THE ACQUISITION OF HUMAN CAPITAL AND ECONOMIC GROWTH: AN INTERNATIONAL SURVEY

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THE ACQUISITION OF HUMAN CAPITAL AND ECONOMIC GROWTH:

AN INTERNATIONAL SURVEY Christopher E.S. WARBURTON, Ph.D.*

Abstract

This paper analyzes the evolution and challenges of acquiring human capital in the US.

It revisits the omitted variable bias in formal and informal pedagogical evaluations and underscores the importance of public investment in human capital. The paper subsequently evaluates the importance of human capital by alluding to exogenous and endogenous growth models. Using time series data from 1990 to 2017 to evaluate the contributions of human capital to macroeconomic growth, empirical findings suggest that exogenous growth theory, more than endogenous growth theory, can still be applied to some countries of the world, where the residual-to-investment ratio is exceedingly high.

Keywords: Endogenous growth, Human capital, Total factor productivity, JEL Classification: I23, I25, I26, N10, O40

1. Introduction

This paper analyzes the evolution and challenges of acquiring human capital in the US.

It revisits the omitted variable bias in formal and informal pedagogical evaluations and underscores the importance of public investment in human capital. The paper subsequently evaluates the importance of human capital by alluding to exogenous and endogenous growth models. Using time series data from 1990 to 2017 to evaluate the contributions of human capital to macroeconomic growth, empirical findings suggest that exogenous growth theory, more than endogenous growth theory, can still be applied to some countries of the world, where the residual-to-investment ratio is exceedingly high.

Human capital has generated interest since the eighteenth century, though the concept attracted widespread interest after Solow’s growth model in the 1950s. The historical significance and scope of the concept have been influentially chronicled by Goldin (2014:1), who traces the use of the expression to Adam Smith’s fourth definition of the concept:

“The acquisition of … talents during … education, study, or apprenticeship, costs a real expense, which is capital in [a] person. Those talents [are] part of his fortune [and] likewise that of society” (Smith, 1776). Goldin further suggests that the expression was probably formalized by Irving Fisher in 1897, after which it became a serious part of economic discussion in the 1950s; especially after Mincer’s (1958)

“Investment in Human Capital and Personal Income Distribution.” A contemporaneous definition of human capital is rather broad, but it reflects the acquisition of skills that are productively employed to generate output. Implicitly, there is an investment dimension to the acquisition of human capital since all humans do not have natural abilities to utilize productive skills.

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*Graduate School of Business Administration, Berkeley College, United States.

Email: [email protected]

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Consider Goldin’s characterization of the expression:

“Human capital is the stock of productive skills, talents, health and expertise of the labor force, just as physical capital is the stock of plant, equipment, machines, and tools. Within each type of capital the performance, vintage and efficiency can vary.

The stocks of human and physical capital are produced through a set of investment decisions, where the investment is costly in terms of direct costs and, for human capital investment, in terms of the opportunity cost of the individual’s time” (Goldin: 22).

At the micro and macro levels, the concept of human capital generically implies that investment in people can enhance their productivity and economic growth. That is, investment must be made in education, training, and health for humans to be productive. Today, learning by doing and formal education are two of the cognizable channels that can facilitate the acquisition of human capital. Therefore, nations that want to grow cannot possibly disregard the importance of human capital, which naturally requires investment for greater returns.

Hence, Goldin finds that:

“In almost all places and during most historical periods, education has been publicly provided and publicly funded. There have been times when the private sector has been larger but the public sector has almost always increased in relative importance compared with the private sector. The reasons for the increasing government involvement in education are many.

The state has various interests in education that increase demand for schools and, in turn, lead the state to subsidize education. A main interest of the state is that education provides public goods of various types including endowing citizens with a set of common values. The state also has interests in correcting market failures concerning schooling” (Goldin: 13).

Apart from the economic reasons that have been pervasively advanced for the acquisition of human capital, including the inability of markets to provide public goods, democratic systems require literate and educated citizens to ensure the sustenance and viability of the democratic system of government (Alexis de Tocqueville, 1835, Sokoloff and Engerman, 2000).

This paper has been developed to: (i) analyze the importance of human capital, (ii) evaluate the challenges confronting contemporary academic institutions (channels for generating human capital), (iii) emphasize the need for public investments in education, and (iv) present a theory that measures growth residuals as a percentage of public investment in human capital; the latter does not consider growth residual (error) to be total factor productivity (TFP). The challenges confronting academic institutions have financial, racial, gender, and ethical connotations, which are extensively discussed in “Pedagogical ethics and economic development”; a complement of this paper. To put this paper in wholesome perspective, I also examine the rise and fall of the value of American public education in the context of the acquisition of human capital, the imprecise measurements of pedagogical assessments for the acquisition of

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human capital, and some of the unethical elitist frictions that impugn the ability to acquire human capital (Warburton, 2020).

The next section (Section II) examines the importance of human capital in the context of empirical models that have been developed over the years to validate the relevance of human capital to economic growth and development. Notably, the acquisition process is impugned when the preconditions for acquisition are tenuous and corrupt by ethical lapses. The auxiliary paper, which should be approached in the context of prevailing development literature, more fully conveys the message that pedagogical rectitude is essential to achieve valuable human capital. Discussions of exogenous and endogenous growth models in Section II are followed by international estimates of the contribution of human capital to economic growth. As a foundation for empirical evaluation of growth residuals, the relevance and functionality of growth- enhancing variables are discussed in Section III. A conclusion is provided at the end of the paper, with particular emphasis on the practical implications of the growth residuals for various countries and regions of the world.

