Interrelationships among government participation, population and growth of per capita income: Inquiry on top twenty income-holding countries in the world

Das, Ramesh Chandra Article Interrelationships among government participation, population and growth of per capita income: Inquiry on top twenty income-holding countries in the world Economies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Das, Ramesh Chandra (2025) : Interrelationships among government participation, population and growth of per capita income: Inquiry on top twenty income-holding countries in the world, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 13, Iss. 2, pp. 1-29, https://doi.org/10.3390/economies13020046 This Version is available at: https://hdl.handle.net/10419/329326 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Academic Editor: Sabina Hodži´c Received: 26 December 2024 Revised: 1 February 2025 Accepted: 5 February 2025 Published: 12 February 2025 Citation: Das, R. C. (2025). Interrelationships Among Government Participation, Population and Growth of per Capita Income: Inquiry on Top Twenty IncomeHolding Countries in the World. Economies,13(2), 46. https://doi.org/ 10.3390/economies13020046 Copyright: © 2025 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article Interrelationships Among Government Participation, Population and Growth of per Capita Income: Inquiry on Top Twenty Income-Holding Countries in the World Ramesh Chandra Das Department of Economics, Vidyasagar University, Midnapore 721102, West Bengal, India; [email protected].ac.in Abstract: The literature on growth in economics encompasses two main facets of thinking: the applicability of diminishing productivity of capital, as has been in the neoclassical growth model with exogenous technological progress, and the applicability of nondiminishing productivity of capital, as has been in the endogenous growth models. The main conclusion of the former is the cross-country convergence to a common steady state while that of the latter is non-convergence. The tremendous history of the growth of the world’s so-called developed economies in the 1980s, diverging with the so-called backward economies, has nullified the applicability of the neoclassical growth model and justified non-steady state positive per capita growth of income and consumption through endogenous technological progress in terms of knowledge capital, human capital, good public institutions, etc. The present study aims to examine whether per capita income growth is explained by the size of government intervention coupled with the working population size in the world’s top twenty countries in terms of aggregate income. With the theoretical setup of the model and using empirical tools, such as cointegration, error correction and causality in a vector autoregression structure, this study reveals that eighteen countries maintain long-run relationships among per capita income growth, government participation, population and the interaction factors between government intervention and population, excepting Germany and Canada. Further, in the short run, for eleven countries on the list, there are instances in which public institutions associated with the population and the interaction term have a causal influence on the growth of per capita income. The empirical results relating to income growth, thus, have sustainability implications. Keywords: public institution; growth; working population; PCGDP; consumption; sustainability; cointegration; VAR; VECM; causality 1. Introduction Economists often are engaged in a popular debate on whether the government sector should take part in economic activities. If yes, in what capacity? The classical (Smith,1776; Say,1834, among others) and neoclassical economists (Solow,1956) had full faith in the working of a market economy in a competitive structure with the complete absence of the government sector as it hampers economic activity. Only the private buyers and sellers will be capable of determining commodity and factor prices with no sunk cost or dead weight loss. But the myth was broken in the 1920s when the world’s industrially developed market economies collapsed and there was a long recession in business activities. Classical economists had no solution at that time. The failure of the laissez faire doctrine of the capitalistic economists in the Great Depression of the 1920s and 1930s has been well known Economies 2025,13, 46 https://doi.org/10.3390/economies13020046 Economies 2025,13, 46 2 of 29 enough to allow public policymakers to promote government interventions in economic activities besides its social and administrative works—a phenomenon supported by the classical and neoclassical economists, philosophers and political scientists. In his General Theory, Professor J. M. Keynes (1936) recommended strong government interventions in economic activities, especially in the short run, to resist depressionary situations. Later, Robert Barro (1990) incorporated the government factor into the endogenous growth models to justify one of the major causes of why growth can be perpetual. But empirical evidence proves that government interventions may be good or bad for economies of different statures. The good effect channels are of two categories: first, the government must have a role in fields like legislation, security of property rights and providing a proper environment for private investment and production through decreasing transaction costs; second, the government must intervene in other fields where it comes to playing roles and/or giving services to sectors like infrastructures, human development, public health and education. The two alternatives support the forward linkage development policy where positive public investment leads to the expansion in the private sector and other associated sectors, leading to the applicability of the crowding-in hypothesis (Ramirez,1998;Erden & Holcombe,2006;Afonso & St. Aubyn,2008;Mahmoudzadeh et al.,2013;Warner,2014;¸Sen & Kaya,2014;Das et al.,2015,2018;Francois et al.,2024; among others). This hypothesis mostly works in the countries or groups of countries from developing nations where the capital markets are relatively underdeveloped compared to developed countries. The economic logic for defending government interventions in economic activities is that it protects the sectors in which the market mechanism fails or it has a comparative advantage over the private sector. However, these interventions involve costs as well. Some of the propositions under this heading are as follows: First, the government has to afford its costs through public borrowing and tax revenues. Receiving taxes from economic agents makes them discouraged in that they reduce their work effort and consume and save less, which hurts economic growth. Second, public borrowing also increases the rate of interest and crowds out private investment and tax increases in the future (Aschauer,1989;Furceri & Sousa,2009; Phetsavong & Ichihashi,2012;¸Sen & Kaya,2014;Das