rough draft econ 690

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SAN FRANCISCO STATE UNIVERSITY Education’s Returns in International Growth Efficient Human Capital Investment within Development and Public Funding Dion Rosete, ID #911507147 4/29/2015 Econ 690 (02) This paper tests to see if the role of human capital as a neoclassical production input can be represented and applied within the effect of a country’s per student public educational expenditures on economic growth. Additionally, it tests to see if the related principle of diminishing marginal returns holds true for this input when put in terms of economic development; the lower the developmental class of a country, the higher the growth. Looking at national growth trends across the world every half decade from 1985 to 2010, we find that such spending on education is significantly negative across all countries. When further broken down into the four development classes designated by the World Bank, the three lowest classes experience negative growth. Only in the case of High Income countries does it seem to be significantly beneficial, suggesting the issue of inefficient spending.

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Page 1: Rough Draft Econ 690

SAN FRANCISCO STATE UNIVERSITY

Education’s Returns in International Growth

Efficient Human Capital Investment within Development and Public

Funding

Dion Rosete, ID #911507147

4/29/2015

Econ 690 (02)

This paper tests to see if the role of human capital as a neoclassical production input can be represented and applied within the effect of a country’s per student public educational expenditures on economic growth. Additionally, it tests to see if the related principle of diminishing marginal returns holds true for this input when put in terms of economic development; the lower the developmental class of a country, the higher the growth. Looking at national growth trends across the world every half decade from 1985 to 2010, we find that such spending on education is significantly negative across all countries. When further broken down into the four development classes designated by the World Bank, the three lowest classes experience negative growth. Only in the case of High Income countries does it seem to be significantly beneficial, suggesting the issue of inefficient spending.

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1. Introduction

Human capital, the stock of knowledge and skills accompanying laborers, is taken as an

input in the neoclassical model of production. Economic and political analysts then believe the

natural policy prescriptions involve inducing government funding to education, the vital source

of human capital. It is plainly evident that education produces vigorous benefits to the whole of

society, but it is widely questioned as to what extent, how it is best measured, and what

methods/conditions can best catalyze it. Additionally, within this model, the supposed

diminishing marginal returns to inputs suggest an inverse relationship between an economy’s

developmental level and growth rate. This has led to the murky, widely debated concept of

convergence – to put in simplest terms, financially poorer, developing countries will tend to

grow faster than financially richer, developed countries, with some suggestion they will

potentially catch up to the same level. By this logic, it could be that the gains made by human

capital are larger for developing countries than for developed countries. This makes one

question, do the current rates of government educational expenditures per student, the current

quality levels of education by proxy, positively contribute to economic growth? And if so, are

these returns greater for less developed countries?

Given this neoclassical production function, one can predict that government

expenditures per pupil will generally have a positive relationship with growth, as it signifies

better quality education, and therefore better quality human capital as a productive input. The

common policy prescription of more public funding will therefore hold true. Given diminishing

marginal returns, I also predict countries that are less developed will have more to gain through

education; therefore, the interaction between lower development and educational expenditures

will exhibit added “bonuses” towards growth.

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2. Literature Survey

Barro (1999) demonstrates how a country’s political, legal, and economic institutions

determine its individual economic growth rates and investment. The article runs two sets of

regressions, one in which the dependent variable is a country’s growth in real GDP per capita in

five year intervals (1965-1995), and the other in which it is the ratio of real investment (both

public and private) to real GDP, or I/Y. These institutions are measured by log(GDP), log(GDP)

squared, rule-of-law index (measuring secure property rights and strong legal system),

democracy index (measuring electoral rights and civil liberties), democracy index squared,

inflation rate, education (ultimately, enrollment for males at the secondary/tertiary level), and

government consumption (G/Y) ratio; in the regression for growth, I/Y was used as an

independent variable as well. G/Y was found to be significantly negative on both growth and

investment. In reference to the log(GDP) variables, it notes the non-linear patterns of growth

show no evidence of absolute convergence, but that of conditional convergence. This study also

finds that the average years of school attainment at the secondary & higher levels for males ages

25 and above is insignificantly related to the investment ratio, but significantly positive on the

economic growth rate. On the other hand, the same measure for females was only significant

when fertility rate was excluded, as Barro (1999) speculates on the discriminatory practices

preventing “the efficient exploitation of females in the formal labor market.” Years of attainment

of males or females at the primary level was found insignificant for growth; the author also

speculates that only higher levels of education are what grant a country the knowledge to access

new technologies. But then, the study investigates even further by including test scores (from

different years), and this new variable was deemed significant; the male secondary and higher

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education variable remained significant despite its inclusion, suggesting that “the quality and

quantity of schooling both matter.”