2. Human capital and economic growth: Why is human capital important?

Countries that cannot channel large amounts of human capital into productive uses will not be able to account for sustainable economic growth. Human capital enhances gross fixed capital formation and ability to produce manufacturing goods in the real sector.

Invariably, human capital also enhances productivity in the service sector, which can be considered to be part of the growth residual, occasioned by human capital.

Traditional growth models have not successfully accounted for the latter (service sector). In the next section, I examine the exogenous and potentially endogenous contribution of human capital to economic growth for a variety of countries.

Prototypical discussions of the concept of human capital were intertwined with economic growth or output. Today, such discussions include development. Though the relevance of human capital to economic growth has a long history, economic models of human capital appeared lately. Following Smith, proponents of economic growth avoided mathematical specifications until the second half of the twentieth century (Gylfason: 24). In the 1940s, and starting with Samuelson’s Foundations of Economic Analysis (1948), economists started to expand their inclusion of mathematical specifications in economic analyses.

Early theories of economic growth did very little justice to human capital. A prototypical foundation of growth theories was provided by Charles Cobb and Paul Douglas (1928). The function barely considered physical capital (K) and labor (L) and the contributions of the input to output (Y):

Y = f (K,L) (1) Y =K L^ ⁽¹⁻^⁾; (2) where α is a parameter with a value that is greater than 0 but less than 1. The parametric measurement ensures that the aggregate contribution of physical capital and labor cannot be greater than 100%. The derivatives of Equation 2 define the rental

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and wage values or the contributions of the inputs to output, denoted by Equations 3 and 4:

Y ^{1 (1} ⁾ K L K

 

 ⁻ ⁻

 =

 , and (3)

Y (1 ) ⁽ ⁾

K L

L

  ⁻

 = −

 , (4) The Solow growth accounting presupposes that labor and physical capital can account for growth in output (Equation 5).

Y K (1 ) L

Y



K



L

 =  + −  . (5)

But what happens when the left hand side of Equation 5 is greater than the right hand side? There must be some omitted variables, which are not necessarily noisy residuals.

The omitted variables were considered to be a residual, which Robert Solow estimated in 1957.

Subsequent models built on the Cobb-Douglas model in the 1930s and 40s, starting with that of Roy Harrod (1939) and Evsey Domar (1946), or the Harrod-Domar (HD) model. The subsequent models did not endogenize human capital or technology. Three concepts defined the theory of Harrod and Domar: (i) the saving rate of households, which is dependent on intertemporal decisions about consumption, (ii) the capital output ratio, which reflects the demand for capital (K) that is related to prospective output, and (iii) the depreciation rate, broadly defined to reflect the quality of investment decisions in the past. The acquisition of knowledge or the capacity of knowledge to enhance production was explicitly excluded. Therefore, saving was incorporated into the idea of earlier production functions that equate output (Y) to capital and labor (L) (Equation 1).

In reality, with less regard for labor, the HD model focused attention on physical capital accumulation as output grows.

1

* K K;

Y K v

v v Y

=    → = = (6)

where v is a constant that is indicative of the prospective growth of output as capital stock changes (see also Perkins, Radelet, Lindauer, and Block: 97). Equation 6 can be used to show the impact on output when capital changes (Δ) incrementally:

K. K.

Y v

v Y

 

 = → =

 (7) The capital intensity denoted by Equation 7 is usually contingent on variable applications of science to production (technology), or the compositions of goods that are produced across nations. Therefore, the incremental representation of Equation 7

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connotes a different meaning from the average representation of Equation 6. However, the average is presumed to be equal to the incremental because v is presumed to be constant. So, what causes the change in capital stock? Saving and depreciation; a fraction of income is saved just as a fraction of capital depreciates:

 =K sY dK− . (8) Re-writing Equation 7 in terms of growth rate and combining Equations 7 and 8 gives:

Y K Y sY s ;

d g d

Y Yv Y Yv v

 =  →  = − → = − where d=ΔK/K. (9)

While the connection between human capital and saving is not readily apparent in the model, higher earning capacity through the education channel is more likely to increase saving capacity; and therefore economic growth. But as Perkins et al noted:

‘Underlying Equation 9 is the view that capital created by investment is the main determinant of economic growth and that saving makes investment possible.’ (Perkins et al: 98).¹

The earlier models were generally considered to be exogenous because they excluded technological change or education. However, the Cobb-Douglas production function is flexible enough to accommodate human capital (education) and technological change.

Consider a re-specification of Equation 2 to include technological change A:

Y = AL K^ ⁽¹⁻^⁾; (10) By endogenizing technological progress, the contributions of education can be estimated when technology is considered to be a function of human capital per person:² A = C^α. (11) Equation 10 becomes Y =cL K^ ⁽¹⁻^⁾;where cL is considered to be the stock of human capital (the human capital per person times the number of persons (Gylfason:

138). The growth in human capital (Δc/c) is contingent on the useful hours that are used to produce goods and services (h), and the amount that is invested in education for subsequent growth in human capital (1-h). In effect, growth (g) is a function of population growth and productive time that is devoted to acquiring an education (1- h=q); where q is for labor productivity. Therefore, Equation 9 endogenizes education and productivity as explanation of the Solow residual. Consider Mankiw’s representation:

Y K (1 ) L A;

Y



K



L A

   

= + − + (12)

1 .

