Master’s Degree
in Management – Accounting&Finance
Final Thesis
Taxation and economic development:
a comparative econometric study of
fiscal policies
Supervisors
Ch. Prof. Donadelli Micheal Ch. Prof. Dasgupta Shouro
Assistant supervisor
Ch. Prof. Zantomio Francesca Graduand
Valentina Zago
Matriculation Number 856767 Academic Year
Index
Abstract ... p.1
Chapter I – Taxation and Growth: An Introduction ... p.3
1.1 Different approaches in the tax system... p.3 1.2 Taxation and development: an overview ... p.6
Chapter II – Early growth accounting and Barro regressions ... p.17
2.1 A model for growth: the theoretical panorama) ... p.17 2.2 Barro Regressions and the 1980-2018 expansion (Base year) ... p.22 2.3 Time series 1960-1985 ... p.37 2.4 Time series 1960-2018 ... p.42 2.5 Time series 1986-2018 ... p.49
Chapter III – The determinants of growth: does taxation matter? ... p.55
3.1 Literature review ... p.55 3.1.1 Macroeconomic variables ... p.57 3.1.2 Public expenditure ... p.59 3.1.3 Trade components and FDI ... p.63 3.1.4 Non-economic determinants ... p.65 3.1.5 Taxation... p.67 3.2 Analysis at World level ... p.74 3.3 Analysis at OECD level ... p.96
Chapter IV – Different tax systems: an enquiry on their relative impact ... p.107
4.1 Tax structure: the framework ... p.108 4.1.1 Income Taxes ... p.108 4.1.2 Consumption Taxes ... p.110 4.1.3 Property Taxes ... p.112
4.1.4 Capital Gains Taxes ... p.113 4.1.5 Payroll Taxes ... p.114 4.1.6 Inheritance/Estate Taxes ... p.114 4.2 Literature review ... p.115 4.3 Empirical Analysis ... p.120
Chapter V – From optimal tax theory to tax policy: redistribution and challenges ... p.129 5.1 Income redistribution: does taxation matter? ... p.129
5.2 Challenges for a second-best analysis ... p.134 5.2.1 The commitment issue ... p.137 5.2.2 Heterogeneous preferences and utility ... p.138 a. Needs ... p.139 b. Disutility of work ... p.139 c. Interdependent utilities ... p.140 d. Other dimensions of taste differences ... p.141 5.2.3 Behavioural issues... p.141 Conclusions ... p.143 Appendix ... p.145 Bibliography... p.175 Sitography ... p.182
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Abstract
In the general opinion, taxation is currently regarded as a barrier to growth and is a very much exploited theme in political debate. Countries have dramatically increased the level of taxation as well as have changed the way in which taxes are raised. Key role for administrative studies and the political motives for fiscal capacity, there are some aspects of economic development that are related to tax systems’ evolution, such as the size of firms, financial transactions, but also the tax system evolution has had a feedback on economic development. It is true that as taxes increase, the burden on private individuals and corporations increases, but it is also true that the higher is tax collection, the more the governments can intervene with investments that enhance the population’s well-being and standards of living. This double and reverse relationship is also influenced by political institutions. Fostering fiscal capacity and enlarging tax collection is in the interests of governments. At the core of the relationship between citizens and the government is the issue of whether taxation is beneficial or not. But is taxation actually intertwined with economic development? What role does it play as far as growth and development of a country are concerned?
From the early works of Adam Smith and Malthus to the present-day researchers have tried to find the most important determinates that influence growth by formulating new and improved theories and models.
In this thesis, I will try to offer my point of view in the evolution of the main factors that have an impact on economic growth. In particular, it will delve into old and new research and also reveal areas in which knowledge is lacking. Through a combination of theory and empirical work, prior research and analysis will be presented and new paths of knowledge will be explored for the first time. Using the R software, new econometric models will be studied in order to improve and test previous studies and to assess new causal relationships.
First of all Barro’s growth relationships will be studies by increasing geographical coverage using as standard point of analysis the base year; then the research will be implemented by extending the research up to nowadays using panel growth regressions divided in three main time sections.
In addition to this, the work will delve in the field of growth accounting, through an intense analysis of the most significant determinants of growth.
Then, the impact of different types of taxation on growth will be assesses and finally, a new model of taxation, through the minimization of differences across the world will be created and analysed.
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CHAPTER I
Taxation and growth: An Introduction
1.1 Different approaches in the tax system
The growth of countries and their ability to extract a significant amount of money from its inhabitants is a compelling and outstanding economic feature that characterised the last two centuries. Economists have always been aware of the importance of growth. Studies concerning economic development languished after the late 1960s and, after a lapse of nearly twenty years, this field of research became brisk again in the mid-1980s. This new path of analysis was characterized by models of the determination of long-run growth, an area that is now called “endogenous growth theory”.
Starting from the mist of times, one of the most important determinants of growth was found to be taxation. Actually, well-designed tax systems minimize efficiency losses created by taxes and at the same time lead to development in endogenous-growth models (Barro, Sala-i-Martin, 1992). Indeed, taxation imposes an economic burden on economic agents’ (especially on lower-band earners), but tax revenue is also raised by governments in order to be spent to increase public welfare, that is, on public goods and investments that make the economy more productive (Barro, 1990).
The milestone relationship between taxation and growth arouse with the so called “standard approach” to taxation (Slemrod and Yitzhaki, 2002), according to which the two most important constraints to the tax take are low levels of revenue and the reliance on narrow tax bases. This model is a basic one: it leaves little room for government influences on taxation and sees economic development and tax systems as two sole horizons influencing each other.
Figure 1: The standard approach
However, economic development does not necessarily translate into increases in the tax take (as this will imply an increasing burden on taxpayers), nor does the reverse (as far as taxation is not the only factor influencing economic development). However, when
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designing a tax system, it has to be kept in mind that “the best tax policy is worth little if it cannot be implemented effectively” (Bird, 2004).
From this reasoning, a new approach arose. This view unfolded by taking into consideration historical accounts of how tax systems have developed: the latter, indeed, have increasingly focused attention on governmental behaviour and the rationale for raising taxes. By looking at historical accounts, it can be asserted that governments put strong conscious efforts to build fiscal capacity over years, and that political factors are to be factored in when considering the extent of tax take, being a crucial factor influencing it.
This approach is aligned with a more modern path of research on development, which sees political motives in addition to economic factors as a central point to understanding how development proceeds and to explain why some countries languish while others ones blossom.