et al.,2015,2018;Nguyen & Trinh, 2018;Ben Zeev et al.,2023; among others). This happens mostly in the case of developed countries where capital markets are developed and have saturation levels depending on the requirements of the economies’ necessities; any more public investment leads to an increase in the rate of interest which leads to a reduction in the demand for investments from private units. Third, it produces inefficient economic outputs, unlike the market forces that bring the economy to optimality through the effective allocation of resources. Thus, government interventions, among others, can promote corruption and bureaucratic rent-seeking activities. Fourth, centralization and bureaucratic activities decrease creativity in both the public and private sectors. In accordance with market mechanisms, rewards and penalties of decisions are directly subject to wise choices, because they will appear in peoples’ wealth and property very soon. A series of positive and negative effects can be added to this. Empirical evidence, including that provided by Grossman (1990), Ghali (1998), Loizides and Vamvoukas (2005), etc., reveals that the effect of government size is the cause of economic growth. On the other hand, studies such as those of Gwartney et al. (1998), Folster and Henrekson (2001), among others, reveal that the effect of government size on economic growth is negative. Furthermore, the theoretical works of Robert Barro (1990), Mourmouras and Lee (1999), etc., and the empirical evidence provided by Barro (1991) and Chiou-Wei et al. (2010) show that in the lower levels of government activities, Economies 2025,13, 46 3 of 29 the effect of government expenditures is positive, but is reversed if it increases, which is shown with an inverted U-shaped curve. Therefore, the activities of the government have both positive and negative effects on economic growth. On the one hand, it increases economic growth by providing a proper environment for private activities, legislation regarding private possession and its guarantee, building infrastructures and public goods, and on the other hand, it decreases economic growth through borrowing and taxation policies, decreasing creativity and increasing inefficiency, where the intensity of the negative effects depends on the amount of money spent and how it is spent (types of expenditures). Thus, the final effect of government expenditures depends on the kind of government expenditures (protection of property rights, subsidies, infrastructures, etc.) and its positive or negative effects on economic growth. The role of the government sector in terms of good public institutions having public good properties in the growth of per capita income in the countries of the West during the 1980s onwards has been justified by an endogenous growth theoretician in the works of Robert Barro (1990,1991). The model establishes that the incorporation of a good public institution under no tax or a lump sum tax system causes the perpetual growth of per capita income and consumption and that these growth rates are dependent upon the size of government in the economy, the population size and the combinations of the two. Therefore, for countries, there should be long-term relationships between per capita income growth, the size of the government, population size and their interactions. 1.1. Objective of This Study This study examines whether public sector participations in line with the endogenous growth model of Robert Barro have long-run relations with the per capita GDP growth rates in the world’s top 20 countries in terms of GDP for the period 1991–2020. 1.2. Contributions of This Study This study contributes to the existing literature in the following manner: • It examines the endogenous growth model involving public institutions for the world’s top 20 countries in GDP • It incorporates the effects of population as a scale factor on growth of per capita GDP • It captures the interaction effects between public participation and labor forces on per capita GDP growth rates and shows the route towards sustainable development The paper is organized as follows: The next section, Section 2, presents the literature review followed by the theoretical model and public sector linkages with sustainable development. Section 3focuses on the materials and methods; Section 4covers results, analysis and discussion; and finally, Section 5concludes this study. 2. Review of Related Literature This study has conducted a literature review of the extant literature and classified it into three sub-sections. First, it covers the studies on the linkages between public spending and growth; then, it presents the theoretical model of Robert Barro (1990) with some modifications in line with the requirements of this study; and then, it covers some studies on the public sector’s linkages with sustainable development. 2.1. Public Spending and Growth Linkages Landau (1983) studied the relevant data of 104 countries on a cross-sectional basis and found significantly negative relations between the growth rate of real per capita GDP and the amount of government consumption expenditure as a ratio to GDP. Using data for each Economies 2025,13, 46 4 of 29 country averaged over roughly 20-year periods for 47 countries, Kormendi and Meguire (1985) found no significant relation between the average growth rates of real GDP and average growth rates or levels of the share of government consumption spending in GDP. Grier and Tullock (1987) extended the Kormendi–Meguire form of analysis to 115 countries, using data on government consumption for a pooled cross-section analysis, and found a significantly negative relation between the growth of real GDP and the growth of the government share of GDP. Barth and Bradley (1987) found a negative relation between the growth rate of real GDP and the share of government consumption spending for 16 OECD countries for the period 1971–1983. Aschauer (1989) argued that the services from government infrastructure were particularly important in the context of growth where the roles of public services as an input to private production were considered. It is this productive role that creates a potentially positive linkage between government and income growth. Barro (1989) showed that in the set of 98 countries for which government consumption spending to GDP was measured, a regression of the average annual growth rate of real per capita GDP from 1960 to 1985 on a set of explanatory variables led to negative coefficients. There was thus an indication that an increase in resources devoted to nonproductive (but possibly utility-enhancing) government services was associated with lower per capita growth rates of income. But with a separate set of 76 countries having the public-investment-to-GDP ratio as the regressor, the findings showed a positive coefficient. This result was consistent with the hypothesis that the typical country came closer to the quantity of public investment that would maximize the income