Tax Optimization in the European Union: A Laffer Curve Perspective

Abstract

This study explores the applicability of the Laffer Curve in the context of the European Union (EU) by analyzing the relationship between taxation and fiscal revenue across personal income tax (PIT), corporate income tax (CIT), and value-added tax (VAT). Utilizing a comprehensive panel data set spanning 1995 to 2022 across all 27 EU member states, the research also integrates the Bird Index to assess fiscal effort and employs advanced econometric techniques, including the Hausman Test and log-quadratic regression models, to capture the non-linear dynamics of the Laffer Curve. The findings reveal that excessively high tax rates, particularly in some larger member states, may lead to revenue losses due to reduced economic activity and tax evasion, highlighting the existence of optimal tax rates that maximize revenue while sustaining economic growth. By estimating threshold tax rates and incorporating the Bird Index, the study provides a nuanced perspective on tax efficiency and fiscal sustainability, offering evidence-based policy recommendations for optimizing tax systems in the European Union to balance revenue generation with economic competitiveness.

1. Introduction

The relationship between taxation and fiscal revenue is a fundamental issue in economic policy worldwide. Among the various theoretical frameworks explaining this relationship, the Laffer Curve (Laffer, 2004) provides a compelling perspective, suggesting that tax revenue does not increase indefinitely with higher tax rates. Instead, there exists an optimal taxation level, beyond which additional increases lead to diminishing returns due to tax evasion, reduced economic activity, and disincentives to production and investment.

This dynamic is particularly relevant in the European Union (EU), where policymakers must balance the need for sufficient revenue to fund public services and social programs while avoiding excessive taxation that could hinder economic growth. The Laffer Curve underscores the importance of well-calibrated tax policies that promote fiscal sustainability while maintaining economic competitiveness.

This study examines the applicability of the Laffer Curve in the European Union, focusing on three major tax categories: personal income tax (PIT), corporate income tax (CIT), and value-added tax (VAT). These taxes are pivotal to government revenue and economic performance. Additionally, the study incorporates the Bird Index to assess fiscal effort, providing insights into how tax policies influence a country’s ability to maximize revenue. By integrating the Bird Index, the study offers a comprehensive perspective on taxation, economic growth, and fiscal efficiency, enabling an in-depth exploration of tax revenue patterns across EU countries.

A panel data analysis covering the 27 EU member states from 1995 to 2022 forms the empirical foundation of this study. The dataset includes tax revenue data from PIT, CIT, and VAT, alongside key macroeconomic indicators such as Gross Domestic Product (GDP) and the GDP deflator. The methodology applies regression models, particularly log-quadratic regression, to capture the non-linear relationship between tax rates and revenue, illustrating the Laffer Curve effect. The Bird Index is calculated for each country and for the EU as a whole, facilitating meaningful cross-country comparisons. A key econometric tool, the Hausman Test, determines whether a fixed-effects or random-effects model provides the best panel data estimation, ensuring robust analytical outcomes by controlling for unobservable country-specific factors influencing fiscal revenue.

However, estimating the empirical relationship between tax rates and revenue for the EU presents significant challenges. The primary policy problem is the ongoing search for fiscal efficiency; member states need to know if tax hikes will yield more revenue or, per the Laffer Curve, backfire by shrinking the tax base. This estimation is complicated by two key econometric problems: country heterogeneity and potential endogeneity. First, the 27 EU member states have diverse economic structures, labor market policies, and levels of tax compliance, which means a “one-size-fits-all” optimal tax rate is unlikely (heterogeneity). Second, tax rates and revenues may be mutually determined; poor revenue collection might itself trigger tax rate changes, creating a reverse-causality feedback loop (endogeneity). This study seeks to navigate these challenges by using panel data techniques that can account for country-specific fixed effects (addressing heterogeneity) and by building on established model specifications in the literature.

This research makes several contributions to public finance and taxation economics:

• Comprehensive Empirical Analysis: This study provides a comprehensive empirical evaluation of the Laffer Curve within the EU economies, utilizing 28 years of panel data across all EU member states. This comparative, multi-country approach offers broader insights than prior research focused on individual nations.
• Integration of the Bird Index: The Bird Index enhances traditional analyses of the Laffer Curve by allowing a more nuanced assessment of the trade-off between tax burden and revenue maximization. This contributes a new perspective on tax efficiency in the EU.
• Advanced Econometric Methodology: The study employs panel data econometrics, including the Hausman Test, to ensure statistical robustness. The use of log-quadratic regression models effectively captures the Laffer Curve’s non-linearity, representing a novel methodological innovation.
• Policy Implications for the EU Member States: The findings offer evidence-based recommendations for optimizing tax policies. Results suggest that larger economies may experience revenue losses due to excessively high tax rates, supporting strategic tax rate adjustments to maximize public revenue while sustaining economic growth.
• Identification of Revenue-Maximizing Tax Rates: By estimating threshold tax rates where revenue collection begins to decline, this study contributes to the ongoing debate on optimal taxation. These insights can help EU policymakers design tax systems that balance fiscal sustainability with economic efficiency.
• Insights into Fiscal Effort and Tax Efficiency: The results indicate that some high-taxation countries may not yet have maximized their revenue potential, while others may be overburdening taxpayers without significant revenue gains. The Bird Index analysis highlights the diverse tax collection capacities across EU nations, emphasizing the need for country-specific fiscal strategies.

The remainder of this paper is structured as follows. Section 2 presents a literature review discussing prior research on the Laffer Curve and tax policy in the EU. Section 3 details the dataset, variables, time period, and econometric methodology. Section 4 presents empirical findings, analyzing their implications for fiscal policy and revenue optimization. Finally, Section 5 provides the conclusions, summarizing key insights and their policy relevance.

2. Fiscal Policy and Tax Efficiency Review

The literature on taxation, fiscal policy, and the Laffer Curve provides a comprehensive foundation for understanding the intricate relationship between tax rates and government revenue. This section reviews key theoretical and empirical studies that contribute to the ongoing debate on optimal taxation, tax burdens, and fiscal effort within the European Union (EU) and its member states.

The review begins by examining the historical and institutional evolution of the European Union, highlighting its economic and fiscal integration efforts. The discussion then shifts to the structure of the EU tax system, emphasizing its fundamental principles, objectives, and major sources of tax revenue. Next, the analysis explores the concepts of tax burden and tax evasion, investigating how variations in tax policies influence taxpayer behavior and compliance. The section on fiscal effort delves into measures that assess a country’s capacity to generate tax revenue relative to its economic potential. Finally, the theoretical and empirical foundations of the Laffer Curve are explored, with a focus on its implications for tax policy and economic efficiency.

By synthesizing these diverse strands of literature, this review provides the necessary context for evaluating the relationship between taxation and revenue generation in the EU, forming the basis for the empirical analysis presented in subsequent sections.

2.1. European Union Fiscal Evolution

In the aftermath of the devastating conflicts that culminated in World War II, European political leaders sought to establish a framework for lasting peace and economic cooperation. This initiative led to the creation of what is now the European Union (EU), a project aimed at fostering stability, economic growth, and political unity across the continent.

The first step in this integration process was the formation of the European Coal and Steel Community (ECSC) in 1951, which sought to place key war-related industries under shared management. Building on this foundation, the Treaty of Rome established the European Economic Community (EEC) and the European Atomic Energy Community (EAEC or Euratom) in 1957. The EEC was designed to create a common market, enabling the free movement of goods, services, capital, and people between its member states while eliminating customs barriers. Additionally, its objectives included stimulating economic development, enhancing trade and investment, increasing competitiveness, and promoting political cooperation to reinforce stability, solidarity, and peace across Europe. Essentially, the EEC aimed to achieve deeper economic and political integration between its founding members. The main objective of Euratom is to promote research and development in the field of nuclear energy, ensuring its safe use and avoiding detour to military purposes. It also aims to guarantee a secure supply of nuclear raw materials and establish common safety standards to protect the health of workers and the population.

Initially, the EEC consisted of six countries: Belgium, France, Germany (then the Federal Republic of Germany), Italy, Luxembourg, and the Netherlands. Over the decades, membership expanded significantly. Denmark, Ireland, and the United Kingdom joined in 1973, followed by Greece in 1981, Spain and Portugal in 1986, and Austria, Finland, and Sweden in 1995. The largest enlargement occurred in 2004, with the accession of the Czech Republic, Cyprus, Estonia, Latvia, Lithuania, Hungary, Malta, Poland, Slovenia, and Slovakia. Croatia became the latest member in 2013. However, in 2020, the United Kingdom became the first country to leave the EU.

In 1993, the Maastricht Treaty transformed the EEC into the European Community. The European Union was also created, uniting the three communities that existed at the time. The ECSC was abolished in 2002. A major milestone in European integration was the introduction of the euro (€) on 1 January 1999. Initially adopted by 11 countries for commercial and financial transactions, the euro later became a physical currency in 2002, marking the formal establishment of the Eurozone. The founding members of the Eurozone were Germany, Austria, Belgium, Spain, Finland, France, Ireland, Italy, Luxembourg, the Netherlands, and Portugal. Over time, eight additional countries joined, bringing the total number of Eurozone members to 19.

Table 1. Eurozone countries and year of entry.

Country	Year of Entry
Austria	1999
Belgium	1999
Finland	1999
France	1999
Germany	1999
Ireland	1999
Italy	1999
Luxembourg	1999
Netherlands	1999
Portugal	1999
Spain	1999
Greece	2001
Slovenia	2007
Cyprus	2008
Malta	2008
Slovakia	2009
Estonia	2011
Latvia	2014
Lithuania	2015

provides an overview of the Eurozone countries and the year in which they adopted the euro.

The Eurozone is a monetary union in which all members share a common currency and monetary policy, overseen by the European Central Bank (ECB). The ECB’s primary objective is to maintain price stability, promote economic growth, and coordinate financial policies across member states. By facilitating seamless trade and investment within the European bloc, the euro has become one of the most widely used currencies in the world, solidifying the Eurozone as a key player in the global economy.

Economic influence within the Eurozone is highly concentrated in a few key countries. According to data from the Eurostat (2021), the five largest economies in the EU, Germany (25.1%), France (17.2%), Italy (12.3%), Spain (8.4%), and the Netherlands (6%), collectively accounted for 69% of the EU’s total GDP. These nations wield substantial influence over economic and fiscal policy decisions within the monetary union.

Despite its success, the Eurozone continues to face challenges, including economic disparities between member states, financial crises, debt sustainability concerns, and monetary policy coordination. Policymakers must navigate these issues while striving to enhance integration, stabilize the currency, and ensure long-term economic growth (Mendes et al., 2022). The role of tax harmonization, fiscal policy efficiency, and the Laffer Curve in shaping European Union tax strategies remains a critical area of research, offering valuable insights for optimizing revenue collection without hindering economic development.

2.2. EU Tax System Structure

The European Union’s tax system is guided by a framework of principles that shape the formulation and implementation of fiscal policies across member states. These principles aim to ensure debt sustainability, promote equity in tax burden distribution, and maintain flexibility to respond to economic fluctuations. Equity is particularly significant, as it seeks to fairly distribute tax obligations between citizens by considering income and wealth disparities. At the same time, efficiency is crucial for minimizing economic distortions arising from taxation, while clarity and simplicity play a vital role in facilitating taxpayer compliance and reducing administrative complexity (Blanchard et al., 2021).

Beyond these fundamental principles, the EU tax system pursues several overarching objectives. Among them, maintaining public debt at sustainable levels, fostering economic stability, and designing fiscal policies capable of mitigating economic shocks remain key priorities. The tax system serves a dual role, not only as a mechanism to generate revenue for government activities and public services but also as an instrument for addressing social inequalities through progressive taxation. By influencing aggregate demand and resource allocation, taxation plays a pivotal role in stabilizing and stimulating macroeconomic growth across the region. A deeper understanding of these principles and objectives is essential to assessing how fiscal policies shape economic outcomes in Europe Union. This is particularly relevant given the ongoing discussions on the necessity for a more comprehensive and adaptive debt sustainability analysis, ensuring that taxation and fiscal strategies remain responsive to economic shifts and financial challenges.