Figure 2: The modern approach
According to this approach, political factors (such as the degree of political instability) influence economic development and shape investments in fiscal capacity. However, it has to be stressed that the extent to which governments can levy taxes are not only dependent on political institutions and their strength, but also mirror both national and international circumstances (such as the risk of fights and revolution) that affect political interests and the creation of a strong state. This model is depicted in Figure 2 and was formalised by Timothy Besley and Torsten Persson in their “Taxation and development” (2013).
In addition to this, another link has to be pointed out. It is the impact that taxation itself has on development. Indeed, taxation can deeply shape the economy of a state, in a positive or negative way (just consider the level of taxation and the different types of taxes). When a state is characterized by a developed tax system, it has the possibility to play an active role in the economy, by contributing to growth, as a complement to its extractive role. Some examples include building high-return infrastructure projects and
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developing the legal system to reduce the extent of informality in the economy.
Figure 3: The extended approach
An approach only focusing on economic theory will therefore lead to a tax system that is shaped and characterised by the constructive effort of politically motivated agents, aimed at an increase in the tax base. However, an important factor is missing. The approach that will be taken on in this work sees tax compliance as something more than a simple abstract issue. This is coherent with the idea boosted by political scientists and sociologists, which expand taxation’s role in the growth of countries even further, by stating that it can be a stimulus for political and economic change. This view is illustrated in Figure 3, where political institutions respond to an expanding tax domain. Demands for transparency and representation are built as part of the need to build a strong fiscal state in a “fiscal contract” between the citizens and the state.
As far as tax revenue is concerned, an additional factor has to be considered: tax evasion. As a matter of fact, there is a gap between expected revenue and actual revenue collected by governments worldwide. According to Richard Murphy’s research, which was conducted for the European Parliament, EU tax gap is estimated to be equal to €825 billion a year, based on data for 2015. Therefore, an additional variable to be factored in is the need for compliance. In modern empirical tax systems, policy makers have to create incentives and ensure that the tax gap is minimized. This approach is related to a vast series of literature, that have studied in several papers different ways in which tax systems can be improved in order to minimize shadow economy and increase the effective collection of tax revenue. For example, Cukierman, Edwards, and Tabellini (1992) discuss on how the use of seigniorage depends on the efficiency of the tax system, and how the strategic choice of the latter depends on factors like political stability and polarization. I myself have studied the impact that government effectiveness and political stability have on tax evasion. In particular, a one-unit increase in political stability leads
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to a decrease of 0.079 in tax evasion rate (measured by the Basel anti-money laundering index, as published by the Basel Institute of Governance).
In economic literature, there have been a variety of studies that have analysed the impact that different variables have on both tax evasion on one hand and those economic growth on the other. A quick list, as far as the development of fiscal capacity evolved, comprises Bonney (1999), Brewer (1989) and O’Brien (2001, 2005). These researchers have studied the impact that of government role have on strengthening fiscal capacity, and in particular the importance that warfare assumes in stimulating demands for fiscal capacity (a feature that will be further explored in this Chapter).
Others focused on other aspects, adopting more generalised view, such as Hoffman and Rosenthal (1997), Levi (1988), Schumpeter (1918), and Tilly (1985).
1.2 Taxation and development – an overview
Before delving into growth accounting and presenting econometric models, it is necessary to provide an overview on States’ growth trends with some background facts about taxation across the World.
Figure 4: Total tax revenues as % of GDP
(Source: ICTD/UNU-WIDER Government Revenue Dataset, September 2019)
According to Madisson (2001), countries in Central Europe1 have raised around 12% of GDP in tax revenue around 1910 and around 46% by the turn of the Millennium. The
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corresponding figures for the US are 8% and 30%. By collecting data from the OECD database and plotting tax revenue versus GDP, it can be said this ratio has generally been characterized an increasing path since the second half of the 1960s. As can be seen in the graphs below, at the edge of 2019, these ratios rose, respectively, up to 46% (France) and declined to 24% (US). All in all, OECD average was 34.3 in 2018 (OECD Revenue Statistics, 2019).
It is to highlight that the largest drop in the tax-to-gross domestic product ratio between 2017 and 2018 has been experienced by the United States, with a decrease equal to 2.5 percentage points. This decline was due to the tax reforms implemented in the Tax Cuts and Jobs Act, which considerably altered the American tax system. Corporate tax rate was lowered from 38.9% in 2017 to 25.8% in 2018. In addition to this, the tax wedge on labour income was reduced through the implementation of further reductions to income tax rates and increases in the standard deduction and the child tax credit.
As a consequence, taxes on income fell by 1.1 percentage-points, PIT was reduced by 0.5 percentage points and CIT was lowered by 0.7 percentage points. Furthermore, property tax revenues were reduced by 1.3 percentage points, due to the one-off deemed repatriation tax on foreign earnings under the Tax Cuts and Jobs Act.
Figure 5: Tax revenues as % of GDP for European countries, 1965-2018 (Source: OECD.org)
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Figure 6: Tax revenues as % of GDP for non-European countries, 1965-2018 (Source: OECD.org)
In particular, it has to be made a distinction between European (as for example those in Madisson’s sample) and non-European countries, and it has to be stressed that the formers’ tax revenue is much higher with respect to the latters’. Furthermore, despite the increasing path, some ups and downs in revenues are visible. Reason behind these changes are a series of tax reforms, among which the most important one was the extension of the income tax to a wide population, which was allowed by large investments in fiscal capacity and political institutions.
The increase in tax revenue, however, is not only due to a higher tax rate, but to some additional and substantial changes in the overall tax systems, as introduced above. Mitchell (2007) studied the evolution of fiscal capacity over time basing his research on a sample of 17 countries2. In particular, he focused his analysis on three kinds of taxation (income tax, income tax witholding and VAT) and plotted their distribution since 1850. The collection of tax revenue assumes investments in fiscal capacity and therefore an evident tendency in the former can be a proxy for the evaluation of a trend in the latter. Figure 7 presents Michell’s research output.
2 The countries in the sample are Argentina, Australia, Brazil, Canada, Chile, Colombia,
Denmark, Finland, Ireland, Japan, Mexico, the Netherlands, New Zealand, Norway, Sweden, Switzerland, the United Kingdom, and the United States. The sample being confident that the data are comparable across countries and time in Mitchell.
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Figure 7: Fiscal capacity evolution Figure 8: Taxes and share of income tax (Source: Besley&Persson) (Source: Besley&Persson)
The solid line shows the proportion of countries that have introduced income taxes, the dashed line the proportion that have implemented income-tax withholding and the line with a mixture of dots and dashes represents the proportion that have adopted value-added taxes.
