Shadows of Resilience: Exploring the Impact of the Shadow Economy on Economic Stability ^†

Abstract

This study analyzes the shadow economy within the European Union and its influence on the economic resilience of member countries. Data spanning almost two decades and covering a broad spectrum provide a unique opportunity to examine the impact of the shadow economy on economic stability across various economic cycles. Regularization techniques such as Lasso and Automatic Relevance Determination (ARD) combat possible collinearity and overfitting arising from the inclusion of irrelevant and redundant variables. The shadow economy interacts with key indicators of economic resilience, such as GDP, national debt, and population, across different phases of economic stability and turbulence. The preliminary findings suggest a complex and varied interaction between the shadow economy and economic resilience. This study provides a valuable foundation for policies aimed at stability and sustainable economic growth.

1. Introduction

As nations grapple with economic crises and strive for sustainable growth, the double-edged potential of the shadow economy to bolster and destabilize the economy demands urgent investigation. Within the European Union, where economic policies and interdependencies shape member states’ resilience, understanding this shadow economy dynamic becomes even more crucial. The shadow economy can significantly affect tax revenue and resource allocation, economic policymaking, and social equity.

Current research, however, provides limited insight into the shadow economy’s impact on resilience during periods of crisis compared to periods of relative stability. This lack of a crisis-focused understanding hinders our ability to anticipate and effectively respond to the unique economic challenges posed by short-term shocks and extended periods of instability.

This study investigates the connection between the size of the shadow economy and key economic resilience indicators within the European Union. Specifically, we focus on the growth rate of the gross domestic product, unemployment, inflation, and the ratio of debt to GDP. We hypothesize that a larger shadow economy will be linked to a lower increase in the unemployment rate during financial crises compared to periods of relative stability. This resilience may result from the shadow economy’s capacity to supply informal employment opportunities and its greater adaptability during economic shocks.

By analyzing a dataset spanning the years from 2003 to 2021 across diverse EU member states, this study offers a nuanced and timely perspective on the complex interaction between the shadow economy and economic resilience. The balance of this paper unfolds as follows. First, we review the literature on the shadow economy, economic resilience, and their connections during crises. We then describe our dataset, variables, and econometric methodologies. Subsequently, we present the results of our analysis, followed by a discussion of those findings. Finally, we summarize the key takeaways, acknowledge the limitations of this study, and contemplate the prospects for future research.

2. Literature Review

While often portrayed as a destabilizing force, the potential role of the shadow economy in fostering resilience during times of crisis remains a compelling and complex question [1]. Some studies suggest that the shadow economy’s informal structures may provide alternative employment sources, lessening the immediate economic shock of a crisis [2]. Others argue that the lack of regulation and diminished tax collection associated with the shadow economy can undermine long-term stability and hinder a robust recovery [3].

Research specifically addressing the shadow economy in the European Union is comparatively limited. Certain studies have examined the shadow economy in individual EU states, but fewer explicitly link this to resilience indicators like unemployment [4]. There appears to be a knowledge gap regarding the impact of the shadow economy on Europe’s diverse economies.

The shadow economy’s influence on resilience appears to be highly context-specific. EU member states vary greatly in terms of the size of their shadow economies and their institutional backdrops [5]. These variations suggest that the shadow economy’s influence on resilience may be affected by factors such as labor market regulations and the effectiveness of government institutions. Studies suggest that the shadow economy may serve as a symptom of underlying economic stresses and a means for individuals to cope with labor market rigidities, particularly during crises [6].

Furthermore, the shadow economy’s impact likely interacts with country-specific factors such as the overall level of competitiveness [7], the strength of governance [8], the efficiency of social safety nets [9], and the degree of financial development [10]. These interactions underscore the need to control for such factors in studies examining the shadow economy’s relationship with resilience.

The debate about the shadow economy’s “buffering” effect remains unresolved. While it might offer temporary employment during a crisis, its undermining effect on tax revenue, social protections, and economic formalization could hinder sustainable recovery [11]. Whether short-term resilience outweighs longer-term risks raises a complex question, particularly in the EU, where economic systems and policies are intertwined.

3. Methodology

3.1. Data

This study’s panel dataset covers Austria, Belgium, Bulgaria, Croatia, Czechia, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, the Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, and Sweden from 2003 to 2021. There are N = 25 countries × 19 years = 475 total observations. The primary data sources include the following:

• Eurostat (for GDP, government debt, population, consumption, government expenditure, VAT, taxes on production, household social contributions, unit labor costs, financial transactions, deposits)
• The International Monetary Fund (IMF) (for foreign direct investment, tax revenues, inflation, general government expenditure)
• The International Labour Organization (ILO) (for the unemployment rate)
• [12] for the shadow economy measure

3.2. Key Variables

Table 1. Dependent variables.

