP ratio is the main explanatory variable on which the estimated critical threshold depends. The investment rate (gross fixed capital formation/GDP) captures the accumulation of physical capital in the [37] tradition. Initial income (the logarithm of real GDP per capita at the start of the period) tests the conditional convergence hypothesis of [26]. The population growth rate controls for the dilutive effect of population on capital per capita. The degree of trade openness ((exports + imports)/GDP) captures the effect of integration into international trade, in line with [35]. Credit to the economy (domestic credit to the private sector/GDP) captures the effect of financial development on growth ([21]), which is particularly relevant in a zone where financial markets remain underdeveloped. Finally, the international price of oil (the Brent price in constant dollars) is introduced as a control variable specific to the CEMAC context, in order to isolate the effect of debt itself from that of the oil cycle and to avoid omitted-variable bias (Table 1).

Source hierarchy: For public debt, the reference series is the IMF’s (Historical Public Debt Database/Fiscal Monitor), supplemented, where a country-year observation is missing or inconsistent with national publications, by BEAC annual reports ([20]). For GDP per capita growth and the control variables (investment, credit to the economy, trade openness, initial income, population growth), the reference source is the World Bank’s World Development Indicators (WDI); the 2026-2027 observations, not yet available in the WDI at the time the panel was constructed, are supplemented by IMF World Economic Outlook (WEO) projections; these WEO-based years enter the dependent variable’s forward-looking four-year average (t to t+3) for the final in-sample observations (t = 2023 and 2024), each of which therefore includes at least one WEO-projected year. The international oil price is drawn from the World Bank’s Commodity Markets (Pink Sheet) database.

Reconciliation rule in case of divergence: Where the IMF, BEAC and WDI series diverge for the same country-year observation, the source closest to the official national publication (BEAC report) is given priority for public debt.

Table 1.Definition of variables.

Source: Authors.

To study the non-linear relationship between public debt and economic growth, we use the PSTR (Panel Smooth Transition Regression) model developed by [13]. This model generalizes [14] threshold model by allowing a gradual and continuous transition between regimes, rather than an abrupt switch at a single threshold—a property considered more realistic for studying the debt-growth relationship, where the adjustments of economic agents are rarely instantaneous.

The two-regime PSTR model is written as:

where ε i t i.i.d. (0, σ2 ε) and G ( q i t ; γ , c ) denotes the transition function associated with the transition variable q i t , the threshold parameter c, and the smoothing parameter, α i and λ t is the dependent variable, and. X i t contains the explanatory variables; β₀ and β₁ denote, respectively, the parameter vectors of the linear and non-linear parts of the model, and ε i t is the vector of error terms.

The transition function G ( q i t ; γ , c ) , which is continuous and bounded between 0 et 1, is a logistic function of order m :

where c = ( c 1 ⋯ c m ) is an m-dimensional vector and γ is the smoothing parameter, which governs the speed of transition between regimes. When γ tends toward infinity, this function converges to an indicator function and the PSTR model approaches the PTR model with an abrupt transition; when γ tends toward zero, the coefficients vary in an almost linear fashion and the model approaches a linear model.

The transition variable retained, q i t , is the public debt-to-GDP ratio itself, measured at t; the dependent variable, real GDP per capita growth, is instead measured as a forward-looking average over t to t + 3. Among the explanatory variables, only public debt carries a regime-varying coefficient (parameter β₁); all other control variables (investment, credit to the economy, trade openness, initial income, population growth, and the change in the oil price) retain a coefficient that is constant across regimes (parameter β₀). The model further includes time fixed effects in the form of annual dummy variables (λt), whose coefficients, not reported in the results tables below, control for shocks common to all countries at a given date.

The panel studied covers six CEMAC countries over the period 1990-2024 (N = 210, balanced panel).

Regarding the dependent variable (Table 2), it averages 1.60% over the period, with a high degree of dispersion (standard deviation = 9.35) reflecting the well-documented structural heterogeneity of regional economic trajectories, between episodes of oil rent and recurrent crises. Regarding the exogenous variables: public debt (the main exogenous variable) ranges from 0.47% to 270.18% of GDP with an average of 67.37%, close to the community ceiling of 70%. Its high standard deviation (51.42, coefficient of variation above 75%) reflects marked heterogeneity, justifying a non-linear specification a priori. Investment averages 24.88% of GDP, with a distribution also skewed to the right (skewness = 2.42), reflecting occasional large oil infrastructure projects. Credit to the economy remains low (9.26% of GDP on average), a sign of the zone’s persistent under-banking. Trade openness averages 71.90%, with fairly marked variability depending on the trade structure of each country. Population growth is the most homogeneous variable (mean 2.99%, standard deviation 1.00). Finally, the price of oil ranges from 12.72 to 111.97 USD/barrel, illustrating the volatility of international markets.