growth rate. The role of government institutions, including the rule of law and well-functioning property rights, in explaining long-run economic performance has emerged from new institutional economics pioneered by North (1989). Devarajan et al. (1996) focus on the link between the level of public expenditure and growth using data from 43 developing countries over 20 years and show that an increase in the share of current expenditure has positive and statistically significant growth effects. Blankenau and Simpson (2004) explore this expenditure–growth relationship in the context of an endogenous growth model in which private and public investment are inputs to human capital accumulation, and the empirical evidence is mixed concerning the effects of public education expenditures on economic growth. Bose et al. (2007) examine the growth effects of government expenditure for a panel of 30 developing countries in the 1970s and 1980s in aggregate and disaggregated government expenditures. The results show that the share of government capital expenditure in GDP is positively and significantly correlated with economic growth, and at the disaggregated level, government investment in education and total expenditures in education are significantly associated with growth. Rajkumar and Swaroop (2008) examined the role of governance in the effectiveness of public spending in achieving social outcomes for a sample of 91 countries and showed that the quality of governance could largely explain differences in the efficacy of public spending. Afonso and Jalles (2011) conducted an empirical analysis of 108 countries for 1970–2008 on government size and institutional quality and found that the size of the government had an adverse effect on economic growth while institutional quality had a positive impact. Wu et al. (2010) examined the causal relationship between government expenditure and economic growth in a panel of 182 countries for 1950–2004 and found that the government played a role in economic growth. Afonso and Furceri (2010) analyzed the effects in terms of size and volatility of government spending and revenue on economic growth in OECD and EU countries and found both variables to be detrimental to economic growth. In their later study, Afonso and Jalles (2014) studied the fiscal composition– growth nexus for a set of OECD countries and found no significant impact of revenues on growth, whereas expenditures had negative effects. In their work, Chakraborty and Krishnankutty (2012) focus on the expenditure on education as a determinant of economic Economies 2025,13, 46 5 of 29 growth in Indian states. Using a panel data model, their study shows that expenditure on education positively influences the growth of the economy. Kurt (2015) investigates the direct and indirect effects of health expenditures on economic growth using the Feder–Ram model for Turkiye in monthly data for the period 2006–2013 and shows that the direct impact of government health expenditures on economic growth in Turkiye is positive and significant and its indirect impact is negative and significant. Malesevic and Golem (2019) obtained the results for EU15 countries during 1995–2014, where the single most important government expenditure item was education among aggregate expenditure for economic growth. Pahlevi (2017), studying an Indonesian panel of 33 states for the period 2008– 2012, shows that governance and health expenditure are found to have a positive impact on human development; meanwhile, health expenditure is discovered to affect human development in a negative direction. Churchill et al. (2015) performed a hierarchical metaregression analysis to review 87 empirical studies that report 769 estimates for the effects of government size on economic growth, and the findings indicate that the relationship between government size and growth is context-specific and the existing evidence is insufficient to establish a negative causal effect. Bhanumurthy et al. (2016) examined public expenditure, good governance and human development in districts of Madhya Pradesh in India, incorporating an interaction term to address the linkage effect of government expenditure; good governance was introduced in addition to other explanatory variables, and the result showed that good governance significantly contributed to better economic performance. Liu et al. (2018) conducted a study on governance quality and economic growth for provinces in China for the period 2001–2015 in a panel data model, and this study affirms that good governance contributes to growth positively. Olaoye et al. (2019) tested for causality between government expenditure and economic growth, but their result shows no evidence of a causal relationship. A list of studies was compiled by Das (2021) in a volume covering the debate on the optimum size of a government intervention which shows in general that the impact depends on several situations across countries and groups; however, no specific conclusion is drawn. Datta and Chakrabarti (2021) show that a government’s budget allocation for development management programs has an optimum level/upper bound negating the confusing results of the impacts on the size of the government intervention as evidenced by many studies in the literature. Sinha et al. (2021) highlight that the extent of FDI inflows is highly influenced by several macro policies of governments other than subsidies; however, government policies towards open economy macroeconomic factors are more effective. Jain and Nagpal (2021) have observed that a rise in the size of the public spending in a selected developing countries and groups results in a substantial increase (decrease) in the growth rate when the public spending is below (above) the optimal threshold level, indicating a non-monotonic association. 2.2. Theoretical Model The weak justification of neoclassical economists such as Solow (1956) on the working of cross-country convergences during the 1980s among the developed nations has influenced the new growth theoreticians such as Rebelo (1991), Lucas (1988), Romer (1994), Ramsey (1928) and Robert Barro (1990), who explained through endogenous growth models how the cross-country convergences did not work. The endogenous growth theories consider the working of increasing returns to scale where the sources of such returns to scale are research and development (the Romer Model), human capital (the Lucas Model), one-factor model (the Rebelo Model with Y = AK type production function) and good public institutions (the Barro Model). The present study uses the basic structure of the Robert Barro (1990) model of endogenous growth and makes some simple modifications of the production function incorporat- Economies 2025,13, 46 6 of 29 ing the interaction effects between government expenditure as a ratio to aggregate output and the working population in the economy. This is because a good public institution (as measured by high G/Y) leads to good-quality public institutional outputs in