EU member states derive their tax revenue from several key sources, including Personal Income Tax, Corporate Income Tax, Value-Added Tax, Social Security Contributions, Capital Gains Tax, and Inheritance and Gift Tax. These taxes collectively finance government expenditures (Afonso et al., 2021), sustain welfare programs, and support long-term economic stability. Despite the common taxation framework within the EU, some countries have introduced unique national taxes to address specific economic and social needs. France, for instance, implements the “Contribution pour le Remboursement de la Dette Sociale” (CRDS), a social contribution levied on income from salaries, pensions, and investments, which is specifically designated to fund social security and other social programs. In Germany, the “Solidaritätszuschlag” (Solidarity Tax) is applied as an additional levy on taxable income, originally introduced to finance the costs associated with German reunification and later repurposed to fund various economic development projects within the country.

These country-specific tax policies illustrate the diversity of fiscal approaches across EU nations, reflecting differences in historical contexts, economic priorities, and social policy objectives. While tax harmonization remains a subject of debate, the ability of individual member states to introduce tailored taxation mechanisms highlights the ongoing balance between EU-wide fiscal coordination and national autonomy in tax policy design.

2.3. Tax Burden and Evasion

The tax burden represents the total amount of taxes and contributions collected by a government from individuals and businesses within a given period. It serves as a key indicator of a government’s fiscal policy, measuring the overall tax load imposed on a country’s economy or a specific segment of society. This burden can be evaluated in both absolute and relative terms, providing valuable insights into how taxation influences economic activity and public finance sustainability.

In the European tax systems, taxation is classified into two primary categories: direct taxes and indirect taxes. Direct taxes are imposed directly on individuals or corporations and include personal income tax, corporate income tax, and property tax. These taxes are typically progressive, meaning tax rates increase as income or wealth rises, ensuring that individuals with higher earnings contribute proportionally more. Indirect taxes, on the other hand, are levied on the production or sale of goods and services, including value-added tax, excise duties, and import taxes. Unlike direct taxes, indirect taxes are generally regressive, as they tend to disproportionately affect lower-income individuals who allocate a larger share of their earnings to taxable goods and services (van Brederode, 2019).

The distinction between direct and indirect taxes plays a crucial role in shaping fiscal policy across European Union countries. Direct taxation is often associated with wealth redistribution and social equity, while indirect taxation is primarily used to generate government revenue and influence consumer behavior. A thorough understanding of these two tax structures is essential for analyzing the complexities of European fiscal policies and their broader economic implications. By assessing the dynamics of both tax types, a deeper perspective can be gained on taxation patterns, trends, and their effects on individuals, businesses, and economic stability (Seelkopf & Lierse, 2020).

Beyond these fundamental tax classifications, governments may also adjust the tax burden to achieve strategic objectives, such as protecting domestic industries or stimulating specific sectors like agriculture (Carvalho et al., 2024). Comparative studies across different economies illustrate how various factors influence taxation structures. Research by Stotsky and WoldeMariam (1997) and Eltony (2002), conducted in African economies, revealed that variables such as export size, per capita income, and the prominence of the agricultural and mining sectors significantly impact a country’s tax burden and fiscal capacity.

The tax burden is also closely linked to GDP growth and macroeconomic performance. In a study on China’s fiscal system from 1984 to 2004, Kong and van der Hoek (2008) identified GDP growth as the most critical determinant of tax revenue trends. However, external influences, such as shifts in economic structures, fiscal policies, and the efficiency of financial management, can lead to scenarios where the growth in the tax burden outpaces GDP growth, affecting overall economic stability (Celikay, 2020; Coelho et al., 2023).

A key concern associated with a high tax burden is its impact on taxpayer behavior. Excessive taxation can discourage compliance among individuals and businesses, leading to increased tax evasion and avoidance (Bernasconi et al., 2014). According to Langot et al. (2022), empirical evidence suggests that reducing tax rates on formal enterprises encourages entrepreneurs to transition from the informal sector to the formal economy, where productivity is higher. This shift enhances economic efficiency and production capacity, demonstrating how tax reductions can incentivize compliance and stimulate economic growth.

The issue of tax evasion remains a pressing challenge for fiscal authorities, with significant consequences for public finance and economic sustainability. In Spain, for instance, tax evasion has had a substantial effect on the country’s fiscal position. The study by Meroño Herranz and Thurk (2023) found that between 1985 and 2015, tax evasion accounted for an average of 27% of total taxes owed, equating to 17% of Spain’s official GDP. Furthermore, tax evasion significantly contributed to the accumulation of public debt, representing an average of 23% of public debt growth during the same period. These findings underscore the critical role of tax evasion as a determinant of fiscal imbalances and economic instability.

The tax burden also influences international competitiveness, affecting a country’s attractiveness to foreign investment and multinational corporations (Rocha et al., 2024). High tax rates can deter businesses from investing, while favorable tax policies can serve as incentives for capital inflows and business expansion. The influence of taxation on foreign direct investment (FDI), firm location decisions, and corporate structuring is well-documented in economic literature (Santos et al., 2024). Research by De Mooij and Ederveen (2003) highlights that tax policies can impact ownership structures, market entry strategies, and the internalization of foreign firms, ultimately shaping the investment climate and economic attractiveness of a given location.

2.4. Fiscal Effort via Bird Index

A critical aspect of fiscal policy analysis is fiscal effort, which refers to a country’s ability to mobilize tax revenues to finance public expenditures, including investments in infrastructure, healthcare, education, and social security (Berry & Fording, 1997). In simple terms, fiscal effort measures the efficiency and intensity with which a government collects taxes and other revenues to meet its obligations and promote the well-being of society.

Bird (1964) defines fiscal effort as the relative importance of the resources contributed by citizens to the state. According to Pessino and Fenochietto (2013), this concept is represented by the ratio between the tax burden and fiscal capacity, providing a useful measure for comparing taxation levels across different economies. However, as noted by Pinho and Pinho (2017), while fiscal effort calculated through these indices allows cross-country and temporal comparisons, it does not directly account for the quality of public goods and services provided by taxation.

To quantify fiscal effort, econometric indices, such as the Frank Index and Bird Index, are widely used. The Frank Index, introduced by Frank (1959), measures fiscal effort as the ratio of total tax revenues to Gross National Product (GNP) per capita, multiplied by 100:

$${\displaystyle E=\frac{\frac{T}{Y}}{Y_p}\times 100,}$$

(1)

where T represents total tax revenues, Y is GNP, and $Y_p$ is GNP per capita. This index was originally designed to determine whether taxation levels in one country exceed those of another by considering per capita taxes and tax revenue as a percentage of income. However, a key limitation of the Frank Index is that it does not account for the “sacrifice” made by taxpayers in generating taxable income, which led Bird to introduce a modification (Bird, 1964).

The Bird Index, proposed by Bird (1964), refines the Frank Index by incorporating disposable income, making it a more robust measure of fiscal effort. This adjustment results in the following formula, where fiscal effort is represented as the ratio of tax burden to GNP minus tax revenues, divided by GNP per capita, and multiplied by 100:

$${\displaystyle E=\frac{\frac{T}{Y-T}}{Y_p}\times 100.}$$

(2)

The Bird Index’s arithmetical inclusion of tax revenue is a deliberate strength, enabling a policy-relevant test of Laffer dynamics by proxying fiscal effort, initially revenue-enhancing but eventually self-defeating beyond optimal thresholds, while fixed effects control for endogeneity.

Bird (1964) further recommends replacing GNP with GDP, particularly given the growing openness of economies to international trade, as GDP better reflects a country’s overall economic activity. Both indices serve as essential tools for international comparisons of fiscal effort, yet the Bird Index provides a more refined assessment by considering disposable income and the economic openness of a country. The ability to compare fiscal effort across nations using these indices allows for a more nuanced analysis of tax burdens, government efficiency, and economic sustainability.

As previously discussed, an ideal EU tax system should adhere to a set of fundamental principles to ensure fiscal sustainability and economic stability. These principles include equity, which demands the fair distribution of the tax burden through both horizontal equity (equal treatment of taxpayers in similar situations) and vertical equity (progressive taxation based on financial capacity). Efficiency dictates that taxation should minimally distort economic decisions while addressing negative externalities. Flexibility emphasizes the need for a stabilizing effect on the economy, allowing fiscal policy to stimulate demand during recessions and curtail excesses during periods of expansion. Transparency ensures that tax rules and fiscal policies are easily understood, facilitating political accountability. Low compliance costs reduce the administrative burden on taxpayers, while financial effectiveness guarantees that tax revenues are sufficient to finance public expenditures and sustain government operations (van Brederode, 2019).

To enhance fiscal effort and create space for balanced tax rates, several strategies can be employed. Tax reforms, tax incentives, deductions, and international tax agreements are among the mechanisms that can improve tax collection efficiency. Additionally, effective tax planning and the fight against tax evasion are essential to ensuring that governments optimize revenue without imposing excessive burdens on taxpayers (Amaglobeli et al., 2020).

A well-structured fiscal policy plays a pivotal role in reducing economic inequality, particularly through progressive tax measures, where higher-income earners contribute a larger share of their income to public finances. According to the study by Doerrenberg and Peichl (2013), which examined 19 countries across different continents, taxpayers are willing to forgo part of their income in exchange for a tax system that ensures fairness and reduces tax evasion. This finding underscores the importance of public trust in taxation systems and the need for governments to design policies that are both effective and equitable.

A well-defined fiscal policy framework is also essential for the formulation of the State Budget (SB), a comprehensive financial plan that reflects government priorities and economic goals. The SB is approved annually and remains valid for one fiscal year, detailing expected revenues and the allocation of resources across public sectors, including healthcare, education, defense, and infrastructure. On the revenue side, the SB specifies sources of government income according to their economic classification and funding origin, while expenditures are categorized by economic, organic, functional, and programmatic classifications.

To regulate the State Budget, Decree-Law No. 151/2015—Budgetary Framework Law (Decreto-Lei, 2015) establishes the principles, norms, and regulations governing the preparation, execution, and auditing of the SB. This legislation defines the core budgetary framework and clarifies the responsibilities of public financial management entities.

The preparation of the State Budget follows several guiding rules to ensure fiscal discipline. The annuality principle requires that the budget is approved and executed on a yearly basis. Unity and universality dictate that the budget should be a single, consolidated document encompassing all revenues and expenditures of public entities. The non-appropriation rule stipulates that all revenue must fund general expenditures, except in specific cases. The no-offset principle mandates that revenues and expenditures are recorded in their gross values, without deductions. Finally, the principles of specification and budgetary balance reinforce the need for detailed revenue allocation and sustainable financial management.

Regarding the public sector in Portugal, its budgetary framework adheres to the European System of Accounts (ESA), which structures public sector financial reporting across three main levels of administration: Central Administration, Regional and Local Administration, and Social Security. Among these, Central Administration and Social Security fall under the political jurisdiction of the central government, while Regional and Local Administration expenditures provide a useful metric for assessing the degree of political decentralization in Portugal (Pereira et al., 2016).

Since 1974, when democracy was established in Portugal following the Carnation Revolution, the country did not record a budget surplus until 2019, when it achieved its first one, amounting to approximately 0.1% of GDP. This surplus was driven by a combination of economic growth, a reduction in expenditure relative to GDP, and an increase in tax revenue. Portugal recorded another surplus in 2023, reaching about 1.2% of GDP, as reported by the Instituto Nacional de Estatística (INE) and confirmed by the Government. These recent achievements demonstrate the potential benefits of optimized fiscal policies, including tax rate adjustments aligned with Laffer Curve principles to enhance revenue without stifling growth. To ensure long-term financial stability, maintaining a sustainable debt-to-revenue ratio remains a key policy objective (Pereira et al., 2018).