( )

v s

g d

 =

+

2 Output and input per person can be defined by dividing through by labor (L) and rewriting Equation 10 in lower case letters. Y CL K⁽¹ ⁾ K

y y k

L L L

  

−   

= = =  → =

 

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where growth in output = contribution of capital + contribution of labor + growth in total factor productivity ( Mankiw: 268).

The Solow rendition and its offspring became known as the neoclassical breed of models; because of the inclusion of population growth, technological change, and to some extent, the concept of diminishing returns to factor input. The older model of Harrod and Domar was considered to be overidentified, largely because a single growth model with technology was sufficient to explain economic growth rather than two equations; one model explaining the role of saving (s), efficiency (E), and depreciation (δ), (Equation 13), and another explaining the role of population growth (n) and technological progress (q), (Equation 14):

g = sE -



, and (13) q = g- n; (14) where Equation 13 is a representation of economic growth per capita (see Gylfason:137).

In 1992, with the inclusion of human capital, the relative performance of the flexible neoclassical model was evaluated by Mankiw et al. (Equation 15):

Y K AH= ^( )⁽¹⁻^⁾; (15) where Y is for output, K is for physical capital, H is for skilled labor, and A is for labor- augmenting technology that grows exogenously at rate g (see also Jones: 48). It is reasonably assumed that individuals accumulate capital by learning new skills instead of working. Therefore, H can be defined as the amount of time that is spent to acquire new skills (u) and the total amount of raw labor (L) that is available for productive use in an economy:

H e L =

^^u

;

(16) where ψ is a positive constant. Incremental increases in u increase H by ψ*100 (in percentage form).³ It is noteworthy that when u is zero, all labor is unskilled. That is, H=L. Unlike the model of Mankiw et al. in which physical and human capital are presumed to grow in tandem, Jones assumes that individuals spend time to acquire human capital. By using the base e, it is assumed that an additional year of schooling increases wages by about 10 percent. Further, it is assumed that physical capital is accumulated by investing a portion of output that is not consumed:

K =s Y dK_K − ; (17) where SK is the investment rate for physical capital and d is for the constant rate of depreciation.

3For log d H .

du =

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So, how did some countries manage to become richer while others became poorer?

The extended Solow model provides an explanation in terms of a steady-state value of output-technology ratio (Equation 20):

( )

/ 1

*( ) s^K ( );

y t hA t

n g d

 −

 

=  + +  (20) The empirical evidence suggests that countries became richer because they had high investment rates in physical capital, spent a lot of time accumulating skills (h= e^ψu ), maintained low population growth rates, and acquired high levels of technology, which propelled per capita output growth (Jones:50). Invariably, acquiring human capital and technology cannot be delinked from stable preconditions (propitious and frictionless environments with the appropriate didactic skills). There are various ways in which the technology of a nation can be improved: international trade, scholarly productivity in scientific journals, domestic education, and immigration of foreign born talent.

Smarter countries gladly absorb foreign talents without liquidating them, and poorer countries will do well to retain human capital and avoid the brain-drain syndrome. The next section examines the relevance and functionality of some growth-enhancing variables.

3. Variables and empirical findings of growth residual-to-investment ratio

In this section, I evaluate the importance of human capital and its contribution to economic growth in rich and relatively poorer countries. Human capital interacts with labor and capital, and to some extent, the improvement of the quality of land. In general, land—a gift of nature—is theoretically considered to be fixed (see Appendix A16). However, land can be reclaimed and its quality can be improved for better economic results or economic growth. Traditional models generally disregard the value of land, which also include marine resources and the interactive capacity of land with human capital. In this paper, variables have been selected to reflect indispensable interaction of the factors of production. The inability to clearly separate the interactive effects gives the growth residual, usually referred to as TFP, very important probative value. The probative value can be contrasted to the individual contributions of the factors of production in regression models.

In this inquiry, gross fixed capital formation, “formerly gross domestic fixed investment, is used to show the interaction of human capital, physical capital and land improvement.” Therefore, the variable includes “land improvements (fences, ditches, drains, and so on); plant, machinery, and equipment purchases; and the construction of roads, railways, and the like, including schools, offices, hospitals, private residential dwellings, and commercial and industrial buildings. According to the 1993 System of National Accounts (SNA), net acquisitions of valuables are also considered capital formation.” The data are in current U.S. dollars and made available by the World Bank and the OECD (see the World Bank’s World Development Indicators (WDI) for 2019).

The stock of capital and land improvement by capital (K) (physical, human, and financial) is instrumental in computing the contribution of human capital [man-made

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facilitators of production] to economic growth or output (K/Y= rK). The growth of the capital stock is captured by gK.

GDP per capita is gross domestic product divided by midyear population. This variable controls for disparities in national wealth and facilitates comparative analysis.

GDP is defined as ‘the sum of gross value added by all resident producers in the economy plus any product taxes, less 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.’ The data are in constant 2010 U.S. dollars and they have been provided by the World Bank (WDI). The notation for the growth of GDP per capita is gy.

