Fiscal Sustainability and the Informal Economy: A Non-Linear Perspective

Abstract

This study examines the issue of fiscal sustainability—measured through the response of the budgetary balance to public debt levels—for 36 OECD countries and candidate countries, and it shows that the relationship is non-linear and depends on the level of the informal economy as a threshold variable. Using the Panel Smooth Transition Regression model, the analysis uncovers regime-dependent fiscal behavior, indicating that the effect of public debt on the budget deficit varies significantly under different economic conditions. In regime 1—at a low level of the informal economy-, the impact of debt on the budgetary deficit is negative and significant, but in regime 2—when the informal economy exceeds the transition threshold-, this impact becomes positive and significant. These results indicate that, in an economic context with a larger informal economy, debt may have a different effect on the budgetary deficit, possibly due to factors such as reduced fiscal efficiency or loss of government revenue. Therefore, fiscal sustainability can be affected by the level of the informal economy.

1. Introduction

Fiscal-budgetary systems, by the nature of their functions (financing, economic adjustment, and combating social inequalities), are dynamic mechanisms subject to frequent adjustments in order to achieve the above-mentioned functions, to monitor the process of fiscal-budgetary consolidation (reducing the deficit and public debt), as well as to pursue medium- and long-term objectives related to the implementation of strategies to ensure sustainable public finances. Moreover, beyond these aspects targeting future performance adjustments in the short, medium, and long term, the foundation of adjustment decisions is based on the historical and current state of fiscal-budgetary systems, which reveals their actual condition (functionalities and dysfunctions, successes, and failures), a situation that also allows the identification of possible causes and the outlining of a fiscal-budgetary profile as a starting point for adjustment efforts.

This study aims to achieve several objectives concerning fiscal sustainability and the influence of the informal economy on budgetary balances in 36 OECD countries and Romania—a candidate for OECD membership, similar in many ways to OECD countries from a level of development perspective. The objectives of this paper include: (i) exploring the potential non-linear relationship between public debt and the budget deficit, to investigate whether fiscal adjustments differ under various economic conditions; (ii) evaluating the informal economy’s role as a threshold variable, examining how its size affects the effectiveness of fiscal policy and the sustainability of public finances; (iii) investigating the presence of fiscal fatigue, to determine if governments struggle to manage budget deficits beyond certain levels of debt; and (iv) assessing the effects of macroeconomic shocks, such as the COVID-19 pandemic, on fiscal sustainability, looking into whether crisis periods exacerbate budgetary imbalances in different economic contexts. Our study extends the existing literature by introducing the size of the informal economy as a structural threshold that shapes fiscal dynamics under crisis conditions—an aspect overlooked in prior work such as Ghosh et al. (2013) and Legrenzi and Milas (2013). By focusing on the nonlinear interaction between debt and deficits in high-informality regimes during periods of overlapping shocks (e.g., the pandemic and the war in Ukraine), we offer a new lens on fiscal fatigue and emphasize the need for context-sensitive, institutionally grounded consolidation strategies.

The concept of the fiscal-budgetary profile, as previously stated, represents an integrated approach and evaluation of as many components of the fiscal-budgetary system as possible, including revenues, expenditures, outcomes, impacts on the economic and social environment, regional integration, and/or alignment with international trends to which the analyzed fiscal-budgetary system has adhered or aspires to adhere, as well as other economic components directly or indirectly related to the fiscal-budgetary environment. The more numerous and complex the fiscal-budgetary and other fiscally relevant elements included in the analysis and evaluation, the more developed and comprehensive the resulting fiscal-budgetary profile becomes, offering a deeper insight into the fiscal-budgetary system at a given point in time (annually) and/or over a longer period.

The approach to the fiscal-budgetary profile can also be further structured at the level of revenues (tax rates, structure, predominance or orientation of taxation toward a specific tax base or production factors), at the level of expenditures (structure, size, orientation, etc.), at the level of consolidated results (budget deficit, public debt), at the level of consequences (financial, economic, social), as well as in terms of the response to various crises that humanity has faced in recent decades (financial, economic, social, health, energy, geopolitical). Additionally, it can address regulation and convergence within the EU or in relation to developments in various sectors (environment, natural resources, demographics, technological changes, digitalization).

The literature in the fiscal budgetary field is primarily oriented toward the structured study and research of fiscal budgetary systems, with analyses focusing on aspects related to those previously mentioned. More integrated approaches are presented in periodic reports prepared at the institutional level, particularly within the EU (the series Taxation Trends in the European Union, the fiscal monitor prepared by the European Fiscal Council), the Eurostat database, and at the level of other international financial and economic organizations (International Monetary Fund, Organization for Economic Co-operation and Development), the Global Economy database, as well as internal reports from member or regional countries. These reports and databases will be useful for achieving the purpose and objectives of the present work. Depending on the scope and complexity of the data and information analyzed for defining the fiscal-budgetary profile, it can provide an overview of a country’s fiscal characteristics, regional fiscal-budgetary features, as well as comparative insights between the countries in the analyzed region, along with information on the positioning of a fiscal-budgetary system relative to the community level to which it has adhered or is in the process of adhering.

Europe’s past economic and fiscal situation has been shaped (necessarily) by the conditions of the Maastricht Treaty and the Stability and Growth Pact to ensure the soundness of public finances. However, developments over the last fifteen years, including the Financial Crisis and the Sovereign Debt Crisis, have shown that this situation can truly change, rapidly leaving the continent in a rather fragile economic state and recovering only slowly. Now, facing the effects of the COVID-19 pandemic and the war in Ukraine, many countries are exposed to yet another severe economic crisis and national intervention efforts to cushion the impact have resulted in unprecedented budget deficits and a surge in public debt.

Thus, debt sustainability and fiscal policy analysis are more critical than ever for understanding and overseeing the state of public finances. The central challenge is to identify the essential elements that drive fiscal responses and the key factors influencing budgetary performance. It is possible to capture different fiscal behaviors based on varying levels of macroeconomic variables, meaning to distinguish distinct government fiscal policy responses depending on different levels of influencing factors, such as debt, interest rates, or the state of economic output.

The dedicated literature on fiscal sustainability is divided into two main research directions, each addressing different aspects of how governments manage and sustain their fiscal policies.

