Too much or too little? Assessing the optimal size of government in inclusive development

University of Minho School of Economics and Management Francisco Tomaz Cabeleira Too much or too little? Assessing the optimal size of government in inclusive development march 2025 University of Minho School of Economics and Management Francisco Tomaz Cabeleira Too much or too little? Assessing the optimal size of government in inclusive development Master’s Dissertation in Economics Dissertation supervised by Professor Francisco José Alves Coelho Veiga march 2025 Copyright and Terms of Use for Third Party Work This dissertation reports on academic work that can be used by third parties as long as the internationally accepted standards and good practices are respected concerning copyright and related rights. This work can thereafter be used under the terms established in the license below. Readers needing authorization conditions not provided for in the indicated licensing should contact the author through the RepositóriUM of the University of Minho. License granted to users of this work: CC BY-NC-ND https://creativecommons.org/licenses/by-nc-nd/4.0/ i Acknowledgements I hereby express my gratitude to all who, directly or indirectly, contributed to the elaboration of this dissertation, whether through supervision or crucial insights. Special recognition goes to my supervisor, Professor Francisco Veiga, for his invaluable guidance and time, which were indispensable for the realization and subsequent improvement of this work. His mentorship was not only commendable and supportive but also excelled in both academic expertise and approachability. I also acknowledge the remarkable importance of external judgment and the exchange of information and opinions with others. Therefore, I would like to extend my gratitude to my family, as well as to my friends, particularly my colleagues Pedro Machado and Francisco Ribeiro, who, as fellow work and academic peers, played a crucial role in discussing topics of both academic and non-academic nature. Their concern and support are also greatly cherished. ii Statement of Integrity I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho. University of Minho, Braga, march 2025 Francisco Tomaz Cabeleira iii Abstract This article aims to contribute to the growing body of research on the optimal size of government when examining non-traditional economic development metrics, specifically by being the first to depict evidence of the Armey Curve for the Inequality-adjusted Human Development Index (IHDI). Furthermore, the evidence, or the variation of optimal government size according to metrics of development, is scarce, and as such this study attempts to test an undermining of the role of government present in the literature, a direct consequence of wrongly proxying welfare by normative economic indicators. The study also attempts to avoid the incorrectly ignored effects of governance by composing a variable of institutional quality through the use of world governance indicators. The results provide evidence of an optimal size of government ranging from 27.22% to 32.54% for Gross Domestic Product (GDP), 33.34% to 42.20% for Human Development Index (HDI), and lastly, 31.23% to 40.69% for IHDI. The results imply that the dependent variable used makes a considerable difference in the optimal size of government computed, nonetheless, it exhibits that while worldwide government size is not overgrown, the broad sentiment of overbearing government presence is factual, at least for the Western World. The results also imply a stronger connection between government size and economic prosperity for developing countries, which contradicts the current literature. Additionally, findings suggest that it is possible that the more disadvantaged a country is in terms of development, the more easily it can derive utility from development policies related to interventions in government size. A study of expenditure components was also conducted, in which public consumption was inferred to report higher evidence of the Armey Curve than public investment. Results also exhibited that for the Classification of the Function of Government (COFOG) components, expenditure in public order and safety emerged as the most fundamental element in the promotion of economic growth (GDP), development (HDI), and even inclusive development (IHDI). Keywords Optimal size of government, Inclusive economic development, Economic development, Economic growth, Composition of public expenditure iv Resumo Este artigo pretende contribuir para o crescente corpo de investigação sobre a dimensão ótima do estado quando se examinam métricas de desenvolvimento económico não tradicionais, especificamente por ser o primeiro a apresentar provas da Curva de Armey para o IHDI. Além disso, a evidência, ou a variação da dimensão ótima do estado de acordo com as métricas de desenvolvimento, são escassas e, como tal, este artigo tenta testar a subvalorização do papel do estado presente na literatura, uma consequência direta de uma representação falaciosa do bem-estar através de indicadores económicos normativos. O estudo também tenta evitar os efeitos erradamente ignorados da governança, compondo uma variável de qualidade institucional através da utilização dos indicadores de governança global. Os resultados fornecem provas de uma dimensão ótima do estado que varia entre 27,22% e 32,54% para o GDP, 33,34% e 42,20% para o HDI e, por último, 31,23% e 40,69% para o IHDI. Os resultados implicam que a variável dependente utilizada faz uma diferença considerável na dimensão ótima do estado calculada, no entanto, mostra que, embora a dimensão do estado a nível mundial não seja excessiva, o sentimento geral de uma presença exagerada do estado é factual, pelo menos para o Mundo Ocidental. Os resultados também sugerem uma ligação mais forte entre o peso do estado e a prosperidade económica nos países em desenvolvimento, o que contraria a literatura atual. Além disso, os resultados sugerem que é possível que quanto mais desfavorecido for um país em termos de desenvolvimento, maior facilidade terá em extrair utilidade de políticas de desenvolvimento relacionadas com alterações no tamanho do estado. Foi também efetuado um estudo das componentes da despesa, em que se inferiu que o consumo público apresenta maior evidência da Curva de Armey do que o investimento público. Os resultados também mostram que, para os componentes COFOG, as despesas com ordem e segurança pública emergem como o elemento mais fundamental na promoção do crescimento económico (GDP), do desenvolvimento (HDI) e mesmo do desenvolvimento inclusivo (IHDI). Palavras-chave Dimensão óptima do estado, Desenvolvimento económico inclusivo, Desenvolvimento económico, Crescimento económico, Composição da despesa pública v Contents 1 Introduction 1 2 Literature review 4 2.1 The measurement and historical dynamics of government size ............. 4 2.1.1 How should we measure the size of government? ............... 4 2.1.2 The history of government intervention .................... 5 2.2 The role of governments: A review of the literature ................... 8 2.2.1 The economic and social role of government ................. 8 2.2.2 Development and economic growth ...................... 10 2.2.3 Prior scholarship ............................... 13 2.3 The influence of governance and the importance of expenditure allocation ....... 16 2.3.1 Government quality .............................. 16 2.3.2 Expenditure components. Do they all matter? ................. 18 3 Methodology and data 20 3.1 Data source and descriptive statistics ......................... 20 3.1.1 Dataset construction ............................. 20 3.1.2 Descriptive statistics and preliminary results ................. 25 3.2 Econometric methodology ............................... 32 3.2.1 Econometric approach for economic growth indicators ............. 32 3.2.2 Econometric approach for economic development indicators .......... 36 4 Results 39 4.1 Main analysis ..................................... 39 4.1.1 Benchmark results .............................. 39 4.1.2 Components of governance .......................... 50 vi VIF Variance Inflation Factor. 23 WB World Bank. 16,21,22,24,28,30,31,88,89,90,91 xiii 1 Introduction Many may ask why the debate about government intervention is still going, even after extensive research regarding its optimal size. The reason partly relies on the substantial divergence in the methodologies and metrics used (Bergh and Henrekson,2011)1. For various decades, most academics have focused on employing the GDP to represent the prosperity of nations worldwide, which has proven useful in unveiling crucial insights about the importance of a central government in establishing a solid foundation for economic prosperity (Mahler 1992;Berry and Lowery 1984). The size of government macroeconomically supports itself through the implications that various models suggest. Many development and growth models, such as the Solow-Swan (Solow,1956), establish that given diminishing returns of production factors, countries would have a harder time continuing to grow after some benchmark. Governments would need some level of presence in economic activity to escape this curse of decreasing marginal returns to growth. Accordingly, other models, such as Romer (1986), depict that at the aggregate level, diminishing marginal returns can be avoided, allowing growth to be self-sustaining through the proliferation of positive externalities that the exchange of know-how (“learningby-doing”) may permit. In this context, the government appears essential, given that it represents the entity responsible for providing the services, such as basic infrastructure and education, that allow for the transfer and proliferation of that know-how. Nonetheless, other models, such as Barro (1990) and Barro and Sala-i-Martin (1995), refer to the fact that there are optimal taxation levels, and by association, optimal government presence, in which the positive externalities are augmented relative to the economic distortions that the required taxes impose. This relationship is similar to that of the Armey Curve, which depicts that there is a point at which the size of government is optimal to promote economic growth, given that after a certain point, augmented governmental presence would only have detrimental effects on growth (Vedder and Gallaway,1998). This research aims to help solve that dilemma, not in the context of optimal taxation, but for a proxy, 1The author also depicts that literature is full of contradictory findings that are not explained just because of the variation in the definitions but also due to the heterogeneity in the countries studied. 1 which is the size of government. Most literature on this topic points to Gross Domestic Product (GDP) as the determinant fact to be maximised, but given the amount of criticism that it received from many Nobel laureates, such as Kuznets (1941), Hicks (1948), and Nordhaus and Tobin (1972)2, as a flawed measure of standard of living, I argue that a more useful goal would be to attempt to assess the government size that maximises a more inclusive measure of economic development. A metric that addresses aspects beyond the monetary would present itself as more adequate to overcome the possible bias that may arise when assessing the optimal size of government with normative metrics such as the GDP, since it greatly overlooks nonconventional interventions that the government enacts, namely in treating social issues and dealing with inequality (van den Bergh,2009). The Human Development Index (HDI) could be an alternative to solve this issue, serving as an improvement from the previous methodologies, with some works such as Martins and Veiga (2014) and Davies (2009) already using it as a benchmark to more adequately improve the computations of the optimal size of government. Nonetheless, as suggested by van den Bergh (2009) and Sagar and Najam (1998), given various measurability problems, it still fails to include some relevant dynamics, with greater emphasis on inequality, a growing concern in modern times. During various years the issue remained unresolved, however, Alkire and Foster (2010) addressed this shortcoming by attempting to reinforce the metric of HDI by discounting inequality in all its subcomponents (health, education, and standard of living). The resulting new metric is designated as the Inequality-adjusted Human Development Index (IHDI). This is the main metric this study attempts to use to enhance the lack of evidence on optimal government size for measures of economic development. Additionally, given the broad evidence regarding the relevance of the quality of government in promoting economic growth and development, such as Acemoglu et al. (2001) and Nirola and Sahu (2019), this dissertation also strives to disentangle the possible mixed-up effects that previous academia may have overlooked through the incorporation and analysis of governance. After this introduction, I present Part 2, which reflects the literature review, where the academic foundations related to the measurement of government size are depicted, alongside any theory necessary for a better understanding of the relationship between government size and economic prosperity, coupled with previous empirical evidence exhibited by other authors. Then, Part 3, the methodology and data, displays how the databases were constructed alongside their data sources. Additionally, this section also describes any database dynamics while trying to assess preliminary results. It also reports the econometric models used to extrapolate the results, coupled with 2The economic study has been blindly obedient to aggregate material progress, neglecting the distortion of national priorities, the worsening of the income distribution, and the environmental damages that it poses. 2 the rationale for the variables used. Following, Part 4, the results, are presented, where any relevant finding is reported, while also trying to compare how it relates to the hypothesis made and to the previous evidence. Here a robustness analysis is also carried out to guarantee the strength of the conclusions, while also using the results to infer adequate policymaking decisions and advocating for further academic research on appropriate topics. Finally, Part 5, the conclusion, wraps up the significant and novel inferences, depicting how they serve to enhance the present scholarship. 3 2 Literature review 2.1 The measurement and historical dynamics of government size 2.1.1 How should we measure the size of government? Economic underperformance and political instability, namely in the ”old world” , have created an emergence in the discussion of governmental presence in the economy, with different electorates advocating for distinct government approaches as well as pushing narratives that are better aligned with the interests of their class-defined core political constituencies (Hibbs,1977). Disregarding ideological biases, those political narratives still present some logical reasoning for their statements, given that the government not only has the purpose of sustaining social cohesion but also, at the same time, guaranteeing stable economic growth in the long term (Aranson and Ordeshook 1981;Tanzi and Schuknecht 1997).1 Consequently, I argue that the government’s real objective should be determining the optimal equilibrium of governmental presence that maximises both social and economic conditions. Nonetheless, although the broad concept of government size is common, there is no standard framework to compute it since there are numerous indicators and methods to do so (Di Matteo 2013;Vedder and Gallaway 1998). Moreover, the reason why scholarship related to government size is quite heterogeneous, frequently producing conflicting results, derives substantially from the distinct measurements and definitions of government size employed by the different authors (Bergh and Henrekson,2011). There is no definitive answer to which measurement of government size is the most accurate one, with many authors using, for instance, the total number of government employees, other nominal expenditures, and even revenues as a percentage of GDP (Labonte,2010). Nonetheless, Labonte (2010) states that there are two main ways by which we can measure government that are commonly accepted to be more 1Aranson and Ordeshook (1981) state that few can deny the beneficial effects of government intervention in domains such as national defence, police protection, and common-law courts. 4 prominent. More specifically, measuring government size according to expenditures (outlays) or revenues (receipts). Both ways are methodologically valid, although some authors suggest that the differences exhibited by the two approaches can still be substantial, and thus it is crucial to only opt for one (Labonte, 2010). We can exhibit two main motives as to why expressing government size as expenditures is more appropriate than by revenues. The first relates to the higher volatility of revenue levels, which can only be indirectly influenced by legislators. Revenues depend a lot on economic conditions and are very prone to changes in the short term due to unexplained or uncontrollable factors. Consequently, using it as a proxy for the size of government would, by association, reflect a false perception of a heterogeneous and volatile nature of government size (Labonte,2010). The second reason concerns the possible divergence that may arise in terms of government size when measuring it by revenues compared to outlays, particularly in the context of budget deficits. In this framework, given that budget deficits cannot last forever and need to reach a neutral state sooner or later, a reduction in taxes that is not accordingly matched by a cut in spending does not lead to any reduction of the size of government. Consequently, what takes place is a temporal manipulation of the tax incidence, and the measurement by revenues ends up providing a misleading reference that the size of the government is smaller than it is (Labonte,2010). Accordingly, this work makes use of government spending as its proxy for government size, given that it exhibits an apparent edge when compared with other metrics, especially when it is measured as a percentage of GDP, as depicted by Vedder and Gallaway (1998) and Labonte (2010)2. 