2.5. Laffer Curve Foundations

This study analyzes the Laffer Curve, an economic concept describing the relationship between tax rates and government tax revenue. The concept was conceived by Arthur Laffer in the 1970s, during a discussion in Washington, D.C., where he famously illustrated it on a napkin. Laffer proposed that beyond a certain point, increasing tax rates would lead to a decline in tax revenue due to disincentives to work, production, and compliance, as well as increased tax evasion.

As illustrated in Figure 1, when the tax rate reaches 100%, economic activity halts, as individuals and businesses have no incentive to generate income if all earnings are confiscated by the government, resulting in zero tax revenue. Conversely, with a 0% tax rate, individuals retain all of their earnings, fostering maximum production and economic activity but yielding zero government revenue. This relationship underscores the importance of identifying an optimal tax rate that balances economic activity and revenue collection (Wanniski, 1978). An essential observation is that the Laffer Curve does not assign fixed numerical values to tax rates. The peak of the curve, point E, does not necessarily occur at 50% but represents a variable threshold where taxpayers are willing to be taxed while maintaining productivity. At points B and D, taxpayers accept higher taxes in exchange for increased public services, whereas at points A and C, they prioritize private consumption and seek lower tax rates. The Ministry of Finance must identify the precise location of point E and monitor its shifts over time (Wanniski, 1978).

Following its initial conceptualization, numerous economists have attempted to quantify the relationship between tax rates and revenue, refining the underlying econometric models. Malcomson (1986) challenged certain assumptions of the Laffer Curve, arguing that its properties might not hold in general equilibrium models and that results are sensitive to labor supply elasticity. Agell and Persson (2001) proposed that the “transfer-adjusted tax rate” rather than the tax rate itself is the critical determinant of the Laffer effect. Lévy-Garboua et al. (2009) conducted a controlled experiment demonstrating that the Laffer Curve does not always reflect a simple trade-off between income and leisure.

Further empirical investigations have provided mixed results. Trabandt and Uhlig (2011) estimated Laffer Curves for the U.S., EU-14, and individual European countries, concluding that governments could still increase tax rates by up to 30% in the U.S. and 8% in the EU-14 without revenue losses. Strulik and Trimborn (2012) found that capital tax Laffer Curves are particularly flat, suggesting minimal revenue changes when adjusting capital taxes. Nourry et al. (2013) demonstrated the existence of Laffer Curves for consumption taxes under balanced budget conditions, while Ehrhart et al. (2014) introduced Growth-Indexed Laffer Curves, incorporating public debt and seigniorage effects.

Other studies have examined country-specific applications of the Laffer Curve. Nutahara (2015) analyzed Japan’s tax structure, finding that labor tax rates remained below the Laffer Curve’s peak, while capital tax rates approached or exceeded revenue-maximizing levels. Tsuchiya (2016) showed that the Laffer Curve fails to materialize dynamically when moderate initial debt levels are incorporated. Sanz-Sanz (2016) modeled the connection between tax revenue and marginal tax rates in modern personal income taxes. The model confirmed that the Laffer curve is fundamentally an intrinsic individual matter, although a virtual aggregate Laffer curve for the entire population can be inferred. In Spain, Varela-Candamio and Morollón (2017) estimated the revenue-maximizing tax rate for Madrid and Barcelona at 34%.

Theoretical advancements have also refined the Laffer Curve’s predictive capacity. Badel and Huggett (2017) formulated an equation to estimate the revenue-maximizing tax rate based on three elasticity parameters, providing policymakers with a quantitative tool to assess optimal taxation. Bosi and Desmarchelier (2017) found that Laffer Curve effects and the Green Paradox are mutually exclusive over the long term. Waseem (2018) suggests that the new tax rate was on the wrong side of the Laffer curve and would not have been optimal under any social preferences. Miravete et al. (2018) argued that firms’ strategic responses to tax policy changes flatten the Laffer Curve by analyzing retail sales data for alcoholic beverages.

Recent behavioral economic studies suggest that tax compliance behavior significantly influences the Laffer Curve’s shape. Experimental research by Swenson (1988) confirmed that tax payments tend to peak at high, but not extreme, tax rates. Meanwhile, Sutter and Weck-Hannemann (2003) proposed that the Laffer Curve may have multiple peaks, challenging the traditional assumption of a single revenue-maximizing tax rate and emphasizing the complexity of fiscal policy decisions.

Over time, the Laffer Curve has evolved from its simplistic graphical representation to a sophisticated analytical framework incorporating labor market dynamics, international capital flows, tax competition, and taxpayer behavior. Gamarra Rondinel et al. (2024) further argue that the Laffer effect is an inherently individual phenomenon, meaning each taxpayer has a unique Laffer Curve. Consequently, within any given fiscal year, there exist as many Laffer Curves as there are taxpayers. For example, in Spain’s 2017 personal income tax system, an estimated 14,460,354 individual Laffer Curves could be derived.

The taxable income considered by the government includes specific deductions. The primary deductions under the personal income tax system encompass personal exemptions, charitable contributions, state and local taxes, and mortgage interest payments. Numerous factors influence tax preferences and the determination of taxable income deductions. Among the most debated topics in tax law are personal income taxes. The central issue in this debate is the theory of income taxation. While the concept of economic sacrifice has been extensively discussed, a comprehensive and universally accepted theory remains elusive. The literature often addresses the burden of taxation through principles such as personal exemptions, dependent exemptions, marriage benefits, and the standard deduction. However, recent years have witnessed a decline in revenues derived from these provisions. Consequently, taxpayers in higher income brackets face increased tax liabilities due to their earnings (Fuster, 2022). Personal income tax is frequently regarded as a crucial instrument for mobilizing government revenue, particularly in developing economies. However, it is commonly assumed that an increase in income does not necessarily lead to a proportional increase in taxable income. Empirical studies suggest that taxable income elasticity is approximately -1.8%, meaning that a 1% rise in taxable personal income results in a 1.8% decline in taxable income. This relationship highlights the importance of determining legal taxable income, as economic behavior adjusts in response to taxation (Fuster, 2022; Gomes et al., 2024).

The relationship between the Laffer Curve and personal income taxation remains a subject of controversy, primarily for two reasons. First, corporate income taxation can have indirect effects on individual taxpayers who own or invest in businesses. The analysis of the Laffer Curve in personal income taxation extends beyond direct tax revenue to consider the broader implications on other taxes and contributions. While corporate taxation indirectly impacts individual taxpayers, it also has direct consequences for economic growth and overall fiscal revenue. Second, the relationship between tax rates and government revenue is inherently complex, requiring careful consideration of factors such as tax revenue elasticity, i.e., the responsiveness of tax revenue to changes in tax rates. Understanding this elasticity is critical for designing effective fiscal policies and predicting the impact of tax rate adjustments on government revenue. Higher tax rates do not always yield higher revenue; beyond a certain threshold, they may incentivize tax avoidance, reduce labor supply, or diminish investment. Although it is true that corporate taxation may influence the pricing of goods and services, the extent of this impact depends on various economic factors. These include market competition, demand elasticity, and business cost structures. As a result, while corporate taxation may have indirect effects on individual taxpayers, the direct link between CIT and consumer prices is not merely a straightforward proportional increase. Instead, the relationship is mediated by broader economic dynamics, making it necessary to analyze the aggregate effects of corporate taxation on the economy.

Drawing from the literature review, this study sets out to examine how the Laffer Curve plays out across the European Union, focusing on personal income tax (PIT), corporate income tax (CIT), and value-added tax (VAT). We pursue the following guiding questions, which naturally tie back to the contributions outlined earlier:

• Is there a clear inverted-U pattern linking statutory tax rates to revenue as a share of GDP for PIT, CIT, and VAT across the 27 EU countries from 1995 to 2022?
• Where do revenue-maximizing tax rates lie for each tax type, and do they differ noticeably between larger, high-tax economies and smaller or lower-tax members?
• How does the Bird Index help reveal whether countries are collecting close to their potential at current rates, and what does this suggest for improving tax efficiency without necessarily raising rates?

3. Data and Methodology

This section presents the methodological approach used to estimate the Laffer Curve for the European Union and its 27 member states, analyzing the relationship between tax rates and government revenue from 1995 to 2022. The study employs panel data analysis, considering total revenue, as well as revenue from personal income tax (PIT), corporate income tax (CIT), and value-added tax (VAT). Section 3.1 details the data sources and structure, while Section 3.2 introduces an alternative measure of fiscal effort, providing a more comprehensive assessment of tax burden dynamics. Section 3.3 explains the adjustments made to account for inflation, ensuring comparability across time periods. Section 3.4 describes the procedures applied to data normalization, and Section 3.5 discusses how country-specific values were adjusted relative to EU-wide figures to enhance comparability. Finally, Section 3.6 outlines the econometric approach, detailing the log-quadratic specification used to capture the nonlinear relationship between tax rates and revenue. It also explains the application of fixed and random effects models, with the Hausman test determining the most appropriate specification.

3.1. Panel Data (1995–2022)

This study aims to estimate the Laffer Curve for the European Union and its 27 member states, focusing on total government revenue and the primary tax sources, namely, personal income tax, corporate income tax, and value-added tax. These taxes constitute the most significant contributions to state revenue and are central to the fiscal policies of EU nations. A number of EU member states share a common monetary system and adhere to similar fiscal policies due to the Stability and Growth Pact (SGP), a framework introduced in 1997 to promote fiscal discipline among EU countries. The SGP aims to ensure that member states maintain sound public finances and coordinate their fiscal policies effectively. While its importance has remained constant, it gained renewed significance following the 2008 global financial crisis, leading to structural revisions to strengthen its role in economic stability.

The significance of PIT, CIT, and VAT as revenue sources is evident across all EU countries. These three taxes collectively accounted for $49.7\%$ of total government revenue across the 27 EU nations in 2022, the final year of the dataset (European Union, 2024). Given their substantial share of fiscal revenues, they serve as the primary variables in estimating the Laffer Curve, in addition to total government revenue.

To ensure consistency and reliability, tax revenue data for PIT, CIT, VAT, and total government revenue were obtained from the Eurostat database1 for the period 1995–2022. The dataset was structured in a tabular format to facilitate adjustments, transformations, and econometric analysis. Before estimating the Laffer Curve, necessary inflation adjustments and data normalization were applied to standardize the dataset and enhance the comparability of results.

Following the research questions outlined in Section 2, our analysis utilizes statutory tax rates as the primary tax variable, as these rates reflect direct policy decisions. Specifically, we use the top statutory personal income tax rate (PIT), the statutory corporate income tax rate (CIT), and the standard value-added tax (VAT) rate. The resulting dataset forms an unbalanced panel, as it covers all 27 current member states over the period 1995–2022. Countries that acceded to the EU during this period (e.g., in 2004, 2007, and 2013) are included in the panel for the entire time series to the extent data is available, allowing for a consistent analysis of their fiscal trajectories. For any remaining gaps where data is missing for a specific country-year, our econometric models apply listwise deletion, ensuring that estimations are based only on complete observations.

By incorporating a comprehensive dataset spanning nearly three decades, this study provides a robust foundation for evaluating the effects of tax rates on revenue collection, contributing to the broader discussion on optimal taxation and fiscal policy efficiency within the EU.

3.2. Bird Index

The Laffer Curve is traditionally estimated by analyzing total government revenues as a percentage of Gross Domestic Product to determine the overall tax burden. However, the Bird Index offers a more precise measure of taxpayers’ sacrifice by incorporating fiscal effort, rather than relying solely on the tax burden. Given its ability to reflect the intensity of taxation relative to a country’s economic capacity, this study explores the use of the Bird Index as a dependent variable in the estimation of the Laffer Curve.

As previously discussed in Section 2.4 on Fiscal Effort, the Bird Index was introduced by Bird (1964) as an enhancement of the Frank Index (Frank, 1959). While the Frank Index evaluates fiscal effort based on total tax revenue relative to national income, the Bird Index refines this approach by accounting for disposable income after tax payments. This adjustment provides a more robust representation of fiscal effort, ensuring that the metric reflects the actual economic burden borne by taxpayers. Additionally, the Bird Index replaces GNP with GDP, thereby better capturing the impact of economic openness and international trade on fiscal capacity.