The first direction revolves around the concept of the fiscal response function, explored in various studies such as those by Bohn (1995, 1998) and Afonso et al. (2009). These studies investigate how a government’s fiscal deficit—essentially the difference between its revenues and expenditures—adjusts in response to fluctuations in the debt-to-GDP ratio. The primary question these studies aim to answer is whether governments proactively respond to rising debt levels by adjusting their fiscal policies to prevent debt from becoming unsustainable. One result of this research is that if the budgetary balance’s response to increasing debt is positive and statistically significant, it indicates that the government takes necessary measures to stabilize debt. This positive response is often interpreted as a sign of “weak sustainability”. In this context, “weak” does not imply fragility but rather that the government is doing enough to prevent debt from rising uncontrollably, even if it is not significantly reduced. Essentially, as long as the government adjusts its budgetary balance in response to rising debt, the debt level can be stabilized over time, ensuring that public finances remain sustainable in the long term.

On the other hand, the second component of the literature focuses on a phenomenon known as “fiscal fatigue”. This concept was brought to prominence by Ghosh et al. (2013), who expanded our understanding of the limits of fiscal sustainability. Fiscal fatigue refers to the idea that the relationship between debt and the budgetary balance may not be straightforward or linear, as previously assumed. Instead, this research suggests that a non-linear dynamic might be at play, particularly in the form of a cubic relationship.

Thus, while governments may initially respond positively to rising debt by increasing their budgetary surplus (thereby attempting to manage and reduce debt), there is a limit to how much adjustment they can or will make. As the debt ratio continues to rise, a point may be reached where the government’s capacity or willingness to maintain a positive fiscal response diminishes. This is where the concept of fiscal fatigue comes into play: beyond a certain debt threshold, the government may no longer be able to increase its budgetary surplus or may even begin to run a budgetary deficit again.

2. Literature Review

The literature addressing fiscal sustainability is divided into two main research strands, each addressing different aspects of how governments manage and support their fiscal policies.

The first direction focuses on the concept of the tax response function, which has been explored by several studies such as those of Bohn (1995, 1998) and Afonso et al. (2009). This research examines how a government’s fiscal deficit—essentially the difference between its revenues and expenditures—adjusts in response to fluctuations in the debt-to-GDP ratio. The main question these studies seek to answer is whether governments are proactively responding to rising debt levels by adjusting their fiscal policies to prevent debt from becoming unsustainable.

A result of the literature review is that if the budgetary balance response to a debt increase is positive and statistically significant, it suggests that the government is taking the necessary steps to stabilize the debt. This positive response is often interpreted as a sign of “poor sustainability”. In this context, “weak” does not mean fragility, but rather that the government is doing enough to prevent debt from growing uncontrollably, even if it is not significantly reduced. Essentially, as long as the government adjusts its budgetary balance in response to rising debt, debt levels can be stabilized over time, ensuring that public finances remain sustainable over the long term.

On the other hand, the second component of the literature focuses on a phenomenon known as fiscal fatigue. This concept was brought to the fore by Ghosh et al. (2013), who expanded our understanding of the limits of fiscal sustainability. Fiscally tiring refers to the idea that the relationship between debt and budgetary balance may not be direct or linear, as previously assumed. Instead, this research suggests that there could be nonlinear dynamics at play, especially in the form of a cubic relationship. Thus, while governments can initially respond positively to rising debts by increasing their budgetary surplus (thus attempting to manage and reduce debt), there is a limit to how much adjustment they can or will make. As the debt ratio continues to rise, there may come a point where the government’s ability or willingness to maintain a positive fiscal response declines. This is where the concept of fiscal fatigue comes in: beyond a certain debt threshold, the government may not be able to increase its budgetary surplus or may even start to run a budgetary deficit again. This turning point is essential because it indicates that the government’s fiscal policy has become less effective in managing debt, and subsequent increases in debt could lead to a vicious cycle in which debt grows uncontrollably.

This second part of the literature highlights the limitations of relying solely on the tax response function to measure fiscal sustainability. While a positive response to debts is required, it may not be sufficient if there are limits to how much adjustment is feasible. The nonlinearities identified by the concept of fiscal fatigue suggest that governments face real constraints in their ability to sustain fiscal adjustments indefinitely. Therefore, even if a government initially shows a positive fiscal response to rising debt, this response may not be sufficient to ensure long-term sustainability if the debt burden becomes too high.

In short, these two branches of literature offer complementary perspectives on fiscal sustainability. The fiscal response function emphasizes the importance of governments’ response to rising debt levels with appropriate fiscal adjustments, while the concept of fiscal fatigue highlights the potential limits of these adjustments, especially in the face of high or rapidly growing debt. Together, they provide a more nuanced understanding of the challenges governments face in managing public finances in the long term.

Overall, research on fiscal adjustments in European countries (Ghosh et al., 2013) suggests that the link between the level of debt and the budgetary balance progresses in three phases. When the debt level is low, the principal balance remains unaffected by the increase in debt, as certain levels consider the debt to increase insignificantly. Second, once rising debt reaches a point where markets react and have a higher probability of default, the authorities will initiate a process of fiscal consolidation aimed at stabilizing the debt-to-GDP ratio. The concept of fiscal fatigue arises in the third phase of fiscal adjustment when the debt exceeds a certain level, despite the adjustment.

As it is well known, the global financial crisis that began in 2008 had some long-lasting repercussions, especially in the period 2009–2011 in the EU, being known as the sovereign debt crisis. As a result, extensive research has addressed the tax backlash function, in particular regarding EU Member States. Medeiros (2012), for example, simulates debt ratios for 15 EU Member States using vector auto-regression (VAR) models and a panel fiscal reaction function (FRF). In addition, Legrenzi and Milas (2013) use nonlinear fiscal response functions with endogenously determined state adjustment thresholds to analyze the behavior of fiscal policy authorities in “good” and “bad” periods, building on previous research on fiscal policy sustainability. Their sample focused on Greece, Ireland, Portugal, and Spain. The study revealed that these countries presented corrective actions to regulate fiscal imbalances only when their debt ratios were considerably high. Specifically, the estimated debt thresholds for initiating these remedies turned out to be 69% for Greece, 49% for Ireland, 47% for Portugal and 43% for Spain. In addition, Greece’s fiscal position differs from the 60% Maastricht Treaty benchmark due to a higher threshold, slower fiscal adjustment, and a non-cyclical budgetary surplus. In addition, under pressure from financial markets, all governments have reduced the level of debt above which corrective measures are taken. In addition, Small et al. (2020) studied the budgetary reaction of 53 developing countries to changes in their debt-to-GDP ratios. According to them, there is a positive link between debt and the budgetary surplus and nations adjust conditionally on the level of income as well as spending margins at almost the same rate.