As visible for this limited sample of countries, all three types of taxes presented an increasing trend from the first half of the nineteenth century up to nowadays. It is also visible that they started to be levied at different points in time. The “oldest” are taxes on income, which arose in the mid-nineteenth century, followed by direct withholding. The latter, however, lagged behind up to the first half on the 90s. Finally, VAT adoption did not start before the end of the second World War. Interestingly, in 2000 a gap still persisted in the cumulative frequency representation. This is due to the fact that at that time, and still nowadays, no value-added tax is levied by one of Mitchell’s sample countries, that is, the United States3. Not by chance, the imposition of VAT requires a high degree of administrative fiscal capacity.
As introduced above, changes in the tax system are related to investments in administrative structures. Stronger and more effective tax systems have allowed the collection of increasing amounts of tax revenue. In more detail, Figure 8 depicts two important features that characterised the twentieth-century evolution of tax systems worldwide:
1. In the twentieth century, average tax take has increased over time from around
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10% of national aggregate income to around 25%4;
2. Income taxation, which only made up about 5% of revenues at the beginning of the century, constitute almost 50% of total revenue at the end of the last century. The trends are mainly characterised by two hikes, corresponding to the two World Wars. Wars are exceptional circumstances during which governments experience higher needs of revenues and are prone to spend more, and as a consequence increase tax rates. However, after the end of these troubled periods, tax rates are no more lowered to the pre-war level, but are kept high, sometimes accompanied by higher services and public social benefits that citizens join. Much literature debate deals with fiscal state’s pattern of war, with only Centeno (1997) arguing that Latin America may be an exception to the Tilly hypothesis of war as a major motive for building fiscal capacity (Tilly, 1985). Some researchers, such as Herbst (2000), have even ventured the hypothesis that some countries in Africa might have been able to strengthen their weak states if external wars had been more frequent on the continent. Having named weaker states, it is to stress that the narrow sample in Figures 7 and 8 does not take into account many of the poorer countries in the world (just think about African countries or the Southern Asian ones).
But how has fiscal capacity evolved across countries and over time?
One of the most striking and acknowledged feature is that richer countries raise more tax revenue as a share of national income than poorer countries do. This is supported by Besley and Persson (2013), who studied the overall tax take as a share of GDP using the Baunsgaard and Keen (2005) dataset. In particular, they divided the dataset in three different subsets according to the level of income (namely, low, medium or high) and studied the relationship between the share of taxes to gross domestic product against the logarithm of GDP per capita (taken from the PennWorld Table’s dataset). From this cross-section analysis, which is depicted in Figure 9, it is evident that the high-income class (characterised by the higher GDP per capita) contributed to a higher level to tax revenue. In addition to this, by using historical data from Mitchell (2007), they also plotted the log of 5-year averages of the tax share from 1900 to 2000 against national income and differentiated observations by time period. As you can see from Figure 9, the share of taxes in aggregate income and the log of the 5-year averages of per capita GDP (the
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variable that was used to also incorporate the time factor) appear to be characterised again by a positive pattern.
Figure 9: Cross-section taxes vs income Figure 10: Time series tax vs GDPpc (Source: Besley&Persson) (Source: Besley&Persson) Both plots are strikingly similar as the correlation pattern is concerned. Indeed, a clear and strong positive correlation emerges: high-income countries currently collect a much larger share of their income in taxes. This means that higher-income countries (that is, more developed ones) today raise a higher level of tax revenues than poorer countries do, and this is mainly due to the fact that they have made larger investments to build fiscal capacity.
As known, different types of taxes are levied both directly and indirectly to individuals and businesses worldwide. Each of them requires different amounts of investments in order to be collected and to be respected by citizens and companies. It is to stress that not all kinds of tax require the same level of investment in order to be applied and be collected. This is why the first and most ancient form of taxation were trade taxes and did not require highly-developed enforcement and compliance systems, but only required to observe trade flows at major shipping ports. On the other hand, other types of taxation became to be applied due to enhanced administrative compliance systems, which were not present or so developed decades ago. Therefore, as years and decades passed, new forms of taxation were born, and some new ones replaced others. The most important of these is the taxation of income.
Holding constant total tax revenue, it is curious to look at both the cross section and time series representations (respectively, Figure 11 and 12) of income taxes versus trade taxes.
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Figure 11: Cross-section income vs trade taxes Figure 12: Time series income vs trade taxes (Source: Besley&Persson) (Source: Besley&Persson)
In Figure 11, the income-tax share is presented on the y-axis, while trade-tax share on the x-axis. The two variables are characterized by a clear pattern that points out negative correlation: countries that rely more on income taxation rely less on trade taxes. Moreover, high-income countries levy to a higher extent income taxes than middle and low-income countries, which mainly depend on trade taxes. Confirming the pattern described above, according to which countries adopt income taxation after massive investments in enforcement and compliance structures, is Figure 12, where income taxation is found out to be started to be applied in the period 1970-1999. Indeed, in the 1990s countries have moved away from trade to income taxes by developing fiscal capacity and developing their tax systems, as they have become richer. Moreover, it is to highlight that both cross-sectional and time-series plots present also similar slope of the regression lines.
Income taxation is the one that generates the higher revenues for governments worldwide. Besley and Persson (2013) further investigated the contributions to income tax by differentiating observations into three different subsets, defined by the level of tax take. The three subsets are the following ones:
• countries that raise more than 25% of taxes in GDP (depicted with a triangle in Figure 13);
• countries that raise 15–25% of taxes in GDP (depicted with an empty circle); • countries that raise less than 15% (depicted with a full circle).
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In Figure 13 all these three different categories all represented in a plot with the income-tax share is on the y-axis and the log of income per capita on the x-axis.
Figure 13: Cross-section income tax vs income Figure 14: Time series income tax vs per capita aggregate income
(Source: Besley&Persson) (Source: Besley&Persson)
The cross-section shows that countries in the high-tax group raise much more of their tax revenues in the form of income taxes, while the historical time series differentiates again observations by time period, highlighting that in the most recent period (1970-1999) an increasing level of income taxes have been levied on population. The historical trend in this sample of older nations and the pattern in the world today is again very similar. According to the 2019 OECD Revenue Statistics, on average, the 37 countries belonging to the Organization for Economic Co-operation and Development collected 34.0% of their tax revenues through taxes on income and profits (both personal and corporate) in 2017. Taxes on personal and corporate incomes remain the most important source of revenues used to finance public spending in 18 OECD countries, and in nine of them (Australia, Canada, Denmark, Iceland, Ireland, Mexico, New Zealand, Switzerland and the United States) the share of income taxes in the 2017 tax mix exceeds 40%. (See the detail of revenue composition in Figure A1 in the Appendix).