terms of good educational attainment, health benefits, legal and judicial supports, internal and external security, etc., increasing the good-quality population size. Thus, following the Barro model, let us suppose that, in the production function, there is G as the additional input (to represent public services or public input without congestion effects and user charges) with L and K (as private inputs) producing output Y. The Cobb–Douglas-type production function for the whole economy is Yi= AL1−α. Kα. G1−α(1) where 0 < α< 1. The production function shows the working of constant returns to scale (CRS) in private inputs, L and K (as the sum of their powers is 1), and the inclusion of G as another factor of production leads the total production system to increasing returns to scale (IRS) as the sum of their powers is greater than 1. ‘A’ stands for technology which, among others, captures the interaction effects between government’s participation in the aggregate economy as measured by G/Y and L (the working population) which is G/Y × L (i.e., A = A(G/Y ×L )). If all other components of A are fixed, then there can be a one-to-one relation between A and G/Y × L, i.e., A = (G/Y) × L. The modified model in the present study, thus, has more flexibility in analyzing the impacts of several components of the public institutional system on economic growth. Assume that the aggregate labor force is constant. In that case, if G is constant, the returns from private capital (K) will be diminishing. On the other hand, if G increases along with K (that means both private and public capitals move in positive directions simultaneously like crowding-in effects), then diminishing MPk will not arise. Here, public capital is complementary to K and L and an increase in G leads to an increase in the MPL and MPk (this is the source of endogenous growth). The production function in per capita form is y=A.kα. G1−α(2) The total output of the economy is Σy=y×L=Y=AL.kα. G1−α= AL. kα. (G/Gα) Or, Gα= (AL. kα. G)/Y = AL. kα. (G/Y) Or. G = (G/Y)1/α. (AL)1/α. k (3) The common budget constraint faced by the aggregate economy is dk/dt = dm/dt = ˙ m= y −c−δk−G/L where G/L is per capita consumption of public goods/services. Here, ‘m’ is the state variable representing asset value, and c is the per capita consumption, which is the inverse of savings in an intertemporal infinite period model. Following the Ramsey model, we set the current value Hamiltonian function for utility maximization with respect to c, G and k. H = u(ct). e−(ρ−n)t +βt[y −c−δk−G/L] Economies 2025,13, 46 7 of 29 Here, βt is the co-state variable, ρ is the discount rate, n is the population growth rate and δ is the rate of depreciation. Assuming the population growth rate is at n and the constant elasticity of substitution utility function, u = (c 1−σ /1 −σ ), σ being the intertemporal elasticity of substitution or constant elasticity of marginal utility of consumption. Thus, the Hamiltonian is now H(c, G, k) = (c1−σ/1−σ). e−(ρ−n)t +βt[y −c−δk−G/L] or, H(c, G, k) = (c1−σ/1−σ). e−(ρ−n)t +βt[A. kα. G1−α−c−δk−G/L] The FOCs are δH/δc = 0, >> c−σ. (1−σ)/(1−σ). e−(ρ−n)t =β(4) δH/δG = 0, >>(1−α). β. A. kα. G−α−β/L = 0 or, (1−α). A. kα. G−α= 1/L (5) δH/δk = −δβ/δt >>β.α. A. kα−1. G1−α−β δ =−δβ/δt (6) And the transversality condition is lim t→∞(βt.mt)=0 Now, we take the derivative of βw.r.t time from (4) and substitute it into (6). We obtain β(α. A. kα−1. G 1−α−δ) = σ.c−σ. [(δc/δt)/c]. e−(ρ−n)t Now, putting the value of βfrom (1) into the above relation c−σ. (1−σ)/(1−σ). e−(ρ−n)t.(α. A. kα−1. G1−α−δ) = σ.c−σ. [(δc/δt)/c]. e−(ρ−n)t or, α. A. kα−1. G1−α−δ=σ. [(δc/δt)/c] or, [(δc/δt)/c] = 1/σ[α. A. kα−1. G1−α−n−δ] (7) Now, from (2), (1−α). A. kα. G−α= 1/L Or, (1−α). A. kα. G1−α= 1/L Or, (1−α). A. L. kα. G1−α= 1 Or. (1−α). Y = G Or, G/Y = (1 −α) (8) This means the government-expenditure-to-GDP ratio (=G/Y) is constant where G/Y stands for the share of productive government expenditures in GDP. In other words, the optimal condition of the government in a country is to maintain a constant G/Y in the model with a lump sum tax. However, the shares vary across the countries depending upon the values of α , which measures the productivity of public services relative to private services. It could vary across countries for a number of reasons related to geography, the share of agricultural production, urban density and so on. Hence, the growth rates of income, consumption and capital accumulation vary across the countries. As the value of αincreases, G/Y falls, and as a result, the growth rate falls. Economies 2025,13, 46 8 of 29 Now, we put the expression of G from (1) in (7) (δc/δt)/c = 1/σ[α. A. kα−1. G1−α−n−δ] Or, (δc/δt)/c = 1/σ[α. A. kα−1. G1−α−n−δ] Or, (δc/δt)/c = 1/σ[α. A. kα−1. {(G/Y)1/α. (AL)1/α. k}1−α−n−δ] Or, (δc/δt)/c = 1/σ[α. A. kα−1. {(1−α)1−α/α. (AL)1−α/α. k1−α−n−δ] Or, (δc/δt)/c = 1/σ[α. A1/α. (1−α)1−α/α. L1−α/α−n−δ] (9) Therefore, the social planner’s optimum solution is identical to that under a decentralized system under the lump sum tax assumption. The optimal rate of growth of k, y and c will be the rate [writing ( δ c/ δ t)/c = . c c ], which is given below as ˙ c/c = 1/σ[α.A1/α. (G/Y)1−α/α. L1−α/α−n−δ] = 1/σ[α.A1/α. (1−α)1−α/α. L1−α/α−n−δ] Let us replace the term A with G/Y × L = (1 −α ) × L (as has been explained in the introductory part of the model), and the revised consumption growth relation becomes ˙ c/c = 1/σ[α. {(1−α)×L}1/α. (1−α)1−α/α. L1−α/α−n−δ] = 1/σ[α. (1−α)(2−α)/α. L(2−α)/α−n−δ](10) It is clear from the expression that the rate of growth of per capita consumption depends on the marginal productivity of per capita capital which again depends upon the endogenous growth component, the G/Y ratio (=1 −α ), population size (=L) and the interactions between G/Y and population size (captured by A = G/Y × L), but not on per capita capital accumulation (=k). The intuition behind the effects of G/Y on population or the reverse is that a good public institution (as measured by high G/Y or high (1 −α )) leads to good-quality public institutional outputs in terms of good educational attainment, health benefits, legal and judicial supports, internal and external security, etc., increasing the good-quality population size (Lucas,1988;Barro & Lee,1993;Barro,2001;Barro & Lee,2001; Verhulst,1838;Das & Mukherjee,2019;Diebolt & Hippe,2019;Das,2020;Hussain & Das, 2024). On the other hand, in countries having good-quality public institutions, the increase in population size of the countries will be able to absorb the good public institutional frameworks that will push up their productivity which will then help in increasing the growth of per capita consumption. The rate of growth of per capita income ( . y /y) will then be positive with G/Y, population and their interaction term (G/Y × L). Hence, as the scale factor, L, increases along with G/Y, the marginal productivity of capital increases, breaks its diminishing nature, and ultimately, . c /c and . y /y increase in the long run without reaching any steady-state solution. 