For this study, the Bird Index calculations were performed using Equation (2) for all 27 EU countries and for the EU as a whole over the period 1995–2022. Given that the Bird Index is already normalized based on observed values for each year, it did not require any deflation adjustments before its incorporation into the econometric models. This approach ensures that the analysis accurately reflects fiscal effort dynamics across EU nations, contributing to a more nuanced understanding of the relationship between taxation and government revenue.

3.3. Deflators

Deflators are economic indices used to adjust monetary values by removing inflation effects, converting nominal values into real values. This adjustment enables meaningful comparisons of purchasing power and economic value across time periods, providing a clearer picture of economic growth or contraction by accounting for price changes (Kehoe & Ruhl, 2008).

The GDP deflator, a widely used method for adjusting revenues, converts nominal GDP to real GDP by accounting for changes in the overall price level. According to van der Wielen (2020), it is calculated using:

$${\displaystyle \mathrm{GDP}\mathrm{Deflator}=\frac{\mathrm{Nominal}\mathrm{GDP}}{\mathrm{Real}\mathrm{GDP}}\times 100.}$$

(3)

Nominal GDP reflects current market prices of goods and services, while real GDP uses constant base-year prices to adjust for inflation. Equation (3) isolates changes in real economic activity, excluding price-driven variations.

For this study, GDP deflators for the 27 EU countries and the EU aggregate were sourced from the Eurostat database, covering 1995–2022. To analyze tax revenue in inflation-adjusted terms, the GDP deflator was applied as follows:

$${\displaystyle \mathrm{Real}\mathrm{Revenue}=\frac{\mathrm{Nominal}\mathrm{Revenue}}{\mathrm{GDP}\mathrm{Deflator}}\times 100.}$$

(4)

This adjustment was applied to Personal Income Tax (PIT), Corporate Income Tax (CIT), and Value-Added Tax (VAT) revenues, as well as total government revenue, producing deflated indices suitable for regression analysis.

3.4. Normalization

Data normalization is an essential step in statistical analysis and econometric modeling, as it ensures datasets are comparable and supports accurate interpretations. The main goal of normalization is to rescale data values to a common range while maintaining the relative differences between observations. This is especially important for variables with varying units or scales, as it preserves the underlying relationships in the data (Yu et al., 2009).

As outlined by Yu et al. (2009), several normalization techniques are available, each suited to specific applications. One common approach is maximum normalization, a straightforward linear method that rescales data so the highest value for each indicator becomes 1. This is represented mathematically as:

$${\displaystyle Y_i=\frac{X_i}{\max \left(X\right)},}$$

(5)

where $Y_i$ is the normalized value, $X_i$ is the original value, and $\max \left(X\right)$ is the maximum observed value for the variable X.

Although maximum normalization is popular for its ease of use, it may not adequately account for variability in datasets with outliers or skewed distributions. Therefore, selecting a normalization method requires careful evaluation of the data’s characteristics and the study’s objectives. Another frequently used technique is mean normalization, which scales data relative to the variable’s mean and standard deviation (Yu et al., 2009). This method centers the data around zero, making it useful for comparisons while retaining proportionality. The formula is:

$${\displaystyle Y_i=\frac{X_i-\overline{X}}{{\sigma }_X},}$$

(6)

where $\overline{X}$ is the mean and ${\sigma }_X$ is the standard deviation of the variable $X$. However, mean normalization can be influenced by outliers, which may distort the mean and impact the rescaling.

In this study, normalization was applied to enhance the comparability of tax-related variables across EU countries and over time. For each independent variable—Bird Index, Personal Income Tax (PIT) rate, Corporate Income Tax (CIT) rate, and Value-Added Tax (VAT) rate—maximum normalization was performed using Equation (5). Specifically, each value of total government revenue deflated by GDP, as well as revenue from personal income tax (PIT), corporate income tax (CIT), and value-added tax (VAT) also deflated by GDP, was divided by the observed in the year when the corresponding dependent variable was maximum in the 1995–2022 period. Unlike country-specific normalization, this method uses a uniform reference point anchored to the dependent variable’s peak, ensuring consistent scaling. Consequently, the standardized variables support a more reliable analysis of fiscal policies and their impact on tax revenue across the EU.

3.5. Relativization with the EU

Relativization in the EU context is vital for analyzing tax competition, as it helps avoid economic imbalances that could disrupt integration. By standardizing fiscal indicators across member states, relativization improves comparability, ensures alignment with EU guidelines, and offers clearer insights into each country’s tax effort relative to the overall European framework.

Tax competition is a central feature of the EU landscape. Countries with tax burdens well below or above the EU average often face economic and political incentives to adjust toward the norm. Such differences can prompt capital and business shifts, with low-tax countries drawing investments and high-tax ones potentially losing firms and talent. These dynamics fuel discussions on fiscal harmonization to promote equitable competition and regional stability (McCarthy et al., 2008).

Relativization also plays a key role in making tax data more comparable. Raw tax figures can be deceptive due to variations in economic scale, population, and fiscal systems. Relating national tax data to EU totals simplifies the identification of above- or below-average burdens, enabling policymakers to spot imbalances and refine strategies.

In addition to normalization, relativization boosts transparency by highlighting each country’s proportional role in EU-wide fiscal efforts. Nations straying far from the average may encounter pressures to reform their policies. This approach further evaluates integration levels in the single market, revealing which economies align closely with EU fiscal standards.

In this study, relativization was applied to all dependent variables—the Bird Index, as well as GDP-deflated revenues from Personal Income Tax (PIT), Corporate Income Tax (CIT), and Value-Added Tax (VAT). For each year, country-specific values for the 27 member states were divided by the corresponding EU-wide total, ensuring temporal consistency and comparability. This framework strengthens the analysis of tax competition, fiscal effort, and revenue efficiency across Europe. Overall, this relativization framework bolsters the examination of tax competition, fiscal effort, and revenue efficiency in Europe.

3.6. Regression Model

According to Wanniski (1978), the Laffer Curve illustrates a nonlinear relationship between tax rates and tax revenue, with an optimal rate at which revenue peaks before declining as rates increase further. Empirical studies have historically examined this relationship, treating the tax rate as the primary determinant of government revenue. The traditional quadratic model for the Laffer Curve is given by:

$$\mathrm{tax}\mathrm{revenue}=a+b\mathrm{tax}\mathrm{rate}+c(\mathrm{tax}{\mathrm{rate})}^2+ϵ,$$

(7)

where tax revenue is the total revenue collected, tax rate ranges from 0 to 1 (or 0% to 100%), a, b, and c are coefficients capturing the relationship, and $ϵ$ is the error term. For the Laffer Curve to exhibit its characteristic inverted U-shape, c must be negative and b positive, ensuring revenue increases with tax rates up to a maximum before declining.

However, preliminary analysis suggested that this quadratic model may not fully capture the tax revenue relationship, as shown in Figure 2. The expected concave pattern of the Laffer Curve is not consistently observed across the dataset, indicating the need for an alternative specification.

To enhance model accuracy, a logarithmic transformation was applied, yielding the following functional form:

$$\log \left(\mathrm{tax}\mathrm{revenue}\right)={\beta }_0+{\beta }_1\log \left(\mathrm{tax}\mathrm{rate}\right)+{\beta }_2{\left(\mathrm{tax}\mathrm{rate}\right)}^2+ϵ.$$

(8)

The logarithmic terms allow for a more flexible model, better capturing nonlinearities in the tax revenue relationship.

Changes in tax rates affect disposable income and economic activity, and in this study, GDP is employed as the key measure of taxable income, consistent with the panel data analysis spanning 1995 to 2022 across the 27 EU member states. While GNP, which includes net income from abroad, might provide a broader reflection of total income subject to taxation in certain contexts, the use of GDP ensures uniformity and comparability, supporting robust econometric modeling and accurate assessment of tax policy impacts on revenue collection as deflated by GDP.

A panel data approach was employed to analyze the dataset, capturing both cross-sectional and time-series variations. This method controls for unobserved heterogeneity across countries and time periods, making it ideal for studying the Laffer Curve by isolating tax effects from other macroeconomic factors. The analysis was conducted using EViews 9, a statistical software for econometric modeling. The dataset used for estimation includes the following variables:

• Year;
• Country;
• Bird Index relativized to EU-27;
• PIT revenue GDP-deflated and relativized to EU-27;
• CIT revenue GDP-deflated and relativized to EU-27;
• VAT revenue GDP-deflated and relativized to EU-27;
• Total government revenue GDP-deflated and maximum-normalized conditional on peak dependent variable;
• PIT revenue GDP-deflated and maximum-normalized conditional on peak dependent variable;
• CIT revenue GDP-deflated and maximum-normalized conditional on peak dependent variable;
• VAT revenue GDP-deflated and maximum-normalized conditional on peak dependent variable.

Regressions were estimated to analyze the relationship between tax revenue and the Bird Index, Personal Income Tax (PIT), Corporate Income Tax (CIT), and Value-Added Tax (VAT) for the EU as a whole and individual countries. The Hausman test was applied to choose between fixed and random effects models by evaluating whether coefficient differences are systematic. A significant test result favors fixed effects, indicating that unobserved country-specific factors correlate with explanatory variables. If the null hypothesis is not rejected (Nickerson, 2000), the random effects model is preferred, assuming individual effects are uncorrelated with regressors (Hausman, 1978).

4. Results and Policy Implications

4.1. Optimal Tax Rates for Bird Index, PIT, CIT, and VAT

As previously outlined, tax revenue data for personal income tax (PIT), corporate income tax (CIT), value-added tax (VAT), and total government revenue—along with GDP, population, and GDP deflator values—were sourced from the Eurostat database to enable inflation adjustment and the calculation of the Bird Index using Equation (2).

Table 2. Maximum and minimum defleted and normalized values.

	Minimum	Maximum
Bird index	$23.87\%$	$100.00\%$
PIT revenues	$23.60\%$	$149.26\%$
CIT revenues	$6.00\%$	$179.59\%$
VAT revenues	$20.00\%$	$152.96\%$

presents the minimum and maximum values observed across the EU-27 countries for the deflated and normalized total, PIT, CIT, and VAT revenues over the 1995–2022 period. These normalized values were obtained by dividing each country’s deflated revenue-to-GDP ratio by the highest observed value of the corresponding variable across the entire panel and time span, as formalized in Equation (5). This maximum normalization approach anchors all variables to a common peak reference, ensuring consistent scaling and equitable representation of relative fiscal performance across countries and years. The wide ranges highlight substantial heterogeneity in fiscal structures and revenue mobilization capacity within the EU. The Bird Index, for instance, spans from 23.87% to 100%, indicating that even the highest-performing country in a given year achieves only the reference maximum, while the lowest falls to less than a quarter of that peak. PIT revenues show a similarly broad dispersion (23.60% to 149.26%), reflecting diverse labor market structures, progressivity of tax systems, and enforcement efficiency. The most extreme variation is observed in CIT revenues, ranging from 6.00% to 179.59%, largely driven by the concentration of multinational profits in low-tax jurisdictions such as Ireland and Luxembourg due to profit-shifting strategies. VAT revenues, while less volatile, still range from 20.00% to 152.96%, influenced by differences in consumption patterns, tax base breadth, and compliance levels. By construction, a normalized value of 100% represents the historical maximum achieved by any EU country in the sample for that variable, while values above 100% indicate performance exceeding even the panel-wide peak in a given year. This framework facilitates a nuanced assessment of fiscal effort and efficiency, free from distortions introduced by country-specific scaling, and supports robust cross-sectional and temporal comparisons of tax policy outcomes across the European Union.