As anticipated earlier, the main issue in the tax panorama is tax evasion. One measure of fiscal capacity can be obtained by comparing statutory tax rates to actual tax revenues collected. Figure 15 plots the top statutory income-tax rates in 1990s for the 67-country sample in Gordon and Lee (2005) against the share of income taxes in GDP from Baunsgaard and Keen (2005).
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Figure 15: Top statutory income vs total tax take (Source: Besley&Persson)
From Figure 15 it is visible that the distribution of the top statutory rates is about the same among the different income categories. With this qualification, the fact that high-income countries raise much more income-tax revenue than low-income countries suggests that a narrow tax base driven by compliance difficulties is a much bigger issue among low-income countries. This reinforces the earlier observation that fiscal capacity is considerably less developed in poor countries. However, it is to say that the dataset used to create this plot does not take into consideration factors such as coverage and progressivity.
Finally, also some facts relating tax structure and politics have to be considered, according to the “new” model of tax system described at the beginning of the Chapter. The indicator of executive constraints from the Polity IV database (see Marshal and Jaggers, 2010) can be used to represent political institutions. The highest value (the variable x-const is equal to 7 on a 1–7 scale) is used to measure the proportion of years since independence that a country had strong constraints on the executive. To demonstrate that this political factor reflects something different than income’s variety, current income has to be controlled for before plotting the partial correlation of high executive constraints total tax share in GDP (Figure 16). A clear positive correlation between this measure of political institutions and fiscal capacity is visible, taking the level of economic development into consideration5. The facts illustrated in these figures illustrate the need to adopt an approach where political factors help shape the level and evolution of fiscal capacity.
5 In Figure 16 the correlation hinges mainly on the countries with very low executive constraints
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Figure 16: Income tax share vs. executive constraints (Source: Besley&Persson)
In conclusion, taken together, the cross-sectional and time-series data analysed in this Chapter suggest the following results. Richer countries have invested in their fiscal capacities over time making major investment in enforcement and compliance systems. As a consequence, nowadays they collect a greater portion of national income in taxes than do poorer countries, even though they apply the same tax rates. In addition to this, they rely to a much larger extent on income taxes as opposed to trade taxes. Moreover, high-tax countries rely to a much larger extent on income taxes as opposed to trade taxes than do low-tax countries. Countries with strong executive constraints collect higher tax revenues, when income per capita is held constant, than do countries with weak executive constraints and rely on a higher share of income taxes in total taxes, when income per capita is held constant, than do countries with weak executive constraints. Together, it can be summarized that rich, high-tax and executive-constrained states have made considerably larger investments in fiscal capacity than have poorer, low-tax, and non-executive-constrained states.
Considering the correlations highlighted by data presented in this Chapter, it is however unexpected that analysts and researchers have not given sufficient importance to dynamic models of macroeconomic, social and political determinants of fiscal capacity. Most normative and positive theories of taxation hardly ever touch upon lacking administrative infrastructure as an important constraint on the taxes that governments can raise. All of these variables will be considered and analysed when empirically studying econometric models concerning economic growth and taxation in the next Chapters.
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CHAPTER II
Early growth accounting and Barro regressions
2.1 A model for growth: Theoretical panorama
One of the most important questions in economics is “What causes economic growth and thus prosperity for the people in the World?”. While an in-depth literature review of the studies concerning the determinants of growth from the mist of times up to more recent research will be presented in Chapter III, the aim of this Chapter is to present the framework of growth accounting starting with a generalised model, which will take into consideration the impact of taxation on growth, and then by focusing on the pioneer model proposed by Barro in the 1990s.
First of all, a distinction between development and growth has to be made. Development is measured by a proxy indicator, which is GDP per capita in a society, and is usually used as a qualitative feature. On the other hand, growth is defined as the GDP variation from one year to the next. Growth accounting is usually defined as the method used to determine the contribution of each factor to the growth of output, this output being growth or development of a country.
At the macroeconomic level, output level Y (e.g. GDP), can be expressed as a function of the level of technical progress and advancement (A), the level of capital employed (K) and labour force employed (L). Moreover, labour can not only be considered in quantitative terms (number of hours worked), but also in qualitative terms (effort put), but this will be taken into account later.
If the variation in the level of these three factors and marginal productivity are considered, they can be expresses in the function:
𝑌 = 𝐹(𝐴, 𝐾, 𝐿)
If these variables are considered across time, the function becomes:
𝑌(𝑡) = 𝐹(𝐴(𝑡), 𝐾(𝑡), 𝐿(𝑡))
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variables and also the change in marginal productivity is considered, the function evolves as such: 𝑑𝑌 𝑑𝑡 = +𝐹𝐴 𝜕𝐴 𝜕𝑡 + 𝐹𝐾 𝜕𝐾 𝜕𝑡 + 𝐹𝐿 𝜕𝐿 𝜕𝑡
How is taxation interfering with A, K and L? Growth depends on the choice of economic agents’ about how much to invest in technological advancement, in capital and their supply of labour (and labour force education). In other words, economic growth can be affected by policy choices through the effect that taxation has upon economic decisions. Let’s give a hint about the possible impact that taxation can have on growth on the basis of the model presented above:
• Impact on technical progress and advancement: Taxation of firms (corporate taxation) in the general opinion reduces the return to innovation, and therefore companies’ optimal level of investment on research and development, with a detrimental effect on technological progress. This because R&D is used to search for new products and new or cheaper innovative materials. Taxation of that profit changes the incentive of corporations to invest, because the overall return to that investment will be lower;
• Impact on the level of capital: Taxation of capital impacts firms’ demand for this factor of production. In other words, taxes on capital impact firms’ decisions regarding the desired stock of capital by affecting the cost of capital in economies. Also human capital is the key input to the research sector, which generates the new products or ideas that underlie technological progress. Thus, countries with a higher level of human capital are characterised by a faster rate of introduction of new goods and thereby tend to have a greater pace of growth. Human capital plays a special role in a number of models of endogenous economic growth. In multicounty models of technological change (Romer, 1990), the spread of new ideas across countries (or firms or industries) is also important. As highlighted d by Nelson and Phelps (1966), countries who are distinguished by human capital also internalize innovations or ideas that have been discovered elsewhere. Therefore, a country with more human capital tends to grow faster, as it catches up more rapidly to the ones in which new ideas blossom. According to Becker, Murphy, and Tamura (1990) the rate of return on human capital increases over
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some range, and that could be due to the “spill-over” benefits from human capital as stressed by Lucas (1988). Increases in the quantity of human capital per person tend to lead to higher rates of investment in human and physical capital, and hence, to higher per capita growth. Personal income taxation reduces the returns to education, which is known to foster growth;
• Impact on labour force: Personal income taxation reduces the returns to savings so must reduce the accumulation of capital, which is known to foster growth. Indeed, people accumulate capital by saving and postponing consumption. Assuming an interest rate equal to r, people can save one euro today to have back (1+r)*t in time t. However, PIT reduces the returns to saving as far as people will have to give up to part of their saving to pay taxes.