The labor force (stock) comprises people in the age category of 15 and older who supply labor for the production of goods and services during a specified period. “It includes people who are currently employed and people who are unemployed but seeking work as well as first-time job-seekers. Not everyone who works is included, however. Unpaid workers, family workers, and students are often omitted, and some countries do not count members of the armed forces. Labor force size tends to vary during the year as seasonal workers enter and leave” (WDI). Using the unemployment rate (the percent of total labor force, national estimate) of the sampled countries—and since everyone in the labor force cannot be productive or gainfully employed—I adjust the labor force to compute the effective labor force (LE); Therefore, the effective labor force defines the contribution of labor to output (LE/Y= wL). The World Bank defines unemployment as “the share of the labor force that is without work but available for and seeking employment.” However, definitions of labor force and unemployment differ by country (WDI). Consequently, the general theoretical specification of the growth residual, which can be found in Perkins et al, (68) can be considered for estimation:

gy- a =(rK*gK) + (wL*gL) (21) where:

gy = GDP growth rate,

gK = growth rate of capital stock, gL= growth rate of the labor force, wL= the share of labor in national income, rK = the share of capital in national income, and

a = omitted variable bias [residual, error, or TFP], a measurement puzzle; the TFP can be estimated with no precise theoretical meaning, except that it is an error in estimation. Rather than truly being TFP growth, a is simply the part of measured growth that cannot be explained by data on the traditional factors of production (Perkins et al: 70).

Public investment in education (IG) is defined as general government expenditure on education (current, capital, and transfers) as a percentage of GDP. It includes expenditure funded by transfers from international sources to government. “General government” usually refers to local, regional and central governments (WDI).

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In traditional regression models, where factor inputs are considered to be binary and made efficient by human capital, the contributions of capital and labor to economic growth must be exhausted. For econometric and theoretical reasons, the quality of land or the use of capital to improve land is not generally considered. Binary allocations of factor returns will not hold when other factors of production are endogenized or considered within unconventional growth models. Therefore, the growth residual must capture omitted variable biases with very high probative value.

The interactive effects of human capital have been well documented for several countries in America, Europe, Eurasia, Africa and Asia –Pacific between 1967 and 2006. Empirical studies show interactions between: (i) education and the production function, (ii) education and investment per inhabitant, (iii) education, fertility and economic development, (iv) education and social capital, (v) human capital, industry and foreign trade, and (vi) human capital and regional development (Guisan and Neira, 2008).

Nine-year averages of time series data are used to estimate a basic growth model of factor inputs. The lower frequency of the data minimizes the occurrences of abnormal changes in the variables of interest and presents a more appealing evidence for the recurrence of observations that impinge on the performance of the variables. It is assumed that the periodization will capture time dynamism and a reasonable amount of stability for meaningful analysis. In fact, macroeconomists routinely utilize lower frequency data to minimize abnormal distortions.⁴

The growth residuals, generally considered to be total factor productivity (TFP), are finally estimated as a percentage of public investment in human capital. For a variety of reasons, unlike some other studies, I have hesitated to characterize the growth residuals of the model as TFP: (i) the model is not an estimated regression model and it does not absorb the regularity conditions of the ordinary least squares (OLS) estimating method; (ii) the residuals can be associated with factors that are unrelated to investment in human capital; and (iii) the percentage of error that is unrelated to investment in human capital is generally unknown.

Thus, expressing the residuals as a margin of error or percentage of public investment in human capital gives the growth residual some probative investment value. This measurement is helpful because it also reflects the extent to which public investment in human capital can target the endogenous factors that are usually given prime importance in growth models. That is, not all spending on human capital can directly and robustly affect the highly regarded inputs of economic growth.

The empirical relevance of this paper is therefore centered on the growth-residual- to-public investment ratio (a/IG). The results of the findings are reported in Table 1 and, more extensively or explicitly, in Appendices A3 to A15; the smaller the ratio, the greater the contribution of public investment in education to economic growth. That is, the error is smaller in relation to public investment in human capital after accounting for the major factors that contribute to economic growth ( labor and capital), and the technological know-how to improve on the quality of land.

4 See also Baumohl: 26.

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For all the sampled countries, the contribution of public investment in human capital to economic growth—as measured by the endogenous factors—increased between 1999 and 2017, except for the African countries of Sierra Leone and Ghana.

Denmark and Finland, which invested more in human capital from 1969 to 2017, an average of about 7 and 6 percent of GDP respectively, account for the greatest contribution of human capital to economic growth (close to 100 percent). Between 2009 and 2017, the US accounted for about 74 percent, which is reasonably high but comparatively lower to the contributions of Germany, France, UK, and Brazil.

“Human capital, in the form of schooling embodied in the labor force, increased in the United States from the beginnings of the nation. It greatly changed in content as the demands for skills in the economy shifted. The increase in years of schooling from the nineteenth century was fairly continuous until the past three decades when it slowed down. The increase followed…three transformations and was often a grass roots movement with the cooperation of communities, states and, at times, the federal government. Compulsion had little effect in the United States but had a greater impact in other nations where it often constrained governments to build and maintain schools” (Goldin:17).

While recent theories of economic growth emphasize endogeneity, TFP cannot clearly explain economic growth in the sampled African countries. The factors that contribute to economic growth are largely extraneous to effective labor and capital.