2.3. Public Sector Linkages with Sustainable Development The United Nations 17-point sustainable development goals (SDGs) include good public institutions having the capability of making economic growth, promoting good health and education, reducing corruption, crimes, etc., which is covered in Goal Number 16. SDG 16 (Global Goal 16) is framed to promote peaceful and inclusive societies for sustainable development; provide access to justice for all; and build effective, accountable and inclusive institutions at all levels. The goal has 12 targets, 23 indicators and 10 outcome targets. The outcome targets related to our analysis are to develop effective, accountable and transparent institutions; ensure responsive, inclusive and representative decision-making; ensure public access to information; and protect fundamental freedoms. The proposed Economies 2025,13, 46 15 of 29 Table 1. Cont. ADF Statistics (Probability) Country G/Y Ratio (Level) Population (Level) (G/Y) × Population (Level) PCGDP Growth (Level) G/Y Ratio (1st Diff.) Population (1st Diff.) (G/Y) × Population (1st Diff.) PCGDP Growth (1st Diff.) S. Korea −2.3 (0.25) −2.40 (0.18) −2.73 (0.0/) −2.26 (0.21) −4.30 (0.00) −4.4 (0.00) * −4.73 (0.00) −5.26 (0.00) Australia −2.1 (0.27) −1.97 (0.35) −2.00 (0.32) −2.79 (0.09) −5.1 (0.00) −2.97 (0.05) −5.00 (0.00) −3.79 (0.00) Mexico −1.8 (0.62) −1.25 (0.83) −2.01 (0.44) −2.72 (0.09) −3.79 (0.00) −3.2 (0.03) * −3.01 (0.04) −4.72 (0.00) Spain −2.1 (0.25) −2.10 (0.24) −1.99 (0.46) −2.85 (0.07) −3.01 (0.05) −3.10 (0.04) −2.99 (0.05) −3.85 (0.00) Indonesia −2.8 (0.08) −2.38 (0.19) −2.66 (0.09) −2.73 (0.08) −5.80 (0.00) −4.38 (0.00) −5.66 (0.00) −3.73 (0.00) Netherlands −2.4 (0.18) −2.21 (0.27) −2.30 (0.26) −2.49 (0.14) −4.34 (0.00) −3.21 (0.03) −4.30 (0.00) −4.49 (0.00) S. Arabia −2.9 (0.07) −2.14 (0.30) −2.71 (0.07) −2.42 (0.15) −4.95 (0.00) −3.14 (0.04) −6.71 (0.00) * −4.42 (0.00) Turkiye −2.1 (0.27) −2.81 (0.07) −2.62 (0.09) −2.61 (0.11) −6.09 (0.00) −4.81 (0.00) −5.62 (0.00) −4.61 (0.00) Switzerland −2.4 (0.18) −1.98 (0.35) −1.58 (0.41) −2.73 (0.08) −4.24 (0.00) −2.98 (0.05) −3.58 (0.01) −4.73 (0.00) Note: * mark indicates I(2) series. Source: author’s calculations. 4.3. Johansen Cointegration Test Results As the number of endogenous variables is more than two, we use the VAR model to identify the optimum lag and cointegration among the four variables. The optimum lag is selected by looking at the minimum values of most of the testing criteria such as LR, final prediction error (FPE), Akaike information criterion (AIC), Schwarz information criterion (SIC) and Hannan–Quinn information criterion (HQIC). In all the cases with each of the four indicators playing the role of dependent variable interchangeably, the optimum lag is observed to be 2 (the results are not shown in tables). The Johansen cointegration test technique is used, and the results are presented in Table 2. This test is performed to see whether the lower-order values are cointegrated. Table 2. Johansen cointegration test results. Country Hypothesized No. of CEs Trace Statistics (Prob) Remarks USA * None * 69.303 (0.00) The variables are cointegrated and there is 1 cointegrating equation at the 0.05 level At most 1 * 23.036 (0.38) At most 2 8.0005 (0.13) At most 3 2.606 (0.11) China * None * 103.4 (0.00) The variables are cointegrated and there are 4 cointegrating equations at the 0.05 level At most 1 * 42.65 (0.00) At most 2 19.96 (0.00) At most 3 5.39 (0.02) Japan None * 54.209 (0.01) The variables are cointegrated and there is 1 cointegrating equation at the 0.05 level At most 1 * 22.017 (0.29) At most 2 9.316 (0.33) At most 3 2.336 (0.12) Germany None * 43.60 (0.11) No cointegration At most 1 * 21.16 (0.34) At most 2 7.25 (0.54) At most 3 1.53 (0.21) Economies 2025,13, 46 16 of 29 Table 2. Cont. Country Hypothesized No. of CEs Trace Statistics (Prob) Remarks India None * 62.52 (0.00) The variables are cointegrated and there is 1 cointegrating equation at the 0.05 level At most 1 * 23.76 (0.21) At most 2 11.47 (0.18) At most 3 3.04 (0.08) UK * None * 49.16 (0.03) The variables are cointegrated and there is 1 cointegrating equation at the 0.05 level At most 1 * 19.57 (0.45) At most 2 7.54 (0.51) At most 3 2.76 (0.09) France None * 80.95 (0.00) The variables are cointegrated and there are 4 cointegrating equations at the 0.05 level At most 1 * 43.05 (0.00) At most 2 19.18 (0.01) At most 3 5.86 (0.01) Italy None * 47.56 (0.00) The variables are cointegrated and there is 1 cointegrating equation at the 0.05 level At most 1 * 28.79 (0.06) At most 2 14.88 (0.06) At most 3 4.68 (0.06) Canada * None * 38.56 (0.22) No cointegration At most 1 * 27.79 (0.11) At most 2 13.88 (0.06) At most 3 5.68 (0.06) Brazil None * 77.33 (0.00) The variables are cointegrated and there are 2 cointegrating equations at the 0.05 level At most 1 * 38.01 (0.00) At most 2 9.86 (0.29) At most 3 0.28 (0.59) Russia * None * 54.36 (0.01) The variables are cointegrated and there are 2 cointegrating equations at the 0.05 level At most 1 * 32.37 (0.02) At most 2 13.18 (0.10) At most 3 3.76 (0.06) S. Korea * None * 70.63 (0.00) The variables are cointegrated and there are 2 cointegrating equations at the 0.05 level At most 1 * 38.50 (0.00) At most 2 11.51 (0.18) At most 3 0.189 (0.66) Australia None * 59.83 (0.00) The variables are cointegrated and there are 2 cointegrating equations at the 0.05 level At most 1 * 19.91 (0.43) At most 2 4.33 (0.87) At most 3 0.15 (0.70) Mexico * None * 98.71 (0.00) The variables are cointegrated and there are 3 cointegrating equations at the 0.05 level At most 1 * 45.36 (0.00) At most 2 18.45 (0.01) At most 3 1.95 (0.16) Economies 2025,13, 46 17 of 29 Table 2. Cont. Country Hypothesized No. of CEs Trace Statistics (Prob) Remarks Spain None * 52.67 (0.00) The variables are cointegrated and there is 1 cointegrating equation at the 0.05 level At most 1 * 23.74 (0.20) At most 2 12.92 (0.11) At most 3 2.59 (0.09) Indonesia None * 68.93 (0.00) The variables are cointegrated and there are 2 cointegrating equations at the 0.05 level At most 1 * 31.05 (0.03) At most 2 5.60 (0.74) At most 3 3.15 (0.08) Netherlands None * 47.99 (0.04) The variables are cointegrated and there is 1 cointegrating equation at the 0.05 level At most 1 * 21.95 (0.29) At most 2 11.25 (0.19) At most 3 3.45 (0.06) S. Arabia * None * 56.16 (0.00) The variables are cointegrated and there are 4 cointegrating equations at the 0.05 level At most 1 * 29.67 (0.01) At most 2 15.47 (0.05) At most 3 5.45 (0.01) Turkiye None * 55.75 (0.00) The variables are cointegrated and there is 1 cointegrating equation at the 0.05 level At most 1 * 28.17 (0.07) At most 2 10.89 (0.27) At most 3 4.56 (0.03) Switzerland None * 78.83 (0.00) The variables are cointegrated and there is 1 cointegrating equation at the 0.05 level At most 1 * 28.87 (0.31) At most 2 13.56 (0.10) At most 3 0.009 (0.94) Note: * marks in the first column indicate the series of the countries following the I(2) feature. Again, * marks