From these three perspectives, taxation just seems to challenge growth, but from the other side of the coin, it has to be acknowledged that growth can be affected by policy choices through growth-enhancing public expenditures (funded by tax revenue). As visible in Figure 17, which homes GDP growth in the vertical axis and government expenses on education on the horizontal axis, growth and government investment are positively correlated. However, this relationship is not only true for investments in education. Think about public investments in other public goods and services such as infrastructures hospitals, streets highways, the creation of a legal and transparent field for foreign investment, fostering investment in R&D, and so on.
Figure 17: GDP growth versus Government expenditure as a % of GDP (Source: Besley&Persson)
Figure 17 is by Besley and Personn (2013) and homes in data concerning 151 countries, taken from Word’s Bank database at the time of their research. If the same relationship is
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plotted using data from the same dataset nowadays, the picture changes:
Figure 18: GDP growth versus Government expenditure as a % of GDP (Source: R Studio)
The scatterplot does not represent a positive correlation between the two variables, but as the best-fit line suggest, they seem to be slightly negatively related. Actually, this is due to the fact that the updated dataset contains data about 264 countries for the period up to nowadays. The difference therefore is not only due to time horizon (more recent data as countries are changing), but also to the fact that the sample size is extended and much more observations are present. This is an initial point of discussion for the work that will be performed in the next chapters of this work.
So, in theory, taxation can have both a negative and a positive effect on growth. Mostly, the difficulty consists in disentangling the positive effect of government expenditure from the negative effect of the taxes used for financing. This is well represented by the Laffer curve, a theory developed by the economist Arthur Laffer in 1979. The Laffer Curve describes how changes in tax rates affect government revenues. In particular, the former affects the latter in two ways. One is immediate, which Laffer describes as “arithmetic.” Every dollar in tax reduction translates directly to one less dollar in government revenue. The other effect is longer-term, which Laffer describes as the “economic” effect. It works in the opposite direction. Lower tax rates put money into the hands of taxpayers, who then spend it. It creates more business activity to meet consumer demand. For this reason, companies hire more workers, who then spend their additional income. This boost to economic growth generates a larger tax base. It eventually replaces any revenue lost from the tax cut. Laffer’s theory can be represented as in Figure 19.
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Figure 19: The Laffer curve
Figure 19 shows how, at the bottom of the curve, a tax rate equal to zero taxes results in no collection of revenue by governments. As far as the tax rate increases, government income suddenly starts to rise. In the normal range, raising taxes has the effect of increasing total revenue, as shown by the flatness of the curve. However, as the government keeps raising taxes, the payoff the marginal revenue becomes less, causing the curve to steepen. At some point, higher taxes place a heavy burden on economic growth. Demand falls so much that the long-term decline in the tax base more than offsets the immediate increase in tax revenue. At this point the curve the curve reaches the apex and then bends backward. Beyond the maximum point on the Laffer hill, additional taxes result in reduced government revenue. This is the part corresponding to the second half of the curve on the chart, which Laffer calls the “prohibitive range”. At the top of the curve, when tax rates are 100%, government revenue is zero. If the government takes all personal income and business profit, then no one works or produces goods. This results in the disappearance of the tax base. Therefore, “the government that thinks that raising taxes is necessary to pay for social programs and other public services is short-changing itself”, argued Laffer. When tax rates are beyond the apex in the curve, that is, in the “prohibitive range” of Figure 19, individuals work less and businesses invest less, smoothing growth and reducing the tax base.
Laffer’s general idea of supply-side stimulus can sometimes work. If in a country tax rates are reduced, this will mainly favour people in the higher-income bracket. At first this kind of policy might be thought to be not fair, as not benefitting poorer people, but in developing countries where there is not enough money to fund the investment needed
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to spur growth, a Laffer-style policy could temporarily help stimulate economic expansion by channelling wealth to potential investors.
But this scenario is not applicable to other developed countries (as for example the US and the majority of European countries). This because private investment tends to follow and flow with the business cycle and when demand is not strong, so is investment. Cutting taxes on a country’s higher-income layer is not going to encourage them to invest more, as they have a higher portion of income that remains unspent with respect to the lower-income bracket. Moreover, by shifting wealth from middle class families to the moneyed few (a group that is able to consume far less than the working masses) this sort of policy suppresses consumption, which in turn discourages investment in productive businesses. Slowing demand drags on growth, causing debt and unemployment to rise.
Nonetheless, the tidy arc of cause and consequence described by Laffer does not occur in the real world. It is true that extremely high tax rates drown economic activity, but there is no reason to assume the relationship between tax revenue and tax rates is perfectly U-shaped. In addition to this, the equilibrium point at which a government collects the highest level of revenue without dragging down the economy is impossible to know and is different from country to country. As a consequence, without detailed data, it is not possible to understand on which point on the curve a country’s economy is.
Up to now, this work has dealt with correlation patterns among growth and other variable potentially affecting it. But now it is time to turn to empirical evidence. Regression analysis allows to control for other variables that might be affecting the dependent variable, which in this case is economic growth.
2.2 Barro Regressions and the 1980-2018 expansion (Base year)
There is a substantial body of literature that seeks to identify from data the factors that determine the rate of growth of a country, but the first scholar who used econometric regressions in order to study the impact of taxation on growth and that became the pioneer of growth accounting was the American macroeconomist Robert J. Barro in 1991. He used both economic and non-economic variables to perform growth regression analysis aimed at studying the determinants of growth. The general form of a Barro growth regression uses the growth rate of GDP as the left-hand side variable. The variables on
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the right-had side were selected from a very wide range of potential regressors. This range included economic variables, such as the ratio of investment to GDP, and non-economic variables, such as political rights and violent wars. The latter were included to capture the stability of the political environment of each country. The data were taken from the Summer and Heston (1998), the United Nations and the World Bank and Bank’s (1979) databases, regarding a cross-section of 98 countries for the period 1960-1985.