Unlike Ghana and South Africa, public investment in human capital is not very robust in Sierra Leone see Appendix A1). Ironically, the growth residual approximates public investment in human capital, implying that the investment in human capital is not translating into economic growth that is driven by the endogenous factors of labor and capital.

Given the structure and/or disturbances in the African economies, this finding is not entirely surprising.⁵ Indeed, the contributions of manufacturing and technological know-how to economic growth are not as robust as those of advanced economies, implying that that private investment, foreign remittances, and the service and nontradable sectors are making more contributions to economic growth rather than government investment in education. In their study of 33 African countries, Schuaibu and Timothy (2016) find that African governments may sustain human capital development through sustained education and health expenditures.

Additional evidence suggests that public investment in education must be targeted to those endogenous factors that significantly contribute to economic growth.

5 The 1999-2008 residual-investment ratio for Sierra Leone can be considered to be the result of a noisy civil war (1991-2002). Similarly, the Ebola epidemic of 2014 and 2015 and falling global commodity prices contracted economic activity in all areas. However, the positive or negative performance of economic growth can be expected to move in tandem with the sources of economic growth or decay.

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Table 1: Unexplained growth as a percentage of public investment in human capital (1990 to 2017)*

United States 1990-98 1999-2008 2009-17

Residual (“TFP”) 0.02 0.02 0.01

RES/Investment -- 0.39 0.26

Canada

Residual (“TFP”) -- 0.02 0.02

Denmark

Residual (“TFP”) -- 0.01 0.001

Finland

Residual (“TFP”) 0.02 0.03 0.001

RES/Investment 0.34 0.53 0.02

France

Residual (“TFP”) 0.02 0.02 0.01

Germany

Residual (“TFP”) 0.02 0.01 0.01

United Kingdom

Residual (“TFP”) 0.02 0.02 0.01

Australia

Residual (“TFP”) 0.03 0.03 0.02

Ghana

Residual (“TFP”) -- 0.04 0.07

Sierra Leone

Residual (“TFP”) -- 0.01 0.04

South Africa

Residual (“TFP”) 0.01 0.03 0.02

Brazil

Residual (“TFP”) 0.02 0.03 0.01

Mexico

Residual (“TFP”) 0.02 0.02 0.02

* See the Appendix for complete computation estimated to be US$1.53 billion at end-2016. The country’s debt increased from 21.3 percent of GDP at end-2013 to 41.3 percent of GDP at end-2016, mainly due to debt contracted for post-Ebola recovery and infrastructure construction need.⁶

In Ghana, agriculture accounts for about 20% of GDP and employs more than half of the workforce, mainly small landholders. Gold, oil, and cocoa exports, and individual remittances, are major sources of foreign exchange. The expansion of Ghana’s nascent oil industry has increased economic growth, but the fall in oil prices since 2015 has reduced Ghana’s oil revenue by about 50%. African countries are

6 See https://www.imf.org/external/pubs/ft/dsa/pdf/2017/dsacr17154.pdf

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heavily saddled with debts, which constrain the ability of the public sector to invest more robustly in education. Public debt stifles capital formation.⁷ For example, Ghana signed a $920 million extended credit facility with the IMF in April 2015 to help it address its growing economic crisis. Sierra Leone’s debt to multilateral creditors was estimated to be US$1.53 billion at end-2016.

The IMF’s fiscal targets require Ghana to reduce the deficit by cutting subsidies, decreasing the bloated public sector wage bill, strengthening revenue administration, boosting tax revenues, and improving the health of Ghana’s banking sector. Fiscal priorities include rescheduling some of Ghana’s $31 billion debt, stimulating economic growth, reducing inflation, and stabilizing the currency.⁸

In the extremely impoverished Sierra Leone, where natural and man-made disasters have compromised living standards, nearly half of the working-age population engages in subsistence agriculture. The country possesses substantial mineral, agricultural, and fishery resources, but it is still recovering from a civil war that destroyed most institutions before the early 2000s. In recent years, economic growth has been driven by mining - particularly iron ore. The principal exports of the country have been iron ore, diamonds, and rutile; the prices of which are susceptible to volatile international price movements. Until 2014, the Sierra Leonean government heavily depended on external assistance to support its budget. The dependence was made worse by the Ebola outbreak of 2014 and 2015, which coincided with falling global commodities prices. Low commodity prices have contributed to the country’s biggest fiscal shortfall since 2001. The African macroeconomic conditions naturally pose challenges for

“TFP” measurements when investments in human capital cannot be channeled into productive uses of those factors that are considered to be the prime drivers of economic growth in more advanced economies.

Alternatively, advanced economies are well positioned to invest in human capital so that the factors of production that greatly account for economic growth can be more productive, thereby reducing the growth residual-investment ratio. While this theory of growth certainly holds generic appeal and persuasion, it is not currently applicable to all countries of the world as a practical matter. Therefore, the evidence suggests that countries that are well positioned to invest and grow can increase the productivity of their factors of production when investment is well-targeted to those factors that enhance economic growth. Such countries can reasonably account for investment in human capital that has a dominant presence in growth models. Less developed countries can increase their human capital via more international cooperation, given the interactive nature of human capital (Guisan and Neira). Of course, institutional and infrastructural development can provide intermediate gains (Shuaibu and Timothy).

7 In May, 2018, at least six African countries - Chad, Eritrea, Mozambique, Congo Republic, South Sudan and Zimbabwe - were considered to be in debt crisis.