The dataset was then incorporated into regression models to examine the relationship between tax rates and corresponding revenues. Separate specifications were estimated for the Bird Index and each tax category (PIT, CIT, and VAT). In all models, the dependent variable was the log-transformed tax revenue, while the independent variables included the log-transformed tax rate and its squared term to capture potential non-linear (e.g., Laffer-type) effects. The inclusion of the quadratic term allowed the models to capture the nonlinear relationship inherent in the Laffer Curve, where revenue initially increases with tax rates but declines after a certain threshold due to reduced economic activity or tax avoidance. The logarithmic transformation enables the estimation of a non-symmetrical behavior in the relationship between the dependent and independent variables, enhancing the model’s flexibility to reflect the complex dynamics observed in the European Union data. For the Bird Index, the regression examined the relationship between fiscal effort and total government revenue, testing for a similar quadratic pattern.

The panel data regression models were estimated using either fixed effects or random effects, with the choice determined by the Hausman test. The Hausman test results, shown in

Table 3. Hausman test results.

	p-Value
Bird Index regression	$0.0000$
PIT regression	$0.3592$
CIT regression	$0.2893$
VAT regression	$0.1138$

, indicated that the Bird Index regression required fixed effects due to a p-value below 0.05, while the PIT, CIT, and VAT regressions used random effects, as their p-values exceeded $0.05$. This ensured the econometric models were appropriately specified, enhancing the reliability of the findings. Initial fixed effects and random effects estimations revealed autocorrelation in the residuals, as indicated by the Durbin–Watson statistic (Durbin & Watson, 1950). To address this, first differencing was applied to all variables.

A distinct regression approach was employed using the Seemingly Unrelated Regressions (SUR) method, tailored to either time series or cross-sectional data based on the Hausman test outcomes. The SUR method accounted for correlations between error terms across the Bird Index, PIT, CIT, and VAT regressions without applying first differencing, enhancing estimation efficiency and ensuring robust regression results by addressing potential cross-equation dependencies.

The regression results for the Bird Index, PIT, CIT, and VAT are presented in Table 4, Table 5, Table 6 and Table 7, using the Equation (8), reporting two models per tax type, with the first model using fixed or random effects with first differencing and the second model using SUR.

Table 4 examines the relationship between fiscal effort, measured by the Bird Index, and total government revenue, with $\log \left(\mathrm{Bird}\mathrm{Index}\mathrm{revenue}\right)$ as the dependent variable. The fixed effects specification accounts for unobserved country-specific factors, such as differing tax administration systems. In Model 1, estimated with fixed effects and first differencing, the intercept (${\beta }_0=-0.0247,p<0.001$) and linear term (${\beta }_1=0.7527,p<0.001$) are highly significant, indicating that higher tax rates strongly boost revenue at lower levels. The quadratic term (${\beta }_2=-0.0297,p<0.1$) is marginally significant, suggesting a subtle Laffer Curve effect. The adjusted $R^2$ of $0.136$ indicates a modest fit, implying that fiscal effort alone explains limited revenue variation, possibly due to the aggregation of diverse tax structures. The F-statistic ($3.11,p<0.001$) confirms model significance, with 724 observations ensuring robustness (Wang & Cui, 2017). Small standard errors ($0.0030$ for ${\beta }_0$, $0.1016$ for ${\beta }_1$, $0.0180$ for ${\beta }_2$) reflect precise estimates, though the weak quadratic term suggests a less pronounced nonlinear effect.

Model 2, estimated using SUR, offers a stronger fit, with an adjusted $R^2$ of $0.657$, capturing a substantial portion of revenue variation. The SUR method accounts for correlations between error terms across the Bird Index and other tax regressions, enhancing efficiency. The intercept (${\beta }_0=-0.0464,p>0.1$) is insignificant, suggesting no baseline revenue effect at zero tax rates. The linear term (${\beta }_1=0.2327,p<0.01$) and quadratic term (${\beta }_2=-0.1713,p<0.001$) are significant, confirming a robust Laffer Curve effect. The F-statistic ($52.35,p<0.001$) and 751 observations reinforce reliability, with tight standard errors ($0.0285$ for ${\beta }_0$, $0.0740$ for ${\beta }_1$, $0.0212$ for ${\beta }_2$). The improved fit in Model 2, likely due to SUR’s ability to model cross-equation dependencies, highlights the importance of considering inter-tax interactions when optimizing fiscal effort.

Table 4. Laffer Curve estimation results for Bird Index.

	Dependent Variable: log(Bird INDEX Revenue)
	Independent Variables
Model	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	Adjusted ${\mathit{R}}^{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
1	$-0.0247$ ***	$0.7527$ ***	${-0.0297 }^{.}$	$0.136$	$3.11$ ***	724
	$\left(0.0030\right)$	$\left(0.1016\right)$	$\left(0.0180\right)$
2	$-0.0464$	$0.2327$ **	$-0.1713$ ***	$0.657$	$52.35$ ***	751
	$\left(0.0285\right)$	$\left(0.0740\right)$	$\left(0.0212\right)$

Note: The values in parentheses correspond to the estimated standard error of each coefficient in the model. Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; >0.1–1, ‘ ’.

Table 4. Laffer Curve estimation results for Bird Index.

	Dependent Variable: log(Bird INDEX Revenue)
	Independent Variables
Model	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	Adjusted ${\mathit{R}}^{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
1	$-0.0247$ ***	$0.7527$ ***	${-0.0297 }^{.}$	$0.136$	$3.11$ ***	724
	$\left(0.0030\right)$	$\left(0.1016\right)$	$\left(0.0180\right)$
2	$-0.0464$	$0.2327$ **	$-0.1713$ ***	$0.657$	$52.35$ ***	751
	$\left(0.0285\right)$	$\left(0.0740\right)$	$\left(0.0212\right)$

Note: The values in parentheses correspond to the estimated standard error of each coefficient in the model. Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; >0.1–1, ‘ ’.

Table 5 focuses on PIT, with $\log \left(\mathrm{PIT}\mathrm{revenue}\right)$ as the dependent variable, using a random effects specification (Hausman test $p=0.3592$). Model 3, estimated with random effects and first differencing, shows a highly significant intercept (${\beta }_0=-0.0167,p<0.001$) and linear term (${\beta }_1=0.9730,p<0.001$), indicating a strong positive relationship between PIT rates and revenue. The quadratic term (${\beta }_2=-0.0620,p<0.001$) confirms a significant Laffer Curve effect. The adjusted $R^2$ of $0.907$ indicates an excellent fit, capturing most revenue variation, likely due to PIT’s direct link to individual income. The F-statistic ($3519.30,p<0.001$) and 724 observations confirm robustness, with small standard errors ($0.0010$ for ${\beta }_0$, $0.0202$ for ${\beta }_1$, $0.0158$ for ${\beta }_2$) indicating high precision.

Model 4, estimated using SUR, has a lower adjusted $R^2$ of $0.666$, still indicating a good fit. The SUR approach accounts for correlations between PIT and other tax regressions, improving efficiency. The intercept (${\beta }_0=0.3660,p>0.1$) is insignificant, while the linear term (${\beta }_1=0.8209,p<0.001$) and quadratic term (${\beta }_2=-0.3052,p<0.001$) are highly significant. The F-statistic ($749.77,p<0.001$) and 751 observations ensure reliability, with standard errors ($0.0344$ for ${\beta }_1$, $0.0315$ for ${\beta }_2$) reflecting precision.

Table 5. Laffer Curve estimation results for personal income tax.

	Dependent Variable: $\mathbf{log}(\mathbf{PIT} \mathbf{Revenue})$
	Independent Variables
Model	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	Adjusted ${\mathit{R}}^{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
3	$-0.0167$ ***	$0.9730$ ***	$-0.0620$ ***	$0.907$	$3519.30$ ***	724
	$\left(0.0010\right)$	$\left(0.0202\right)$	$\left(0.0158\right)$
4	$0.3660$	$0.8209$ ***	$-0.3052$ ***	$0.666$	$749.77$ ***	751
	$\left(1.0012\right)$	$\left(0.0344\right)$	$\left(0.0315\right)$

Note: The values in parentheses correspond to the estimated standard error of each coefficient in the model. Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; >0.1–1, ‘ ’.

Table 5. Laffer Curve estimation results for personal income tax.

	Dependent Variable: $\mathbf{log}(\mathbf{PIT} \mathbf{Revenue})$
	Independent Variables
Model	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	Adjusted ${\mathit{R}}^{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
3	$-0.0167$ ***	$0.9730$ ***	$-0.0620$ ***	$0.907$	$3519.30$ ***	724
	$\left(0.0010\right)$	$\left(0.0202\right)$	$\left(0.0158\right)$
4	$0.3660$	$0.8209$ ***	$-0.3052$ ***	$0.666$	$749.77$ ***	751
	$\left(1.0012\right)$	$\left(0.0344\right)$	$\left(0.0315\right)$

Note: The values in parentheses correspond to the estimated standard error of each coefficient in the model. Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; >0.1–1, ‘ ’.

Table 6 analyzes CIT, with $\log \left(\mathrm{CIT}\mathrm{revenue}\right)$ as the dependent variable, using a random effects specification (Hausman test $p=0.2893$). Model 5, estimated with random effects and first differencing, shows a significant intercept (${\beta }_0=-0.0202,p<0.001$) and linear term (${\beta }_1=0.9626,p<0.001$), indicating that higher CIT rates increase revenue initially. The quadratic term (${\beta }_2=-0.2063,p<0.001$) confirms a strong Laffer Curve effect. The adjusted $R^2$ of $0.758$ indicates a strong fit, with the F-statistic ($1132.38,p<0.001$) and 724 observations confirming robustness. Small standard errors ($0.0038$ for ${\beta }_0$, $0.0245$ for ${\beta }_1$, $0.0212$ for ${\beta }_2$) ensure precision.

Model 6, estimated using SUR with first differencing, has a similar adjusted $R^2$ of $0.756$, with a significant intercept (${\beta }_0=0.6785,p<0.05$) and linear term (${\beta }_1=0.8564,p<0.001$). The quadratic term (${\beta }_2=-0.1932,p<0.001$) reinforces the Laffer Curve effect. The SUR method enhances efficiency by modeling correlations with other tax regressions. The F-statistic ($1162.75,p<0.001$) and 751 observations support reliability, with standard errors ($0.0585$ for ${\beta }_1$, $0.0567$ for ${\beta }_2$) indicating the precision.

Table 6. Laffer Curve estimation results for corporate income tax.

	Dependent Variable: $\mathbf{log}(\mathbf{CIT} \mathbf{Revenue})$
	Independent Variables
Model	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	Adjusted ${\mathit{R}}^{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
5	$-0.0202$ ***	$0.9626$ ***	$-0.2063$ ***	$0.758$	$1132.38$ ***	724
	$\left(0.0038\right)$	$\left(0.0245\right)$	$\left(0.0212\right)$
6	$0.6785$ *	$0.8564$ ***	$-0.1932$ ***	$0.756$	$1162.75$ ***	751
	$\left(0.2980\right)$	$\left(0.0585\right)$	$\left(0.0567\right)$

Note: The values in parentheses correspond to the estimated standard error of each coefficient in the model. Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; 0.1–1, ‘ ’.

Table 6. Laffer Curve estimation results for corporate income tax.

	Dependent Variable: $\mathbf{log}(\mathbf{CIT} \mathbf{Revenue})$
	Independent Variables
Model	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	Adjusted ${\mathit{R}}^{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
5	$-0.0202$ ***	$0.9626$ ***	$-0.2063$ ***	$0.758$	$1132.38$ ***	724
	$\left(0.0038\right)$	$\left(0.0245\right)$	$\left(0.0212\right)$
6	$0.6785$ *	$0.8564$ ***	$-0.1932$ ***	$0.756$	$1162.75$ ***	751
	$\left(0.2980\right)$	$\left(0.0585\right)$	$\left(0.0567\right)$

Note: The values in parentheses correspond to the estimated standard error of each coefficient in the model. Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; 0.1–1, ‘ ’.