The variables that Barro used were the following:
• The variable γy6085 (also named GR6085) is the growth rate of real per capita GDP from 1960 to 1985;
• GDP60 is 1960 value of real per capita GDP (using 1980 as base year); • GDP60SQ is the square of GDP60;
• i/y is the average from 1960 to 1985 of the ratios of real domestic investment to real GDP;
• gt/y is the average from 1970 to 1985 of the ratios of real public domestic investment to real GDP;
• gt/I is the average from 1970 to 1985 of the ratio of real public domestic investment to real domestic investment;
• gc/y is the average from 1970 to 1985 of the ratio of real government consumption (that is, investment) to real GDP (government consumption spending);
• FERT is the total fertility rate (as indicated by the number of children per woman), average of 1965 and 1985;
• MORT is the mortality rate for age 0 through 4, average of 1965 and 1985; • FERTNET is equal to FERT(1-MORT);
• GPOP is the growth rate of population from 1960 to 1985;
• POP is the geometric average of population (in millions) from 1960 to 1985; • SEC60 is the 1960 secondary-school enrolment rate. It measures the number of
students enrolled in the designated grade levels relative to the total population of the corresponding age group;
• PRIM60 is the 1960 primary-school enrolment rate;
• STTEAPRI is the student-teacher ratio in primary schools in 1960; • STTEASEC is the student-teacher ratio in secondary schools in 1960; • LIT60 is adult literacy rate in 1960;
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• ASSASS is the number of assassinations per million population per year;
• PPPI60 is 1960 purchase power parity value for the investment deflator (US=1.0); • PPIDEV is magnitude of the deviation of the 1960 purchasing power parity value
for the investment deflator from the sample mean. • PPPY60 is the value for the GDP deflator (US=1.0).
In addition to these variables, Barro used other four regressors (SOC, MIXED, AFRICA and LAT.AMER) as dummy variables for, respectively, socialist economic system, mixed/free enterprise/socialistic economic system, sub-Saharan Africa and Latin America. These variables were used in order to incorporate the country fixed effects in the regression equation and exclude biases. Barro wisely introduced other variable to incorporate political instability (REV and ASS), the economic system and role of government and market distortions (PPP variables). See Figure A2 in the Appendix for the descriptive statistics of all the variables included in Barro’s analysis.
It has to be noted that Barro did not perform time-series analysis, but used as independent variables the data of the base year of his model (that is, 1960). The regressors that Barro used are wisely incorporated with neoclassical growth model. In particular, Barro used GDP60 as the omni-present independent variable, and almost all regressors were calculated on the basis of 1960. This means that 1960 is the base year for Barro regressions models. This is a very important thing to stress, as Barro also used his regression to further test neoclassical growth models’ assumptions. In particular, according to Solow (1956), Cass (1965) and Koopmans (1965), a country’s per capital growth rate tends to be inversely related to its starting level of income per person. This means that, assuming that countries are similar with respect to structural parameters for preferences and technology, poor ones tend to grow faster than rich ones. This is called “convergence” in the levels of per capita income across countries6.
Among the different models tested, the fitted regression equation of the best one is the following:
6 Barro and Sala i Martin (1990) show that the tendency for poor countries to grow faster than
rich countries, termed -convergence, need not imply a reduction in the dispersion of income levels, termed -convergence, if each country's level of income is continually subject to random disturbances. The present study deals only with -convergence.
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γy6085=0.0302-0.0075GDP60+0.0305SEC60+0.0250PRIM60 -0.119 gc/y-0.0195REV-0.0333ASSASS-0.0143PPI60DEV
From the regression above, the following results can be inferred.
Since GDP60 is measured in thousands of 1980 dollars, regression output suggests that an increase in per capita real GDP by one thousand dollars lowers the real per capita growth rate (GR6085) by 0.75 percentage points per year. This is an evidence of “convergence”: countries with initial lower GDP grow faster than those with higher initial GDP. The main element behind the convergence result in neoclassical growth models is diminishing returns to reproducible capital. Poor countries, which are characterized by low ratios of capital to labour, have high marginal products of capital and therefore tend to grow faster. This tendency for low-income countries to grow at high rates is reinforced in extensions of the neoclassical models that allow for international mobility of capital and technology.
The growth of per capita GDP is positively related to the initial level of human capital. The empirical analysis in Barro’s paper uses school-enrolment rates as proxies for human capital. For a given starting value of per capita GDP, a country’s subsequent growth rate is positively related to these measures of initial human capital. In particular, a one-percentage point increase in primary-school or secondary-school enrolment rates, will lead to an increase in GDP per capita growth respectively, by 3.05 and 2.05% per year. Growth is shown to be negatively related to the variables measuring political instability (REV and ASS). These relations could involve the adverse effects of political instability on property rights and the linkage between property rights and private investment. Political instability and little political cohesion (weak executive constraints) generally mean that the incentives to invest in fiscal capacity are very weak, so as a consequence compliance and hence tax revenues are threatened under these conditions. According to the analysis made in Chapter I, countries that have operated on more cohesive institutions in the past are expected to have higher stock of fiscal capacity today. Barro’s regression output confirms this: the higher is political instability, the lower will be growth. Besley and Persson (2011) show that this is indeed the case when fiscal capacity is measured in different ways and cohesive political institutions are measured by executive constraints, as they found evidence that more stability is correlated with higher fiscal capacity and therefore higher growth.
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Also price distortions affect growth. The regressions equation indicates a significantly negative relation between growth and the magnitude of the 1960 purchasing power parity deviation from the sample mean (denoted PPI60DEV). The estimated coefficient is -0.014, with a standard error equal to 0.0053. This result implies that a one-standard error (0.25) increase in the magnitude of PPPIGO is associated with a reduction in the per capita growth rate by 0.4 percentage point.
Growth is also shown to be inversely related to the average ratio of the share of government consumption to GDP. It has to be stressed that Barro did not use in his regression tax rates, but only government consumption spending, which is an indirect way of measuring the impact of tax rates on growth. The negative coefficient on the government expenditure variable has several interpretations. It is important to observe that it is consumption expenditure by government, so the negative coefficient does not conflict with modelling of productive government expenditure leading to growth. The negative value seems to demonstrate that government spending is somehow purely wasteful, something that will be deeply investigated in the following pages and Chapters.
In his research, Barro obviously ran different regression models, the most significant one has been analysed, while the other significant ones are reported below:
Figure 20: Barro’s baseyear regression models (Source: Barro, 1991)
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As is visible from Figure 20, some other variables proved to be significant to Barro, so they will be tested below, in order to understand whether there is a real causal relationship between them and growth rate.
In the pages that will follow, Barro’s analysis will be replicated using time series data from the World Banks’s World Government Indicators database using the same technique that Barro used, that is, base years. In the first part of the analysis Barro’s baseyear regressions will be replicated using another data source from the original one, in order to understand if results keep on being consistent even if the data sample is extended from the geographical and temporal point of view. As anticipated, in this section the Barro regression models will be presented, after an analysis performed with the R Software. In particular, 264 countries have been analysed over the years 1980-2018 versus 89 ones over the years 1960-85 studied by Barro.