8 See the CIA’s World Factbook et al in https://theodora.com/wfbcurrent/ghana/

ghana_economy.html

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17 4. Conclusion and policy implications

This paper finds that it is critical and very important for the public to investment in human capital. This finding is not unrelated to the preconditions for the acquisition of human capital, which are being discussed elsewhere (Warburton 2019, 2020). Episodes of market failure indicate that a public good cannot be reliably produced by the private sector, and that the enlightenment and system of government of a nation is endangered when its populace is highly uneducated.

The empirical evidence suggests that endogenous growth cannot be applied to all countries of the world; especially to those countries with insufficient investment in human capital; and for which the traditional growth-enhancing factors cannot be adequately accounted for in growth models. Omitted variables are confounding, but they can provide useful probative value when their relationship to public investment in human capital is taken into consideration. Accordingly, countries that have consistently targeted human capital for economic growth can better account for their investment in growth models. The historical data (information) provides incontrovertible evidence that public investment in education is rewarding, and that the conditions that inhibit acquisition of human capital are economically destructive. Inhibiting conditions are multifarious; pedagogical preconditions, institutional policies, financial infrastructure, and public policies.

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Appendix on line a the journal Website: https://www.usc.gal/economet/eaat.htm

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19

Appendix 1.

A1: Average per capita spending on education 1969-2018 (percent of GDP)*

America

1969-78 1979-88 1989-98 1999-2008 2009-2017

United States N/A N/A N/A N/A 5.154408

Canada 7.005984 6.443131 6.49578 5.024719 5.16567 Europe

1969-78 1979-88 1989-98 1999-2008 2009-2017 Denmark 6.227096 5.949812 7.16307 7.968067 8.143398 Finland 5.080557 4.917053 6.407941 5.930953 6.871759 France 3.896531 4.661916 5.204269 5.566696 5.555713

Germany N/A N/A 4.421226 4.343957 4.887826

United

Kingdom 5.683913 4.791428 4.370681 4.644144 5.57998 Australasia

1969-78 1979-88 1989-98 1999-2008 2009-2017 Australia 6.01041 5.385921 5.008234 4.774818 5.19238

India N/A N/A 3.513835 3.722968 3.65732

Japan 4.375638 5.173353 3.974397 N/A 3.603922

Latin America

1969-78 1979-88 1989-98 1999-2008 2009-2017

Brazil N/A N/A 4.66241 4.32354 5.819036

Mexico N/A N/A 2.974511 4.507928 5.107537

Africa

1969-78 1979-88 1989-98 1999-2008 2009-2017

Ghana 4.9082 2.65434 N/A 5.851447 6.154889

Sierra Leone N/A N/A N/A 3.257971 2.955925

South Africa N/A N/A 5.22746 5.497258 5.145418

*Values for available data. Data Source: World Bank’s World Development Indicators (2019)

The US spends more per hour on secondary-level teachers for comparatively lower international scores in science, math, and reading (see Table 1, Warburton 2020);

indicating that there is some amount of inefficiency in the system that coincides with a substantial amount of indigent students trying to get an education. Of course, salaries are also based on ancillary economic conditions, including levels of inflation or cost of living.

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20 A2: Average per capita Income 1969-2018

America

1969-78 1979-88 1989-98 1999-2008 2009-2017 United

States 25,420.8 31,054.6873 38,151.6782 47,089.4347 50,407.48 Canada 27,356.9 33,302.2628 37,078.7401 45,803.3706 49,197.87

Europe

1969-78 1979-88 1989-98 1999-2008 2009-2017 Denmark 22,075 27,404.0626 34,063.8036 39,255.9742 44,267.09 Finland 20,771.6 27,826.2456 32,596.9884 44,019.0904 46,109.54 France 22,641.9 28,156.1986 33,669.7375 39,706.6245 41,414.28 Germany 22,075 27,404.0626 34,063.8036 39,255.9742 44,267.09 United

Kingdom 19,489.9 23,869.4558 30,093.8542 38,213.0286 40,529.97 Australasia

1969-78 1979-88 1989-98 1999-2008 2009-2017 Australia 27,135.3 31,387.9599 37,349.4954 47,315.8918 53,903.74 India 400.884 468.849995 645.893327 980.330534 1,591.495 Japan 21,280.5 29,270.5327 39,689.0157 43,435.5557 45,908.13

Latin America

1969-78 1979-88 1989-98 1999-2008 2009-2017 Brazil 6,154.57 7,895.94584 8,281.00531 9,339.19406 11,324.38 Mexico 6,029 7,659.02413 7,927.8346 9,012.2736 9,422.416

Africa

1969-78 1979-88 1989-98 1999-2008 2009-2017 Ghana 1,016.04 795.794416 873.169333 1,058.11792 1,545.633 Sierra

Leone 480.53 469.115802 353.415419 336.542904 459.447 South

Africa 6,138.44 6,223.91797 5,668.63762 6,399.08669 7,452.922

*Constant US $ 2010

Data Source: World Bank’s World Development Indicators (2019)

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21

Growth Residuals as Percentages of Public Investment in Education

A3: Growth residual, United States (1990 to 2017)