Hanushek & Kim (1995) questions common measures of human capital, particularly in

that they are more geared towards quantity, rather than quality. So, alongside quantitative

variables such as primary enrollment rates, the study also proposes and regresses several

qualitative alternatives, such as standardized test scores in math and science, pupil-teacher ratios,

and expenditures. While constructing a production function and controlling for annual population

growth, they found the education of parents (quantity of schooling of the population) and the

many test score variables to be positively significant, while school resources were found to be

either insignificant or significant with the wrong signs. Pupil-teacher ratio was found to be

significantly positive; ratio of recurring education expenditures on GDP was significantly

negative; ratio of total education expenditures was mostly insignificant and always negative.

After “splicing together” scores for different standardized tests into fewer variables, and

controlling for initial GDP and population growth, they find that “both cognitive skills and

schooling quantity positively contribute to explaining variations in per capita growth rates.”

Barro (1992) aims to assess the interplay between human capital and economic growth

across countries within a lengthy discussion of convergence, looking at rate of GDP per capita in

five-year intervals from 1960 to 1985. It’s key independent variable is log(School), looks at the

natural logarithmic form of 1 plus the average number of years of educational attainment for the

population 25 and over, at the start of each interval. While controlling initial GDP, the

government consumption ratio, the period average of the black market premium on foreign

exchange, the interaction between “natural openness” and tariff rates, and the frequency of

revolutions and coups (as a proxy for political stability), log(School) was found to be

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significantly positive. Upon adding the investment ratio and fertility rate variables, the variable

remained significantly positive, but its coefficient was reduced roughly in half, suggesting

human capital’s “channels of effect” on human growth are investment positively, and fertility

negatively. It clarifies, higher human capital means higher wage, and therefore a bigger

opportunity cost to having children.

Keller (2006b) studies the role of education in Asia’s growth since the 1960s. She runs

three sets of regressions for three different measures of education - enrollment rates, public

expenditures, and expenditures per student – each with three separate variables for the primary,

secondary, and tertiary levels. Within each set, each of these three variables are first regressed

individually, then collectively, gradually adding other control variables similar to that of Barro

(1999) - initial GDP, investment ratio, government spending ratio, inflation rate, trade rate,

fertility rate, and public rights index. Within enrollment rates, when regressed individually, all

three education levels are found to be beneficial to economic growth, w/ secondary & higher

education highly significant; regressed together, secondary education was found to be most

crucial, only losing significance when fertility rate was added, while the other two levels

gradually lost significance. The coefficients for public expenditures are the largest; regressed

individually, primary education was only significant; regressed altogether, and with control

variables, secondary and higher education had a significantly negative effect. For public

expenditures per student, once again, fertility rates are added, they all lose significance; tested

individually and collectively, secondary & tertiary spending were insignificantly negative. Keller

concludes faster growing Asian countries have spent more on primary education (both total and

per student) and have more students enrolled in secondary education. Enrollment rates have

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indirect effects on increasing growth through decreasing fertility and increasing international

trade. To spend more on secondary and tertiary would be inefficient in granting less growth.

Keller (2006a) uses the same process as Keller (2006b), only this time repeated globally,

for less developed countries (LDCs), and developed countries (DCs). Keller concludes for every

situation, countries raising enrollment rates in secondary education grow faster during this

period. In the global and DC situations, tertiary enrollment is beneficial as well. The global and

LDC results suggest that in the face of scarce resources, public resources appear better allocated

towards basic, primary education, rather than higher. For LDCs, college enrollment rates were

less significant and possessed smaller coefficients; their secondary education’s significant

negative effect of expenditures suggest inefficient spending unless enrollment rates are

increased. For DCs, when inflation is added, expenditures on secondary and primary education

are negative. Globally, given the other stages, primary enrollment was significantly negative;

tertiary’s expenditures & expenditures per student suggest inefficient spending.