2.1.2 The history of government intervention The size of government is rather volatile, given that it changes according to society’s needs in each period. Before World War 1, most economists advocated for a minimal government (”Laissez-faire”) in which its only functions would be the maintenance of law enforcement, administration, and national defence, given the assumed ability of the market to self-regulate.3As depicted in Figure 1, at that time, the average share of public expenditure worldwide was no more than 10% of GDP. Nonetheless, the impact of the 1st World War, in 1914, proposed incremental government intervention both during, due to war efforts, but also after the conflict, given the requirement for public measures and policies to solve poverty, instability, 2Labonte (2010) also exhibited that government expenditures have distinct impacts on the economy, more specifically, in the case of government transfers and government purchases of goods and services. 3The ideology of self-regulating markets, or, in other words, the market economy, was an economic thought that originated in England, which depicted that prices must be allowed to regulate themselves in a system of minimal outside interference. 5 and unemployment (Mueller,2003). Consequently, after the conflict, even though downward pressures of governmental presence were reported, government expenditures did not fall to pre-war levels and consistently continued to grow. The Great Depression, from 1929 until 1939, also presented an important mark in the relevance of government presence in the economy, given the required public incentives that the crisis made imperative (Bernanke, 2000).4 0% 5% 10% 15% 20% 25% 30% 35% 40% 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 Figure 1: World average government size (% of GDP). Source: International Monetary Fund (IMF)/Own Computations. The 2nd World War proposed a similar phenomenon to that of the first one, in which war efforts increased the size of government, and by its end in 1945, the global average weight of government had already surpassed 20% of GDP, which, although suffering a short-term downturn in the following years, kept expanding until the nineties. One foundational factor for that growth appears in the form of the partial emergence of social insurance programs, which Dryzek and Goodin (1986) found to be linked to the events of the 2nd World War, at least for Great Britain. Another reason that partially explains that upsurge derives from the incremental distrust of the idea of a self-regulating market proposed by Adam Smith (Smith, 1776), which was losing relevance to the ideas of other esteemed scholars, more particularly, to those of John Maynard Keynes (Mueller 2003;Bernanke 2000). As Keynes commonly used to state, given the unreasonable long period markets require to self-regulate, governmental intervention is essential to solve issues such as low growth and high unemployment, given that ”in the long run, we are all dead” (Keynes,1923).5Furthermore, given the growing ubiquity of social 4The augmented government intervention during this time was an evident signal that the public was losing confidence in the self-correcting mechanisms of a market economy. 5Keynes suggested that both wages and prices were ”sticky” , in the sense that they were not capable of efficiently responding to market demand, at least in a 6 security systems and non-monetary programs (Mueller,2003), the average size of public expenditure peaked in 1992, when the world average government expenditure was more than 35% of GDP. At the time, there were strong beliefs that most developed nations, particularly in Europe and North America, were in unsustainable tax brackets and had government presence that endangered economic flourishing. Additionally, scholarship criticising the adverse effects of oversized governments became common, with many academics suggesting that the negative externalities exhibited by the public sector could be as bad as those of the private (Gwartney et al. 1998;Mueller 2003). Some of the critiques derive from the economic distortions that the associated income tax burdens originate, namely in the context of loss of efficiency and the blurring of price signals (Mueller,2003). This effect alters the choice between work and leisure, and as exhibited by Alesina and Perotti (1997), the increment of tax brackets in labour can cause an artificial increase in labour costs, which, by association, causes higher unemployment and an overall loss of competitiveness. Overtaxing can also have corruptive effects on the economy by promoting economic activity in the shadow economy and underreporting of revenues. Instead of being influenced to work less, taxes can induce individuals to simply report that they gain less by attempting to receive their income through the underground economy (Mueller,2003). For instance, Andreoni et al. (1998) suggest that this problem is substantial, at least in the United States, where roughly 17% of all potential tax revenue from income tax (federal) is lost due to tax evasion. A large governmental presence can also instigate corruption, given that the provision of public goods and services can have both direct and indirect benefits for individual entities. In this sense, corruption emerges due to the temptation of the private sector to interfere in public decision-making by bribing bureaucrats, which will sacrifice the public interests to those of their own and their corruptors (Mueller, 2003). Nonetheless, corruption can be substantially dealt with by endowing higher compensations, as proposed by Goel and Nelson (1998), who found corruption to be inversely related to the wages paid to the employees of the public sector. However, the affiliated costs of increasing wages to eliminate all corruption are too high and not justifiable for the gains that result from reduced corruption, and in this sense, there will always be a trade-off between bureaucrats’ wages and corruption standards. Subsequently, all these critiques led most nations to undertake slight decreases in the sizes of government in the late nineties, dropping to values similar to those of the early eighties. Nonetheless, the emergence of the global financial crisis made it unreliable for governments to become less present in the reasonable amount of time. 7 economy (Laeven et al.,2010), even when knowing of the dangers of over-interventionism. As of the second decade of the 21st century, although the idea of reducing government still prevails, most nations have been incapable of substantially doing so, even more so with the manifestation of the COVID-19 pandemic (World Bank,2022).6 2.2 The role of governments: A review of the literature 2.2.1 The economic and social role of government Even though the role of government in dealing with shocks, such as crisis and instability, was previously exhibited, it is important to focus on its relevance from a macroeconomic standpoint. To fully explain the macroeconomic role of government per se, we need to first understand the determinants of growth (GDP). The Solow (1956) model is one of the most fundamental frameworks in this context, and it describes that GDP levels are determined by three main factors: capital stock (equipment and buildings available for production), labour (hours worked), and technology. The share of GDP growth that is not explained by labour or capital is what we refer to as the Solow Residual or Total Factor Productivity (TFP), which relates to the effect of technology.7One assumption that this model proposes is economic convergence, given that those production factors, particularly capital and labour, present diminishing returns, thus, without any exogenous change in TFP, all countries conditionally converge (they converge to the same point if they possess the same populational growth rate, savings rate, and capital depreciation rate) to the same GDP per capita in the long run. The proposition for convergence, particularly for absolute convergence, is not homogeneous as of the late 20th and early 21st centuries, given that the evidence worldwide is not broadly supportive and commonly presents opposite implications. The scholarship is substantially divided, with many authors suggesting that convergence holds, even absolutely (Nahar and Inder,2002), and others suggesting the opposite relationship (Quah,1993,1997), and there are even some cases where absolute convergence is dependent on the time frame and set of countries that are used in the analysis (Mathur,2005). The nature of absolute convergence is undoubtedly ambiguous, nonetheless, that relation does not seem to transpose to conditional convergence. Although some authors, such as Nell (2020), exposed no conditional convergence for the post-1989 globalisation era, and Boldrin and Canova (2001) and Canova 6During the pandemic period, there was unprecedented government intervention and regulatory forbearance, with great emphasis on the financial sector, where those policies aided banks in maintaining capital levels and liquidity. 7Increases in TFP are commonly attributed in their entirety to technological progress, nonetheless, it can also be influenced by education and government regulation. 8 and Marcet (1995) provide evidence suggesting that it either is non-existent or simply not substantial enough to strongly affirm its widespread presence, these views are relatively isolated. Most of the growth literature, in contrast, finds empirical evidence of conditional income convergence. The wide bulk of empirical evidence suggests that economies that are placed at lower initial income levels tend to grow at faster rates than those established with higher initial incomes, after controlling for saving and population growth rates, corroborating the commonness of conditional convergence (Barro et al. 1991,1992;Cho and Graham 1996;Kaitila 2004;Nonneman and Vanhoudt 1996;Murthy and Chien 1997). Considering this conflicting reality, one might ask oneself which other factors can help explain growth, as Romer (1986) learning-by-doing model exhibits. His work depicts that even though at the individual level diminishing returns still hold, at the aggregate level, that issue can be dealt with through the proliferation of positive externalities. Those arise due to the exchange of know-how between enterprises, which makes it possible to overcome the problem of diminishing returns, enabling growth to be self-sustaining. This dynamic proposes the relevance of governmental economic presence since the public sector serves as the entity responsible for providing basic research, infrastructure, and education that allows for the proliferation of that know-how and associated positive externalities8. Despite that, those services must be funded by taxes, which on their own can also create economic distortions. Following this rationale, Barro (1990) and Barro and Sala-i-Martin (1995) propose that there is an optimal taxation level for investing in those services, given that there is a point at which the net benefit in terms of economic growth that derives from providing those public services is maximised.9By proxy, the existence of optimal taxation levels to maximise growth implies that governmental presence is highly beneficial for augmenting economic performance, nonetheless, only until a threshold. The rationale for governmental interference is also shared with Vedder and Gallaway (1998), who state that the effect of government size on economic growth behaves as the Armey Curve proposes, in a quadratic form (inverted U-shape), where too little government prevents the creation of an optimal layout for growth, while too much government punishes the private sector. “Why?” is what one might ask. Vedder and Gallaway (1998) state that it partially relates to the fragility that a lacking government would create, namely in lack of property rights (rule of law), which would put forward a disincentive to both save and invest, given that expropriation would be real and common. The Armey Curve, depicted in Figure 2, 8In the case of network externalities, there is a lack of private incentive to develop them, and in this sense, public policy plays a crucial role in both the implementation and distribution of the associated infrastructure and ”know-how” . 9All and any public expenditure must be financed by tax in present or future private wealth, which reduces the net return on investment while also slowing down private capital accumulation. 9 government size in inclusive development (IHDI) as a primary result while also striving to determine if the results showcased by the alternative metrics could propose a possible under-representation of the role of government in the present literature. 2.3 The influence of governance and the importance of expenditure allocation 2.3.1 Government quality As previously established, governmental involvement is relevant to support and facilitate both economic growth and development. Even so, the existence of extremely successful nations that have not only commonly reported higher growth rates than the world average but also depicted much higher GDP per capita levels, such as Ireland, South Korea, Singapore, Qatar, and even Switzerland, that have relatively low public sectors (21.23%, 28.68%, 15.39%, 24.25%, and 31.53% as of 2022), might drive us to scrutinise what other factors may be at play. One contributing factor is the quality of government, which we can define as governance, a concept that depicts how well a nation manages its resources and how transparent and accountable its institutions are (Baland et al.,2010). Governance is of dire importance to promote economic prosperity, with Wolfowitz (2006), former President of the World Bank (WB), even suggesting that dysfunctional governance is the largest threat to development in most of the underdeveloped world. The relevance of governance is not necessarily recent, with Acemoglu et al. (2001)19 and North and Thomas (1973) depicting that there is a causal effect of economic institutions and governance on development, with the heterogeneity in their quality being a major explanation for the contemporary discrepancy between rich and poor countries. Recently, however, economists started to jointly tackle the dynamics and effects of size and quality of government on growth, with Nirola and Sahu (2019) suggesting that to enhance both state-level and national-level economic growth, nations should accentuate their efforts on promoting the quality of institutions, alternatively to blindly employing too much attention to the size of governments. There is also empirical evidence of a seemingly interactive relationship between government size and quality, given that in some cases, incrementing both can have positive effects on growth outcomes, despite that, countries with higher governance make more effective use of incremental government size than those 19 Acemoglu et al. (2001) showcase the example of British colonies compared to those of the French, Spanish, and Portuguese, which, due to good economic and political institutions that they inherited from Britain, exhibit much superior prosperity than the latter. 16 with lower governance (Cooray,2009). Afonso and Jalles (2016) also portray that the study of the optimal level of government falls under the interaction of size and governance, depicting that institutional quality has a positive and significant impact on the level of real GDP per capita and that the supposedly negative impact of government size on growth is more significant for nations in a setting of low quality of governance. Kim et al. (2018) also exhibit similar relationships, stating that both the size and quality of governments serve as fundamental tools to promote productivity and, hence, economic growth. More precisely, their results suggest that better governance facilitates countries in benefiting from enlarged government size, given that they act as complements in promoting efficiency and output growth20. In this context, my last research topic attempts to disentangle the possible mixed-up effects of government size and quality on growth and development, to suggest policy recommendations in terms of governmental resource allocation, and to guarantee that any bias is avoided in the computation of the optimal size of government. Following this premise, coupled with Goh and Mohd Aznan (2023) recommendations21, this study incorporates governance indicators as variables of control. There is a possibility that previous literature may have wrongly estimated the size of the government, potentially due to the correlation of the government size with an unobserved variable, governance. This problem is what we refer to as endogeneity, and the omission of government quality could partially explain why government size tends to be so highly relevant in most empirical studies, even though, punctually, some empirical works still find evidence of inexistent effects of government size on both growth and development. The greater bulk of academic studies imply the foundational role that good governance has in endorsing growth, nonetheless, there are still authors that contradict the leading wave by suggesting other dynamics. For instance, Sachs et al. (2004) exhibit that poor countries are not poor due to bad governance, but rather because they lack the economic resources to afford good governance in the first place, and that surprisingly, many underdeveloped nations report relatively favourable levels of governance. Furthermore, Hausmann et al. (2008) argue that governance is indeed a relevant issue, nevertheless, it represents only one of many other factors that may sabotage development. 20 Kim et al. (2018), by dividing their sample into highand low-resource countries, identify that this relationship is relatively more pronounced for countries with an abundance of natural resources. 21 Goh and Mohd Aznan (2023) stress the pertinence of incorporating governance in the methodology while also exhibiting that different regions may unveil distinct results. 