Table 2. General descriptive statistics.

Source: Authors.

Figure 1 confirms the weakness of the simple linear relationship between public debt and growth (r = 0.112), and supports the choice of a non-linear specification.

Source: R Output.

Figure 1.Average public debt and GDP per capita growth.

Investment unsurprisingly appears positively correlated with growth (r = 0.629), confirming its role as a growth driver, consistent with neoclassical growth models (Table 3). Credit to the economy, for its part, shows a negative correlation with growth (r = −0.221). The price of oil is negatively correlated with both public debt (r = −0.548) and growth (r = −0.245), reflecting the macro-fiscal sensitivity of the zone’s oil economies to world price cycles. No correlation coefficient between explanatory variables exceeds the critical threshold of 0.70; only two pairs show a moderate correlation (investment-openness, r = 0.505; initial income-openness, r = 0.639), posing no risk of problematic multicollinearity for the estimation.

Table 3.Correlation matrix of model variables.

Source: Authors.

The estimation of the econometric model proceeds in several successive steps. Pesaran’s cross-sectional dependence test is applied first, in order to determine the unit-root test appropriate to each variable and to identify those requiring differencing to ensure stationarity. Linearity tests and tests for selecting the number of regimes are then conducted to validate the chosen PSTR specification, prior to the actual estimation of the model. Finally, specification tests are carried out to assess the robustness of the results obtained.

Preliminary tests

Since cross-sectional dependence in macroeconomic panels can bias first-generation unit-root tests, Pesaran’s dependence test (CD-test) is applied to each variable in order to determine the appropriate stationarity test—LLC ([24]) or CIPS (Cross-sectionally Augmented IPS) (Table 4).

Table 4.Cross-sectional dependence and stationarity of variables.

Source: Authors.

The CD-test results lead to a distinction between two groups of variables: those exhibiting significant cross-sectional dependence (debt, investment, credit to the economy, openness, oil price), for which the CIPS test or the univariate Dickey-Fuller test is used, and those for which independence is not rejected (GDP per capita growth, initial income, population growth), tested using LLC. All variables are stationary in levels, except for initial income and the oil price. The latter, integrated of order one, is differenced for the estimation (DF statistic = −5.348, p < 0.01). Initial income is kept in levels, since differencing it would correspond approximately to the growth rate of GDP per capita, creating a tautological relationship with the dependent variable. This is confirmed empirically: the correlation between differenced initial income and GDP per capita growth is 0.94, and a random-effects panel regression of growth on differenced initial income alone yields a within R² of 0.874, with a coefficient of 117.08 (p < 0.001); differencing initial income would therefore amount to duplicating the dependent variable rather than introducing an independent control. This choice, common in the conditional-convergence literature (where initial income in level is precisely what captures the gap to the long-run growth path), nonetheless exposes the model to the usual spurious-regression risk associated with non-stationary panel variables; it constitutes, in that sense, a deliberate trade-off between strict econometric validity and the economic interpretability of the coefficient, rather than a complete neutralization of the issue.

Before estimating the PSTR model, the linearity hypothesis must be tested against the alternative of a threshold specification, and the number of transition functions to retain must then be determined, following the sequential procedure of [13].

The LM_X and LM_F statistics reject the linearity hypothesis at conventional thresholds (1% to 5%) for all three values of m tested, confirming the existence of a non-linear relationship between public debt and growth (Table 5). The versions corrected for heteroskedasticity and autocorrelation (HAC_X, HAC_F), as well as the cluster wild-bootstrap p-value (WCB_PV), do not, by contrast, reject the linearity hypothesis at the 5% level, and only the wild-bootstrap p-value (WB_PV) rejects it marginally; this divergence, expected given the small number of countries in the panel (N = 6), which reduces the power of the corrected asymptotic tests, cautions against over-interpreting the rejection of linearity as a clear-cut result. Since the LM statistics remain the usual reference in the literature [19], linearity is treated as a working hypothesis and the PSTR model is preferred over a linear specification; this relative fragility of the corrected tests nonetheless echoes the indicative (rather than strictly delimited) reading adopted below for the estimated threshold.

The sequential test shows that the first test (r = 0 against r = 1) rejects linearity (LM_X and LM_F significant at 5%), confirming the need for at least one transition function. The second test (r = 1 against r = 2) does not reject the null hypothesis, so the procedure stops at r = 1. The PSTR model with a single transition function is therefore retained, in line with the most parsimonious specification validated by the data.