4. Research Hypothesis and Empirical Model

The hypothesis I desire to test is if a) greater education expenditures per student induces

positive economic growth for country, and b) such an effect is stronger for less developed

countries. The following parameters of the regression equation will be used to analyze and

answer this statistically:

𝑔 = 𝛽0 + 𝑠𝑐,𝑡(𝛽1 + 𝛽2𝑢𝑐,𝑡, + 𝛽3𝑙𝑐,𝑡 + 𝛽4𝑏𝑐,𝑡) + 𝛽5𝑦𝑐,𝑡 + ∑ 𝛽𝑖 𝑥𝑖 + 𝜀𝑖

Where:

𝑔 = Rate of change in Real GDP per capita

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𝑠𝑐,𝑡 = Total public educational expenditure per student for all levels, expressed as a percentage

of real GDP per capita

𝑢𝑐,𝑡 = Dummy variable indicating whether or not a country was designated as Upper Middle

Income, according to World Bank Development Classification, interacting with educational

expenditures

𝑙𝑐,𝑡 = Interacting Dummy variable likewise indicating Lower Middle Income classification

𝑏𝑐,𝑡 = Interacting Dummy variable indicating Low(est) Income classification

𝑦𝑐,𝑡 = Initial GDP per capita, the starting economic level of each time period

𝑥𝑖 = Control variable, 𝑖

I will use this equation to test whether or not the data shows such a positive relationship

between educational expenditures per pupil and economic growth exists, while also testing if this

relationship is particularly stronger for developing countries. A fourth related dummy

variable,𝑡𝑐,𝑡, indicates a country of High Income status, but is omitted from the equation to serve

as the point of reference.

The aggregate data will come from many different countries (𝑐) at different periods of

time (𝑡) – specifically, every half of a decade from 1985 to 2010, providing five, five year long

periods. Most variables will be presented as averages of each period; the exceptions are the

dependent variable, rate of change in real GDP per capita between the last year and the first year

of each period; the independent variable initial GDP per capita, which will be taken from the

start of each period; and the independent dummy variables, which come from the earliest

available classification in each period. The key independent variables are the aforementioned

dummy variables and public educational expenditure per student for all levels.

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The results of the regression analysis will allow me to test whether the data suggests this

notion that greater educational expenditures per student lead to greater economic growth, and

that developing countries achieve greater economic growth than developed countries through

said expenditures. This can be formally analyzed by a hypothesis test on the signs of the

parameters for such spending:

𝐻0: 𝛽1,2,3,4 = 0

𝐻𝐴: 𝛽1,2,3,4 > 0

If the results indicate I can reject these null hypotheses, it would statistically support my

research hypothesis, that through the human capital productive input, higher educational

expenditures per student increase economic growth, and through the principle of diminishing

returns, less developed countries achieve “bonus” gains from educational expenditures than their

more developed counterparts. If only one or two of null hypotheses can be rejected, than that

would suggest conditional, rather than absolute, diminishing returns are the case; countries will

achieve greater gains at lower stages of production, but only under the certain right conditions.

The equation includes a set of independent variables (x variables) to control for other

probable factors affecting economic growth: inflation, population growth, ratios of government

consumption and investment (recently renamed “gross capital formation” by the World Bank),

terms of trade index, Gini inequality index, Democratic Rights index, and Rule of Law index.

The natural logarithm of starting real GDP per capita will also lend support to this theory of

diminishing returns.

I will use the traditional process of regressing the independent variables all together, and

then whittling out the most insignificant ones, until the key independent variables are rendered

insignificant, or otherwise become part of a model in which all remaining variables are

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significant - perhaps at least at a 50% significance level, a moderately generous decision rule. In

doing so, emulating the methods used by Barro (1992), Keller (2006a), and Keller (2006b), I will

be observing if each time a control variable is omitted, the key independent variables’

significance increases, signified by decreasing p-values. This would indicate these dropped

control variables are “indirect effects” or “channels of effect” for education to induce growth.

5. Data and Variable Description

In my empirical test, I collected aggregate data from several sources, from the time

periods 1985-1990, 1990-1995, and so on, until 2005-2010. Observations for 213 national

economies were taken from the World Bank, my primary data source, in GDP per capita,

development classification, government spending, investment, Gini index, inflation, population

growth, and the Terms of Trade index.