Variable Name	Definition	Unit of Measurement	Source
GDP Growth	Annual percentage change in gross domestic product	Percentage	Calculated
Unemployment Rate	Share of the labor force without work, available, seeking	Percentage	ILO
Inflation	Annual percentage change in the consumer price index	Percentage	IMF
Debt-to-GDP Ratio	Government debt as a percentage of gross domestic product	Percentage	Calculated

lists the dependent variables, their definitions, and sources:

A complete list of variables, sources, and descriptive analysis appears in Appendix A.

3.3. Econometric Models

This study will apply the following econometric approaches in examining the relationship between the shadow economy and economic resilience, with a particular emphasis on the financial crisis of 2007 to 2011.

• Ordinary Least Squares (OLS)

To address omitted variable bias, we estimate all four OLS models. The basic model specification is as follows:

$$Resilience Indicato{r}_{it}={\beta }_0+{\beta }_1\ast Shadow Econom{y}_{it}+{\beta }_2\ast Control{s}_{it}+{\epsilon }_{it}$$

where $i$ denotes a country, and t denotes time.

To probe more deeply into the connections between the shadow economy and economic resilience, we employed two advanced econometric techniques: Lasso regression and Automatic Relevance Determination (ARD). These methods address specific challenges, such as multicollinearity and the high dimensionality of the predictors.

• Lasso Regression

Lasso (least absolute shrinkage and selection operator) regression identifies relevant variables and mitigates overfitting [13]. This technique enhances the model’s interpretability by performing variable selection and regularization simultaneously. The Lasso model imposes an ℓ₁ penalty on the regression coefficients, shrinking some of them to zero. This property is particularly useful in reducing the complexity of the model where a large number of predictors may exist but only a few are significant. We implemented Lasso regression using a cross-validated LassoCV model from the sklearn.linear_model module, which optimizes the regularization strength (λ) based on cross-validation [14].

• Automatic Relevance Determination (ARD) Regression

As with Lasso regression, ARD regression refines our understanding of variable relevance. ARD regression, a Bayesian extension of linear models, introduces sparsity by formulating the regression problem with Gaussian priors on the regression coefficients [15]. This method not only estimates the weights of the predictors but also infers their relevance through the posterior distribution of the weights. We used the ARDRegression class from sklearn.linear_model for Python 3.7.

• Model Evaluation

Both models were assessed based on their r² values and the interpretability of their coefficients. We performed the analysis using a standard train/test 80/20 split to validate the models’ predictive performance and ensure that they generalized well to new data.

Our dataset underwent rigorous preprocessing. This involved the imputation of missing values using mean substitution, ensuring no loss of critical information. Additionally, the data were standardized to bring all variables to a comparable scale, thus eliminating any potential bias arising from differing variable units. To prevent leakage between the training and test data, which is a lamentable and preventable source of contaminating bias, we conducted Gaussian scaling based entirely on the statistical properties of the training data [16] (pp. 138–140)

3.4. Analysis

Τhe analysis begins with a correlation matrix connecting the shadow economy size to various economic indicators (Figure 1):

The correlation analysis provides the following insights:

• Shadow Economy and GDP Growth: The size of the shadow economy and GDP growth are positively correlated ($r=0.229$). As the shadow economy increases, GDP growth also tends to be higher.
• Shadow Economy and Unemployment: The shadow economy and unemployment are also positively correlated ($r=0.290$). A larger shadow economy could be associated with higher unemployment.
• Shadow Economy and Inflation: The shadow economy shows a moderate positive correlation with inflation ($r=0.344$), suggesting that an increase in the shadow economy may be connected to higher inflation.
• Shadow Economy and Debt-to-GDP Ratio: A negative correlation ($r=-0.162$) implies that a larger shadow economy might be connected to a lower debt-to-GDP ratio.

These correlations provide an initial view of the relationships but do not account for other variables that might influence these outcomes.

3.5. Regression Results

We employed robust econometric methodologies to derive insights into the connections linking the shadow economy to pivotal economic variables, including GDP growth, unemployment, the debt-to-GDP ratio, and inflation. Because we conducted regression on standardized data, the resulting beta coefficients are dimensionless units that must be understood in terms of z-scores and Gaussian distance, rather than percentage points or other (human-friendly) units of measurement. Using robust standard errors to address issues such as autocorrelation and heteroscedasticity, we derived the following conclusions:

• GDP Growth: The results indicate a positive relationship between the shadow economy and GDP growth. A 1z increase in the size of the shadow economy is associated with a corresponding 0.117z increase in GDP growth, controlling for factors like unemployment, inflation, and debt levels. In some contexts, the shadow economy may contribute positively to economic output.
• Unemployment: A larger shadow economy correlates with higher unemployment rates. Specifically, a 1z increase in the shadow economy size is linked to a 0.249z increase in unemployment. While the shadow economy might supplement economic output, it could also be associated with less stable job markets.
• Debt-to-GDP Ratio: The shadow economy is inversely related to the debt-to-GDP ratio. An increase in the size of the shadow economy by 1z is associated with a 1.2255% decrease in the debt-to-GDP ratio. The shadow economy might alleviate some of the fiscal pressures on official economies. It remains unclear whether this effect arises from reduced reliance on government benefits, an increase in tax revenue, or a combination of these fiscal effects.
• Inflation: The shadow economy has a mildly positive impact on inflation. A 1z increase in the shadow economy leads to a 0.0796z increase in inflation. The shadow economy could contribute to inflationary pressures, possibly through increased money circulation outside formal channels.

These results yield important perspectives on the dual role of the shadow economy in economic resilience. They reveal potential benefits, as well as potential costs. The shadow economy can spur economic activity and reduce fiscal pressures. But it may also contribute to higher unemployment and inflation.

• Results Table:

Table 2. Summary table.

Indicator	Coefficient of Shadow Economy	p-Value	Implications
GDP Growth	0.117	<0.01	Positive impact on economic output
Unemployment	0.249	<0.001	Potential destabilization of job markets
Debt-to-GDP Ratio	−1.2255	<0.001	Reduction in fiscal pressures
Inflation	0.0796	<0.001	Contribution to inflationary pressures

summarizes the regression results:

Each model included controls for other economic variables to isolate the effect of the shadow economy on these variables of interest. Below are the equations for each regression model, formatted to include the coefficients and variables as derived from our analyses. These equations clearly outline how each dependent variable is modeled in relation to the shadow economy and the other control variables.

• Regression Model Equations:

1.

GDP Growth Model:

$$\begin{array}{cc}\hfill GDP Growt{h}_i& =0.117\times Shadow Econom{y}_i-0.224\times Unemploymen{t}_i+0.980\times Inflatio{n}_i\hfill \\ \hfill & -0.0245\times Debt\_to\_GDP\_Rati{o}_i+0.0327\times FD{I}_i+0.0014\times Financial Transaction{s}_i\hfill \\ \hfill & +{ϵ}_i\hfill \end{array}$$

2.

Unemployment Model:

$$\begin{array}{cc}\hfill Unemploymen{t}_i& =0.249\times Shadow Econom{y}_i-0.1159\times GDP Growt{h}_i-0.2013\times Inflatio{n}_i\hfill \\ \hfill & +0.0469\times Debt\_t{o}_{GDP}Rati{o}_i-0.0002\times FD{I}_i+0.0011\times Financial Transaction{s}_i+{ϵ}_i\hfill \end{array}$$

3.

Debt-to-GDP Ratio Model:

$$\begin{array}{cc}\hfill Debt\_to\_GDP\_Rati{o}_i& =-1.2255\times Shadow Econom{y}_i-0.9742\times GDP Growt{h}_i+3.6063\times Unemploymen{t}_i\hfill \\ \hfill & -2.1842\times Inflatio{n}_i+0.0081\times FD{I}_i-0.0339\times Financial Transaction{s}_i+{ϵ}_i\hfill \end{array}$$

4.

Inflation Model:

$$\begin{array}{cc}\hfill Inflatio{n}_i& =0.0796\times Shadow Econom{y}_i+0.1271\times GDP Growt{h}_i-0.0504\times Unemploymen{t}_i\hfill \\ \hfill & -0.0071\times Debt\_to\_GDP\_Rati{o}_i+0.0016\times FD{I}_i-0.0002\times Financial Transaction{s}_i\hfill \\ \hfill & +{ϵ}_i\hfill \end{array}$$

• Lasso and ARD Regression Analysis

Table 3. Results for Lasso and ARD models.

Variable	Lasso GDP Growth	Lasso Unemployment	ARD GDP Growth	ARD Unemployment
Inflation	1.9159	−0.9190	1.9447	−0.9210
comp	0.5077	−1.6485	0.4637	−1.6312
consumption_expenditure_perc	−0.3366	0.8397	−0.0009	0.8221
debt_to_gdp	−0.5626	1.6539	−0.4157	1.6638
deposits	0.0111	0.1950	0.0005	0.1763
fdi	0.4369	−0.0368	0.3640	−0.0005
financial_transactions	−0.0981	0.0727	−0.0002	0.0023
gov_expenditure_perc	−2.8357	0.5300	−3.2432	0.5087
household_social_contr_perc	0.8048	−1.6132	0.8048	−1.6176
sdg	0.0000	−0.4304	0.0002	−0.4304
shadow	−0.0204	0.0000	−0.0013	−0.0010
tax_revenue	0.7532	−1.1878	0.7120	−1.2140
taxes_prod_imports_perc	1.5645	−0.4699	1.6691	−0.4151
unit_labour_cost	−0.6567	−0.6250	−0.6019	−0.6267

reports the results of the Lasso and ARD regressions for the GDP growth and inflation models:

The Lasso regression model revealed several variables that influence GDP growth and unemployment rates within the European Union. For GDP growth, the model identified inflation, foreign direct investment (FDI), and household social contributions as positive influencers. The government expenditure percentage reports a negative coefficient. While business investments, especially from abroad, may affect economic output, greater overall government spending may be associated with slower growth.