in the second column denote rejection of the ‘no cointegration’ hypothesis at the 0.05 level. Source: author’s calculations. It is observed from the table that the Trace Statistics show cointegration results among the variables in 18 countries at the 0.05 level of significance, but this was not shown for Germany and Canada. This means the four growth indicators as per the Barro model are cointegrated and there are long-run relationships among them. This is a valid justification for whether the government sector in terms of good institutions has good impacts on per capita income growth. The leading countries in the world in terms of GDP have experienced higher growth of outputs due to their strong public institutions, their labor force and the coordination between public spending and labor force. Now, we test for short-run dynamics among the four variables around the equilibrium relations by VECM to see whether the cointegrating relations are stable. Further, VECM analysis is performed for those countries that have long-run relations among the variables. The results of VECM are given in Table 3. Economies 2025,13, 46 18 of 29 Table 3. Long-run causality test results through VECM. Country Dependent Variables Independent Variables EC Term(η) Prob. Remarks China G/Y G/Y ×L, Population, PCGDP 15.59 0.00 No LR causality G/Y ×L G/Y, Population, PCGDP 0.0001 0.00 No LR causality Population G/Y, G/Y ×L, PCGDP −271,179 0.31 No LR causality PCGDP Growth G/Y, G/Y ×L, Population 579.21 0.26 No LR causality Japan G/Y G/Y ×L, Population, PCGDP −23.59 0.02 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP −2.0000 0.02 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 401,023 0.39 No LR causality PCGDP Growth G/Y, G/Y ×L, Population 37,322 0.00 No LR causality India G/Y G/Y ×L, Population, PCGDP 2.003 0.14 No LR causality G/Y ×L G/Y, Population, PCGDP 1,790,000 0.09 No LR causality Population G/Y, G/Y ×L, PCGDP −294,086 0.01 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 61.67 0.22 No LR causality UK G/Y G/Y ×L, Population, PCGDP −0.063 0.98 No LR causality G/Y ×L G/Y, Population, PCGDP 4,112,746 0.97 No LR causality Population G/Y, G/Y ×L, PCGDP 79,800 0.00 No LR causality PCGDP Growth G/Y, G/Y ×L, Population −2353 0.46 No LR causality France G/Y G/Y ×L, Population, PCGDP −1.02 0.19 No LR causality G/Y ×L G/Y, Population, PCGDP −39,756,754 0.22 No LR causality Population G/Y, G/Y ×L, PCGDP 39,862 0.00 No LR causality PCGDP Growth G/Y, G/Y ×L, Population −1219 0.31 No LR causality Brazil G/Y G/Y ×L, Population, PCGDP 0.07 0.03 No LR causality G/Y ×L G/Y, Population, PCGDP 9,181,923 0.03 No LR causality Population G/Y, G/Y ×L, PCGDP −338.3 0.26 No LR causality PCGDP Growth G/Y, G/Y ×L, Population −26.16 0.18 No LR causality Russia G/Y G/Y ×L, Population, PCGDP −23.42 0.00 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP −23,500,000 0.00 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP −233,665 0.05 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 3318 0.13 No LR causality S. Korea G/Y G/Y ×L, Population, PCGDP −14.58 0.03 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP −5,040,000 0.03 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP −64,407 0.70 No LR causality PCGDP Growth G/Y, G/Y ×L, Population −23.39 0.00 G/Y, G/Y ×L, Population→PCGDP Australia G/Y G/Y×L, Population, PCGDP −0.31 0.03 No LR causality G/Y ×L G/Y, Population, PCGDP −2,040,000 0.13 No LR causality Population G/Y, G/Y ×L, PCGDP −64,407 0.70 No LR causality PCGDP Growth G/Y, G/Y ×L, Population 0.49 0.01 No LR causality Mexico G/Y G/Y ×L, Population, PCGDP 4.77 0.08 No LR causality G/Y ×L G/Y, Population, PCGDP 45,600,000 0.03 No LR causality Population G/Y, G/Y ×L, PCGDP −14,147 0.74 No LR causality PCGDP Growth G/Y, G/Y ×L, Population 8.89 0.04 No LR causality Spain G/Y G/Y ×L, Population, PCGDP 6.085 0.00 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP −17,000,000 0.00 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 99,605 0.41 No LR causality PCGDP Growth G/Y, G/Y ×L, Population 6.475 0.00 No LR causality Economies 2025,13, 46 19 of 29 Table 3. Cont. Country Dependent Variables Independent Variables EC Term(η) Prob. Remarks Indonesia G/Y G/Y ×L, Population, PCGDP −2.76 0.33 No LR causality G/Y ×L G/Y, Population, PCGDP −30,900,000 0.41 No LR causality Population G/Y, G/Y ×L, PCGDP 79,385 0.00 No LR causality PCGDP Growth G/Y, G/Y ×L, Population −0.91 0.05 G/Y, G/Y ×L, Population→PCGDP Netherlands G/Y G/Y ×L, Population, PCGDP 3.62 0.55 No LR causality G/Y ×L G/Y, Population, PCGDP 41,572,903 0.52 No LR causality Population G/Y, G/Y ×L, PCGDP 39,787 0.00 No LR causality PCGDP Growth G/Y, G/Y ×L, Population −0.87 0.77 No LR causality S. Arabia G/Y G/Y ×L, Population, PCGDP −4.24 0.00 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP −87,856,447 0.00 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 45,042 0.47 No LR causality PCGDP Growth G/Y, G/Y ×L, Population 0.14 0.00 No LR causality Turkiye G/Y G/Y ×L, Population, PCGDP −1.44 0.00 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP −53,429,008 0.01 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 32,999 0.03 No LR causality PCGDP Growth G/Y, G/Y ×L, Population −0.46 0.41 No LR causality Switzerland G/Y G/Y ×L, Population, PCGDP −0.936 0.12 No LR causality G/Y ×L G/Y, Population, PCGDP −4,546,936 0.16 No LR causality Population G/Y, G/Y ×L, PCGDP −1776 0.36 No LR causality PCGDP Growth G/Y, G/Y ×L, Population −9.91 0.01 G/Y, G/Y ×L, Population→PCGDP Note: PCGDP in columns 3 and 6 represents the growth of PCGDP. Source: author’s own calculations. It is observed that the errors in maximum of the models are not corrected as the signs of the error correction terms are not negative and significant. Though there are some negative values of the said term, they are not statistically significant in most of the cases. Only in the case of three countries, S. Korea, Indonesia and Switzerland, are there significant error corrections when PCGDP Growth is the endogenous dependent variable. It can also be said that good public institutions, population and their interaction terms affect or rather have a causal influence on the per capita GDP growth rate in the long run. On the other hand, PCGDP Growth, population and the interaction term have a causal influence on the government share of GDP in the long run in the case of some countries such as Japan, Russia, S. Korea, Spain, S. Arabia and Turkiye. Again, population is influenced by the rest of the factors in the long run in the case of India and Russia. This study does not find any error correction or long-run causality in any of the four combinations of the variables in the case of China, the UK, France, Italy, Brazil, Australia, Mexico and the Netherlands. 