As previously suggested, most of the available raw data was converted to attain the

average/mean for each half of a decade, in “level-level” format. However, the raw GDP per

capita data, expressed in US dollars, was used to construct Initial or Starting GDP , the GDP per

capita at the beginning of each five-year period, but transformed into natural logarithmic form;

and GDP Growth, the percentage rate of change between the beginning and end of each period,

to signify this economic growth. Also, the World Bank classification is taken from the earliest

available designation within each period; the classifications are based on annually adjusted

brackets in Gross National Income per capita. As previously stated, the High(est) Income

countries are assigned a 1 in the dummy variable 𝑡𝑐,𝑡, Upper Middle Income countries are

assigned a 1 in the dummy variable 𝑢𝑐,𝑡, Lower middle Income a 1 in 𝑙𝑐,𝑡, and Low(est) Income a

1 in 𝑏𝑐,𝑡.

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Government Expenditures and Investment (renamed Gross Capital Formation by the

World Bank) are expressed as percentages of the GDP. Inflation and population growth are

expressed in percentage change. The Gini index, “measures the extent to which the distribution

of income or consumption expenditure among individuals or households within an economy

deviates from a perfectly equal distribution,” on a scale from 0 to 100 – 0 indicating perfect

income equality, 100 perfect inequality. (Net Barter) Terms of Trade Index is the percentage

ratio of exports over imports, measured relative to the base year 2000 (=100). The Rule of Law

Index, which “captures perceptions of the extent to which agents have confidence in and abide

by the rules of society, and in particular the quality of contract enforcement, property rights, the

police, and the courts, as well as the likelihood of crime and violence,” scores countries in units

of normal distribution, from a weak rule of -2.5, to a strong rule of 2.5.

The Democracy Index was constructed by Freedom House and covers 209 countries. The

index is constructed on a scale of 1 to 7, with 1 being “most free,” and 7 being “least free.” The

index itself is an average of their Political Rights Index and Civil Liberties Index, each with a

parallel scale.

Due to the severity of gaps in information, I switched from using World Bank’s Primary,

Secondary, and Tertiary expenditures per students data for United Nations Educational,

Scientific, and Cultural Organization’s (UNESCO) Total Educational Expenditure Per Student

for All Levels, covering 165 countries. Along with the interaction variables, this is my key

independent variable, and it is expressed as a percentage of GDP per capita.

Data collection and organization was a particularly arduous task, as the sources had less

sufficient data than anticipated, containing these severe gaps, especially sparse in the older

periods 1985-1990 and 1990-1995. There was also an issue of matching, as each of the sources

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had a different list of countries, with some countries referred to by alternate names, such as

Myanmar versus Burma, or Congo Brazzaville versus Republic of Congo. The Rule of Law

Index measure only lasted 1996-2009, and the Gini Index was especially sparse for the older

periods.

As illustrated in Table 1, the average country growth rate for five years is 39.29%. The

average percentage of Educational Expenditures Per Student is 19.93% of GDP per capita.

Terms of Trade Index is on average 23.38, suggesting that most countries are severely dependent

on imports. The average Rule of Law normal distribution score is -.04, meaning most observed

countries have just slightly below average legal systems. Educational Expenditures, Rule of Law,

and Gini have the least amount of observations; while all the others each have over 800 pieces of

data, these three each have less than 600. The average Democracy Index rating of 3.65 suggests

that the countries in the sample are what Freedom House deems “less free.” A bit over half of the

sample consists of less developed countries, which proves convenient for the aspect of my study

concerning diminishing marginal returns – 28.40% are of Lower Middle Income and 26.60% are

of Low Income. The Gini Index average of 39.86 suggests countries lean a little bit towards

having a more even distribution of income. Government Expenditure and Investment account for

16.8% and 23.5% respectively for the average national economy. The mean starting GDP per

capita is $7801.80 per “citizen,” the average standard of living from 1985-2005.