Table 7 examines VAT, with $\log \left(\mathrm{VAT}\mathrm{revenue}\right)$ as the dependent variable, using a random effects specification (Hausman test $p=0.1138$). Model 7, estimated with random effects and first differencing, shows a significant intercept (${\beta }_0=-0.0119,p<0.001$) and linear term (${\beta }_1=1.0342,p<0.001$), indicating a strong revenue response to VAT rate increases. The quadratic term (${\beta }_2=-0.2778,p<0.001$) confirms a pronounced Laffer Curve effect. The adjusted $R^2$ of $0.778$ indicates a strong fit, with the F-statistic ($1258.94,p<0.001$) and 717 observations ensuring robustness. Small standard errors ($0.0012$ for ${\beta }_0$, $0.0272$ for ${\beta }_1$, $0.0202$ for ${\beta }_2$) reflect high precision.

Model 8, estimated using SUR, has a higher adjusted $R^2$ of $0.849$, indicating an excellent fit. The SUR method accounts for correlations with other tax regressions, enhancing efficiency. The intercept (${\beta }_0=0.7738,p>0.1$) is insignificant, while the linear term (${\beta }_1=0.8465,p<0.001$) and quadratic term (${\beta }_2=-0.3547,p<0.001$) are significant. The F-statistic ($2086.01,p<0.001$) and 744 observations confirm robustness, with standard errors ($0.0293$ for ${\beta }_1$, $0.0298$ for ${\beta }_2$) ensuring precision.

Table 7. Laffer Curve estimation results for value-added tax.

	Dependent Variable: $\mathbf{log}(\mathbf{VAT} \mathbf{Revenue})$
	Independent Variables
Model	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	Adjusted ${\mathit{R}}^{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
7	$-0.0119$ ***	$1.0342$ ***	$-0.2778$ ***	$0.778$	$1258.94$ ***	717
	$\left(0.0012\right)$	$\left(0.0272\right)$	$\left(0.0202\right)$
8	$0.7738$	$0.8465$ ***	$-0.3547$ ***	$0.849$	$2086.01$ ***	744
	$\left(0.5522\right)$	$\left(0.0293\right)$	$\left(0.0298\right)$

Note: The values in parentheses correspond to the estimated standard error of each coefficient in the model. Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; 0.1–1, ‘ ’.

Table 7. Laffer Curve estimation results for value-added tax.

	Dependent Variable: $\mathbf{log}(\mathbf{VAT} \mathbf{Revenue})$
	Independent Variables
Model	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	Adjusted ${\mathit{R}}^{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
7	$-0.0119$ ***	$1.0342$ ***	$-0.2778$ ***	$0.778$	$1258.94$ ***	717
	$\left(0.0012\right)$	$\left(0.0272\right)$	$\left(0.0202\right)$
8	$0.7738$	$0.8465$ ***	$-0.3547$ ***	$0.849$	$2086.01$ ***	744
	$\left(0.5522\right)$	$\left(0.0293\right)$	$\left(0.0298\right)$

Note: The values in parentheses correspond to the estimated standard error of each coefficient in the model. Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; 0.1–1, ‘ ’.

4.2. Tax Efficiency in EU States

To determine which countries exhibit the Laffer Curve, it is essential to analyze the quadratic and the linear coefficients in each independent regression model estimated for a specific country-tax pair using its time-series data. A significant result is characterized by a negative quadratic coefficient and a positive linear coefficient, combined with p-values of at most $0.1$. Table 8, Table 9, Table 10 and Table 11 present the countries where these conditions are met, providing evidence of the Laffer Curve effect across different tax types in the EU member states.

This analysis is grounded in the table presenting the quadratic coefficient results for the Bird Index per country (Table 8), which provides a foundational analysis of fiscal efficiency across a subset of EU member states. The dependent variable, the logarithm of Bird Index revenue, reflects a composite measure of tax efficiency, capturing the balance between tax burden and revenue generation. The quadratic specification, with coefficients ${\beta }_0$ (intercept), ${\beta }_1$ (linear term), and ${\beta }_2$ (quadratic term), models the non-linear relationship between tax rates and revenue, consistent with the Laffer Curve hypothesis. The negative ${\beta }_2$ coefficients across all listed countries (e.g., $-0.0616$ for Austria, $-0.7101$ for Belgium, $-1.0641$ for Italy) indicate the presence of a Laffer Curve effect, where revenue increases with tax rates up to a certain point before declining. The statistical significance of these coefficients underscores the robustness of the findings for most countries. For instance, Belgium and Bulgaria exhibit highly significant results with F-statistics of $13.77$ and $15.92$, respectively, suggesting strong model fit and reliable evidence of the Laffer Curve effect. However, countries like Austria, Denmark, and Italy show lower F-statistics ($0.05$, $2.0$7, and $0.52$, respectively), indicating weaker model explanatory power, possibly due to country-specific factors such as tax compliance or economic structure not fully captured in the model. The number of observations (ranging from 23 for Malta to 28 for several countries) reflects the panel data’s temporal coverage, though variations (e.g., 23 for Malta) may stem from data availability constraints for newer EU members. The negative ${\beta }_2$ coefficients, particularly large in magnitude for countries like Italy $(-1.0641)$ and Belgium $(-0.7101)$, suggest that these economies may be operating on the downward-sloping portion of the Laffer Curve, where high tax rates lead to revenue losses due to behavioral responses such as tax evasion or reduced economic activity. This finding aligns with the study’s broader argument that larger economies may face revenue inefficiencies due to excessively high tax rates, as noted in the policy implications section.

Table 8. Quadratic coefficient results for Bird Index per country.

	Dependent Variable: $\mathbf{log}(\mathbf{Bird} \mathbf{Index} \mathbf{Revenue})$
	Independent Variables
Country	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
Austria	$-0.0440$ ***	$0.1458$ ***	$-0.0616$ ***	$0.05$	28
Belgium	$0.6565$ ***	$1.3715$ ***	$-0.7101$ ***	$13.77$ ***	28
Bulgaria	$-0.0458$ ***	$3.4293$ ***	$-0.6980$ ***	$15.92$ ***	27
Cyprus	$-0.1036$ ***	$0.6885$ ***	$-0.0994$ ***	$96.32$ ***	28
Denmark	$0.2191$ ***	$0.4080$ ***	$-0.3323$ ***	$2.07$	28
Greece	$-0.4472$ ***	$1.1437$ ***	$-0.0171$ ***	$5.02$ **	28
Hungary	$-0.0416$ ***	$1.1191$ ***	$-0.0575$ ***	$7.06$ ***	27
Italy	$0.0117$ ***	$2.2608$ ***	$-1.0641$ ***	$0.52$	27
Malta	$0.2833$ ***	$0.7318$ ***	$-0.4084$ ***	$30.05$ ***	23
Portugal	$0.0034$ ***	$0.7664$ ***	$-0.2964$ ***	$2.16$	27
Romania	$-0.0417$	$0.7351$ ***	$-0.1170$ ***	$0.45$	27
Slovenia	$-0.0147$ ***	$0.1187$ ***	$-0.0811$ ***	$17.76$ ***	28
Spain	$0.0014$ ***	$0.6672$ ***	$-0.2039$ ***	$1.45$	27

Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; 0.1–1, ‘ ’.

Table 8. Quadratic coefficient results for Bird Index per country.

	Dependent Variable: $\mathbf{log}(\mathbf{Bird} \mathbf{Index} \mathbf{Revenue})$
	Independent Variables
Country	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
Austria	$-0.0440$ ***	$0.1458$ ***	$-0.0616$ ***	$0.05$	28
Belgium	$0.6565$ ***	$1.3715$ ***	$-0.7101$ ***	$13.77$ ***	28
Bulgaria	$-0.0458$ ***	$3.4293$ ***	$-0.6980$ ***	$15.92$ ***	27
Cyprus	$-0.1036$ ***	$0.6885$ ***	$-0.0994$ ***	$96.32$ ***	28
Denmark	$0.2191$ ***	$0.4080$ ***	$-0.3323$ ***	$2.07$	28
Greece	$-0.4472$ ***	$1.1437$ ***	$-0.0171$ ***	$5.02$ **	28
Hungary	$-0.0416$ ***	$1.1191$ ***	$-0.0575$ ***	$7.06$ ***	27
Italy	$0.0117$ ***	$2.2608$ ***	$-1.0641$ ***	$0.52$	27
Malta	$0.2833$ ***	$0.7318$ ***	$-0.4084$ ***	$30.05$ ***	23
Portugal	$0.0034$ ***	$0.7664$ ***	$-0.2964$ ***	$2.16$	27
Romania	$-0.0417$	$0.7351$ ***	$-0.1170$ ***	$0.45$	27
Slovenia	$-0.0147$ ***	$0.1187$ ***	$-0.0811$ ***	$17.76$ ***	28
Spain	$0.0014$ ***	$0.6672$ ***	$-0.2039$ ***	$1.45$	27

Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; 0.1–1, ‘ ’.

The turning point, where revenue maximizes, is calculated as $\sqrt{-{\displaystyle \frac{{\beta }_1}{2{\beta }_2}}}$, where ${\beta }_1$ and ${\beta }_2$ are the coefficients from the log-quadratic model, derived from setting the partial derivative with respect to $\log \left(\mathrm{tax}\mathrm{rate}\right)$ to zero. The resulting value is expressed in percentage points (e.g., a turning point of 0.92 corresponds to a 92% tax rate). This point represents the tax burden (as measured by the Bird Index) at which further rate increases begin to reduce revenue. For example, in Belgium (${\beta }_1=1.3715$, ${\beta }_2=-0.7101$), the turning point is $\sqrt{-{\displaystyle \frac{1.3715}{2\times (-0.7101)}}}\approx \sqrt{0.9658}\approx 0.983$, implying maximum revenue near a Bird Index of approximately 0.98 (close to the sample maximum, indicating operation near or beyond the peak). In contrast, Cyprus (${\beta }_1=0.6885$, ${\beta }_2=-0.0994$) yields a turning point of $\sqrt{-{\displaystyle \frac{0.6885}{2\times (-0.0994)}}}\approx \sqrt{3.464}\approx 1.86$, well above observed Bird Index values, suggesting room for rate increases without revenue loss. Bulgaria (${\beta }_1=3.4293$, ${\beta }_2=-0.6980$) shows a turning point at $\sqrt{-{\displaystyle \frac{3.4293}{2\times (-0.6980)}}}\approx \sqrt{2.457}\approx 1.57$, again indicating potential for higher rates. These examples, selected for their statistical robustness and contrasting positions, highlight heterogeneity in fiscal space across EU states.

Table 9 presents the quadratic coefficient results for personal income tax (PIT) revenue, offering a detailed examination of how PIT rates influence revenue across selected EU countries. The dependent variable, the logarithm of PIT revenue, is regressed against a quadratic function of tax rates, with ${\beta }_0$, ${\beta }_1$, and ${\beta }_2$ capturing the intercept, linear, and quadratic effects, respectively. The consistently negative ${\beta }_2$ coefficients (e.g., $-1.3393$ for Finland, $-1.4167$ for Italy, $-0.5366$ for France) confirm the Laffer Curve’s inverted U-shape, where increasing PIT rates initially boost revenue but eventually lead to declines due to disincentives such as reduced labor supply or tax avoidance. The high statistical significance of these coefficients, particularly for France ($F=299.20,p<0.001$) and Croatia ($F=134.40,p<0.001$), indicates strong evidence of the Laffer Curve effect in these countries. Notably, Italy’s large ${\beta }_0\left(4.3815\right)$ and ${\beta }_2(-1.4167)$ suggest a pronounced sensitivity of PIT revenue to tax rate changes, potentially reflecting a complex tax system or high tax evasion rates, as discussed in the literature review section on tax burden and evasion. In contrast, Slovakia’s ${\beta }_2$ coefficient $(-0.2668)$ is only marginally significant $(p<0.1)$, suggesting a weaker Laffer Curve effect, possibly due to its relatively flat tax structure, which may limit behavioral responses to tax rate changes. The high F-statistics across most countries (e.g., $134.40$ for Croatia, $61.50$ for Poland) indicate robust model fit, reinforcing the reliability of the quadratic specification in capturing the non-linear dynamics of PIT revenue.

Table 9. Quadratic coefficient results for personal income tax per country.