17 2.3.2 Expenditure components. Do they all matter? When assessing the optimal size of government, a substantial number of academics rely on the assumption that all government expenditures behave similarly, ignoring any possible heterogeneous effects that distinct components of expenditure could have on growth (Vedder and Gallaway 1998;Asimakopoulos and Karavias 2016;Altunc and Aydın 2013;Makin et al. 2019;Aly and Strazicich 2000). Nonetheless, one might question the validity of that assumption, given that, for instance, investment and consumption expenditures could lead to distinct results, both in absolute terms and in terms of temporal incidence. Other scholars have attempted to address this dynamic, namely by decomposing government size into adequate components and computing the optimal size of government accordingly. Hajamini and Falahi (2018)22 for instance, use distinct metrics and components to make their computations, more particularly by decomposing government size into final consumption expenditure and current expenditure other than final consumption. Similarly, Chen and Lee (2005) also decompose the overall government size, expressed as government expenditure (as a % of GDP), into two categories, specifically government consumption expenditure and government investment expenditure. His idea derived from Lin (1994) hypothesis that while both components could have beneficial repercussions on growth, the impact of government consumption will be less significant than the contribution of government investment, given that the latter has an uplifting effect on private investment. Likewise, Barro (1991) found that public investment tends to be positively correlated with both growth and private investment, nonetheless, contrary to the previous case, he exhibited that public consumption spending has adverse effects on growth and private investment. Davies (2009), in his attempt to use HDI to compute the optimal size of government, follows a similar methodology, namely by assessing the optimal size of government separately to government consumption and government investment expenditures and reporting the optimal size of government as the summation of the precedent optimal sizes. Accordingly, his results address not only the distinct effects of the expenditures’ components but also their optimal allocation. Similarly, Afonso and Furceri (2010) also decompose government sizes according to expenditures, however, contrary to Davies (2009), they find that government investment has statistically significant negative effects on growth. Martins and Veiga (2014) decompose the size of government to an even further level, specifically according to defence, health, education, social protection, and a clustered group of the remaining expenditure subcomponents. This disaggregation made it possible to reach findings slightly different from previous academia, explicitly in the context that although non-linear relationships were found for HDI growth 22 Hajamini and Falahi (2018), in contrast to other studies, use government gross fixed capital formation as their proxy for government size. 18 in all subcomponents, the impact was heterogeneous according to the component analysed. Defence, education, and social protection expenditure had relationships similar to that of the Armey Curve (inverted U-shape), where increments would lead to augmented growth prospects until a benchmark. Health and the rest of the subcomponents display opposite dynamics, given that they behaved oppositely to the Armey Curve, or in a U-shaped relationship, where increases in expenditure always lead to detrimental effects, nonetheless, after a baseline, all and any incremental expenditure would have beneficial effects on growth outlooks. Devarajan et al. (1996) even suggest that an optimal mix of public spending could lead to higher steady states of economic growth, given that seemingly productive expenditures could become pointless when used in excess. Their findings put forward that, for its set of developing countries, increments in capital expenditure have negative effects on growth prospects, and contrary to the standard sentiment23, developing nations have been misallocating public resources in favour of capital expenditures at the expense of current expenditures. Nevertheless, Bose et al. (2007), in a similar analysis of developing countries, found conflicting results, reporting positive effects on growth for capital expenditure and insignificant effects for current expenditure. Additionally, at a disaggregated level, Bose et al. (2007) uncovered that the only components to have a constructive impact on growth are the investment in education and total expenditure in education24. Distinguishing the different components of expenditure is highly relevant to acquiring robust results, given that the absence of decomposition may explain why the heterogeneity in empirical evidence is still strong. The traditional assumption that all the effects of government expenditure are the same might be creating noise that disturbs the accurate effect of government size, obstructing the optimal computation of the size of government, and consequently, damaging the discussion of the role of government. 23 At the time, scholars believed that overspending in current expenses was damaging growth in developing countries, nonetheless, Devarajan et al. (1996) exhibited that the bias was in the opposite direction. 24 Bose et al. (2007) conclusions were paradoxical to those of Devarajan et al. (1996) not only on the relevance of current expenditure but also on the effects of education, which the latter depicted to be negative. 19 3 Methodology and data 3.1 Data source and descriptive statistics 3.1.1 Dataset construction Referencing subsection 2.1.1, my primordial indicator reflects the size of the government, which was argued to be more precisely represented by government expenditure as a percentage of GDP (Vedder and Gallaway,1998;Labonte,2010). Such an indicator was employed according to data made available by the IMF, which, although not the only source of information for government sizes, is the one that depicts more robust and long-lasting data, which can go back as early as two centuries. Commonly, the data for government size tends to range from zero to 100 percent of GDP, nonetheless, issues such as foreign aid can bring forward anomalies in terms of that size, with punctual cases where the range is breached. The few outliers that fall outside that scope were excluded from the dataset to avoid bias and miscomputations. Additionally, considering the hypothesis of the heterogeneous nature and relevance of distinct expenditure components made in subsection 2.3.2, data from the Governance Finance Statistics of the IMF is also incorporated to depict the allocation of expenditure components, more particularly to depict government intervention according to Classification of the Function of Government (COFOG) components. Contrary to many authors’ procedures, such as Hajamini and Falahi (2018) and Chen and Lee (2005), which only aggregate government expenditure in a considerable few clusters, this information allows for a more particular analysis of the impact of government expenditure by decomposing it at a more in-depth level. More specifically, such data portrays, as a percentage of GDP, government expenditure in general public services; defence; public order and safety; economic affairs; environmental protection; housing and community amenities; health; recreation, culture, and religion; education; and lastly, social protection. This disaggregation should be sufficient to address the heterogeneity of the component level and, similarly to Lin (1994), enable the distinguishment between productive and unproductive government intervention. 20 The extreme disaggregation, although beneficial in some respects, can limit the robustness of the results, giving their higher dependence on randomness, contrary to broad government expenditure, which is better at providing broad structural changes in the government’s approaches to economic intervention. As such, and considering the different impacts of government consumption and investment depicted by Lin (1994), a broader aggregation of government components is also used, more particularly for government expenditure in consumption and government expenditure in investment. Given calculation misadjustments from different data sources, the government investment as a percentage of GDP was retrieved from the IMF at the similarity of the overall government expenditure, and the government consumption was proxied by subtracting the investment from the overall government expenditure (in % of GDP). The study of optimal values of government size tends to address heterogeneity at the level of both development and income levels, and as such, data was retrieved for both indicators. A dummy variable was constructed (=1 if developed, =0 if developing) representing the country’s development status in the year 2023 according to the IMF. The time variation of development status was ignored due to two basic reasons, the first being a lack of data to accompany the development dynamics over time, and secondly, with the relatively small time dimension, is plausible to state that the change in development status is too small to effectively damage the consequential results that derive from this indicator. For income levels, a categorical variable was constructed for the cluster of income levels according to data from the WB for 2022 (=0 if low income, =1 if lower medium income, =2 if upper medium income, =3 if high income). Similarly to the previous case and, for the same reasons, the time dynamics of the variable are also ignored. To assess the impact of the size of government expenditure on economic growth, information from the WB for GDP in constant 2015 US$ was retrieved. Additionally, from the same source, the population depicted by the total number of individuals was also incorporated into the dataset, and coupled with the previous indicator, it was possible to construct an indicator of real GDP per capita in constant US$. This indicator is later incorporated as one of the variables that I attempt to explain, given that it is in the study of the optimal size of government, considered by many to be the most used and appropriate metric to measure the increment in welfare that results from intrinsic changes in government structures. The United Nations Development Program (UNDP) makes available most data related to development metrics, more particularly HDI and IHDI, which are both used in this work. As represented in section 2.2, the HDI is computed by the geometric mean of normalised indices for three key dimensions of human development: a long and healthy life (health index), access to knowledge (education index), and decent 21 standards of living (income index). The health index is calculated using information about the life expectancy at birth and education by using a mix of data for expected years of schooling and mean years of schooling, and the latter is estimated using data for the Gross National Income (GNI) per capita in constant 2017 Purchasing Power Parity (PPP). Table 1: Dimensions of HDI and IHDI. Dimension Indicator Health Life expectancy at birth (years) Education Expected years of schooling (years) Mean years of schooling (years) Standard of living GNI per capita (2017 PPP$) Dimension index = Actual value − Minimum value Maximum value − Minimum value HDI =3 √ Income index · Education index · Health index The IHDI, similarly to its predecessor, can only vary between zero and one, with higher values corresponding to higher levels of development, nonetheless, the IHDI tends to present lower values given that it follows the same computations as the HDI but is later discounted according to the within-country inequality (A) at each of the key components of development. IHDI =3 √ Income index* · Education index* · Health index* =3 √(1 −A Health )·(1 −A Education )·(1 −A Income ) The inequality function (A) represents the inequality or discount factor for each of the underlying development factors, which will lead to higher divergence between the HDI and the IHDI the higher its value. For interpretation purposes, the values of both HDI and IHDI were rescaled to range from zero to 100. Ax= 1 − n √X1···Xn ¯ X The current database, following Goh and Mohd Aznan (2023) suggestions, also incorporated WB world governance indicators to appraise the development and growth dynamics more accurately. Such 22 indicators are essential to proxy for management and institutional competencies, given that they describe broad patterns in the perceptions of the quality of governance over time. More particularly, they are comprised of six metrics that attempt to depict certain crucial factors of governance, such as voice and accountability, an indicator that captures the perceived extent to which citizens can select their government as well as freedom of speech; political stability and absence of violence/terrorism, which measures the perceived likelihood of political instability or associated violence; and lastly, government effectiveness, which captures perceptions related to the quality of public services along with its independence from political influence. The other three indicators correspond to regulatory quality, the perception of the ability of governments to formulate and implement policies and regulations to promote and regulate the private sector; rule of law, which depicts the perceived confidence in abiding by the rules of society by law enforcement, more particularly property rights, police, and courts; and lastly, control of corruption, which reflects the perceived extent to which public power is exercised for private gain. All governance indicator estimates are bound to a range of values of -2.5 and 2.5, with higher values corresponding to better governance. The rule of law in particular has commonly been cited as particularly relevant to address according to Vedder and Gallaway (1998) and Goh and Mohd Aznan (2023), nonetheless, the implementation of all governance indicators is econometrically invalid, given that they are prone to replicate and represent similar aspects of governance, and, as a direct consequence, they tend to be highly vulnerable to multicollinearity issues. Accordingly, the econometric guidelines of the Variance Inflation Factor (VIF) only allow for the implementation of a certain amount of world governance indicators, and as such, a new variable is constructed to allow for the implementation of the full amount of world governance indicators. Using the data for the six governance indicators, an overall governance indicator is constructed by making use of the principal component analysis. The objective of principal component analysis is to reduce the number of variables in a dataset while preserving as much information as possible. Broadly, this technique transforms a set of highly correlated variables into a smaller set of uncorrelated variables, which we refer to as principal components, without losing the broad statistical relevance and significance of the original variables. Governance it =f( Voice it, Law it, Regulatory it, Stability it, Efficiency it, Corruption it) In this approach, only the first principal component is used to represent governance, given that it is capable of explaining up to roughly 80% of the variance of the original governance indicators. 23 Given the distinct nature of growth and development dynamics, a bipolar econometric approach will later be implemented, and accordingly, also different data. For economic growth dynamics, additional data from the WB is incorporated, more particularly the gross capital formation as a percentage of GDP, trade openness, which reflects the proportion of the monetary value of exports and imports on the GDP, and lastly tertiary school enrolment (% gross). For development metrics, the data employed slightly differs, although most of it also derives from the WB. In this case, complementary information for the infant mortality rate (per 1000 births) is also incorporated. The data incorporated was standardised to depict values in percentages, and as such, most data was, when appropriate, multiplied by 100 at the similarity of development indicators. Additionally, it is relevant to refer to the lack of a uniform designation for country names and country codes, which made it essential to opt for a uniform approach to depict the individuals being addressed, as such, this database also makes use of information retrieved from the International Organization for Standardization (ISO) to uniformly designate countries. After merging the data and transforming it to ensure safe specifications of the variables, it was later divided into three separate databases, which are used to address the difficult interplay between statistical relevance and econometric adequacy, which is common within the study of optimal expenditure due to a consistently low number of observations. The first dataset corresponds to an annual database that ranges from 1960 to 2023 for a set of 228 countries, which will later be useful to assess predictive and preliminary dynamics, as well as some additional estimations. The second corresponds to a database with econometric usefulness, in which the years were dropped and were transformed into non-overlapping 3-year period averages for most variables, except GDP per capita, HDI,IHDI, population, and tertiary school enrolment. XT=xt+xt−1+xt−2 3or XT=xt, T ={1, . . . , 21}, t ={1962, . . . , 2023} The latter database depicts information for twenty-one non-overlapping 3-year periods (1962-1964, 1965-1967, 1968-1970, 1971-1973, 1974-1976, 1977-1979, 1980-1982, 1983-1985, 1986-1988, 19891991, 1992-1994, 1995-1997, 1998-2000, 2001-2003, 2004-2006, 2007-2009, 2010-2012, 2013-2015, 2016-2018, 2019-2021, 2022-2023), and, similarly to the annual database, it is also for a set of 228 countries. The rationale as to why this technique was carried out and the motive to only estimate averages for certain variables are related to economic theory and econometric implementation, and as such will only 24 be exhibited in the accordant section. Additionally, the third database corresponds to the same approach, but only for 5-year periods. As for GDP per capita, HDI,IHDI, population, and tertiary school enrolment, the values are not averages since the values represent the observations of the last year of the respective 3-year or 5-year periods. Additionally, using such variables, except for school enrolment, logarithmic growth rates were constructed. log Yt=log Y0+gY·t gY·t=log Yt−log Y0 gY·100 = 1 t·(log Yt−log Y0)·100 Given that we use periods, the growth rates were constructed by using the logarithmic change between periods for those variables, divided by the number of years of the periods. Such a procedure allows for the computation of the average annual growth rates of such indicators. Lastly, when multiplied by 100, it is possible to depict the percentage growth rate in continuous time. 3.1.2 Descriptive statistics and preliminary results In this section, it is possible to address any issue that might be present in the data used in the empirical methodology. Table 2presents the joint descriptive statistics for the non-overlapping 3-year period averages database, which will be used to compute the optimal government expenditure estimates for growth and development metrics. The first notable dynamic is the number of observations for different economic indicators, which are notably sparse. As mentioned above, the country’s dynamics for optimal government expenditure suffer from data availability issues, a phenomenon similar to most of the previous literature. Although such data is macroeconomically fundamental to uncovering relationships related to government size, one must account for its nature, as a low number of observations can introduce delicacy when working with such data. The roughly 800 observations for GDP per capita and HDI do not present the biggest issue, as this is common in this field of study, and when correctly addressed, should not pose risks to the validity of the results. Davies (2009), Martins and Veiga (2014), and Asimakopoulos and Karavias (2016), for instance, present a similar or even lower number of observations. Nonetheless, given the recent tenure of IHDI, this metric raises the most pressing concern, especially as it is central to this study, with only 355 observations. While other works occasionally use similar sample sizes, careful interpretation is crucial to mitigate potential small sample bias. 25 literature, to conduct a disaggregated scrutiny. A unified analysis that ignores such heterogeneity could obscure the Armey Curve relationship. It is important to note that the previous assessment only shows trend lines, which are useful for making predictions and preliminary assumptions about potential future relationships. They do not, however, provide robust or statistically significant tools for extrapolating empirical inferences on the optimal size of government. Their applicability lies in guiding expectations regarding relationships and challenges that may arise. Overall, they suggest that future evidence may support the existence of the Armey Curve or that aggregation of developed and developing countries may obscure such relationships. Furthermore, these preliminary findings suggest that conclusions may vary depending on the metric used, with particular alienation for economic growth. 