In detail, the variables used are:
• RealGDP_80 (1980 Real GDP): GDP at purchaser’s prices is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources. Data are in current U.S. dollars. Dollar figures for GDP are converted from domestic currencies using 1980 official exchange rates7.
• GDPpc_80 (1980 GDP per capita): GDP per capita is gross domestic product divided by midyear population. GDP is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources. Data are in current U.S. dollars7.
• GDPpcsq_80 (1980 GDP per capita squared): it is the square of GDPpc_80; • GDPpcgr_8018 (per capita GDP growth rate 1980-2018): it is the growth rate in
GDP per capita from 1980 to 2018;
• Prim_80 (1980 primary-school net enrolment rate): Net enrolment rate is the ratio of children of official school age who are enrolled in school to the population of
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the corresponding official school age. Primary education provides children with basic reading, writing, and mathematics skills along with an elementary understanding of such subjects as history, geography, natural science, social science, art, and music8.
• Sec80 (1980 secondary-school enrolment rate): Secondary education completes the provision of basic education that began at the primary level, and aims at laying the foundations for lifelong learning and human development, by offering more subject- or skill-oriented instruction using more specialized teachers8.
• AvgInv_8018 (1980 net investment in government nonfinancial assets): it includes investments in fixed assets, inventories, valuables, and non-produced assets. Nonfinancial assets are stores of value and provide benefits either through their use in the production of goods and services or in the form of property income and holding gains. Net investment in nonfinancial assets also includes consumption of fixed capital9.
• FertilityBase_80 (1980 total fertility rate): it represents the number of children that would be born to a woman if she were to live to the end of her childbearing years and bear children in accordance with age-specific fertility rates of the specified year10.
• AvgFert_8018 (average fertility rate from 1980 to 2018): average of fertility as described above from 1980 to 2018 values;
• MortBase_80 (1980 mortality rate): Under-five mortality rate is the probability per 1.000 that a new-born baby will die before reaching age five, if subject to age-specific mortality rates of the specified year11.
• AvgMort_8018 (average mortality rate from 1980 to 2018): average of mortality as described above from 1980 to 2018 values;
• AvgVio_80 (Internally displaced persons, new displacement associated with conflict and violence in 1980): Internally displaced persons are defined according to the 1998 Guiding Principles as people or groups of people who have been
8 UNESCO Institute for Statistics (http://uis.unesco.org/)
9 International Monetary Fund, Government Finance Statistics Yearbook and data files.
10 (1) United Nations Population Division. World Population Prospects: 2019 Revision. (2) Census reports
and other statistical publications from national statistical offices, (3) Eurostat: Demographic Statistics, (4) United Nations Statistical Division. Population and Vital Statistics Reprot (various years), (5) U.S. Census Bureau: International Database, and (6) Secretariat of the Pacific Community: Statistics and Demography Programme.
11 Estimates Developed by the UN Inter-agency Group for Child Mortality Estimation (UNICEF, WHO,
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forced or obliged to flee or to leave their homes or places of habitual residence, in particular as a result of armed conflict, or to avoid the effects of armed conflict, situations of generalized violence, violations of human rights, or natural or human-made disasters and who have not crossed an international border. The variable represents the number of new cases or incidents of displacement recorded over the specified year, rather than the number of people displaced. This is done because people may have been displaced more than once12.
• LIT_80 (1980 adult literacy rate): it is the percentage of people ages 15 and above who can both read and write with understanding a short simple statement about their everyday life8.
• STTEAPR_80 (1980 primary school pupil-teacher ratio): it is the average number of pupils per teacher in primary school in 19808.
• STTEASEC_80 (1980 secondary school pupil-teacher ratio): it is the average number of pupils per teacher in secondary school in 19808.
• RealPopbase_80 (1980 total population): it is based on the de facto definition of population, which counts all residents regardless of legal status or citizenship. The values shown are midyear estimates10.
• GeomavgPop_8018: geometric average of Realpopbase_80 as above from 1980 to 2018.
Before running regressions, some descriptive statistics has been performed with the help of R Software. First of all, attention must be put to the five-number summary, which is a set of descriptive statistics that provides information about measures of positions of the variables studied. It consists in the five most important sample percentiles: the sample minimum (smallest observation), the lower quartile or first quartile, the median (the middle value), the upper quartile or third quartile and the sample maximum (largest observation). By subtracting the first quartile from the third quartile we obtain the interquartile range, which helps to describe the spread of the data, and determine whether or not any data points are outliers (values outside the upper and lower limits of the datasets Q1–1.5 x IQR; Q3+1.5 x IQR). All these figures (together with the means) are presented in Figure A3 in the Appendix and in the R code file and can be used to draw graphical representations of the variables based on quartiles, that is, the boxplots (see the
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Appendix). Comparing the five-number summary of the dataset used to that of Barro’s one13 (in Figure A2 in the Appendix), it is visible that the mean of GDP growth rate from 1980 to 2018 (GDPgr_8018) is much higher than the mean from 1960 to 1985 (GR6085), and this is for sure correct, as GDP per capita has followed an increasing path since after-wars years. Variables representing educational attainment have been generally stable around the mean, however presenting a slightly higher standard deviation (due to higher differentiation of the dataset at the world level). Also fertility and mortality remain more or less in the average. Literacy rate, on the other hand, has increased, as expected.
From boxplots can been identified outliers, that is, data points that are located outside the fences (or “whiskers”) of the boxplot (outside 1.5 times the interquartile range above the upper quartile and below the lower quartile, as has been said before). Looking at the particular variables, it can be seen that in some countries there are very high or low values with respect to the other ones, and this is the reason why these outliers appear in the boxplot.
The variables which present more outliers are those related to GDP (RealGDP_80, GDPpc_80, GDPpcgr_8018, GDPpcsq_80) and population (Realpopbase_80, GeomavgPop_8018). This is due to the fact that world-wide data are analysed using a single plot. Obviously, there are countries that are extremely highly populated and ones that present a really high GDP with respect to others, if the overall worldwide picture is considered. For example, if we look at the boxplot of RealGDP_80 and GDPpc_80, it is visible this variable exhibited extraordinary high numbers in extremely populated countries (Japan and East Asia countries) and very low numbers in small countries or island (Kiribati, Maldives, Guinea, Tonga, etc.). The opposite can be said for growth rates (eg. GDPpcgr), where the higher percentages are present in highly-developing countries (China, Maldives, Korea), and lower in ones who were characterised more turbulent economies (Syrian Arab Republic, Niger, Congo, Burundi, Gabon). All these results are perfectly correct and expected, because it is true that this high numbers are due to some particular features of the counties, that are visible only with a simple and basic analysis of the datasets.