In terms of unemployment, the Lasso model assigned strongly positive coefficients to debt-to-GDP ratio, consumption expenditure percentage, and government expenditures. These results imply that higher debt levels and higher consumer and government spending are linked with higher unemployment. Conversely, competitiveness, household social contributions, and tax revenue were associated with lower unemployment rates. Economic efficiency and higher tax collections may strengthen labor markets.

Automatic Relevance Determination (ARD) Regression

ARD regression provided further insight into the predictive importance of the variables. The model supported the findings from the Lasso analysis but offered additional nuance. For example, competitiveness and tax revenue showed positive impacts on GDP growth, suggesting that a competitive economic environment and efficient tax collection are crucial to enhancing economic output. On the other hand, the debt-to-GDP ratio was a negative factor, reaffirming the complex role played by fiscal policy in economic growth.

4. Discussion

This paper highlights the complex and multifaceted nature of the shadow economy in the European Union. By examining the impact of the shadow economy on key economic indicators—GDP growth, unemployment, debt-to-GDP ratio, and inflation—we provide nuanced insights into its potential benefits and drawbacks.

• Economic Growth and Stability: The positive correlation between the shadow economy and GDP growth suggests that informal economic activities might enhance output, particularly in times of crisis or when formal markets otherwise underperform. The shadow economy may offer alternative avenues for economic activities and transactions that might not otherwise occur, possibly cushioning the impact of economic downturns. However, the sustainability of such growth is questionable, as it may bypass regulatory frameworks and taxation, potentially leading to long-term challenges in governance and economic management.
• Employment and Labor Markets: The association of the shadow economy with higher unemployment supports mixed interpretations. While informal sectors can provide immediate, albeit unstable, employment opportunities, their growth could undermine formal employment sectors. The diversion of resources and labor from the formal to the informal sector might exacerbate job insecurity and degrade employment conditions.
• Fiscal Implications: The relationship between the shadow economy and the debt-to-GDP ratio underscores the potential of the shadow economy to alleviate immediate fiscal pressures. However, this might come at the cost of reduced tax revenues and the diminished long-term ability of governments to invest in public goods and services.
• Inflationary Pressures: The link between the shadow economy and inflation highlights the potential of informal economic activities to contribute to inflationary pressures. This might occur through increased money circulation that is not matched by formal economic output or productivity, leading to price increases and potential economic overheating.

The Lasso and ARD analyses both illuminate the multifaceted impact of the shadow economy, alongside other drivers of GDP growth and unemployment. While the shadow economy might provide short-term relief during crises, it erodes labor markets in the long term, perhaps because it undermines formal economic structures.

Moreover, the positive association between government fiscal measures (such as tax revenue and expenditures) and economic indicators highlights the critical role of effective fiscal management. The influence of competitiveness on both GDP growth and reducing unemployment further emphasizes the importance of policies aimed at improving economic efficiency and innovation.

These insights are crucial as policymakers and economic strategists try to integrate shadow economies into formal economic frameworks while fostering economic resilience and stability. The nuanced understanding provided by this study’s econometric models offers a valuable foundation for future research and policymaking.

• Policy Implications:

Our findings suggest that policymakers should adopt a balanced approach toward the shadow economy. While the immediate benefits in terms of economic output and fiscal relief are evident, the long-term implications for economic stability, employment quality, and inflation are concerning. Policies aimed at integrating informal activities into the formal economy could help mitigate these issues. This could include simplifying business registration processes, reducing tax burdens for small businesses, and strengthening labor rights within informal sectors. Accounting for the European Union’s diverse economic landscape demands more nuance than a one-size-fits-all policy can provide. Tailored strategies should consider the economic, cultural, and regulatory diversity of Europe’s member states.

• Future Research:

Further research could more extensively elaborate the causal relationships between the shadow economy and other facets of the economy. Longitudinal studies could help clarify the directionality of these relationships and their potential lag effects. Additionally, qualitative studies on the nature of employment within the shadow economy could provide deeper insights into labor markets. Economic and social diversity within the European Union invites the application of tools such as fixed-effects regression and clustering analysis. Finally, the gathering and preprocessing of the data for this study invite the application of supervised machine learning methods, especially decision tree ensembles, gradient boosting machines, and support vector machines.