Furthermore, Everaert and Jansen (2018) investigate whether fiscal fatigue is a solid property of the tax response function in a group of OECD nations from 1970 to 2014. The results demonstrated a heterogeneous response of the budgetary balance to the public debt, with fiscal fatigue not being identified as a common characteristic of the fiscal reaction function manifested by all the nations in the panel.

Furthermore, financial intermediation has a strong connection to a country’s fiscal position, as it influences the allocation of resources and the management of government finances. In addition, banks play an important role in channeling funds from depositors to individuals, thus supporting the movement of capital within an economy. This intermediation role has a direct impact on a government’s fiscal condition, as it dictates interest rates on loans and, implicitly, the availability of cash for public spending. In addition, Demirgüç-Kunt and Huizinga (1999) argue that the efficiency of the banking sector in mobilizing household and business savings and then allocating these resources to investments such as infrastructure can influence both government borrowing costs and its ability to finance public projects, ultimately shaping the country’s fiscal position.

Neaime (2015) analyzed the level of sustainability of public debt and budget deficit for a considerable number of countries in the European Union, for a time horizon of 30 years. The results suggested that after the economic crisis, European economies suffered deeply from the perspective of public finances, which also generated the debt crisis. There is a sharp deterioration in the level of public debt, with only a few economies having a sustainable level of it, most of them well above the threshold of 60% of GDP regulated by the Maastricht treaty.

Reed et al. (2019) used a VAR model to study the link between twin deficits and public debt sustainability. Using variance decomposition, they demonstrated that there is a persistent link over time between the current account deficit and the budget deficit on the one hand, respectively, and the level of sustainability of public debt. To keep the public debt at an optimal level, an adjustment of the twin deficits is necessary; this problem is specific to states with a high level of both imports and exports.

Saleh and Harvie (2005) carry out an extensive analysis of the impact of the budget deficit on a considerable number of macroeconomic variables such as market interest rates, exchange rates, economic growth, different types of spending, but also on taxation. The results suggest that a high level of budget deficit can stimulate the economy if this expansionary policy is maintained for a longer period of time. However, it must be borne in mind that after such a period the government must intervene strongly in the tax area, respectively, to counterbalance the policy in a restrictive area. This can be achieved only if the multiplier effect of the additional expenses incurred is higher than one.

Dumitrescu (2014), starting from the equations of public debt and budgetary constraint, analyzes the evolution of the public debt-to-GDP ratio for the Romanian economy, identifying the main factors influencing its sustainability. It suggests that the level of public debt and the long-term anticipation of influencing factors ensure that it improves its stability and sustainability.

A relevant aspect of analysis in the evaluation of public finances is the budgetary expenditure on social protection. Kotlikoff and Hagist (2005) analyzed the fact that health expenditure has increased more than GDP; therefore, if social spending increases at the same rate, in many economies large and unsustainable budget deficits will lead to long-term imbalances. At the same time, Corsetti and Roubini (1991) and Alesina (2000) analyzed the effects of the increase in social public spending on the level of fiscal policy sustainability.

The vulnerabilities of fiscal policies have been analyzed over time by a series of authors such as Greiner and Semmler (1999), Afonso and Raul (2008), and Corsetti and Roubini (1991), who have argued that an increase in social protection spending, to the detriment of other categories of spending, can lead to an economic stimulus, but in the very short term, which characterizes the fiscal-budgetary policy as unsustainable. At the same time, authors such as Fatas and Mihov (2009), Claeys (2007), and Afonso et al. (2009) suggest that governments have difficulty adjusting public policies, probably for political reasons choosing to maintain a procyclical policy.

Another aspect to analyze is the existence of fiscal vulnerabilities. Ghosh et al. (2013) state that a significant increase in budgetary deficits and public debt is generated by a lower level of tax revenues and a high amount of public stimulus expenditures. This leads to the emergence of vulnerabilities in fiscal policy. These vulnerabilities must be eliminated quickly; otherwise, they will lead to major imbalances in public finances.

Hemming et al. (2003) substantiated that fiscal vulnerabilities significantly increased the probability of crises. Subsequently, Rial and Vicente (2004) using a sensitivity analysis studied the vulnerability of public debt. They defined fiscal vulnerability as any violation of liquidity and/or solvency requirements because of changes in macroeconomic conditions. At the same time, Ghezzi et al. (2010) built a fiscal vulnerability index, using indicators such as solvency, financing needs, dependence on external financing, health of the financial sector, and institutional strength. Baldacci et al. (2011) contributed to the development of a methodology for assessing fiscal policies by using a vulnerability index calculated as a deviation from the 10-year national averages, a set of indicators, and a fiscal stress index. Schaechter et al. (2012) built a toolkit for assessing vulnerability and fiscal risks. They introduced six instruments such as indicators measuring short-term pressures, including gross financing needs, market-based measures of sovereign risk, a measure of potential spillovers, and indicators assessing medium- and long-term vulnerabilities, comprising a measure of the fiscal effort required to stabilize debt, a measure assessing the negative impact of growth and interest shocks on the debt trajectory, and a measure that reflects the risks associated with the underlying debt projections.