3.2 Econometric methodology 3.2.1 Econometric approach for economic growth indicators As previously exhibited, the substantial contrast between economic growth and economic development can imply heterogeneity in the conclusions inferred, and as such, distinct econometric approaches are imperative. Consequently, a dual regression methodology is applied, one for economic growth and the other for development indicators, although both share particular characteristics in their estimation. For instance, as referred to in subsection 3.1.1, the data is averaged over 3-year periods for most variables, and accordingly, lags and logarithmic growth rates are implemented to construct appropriate dependent and explanatory variables. What hasn’t been discussed nonetheless is the rationale for such a procedure. The main motive for such a technique relies on controlling for the effects of business cycles in cross-country and time-series studies and emphasising the relevant variables’ impacts on long-term economic or development growth (Sturn and Epstein,2021;Beck and Levine,2004). Broadly, the use of non-overlapping periods allows for smoothing out short-term fluctuations and focusing on the impact of structural changes by reducing the noise from such anomalies and emphasising long-term economic dynamics. As cited by Beck and Levine (2004), averaging annual data into nonoverlapping 5-year periods allows for the purging of cyclical bias and consequently depicts more accurate conclusions. The literature, however, stresses the dilemma of how many years should be used to construct the 32 non-overlapping periods, with some even suggesting that averaging in 5-year periods may not be enough to effectively control for such cycles, given that they can commonly be persistent for larger durations (Schularick and Solomou,2011;Loayza and Rancière,2006). Even so, in the current framework, smaller periods of only 3-year periods were exercised, considering the vulnerability and the necessity of counterbalancing econometric suitability with statistical relevance. Such judgement relates to the fact that the increment in the robustness of results resulting from incremental observations from changing from 5-year periods to 3-year periods might likely compensate for the loss in robustness that derives from not controlling as accurately the business cycles. Accordingly, given this limitation, it is of foremost concern to approach carefully resulting computations, and as such, future results will commonly be computed also for 5-year periods to ensure the sturdiness of the causal inference. Additionally, most literature focuses on economic growth and its probably quantitatively important connection with business cycles, which may also reinforce economic growth (Kaihatsu et al.,2019;Pedersen and Elmer,2003). Nonetheless, evidence on business cycle dynamics with development indicators is lacking, and thus, the assumption that averaging for 5-year periods for both growth and development is unfounded. Consequently, adopting the same non-overlapping periods might imply fallacies, given that it assumes that both indicators of economic and development performance are prone to the same duration of business cycles. By rationale, given that development implies more structural changes, while economic growth has more fast-paced dynamics, it might be relevant to appraise if longer averages may be more appropriate for the development indicators, while for growth shorter averages might be sufficient, thus further validating the use of different periods to address business cycles incidence and its mechanisms. With this topic sorted, the construction of the econometric estimation can be assembled. Model 1 depicts the current estimation, which is used to assess the benchmark results for dynamics relating to the size of government and economic growth. At the similarity to most literature, this model attempts to estimate an optimal government expenditure level or turning point, if existent, according to the maximisation of economic growth, which, in this scenario, is represented by the GDP per capita annual average growth rate for a country iat period t(∆GDP), and as stated in the previous section, is computed using the logarithmic change rate between two consecutive periods. 33 ∆ GDP i,t =αi+β0log GDP i,t−1+β1 Education i,t−1+β2 Size i,t+ β3 Size 2 i,t +β4 GCF i,t +β5 Governance i,t +β6∆ Population i,t+ β7 Trade i,t +γt+ϵi,t (Model 1) Given the literature on economic convergence, which tends to support the existence of conditional convergence, it is expected that the present level of economic advancement might explain a considerable amount of future growth, given that countries tend to end in a country-specific steady state that is dependent on their specific labour force and savings specifications (Barro et al.,1991,1992;Cho and Graham, 1996;Kaitila,2004;Nonneman and Vanhoudt,1996;Murthy and Chien,1997). Consequently, the logarithm of the last year of the 3-year periods of GDP per capita for country iat period t−1(log GDP) was implemented as a control variable. As suggested by Barro (2016), this variable is anticipated to have a negative coefficient if conditional convergence holds, since with increasing economic prosperity, decreasing marginal returns to growth start to take form, making it increasingly harder to sustain high rates of growth. Additionally, the inclusion of such a variable allows the econometric model to be dynamic and, as such, depicts the past values of the dependent variable to influence its present value, which helps capture the serial persistence of economic mechanisms of growth (Bhargava and Sargan, 1983;Arellano and Bond,1991). As previously referred to, however, that variable only tests conditional convergence if controlled for country-specific labour and saving settings, given that if that does not hold, what is being tested is absolute convergence. In this sense, to control for the labour force, the population annual average growth rate for country iat period t(Population) computed by the logarithmic change is also included, giving Ram (1986) suggestions that it serves as a proxy for labour force growth. Although a stable and robust labour force is an essential foundational tool to sustain a consistent tax base and working force, an abusive incremental population might make it harder to keep up with a fast-tracked demand for jobs and central services, and therefore we can project such a variable to be non-significant or even to stifle growth. Analogously to Asimakopoulos and Karavias (2016), the average gross capital formation as a percentage of GDP for country iat period t(GCF) is also incorporated, for mainly two main reasons. The first relies on the necessity of controlling for the savings dynamics to infer conditional convergence, given the proposal of Hajamini and Falahi (2018) that investment as a percentage of GDP can be used as a substitute for the savings rate. Additionally, capital formation is also relevant to factoring in the relevance of private investment and 34 its multiplying impact on economic growth.1Consequently, it is foreseen that it will have an encouraging and significant impact on the growth prospects. The main explanatory variable under analysis refers to government size, which is represented here as the average government expenditure as a percentage of GDP for country iat period t(Size), which is also incorporated in its quadratic form (Size2). The quadratic approach is implemented as a default considering that most recent academics confronted the traditional approach of linear relations and found the statistical pertinence of carrying out non-linear relationships (Hajamini and Falahi,2018). As a result, for the relationship of the Armey Curve, which is expected, the government size should depict a positive coefficient while its square should exhibit a negative effect, with the resulting turning point where increases in government expenditure no longer imply marginal enhancements in economic growth, conveying the optimal government size. Furthermore, trade openness, the share of the monetary value of exports and imports on the overall GDP in country iat period t(Trade), is also included, following the econometric methodology of both Afonso and Furceri (2010) and Asimakopoulos and Karavias (2016), to account for the effect that the insertion in international trade or even trade liberalisation policies exert on economic growth. Therefore, we might anticipate a positive and significant impact of that variable similar to Afonso and Furceri (2010), or at least for developing countries alike Asimakopoulos and Karavias (2016). Given the relevance to control for the impact of education on growth, the tertiary school enrolment, expressed as a percentage of the population of tertiary education age, of the last year of the 3-year periods for country iat period t−1(Education) was also integrated. Contrary to other scholarship, such as Martins and Veiga (2014), secondary school enrolment was not used, given that nowadays it lacks heterogeneity according to the level of economic prosperity given the recent worldwide improvement in basic levels of education prospects. Given the probable beneficial impact of a qualified workforce on growth, it is expected that the variable will provide a positive coefficient. Lastly, as depicted in subsection 2.3.1, governance is of dire relevance in explaining most of the heterogeneity in economic prosperity between rich and poor countries (Acemoglu et al.,2001;North and Thomas,1973). Hence, the indicator of broad governance for country iat period t(Governance), constructed using principal component analysis, was also incorporated. According to inferences from the literature, it should have a positive and statistically significant effect on economic growth. Given the substantial endogeneity present in dynamic models of economic growth, particularly due to the correlation between the lagged dependent variable and the error term, a two-step System1Gross capital formation is used as a proxy for private investment, given that public sector investment represents only a negligeable share of total investment. 35 Generalised Method of Moments (GMM) estimator with time Fixed Effects (FE) is used to reduce bias and increase the estimation precision (Bond,2002).2 The use of System-GMM is most appropriate when the panel units, such as countries, are large, while the periods are relatively small, a characteristic shared by the present 3-year and 5-year period database. Additionally, the Difference-GMM has been found to have poor finite sample properties, particularly in cases where the time series are highly persistent (Blundell and Bond,1998;Bond et al.,2001). Furthermore, applying the Bond rule of thumb suggests that System-GMM is likely more appropriate than Difference-GMM. In Model 1, all explanatory variables are treated as endogenous, except for the period dummies, which serve as exogenous instruments. For endogenous variables, lagged values from at least two periods are used as instruments. Moreover, to ensure the robustness of my empirical inferences, I compute the results using robust standard errors to correct for heteroskedasticity and potential serial correlation in the error terms. The integration of System-GMM is also highly relevant because it helps address a multitude of sources of endogeneity, such as unobserved, simultaneity, and dynamic endogeneity (Ullah et al.,2018). Tackling endogeneity deriving from simultaneity is of special importance in this particular model, given that although government size might theoretically affect growth, there is also evidence that growth can also affect government size (Peacock and Scott,2000). 3.2.2 Econometric approach for economic development indicators In the estimation used to assess development and inclusive development, the econometric methodology is similar, as a direct consequence of the parallel nature of HDI and IHDI, and as such are explained by the same variables (except for their lags). Similar to the methodology referred to in economic growth modelling, the dynamics related to business cycles imply the main use of 3-year periods but also 5-year periods due to robustness issues and business cycle duration. Model 2 exhibits the construction of the econometric model for development indicators, which is similar to Model 1 given the structural similarities between economic growth and development. Consequently, similarly to Model 1, this new model also attempts to compute the turning point of the government size, although presently for both development and inclusive development, the first represented here by the HDI annual average growth rate for country iin period t(∆HDI) and the latter depicted by the IHDI annual average growth rate for country iat period t(∆IHDI), both computed by logarithmic growth rates. 2Given the potential lack of statistical significance in System-GMM estimates, individual and time FE regressions are also used to ensure robustness. 36 ∆ HDI/IHDI i,t =αi+β0log HDI/IHDI i,t−1+β1 Education i,t−1+ β2 Size i,t +β3 Size 2 i,t +β4 GCF i,t +β5 Governance i,t+ β6 Infant i,t +γt+ϵi,t (Model 2) Given the similarity of both economic growth and development indicators, corroborated by other authors’ econometric approaches to development such as Davies (2009) and Martins and Veiga (2014), we could expect that certain explanatory variables should remain relevant when applied to assess development dynamics. In this sense, the tertiary school enrolment, gross capital formation, governance, and surely government expenditure in its quadratic form are all explanatory variables that were also implemented in Model 2. Given the similarity of both models, we could anticipate the statistical relevance and the direction of the impact of such indicators to be a close reflection of their anticipated behaviour in Model 1. Building on this argument, we could anticipate that tertiary school enrollment, governance, and gross capital formation would have a positive and statistically significant impact on both metrics of development. As for government size, the effect should be quadratic, similar to that of the Armey Curve, with Davies (2009) and Martins and Veiga (2014) reinforcing such plausibility due to their findings of quadratic impacts of government size on HDI. Only the variables of trade openness and population growth were dropped in the present model. The trade openness was removed due to the intrinsic monetary relevance of trade, which does not transpose as well to development indicators as one should expect. Given that increments in development are often a result of structural changes in a country, the too-diluted effect of trade on development leads to a lack of statistical relevance for that variable. Given that trade impacts economic prosperity, which is only one of many components of development, its impact would only be observed through indirect mechanisms, and consequently, the inclusion of trade would imply more noise in the estimation than actual empirical robustness. Similarly, this partially holds for population growth, given that economic growth accounting often displays population growth as an important foundational factor for economic growth, nonetheless, that does not convert well for development, in which said variable seems to lack explanatory power. The feasibility of a too overly vague transmission mechanism between population and development and its overfitting in Model 2 ultimately led to its withdrawal. To also apply dynamic models, along with the theory of conditional convergence, the logarithms of the last year of the period of both HDI and IHDI for country iat period t−1(log HDI, log IHDI) were also 37 incorporated as control variables. Although population growth is now lacking in the model, the theory of conditional convergence should still be able to hold, and therefore, it is anticipable that the lags of the metrics of development provide a negative coefficient, given that as development grows, decreasing marginal returns start to punish development prospects, ultimately leading countries to their own steady states. The practice is also implemented by Davies (2009) and Martins and Veiga (2014), in which the latter found evidence of convergence. Given the health component of the development indicators, a new variable is added to Model 2 which was not present in Model 1. That variable is the average infant mortality rate for country iat period t−1(Infant), which is expected to exhibit a negative and statistical impact on development, given that the worse the health conditions of a country, the worse its development outcomes. The econometric dilemmas and the critical obstacle of endogeneity are still present in the current model of economic development, and as such, the same approach of Model 1 is implemented here, particularly by running a two-step System-GMM with time FE.3Model 2 also treats all variables as endogenous and uses for instrumental variables the period dummies as well as at least the two-period lags of the explanatory variables. The results are also expressed with robust standard errors to guarantee higher accuracy. 