Table 5.Linearity test and selection of the number of regimes.

Source: prepared by the authors based on R output.

Model estimation

The PSTR model with a single threshold and a single transition function, whose specification was validated by the preceding linearity tests, is estimated using the BFGS optimizer (Table 6).

The transition threshold is estimated at 51.31% of GDP. The confidence interval reported in Table 6, computed from the asymptotic standard error, is narrow ([51.18; 51.44]), but this is unreliable in itself: the distribution of the threshold parameter in a PSTR model is non-standard. A block bootstrap accounting for within-country residual dependence (block length of 4 years, warm-started BFGS re-estimation, 496 valid replications out of 500) yields a substantially wider 95% confidence interval: [49.83; 55.50] using the percentile method, or [47.13; 52.79] using the bias-corrected basic method (bootstrap mean = 51.49%, median = 51.29%, standard deviation = 1.23 points). This confirms that the naive asymptotic interval understates the true uncertainty around the threshold, and that 51.31% of GDP is better read as an indicative transition point situated in the neighborhood of 50%, rather than as a value precisely delimited to two decimal places. It nevertheless remains markedly below the community ceiling of 70% of GDP, which is consistent with hypothesis H2, according to which this ceiling does not reflect the current empirical realities of CEMAC.

Table 6.PSTR model estimation results.

Source: Authors (based on R output). Significant level: ***1%, **5%, *10%.

Specification tests and post-estimation diagnostics

The diagnostic tests complete the validation of the PSTR model. The parameter constancy test checks the temporal stability of the estimated coefficients, a necessary condition for the robustness of the results. The no-remaining-heterogeneity test examines whether the single-transition-function model (m = 1) captures all of the non-linearity in the data, by searching for any residual non-linear structure in the errors (Table 7).

Table 7.Post-estimation specification tests (m = 1, m = 2).

Source: Authors (based on R output).

The diagnostic tests confirm the robustness of the model retained. Regarding parameter constancy, only the LM_X statistic marginally rejects the stability hypothesis, while the other tests (LM_F, HAC, WB, WCB) show no evidence of temporal instability in the coefficients. For the no-remaining-heterogeneity test, although the non-robust statistics (LM_X and, to a lesser extent, LM_F) suggest residual non-linearity, this conclusion is not confirmed by the robust tests (HAC, WB, WCB), which are better suited to the small cross-sectional dimension of the sample in the case of the residual heterogeneity test. These results indicate that the parameters are stable over time and that a single transition function is sufficient to capture the non-linearity of the debt-growth relationship, thereby validating the final specification of the PSTR model.

The transition coefficient is negative and significant (β₁ = −0.058), confirming a regime shift around this threshold. Below 51.31% of GDP, public debt has a positive effect on growth (β₀ = 0.044). Beyond this threshold, its effect becomes statistically indistinguishable from zero (β₀ + β₁ = −0.014), indicating that debt no longer stimulates growth without being significantly detrimental to it either. The smoothing parameter (γ = 53.41) reflects a relatively rapid transition between the two regimes.

Among the control variables, investment has a positive and significant effect on growth, while credit to the economy has a negative effect, which may reflect an inefficient allocation of financial resources or the shallow depth of CEMAC’s financial system. Similarly, changes in oil prices negatively affect growth, illustrating the sub-region’s vulnerability to commodity shocks. Trade openness, on the other hand, has no significant effect, which probably reflects international integration based mainly on the export of natural resources. Finally, initial income shows a negative and significant coefficient, confirming the conditional convergence hypothesis. These results highlight the specific features of growth mechanisms within CEMAC, while recalling that the PSTR model does not allow a causal link to be established between the variables.

The 51.31% threshold estimated in this study is markedly lower than all of the thresholds reported in the prior empirical literature, whether from studies on samples of developed countries (84% - 115%), developing countries (50% - 88%), or specifically on the CEMAC zone (62.7%).

Several factors may explain this gap. First, the study period was extended from 2017 to 2024, thus including the global health crisis and its train of fiscal deterioration, which is likely to lower the tipping point beyond which the accumulation of debt ceases to be beneficial for growth. Second, several methodological choices differ: the correction of public debt data using BEAC annual reports ([20]), the use of income per capita in constant-price purchasing power parity rather than in current currency, and a different decomposition of the control variables. Finally, the robustness of the result, discussed in the following section, suggests that this threshold should be viewed as one empirical benchmark among others rather than as a definitive estimate.