4.4. Short-Run Causality Test Results Although there are absences in the long-run causal relations in most of the countries, at least for the occasions where PCGDP Growth is held as an endogenous dependent variable, there may be the possibilities of short-run causal interplays among the variables. The Wald test is used to test for short-run causality among the variables. The results are given in Table 4. The decision rule is through the values of Chi-Square test statistics with probabilities less than 0.05. Economies 2025,13, 46 20 of 29 Table 4. Short-run causality test results (Wald test). Country Dependent Variables Independent Variables Chi-Square Value Prob. Remarks USA G/Y G/Y ×L, Population, PCGDP 2.468 0.480 No SR causality G/Y ×L G/Y, Population, PCGDP 7.768 0.051 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 3.722 0.293 No SR causality PCGDP Growth G/Y, G/Y ×L, Population 4.035 0.257 No SR causality China G/Y G/Y ×L, Population, PCGDP 17.95 0.00 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP 19.66 0.00 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 3.15 0.78 No SR causality PCGDP Growth G/Y, G/Y ×L, Population 6.38 0.38 No SR causality Japan G/Y G/Y ×L, Population, PCGDP 5.28 0.50 No SR causality G/Y ×L G/Y, Population, PCGDP 6.078 0.41 No SR causality Population G/Y, G/Y ×L, PCGDP 2.27 0.89 No SR causality PCGDP Growth G/Y, G/Y ×L, Population 19.53 0.003 G/Y, G/Y ×L, Population→PCGDP Germany G/Y G/Y ×L, Population, PCGDP 1.38 0.96 No SR causality G/Y ×L G/Y, Population, PCGDP 1.53 0.95 No SR causality Population G/Y, G/Y ×L, PCGDP 19.60 0.00 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 1.55 0.00 No SR causality India G/Y G/Y ×L, Population, PCGDP 6.48 0.37 No SR causality G/Y ×L G/Y, Population, PCGDP 7.64 0.26 No SR causality Population G/Y, G/Y ×L, PCGDP 13.06 0.04 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 3.40 0.75 No SR causality UK G/Y G/Y ×L, Population, PCGDP 4.25 0.64 No SR causality G/Y ×L G/Y, Population, PCGDP 4.27 0.63 No SR causality Population G/Y, G/Y ×L, PCGDP 16.11 0.01 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 15.81 0.05 G/Y, G/Y ×L, Population→PCGDP France G/Y G/Y ×L, Population, PCGDP 3.11 0.79 No SR causality G/Y ×L G/Y, Population, PCGDP 3.95 0.68 No SR causality Population G/Y, G/Y ×L, PCGDP 50.40 0.00 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 3.25 0.77 G/Y, G/Y ×L, Population→PCGDP Italy G/Y G/Y ×L, Population, PCGDP 13.06 0.04 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP 12.58 0.05 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 3.09 0.79 No SR causality PCGDP Growth G/Y, G/Y ×L, Population 3.12 0.79 No SR causality Canada G/Y G/Y ×L, Population, PCGDP 6.27 0.39 No SR causality G/Y ×L G/Y, Population, PCGDP 6.29 0.39 No SR causality Population G/Y, G/Y ×L, PCGDP 1.34 0.96 No SR causality PCGDP Growth G/Y, G/Y ×L, Population 8.70 0.19 No SR causality Brazil G/Y G/Y ×L, Population, PCGDP 27.10 0.00 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP 28.22 0.00 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 17.08 0.00 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 12.30 0.05 G/Y, G/Y ×L, Population→PCGDP Russia G/Y G/Y ×L, Population, PCGDP 9.30 0.15 No SR causality G/Y ×L G/Y, Population, PCGDP 9.03 0.17 No SR causality Population G/Y, G/Y ×L, PCGDP 19.87 0.00 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 6.68 0.35 G/Y, G/Y ×L, Population→PCGDP Economies 2025,13, 46 21 of 29 Table 4. Cont. Country Dependent Variables Independent Variables Chi-Square Value Prob. Remarks S. Korea G/Y G/Y ×L, Population, PCGDP 6.94 0.32 No SR causality G/Y ×L G/Y, Population, PCGDP 7.41 0.28 No SR causality Population G/Y, G/Y ×L, PCGDP 26.41 0.00 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 27.99 0.00 G/Y, G/Y ×L, Population→PCGDP Australia G/Y G/Y ×L, Population, PCGDP 4.62 0.59 No SR causality G/Y ×L G/Y, Population, PCGDP 6.62 0.35 No SR causality Population G/Y, G/Y ×L, PCGDP 4.12 0.66 No SR causality PCGDP Growth G/Y, G/Y ×L, Population 18.59 0.00 G/Y, G/Y ×L, Population→PCGDP Mexico G/Y G/Y ×L, Population, PCGDP 10.12 0.12 No SR causality G/Y ×L G/Y, Population, PCGDP 11.56 0.07 No SR causality Population G/Y, G/Y ×L, PCGDP 18.86 0.00 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 25.025 0.00 G/Y, G/Y ×L, Population→PCGDP Spain G/Y G/Y ×L, Population, PCGDP 51.77 0.00 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP 44.47 0.00 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 2.51 0.86 No SR causality PCGDP Growth G/Y, G/Y ×L, Population 22.86 0.00 G/Y, G/Y ×L, Population→PCGDP Indonesia G/Y G/Y ×L, Population, PCGDP 7.85 0.24 No SR causality G/Y ×L G/Y, Population, PCGDP 8.75 0.19 No SR causality Population G/Y, G/Y ×L, PCGDP 15.67 0.01 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 32.92 0.00 G/Y, G/Y ×L, Population→PCGDP Netherlands G/Y G/Y ×L, Population, PCGDP 1.07 0.98 No SR causality G/Y ×L G/Y, Population, PCGDP 1.09 0.98 No SR causality Population G/Y, G/Y ×L, PCGDP 13.19 0.05 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 0.82 0.99 No SR causality S. Arabia G/Y G/Y ×L, Population, PCGDP 19.52 0.00 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP 15.75 0.01 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 2.84 0.83 No SR causality PCGDP Growth G/Y, G/Y ×L, Population 7.77 0.25 No SR causality Turkiye G/Y G/Y ×L, Population, PCGDP 12.98 0.05 G/Y ×L, Population, PCGDP→G/Y G/Y ×L G/Y, Population, PCGDP 12.65 0.05 G/Y, Population, PCGDP→G/Y ×L Population G/Y, G/Y ×L, PCGDP 6.56 0.36 No SR causality PCGDP Growth G/Y, G/Y ×L, Population 5.82 0.44 No SR causality Switzerland G/Y G/Y ×L, Population, PCGDP 5.44 0.48 No SR causality G/Y ×L G/Y, Population, PCGDP 4.95 0.54 No SR causality Population G/Y, G/Y ×L, PCGDP 23.66 0.00 G/Y, G/Y ×L, PCGDP→Population PCGDP Growth G/Y, G/Y ×L, Population 34.26 0.00 G/Y, G/Y ×L, Population→PCGDP Note: PCGDP in columns 3 and 6 represents the growth of PCGDP. Source: author’s own calculations. In 11 countries on the list, public institutions associated with population and the interaction term have a causal influence on the growth of PCGDP. These countries are Japan, the UK, France, Brazil, Russia, S. Korea, Australia, Mexico, Spain, Indonesia and Switzerland. Thus, in most of the countries, the growth of PCGDP is explained by good public participation coupled with its impacts on the population. In other words, the Barro model of endogenous growth incorporating public institutions works well in the world’s leading countries in terms of the gross domestic product. It is also observed that the growth of income and population have a causal influence on government participation in countries Economies 2025,13, 46 22 of 29 like China, Italy, Brazil, Spain, S. Arabia and Turkiye. On the other hand, the interaction factor is influenced by income growth, labor force and government participation in the countries such as the USA, China, Italy, Brazil, Spain, S. Arabia and Turkiye. There are common results in the case of G/Y and G/Y × L for the above sets of countries. Brazil is the only country in the list where all four occasions of causal interplays have worked. Canada is the only country in the list where no causal interplays among the four associated variables are observed. 