1969-78 1979-88 1989-98

1999-

2008 2009-17

GDP growth 0.0323 0.0309 0.0313 0.0256 0.0163

Gross fixed capital

formation 0.0614 0.0345 0.0432 0.0238 0.0215

Capital/output -- -- 0.1585 0.1345 0.1192

Labor force (% change) -- -- 0.0139 0.0096 0.0050

Effective labor

force/output -- -- 0.0000 0.0000 0.0000

Factor contribution to

output -- -- 0.0068 0.0032 0.0026

Residual (RES) (TFP) -- -- 0.0245 0.0224 0.0138

Investment in education 0.0540 0.0500 0.0500 0.0580 0.0530 RES/Investment in

education -- -- -- 0.3868 0.2600

Notes: GDP growth at market prices; gross fixed capital (GFC) formation annual percentage change; effective labor force is the labor force adjusted for unemployment; investment in education is the percentage of budgeted public spending in education (human capital)

A4: Growth residual, Canada (1990 to 2017)

1969-78 1979-88 1989-98

1999-

2008 2009-17

GDP growth 0.04317 0.03021 0.02083 0.02890 0.01757

Gross fixed capital

formation 0.04682 0.03993 0.01936 0.04986 0.00901

Capital/output -- -- -- 0.11600 0.10210

Labor force (% change) -- -- 0.00813 0.01698 0.00925 Effective labor

force/output -- -- 0.00001 0.00001 0.00001

output -- -- -- 0.00578 0.00092

Residual -- -- -- 0.02312 0.01665

Investment in education -- -- 0.06600 0.05000 0.05200 RES/Investment in

education -- -- -- 0.46237 0.32022

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22 Europe A5: Growth residual, Denmark (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17

GDP growth 0.0275 0.0223 0.0222 0.0177 0.0090

Gross fixed capital formation 0.0362 0.0272 0.0359 0.0281 0.0100 Capital/output 0.1629 0.1549 0.1459 0.1301 0.1179 Labor force (% change) -- -- -0.0010 0.0041 0.0009 Effective labor force/output* -- -- -- 0.0000 0.0000 Factor contribution to output -- -- -- 0.0037 0.0012

Residual -- -- -- 0.0140 0.0078

Investment in education 0.0622 0.0595 0.0720 0.0797 0.0814 RES/Investment in education -- -- -- 0.1761 0.0006 *UR =expected value for 2001 to 2008 (rolling average 1999:2008).

A6: Growth residual, Finland (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17 GDP growth 0.04055 0.03826 0.01928 0.03300 0.00045 Gross fixed capital formation 0.02776 0.05047 0.00993 0.03182 -0.00355 Capital/output 0.22877 0.22300 0.20422 0.22323 0.15380 Labor force (% change) -- -- -0.00481 0.00753 -0.00055 Effective labor force/output* -- -- 0.00001 0.00001 0.00001 Factor contribution to output -- -- 0.00203 0.00710 -0.00055

Residual -- -- 0.01725 0.02590 0.00099

Investment in education 0.05800 0.04920 0.05081 0.04917 0.06408 RES/Investment in education -- -- 0.33950 0.52670 0.01551

*Unemployment rates for 1995 and 2000 are unavailable A7: Growth residual, France (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17 GDP growth 0.04380 0.02280 0.02101 0.02050 0.00834 Gross fixed capital formation 0.02710 0.02067 0.01535 0.03418 0.00323 Capital/output 0.19871 0.17476 0.15235 0.12903 0.10355 Labor force (% change) -- -- 0.00388 0.00921 0.00313 Effective labor force/output* -- -- 0.00001 0.00001 0.00001 Factor contribution to output -- -- 0.00234 0.00441 0.00033

Residual -- -- 0.01867 0.01609 0.00801

Investment in education 0.03897 0.04662 0.05204 0.05567 0.05556 RES/Investment in education -- -- 0.35868 0.28905 0.14413

*LF not adjusted for unemployment in 1990

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23 A8: Growth residual, Germany (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17

GDP growth 0.02942 0.01981 0.02407 0.01585 0.01269

Gross fixed capital

formation 0.01100 0.01337 0.02825 0.01125 0.01386

Capital/output -- -- 0.21548 0.20428 0.20258

force/output* -- -- 0.00001 0.00001 0.00001

output -- -- 0.00609 0.00230 0.00281

Residual -- -- 0.01798 0.01356 0.00988

education -- -- 0.11389 0.12451 0.11105

*LF not adjusted for unemployment (1991:2008)

A9: Growth residual, UK (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17

GDP growth 0.02856 0.02783 0.02118 0.02501 0.01338

Gross fixed capital

formation 0.00920 0.03998 0.02078 0.01724 0.01832

Capital/output -- -- 0.15790 0.10887 0.08896

Labor force (% change) -- -- -0.00120 0.00962 0.00752 Effective labor

force/output* -- -- 0.00002 0.00001 0.00001

output -- -- 0.00328 0.00188 0.00163

Residual -- -- 0.01790 0.02313 0.01175

education -- -- 0.40952 0.49809 0.21059

*Labor force values for 1990 to 2008 are not adjusted for unemployment; Unemployment in 2008 was 5.6%.