Finally, recent literature emphasizes that fiscal sustainability is inherently nonlinear and contingent on the debt-to-GDP ratio, particularly within the euro area. Owusu et al. (2023) employ a Panel Smooth Transition Regression (PSTR) approach to reveal two distinct fiscal regimes: a low-debt regime with a statistically insignificant fiscal response and a high-debt regime characterized by a significant and positive primary balance reaction to rising debt, suggesting sustainability only in high-debt scenarios. This regime-dependent behavior aligns with findings by Ghosh et al. (2013) on “fiscal fatigue” and by Fournier and Fall (2015), who highlight threshold effects and diminishing fiscal responsiveness. Supporting evidence from Legrenzi and Milas (2012) and Afonso and Jalles (2019) confirms heterogeneity in fiscal behavior across EU states, indicating that uniform debt rules may not be equally effective. Moreover, institutional and political economy factors play a significant role in shaping fiscal responses. Studies such as Afonso et al. (2011) and Ricci-Risquete et al. (2016) document regime-switching behavior in fiscal policy due to electoral cycles and rule-of-law effectiveness. Aldama and Creel (2019) show that regime changes in France and the US often reflect macroeconomic shocks and institutional constraints. The robustness of non-linear specifications is further supported by Gootjes and de Haan (2022) and Larch et al. (2021), who demonstrate pro-cyclical fiscal behavior, especially in high-debt regimes. Collectively, these contributions underscore the necessity of flexible fiscal frameworks that account for debt levels, institutional quality, and cyclical conditions to ensure sustainable public finances across diverse economic landscapes.

3. Materials and Methods

As mentioned in the introduction, the aim of this study is to identify the factors that influence the level of the budget deficit, with a focus on the deficit-debt relationship. Thus, the construction of the data sample is formed by 36 countries globally (Austria, Belgium, Canada, Chile, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Korea, Latvia, Lithuania, Luxembourg, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey, United Kingdom, and United States), the vast majority of which are from the OECD, to which is added Romania—a candidate country, for the period 2004–2021. By examining this wide range of economies, the study highlights how different economic structures and policy environments influence fiscal responses to public debt and the informal economy. The complete definition of all the variables included in the analysis is presented in

Table 1. Data description.

Variable	Description	Source
Deficit (dependent variable)	Fiscal balance, percentage of GDP. The fiscal (budgetary) balance is the difference between government revenues and government expenditures. The value is expressed as a percentage of GDP to relate it to the size of the economy.	The Global Economy
Informal (threshold variable)	The World Bank’s MIMIC model uses the following variables as determinants of the informal economy: (1) government size, (2) share of direct taxation, (3) fiscal freedom index, (4) business freedom index, (5) unemployment rate, and GDP per capita, and (6) government efficiency. It proposes that the following variables are affected by the informal economy: (1) GDP per capita growth rate, (2) labor force participation rate, and (3) money supply as the M0 ratio. These variables are used in a structural equation model (SEM) with a latent variable that measures the size of the informal economy.	The Global Economy
Debt	Government debt as a percentage of GDP. It includes both domestic and external liabilities, such as foreign currency deposits and money, other securities than stocks, and loans. It is the gross value of government liabilities minus the value of equity and financial derivative instruments held by the government.	The Global Economy
Stability	The Political Stability and Absence of Violence/Terrorism index measures the perception of the likelihood that the government will be destabilized or overthrown by unconstitutional or violent means, including politically motivated violence and terrorism.	The Worldwide Governance Indicators
GAP	The output gap measures the difference between the actual output of an economy and its maximum potential output, expressed as a percentage of the gross domestic product.	OECD Database
INF	Inflation measured by the consumer price index reflects the annual percentage change in the cost for the average consumer to purchase a basket of goods and services, which may be fixed or adjusted at specified intervals, such as annually.	The Global Economy
Interest	Short-term interest rates are the rates at which short-term loans are made between financial institutions or the rate at which short-term government securities are issued or traded on the market.	OECD Database
FDI	Foreign direct investment, percentage of GDP. It is the sum of equity capital, reinvested earnings, other long-term capital, and short-term capital, as shown in the balance of payments.	The Global Economy
Crisis	Dummy variable that takes the value of 1 during the period 2009–2011 and 0 otherwise.	Own calculations
COVID	Dummy variable that takes the value of 1 in 2020 and 2021, and 0 otherwise.	Own calculations
Elections	Dummy variable that takes the value of 1 in years with presidential/parliamentary elections and 0 otherwise.	The Global Economy

Source: Authors’ own research.

, while additional evidence regarding the descriptive statistics is presented in Appendix A.

As mentioned, this paper uses the Panel Smooth Transition Regression (PSTR) model, and it is appropriate because it effectively captures non-linear and regime-dependent economic relationships. This model offers a more adaptable alternative to traditional approaches that often impose strict separations between different regimes. In contrast to models that feature sudden transitions, PSTR facilitates a gradual shift between economic regimes, which more accurately represents the interaction of fiscal and economic factors as the informal economy changes in size. This approach is crucial for pinpointing inflection points in the relationship between the budget deficit, public debt, and other explanatory variables, emphasizing how fiscal policy and market responses evolve progressively in reaction to shifting economic conditions.

To ensure the reliability of the analysis, stationarity tests were applied to the selected sample, rather than investigating the concept itself. To do this, the test proposed by Levin et al. (2002) was performed, which is recommended given the structure of our data. The null hypothesis of this test assumes that all panels have a common non-stationary autoregressive parameter. In contrast, the alternative hypothesis indicates stationarity, implying that they exhibit stationary behavior.

The results presented in

Table 2. Levin-Lin-Chu test results.

Variable	Test Value	p-Value
Deficit	−4.77264	0.0000
Informal	−11.4649	0.0000
Debt	−2.22584	0.0130
Stability	−3.17722	0.0007
GAP	−1.63315	0.0512
INF	−10.3027	0.0000
Interest	−9.98313	0.0000
FDI	−4.30917	0.0000

Source: Authors’ own research.

indicate that all variables are stationary at a 10% threshold, ensuring the validity and reliability of the econometric analysis.

The results of the Levin-Lin-Chu test indicate that most variables, such as “Deficit”, “Informal”, “Debt”, “Stability”, “INF”, “Interest”, and “FDI”, are stationary, as shown by the test values, most of which are corroborated by p-values under 5%. However, the variable “GAP” has a p-value of 0.0512, slightly above the threshold, suggesting that it may be non-stationary or near-stationary, although it can reject the null hypothesis of non-stationarity at a 90% significance level. Accordingly, the PSTR model was estimated under conditions that ensured consistency, as confirmed by stationarity tests. The dummy variables were not included in the analysis due to their structure, which is incompatible with the specifications of the chosen stationarity test.

Another phenomenon that can affect the quality of the estimates used is multicollinearity. As a technique for analyzing this phenomenon, the first step was to create a correlation matrix for all the explanatory variables, and then run a standard panel regression and report the VIF values. The correlation matrix of the explanatory variables is shown in

Table 3. Correlation matrix.