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Indeed, three whiskers are present, for example, in the lower part of the boxplot of PRIM_80 as far as a really low enrolment rate characterised primary-school enrolment rates in Burkina Faso, that is, 14.31% (lowest overall score, hence identifying a country with the smaller development of human capital), Somalia (14.45%) and Burundi (18.70%). It is interesting also to see that both STTEAPRI_80 and STTESEC_80 present outliers in the upper part of the plot, where these whiskers represent extremely high number of students per teacher in both primary and secondary school in countries such as Togo (respectively, 54.29 and 39.76), Korea (48.09 and 38.14), Nepal, Myanmar, Nicaragua and Nigeria, which are extremely populated counties.
The same is true for VIO_80, as some countries exhibited some extremely high values of violence. The increase in the number of internally displaced persons associated with conflict and violence is even above 6% in Iraq, with Congo, Pakistan, Ethiopia, Sudan and Nigeria being in the top-rates.
These figures are further reinforced by the calculation of the variances and standard deviations (in the R code), that are much higher for the variables that present outliers and hence higher dispersion.
The next step is to look if the variables have a relationship among each other, and in particular, if they are associated with growth (GDPpcgr_8018). To see this, a correlation matrix has been created in order to shows how strong correlation is among each pair of variables.
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Figure 21: Correlation matrix (Barro base-year 1980-2018)
Some patterns are more evident than others in the figure above. However, in order to clearly understand and identify the relationships among these variables, the covariances and correlations matrices and the scatter plots must be observed carefully (See Figures A16-A17-A18 in the Appendix).
As it is known, when the correlation coefficient is zero there is no correlation between two variables, when it lies below ± 0.29 they are little correlated, if it lies between ± 0.30 and ± 0.59 they are moderately correlated, starting from ±0.70 they are highly correlated and perfectly correlated if it is ± 1. Looking at the correlation matrices, but also at the scatterplots, it can be said that GDP per capita growth is positively correlated with PRIM_80, SEC_80, INV_80 and LIT_80, while it is negatively correlated with AvgFert_8018, AvgMort_8018, Fertbase_80, Mortbase_80 and VIO_80. As far as correlations with this are concerned, no extremely significant patterns are present.
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(To complete the descriptive statistics analysis of the variables, the plots of empirical cumulative distribution functions and histograms of every variable with superimposed a normal curve are available in Appendix)
To test Barro’s regression using as base year 1980, different econometric models have been created to test the significance of the different independent variables in each one, and then the best one that describes that relationship has been identified and further analysed. Analysis has started from models with only the regressors that revealed to be majorly correlated with GDP per capita growth and therefore considered the most important factors that can impact growth, according to Barro. Then regressors have been added one at a time, in order to understand whether they were statistically significant and therefore caused better fit.
The models which revealed to be the most appropriate and precise are the following ones:
Figure 22: Best regression models (Barro base-year 1980-2018)
By looking at the models, it is visible that the latter have the highest explanatory power, since they are characterised by the highest R2 index. All the independent variables in the last two models are statistically significant because the significance levels of each variable are higher than their p-values. The one presented as third regression in Figure 22
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seems to be the best regression on GDPpcgr_80 as far it is characterized by the highest number of extremely significant variables. However, an important feature has to be stressed. If you look at the value of the constants, it is visible that in model (3) it does not appear to be statistically significant. This means that if all independent variable are equal to 0, then also the dependent variable will be equal to 0. However, that does not mean that the constant should be taken out because it is a “garbage” term and it forces the residuals to have a zero mean.
On the other hand, in model (4) when all the independent variables are 0, the estimated growth rate is 43.469 (but also in the case it is meaningless to hypothesize that a country with zero literacy rate and zero enrolment rate, etc). In model (3) the control variables explain 76.6% of the changes in growth rate, while in model (4) they explain 67.0% of the changes. However, attention must be paid when interpreting this value. Correlation does not imply causation, and most of all, whenever a variable is added to a model and the value of its estimated coefficient is different from zero (otherwise the proportion of explained variance stays unchanged), the quality of the fit improves and hence R2 tends to increase. This is to say that R2 is not a good indicator of goodness of fit in this case. Also in this model the F-statistic has a really low p-value, so H0: β1= β2= β3=0 can be rejected, in favour of the alternative H1: “H0 does not hold”, so we can state that the model is jointly statistically significant.
But here we come to interesting part of the research. As it has been stated before, the R2 is not a good pattern for determining which is the best model of the two, as far as model (4) has a higher R2 but model (3) has the higher number of statistically significant variable. This is the problem: with R2 significance is not taken into account, but only accounts of joint explanatory value, so how is it possible to choose among different models?
Since all the predictors that are control for in the fourth model presented are present also in the third one, it can be asserted that the variables in the latter regression are nested in the former. This allows to test if all the parameters associated to the predictor not included in model (4) is equal to 0 versus the alternative that it is different from 0 performing a comparative Anova test. So, looking at the Variance Table, some extremely significant results can be analysed:
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Figure 23: Variance analysis model (3) Figure 24: Variance analysis model (4)
From econometric theory, it is known that the lower the residual sum of squares (SSR), the higher the proportion of the variability in y (total sum of squares or SST) explained by the model (explained sum of squares or SSE), hence, the greater the explanatory power of systemic part of the regression. By comparing the third and the fourth model presented, where not all the variables were included, it is visible that both ones are characterised by the same SSR (480.059). Actually, looking at the percentiles, you see that model (3) has a higher percentage of residuals in the lowest fence with respect to model (4), meaning that even if the sum of errors is the same, single errors are smaller. However, this still does not enable to evaluate with certainty which model has the highest explanatory power.
Therefore, it has to be performed the Akaike’s Information Criterion (AIC) test. This test is really useful as it considers both the fit of the model and the numbers of parameters, where more parameters result in a “penalty”. The model fit is measured as likelihood of the parameters being correct for the population based on the observed sample. The number of parameters is derived from the degrees of freedom that are left. Put simply, AIC roughly equals the number of parameters minus the likelihood of the overall model, therefore the lower the AIC value, the better the model. The AIC for the model which contains all the variables (model 3) is smaller than that of the model with less variables (97.94578 versus 103.4171), hence that does not support dropping the variable STTEAPR_8018. In order to be sure that this could be the right model it is possible to drop each single remaining covariate and see what happens.