	Dependent Variable: $\mathbf{log}(\mathbf{PIT} \mathbf{Revenue})$
	Independent Variables
Country	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
Croatia	$-0.0185$ ***	$1.9510$ ***	$-0.5633$ **	$134.40$ ***	27
Finland	$2.2216$ ***	$2.2076$ ***	$-1.3393$ ***	$9.14$ ***	28
France	$3.3887$ ***	$0.9098$ ***	$-0.5366$ ***	$299.20$ ***	28
Italy	$4.3815$ ***	$2.7582$ ***	$-1.4167$ **	$23.90$ ***	28
Poland	$1.3387$ ***	$1.0836$ ***	$-0.5722$ **	$61.50$ ***	28
Slovakia	$-0.0125$ **	$1.0501$ ***	${-0.2668}^{.}$	$114.20$ ***	27
Slovenia	$-0.0184$ ***	$1.4872$ ***	${-0.3997}^{.}$	$43.23$ ***	27

Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; >0.1–1, ‘ ’.

Table 9. Quadratic coefficient results for personal income tax per country.

	Dependent Variable: $\mathbf{log}(\mathbf{PIT} \mathbf{Revenue})$
	Independent Variables
Country	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
Croatia	$-0.0185$ ***	$1.9510$ ***	$-0.5633$ **	$134.40$ ***	27
Finland	$2.2216$ ***	$2.2076$ ***	$-1.3393$ ***	$9.14$ ***	28
France	$3.3887$ ***	$0.9098$ ***	$-0.5366$ ***	$299.20$ ***	28
Italy	$4.3815$ ***	$2.7582$ ***	$-1.4167$ **	$23.90$ ***	28
Poland	$1.3387$ ***	$1.0836$ ***	$-0.5722$ **	$61.50$ ***	28
Slovakia	$-0.0125$ **	$1.0501$ ***	${-0.2668}^{.}$	$114.20$ ***	27
Slovenia	$-0.0184$ ***	$1.4872$ ***	${-0.3997}^{.}$	$43.23$ ***	27

Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; >0.1–1, ‘ ’.

The turning point represents the PIT rate at which revenue is maximized. For France (${\beta }_1=0.9098$, ${\beta }_2=-0.5366$), it occurs at $\sqrt{-{\displaystyle \frac{0.9098}{2\times (-0.5366)}}}\approx \sqrt{0.847}\approx 0.92$ (or 92% effective rate), a level far exceeding typical top marginal rates, indicating substantial fiscal space before reaching the revenue peak. In contrast, Italy (${\beta }_1=2.7582$, ${\beta }_2=-1.4167$) has a turning point at $\sqrt{-{\displaystyle \frac{2.7582}{2\times (-1.4167)}}}\approx \sqrt{0.974}\approx 0.99$ (99%), suggesting operation near or beyond the peak, consistent with high progressive taxation and potential overtaxation. Croatia (${\beta }_1=1.9510$, ${\beta }_2=-0.5633$) yields a turning point of $\sqrt{-{\displaystyle \frac{1.9510}{2\times (-0.5633)}}}\approx \sqrt{1.732}\approx 1.32$ (132%), well above observed rates, implying room for rate increases without revenue loss. These examples—chosen for strong statistical fit and policy relevance—illustrate diverse positions on the Laffer Curve, with larger, high-tax economies like Italy closer to the downward slope, while others retain upward potential. These results support the study’s policy implications, particularly the suggestion that larger economies like France may be overtaxing, leading to revenue losses, and highlight the need for tailored tax policies that account for country-specific economic conditions and taxpayer behavior.

Table 10 focuses on the quadratic coefficient results for corporate income tax (CIT) revenue, providing insights into how CIT rates affect revenue generation in selected EU countries. The negative ${\beta }_2$ coefficients (e.g., $-0.5391$ for Bulgaria, $-0.4912$ for Czechia, $-0.7404$ for Finland) confirm the Laffer Curve effect for CIT, where excessively high corporate tax rates reduce revenue by discouraging investment or encouraging profit shifting. The statistical significance of these coefficients varies, with Czechia and Latvia showing strong significance $(p<0.001)$ and high F-statistics ($18.90$ and $388.60$, respectively), indicating robust evidence of the Laffer Curve effect. Finland’s ${\beta }_2$ coefficient $(-0.7404)$ is significant at the $0.01$ level, but its lower F-statistic $(2.93,p<0.1)$ suggests weaker explanatory power, possibly due to Finland’s unique economic structure or tax incentives that mitigate the impact of high CIT rates. Countries like Croatia, Cyprus, and Germany have marginally significant ${\beta }_2$ coefficients $(p<0.1)$, suggesting that the Laffer Curve effect may be less pronounced, potentially due to lower baseline CIT rates or effective tax enforcement mechanisms. The high F-statistic for Latvia $\left(388.60\right)$ stands out, indicating an exceptionally strong model fit, possibly driven by Latvia’s economic reforms and sensitivity to tax rate changes during the study period.

The turning point represents the CIT rate at which revenue is maximized. For Latvia (${\beta }_1=1.0494$, ${\beta }_2=-0.4100$), it occurs at $\sqrt{-{\displaystyle \frac{1.0494}{2\times (-0.4100)}}}\approx \sqrt{1.279}\approx 1.13$ (113%), far above typical statutory rates, implying substantial room for rate increases before revenue declines. In contrast, Finland (${\beta }_1=0.6119$, ${\beta }_2=-0.7404$) yields a turning point of $\sqrt{-{\displaystyle \frac{0.6119}{2\times (-0.7404)}}}\approx \sqrt{0.413}\approx 0.64$ (64%), suggesting that current rates may already exceed the revenue-maximizing level, consistent with potential overreliance on corporate taxation. Czechia (${\beta }_1=1.8453$, ${\beta }_2=-0.4912$) has a turning point at $\sqrt{-{\displaystyle \frac{1.8453}{2\times (-0.4912)}}}\approx \sqrt{1.879}\approx 1.37$ (137%), indicating significant fiscal space. These examples, selected for statistical strength and contrasting implications, highlight varied positions on the CIT Laffer Curve, with high-tax environments like Finland potentially on the prohibitive side, while reform-oriented economies like Latvia retain upward potential. These findings align with the study’s discussion of fiscal effort, which emphasizes the importance of aligning tax rates with economic potential to maximize revenue without stifling corporate activity. The results suggest that countries like Hungary and Lithuania, with significant ${\beta }_2$ coefficients ($-0.4679$ and $-0.5448$, respectively), may benefit from reducing CIT rates to move closer to the revenue-maximizing point on the Laffer Curve.

Table 10. Quadratic coefficient results for corporate income tax per country.

	Dependent Variable: $\mathbf{log}(\mathbf{CIT} \mathbf{Revenue})$
	Independent Variables
Country	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
Bulgaria	$0.7176$ ***	$0.5230$ ***	${-0.5391}^{.}$	$8.20$ ***	28
Croatia	$-0.0192$	$1.0700$ ***	${-0.1819}^{.}$	$29.65$ ***	27
Cyprus	$-0.0061$	$0.9962$ ***	${-0.3219}^{.}$	$10.11$ ***	27
Czechia	$-0.0094$	$1.8453$ ***	$-0.4912$ ***	$18.90$ ***	27
Finland	$0.8754$ ***	$0.6119$ **	$-0.7404$ **	${2.93}^{.}$	28
Germany	$-0.0119$	$0.8698$ ***	${-0.2424}^{.}$	$25.52$ ***	27
Hungary	$-0.0312$	$1.5514$ ***	$-0.4679$ **	$35.50$ ***	27
Latvia	$-0.0303$	$1.0494$ ***	$-0.4100$ ***	$388.60$ ***	27
Lithuania	$-0.0143$	$1.1588$ ***	$-0.5448$ ***	$168.50$ ***	27
Slovenia	$-0.0092$	$0.8728$ ***	$-0.3734$ **	$32.93$ ***	27

Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; >0.1–1, ‘ ’.

Table 10. Quadratic coefficient results for corporate income tax per country.

	Dependent Variable: $\mathbf{log}(\mathbf{CIT} \mathbf{Revenue})$
	Independent Variables
Country	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
Bulgaria	$0.7176$ ***	$0.5230$ ***	${-0.5391}^{.}$	$8.20$ ***	28
Croatia	$-0.0192$	$1.0700$ ***	${-0.1819}^{.}$	$29.65$ ***	27
Cyprus	$-0.0061$	$0.9962$ ***	${-0.3219}^{.}$	$10.11$ ***	27
Czechia	$-0.0094$	$1.8453$ ***	$-0.4912$ ***	$18.90$ ***	27
Finland	$0.8754$ ***	$0.6119$ **	$-0.7404$ **	${2.93}^{.}$	28
Germany	$-0.0119$	$0.8698$ ***	${-0.2424}^{.}$	$25.52$ ***	27
Hungary	$-0.0312$	$1.5514$ ***	$-0.4679$ **	$35.50$ ***	27
Latvia	$-0.0303$	$1.0494$ ***	$-0.4100$ ***	$388.60$ ***	27
Lithuania	$-0.0143$	$1.1588$ ***	$-0.5448$ ***	$168.50$ ***	27
Slovenia	$-0.0092$	$0.8728$ ***	$-0.3734$ **	$32.93$ ***	27

Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; >0.1–1, ‘ ’.

Table 11 examines the quadratic coefficient results for value-added tax (VAT) revenue, offering a comprehensive analysis of how VAT rates influence revenue across a broader set of EU countries. The negative ${\beta }_2$ coefficients (e.g., $-0.6154$ for Belgium, $-0.6638$ for Slovenia, $-0.7039$ for Sweden) confirm the Laffer Curve effect for VAT, where high VAT rates may reduce revenue by decreasing consumption or increasing tax evasion. The statistical significance of these coefficients is generally strong, with countries like Bulgaria $(F=358.30,p<0.001$) and Malta $(F=818.30,p<0.001)$ showing exceptionally high F-statistics, indicating robust model fit and strong evidence of the Laffer Curve effect. The large negative ${\beta }_2$ for Sweden $(-0.7039)$ suggests a pronounced sensitivity of VAT revenue to rate increases, consistent with the high tax burden in Nordic countries noted in the literature review. In contrast, countries like the Netherlands and Sweden have lower F-statistics ($2.57$ and $3.16$, respectively, $p<0.1$), indicating weaker model explanatory power, possibly due to stable consumption patterns or effective VAT enforcement mechanisms that mitigate revenue losses at higher rates. The variation in the number of observations (e.g., 24 for Croatia and Slovenia, 23 for Malta) reflects data availability differences, particularly for newer EU members, but does not appear to compromise the overall robustness of the findings.

The turning point represents the VAT rate at which revenue is maximized. For Malta (${\beta }_1=0.7718$, ${\beta }_2=-0.1771$), it occurs at $\sqrt{-{\displaystyle \frac{0.7718}{2\times (-0.1771)}}}\approx \sqrt{2.179}\approx 1.48$ (148%), far above standard rates, indicating substantial fiscal space for rate increases without revenue loss. In contrast, Belgium (${\beta }_1=0.9984$, ${\beta }_2=-0.6154$) yields a turning point of $\sqrt{-{\displaystyle \frac{0.9984}{2\times (-0.6154)}}}\approx \sqrt{0.811}\approx 0.90$ (90%), suggesting operation near or slightly beyond the revenue peak, especially when considering effective rates across multiple VAT bands. Slovenia (${\beta }_1=1.3195$, ${\beta }_2=-0.6638$) has a turning point at $\sqrt{-{\displaystyle \frac{1.3195}{2\times (-0.6638)}}}\approx \sqrt{0.994}\approx 1.00$ (100%), implying proximity to the maximum, consistent with its high standard rate and compliance challenges. These examples, selected for strong statistical support and policy contrast, illustrate heterogeneity in VAT efficiency: smaller, high-enforcement economies like Malta retain upward potential, while mature high-tax systems like Belgium and Slovenia may already face diminishing returns. These results reinforce the study’s policy implications, suggesting that countries with high VAT rates, such as Belgium and Slovenia, may be operating beyond the revenue-maximizing point, necessitating rate adjustments to enhance fiscal efficiency.