	Debt	Stability	GAP	INF	Interest	FDI	Crisis	COVID	Elections
Debt	100%	−5%	−27%	−34%	−35%	−9%	2%	8%	−8%
Stability	−5%	100%	11%	−18%	−21%	10%	0%	−1%	−5%
GAP	−27%	11%	100%	40%	35%	8%	−16%	−36%	−2%
INF	−34%	−18%	40%	100%	72%	5%	9%	−14%	7%
Interest	−35%	−21%	35%	72%	100%	6%	−2%	−17%	9%
FDI	−9%	10%	8%	5%	6%	100%	0%	1%	−6%
Crisis	2%	0%	−16%	9%	−2%	0%	100%	−9%	−2%
COVID	8%	−1%	−36%	−14%	−17%	1%	−9%	100%	−1%
Elections	−8%	−5%	−2%	7%	9%	−6%	−2%	−1%	100%

Source: Authors’ own research.

below.

The correlation matrix suggests that multicollinearity is not a significant issue overall, as most correlations are moderate or low. However, the 72% correlation between Inflation and Interest Rate indicates a strong relationship that could lead to some concerns about multicollinearity in regression analyses involving these variables. Although this correlation is below the typical threshold for severe multicollinearity (usually 0.8 or higher), it still suggests that these two variables may significantly influence each other, complicating the interpretation of their individual effects in a model.

To eliminate any doubt regarding the multicollinearity phenomenon, we ran a fixed effects model with the explanatory variables mentioned above, and the corresponding VIF results for each explanatory factor are shown in

Table 4. VIF test.

Variable	Centered VIF
Debt	1.7992
Stability	1.0510
GAP	2.2242
INF	1.9819
Interest	2.0263
FDI	1.0255
Crisis	1.1276
COVID	1.2224
Elections	1.0034

Source: Authors’ own research.

.

The VIF values presented for each variable are all well below the threshold of 5, indicating that multicollinearity is not a significant issue. The highest VIF observed is 2.2242 for the variable “GAP”, which is still within acceptable limits, suggesting that none of the variables are excessively correlated with each other. This low level of multicollinearity means that the regression coefficients can be interpreted with confidence, as their variations are not significantly inflated by the interdependence between variables. Furthermore, variables such as “Elections” and “FDI” have VIF values very close to 1, leading us to the conclusion that the results will not be distorted by the presence of multicollinearity.

To investigate the presence of a threshold effect for the deficit level, the smooth transition regression (PTR—panel transition regression) developed by Hansen (1999) was used which can be described by Equation (1):

$$Y_{it}=\left\{\begin{array}{c}{\mu }_i+{\alpha }_1^{\prime }{X}_{it}+{\epsilon }_{it},S_{it}\le \tau \\ {\mu }_i+{\alpha }_2^{\prime }{X}_{it}+{\epsilon }_{it},S_{it}>\tau \end{array}\right.$$

(1)

For $i=1,\dots ,N$ and $t=1,\dots ,T$ where N and T represent the number of countries and years, respectively. In Equation (1), the dependent variable ${\mathit{Y}}_{\mathit{i}\mathit{t}}$ is the level of the budget deficit, ${\mathit{S}}_{\mathit{i}\mathit{t}}$ it is the transition variable—i.e., the level of the informal economy, ${\mathit{X}}_{\mathit{i}\mathit{t}}$ it is the matrix of explanatory variables, ${\mathit{\mu }}_{\mathit{i}}$ it is the fixed effects of the country while ${\mathit{\epsilon }}_{\mathit{i}\mathit{t}}$ are the estimation errors. Our decision to use the size of the informal economy as the transition variable is grounded in both theoretical and empirical considerations. As emphasized by Dumitrescu et al. (2022), the informal sector plays a fundamental role in shaping the macroeconomic effects of fiscal policy, especially in emerging economies. A large shadow economy reduces the government’s capacity to collect taxes, weakens the efficiency of automatic stabilizers, and amplifies fiscal vulnerabilities. In line with this, we hypothesize that the fiscal reaction function—measured by the response of the budget deficit to macroeconomic variables—varies depending on the extent of informality in the economy. From a methodological perspective, the shadow economy as a transition variable fulfills the key requirement of the PSTR model: it is continuous, bounded, and economically meaningful, allowing for smooth transitions between low- and high-informality regimes. Following the approach of Dumitrescu et al. (2022), we allow the marginal effect of variables such as public debt or economic growth on the budget balance to vary according to the level of informality, capturing regime-dependent fiscal behavior.

In the PTR model, the two groups of observations, below and above the threshold, are precisely identified and distinct with a sudden transition from one regime to another. In order to consider smooth and gradual changes through the $\mathit{j}=\overline{\mathbf{1},\mathit{r}}$ transition between $\mathit{r}+\mathbf{1}$ distinct regimes, González et al. (2005) introduced an extension of the PTS model, namely PSTR (Panel Smooth Transition Regression). According to them, the model is defined as follows.

$$Y_{it}={\mu }_i+{\beta }_0^{\prime }{X}_{it}+{\sum }_{j=1}^r{\beta }_j^{\prime }{X}_{it}F\left(S_{it}^{\left(j\right)};{\gamma }_j,{\tau }_j\right)+{\epsilon }_{i,t}$$

(2)

In Equation (2), the existence of transition functions $\mathit{F}\left({\mathit{S}}_{\mathit{i}\mathit{t}}^{\left(\mathit{j}\right)};{\mathit{\gamma }}_{\mathit{j}},{\mathit{\tau }}_{\mathit{j}}\right)$ whose values are set in the range (0, 1) will be accepted having three key characteristics: the threshold variable, ${\mathit{S}}_{\mathit{i}\mathit{t}}$, the slope of the transition function, ${\mathit{\gamma }}_{\mathit{j}}$., as well as the location paprametries ${\mathit{\tau }}_{\mathit{j}}$.