3Similarly to the previous case, the potential lack of statistical relevance in System-GMM estimations also prompts the use of individual and time FE estimations to ensure robustness. 38 4 Results 4.1 Main analysis 4.1.1 Benchmark results Table 3reports the benchmark results derived from the baseline econometric models for 3-year periods. The notes describe the econometric specifications, particularly their autocorrelation validity, the Hansen test, the number of instruments, and an additional number of statistical specifications. In column (1), we can observe that the government size is highly related to increments in the GDP growth rate in a quadratic form. Consequently, the augment in government expenditure provides high and significant bonuses to economic growth prospects at its first stages but later tends to provide lower and lower incentives, even ultimately reaching hazardous impacts on GDP, similar to the Armey Curve. Column (2), which also tests GDP growth but uses FE depicts similar relationships. Consequently, by deriving the equation on government size, we can infer the optimal government size according to economic growth maximisation. Consequently, we can depict that for the System-GMM estimation, the results indicate that the optimum government size or expenditure should be allocated at roughly 32.54% of GDP, while for FE that size is substantially similar, situated at roughly 27.22% of GDP. For both columns, the rest of the explanatory variables seem to behave as expected, with higher values of past GDP implying lower growth rates in the present, similar to the rationale of conditional convergence. The gross capital formation also exhibits a substantial and positive impact on economic growth. The beneficial and closely related impact of trade on growth is also exhibited by its positive coefficient. The population growth negative effect was also anticipated. Education also seems to behave similarly to what was previously projected, with a beneficial impact on growth prospects, nonetheless, only for the System-GMM. Governance behaves contrarily, given that it provides a substantial positive impact on growth, nonetheless, only on the FE regression. 39 Table 3: Government size, growth, development, and inclusive development for 3-year periods (1) (2) (3) (4) (5) (6) Variables Sys-GMM FE Sys-GMM FE Sys-GMM FE Log GDPt−1-2.393*** -5.478*** (0.850) (0.838) Log HDIt−1-8.406*** -10.174*** (3.038) (1.038) Log IHDIt−18.483** -18.145*** (3.342) (2.467) Educationt−10.043** 0.012 0.016** 0.002 0.006 0.002 (0.020) (0.011) (0.007) (0.003) (0.016) (0.005) Size 0.621*** 0.304*** 0.026 0.053** -0.223** -0.058 (0.218) (0.098) (0.049) (0.021) (0.103) (0.059) Size2-0.010*** -0.006*** 0.000 -0.001** 0.003** 0.001 (0.003) (0.001) (0.001) (0.000) (0.001) (0.001) GCF 0.225*** 0.145*** 0.002 0.015*** 0.049* 0.019 (0.047) (0.027) (0.013) (0.005) (0.029) (0.014) Governance 0.256 0.739** 0.328* 0.059 -0.470* 0.315 (0.608) (0.288) (0.175) (0.067) (0.274) (0.218) Population -0.682** -0.446*** (0.279) (0.160) Trade 0.029** 0.017* (0.012) (0.009) Infant -0.021 -0.025*** 0.141** -0.060 (0.021) (0.006) (0.067) (0.037) Observations 838 834 820 814 355 343 Countries 130 126 130 124 112 124 AR(1) 0.000267 0.00884 0.00267 AR(2) 0.947 0.136 0.996 Hansen test 0.408 0.458 0.440 Instruments 122 102 44 Adj. R20.498 0.699 0.586 Notes: Two-step System-GMM and Fixed effects regressions, including 3-year period dummies. GMM estimations use robust standard errors. FE estimations use standard errors clustered by country and robust to heteroskedasticity. All variables are treated as endogenous in System-GMM estimations with the exception of period dummies. The dependent variable is the average annual growth rate of GDP per capita for (1) and (2), of HDI for (3) and (4), and of IHDI for (5) and (6). Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 40 Columns (3) and (4) display HDI dynamics for System-GMM and FE, respectively, with a noticeable reduction in the statistical relevance of such a model, at least for 3-year periods. Column (3) does not even depict a statistical effect of government size, with the only variables reporting statistical significance being the lagged dependent variable, with a negative impact, and education and governance with a positive one. Using FE, the statistical significance seems to be augmented, with the quadratic effect of government size being displayed here. Therefore, by decomposing it, we can detect that the optimal government size for HDI, at least in this case, is situated at around 42.20% of GDP. As for the rest of the variables, at least the significant ones, they all seem to behave as anticipated in the previous section. For columns (5) and (6), we can also infer the mechanisms of IHDI, however, as displayed previously, with caution given the lacking number of observations. For both System-GMM and FE, it is first visible that conditional convergence applies, given that the lags of the dependent provide a hazardous impact on inclusive development growth. We can observe, however, that probably due to small sample bias, the effects of most variables appear as rather peculiar in System-GMM. Although the gross capital formation appears as positive, as anticipated, the governance displays a negative impact on IHDI, with government size also displaying an awkward relationship. Particularly, government size, although providing a quadratic effect, is in the opposite direction, where size increments always imply negative effects on IHDI until a certain point, from where any increment always leads to beneficial effects. Not only does this effect contradict most theories, but it also implies that there is no maximisation point for IHDI. Contradictorily, it provides a minimising point where the negative effect of government size on IHDI growth peaks, corresponding in this case to 44.10% of GDP. As for FE, the results provide almost null statistical relevance, except for the lag of IHDI, which implies a negative impact of the present level of IHDI on future IHDI growth prospects. As previously depicted, the business cycle incidence of economic growth and development might differ, and as such, results for 5-year periods are also exhibited in Table 4, in an attempt to assess more robust results, given the commonly slippery and statistically mediocre resilience of this type of data. Columns (1) and (2) depict the 5-year periods results for economic growth, where, for both, the statistical implications of conditional convergence also seem to be present. The System-GMM regression appears as statistically weaker than when computed for 3-year periods in Table 3. Except for the lag of GDP, only the gross capital formation provides statistical and positive effects on economic growth. The FE, however, seems statistically significant, with all statistically significant variables providing results that were previously anticipated. As for government size, we can also derive that the government size is quadratic 41 until roughly 40% of GDP, and beyond that, although the direction becomes negative, there is no statistical significance. In Figure 11, it is visible that the impact of the size of the government on IHDI growth is puzzling, with the marginal impacts providing no clear insight into why such an indicator behaves as it did in the econometric model. It is evident, however, that the effect of government size on IHDI growth probably does not behave like in a U-shaped form, given the opposite and random directions of the marginal models. As such, it is plausible that small sample bias may be damaging the direction of the results, with the consequence being somewhat random effects of government size on IHDI. Considering those ongoing concerns, alternative econometric approaches are implemented to judge the detrimental effects of small sample biases on results related to IHDI. Table 5reflects the equivalent results, where some econometric controls are relaxed to increment sample dimensions and consequently depict possibly more accurate results by trading off econometric rigour for more sample robustness. Column (1) loosens the 3-year System-GMM regression by dropping the gross capital formation, governance, and tertiary enrolment, and as a result, increasing observations by roughly 30%. In this case, the quadratic effect takes form, with an optimal government size of 39.04% of GDP. Column (2), which uses FE, only depicts similar associations if it further excludes infant mortality. In this case, the optimal value is roughly 40.69%. It is clear that the small sample partially conceals the evidence of the Armey Curve, nonetheless, the dismissal of such a large number of controls might imply too much delicacy to the results, while at the same time, expressing an academic fallacy of selection bias by only removing the variables that are fitting for my narrative. Consequently, to depict the empirical veracity and not author tampering, columns (3) and (4) exert the same practice for 5-year periods, with the first only removing the education enrolment, the variable that allows us to extract the largest number of observations, while the latter also removes gross capital formation. The results of both columns (3) and (4) also exhibit evidence for the Armey Curve, with optimal sizes of 37.72% and 31.23% of GDP, respectively. Considering the evidence here conveyed, there is satisfactory reason to assume that the results depicted express the first empirical evidence of an Armey Curve relationship for IHDI, nonetheless, at least for now, with substantially less statistical robustness. Given that the results for IHDI were not computed using procedures equivalent to HDI, it is not accurate to represent if the optimal government size for IHDI is greater than HDI, nevertheless, it is clear that the general tendency is for IHDI to report at least sizes similar to those of HDI. Specifically, we could infer that the optimal government size for IHDI ranges from 48 Table 5: Alternative estimations for inclusive development 3-year periods 5-year periods (1) (2) (3) (4) Variables Sys-GMM FE Sys-GMM FE Log IHDIt−11.311 -14.910*** 4.761 -16.544*** (2.362) (1.160) (3.142) (1.816) Size 0.214*** 0.110** 0.150* 0.115* (0.059) (0.051) (0.078) (0.069) Size2-0.003*** -0.001* -0.002** -0.002* (0.001) (0.001) (0.001) (0.001) GCF 0.049* (0.028) Governance -0.212 0.430* (0.299) (0.231) Infant 0.064 0.107** -0.039 (0.046) (0.043) (0.036) Observations 461 462 327 335 Countries 128 126 121 125 AR(1) 0.000147 0.0340 AR(2) 0.193 Hansen test 0.126 0.324 Instruments 65 35 Adj. R20.515 0.404 Notes: Two-step System-GMM and Fixed effects regressions, including 3-year or 5-year period dummies. GMM estimations use robust standard errors. FE estimations use standard errors clustered by country and robust to heteroskedasticity. All variables are treated as endogenous in System-GMM estimations with the exception of period dummies. The dependent variable is the average annual growth rate of IHDI for all regressions. Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 49 31.23% to 40.69% of GDP. In order not to implement too much noise in the analysis and avoid overcomplication of results by alternating between variables, future results reported for IHDI will be computed using the original controls used in HDI, nonetheless, the concern of small sample is not ignored, and confusing or lacking evidence may be expressed as a direct consequence of small sample, and not of causality. 4.1.2 Components of governance As depicted in the literature, this dissertation also tries to elucidate some of the inferences and mechanisms by which governance affects welfare, which in the previous results has already been empirically highly beneficial and favourable to many economic indicators. Tables 6and 20 depict results to address which particular components of governance seem to affect most economic growth. One conclusion, which is parallel to both tables, is easily noticeable. That relates to the fact that two indicators of governance appear to be particularly relevant for GDP growth, particularly government effectiveness and political stability and absence of violence/terrorism. As for the rest of the variables, they do not seem as relevant to explain growth, at least when addressed individually. The results for HDI and IHDI are not depicted due to the statistical insignificance of all individual governance indicators, which might lead us to question if we can extrapolate that governance is only broadly relevant to both measures of development and that the particular emphasis on specific components appears as irrelevant, contrary to GDP, where a focus on the specified world governance indicators is more pertinent. This might prompt us to inquire whether effectiveness and political stability are primordial to promote private sector activity and economic prosperity, nonetheless, only focusing on those indicators may not benefit every individual equally, and as such, particular governance components appear irrelevant to development metrics. Consequently, to promote distributed welfare, the equal and widespread focus on all governance appears as more appropriate. 50 Table 6: Governance components and economic growth for 3-year periods (1) (2) (3) (4) (5) (6) Variables FE FE FE FE FE FE Log GDPt−1-4.809*** -4.795*** -4.961*** -5.327*** -5.525*** -5.100*** (0.692) (0.788) (0.756) (0.768) (0.777) (0.765) Educationt−10.011 0.010 0.011 0.011 0.009 0.012 (0.011) (0.010) (0.011) (0.011) (0.011) (0.011) Size 0.327*** 0.331*** 0.327*** 0.308*** 0.293*** 0.321*** (0.103) (0.101) (0.099) (0.102) (0.094) (0.102) Size2-0.006*** -0.006*** -0.006*** -0.006*** -0.005*** -0.006*** (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) GCF 0.148*** 0.147*** 0.146*** 0.138*** 0.146*** 0.146*** (0.027) (0.027) (0.027) (0.028) (0.027) (0.027) Population -0.438*** -0.426*** -0.432*** -0.446*** -0.419** -0.435*** (0.152) (0.153) (0.157) (0.153) (0.161) (0.153) Trade 0.016* 0.016* 0.016* 0.019** 0.018* 0.016* (0.009) (0.009) (0.009) (0.009) (0.009) (0.009) Voice 0.495 (0.540) Law 0.064 (0.600) Regulatory 0.544 (0.479) Stability 1.203*** (0.346) Effectiveness 1.418*** (0.484) Corruption 0.771 (0.499) Observations 834 834 834 834 834 834 Countries 126 126 126 126 126 126 Adj. R20.491 0.490 0.491 0.505 0.498 0.492 Notes: Fixed effects regressions, including 3-year period dummies. FE estimations use standard errors clustered by country and robust to heteroskedasticity. The dependent variable is the average annual growth rate of GDP per capita for all regressions. Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 51 4.1.3 The interplay of government quality and quantity Although government size is the primary focus of this study, its implications and interconnection with institutional quality, as highlighted by Cooray (2009), are also highly relevant. Accordingly, this section examines this dynamic. In particular, following a methodology similar to Cooray (2009), Table 7presents the results for the interaction between government size and a categorical variable for quantiles of governance, namely, low, middle, and high governance countries. The empirical evidence for IHDI, in particular, is notably lacking. However, for GDP and HDI, statistical significance is abundant, particularly in low governance countries, which, surprisingly, show stronger evidence of the Armey Curve relationship for both indicators. This finding is not only peculiar but also directly contrasts with the evidence of Cooray (2009) and Afonso and Jalles (2016), which suggest that countries with weaker institutions should be less efficient in managing public expenditure. Furthermore, the evidence for the Armey Curve weakens as governance improves. As a result, the effect is less pronounced for middle governance countries and even completely disappears for high governance countries. Specifically, for low governance countries, the estimated optimal government size ranges from 27.38% to 28.38% for GDP and from 28.15% to 30.97% for HDI. For middle governance countries, the optimal size is 26.74% for GDP and ranges from 29.60% to 37.97% for HDI. Although these results may appear paradoxical, their statistical consistency supports their potential validity. If verified, these findings could suggest the need to reconsider current development strategies employed by nations worldwide. The causal relationship depicted here highlights that while governance is crucial for prosperity, adjusting government size as a policy to stimulate prosperity might be even more important than what previously thought in overcoming poverty traps, even in countries with weak institutional foundations. 52 Table 7: Interactions of government size and government quality 3-year periods 5-year periods (1) (2) (3) (4) (5) (6) Variables FE FE FE FE FE FE Log GDPt−1-4.759*** -5.019*** (0.715) (0.698) Log HDIt−1-10.070*** -11.134*** (0.971) (1.132) Log IHDIt−1-18.412*** -17.646*** (2.650) (3.125) Educationt−10.012 0.003 -0.000 0.034*** 0.006*** 0.007 (0.009) (0.003) (0.005) (0.010) (0.002) (0.006) Size·Govern=0 0.677*** 0.131*** -0.028 0.696*** 0.147*** 0.153 (0.134) (0.031) (0.121) (0.153) (0.035) (0.116) Size2·Govern=0 -0.012*** -0.002*** 0.000 -0.012*** -0.003*** -0.004*** (0.002) (0.001) (0.002) (0.003) (0.001) (0.001) Size·Govern=1 0.207 0.049** -0.074 0.242** 0.063** -0.000 (0.137) (0.022) (0.057) (0.100) (0.025) (0.105) Size2·Govern=1 -0.004 -0.001** 0.001 -0.005** -0.001*** -0.001 (0.003) (0.000) (0.001) (0.002) (0.000) (0.002) Size·Govern=2 -0.170 -0.016 -0.100 -0.142 -0.013 -0.100 (0.147) (0.032) (0.061) (0.144) (0.032) (0.084) Size2·Govern=2 -0.000 0.000 0.001* 0.000 0.000 0.001 (0.002) (0.000) (0.001) (0.002) (0.000) (0.001) GCF 0.146*** 0.017*** 0.025** 0.144*** 0.012** 0.014 (0.026) (0.004) (0.011) (0.034) (0.005) (0.017) Govern 7.301*** 1.067** 1.525 6.929*** 1.086*** 2.179 (1.903) (0.420) (1.196) (1.898) (0.402) (1.544) Population -0.437*** -0.249 (0.159) (0.200) Trade 0.015* 0.013 (0.009) (0.009) Infant -0.023*** -0.074** -0.029*** -0.051 (0.005) (0.035) (0.007) (0.041) Observations 834 814 343 565 553 247 Countries 126 124 100 121 119 93 Adj. R20.509 0.705 0.597 0.554 0.729 0.485 Notes: Fixed effects regressions, including 3-year or 5-year period dummies. FE estimations use standard errors clustered by country and robust to heteroskedasticity. The dependent variable is the average annual growth rate of GDP per capita for (1) and (4), of HDI for (2) and (5), and of IHDI for (3) and (6). Govern corresponds to quantiles according to the variable of governance (=0 if low governance, =1 if middle, =2 if high). Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 53 4.1.4 Levels of development and income The literature also stresses that the effects of development, particularly when clustered by developed or developing countries, are relevant to addressing the different impacts of government size. Asimakopoulos and Karavias (2016) and Martins and Veiga (2014) depict that the quadratic effect of developed countries is higher than that of the developing ones, particularly because developed countries possess institutions of higher quality, and thus the central resources are better employed. As stressed in the literature, however, that somewhat hints at an possible error in the reasoning, given that they are capturing the effect of institutional quality, here proxied by governance, and not the mechanisms of development status. From this perspective, controlling for governance should lead to distinct results, something which Goh and Mohd Aznan (2023) had already advocated. Consequently, Tables 8and 21 depict a similar approach to Martins and Veiga (2014), but now controlling for institutional quality. Table 8uses 3-year periods and exhibits different inferences than what most literature depicted. Particularly, the results depict inverted U-shaped effects of government size on economic growth and development for developing countries, with respective optimal government sizes ranging from 28.45% to 31.99% for GDP and 33.94% for HDI. Developed countries appear to behave quadratically, nonetheless uniquely for economic growth, reporting an optimal size of government of 39.26%. Table 21 depicts the results for 5-year periods, where the quadratic significance for developing countries still holds, nevertheless, now not only for GDP and HDI but also for IHDI. The respective results depict an optimal size of government of 29.55% for GDP, 29.26% for HDI, and 19.30% for IHDI. For developed ones, the effect is also quadratic for all metrics, nonetheless, the direction is quite distinct. Peculiarly, the results depict U-shaped effects of government size for GDP and IHDI, while only the HDI depicts the expected inverted U-shaped effect with an optimal government size of 29.26%. Overall, there is strong corroboration that after controlling for governance, there is evidence that developing countries benefit more from increments in government size, nonetheless, they are later also more penalised for too much government, which depicts a stronger Armey Curve for developing countries. As for developed countries, it is clear that the effect is a lot weaker, with the quadratic effect being substantially random and often paradoxical according to the metric and period established. The rationale for such structure may rely on the fact that developing countries lack the basic structure to promote growth, and consequently, any marginal improvement in government size is more significantly felt, nonetheless, only when governance is controlled. This may also reflect that since the private sector is extremely inefficient in that cluster, there is room to grow the public sector without too much of a cost to private sector efficiency. 54 Table 8: Development dynamics for 3-year periods (1) (2) (3) (4) (5) (6) Variables Sys-GMM FE Sys-GMM FE Sys-GMM FE Log GDPt−1-3.587** -5.604*** (1.699) (0.774) Log HDIt−112.340** -10.239*** (4.987) (1.016) Log HDIt−2-12.422*** (3.441) Log IHDIt−17.770** -18.156*** (3.151) (2.408) Educationt−10.074* 0.017* 0.005 0.002 -0.013 0.001 (0.040) (0.010) (0.007) (0.003) (0.014) (0.005) Developing·Size 0.837* 0.473*** 0.054 0.093*** -0.054 0.020 (0.431) (0.161) (0.091) (0.027) (0.189) (0.078) Developing·Size2-0.013* -0.008*** -0.000 -0.001*** -0.001 -0.001 (0.007) (0.003) (0.001) (0.000) (0.003) (0.001) Developed·Size 0.690* -0.431** 0.094 -0.017 -0.103 -0.079 (0.393) (0.215) (0.077) (0.036) (0.166) (0.055) Developed·Size2-0.009* 0.003 -0.001 0.000 0.002 0.001* (0.005) (0.002) (0.001) (0.000) (0.002) (0.001) GCF 0.186** 0.137*** -0.001 0.016*** 0.069** 0.020 (0.076) (0.028) (0.016) (0.005) (0.032) (0.014) Governance 0.238 0.752*** -0.239 0.061 -0.757* 0.318 (0.841) (0.285) (0.189) (0.068) (0.423) (0.216) Population -0.673* -0.456*** (0.374) (0.160) Trade 0.036*** 0.016* (0.014) (0.009) Infant 0.031* -0.024*** 0.094* -0.059 (0.016) (0.006) (0.050) (0.037) Observations 838 834 807 814 355 343 Countries 130 126 130 124 112 100 AR(1) 0.000502 0.000357 0.00482 AR(2) 0.778 0.230 Hansen test 0.126 0.271 0.551 Instruments 49 53 31 Adj. R20.508 0.703 0.588 Notes: See Table 3 55 As for developed countries, the lack of consistency may express that they are developed for a reason, given that they possess structures and infrastructure enough to sustain growth, and as such, even if incremental government expenditure is applied, contrary to developing countries, it comes at too high of a cost due to the detrimental effects on their highly efficient private sectors. Broadly, it partially reflects the behaviour of not altering a winning formula. This broadly suggests that although the Armey Curve may still exist in developed countries, nonetheless, purely government expenditure dynamics are more indirect and thus harder to assess. Accordingly, this depiction slightly contradicts the impact for developed countries exhibited by Asimakopoulos and Karavias (2016) and Martins and Veiga (2014). Furthermore, this finding might stem from these studies addressing the effect of government expenditure without accounting for the possible bias that may arise from the omission of institutional quality. In contrast, here the impact of governance is accounted for, and as such, consequential results provide innovative inferences, whose policymaking relevance will be outlined later. Similar to Martins and Veiga (2014), the income categorisation is also addressed, nonetheless, given the lack of statistical significance, four categories of income were used rather than two. Tables 9and 22 depict such dynamics for 3-year and 5-year periods, respectively. Assuming the intrinsic correlation between development and income levels, one could anticipate that low income countries could also be more affected by changes in government expenditure, nonetheless, this does not appear to be the case. For GDP in particular, the quadratic effect of government expenditure appears at least in one specification present in every cluster of income, thus obstructing the inference of causality according to level of income. The relation for HDI is similar, nonetheless, in this case, the cluster in which government expenditure has no statistical significance in lower-income countries. For IHDI, that cluster is middle-lower income countries, although in this case, it is common for the relationships to be odd, particularly since it is not uncommon for the quadratic relationship to be in a U-shape. In a broad sense, it is hard to uncover if the upper bound or the lower bound of the percentile of income provides different impacts on government expenditure, however, in a more elastic approach, we could state that it appears to be a very slight statistical superiority for upper middle and high-income countries than for the rest. If greatly accommodating and choosing the latter inference, we could depict that the results are on par with Martins and Veiga (2014), nonetheless, precaution is suggested, given the lack of statistical robustness for such a statement. 56 Table 9: Income dynamics for 3-year periods (1) (2) (3) (4) (5) (6) Variables Sys-GMM FE Sys-GMM FE Sys-GMM FE Log GDPt−1-3.912*** -5.851*** (1.318) (0.753) Log HDIt−11.002 -10.468*** (4.193) (1.156) Log GDPt−2-7.899** (3.455) Log IHDIt−1-4.900 -18.757*** (3.417) (2.286) Educationt−10.007 0.020* 0.009 0.003 -0.004 0.001 (0.027) (0.011) (0.006) (0.003) (0.013) (0.005) Low.I·Size 0.393 0.216 -0.089 0.084 -0.461** -0.424** (0.384) (0.222) (0.118) (0.089) (0.229) (0.166) Low.I·Size2-0.009 -0.004 0.002 -0.001 0.007 0.008** (0.009) (0.005) (0.002) (0.002) (0.006) (0.003) L.M.I·Size 0.540* 0.667** 0.060 0.125** -0.316* 0.147 (0.306) (0.292) (0.100) (0.060) (0.170) (0.117) L.M.I·Size2-0.008 -0.011** 0.000 -0.002* 0.004 -0.002 (0.007) (0.005) (0.003) (0.001) (0.003) (0.002) U.M.I·Size 0.725*** 0.715*** 0.152*** 0.083** -0.070 -0.023 (0.248) (0.138) (0.057) (0.041) (0.122) (0.112) U.M.I·Size2-0.009** -0.012*** -0.002** -0.002** -0.000 -0.001 (0.004) (0.002) (0.001) (0.001) (0.002) (0.001) High.I·Size 0.908*** -0.387** 0.167** 0.004 -0.093 -0.144** (0.289) (0.174) (0.068) (0.029) (0.111) (0.055) High.I·Size2-0.013*** 0.002 -0.002* 0.000 0.001 0.002*** (0.004) (0.002) (0.001) (0.000) (0.001) (0.001) GCF 0.171*** 0.136*** 0.015 0.016*** 0.044 0.018 (0.052) (0.026) (0.016) (0.005) (0.029) (0.014) Governance 0.134 0.734*** 0.000 0.071 0.043 0.293 (0.530) (0.278) (0.127) (0.070) (0.346) (0.211) Population -0.412 -0.440*** (0.302) (0.148) Trade 0.043*** 0.015* (0.012) (0.008) Infant 0.006 -0.024*** -0.006 -0.065** (0.016) (0.006) (0.045) (0.031) Observations 838 834 806 814 355 343 Countries 130 126 129 124 112 100 AR(1) 0.000150 0.00121 0.00868 AR(2) 0.698 0.240 Hansen test 0.405 0.253 0.399 Instruments 121 73 104 Adj. R20.515 0.706 0.608 Notes: See Table 3 57 Table 12: Economic growth and COFOG components for 3-year periods (1) (2) (3) Variables Sys-GMM FE FE Defense 2.855*** (1.049) Defense2-0.375*** (0.122) Safety 5.250** (2.516) Safety2-1.354** (0.566) Social -0.631* (0.369) Observations 424 420 427 Countries 68 63 65 AR(1) 0.0481 AR(2) 0.374 Hansen test 0.833 Instruments 25 Adj. R20.560 0.487 Notes: Statistically relevant Two-step System-GMM and Fixed effects regressions, including 3-year period dummies. Controls equal to Table 1, but omitted due to size constraints. GMM estimations use robust standard errors. FE estimations use standard errors clustered by country and robust to heteroskedasticity. All variables are treated as endogenous in System-GMM estimations with the exception of period dummies. The dependent variable is the average annual growth rate of GDP per capita for all regressions. Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 64 Table 13: Economic development and COFOG components for 3-year periods (1) (2) (3) (4) (5) (6) (7) Variables FE Sys-GMM FE Sys-GMM Sys-GMM FE FE Defense -0.140** (0.054) Public -0.051* -0.041*** (0.027) (0.012) Public20.001* 0.001*** (0.001) (0.000) Health -0.288* (0.164) Health20.036*** (0.013) Safety 1.079** 0.602*** (0.470) (0.166) Safety2-0.220** -0.132*** (0.087) (0.034) Social -0.040** (0.018) Social20.002** (0.001) Observations 404 419 413 418 413 406 413 Countries 60 69 63 68 68 61 63 AR(1) 0.00216 0.00520 0.00446 AR(2) 0.932 0.929 0.853 Hansen test 0.153 0.294 0.124 Instruments 65 51 65 Adj. R20.695 0.673 0.696 0.671 Notes: Statistically relevant Two-step System-GMM and Fixed effects regressions, including 3-year period dummies. Controls equal to Table 1, but omitted due to size constraints. GMM estimations use robust standard errors. FE estimations use standard errors clustered by country and robust to heteroskedasticity. All variables are treated as endogenous in System-GMM estimations with the exception of period dummies. The dependent variable is the average annual growth rate of HDI for all regressions. Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 65 Table 14: Inclusive economic development and COFOG components for 3-year periods (1) (2) (3) (4) (5) (6) Variables Sys-GMM FE Sys-GMM FE Sys-GMM Sys-GMM Defense -0.362*** -0.196*** (0.135) (0.058) Economic 0.244** (0.114) Economic2-0.006*** (0.002) Gov.Education -0.148* (0.074) Environment -4.100** (1.986) Environment22.778** (1.246) Health -0.478** (0.241) Health20.046*** (0.015) Observations 205 200 207 203 207 207 Countries 62 57 62 58 62 62 AR(1) 0.0592 0.00974 0.00695 0.0173 AR(2) 0.872 0.730 0.203 0.450 Hansen test 0.421 0.323 0.193 0.233 Instruments 52 38 32 44 Adj. R20.652 0.621 Notes: Notes: Statistically relevant Two-step System-GMM and Fixed effects regressions, including 3-year period dummies. Controls equal to Table 1, but omitted due to size constraints. GMM estimations use robust standard errors. FE estimations use standard errors clustered by country and robust to heteroskedasticity. All variables are treated as endogenous in System-GMM estimations with the exception of period dummies. The dependent variable is the average annual growth rate of IHDI for all regressions. Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 66 Table 15: Inclusive economic development and COFOG components for 3-year periods (extension) (1) (2) (3) (4) (5) Variables FE Sys-GMM FE Sys-GMM FE Housing -0.284*** (0.102) Safety 1.092* 0.612* (0.657) (0.364) Safety2-0.260*** -0.151*** (0.100) (0.047) Culture 1.715** (0.759) Culture2-0.352* (0.182) Social -0.129*** (0.038) Social20.006** (0.002) Observations 203 205 200 207 203 Countries 58 62 57 62 58 AR(1) 0.0295 0.0157 AR(2) 0.748 0.859 Hansen test 0.238 0.238 Instruments 56 56 Adj. R20.621 0.657 0.631 Notes: Notes: Statistically relevant Two-step System-GMM and Fixed effects regressions, including 3-year period dummies. Controls equal to Table 1, but omitted due to size constraints. GMM estimations use robust standard errors. FE estimations use standard errors clustered by country and robust to heteroskedasticity. All variables are treated as endogenous in System-GMM estimations with the exception of period dummies. The dependent variable is the average annual growth rate of HDI for all regressions. Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 67 4.2 Robustness analysis As suggested in Part 2,Labonte (2010) and Vedder and Gallaway (1998) depict that government expenditure is a more appropriate metric to measure government size than government revenue, nonetheless, using the latter is still reasonable. Therefore, this section depicts the basic results using government revenue as a percentage of GDP as a proxy for government size to ensure that the basic results in Tables 3and 4hold. Table 16 displays the results using 3-year periods, with the fundamental results corroborating the hypothesis of conditional convergence, implying that after controlling for country-specific characteristics, they tend to their steady states, independently of the metric adopted as dependent. Although at times less significant, the rest of the explanatory variables still hold their effects on economic indicators. Particularly, education and trade still present beneficial impacts on prosperity. Governance and gross capital formation remain beneficial to GDP and HDI. Additionally, the population growth rate and infant mortality remain nefarious, the first to GDP growth and the latter to HDI and IHDI. As for government size, the quadratic effect of the Armey Curve is still present, at least for HDI, with the respective optimum of 43.73% for System-GMM and 36.71% for FE. In Table 29, explanatory variables behave as anticipated. Regarding government size, the quadratic effect is significant for both GDP and HDI, with optimums of 42.46% and 35.96% of GDP for the latter. Similarly to subsection 4.1.1, the lack of statistical relevance may not necessarily indicate the inexistence of the Armey Curve but rather a direct repercussion of the small sample size. As such, the same exercise is practised here, where controls are discarded to augment sample size, nonetheless, now using revenues. In Table 17, the main inferences are clear, particularly that, in most regressions, the quadratic effect of government size appears, similar to the Armey Curve. Respective optimums are 39.78% and 32.24% for 3-year System-GMM and FE estimations. For 5-year periods, only System-GMM provides results, with an optimal size of 43.69%. Summarising, it is clear that government revenue presents a partial loss of statistical capability than when government size is represented by expenditure, nonetheless, the robust empirical evidence, for at least economic growth and development, and less robustly, for inclusive economic development, strongly supports the existence of the Armey Curve. 68 Table 16: Robustness check using government revenue for 3-year periods (1) (2) (3) (4) (5) (6) Variables Sys-GMM FE Sys-GMM FE Sys-GMM FE Log GDPt−1-3.006*** -5.487*** (0.854) (0.852) Log HDIt−1-8.590*** -9.843*** (3.124) (1.025) Log IHDIt−15.844* -18.326*** (3.141) (2.465) Educationt−10.025 0.007 0.014** 0.002 0.013 0.002 (0.019) (0.012) (0.007) (0.002) (0.018) (0.005) Size (revenue) 0.458** 0.213** 0.248*** 0.058*** -0.112 0.024 (0.193) (0.106) (0.075) (0.020) (0.095) (0.069) Size (revenue)2-0.005 -0.002 -0.003** -0.001*** 0.002 -0.000 (0.003) (0.002) (0.001) (0.000) (0.001) (0.001) GCF 0.230*** 0.138*** 0.005 0.015*** 0.049 0.019 (0.051) (0.031) (0.014) (0.005) (0.045) (0.014) Governance 0.177 0.890*** 0.358* 0.063 -0.279 0.292 (0.536) (0.309) (0.195) (0.065) (0.354) (0.215) Population -0.755* -0.432** (0.403) (0.170) Trade 0.025** 0.018* (0.012) (0.010) Infant -0.006 -0.023*** 0.127** -0.062* (0.025) (0.006) (0.064) (0.033) Observations 838 834 820 814 355 343 Countries 130 126 130 124 112 100 AR(1) 0.000291 0.0216 0.00530 AR(2) 0.610 0.254 0.751 Hansen test 0.366 0.258 0.291 Instruments 129 102 38 Adj. R20.480 0.700 0.585 Notes: Two-step System-GMM and Fixed effects regressions, including 3-year period dummies. GMM estimations use robust standard errors. FE estimations use standard errors clustered by country and robust to heteroskedasticity. All variables are treated as endogenous in System-GMM estimations with the exception of period dummies. The dependent variable is the average annual growth rate of GDP per capita for (1) and (2), of HDI for (3) and (4), and of IHDI for (5) and (6). Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 69 Table 17: Alternative estimations for inclusive development using government revenue 3-year periods 5-year periods (1) (2) (3) (4) Variables Sys-GMM FE Sys-GMM FE Log IHDIt−10.332 -14.913*** 4.616 -13.660*** (2.471) (1.543) (5.186) (1.823) Size (revenue) 0.156*** 0.131* 0.141** 0.069* (0.051) (0.074) (0.056) (0.041) Size (revenue)2-0.002* -0.002* -0.002* -0.001 (0.001) (0.001) (0.001) (0.001) GCF 0.021* 0.048* (0.011) (0.025) Governance 0.247 -0.448 (0.206) (0.448) Infant 0.050 0.094 (0.051) (0.068) Observations 461 441 327 338 Countries 128 119 121 122 AR(1) 0.000115 0.0334 AR(2) 0.139 Hansen test 0.102 0.276 Instruments 59 35 Adj. R20.523 0.385 Notes: Two-step System-GMM and Fixed effects regressions, including 3-year or 5-year period dummies. GMM estimations use robust standard errors. FE estimations use standard errors clustered by country and robust to heteroskedasticity. All variables are treated as endogenous in System-GMM estimations with the exception of period dummies. The dependent variable is the average annual growth rate of IHDI for all regressions. Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 70 4.3 Policy and research recommendations The innovative relations this dissertation depicts allow us to ponder the current situation related to government expenditure worldwide. The worldwide average government size, around 32%, is not much further from the roughly 30% provided by the GDP, while it is still somewhat lower than the 35% to 40% provided by the HDI or IHDI. Considering this, there are no worldwide applicable policy recommendations in this aspect. Rather, the worldwide heterogeneity makes it clear that certain clusters should follow certain policies. For instance, it is clear that the Western World, mainly European countries, report much larger government sizes than the optimum, commonly even larger than 50%. Table 18: Optimal government size by indicator Optimal Government Size GDP HDI IHDI 27.22% - 32.54% 33.34% - 42.20% 31.23% - 40.69% Table 19: Actual government size as of 2022 across different regions Actual Government Size as of 2022 Developed Developing European Union 43.20% 28.33% 45.36% Sub-Saharan Africa Europe Western World 24.48% 43.29% 44.67% Even though each country should consider their specific cases, the evidence of overgrown governments is real for the Western World, and as such, it is highly recommended for such governments to start to consider trimming governmental presence in the economy, given that, independently of the metric used, whether it is more economic or social, there does not seem to be much to gain from incremental governmental presence. Such policymaking could be a tool to oppose the recent history of deficient growth that has been taking place in Europe, particularly in the European Union (EU) member states, and broad efforts to lower government size to roughly 30-40% would be optimal, however, taking into account the private sector and social responses, given that it is important to guarantee that government cuts do not impose unequal 71 social damage on the most vulnerable layers of society. Instituting European margins controlling the size of government in state members could be a method in which some inefficient central interference is replaced by private sector activity in an attempt to stimulate corporate strength and competitiveness. The results, however, also stress that governance still takes a major role, and consequently, the European institutions, such as the EU and its branches, should continue to focus on further guaranteeing institutional robustness and efficiency, although that recommendation applies to the rest of the world. The situation is the opposite for developing countries, where the government size is largely lower than any of the optimums computed, where it is common, particularly for regions such as sub-Saharan Africa, to report values of only 15% of government size. Contrary to the expectations, the evidence does not indicate that manipulations in government size are only valuable when accompanied by institutional quality, although the latter remains highly relevant for prosperity. In other words, while puzzling, it appears that countries severely hindered by weak institutional settings may, in some cases, be better positioned to extract greater utility from adjustments in government presence. Consequently, at least theoretically, countries that lack sufficient governance resilience to effectively and significantly promote prosperity could utilize development policies involving adjustments to the size of government to enhance their overall economic prosperity. This, in turn, could enable countries that could not initially afford good governance to overcome stagnation and gain momentum. Regarding overall governance, the most significant takeaway for policymakers, particularly international aid institutions, is the need to shift their focus away from merely funding precarious nations. Instead, they should prioritize implementing and sharing knowledge to help strengthen their lacking institutions, resorting to financial assistance only when absolutely necessary. Structuring development policies in this way would enable developing countries to enhance institutional efficiency in a manner that fosters growth and development. At the same time, international oversight would help ensure that the newly established institutions are stimulative rather than extractive. Such a distinct approach could be a method by which developing countries overcome the poverty trap that has been sabotaging the convergence of some regions, particularly sub-Saharan Africa. In general, this practice would focus on investing in teaching rather than just providing and thus enabling independence rather than dependence. Additionally, to guarantee prosperity, both developed and developing countries should take into account the distinct dynamics of certain expenditures and guarantee that the financial needs for public order and 72 safety are the first to be satisfied, given their pivotal role in the promotion of economic and social welfare. It is, however, important to stress that no metric of welfare is perfect, consequently, it is essential to continue to elaborate more perfected measures to represent quality of life. Particularly, although HDI and IHDI represent, at least in theory, enhancements from GDP, it is clear that they also have their shortcomings. The reason that most economists still use GDP to capture welfare may indicate that the new development indicators cannot still do what they were supposed to do, particularly to replace GDP in most studies of development. For HDI and IHDI, specifically, their bounding from zero to one may present a disadvantage rather than an advantage, given that it furthers itself too much from the numeric and benefic nature of GDP, which allows it to provide more accurate results. Such ranges do not allow so much heterogeneity and, consequently, commonly do not have as much statistical relevance as one hopes for. While GDP disregards inequality, the HDI and IHDI may be focused too much on the social aspect by disconnecting themselves too much from the intrinsic economic validity of normative indicators. Additionally, controlling for inequality may even be more appropriate than including health and education in the construction of HDI and IHDI. The rationale focuses on the fact that the inclusion of health prospects and education prospects does not allow economic variability, while at the same time, it is extremely rare for countries to have good incomes and satisfactory income distributions while lacking in levels of education and health. Consequently, including health and education could cause more harm than benefits, and thus, for future analysis, it could be more interesting to assess dynamics for a new variable that connects GDP and income inequality. The IHDI has a similar construction to its income component, but unfortunately, it computes it to be in the range from zero to one. Inequality-adjusted GDP per capita = Real GDP per capita 1 + ( Gini Index 100 ) For new dynamics, I recommend the construction of a new variable of GDP per capita adjusted for inequality, which allows us to guarantee that we focus on the numerical nature of GDP while at the same time guaranteeing that we are capturing citizens welfare, penalising an unequal distribution of economic power. A simple computation of GDP per capita discounted according to the Gini index could be a good starting point for the construction of that variable. The study of government size is highly relevant to assess the relevance of a central government and its presence in society and consequently addressing how the mechanisms change when attempting to 73 Barro, R. J., Sala-I-Martin, X., Blanchard, O. J., and Hall, R. E. (1991). Convergence across states and regions. Brookings Papers on Economic Activity , 1991(1):107–182. https://doi.org/10.2307/ 2534639. Beck, T. and Levine, R. (2004). Stock markets, banks, and growth: Panel evidence. Journal of Banking & Finance , 28(3):423–442. https://doi.org/10.1016/S0378-4266(02)00408-9. Bergh, A. and Henrekson, M. (2011). Government size and growth: a survey and interpretation of the evidence. Journal of Economic Surveys , 25(5):872–897. https://doi.org/10.1111/j. 1467-6419.2011.00697.x. Bernanke, B. S. (2000). Essays on the Great Depression . Princeton University Press, stu - student edition edition. http://www.jstor.org/stable/j.ctt7s5dh. Berry, W. D. and Lowery, D. (1984). The measurement of government size: Implications for the study of government growth. The Journal of Politics , 46(4):1193–1206. https://doi.org/10.2307/ 2131249. Bhargava, A. and Sargan, J. D. (1983). Estimating dynamic random effects models from panel data covering short time periods. Econometrica: Journal of the Econometric Society , pages 1635–1659. https://doi.org/10.2307/1912110. Blundell, R. and Bond, S. (1998). Initial conditions and moment restrictions in dynamic panel data models. Journal of econometrics , 87(1):115–143. https://doi.org/10.1016/S0304-4076(98) 00009-8. Boldrin, M. and Canova, F. (2001). Inequality and convergence in Europe’s regions: reconsidering European regional policies. Economic Policy , 16(32):206–253. https://doi.org/10.1111/ 1468-0327.00074. Bond, S. (2002). Dynamic panel data models: A guide to micro data methods and practice. Portuguese Economic Journal .https://doi.org/10.1007/s10258-002-0009-9. Bond, S., Hoeffler, A., and Temple, J. (2001). Gmm estimation of empirical growth models. Centre for Economic Policy Research Discussion Papers .https://ssrn.com/abstract=290522. Bose, N., Haque, M. E., and Osborn, D. R. (2007). Public expenditure and economic growth: A disaggregated analysis for developing countries. The Manchester School , 75(5):533–556. https: //doi.org/10.1111/j.1467-9957.2007.01028.x. 80 Canova, F. and Marcet, A. (1995). The poor stay poor: Non-convergence across countries and regions, discussion paper no. 1265. Center for Economic PolicyResearch (CEPR), London. https://ssrn. com/abstract=289497. Chen, S.-T. and Lee, C.-C. (2005). Government size and economic growth in taiwan: A threshold regression approach. Journal of Policy Modeling , 27(9):1051–1066. https://doi.org/10.1016/j. jpolmod.2005.06.006. Chiou-Wei, S.-Z., Zhu, Z., and Kuo, Y.-H. (2010). Government size and economic growth: an application of the smooth transition regression model. Applied Economics Letters , 17(14):1405–1415. https: //doi.org/10.1080/13504850902984295. Cho, D. and Graham, S. (1996). The other side of conditional convergence. Economics Letters , 50(2):285– 290. https://doi.org/10.1016/0165-1765(95)00745-8. Cooray, A. (2009). Government expenditure, governance and economic growth. Comparative economic studies , 51:401–418. https://doi.org/10.1057/ces.2009.7. Dar, A. A. and AmirKhalkhali, S. (2002). Government size, factor accumulation, and economic growth: evidence from oecd countries. Journal of Policy Modeling , 24(7):679–692. https://doi.org/10. 1016/S0161-8938(02)00163-1. Davies, A. (2009). Human development and the optimal size of government. The Journal of SocioEconomics , 38(2):326–330. https://doi.org/10.1016/j.socec.2008.07.015. Derviş, K. and Qureshi, Z. (2016). Income distribution within countries: Rising inequality. Global Economy and Development. Brookings .https://www.brookings.edu/articles/ income-distribution-within-countries-rising-inequality/. Devarajan, S., Swaroop, V., and fu Zou, H. (1996). The composition of public expenditure and economic growth. Journal of Monetary Economics , 37(2):313–344. https://doi.org/10.1016/ S0304-3932(96)90039-2. Di Matteo, L. (2013). Measuring government in the 21st century: An international overview of the size and efficiency of public spending . Fraser Institute. https://www.fraserinstitute.org/studies/ measuring-government-21st-century. 81 DiPeitro, W. R. and Anoruo, E. (2012). Government size, public debt and real economic growth: a panel analysis. Journal of Economic Studies , 39(4):410–419. https:doi.org/10.1108/ 01443581211255620. Dryzek, J. and Goodin, R. E. (1986). Risk-sharing and social justice: The motivational foundations of the post-war welfare state. British Journal of Political Science , 16(1):1–34. https://doi.org/10. 1017/S0007123400003781. Easterlin, R. A. (2001). Income and happiness: Towards a unified theory. The Economic Journal , 111(473):465–484. https://doi.org/10.1111/1468-0297.00646. Easterlin, R. A. (2015). Happiness and Economic Growth – The Evidence , pages 283–299. Springer Netherlands, Dordrecht. https://doi.org/10.1007/978-94-017-9178-6_12. Friedman, M. (2016). 61. Capitalism and Freedom , pages 344–349. Columbia University Press, New York Chichester, West Sussex. https://doi.org/10.7312/blau17412-074. Goel, R. K. and Nelson, M. A. (1998). Corruption and government size: A disaggregated analysis. Public choice , 97(1):107–120. https://doi.org/10.1023/A:1004900603583. Goh, H.-H. and Mohd Aznan, M. S. B. (2023). The optimal government size and economic growth: A comparative study between malaysia and south korea. Heliyon , 9(12):e22834. https://doi.org/ 10.1016/j.heliyon.2023.e22834. Guseh, J. S. (1997). Government size and economic growth in developing countries: A politicaleconomy framework. Journal of Macroeconomics , 19(1):175–192. https://doi.org/10.1016/ S0164-0704(97)00010-4. Gwartney, J. D., Lawson, R., and Holcombe, R. G. (1998). The size and functions of government and economic growth . Joint Economic Committee, Washington. https://ohu.people.ysu.edu/ articles/govt_size_economic_growth.pdf. Hajamini, M. and Falahi, M. A. (2018). Economic growth and government size in developed european countries: A panel threshold approach. Economic Analysis and Policy , 58:1–13. https://doi. org/10.1016/j.eap.2017.12.002. Hausmann, R., Rodrik, D., and Velasco, A. (2008). 32415 Growth Diagnostics. In The Washington Consensus Reconsidered: Towards a New Global Governance . Oxford University Press. https:// doi.org/10.1093/acprof:oso/9780199534081.003.0015. 82 Hibbs, D. A. (1977). Political parties and macroeconomic policy. American Political Science Review , 71(4):1467–1487. https://doi.org/10.2307/1961490. Hicks, D. A. (1997). The inequality-adjusted human development index: A constructive proposal. World Development , 25(8):1283–1298. https://doi.org/10.1016/S0305-750X(97)00034-X. Hicks, J. R. (1948). Value and Capital (2nd ed.) . Oxford University Press. https://global.oup. com/academic/product/value-and-capital-9780198282693?cc=pt&lang=en&. Kaihatsu, S., Koga, M., Sakata, T., Hara, N., et al. (2019). Interaction between business cycles and economic growth. Monetary and Economic Studies , 37(1):99–126. https://www.imes.boj.or. jp/research/papers/english/me37-6.pdf. Kaitila, V. (2004). Integration and conditional convergence in the enlarged eu area. ETLA Discussion Papers 935, ETLA Discussion Papers, Helsinki. https://hdl.handle.net/10419/63931. Karras, G. (1996). The optimal government size: Further international evidence on the productivity of government services. Economic Inquiry , 34(2):193–203. https://doi.org/10.1111/j. 1465-7295.1996.tb01372.x. Karras, G. (1997). On the optimal government size in europe: Theory and empirical evidence. The Manchester School , 65(3):280–294. https://doi.org/10.1111/1467-9957.00057. Keynes, J. M. (1923). A tract on monetary reform . Cosimo Classics. https://hdl.handle.net/ 2027/mdp.35112104085974. Kim, D.-H., Wu, Y.-C., and Lin, S.-C. (2018). Heterogeneity in the effects of government size and governance on economic growth. Economic Modelling , 68:205–216. https://doi.org/10.1016/j. econmod.2017.07.014. Kuznets, S. (1941). National income . National Bureau of Economic Research New York. http://www. nber.org/books/kuzn41-2. Labonte, M. (2010). The size and role of government: Economic issues, june 14, congressional research service 7-5700, rl32162. https://hdl.handle.net/1813/77640. Laeven, M. L., Igan, M. D., Claessens, M. S., and Dell’Ariccia, M. G. (2010). Lessons and policy implications from the global financial crisis. IMF Working Papers .https://doi.org/10.5089/ 9781451963021.001. 83 Landau, D. (1983). Government expenditure and economic growth: A cross-country study. Southern Economic Journal , 49(3):783–792. https://doi.org/10.2307/1058716. Lin, S. A. (1994). Government spending and economic growth. Applied Economics , 26(1):83–94. https: //doi.org/10.1080/00036849400000064. Loayza, N. V. and Rancière, R. (2006). Financial development, financial fragility, and growth. Journal of Money, Credit and Banking , 38(4):1051–1076. http://www.jstor.org/stable/3838993. Mahler, V. A. (1992). Measuring public sector size in the advanced market economy countries: The problem of deflators. Social Indicators Research , 27:311–325. https://doi.org/10.1007/ BF00303852. Makin, A. J., Pearce, J., and Ratnasiri, S. (2019). The optimal size of government in australia. Economic Analysis and Policy , 62:27–36. https://doi.org/10.1016/j.eap.2018.12.001. Martins, S. and Veiga, F. J. (2014). Government size, composition of public expenditure, and economic development. International Tax and Public Finance , 21:578–597. https://doi.org/10.1007/ s10797-014-9313-4. Mathur, S. K. (2005). Economic growth & conditional convergence: Its speed for selected regions for 19612001. Indian Economic Review , 40(2):185–208. http://www.jstor.org/stable/29793843. McKinley, T. (2010). Inclusive growth criteria and indicators: An inclusive growth index for diagnosis of country progress. Technical report, Asian Development Bank. https://www.adb.org/ publications. Mueller, D. C. (2003). Public Choice III . Cambridge University Press, 3 edition. https://doi.org/ 10.1017/CBO9780511813771. Murthy, N. V. and Chien, I. (1997). The empirics of economic growth for oecd countries: Some new findings. Economics Letters , 55(3):425–429. https://doi.org/10.1016/S0165-1765(97) 00092-X. Nahar, S. and Inder, B. (2002). Testing convergence in economic growth for oecd countries. Applied Economics , 34(16):2011–2022. https://doi.org/10.1080/00036840110117837. 84 Nell, K. S. (2020). Evaluating the conditional convergence hypothesis in the post-1989 globalization period. Applied Economics , 52(30):3308–3326. https://doi.org/10.1080/00036846.2019. 