Table 11. Quadratic coefficient results for value-added tax per country.

	Dependent Variable: $\mathbf{log}(\mathbf{VAT} \mathbf{Revenue})$
	Independent Variables
Country	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
Belgium	$1.8130$ ***	$0.9984$ ***	$-0.6154$ **	$8.43$ **	28
Bulgaria	$-0.4625$ ***	$0.8624$ ***	$-0.2758$ ***	$358.30$ ***	28
Croatia	$-0.0098$ *	$1.3855$ ***	$-0.4182$ **	$23.45$ ***	24
Cyprus	$-0.0102$	$0.9798$ ***	$-0.2901$ **	$85.27$ ***	27
Czechia	$-0.0092$	$1.1978$ ***	$-0.4917$ **	$16.12$ ***	27
Estonia	${-0.0136}^{.}$	$1.2126$ ***	$-0.4152$ **	$50.71$ ***	27
Finland	$1.1551$ ***	$0.8004$ ***	$-0.3940$ ***	$49.39$ ***	28
Ireland	$-0.0103$ **	$0.8857$ ***	${-0.1714}^{.}$	$91.51$ ***	27
Latvia	$-0.0114$	$0.9860$ ***	${-0.3027}^{.}$	$66.55$ ***	27
Lithuania	$-0.0080$	$1.0519$ ***	$-0.3732$ **	$65.07$ ***	27
Malta	$-2.2083$ ***	$0.7718$ ***	$-0.1771$ **	$818.30$ ***	23
Netherlands	$-0.0030$	$0.9145$ **	${-0.4992}^{.}$	${2.57}^{.}$	27
Romania	$0.5637$ ***	$0.8148$ ***	${-0.2452}^{.}$	$217.60$ ***	28
Slovakia	$-0.0112$	$1.3858$ ***	$-0.5973$ ***	$27.82$ ***	27
Slovenia	$-0.2583$ ***	$1.3195$ ***	$-0.6638$ ***	$216.30$ ***	24
Spain	$-0.0122$ **	$1.0388$ ***	$-0.2123$ ***	$238.50$ ***	27
Sweden	$0.0054$	$0.8717$ **	$-0.7039$ **	${3.16}^{.}$	27

Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; >0.1–1, ‘ ’.

Table 11. Quadratic coefficient results for value-added tax per country.

	Dependent Variable: $\mathbf{log}(\mathbf{VAT} \mathbf{Revenue})$
	Independent Variables
Country	${\mathit{\beta }}_{\mathbf{0}}$	${\mathit{\beta }}_{\mathbf{1}}$	${\mathit{\beta }}_{\mathbf{2}}$	$\mathit{F}$-Statistic	No. of Obs.
Belgium	$1.8130$ ***	$0.9984$ ***	$-0.6154$ **	$8.43$ **	28
Bulgaria	$-0.4625$ ***	$0.8624$ ***	$-0.2758$ ***	$358.30$ ***	28
Croatia	$-0.0098$ *	$1.3855$ ***	$-0.4182$ **	$23.45$ ***	24
Cyprus	$-0.0102$	$0.9798$ ***	$-0.2901$ **	$85.27$ ***	27
Czechia	$-0.0092$	$1.1978$ ***	$-0.4917$ **	$16.12$ ***	27
Estonia	${-0.0136}^{.}$	$1.2126$ ***	$-0.4152$ **	$50.71$ ***	27
Finland	$1.1551$ ***	$0.8004$ ***	$-0.3940$ ***	$49.39$ ***	28
Ireland	$-0.0103$ **	$0.8857$ ***	${-0.1714}^{.}$	$91.51$ ***	27
Latvia	$-0.0114$	$0.9860$ ***	${-0.3027}^{.}$	$66.55$ ***	27
Lithuania	$-0.0080$	$1.0519$ ***	$-0.3732$ **	$65.07$ ***	27
Malta	$-2.2083$ ***	$0.7718$ ***	$-0.1771$ **	$818.30$ ***	23
Netherlands	$-0.0030$	$0.9145$ **	${-0.4992}^{.}$	${2.57}^{.}$	27
Romania	$0.5637$ ***	$0.8148$ ***	${-0.2452}^{.}$	$217.60$ ***	28
Slovakia	$-0.0112$	$1.3858$ ***	$-0.5973$ ***	$27.82$ ***	27
Slovenia	$-0.2583$ ***	$1.3195$ ***	$-0.6638$ ***	$216.30$ ***	24
Spain	$-0.0122$ **	$1.0388$ ***	$-0.2123$ ***	$238.50$ ***	27
Sweden	$0.0054$	$0.8717$ **	$-0.7039$ **	${3.16}^{.}$	27

Significance codes: 0–0.001, ‘***’; >0.001–0.01, ‘**’; >0.01–0.05, ‘*’; >0.05–0.1, ‘^.’; >0.1–1, ‘ ’.

Integrating these findings with the broader context of the study, the tables collectively provide compelling evidence of the Laffer Curve effect across different tax types in the EU member states. The negative quadratic coefficients across all tables confirm that excessively high tax rates lead to revenue losses, supporting the study’s argument that larger economies may face inefficiencies due to overtaxation. The use of the Bird Index in Table 8 adds a novel dimension by assessing overall tax efficiency, revealing that countries like Italy and Belgium may be particularly vulnerable to revenue losses due to high tax burdens. The advanced econometric methodology, including the Hausman Test and log-quadratic regression, ensures that the results are robust and account for country-specific factors, as emphasized in the methodology section. The policy implications are clear: EU member states must carefully calibrate tax rates to balance revenue generation with economic incentives, with smaller economies like Latvia and Malta potentially benefiting from lower rates to stimulate growth, while larger economies may need to reduce rates to avoid revenue losses. The literature review’s discussion of tax evasion and fiscal effort further contextualizes these findings, highlighting the role of compliance and economic potential in shaping revenue outcomes. Overall, these tables provide a critical empirical foundation for evidence-based tax policy recommendations, advancing the understanding of tax optimization in the European Union.

5. Conclusions

This study provides a comprehensive examination of the Laffer Curve’s applicability within the European Union, offering significant insights into the complex relationship between taxation and fiscal revenue across personal income tax (PIT), corporate income tax (CIT), and value-added tax (VAT). By leveraging an extensive panel data set spanning 1995 to 2022 and covering all 27 EU member states, the research establishes that the relationship between tax rates and revenue is inherently non-linear, as hypothesized by the Laffer Curve. The empirical findings confirm that there exists an optimal tax rate for each tax category, beyond which further increases lead to diminishing returns. This phenomenon is driven by factors such as heightened tax evasion, reduced economic activity, and weakened incentives for production and investment, which become particularly pronounced in larger economies. In these countries, the analysis reveals that excessively high tax rates have likely contributed to revenue losses, highlighting the critical need for strategic adjustments to tax policies to maximize fiscal outcomes while fostering economic growth.

The incorporation of the Bird Index into the analysis represents a significant advancement, providing a nuanced measure of fiscal effort that complements the Laffer Curve framework. By assessing the efficiency of tax collection relative to economic capacity, the Bird Index reveals substantial variations in tax performance across EU member states. For instance, smaller economies with lower tax rates often exhibit higher fiscal efficiency, suggesting that moderate tax regimes can enhance revenue collection without stifling economic activity. In contrast, high-tax jurisdictions face challenges in maintaining revenue growth due to behavioral responses such as reduced labor supply or capital flight. This cross-country comparison underscores the importance of tailoring tax policies to the specific economic and institutional contexts of each member state, ensuring that tax systems are both equitable and conducive to long-term fiscal sustainability.

The estimated revenue-maximizing thresholds exhibit considerable variation across tax categories and EU member states, yet turning points for personal income tax (PIT) and corporate income tax (CIT) are broadly comparable to those for value-added tax (VAT) in countries with statistically significant Laffer Curve effects. PIT peaks range from 91% (Finland) to 140% (Slovakia), CIT from 64% (Finland) to 171% (Croatia), and VAT from 79% (Sweden) to 161% (Ireland), with substantial overlap in the 90–140% interval across all three tax types. This similarity reflects comparable behavioral sensitivities: direct taxes (PIT and CIT) deter labor and investment, while indirect taxes (VAT) curb consumption, yielding revenue ceilings that are more alike than distinct in practice.

Methodologically, the study employs advanced econometric techniques to ensure the robustness of its findings. The application of the Hausman Test facilitates the selection of appropriate fixed or random effects models, accounting for unobserved heterogeneity across countries. Additionally, the use of log-quadratic regression models effectively captures the non-linear dynamics of the Laffer Curve, allowing for precise estimation of revenue-maximizing tax rates. These rates vary by tax type and country, with the analysis indicating that PIT and CIT thresholds are generally lower than those for VAT, reflecting the differing behavioral impacts of these taxes. For example, high PIT rates may discourage labor participation, while elevated CIT rates can deter investment and entrepreneurship, both of which undermine revenue potential. The identification of these thresholds provides actionable insights for policymakers, enabling them to design tax systems that balance revenue needs with economic incentives.

The policy implications of this study are particularly relevant for the EU member states, where fiscal harmonization remains a contentious issue. The findings suggest that policymakers should prioritize tax policies that avoid pushing rates beyond their revenue-maximizing thresholds, as this can lead to adverse economic outcomes without corresponding fiscal gains. For larger economies, reducing excessively high tax rates could stimulate economic activity and broaden the tax base, ultimately increasing revenue. Conversely, smaller economies with already efficient tax systems may benefit from maintaining moderate rates while focusing on administrative improvements to curb tax evasion. The study also highlights the importance of considering macroeconomic indicators, such as GDP growth and inflation (captured via the GDP deflator), when designing tax policies, as these factors influence the revenue potential of different tax categories.

Furthermore, this research contributes to the broader literature on public finance by integrating the Laffer Curve with the Bird Index, offering a novel framework for evaluating tax efficiency in a multi-country context. The comprehensive, 28-year dataset and rigorous econometric approach provide a robust foundation for these findings, addressing gaps in prior studies that often focused on single countries or shorter time periods. By identifying revenue-maximizing tax rates and highlighting the role of fiscal effort, the study equips European Union policymakers with evidence-based tools to optimize tax systems. These tools are critical for balancing the competing demands of funding public services and social programs with the need to maintain economic competitiveness in an increasingly integrated European market.

Finally, the findings of this study should be interpreted in light of several limitations. First, our analysis relies on statutory tax rates as proxies for the overall tax burden. These rates may not fully capture the true effective tax rates experienced by individuals and corporations after accounting for various deductions, exemptions, and credits. Similarly, our definitions of the potential tax base (e.g., $Y_p$) are proxies and may not perfectly represent the complex, real-world base upon which taxes are levied. Second, while our panel data model accounts for country-specific fixed effects, the potential for endogeneity cannot be fully ruled out. It is plausible that tax rates and revenues are jointly determined; for instance, a national-level shock or poor revenue performance could itself trigger policy changes in tax rates, a reverse-causality dynamic that our model does not explicitly address. Third, our model does not control for significant cross-country heterogeneity in tax enforcement and compliance. Differences in the efficiency of tax administration, the size of the shadow economy, and varying levels of unobserved institutional quality (such as perceived corruption or political stability) undoubtedly influence the tax-revenue relationship.

These limitations highlight valuable avenues for future research. For instance, exploring the interaction between tax policies and other fiscal instruments, such as public spending or debt management, could provide a more holistic understanding of fiscal sustainability. Another topic could be the use of micro-data to construct more precise effective tax rates or the inclusion of specific governance indicators as control variables. Additionally, extending the analysis to incorporate dynamic effects, such as the long-term impact of tax changes on economic growth, could further refine the identification of optimal tax rates. The study’s framework could also be applied to other regional or global contexts to assess the generalizability of the Laffer Curve and Bird Index in diverse economic settings.

In conclusion, this research underscores the critical importance of well-calibrated tax policies in the EU member states, offering a robust empirical and methodological foundation for policymakers to enhance fiscal sustainability while promoting economic vitality across member states.