According to Teräsvirta (1994) and Colletaz and Hurlin (2006), the structure of the transition function can be defined based on a logistic representation:

$$F\left(S_{it}^{\left(j\right)};{\gamma }_j,c_j\right)={\left[1+exp\left(-\gamma {\prod }_{l=1}^m\left(S_{it}-{\tau }_l\right)\right)\right]}^{-1}$$

(3)

With $\mathit{\gamma }>\mathbf{0}$ and ${\mathit{\tau }}_{\mathbf{1}}\le {\mathit{\tau }}_{\mathbf{2}}\le \dots \le {\mathit{\tau }}_{\mathit{m}}$. According to the suggestions of Omay and Öznur Kan (2010), values of 1 or 2 for m can capture all variations between the dynamics of the explanatory variables and the dependent variable. When m = 1 it is dealing with a transition function with a first-order logistical representation. In this situation, if: (i) $\mathit{\gamma }\to \mathbf{0}$, there is no transition, so the PSTR model becomes a standard linear model with fixed effects with homogeneous coefficients; (ii) $\mathit{\gamma }\to \mathbf{\infty }$ the model becomes a PTR model of Hansen (1999), because the transition from one regime to another is sudden; (iii) if $\mathit{\gamma }\nrightarrow \mathbf{0}$ and $\mathit{\gamma }\nrightarrow \mathbf{\infty }$, the low and high values of it correspond to the two extreme regimes with a single smooth transition function. For $\mathit{m}=\mathbf{2}$ cu $\mathit{\gamma }\nrightarrow \mathbf{0}$ and $\mathit{\gamma }\nrightarrow \mathbf{\infty }$ with and the transition, the function is 1 for both the upper and lower values of it, reaching the minimum point at $\left({\mathit{\tau }}_{\mathbf{1}}+{\mathit{\tau }}_{\mathbf{2}}\right)/\mathbf{2}$ and $\mathit{\gamma }\to \mathbf{\infty }$ when it is a PSTR model with three regimes and a standard linear model with fixed effects when $\mathit{\gamma }\to \mathbf{0}$:

$$Y_{it}={\mu }_i+{\beta }_0^{\prime }{X}_{it}+{\beta }_1^{\prime }{X}_{it}F\left(q_{it};\mathrm{}\gamma ,\tau \right)+u_{it}$$

(4)

To calculate the parameters in Equation (4), the fixed effects must first be eliminated by eliminating the individual averages that will lead to

$${\overline{Y}}_i={\mu }_i+{\beta }_0^{\prime }{\overline{X}}_i+{\beta }_1^{\prime }{W}_i\left(\gamma ,\tau \right)+{\overline{u}}_i$$

(5)

where, ${\overline{Y}}_i=\frac{1}{T}{\sum }_{t=1}^T{Y}_{it},{\overline{X}}_i=\frac{1}{T}{\sum }_{t=1}^T{X}_{it},{\overline{u}}_i=\frac{1}{T}{\sum }_{t=1}^T{u}_{it}\mathrm{a}\mathrm{n}\mathrm{d}{W}_i\left(\gamma ,\tau \right)=\frac{1}{T}{\sum }_{t=1}^T{X}_{it}F\left(S_{it};\gamma ,\tau \right)$.

By removing Equation (5) from Equation (4), the following was obtained:

$$\left(Y_{it}-{\overline{Y}}_i\right)=\left({\mu }_i-{\mu }_i\right)+{\beta }_0^{\prime }\left(X_{it}-{\overline{X}}_i\right)+{\beta }_1^{\prime }\left(X_{it}F\left(S_{it};\gamma ,\tau \right)-W_i\left(\gamma ,\tau \right)\right)+u_{it}-{\overline{u}}_i$$

(6)

Noting ${\tilde{Y}}_{it}=Y_{it}-{\overline{Y}}_i,{\tilde{X}}_{it}=X_{it}-{\overline{X}}_i{,\tilde{u}}_{it}=u_{it}-{\overline{u}}_i$, Equation (6) can be rendered in a vector representation as follows:

$${\tilde{Y}}_{it}={\beta }^{\prime }{\tilde{X}}_{it}\left(\gamma ,\tau \right)+{\tilde{u}}_{it}$$

(7)

where ${\tilde{X}}_{it}\left(\gamma ,\tau \right)={\left(X_{it}^{\prime }-{\overline{X}}_i^{\prime },X_{it}^{\prime }F\left(S_{it};\gamma ,\tau \right)-W_i^{\prime }\left(\gamma ,\tau \right)\right)}^{\prime }$.

Once the first step is complete, the model can be estimated using a nonlinear least squares (NLS) method. However, as González et al. (2005) explained that ${\tilde{\mathit{X}}}_{\mathit{i}\mathit{t}}\left(\mathit{\gamma },\mathit{\tau }\right)$ is sensitive to the values of $\mathit{\gamma }$ and $\mathit{c}$. Consequently, the cornerstone of the NLS approach is to estimate $\mathit{\gamma }$ and $\mathit{\tau }$ to quantify and retain those evils that lead to the destruction of the valley of the major down, the minimization being centered on $\widehat{\mathit{\beta }}$:

$$Q^c\left(\gamma ,c\right)=Arg\mathrm{M}\mathrm{i}\mathrm{n}{\sum }_{i=1}^N{\sum }_{t=1}^T{\left(\left({\tilde{Y}}_{it}-{\widehat{\beta }\left(\gamma ,\tau \right)}^{\prime }{\tilde{X}}_{it}\left(\gamma ,\tau \right)\right)\right)}^2$$

(8)

After effecting this optimization conditioned by an initial set of values $\left(\mathit{\gamma },\mathit{\tau }\right)$, it was estimated ${\mathit{\beta }}_{\mathbf{0}}^{\mathbf{\prime }}{\mathit{\beta }}_{\mathbf{1}}^{\mathbf{\prime }}$ via OLS and then applied NLS $\left(\widehat{\mathit{\gamma }},\widehat{\mathit{\tau }}\right)$.

4. Results

It is important to explore the potential nonlinearities present in the empirical model, as shown in Equation (2). For all the specifications to be run, the null hypothesis is that of a linear relationship between the budget deficit and the selected explanatory factors (H0: r = 0), in favor of the alternative (H1: r = 1. Moreover, it can also be considered two transition functions in the specifications (H1: r = 2). Most of the time, in practice, for simplicity, a single transition function is chosen to capture the non-linear impact induced by the public debt as well as the other variables on the budget deficit. The results of the linearity tests are shown in the table below in

Table 5. Linearity Tests.