1710451. Nirola, N. and Sahu, S. (2019). The interactive impact of government size and quality of institutions on economic growthevidence from the states of india. Heliyon , 5(3):e01352. https://doi.org/10. 1016/j.heliyon.2019.e01352. Nonneman, W. and Vanhoudt, P. (1996). A Further Augmentation of the Solow Model and the Empirics of Economic Growth for OECD Countries*. The Quarterly Journal of Economics , 111(3):943–953. https://doi.org/10.2307/2946677. Nordhaus, W. D. and Tobin, J. (1972). Economic Research: Retrospect and Prospect, Volume 5, Economic Growth . NBER. http://www.nber.org/chapters/c7620. North, D. C. and Thomas, R. P. (1973). The Rise of the Western World: A New Economic History . Cambridge University Press. https://doi.org/10.1017/CBO9780511819438. OECD (2024). Society at a Glance 2024: OECD Social Indicators . OECD Publishing, Paris. https: //doi.org/10.1787/918d8db3-en. Peacock, A. and Scott, A. (2000). The curious attraction of wagner’s law. Public choice , 102(1):1–17. https://doi.org/10.1023/A:1005032817804. Pedersen, T. M. and Elmer, A. M. (2003). International evidence on the connection between business cycles and economic growth. Journal of Macroeconomics , 25(2):255–275. https://doi.org/ 10.1016/S0164-0704(03)00028-4. Quah, D. (1993). Galton’s fallacy and tests of the convergence hypothesis. The Scandinavian Journal of Economics , 95(4):427–443. https://doi.org/10.2307/3440905. Quah, D. T. (1997). Empirics for growth and distribution: Stratification, polarization, and convergence clubs. Journal of economic growth , 2:27–59. https://doi.org/10.1023/A:1009781613339. Ram, R. (1986). Government size and economic growth: A new framework and some evidence from cross-section and time-series data. The American Economic Review , 76(1):191–203. http://www. jstor.org/stable/1804136. 85 Rauniyar, G. and Kanbur, R. (2010). Inclusive growth and inclusive development: a review and synthesis of asian development bank literature. Journal of the Asia Pacific Economy , 15(4):455–469. https: //doi.org/10.1080/13547860.2010.517680. Romer, P. M. (1986). Increasing returns and long-run growth. Journal of Political Economy , 94(5):1002– 1037. https://doi.org/10.1086/261420. Sachs, J. D., McArthur, J. W., Schmidt-Traub, G., Kruk, M., Bahadur, C., Faye, M., and McCord, G. (2004). Ending africa’s poverty trap. Brookings Papers on Economic Activity , 2004(1):117–216. http:// www.jstor.org/stable/3217964. Sagar, A. D. and Najam, A. (1998). The human development index: a critical review. Ecological Economics , 25(3):249–264. https://doi.org/10.1016/S0921-8009(97)00168-7. Samuelson, P. A. (1961). The Evaluation of ‘Social Income’: Capital Formation and Wealth , pages 32–57. Palgrave Macmillan UK, London. https://doi.org/10.1007/978-1-349-08452-4_3. Schularick, M. and Solomou, S. (2011). Tariffs and economic growth in the first era of globalization. Journal of Economic Growth , 16:33–70. https://doi.org/10.1007/s10887-011-9061-6. Seth, S. (2009). Inequality, interactions, and human development. Journal of Human Development and Capabilities , 10(3):375–396. https://doi.org/10.1080/19452820903048878. Shearer, R. A. (1961). The concept of economic growth. Kyklos , 14(4):497–532. https://doi.org/ 10.1111/j.1467-6435.1961.tb00368.x. Smith, A. (1776). An Inquiry into the Nature and Causes of the Wealth of Nations . History of Economic Thought Books. McMaster University Archive for the History of Economic Thought. https://doi. org/10.7208/chicago/9780226763750.001.0001. Solow, R. M. (1956). A contribution to the theory of economic growth. The Quarterly Journal of Economics , 70(1):65–94. https://doi.org/10.2307/1884513. Streeten, P. (1994). Human development: Means and ends. The American Economic Review , 84(2):232– 237. http://www.jstor.org/stable/2117835. Sturn, S. and Epstein, G. (2021). How much should we trust five-year averaging to purge business cycle effects? a reassessment of the finance-growth and capital accumulation-unemployment nexus. Economic Modelling , 96:242–256. https://doi.org/10.1016/j.econmod.2020.12.028. 86 Tanninen, H. (1999). Income inequality, government expenditures and growth. Applied Economics , 31(9):1109–1117. https://doi.org/10.1080/000368499323599. Tanzi, V. and Schuknecht, L. (1997). Reconsidering the fiscal role of government: The international perspective. The American Economic Review , 87(2):164–168. https://www.jstor.org/stable/ 2950906. Terasawa, K. L. and Gates, W. R. (1998). Relationships between government size and economic growth: Japan’s government reforms and evidence from oecd. International Public Management Journal , 1(2):195–223. https://doi.org/10.1016/S1096-7494(99)80091-9. Ullah, S., Akhtar, P., and Zaefarian, G. (2018). Dealing with endogeneity bias: The generalized method of moments (gmm) for panel data. Industrial Marketing Management , 71:69–78. https://doi.org/ 10.1016/j.indmarman.2017.11.010. van den Bergh, J. C. (2009). The gdp paradox. Journal of Economic Psychology , 30(2):117–135. https: //doi.org/10.1016/j.joep.2008.12.001. Vedder, R. K. and Gallaway, L. E. (1998). Government Size and Economic Growth . The Committee. https://hdl.handle.net/2027/osu.32435069311363. Whajah, J., Bokpin, G. A., and Kuttu, S. (2019). Government size, public debt and inclusive growth in africa. Research in International Business and Finance , 49:225–240. https://doi.org/10.1016/j. ribaf.2019.03.008. Wolfowitz, P. (2006). Good governance and development: a time for action, jakarta, indonesia. Remarks by President, Paul Wolfowitz (English). Presidential speech Washington, D.C. : World Bank Group. http://documents.worldbank.org/curated/en/938181467987875500. World Bank (2022). World development report 2022: Finance for an equitable recovery (vol. 1 of 2) (english). Technical report, World Bank Group. World Development Indicators | World Development Report, Washington, D.C. http://documents.worldbank.org/curated/en/ 408661644986413472. 87 A Annex 0 7.5 15 Logarithm of GDP per capita 3 4 5 Logarithm of HDI -100 0 100 GDP per capita growth rate (%) -25 0 25 HDI growth rate (%) Observations 95% Confidence interval Predicted values Figure 12: Trend lines of GDP per capita and HDI. Source: UNDP/WB. 5 10 15 Logarithm of GDP per capita 2.5 4 5.5 Logarithm of IHDI -100 0 100 GDP per capita growth rate (%) -20 0 20 IHDI growth rate (%) Observations 95% Confidence interval Predicted values Figure 13: Trend lines of GDP per capita and IHDI. Source: UNDP/WB. 88 3 4 5 Logarithm of HDI 2.5 4 5.5 Logarithm of IHDI -20 0 20 HDI growth rate (%) -20 0 20 IHDI growth rate (%) Observations 95% Confidence interval Predicted values Figure 14: Trend lines of HDI and IHDI. Source: UNDP. 0 5 10 15 Logarithm of GDP per capita 0 25 50 75 100 Government expenditure (% of GDP) -75 0 75 GDP per capita growth rate (%) 0 25 50 75 100 Government expenditure (% of GDP) Observations 95% Confidence interval Predicted values Figure 15: Trend line of government size and the GDP per capita growth rate. Source: WB/IMF. 89 Table 23: Consumption and investment for 5-year periods (1) (2) (3) (4) (5) (6) Variables Sys-GMM FE Sys-GMM FE Sys-GMM FE Log GDPt−10.194 -5.871*** (1.773) (1.029) Log GDPt−2-1.768 (1.658) Log HDIt−16.116 -11.042*** (5.128) (1.392) Log HDIt−2-6.492*** (2.104) Log IHDIt−1-3.655 -18.388*** (5.805) (4.374) Educationt−1-0.013 0.002 -0.006 -0.001 0.003 -0.008 (0.019) (0.013) (0.013) (0.002) (0.028) (0.008) Consumption 0.440 0.271*** 0.281** 0.024 0.384** 0.037 (0.317) (0.092) (0.123) (0.018) (0.183) (0.076) Consumption2-0.007 -0.005*** -0.004*** -0.000 -0.006** -0.000 (0.005) (0.001) (0.002) (0.000) (0.003) (0.001) Investment -1.466** 0.082 -0.303* 0.072** 0.162 -0.245 (0.678) (0.175) (0.167) (0.030) (0.336) (0.293) Investment20.104** -0.012 0.037** -0.004* -0.022 0.027 (0.053) (0.010) (0.017) (0.002) (0.023) (0.031) GCF 0.147** 0.144*** 0.014 0.007 0.060 0.049*** (0.069) (0.035) (0.024) (0.006) (0.048) (0.011) Governance -0.014 1.230*** 0.424** 0.003 0.187 0.401 (0.533) (0.335) (0.201) (0.071) (0.538) (0.260) Population -1.747** -0.621*** (0.737) (0.207) Trade 0.016* 0.015* (0.009) (0.009) Infant 0.059 -0.034*** -0.020 -0.095 (0.049) (0.008) (0.064) (0.063) Observations 451 443 432 435 165 128 Countries 122 114 121 112 101 64 AR(1) 0.0428 0.00621 AR(2) 0.215 0.815 Hansen test 0.331 0.116 0.952 Instruments 34 31 20 Adj. R20.614 0.796 0.708 Notes: See Table 4 96 Table 24: Economic growth quantile regression (1) (2) (3) (4) (5) 3-year periods τ= 0.1τ= 0.25 τ= 0.5τ= 0.75 τ= 0.9 Log GDPt−10.823* 0.829*** 0.836*** 0.842*** 0.846*** (0.445) (0.304) (0.142) (0.038) (0.100) Educationt−10.000 0.000 0.000 0.000 0.000 (0.006) (0.004) (0.002) (0.001) (0.001) Size 0.016 0.013 0.009 0.006 0.003 (0.056) (0.039) (0.018) (0.005) (0.013) Size2-0.000 -0.000 -0.000 -0.000 -0.000 (0.001) (0.001) (0.000) (0.000) (0.000) GCF 0.003 0.004 0.004 0.005*** 0.005 (0.015) (0.010) (0.005) (0.001) (0.003) Governance 0.030 0.026 0.022 0.018 0.016 (0.160) (0.109) (0.051) (0.014) (0.036) Population -0.004 -0.008 -0.014 -0.018* -0.021 (0.108) (0.074) (0.035) (0.009) (0.024) Trade 0.000 0.000 0.001 0.001* 0.001 (0.004) (0.003) (0.001) (0.000) (0.001) Observations 838 838 838 838 838 (1) (2) (3) (4) (5) 5-year periods τ= 0.1τ= 0.25 τ= 0.5τ= 0.75 τ= 0.9 Log GDPt−10.687*** 0.693*** 0.703*** 0.713*** 0.718*** (0.128) (0.094) (0.052) (0.047) (0.066) Educationt−10.001 0.001 0.001 0.001 0.001 (0.002) (0.001) (0.001) (0.001) (0.001) Size 0.015 0.014 0.014** 0.014** 0.014 (0.016) (0.012) (0.007) (0.006) (0.008) Size2-0.000 -0.000 -0.000** -0.000** -0.000 (0.000) (0.000) (0.000) (0.000) (0.000) GCF 0.006 0.006* 0.006*** 0.007*** 0.007*** (0.005) (0.003) (0.002) (0.002) (0.002) Governance 0.042 0.040 0.037* 0.033* 0.031 (0.047) (0.034) (0.019) (0.017) (0.024) Population -0.012 -0.012 -0.012 -0.012 -0.012 (0.030) (0.022) (0.012) (0.011) (0.016) Trade 0.000 0.001 0.001 0.001* 0.001 (0.001) (0.001) (0.001) (0.000) (0.001) Observations 573 573 573 573 573 Notes: Quartile regressions using the quantiles of 0.1, 0.25, 0.5, 0.75 and 0.9. The dependent variable is the logarithm of GDP per capita for all regressions. Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 97 Table 25: Inclusive economic development quantile regression (1) (2) (3) (4) (5) 3-year periods τ= 0.1τ= 0.25 τ= 0.5τ= 0.75 τ= 0.9 Log IHDIt−10.523*** 0.499*** 0.460*** 0.417*** 0.391*** (0.162) (0.125) (0.083) (0.099) (0.134) Educationt−10.000 0.000 0.000 0.000 0.000 (0.000) (0.000) (0.000) (0.000) (0.000) Size -0.002 -0.002 -0.002 -0.002 -0.002 (0.003) (0.003) (0.002) (0.002) (0.003) Size20.000 0.000 0.000 0.000 0.000 (0.000) (0.000) (0.000) (0.000) (0.000) GCF 0.001 0.001 0.001 0.000 0.000 (0.001) (0.001) (0.000) (0.000) (0.001) Governance 0.009 0.009 0.009 0.010 0.010 (0.012) (0.009) (0.006) (0.007) (0.010) Infant -0.002 -0.002 -0.002* -0.002 -0.002 (0.002) (0.002) (0.001) (0.001) (0.002) Observations 355 355 355 355 355 (1) (2) (3) (4) (5) 5-year periods τ= 0.1τ= 0.25 τ= 0.5τ= 0.75 τ= 0.9 Log IHDIt−10.098 0.106 0.121 0.136 0.142 (0.210) (0.164) (0.102) (0.127) (0.157) Educationt−10.000 0.000 0.000 0.000 0.000 (0.000) (0.000) (0.000) (0.000) (0.000) Size 0.002 0.002 0.001 -0.001 -0.001 (0.005) (0.004) (0.002) (0.003) (0.004) Size2-0.000 -0.000 -0.000 -0.000 0.000 (0.000) (0.000) (0.000) (0.000) (0.000) GCF 0.001 0.001 0.001 0.001 0.001 (0.001) (0.001) (0.001) (0.001) (0.001) Governance 0.026 0.022* 0.015* 0.009 0.006 (0.016) (0.012) (0.008) (0.010) (0.012) Infant -0.003 -0.003 -0.002 -0.002 -0.002 (0.003) (0.002) (0.001) (0.002) (0.002) Observations 263 263 263 263 263 Notes: Quartile regressions using the quantiles of 0.1, 0.25, 0.5, 0.75 and 0.9. The dependent variable is the logarithm of IHDI for all regressions. Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 98 Table 26: Economic growth and COFOG components for 5-year periods (1) (2) (3) (4) (5) Variables Sys-GMM FE FE Sys-GMM FE Defense 1.912*** (0.619) Defense2-0.254*** (0.073) Public -1.507*** (0.416) Public20.074*** (0.024) Housing -3.138** (1.403) Housing20.881** (0.334) Safety 3.101** 3.621*** (1.578) (1.226) Safety2-0.715*** -0.900*** (0.242) (0.152) Observations 297 294 294 297 290 Countries 69 63 63 69 62 AR(1) 0.0110 0.00179 AR(2) 0.818 0.449 Hansen test 0.428 0.458 Instruments 60 70 Adj. R20.503 0.479 0.578 Notes: Equal approach as Table 12 but using 5-year period dummies. 99 Table 27: Economic development and COFOG components for 5-year periods (1) (2) (3) (4) (5) (6) (7) Variables FE FE FE FE Sys-GMM Sys-GMM FE Defense -0.160*** (0.047) Economic 0.174*** (0.059) Economic2-0.015*** (0.004) Gov.Education 0.419** (0.166) Gov.Education2-0.041*** (0.014) Public -0.031* (0.017) Health -0.444** (0.211) Health20.037** (0.016) Housing -0.841* (0.432) Housing20.274** (0.112) Safety 0.572*** (0.150) Safety2-0.132*** (0.022) Observations 282 286 286 286 291 291 282 Countries 61 62 62 62 67 67 61 AR(1) 0.0218 0.0282 AR(2) 0.530 0.402 Hansen test 0.208 0.130 Instruments 56 56 Adj. R20.637 0.592 0.582 0.583 0.651 Notes: Equal approach as Table 13 but using 5-year period dummies. 100 Table 28: Inclusive economic development and COFOG components for 5-year periods (1) (2) (3) (4) (5) Variables FE Sys-GMM FE Sys-GMM FE Defense 0.332* (0.188) Defense2-0.038*** (0.012) Gov.Education 2.243* (1.249) Gov.Education2-0.256** (0.128) Health 0.106* (0.063) Housing -3.135** (1.487) Housing20.991* (0.567) Safety 0.867** (0.428) Safety2-0.173*** (0.044) Observations 146 154 147 154 146 Countries 54 61 54 61 54 AR(1) 0.0884 0.0673 AR(2) Hansen test 0.611 0.518 Instruments 30 17 Adj. R20.543 0.421 0.536 Notes: Equal approach as Table 15 but using 5-year period dummies. 101 Table 29: Robustness check using government revenue for 5-year periods (1) (2) (3) (4) (5) (6) Variables Sys-GMM FE Sys-GMM FE Sys-GMM FE Log GDPt−1-2.317*** -5.686*** (0.896) (0.749) Log HDIt−1-5.405*** -10.807*** (1.790) (1.098) Log IHDIt−10.956 -18.701*** (4.287) (3.018) Educationt−10.044 0.027*** 0.013*** 0.004* -0.004 0.013** (0.029) (0.010) (0.005) (0.002) (0.013) (0.005) Size (revenue) 0.292* 0.242** 0.108*** 0.057*** 0.081 0.057 (0.168) (0.101) (0.040) (0.019) (0.073) (0.053) Size (revenue)2-0.004 -0.003* -0.001 -0.001*** -0.000 -0.001 (0.003) (0.002) (0.001) (0.000) (0.001) (0.001) GCF 0.177*** 0.148*** 0.031** 0.012** 0.113** 0.004 (0.045) (0.034) (0.012) (0.005) (0.046) (0.023) Governance 0.288 0.869*** 0.157 0.031 -0.179 0.357 (0.499) (0.266) (0.106) (0.050) (0.304) (0.305) Population -0.468 -0.207 (0.324) (0.246) Trade 0.008 0.015 (0.008) (0.009) Infant 0.001 -0.029*** 0.039 -0.058 (0.013) (0.007) (0.065) (0.036) Observations 573 565 563 553 263 247 Countries 129 121 129 119 109 93 AR(1) 0.000844 0.000367 0.0573 AR(2) 0.106 0.837 Hansen test 0.294 0.379 0.759 Instruments 67 81 41 Adj. R20.539 0.717 0.429 Notes: Two-step System-GMM and Fixed effects regressions, including 5-year period dummies. GMM estimations use robust standard errors. FE estimations use standard errors clustered by country and robust to heteroskedasticity. All variables are treated as endogenous in System-GMM estimations with the exception of period dummies. The dependent variable is the average annual growth rate of GDP per capita for (1) and (2), of HDI for (3) and (4), and of IHDI for (5) and (6). Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 102 Table 30: Goverrnment size, growth, development, and inclusive development for annual periods (1) (2) (3) Variables FE FE FE Log GDPt−1-5.332*** (1.006) Log HDIt−1-9.907*** (1.336) Log IHDIt−1-22.120*** (2.964) Educationt−10.005 0.002 0.005 (0.011) (0.003) (0.007) Size 0.226** 0.040* 0.001 (0.105) (0.021) (0.058) Size2-0.005*** -0.001* -0.000 (0.001) (0.000) (0.001) GCF 0.155*** 0.017*** 0.034*** (0.024) (0.005) (0.012) Governance 0.979*** 0.037 0.329 (0.307) (0.091) (0.233) Population -0.345** (0.133) Trade 0.027*** (0.008) Infant -0.017** -0.059* (0.008) (0.032) Observations 2,286 2,245 1,076 Coutries 129 128 110 Adj. R20.471 0.485 0.309 Fixed effects regressions, including year dummies. FE estimations use standard errors clustered by country and robust to heteroskedasticity. The dependent variable is the annual growth rate of GDP per capita for (1), of HDI for (2), and of IHDI for (3). Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 103 Table 31: Development dynamics for annual periods (1) (2) (3) Variables FE FE FE Log GDPt−1-5.546*** (0.948) Log HDIt−1-9.975*** (1.346) Log IHDIt−1-22.136*** (2.899) Educationt−10.011 0.003 0.004 (0.010) (0.003) (0.007) Developing·Size 0.452*** 0.077*** 0.090 (0.146) (0.026) (0.062) Developing·Size2-0.009*** -0.001*** -0.002** (0.002) (0.000) (0.001) Developed·Size -0.501*** -0.022 -0.069 (0.188) (0.032) (0.054) Developed·Size20.003* 0.000 0.001 (0.002) (0.000) (0.001) GCF 0.153*** 0.018*** 0.034*** (0.025) (0.005) (0.013) Governance 0.984*** 0.038 0.323 (0.307) (0.091) (0.228) Population -0.379*** (0.117) Trade 0.024*** (0.007) Infant -0.017** -0.059* (0.008) (0.032) Observations 2,286 2,245 1,076 Countries 129 128 110 Adj. R20.478 0.488 0.316 Fixed effects regressions, including year dummies. FE estimations use standard errors clustered by country and robust to heteroskedasticity. The dependent variable is the annual growth rate of GDP per capita for (1), of HDI for (2), and of IHDI for (3). Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 104 Table 32: Income dynamics for annual periods (1) (2) (3) Variables FE FE FE Log GDPt−1-5.598*** (0.908) Log HDIt−1-10.101*** (1.389) Log IHDIt−1-22.406*** (2.911) Educationt−10.011 0.003 0.004 (0.010) (0.003) (0.006) Low.I·Size 0.319 0.043 -0.262** (0.340) (0.058) (0.116) Low.I·Size2-0.006 -0.000 0.004** (0.006) (0.001) (0.002) L.M.I·Size 0.250 0.072 0.279 (0.164) (0.050) (0.174) L.M.I·Size2-0.004* -0.001 -0.004 (0.002) (0.001) (0.003) U.M.I·Size 0.652*** 0.066* 0.002 (0.211) (0.039) (0.076) U.M.I·Size2-0.012*** -0.001** -0.001* (0.003) (0.001) (0.001) High.I·Size -0.386*** -0.000 -0.113** (0.140) (0.033) (0.049) High.I·Size20.002 0.000 0.001** (0.001) (0.000) (0.001) GCF 0.151*** 0.016*** 0.032** (0.025) (0.005) (0.013) Governance 0.975*** 0.057 0.356 (0.308) (0.093) (0.228) Population -0.411*** (0.105) Trade 0.024*** (0.007) Infant -0.017** -0.057* (0.008) (0.032) Observations 2,286 2,240 1,076 Countries 129 127 110 Adj. R20.480 0.492 0.325 Fixed effects regressions, including year dummies. FE estimations use standard errors clustered by country and robust to heteroskedasticity. The dependent variable is the annual growth rate of GDP per capita for (1), of HDI for (2), and of IHDI for (3). Significance level at which the null hypothesis is rejected: ***, 1%; **, 5%, and *, 10%. 105