4.5. Robustness of the Results To check the robustness of the results of the model, this study tests for the normality of the residuals. Table 5presents the results of the different models specified against the criteria of serial autocorrelation, heteroskedasticity and normality checks of the residuals through the Breusch–Godfrey Serial Correlation LM Test, Breusch–Pagan–Godfrey Heteroskedasticity Test and Histogram-Normality Test, respectively. Table 5. Residuals’ diagnostic checking (only probabilities are noted). Country Dependent Variables Breusch–Godfrey Serial Correlation LM Test Breusch–Pagan– Godfrey Heteroskedasticity Test HistogramNormality Test Remarks China G/Y 0.999 0.853 0.934 Model has good fit as the errors satisfy all the diagnostic checking G/Y ×L 0.999 0.838 0.22 Model has partially good fit as the errors do not satisfy the normality property Population 0.999 0.98 0.037 Model has partially good fit as the errors do not satisfy the normality property PCGDP Growth 0.995 0.70 0.72 Model has good fit as the errors satisfy all the diagnostic checking Japan G/Y 0.992 0.36 0.95 Model has good fit as the errors satisfy all the diagnostic checking G/Y ×L 0.995 0.27 0.96 Model has good fit as the errors satisfy all the diagnostic checking Population 0.99 0.54 0.21 Model has partially good fit as the errors do not satisfy the normality property PCGDP Growth 0.99 0.70 0.60 Model has good fit as the errors satisfy all the diagnostic checking India G/Y 0.20 0.93 0.65 Model has good fit as the errors satisfy all the diagnostic checking G/Y ×L 0.99 0.59 0.005 Model has partially good fit as the errors do not satisfy the normality property Population 0.89 0.32 0.48 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.98 0.12 0.96 Model has good fit as the errors satisfy all the diagnostic checking UK G/Y 0.96 0.40 0.50 Model has good fit as the errors satisfy all the diagnostic checking G/Y ×L 0.99 0.65 0.83 Model has good fit as the errors satisfy all the diagnostic checking Population 0.58 0.30 0.54 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.99 0.12 0.96 Model has good fit as the errors satisfy all the diagnostic checking Economies 2025,13, 46 23 of 29 Table 5. Cont. Country Dependent Variables Breusch–Godfrey Serial Correlation LM Test Breusch–Pagan– Godfrey Heteroskedasticity Test HistogramNormality Test Remarks France G/Y 0.98 0.54 0.60 Model has good fit as the errors satisfy all the diagnostic checking G/Y ×L 0.85 0.64 0.72 Model has good fit as the errors satisfy all the diagnostic checking Population 0.78 0.88 0.69 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.84 0.91 0.84 Model has good fit as the errors satisfy all the diagnostic checking Brazil G/Y 0.99 0.88 0.81 Model has good fit as the errors satisfy all the diagnostic checking G/Y ×L 0.85 0.78 0.68 Model has good fit as the errors satisfy all the diagnostic checking Population 0.97 0.83 0.59 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.85 0.78 0.68 Model has good fit as the errors satisfy all the diagnostic checking Russia G/Y 0.99 0.47 0.41 Model has good fit as the errors satisfy all the diagnostic checking G/Y ×L 0.94 0.58 0.56 Model has good fit as the errors satisfy all the diagnostic checking Population 0.88 0.66 0.60 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.91 0.63 0.55 Model has good fit as the errors satisfy all the diagnostic checking S. Korea G/Y 0.97 0.26 0.72 Model has partially good fit as the errors do not satisfy the normality property G/Y ×L 0.92 0.48 0.77 Model has good fit as the errors satisfy all the diagnostic checking Population 0.95 0.65 0.66 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.94 0.71 0.58 Model has good fit as the errors satisfy all the diagnostic checking Australia G/Y 0.99 0.80 0.14 Model has partially good fit as the errors do not satisfy the normality property G/Y ×L 0.98 0.85 0.45 Model has good fit as the errors satisfy all the diagnostic checking Population 0.96 0.86 0.58 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.97 0.91 0.68 Model has good fit as the errors satisfy all the diagnostic checking Mexico G/Y 0.99 0.57 0.19 Model has partially good fit as the errors do not satisfy the normality property G/Y ×L 0.88 0.61 0.43 Model has good fit as the errors satisfy all the diagnostic checking Population 0.95 0.64 0.54 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.96 0.75 0.62 Model has good fit as the errors satisfy all the diagnostic checking Economies 2025,13, 46 24 of 29 Table 5. Cont. Country Dependent Variables Breusch–Godfrey Serial Correlation LM Test Breusch–Pagan– Godfrey Heteroskedasticity Test HistogramNormality Test Remarks Spain G/Y 0.99 0.51 0.007 Model has partially good fit as the errors do not satisfy the normality property G/Y ×L 0.99 0.60 0.78 Model has good fit as the errors satisfy all the diagnostic checking Population 0.98 0.62 0.71 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.97 0.71 0.65 Model has good fit as the errors satisfy all the diagnostic checking Indonesia G/Y 0.91 0.69 0.66 Model has good fit as the errors satisfy all the diagnostic checking G/Y ×L 0.97 0.72 0.68 Model has good fit as the errors satisfy all the diagnostic checking Population 0.95 0.75 0.78 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.98 0.82 0.58 Model has good fit as the errors satisfy all the diagnostic checking Netherlands G/Y 0.99 0.72 0.012 Model has partially good fit as the errors do not satisfy the normality property G/Y ×L 0.96 0.81 0.002 Model has partially good fit as the errors do not satisfy the normality property Population 0.98 0.77 0.15 Model has partially good fit as the errors do not satisfy the normality property PCGDP Growth 0.99 0.68 0.22 Model has partially good fit as the errors do not satisfy the normality property S. Arabia G/Y 0.99 0.87 0.42 Model has good fit as the errors satisfy all the diagnostic checking G/Y ×L 0.98 0.78 0.56 Model has good fit as the errors satisfy all the diagnostic checking Population 0.95 0.88 0.62 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.98 0.74 0.57 Model has good fit as the errors satisfy all the diagnostic checking Turkiye G/Y 0.99 0.80 0.51 Model has good fit as the errors satisfy all the diagnostic checking G/Y ×L 0.98 0.74 0.59 Model has good fit as the errors satisfy all the diagnostic checking Population 0.95 0.75 0.65 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.96 0.81 0.71 Model has good fit as the errors satisfy all the diagnostic checking Switzerland G/Y 0.97 0.45 0.01 Model has partially good fit as the errors do not satisfy the normality property G/Y ×L 0.98 0.66 0.62 Model has good fit as the errors satisfy all the diagnostic checking Population 0.99 0.85 0.71 Model has good fit as the errors satisfy all the diagnostic checking PCGDP Growth 0.88 0.71 0.56 Model has good fit as the errors satisfy all the diagnostic checking Note: PCGDP in columns 3 and 6 represents the growth of PCGDP. Source: author’s own calculations.