Test	H0: r = 0 vs. H1: r = 1	H0: r = 1 vs. H: r = 2
Lagrange Multiplier—Wald (LMW)	90.329 (0.00)	32.937 (0.00)
Lagrange Multiplier—Fischer (LMF)	9.844 (0.00)	3.106 (0.00)
Likelihood Ratio	97.970 (0.00)	33.884 (0.00)

Source: Authors’ own research.

:

The results of the Lagrange Multiplier-Wald (LMW), Lagrange Multiplier-Fischer (LMF), and Likelihood Ratio linearity tests suggest that the null hypothesis (H0: r = 0), according to which the relationship between the budget deficit and the selected explanatory factors is linear, is rejected at a 99% confidence level. This indicates the existence of very strong arguments against a purely linear relationship, suggesting the presence of a nonlinear relationship between variables. More specifically, the concept of Fiscal Fatigue brings into question the possibility of the existence of a complex nonlinear relationship, such as a quadratic relationship, between public debt and budgetary deficit. The tests indicate that the nonlinear model is better suited to capture the dynamics between public debt and budget deficit than a simple linear model.

Furthermore, although the possibility of a specification with two transition functions (H1: r = 2) was considered, it was rejected at a relevance level of 90%. This indicates that although nonlinearity is present, a simpler transition function (a single inflection point or a quadratic relationship) is sufficient to capture the nonlinearities between variables.

This is essential in this analysis, as it suggests that there is a threshold point in the structure of the level of the informal economy from which governments can no longer respond effectively to rising debts. In conclusion, the tests in Table 5 confirm that the relationship between the budget deficit and the explanatory factors is non-linear, and this requires a more complex analysis to capture the fiscal response to the increase in debts.

In

Table 6. Results of the PSTR (Budget Deficit as a Dependency).

Variable	Regime 1: β0	Nonlinear Part: β1	Regime 2: B0 + B1	Regime 1: β0	Nonlinear Part: β1	Regime 2: B0 + B1
Debt	−0.0219 *	0.1086 ***	0.0867 *	−0.0117	0.1050 ***	0.1050 ***
Debt2				0.0114	−0.0035	0.0000
Stability	−0.1713	−0.5704	0.0000	0.0539	−0.4033	0.0000
GAP	0.2575 ***	−0.2553 ***	0.0022 ***	0.2440 ***	−0.2669 ***	0.0013 ***
Inflation	−0.1146	0.0690	0.0000	−0.1115	0.0885	0.0000
Interest	−0.1925 *	0.0324	−0.1925 *	−0.1778 *	−0.0702	−0.1778 *
ISD	−0.0028	0.0042	0.0000	−0.0034	0.0001	0.0000
Crisis	−1.8180 ***	−0.2817	−1.8180 ***	−1.8499 ***	−0.3736	−1.8499 ***
COVID	−1.3192 **	−3.4635 **	−4.7827 ***	−1.4002 **	−3.2707 ***	−4.6709 ***
Election	−0.0557	0.1725	0.0000	−0.0226	0.1276	0.0000
Informal economy threshold	20.66%			19.23%
Slope	0.9670			0.7422

*, ** and *** indicate statistical significance at the levels of 10%, 5%, and 1%, respectively. In regime 2, all statistically significant coefficients were considered; otherwise, the values are set to zero.

, the results of the PSTR model for more specifications are shown.

The results presented in the table above highlight the coefficients of the variables in both regimes and their statistical significance, conditioned by the level of the informal economy each year. Essentially, the model allows for the analysis of nonlinear relationships and the change of these relationships according to certain economic thresholds or conditions.

In the case of public debt, a negative coefficient (−0.0219) is observed in Regime 1 (β0), indicating that, in a specific economic context, an increase in this indicator can be associated with a reduction in the budget deficit, the coefficient being significant at a relevance threshold of 90%. However, as the economy transitions to Regime 2 (from increased collection efficiency to a lower one), the nonlinear part (β1) with a positive coefficient of 0.1086 suggests that the relationship is reversed, and the accumulation of debt begins to contribute to the increase in the deficit. In Regime 2, the combination of these coefficients (β0 + β1) results in a positive net coefficient (0.0867), indicating that in this regime, an increase in public debt is associated with a larger budget deficit. Moreover, there is no curved or square-shaped relationship between the debt and the budget deficit that is strong enough to significantly influence the results. As a result, the model indicates that only the linear debt-to-deficit ratio is significant, while the quadratic component does not clearly contribute to the change in the budget deficit.

In the case of political stability, the coefficients in Regime 1 and the non-linear part are not significant, suggesting that economic stability does not have a clear impact on the budget deficit in Regime 1. On the other hand, for Output GAP, the coefficients show a very interesting relationship: a positive coefficient in Regime 1 (0.2575 ***) indicates that when the economy is below its potential, the deficit tends to increase. The nonlinear part (β1) is negative (−0.2553 ***), which indicates that as the economy approaches its maximum potential, this effect diminishes. In Regime 2, the combined coefficient becomes very low (0.0022 ***), suggesting that once the informal economy reaches a certain threshold, the GAP no longer significantly influences the budget deficit.

For variables related to major events, such as the global financial crisis 15 years ago and the COVID-19 pandemic, the impact on the budget deficit is negative in both regimes. For example, in the case of the pandemic, the coefficient is negative in both regimes but amplified in cases where the informal economy is at higher levels, i.e., in Regime 2 (−4.7827 ***), reflecting the adverse effects of the pandemic on public finances. This suggests that in times of crisis, the budget deficit increases considerably, and this effect is amplified in the second regime. In contrast, other variables, such as short-term interest rates and inflation, have coefficients that are not significant, suggesting that they have a limited impact on the budget deficit regardless of the level of the informal economy.

To sum up, the results of this PSTR model highlight a complex and dynamic relationship between the budget deficit and the explanatory variables, with notable differences between the two economic regimes. This suggests that economic policies need to be adapted to the specific economic context, as the factors influencing the budget deficit can vary significantly depending on macroeconomic conditions. For example, while increasing public debt can reduce the deficit under certain conditions, in others it can exacerbate fiscal problems, and the effects of economic crises and the pandemic show the need for robust fiscal measures to counter the negative impact on the public budget.