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24 Australasia A10: Growth residual, Australia (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17

GDP growth 0.03728 0.03360 0.03176 0.03534 0.02517

Gross fixed capital

formation 0.02778 0.05172 0.04092 0.06234 0.01426

GFC/output -- -- 0.12883 0.10567 0.06885

force/output -- -- 0.00001 0.00001 0.00001

output -- -- 0.00527 0.00659 0.00098

Residual -- -- 0.02648 0.02876 0.02419

education -- -- 0.52883 0.60225 0.46583

Africa

A11: Growth residual, Ghana (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17

GDP growth 0.02298 0.01233 0.04334 0.05320 0.06674

Gross fixed capital

formation 0.00000 0.00000 0.00000 0.11875 -0.00233

GFC/output 0.11466 0.07844 0.09286 0.08833 0.09078

Labor force/output* -- -- 0.00049 0.00041 0.00027

output -- -- -- 0.01050 -0.00021

Residual -- -- -- 0.04270 0.06694

Investment in education 0.04908 0.02654 -- 0.05851 0.06155 RES/Investment in

education -- -- -- 0.72969 1

Labor force is not adjusted for unemployment: 4.7% (1992), 8.2% (1998), 10.1%

(1999), 10.36% (1992), 4.6% (2006), 5.3% (2010), 2.17% (2013), 6.81 % (2015). An adjustment of about 6% rate of unemployment would not have made a difference.

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25

A12: Growth residual, Sierra Leone (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17

GDP growth 0.0309 0.0151 -0.0235 0.0628 0.0500

Gross fixed capital

formation -- -- -0.1971 2.3594 0.2667

GFC/output -- -- -0.0232 0.0233 0.0294

Labor force/output* -- -- 0.0010 0.0011 0.0007

output -- -- 0.0046 0.0551 0.0079

Residual -- -- -0.0281 0.0078 0.0421

Investment in education -- -- -- 0.0326 0.0296

RES/Investment in

education -- -- -- 0.2385** 1

*Labor force is not adjusted for unemployment. However, the labor force-output ratio is also consistent with growth theory. A 6% adjustment for unemployment would not have changed the result. Available data show that the unemployment rate was 3.42%

in 2004, and 4.7% in 2014; the endogenous factors weakly account for economic growth.

**The country had over a decade of civil war; formally, between 1991 and 2002.

A13: Growth residual, South Africa (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17

GDP growth 0.03345 0.02375 0.01386 0.03994 0.01610

Gross fixed capital

formation 0.05500 0.00489 0.02941 0.07544 0.00571

Capital/output 0.20799 0.21108 0.19768 0.16360 0.12215 Labor force (% change) -- -- 0.03289 0.01878 0.01603 Effective labor

force/output -- -- 0.00005 0.00004 0.00004

output -- -- 0.00582 0.01234 0.00070

Residual -- -- 0.00804 0.02759 0.01541

Investment in education 0.05227 0.05497 0.05145 0.05932 RES/Investment in

education 0.14624 0.53629 0.25970

* 1998 value

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26 Latin America

A14: Growth residual, Brazil (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17

GDP growth 0.08771 0.03335 0.02158 0.03453 0.01224

Gross fixed capital

formation 0.10831 0.00487 0.03150 0.03316 -0.00404

GFC/output 0.25749 0.29626 0.18963 0.13740 0.11211

force/output* -- -- 0.00005 0.00005 0.00004

output -- -- 0.00597 0.00456 -0.00045

Residual -- -- 0.01560 0.02997 0.01270

education -- -- 0.33468 0.69321 0.21818

*Unemployment data unavailable for 1990-1; 1994; 2010; and 2012:15

A15: Growth residual, Mexico (1990 to 2017)

1969-78 1979-88 1989-98 1999-2008 2009-17

GDP growth 0.05806 0.02898 0.03641 0.02286 0.02169

Gross fixed capital

formation 0.06677 0.01662 0.06130 0.03800 0.01123

GFC/output 0.21405 0.19277 0.19202 0.17101 0.16154

force/output -- -- 0.00005 0.00004 0.00004

output -- -- 0.01177 0.00650 0.00181

Residual -- -- 0.02464 0.01636 0.01988

education -- -- 0.82834 0.36286 0.38919

Unemployment Rate 1990 unavailable

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27 A16: Land Area (Sq. km)

America

1969-78 1979-88 1989-98 1999-2008 2009-2017 United States 241,930 241,930 241,930 241,930 241,930 Canada 9,093,510 9,093,510 9,093,510 9,093,510 9,093,510

Europe

1969-78 1979-88 1989-98 1999-2008 2009-2017

Denmark 42,370 42,382 42,418 42,430 42,136.67

Finland 304,590 304,590 304,590 304,423 303,898.9

France 547,566 547,566 547,566 547,592.9 547,557

Germany 349,130 349,130 349,101 348,805 348,848.8

United

Kingdom 241,930 241,930 241,930 241,930 241,930

Australasia

1969-78 1979-88 1989-98 1999-2008 2009-2017 Australia 6.01041 5.385921 5.008234 4.774818 5.19238

Africa

1969-78 1979-88 1989-98 1999-2008 2009-2017

Ghana 227,540 227,540 227,540 227,540 227,540

Sierra Leone 72,180 72,180 72,180 72,180 72,80

South Africa 1,213,090 1,213,090 1,213,090 1,213,090 1,213,090 Latin America

1969-78 1979-88 1989-98 1999-2008 2009-2017 Brazil 8,358,140 8,358,140 8,358,140 8,358,140 8,358,140 Mexico 1,943,950 1,943,950 1,943,950 1,943,950 1,943,950

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