Furthermore, the transition from one regime to another in both specifications is made on the basis of quite clearly outlined logistical functions, the thresholds being quite close, which indicates an increase in the robustness of the presented results. Additionally, we explored alternative transition variables such as the structure of taxation (proxied by the share of indirect taxes in total revenues) and economic inequality (measured by the GINI index). Despite their theoretical relevance, the linearity and homogeneity tests required for PSTR model identification indicated that these variables do not induce significant threshold effects, as the null hypothesis of linearity could not be rejected. While alternative nonlinear modeling approaches, such as Markov Switching models, could provide additional perspectives on regime-dependent fiscal behavior, these techniques are not explored in the current analysis. Their application, particularly in a panel data set, will be considered in future research as a complementary strategy to validate and extend the findings presented here. Overall, the robustness checks confirm the empirical validity of our main results and support the use of the shadow economy as a meaningful threshold variable in explaining fiscal dynamics in a nonlinear framework.

In conclusion, the results of the PSTR model suggest that the relationship between the budget deficit and the level of public debt is complex and varies depending on the economic regime. In Regime 1, the increase in debt seems to have a negative effect on the budget deficit, which may indicate an initial reaction of fiscal consolidation; the authorities do not feel the pressure to adjust fiscal policy immediately. But as it transitions to Regime 2, the relationship becomes positive, suggesting that at some point, rising debt begins to worsen the deficit. This change reflects the possible reaching of a critical debt threshold, at which point markets and authorities perceive an increased risk of default, and fiscal adjustment measures become more aggressive, according to the “fiscal fatigue” hypothesis discussed in the literature.

From a public policy perspective, these results point to the need for careful monitoring of the level of public debt and effective fiscal consolidation mechanisms before debt reaches critical thresholds. In the European context, where the sovereign debt crisis has demonstrated the fragility of economies at high debt levels, the authorities should implement early fiscal adjustment measures to avoid the negative effects of Regime 2, i.e., when the collection to the state budget suffers. Greater attention should also be paid to black swan events, such as economic or pandemic crises, which can amplify fiscal imbalances and impose the need for effective countercyclical fiscal policies. One recommendation would be to introduce strict fiscal rules that include clear thresholds for public debt, combined with measures to stimulate economic growth and make the banking sector more efficient, to ensure the long-term sustainability of public finances.

5. Discussion

The current global fiscal landscape is characterized by persistently high budget deficits, a legacy of successive and overlapping crises—first the COVID-19 pandemic, and more recently, the geopolitical and economic disruptions triggered by the war in Ukraine. These events have put extraordinary pressure on public finances, forcing governments to engage in large-scale spending to stabilize health systems, support households and firms, and manage energy insecurity. The results of our model provide timely insights into how public debt dynamics interact with fiscal balances under these conditions. The transition between the two regimes identified in the model suggests that beyond a certain structural fragility—here proxied by the size of the informal economy—the accumulation of public debt no longer serves as a stabilizing tool but begins to amplify budget deficits. This is especially concerning given the growing number of countries operating close to or beyond such thresholds.

Against this background, our findings underscore the urgent need for a recalibration of fiscal policy—one that avoids abrupt austerity measures, which could undermine investment and growth, but still ensures a credible path toward medium-term consolidation. The nonlinear relationship identified between debt and the deficit implies that early fiscal corrections can be more effective and less painful if implemented before debt levels trigger adverse market reactions or institutional fatigue. In regimes characterized by high informality, however, standard fiscal tools may be less effective, requiring complementary efforts to broaden the tax base, improve compliance, and formalize segments of the economy. Simply put, spending adjustments must be paired with institutional strengthening to restore fiscal space without eroding public investment or confidence.

Moreover, the fact that the effects of economic crises—such as the pandemic—are significantly more damaging in high-informality regimes should serve as a warning to fiscal authorities. Large informal sectors not only reduce the capacity to collect taxes during normal times but also drastically weaken the ability to cushion external shocks. This calls for a more targeted fiscal strategy, with differentiated approaches based on structural characteristics rather than one-size-fits-all deficit targets. Policymakers should view informal economy reform not merely as a development goal, but as a fiscal resilience imperative. The results of the model thus offer not only an empirical diagnosis of current fiscal fragilities but also a strong argument in favor of gradual, context-sensitive consolidation strategies anchored in structural transformation.

6. Conclusions

The results of the Panel Smooth Transition Regression (PSTR) model indicate that the relationship between the budget deficit and public debt is non-linear and influenced by the informal economy. The PSTR model, which uses the informal economy as a transition variable, reveals a different behavior of debt depending on the economic regime (determined by the level of the informal economy).

In regime 1 (at a low level of the informal economy), the impact of debt on the deficit is negative and significant (−0.0219), but in regime 2 (when the informal economy exceeds the transition threshold), this impact becomes positive and significant (0.0867). This change in sign reflects a non-linear relationship and suggests that, in an economic context with a larger informal economy, debt may have a different effect on the budget deficit, possibly due to factors such as reduced fiscal efficiency or loss of government revenue.

Thus, the PSTR model provides a more nuanced understanding of how debt can affect the budget deficit under different economic conditions, suggesting that the effects can vary significantly depending on the level of the informal economy.

The results of the PSTR model suggest that the relationship between the budget deficit and the level of public debt is complex and varies depending on the economic regime. In Regime 1, the increase in debt seems to have a negative effect on the budget deficit, which may indicate an initial reaction of fiscal consolidation, similar to the phase described in the literature, where at low levels of the informal economy (i.e., efficient collection), the authorities do not feel the pressure to adjust fiscal policy immediately. But as it transitions to Regime 2, the relationship becomes positive, suggesting that at some point, rising debt begins to worsen the deficit. Therefore, fiscal sustainability can be affected by the level of the informal economy.

This change reflects the possible reaching of a critical debt threshold, at which point markets and authorities perceive an increased risk of default, and fiscal adjustment measures become more aggressive, according to the “fiscal fatigue” hypothesis discussed in the literature.

From a public policy perspective, these results point to the need for careful monitoring of the level of public debt and effective fiscal consolidation mechanisms before debt reaches critical thresholds. In the European context, where the sovereign debt crisis has demonstrated the fragility of economies at high debt levels, the authorities should implement early fiscal adjustment measures to avoid the negative effects of Regime 2, i.e., when the collection to the state budget suffers.