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Table 1 - Summary Statistics

Quantitative Variables Observations Mean Standard Deviation

Growth in GDP per Capita 924 39.29881 59.24064

Starting GDP per Capita 924 7801.801 13599.44

Educational Expenditures Per Student, All Levels 502 19.92992 10.06454

Inflation 949 51.45821 308.7874

Population Growth 1055 1.60111 1.534073

(Net Barter) Terms of Trade Index 829 23.38155 85.67619

Gini Index 547 39.86508 10.25401

Democracy Index 804 3.652551 1.971318

Rule of Law Index 595 -0.0431787 0.9967398

Government Expenditure, G/Y 880 16.79178 8.714286

Investment, I/Y 887 23.49862 10.12747

Categorical Variables Categories Percentages

World Bank Income Classification Low Income 26.6038%

Lower Middle Income 28.3962%

Upper Middle Income 15.7547%

High Income 22.6415%

6. Empirical Test

First, one must pick an appropriate starting point for this model. As shown in Table 1, I

started with 4 regressions, the first with all variables, the second with the Gini Index omitted, the

third with Rule of Law omitted, and the fourth with both omitted. I tinkered with these two

variables in particular because their data was especially sparse for earlier years. In fact, Gini was

never used in the literature review. I found that it was necessary to keep Rule of Law index, but

drop Gini Index, establishing the Regression 2 as my starting point. The second regression not

only had a slight increase in observations compared to the first, from 206 to 277, it also had a

significant boost in explanatory power, becoming higher than all the other regressions.

According to R-squared, 47.17% of the variation of GDP Growth was explained in the second

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regression, and after compensating for the amount of variables, 44.77% of the variation could be

explained.

However, the Gini Index variable itself was fairly significant, having a P-value of .33 and

.087 respectively for the first and third regressions. Interestingly, its exclusion made the variables

related to educational expenditures become more significant, decreasing their P-values, which

implies some interplay between inequality and human capital.

If using a fairly generous 30% significance level, one could already judge my

hypothesis. Educational expenditures per student do have a positive effect on economic growth,

but only the most highly developed countries are the ones to gain the most from it. This is

indicated by the interaction variables between the less developed categories and these

expenditures being significantly negative and of great value; with the highly developed countries

as the point of reference, only the bare Educational Expenditure variable was positive. Given the

relative size of their (absolute) values, it may be that countries of lower status may actually lose

out, perhaps due to inefficiently spending at the wrong levels. According to this, all else equal,

for every percentage point increase in educational expenditures per student compared to GDP per

capita, a highly developed country gains .85 percentage point in GDP per capita. Though

inelastic in general terms, it has one of the highest elasticities in the equation – for every 1%

increase in educational expenditures per student/GDP per capita, Real GDP per capita increases

by .43%. This somewhat stresses the role of human capital in the neoclassical production

function.

However, the concept of diminishing returns seems to hold true in some respect, based on

starting per capita GDP’s negative coefficient. Then again, with any reasonable significance

level, it is worth noting it is insignificant, possessing a P-value of .67.

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It makes sense that Democracy Index’s coefficient would be negative – a higher score

means less democracy, and less democracy can be detrimental economically. But, it does not

make so much sense for Rule of Law Index to be negative and of such high value – a higher

score means stronger rule of law. Perhaps, the law system serves as an impediment in achieving

economic goals, in which one must “cut through the red tape.” I had no predictions for

Population Growth - it could have gone either way. Population growth could either spread

resources thin, or provide a wider pool of potential workers and producers; the latter seems to be

true, since the coefficient was positive. Meanwhile, the negative coefficient on the Government

Expenditure ratio/percentage suggests inefficient spending is contributing negatively to growth;

however, it is highly insignificant. Investment consistently displayed significant positive

influence and high elasticity. Inflation could have gone either way as well – increasing prices

could force people to cut back on consumption, or it can induce employers to increase wages to

compensate; the former seems to hold true, given the negative coefficient, but it seems more

“mixed” given its low significance.

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Table 2 - Preliminary Regression Results

Dependent Variable: Change In Real GDP per Capita

All Variables Included 1

Number of observations 206

R-squared 0.2501

Adjusted R-squared 0.1994

Independent Variables Coef. t-stat P-value Elasticity

Educational Expenditures Per Student 1.01104 1.08 0.284 0.512737

Upper Middle Income & Educational Expenditure/Student Interaction -0.95683 -1.39 0.165

Lower Middle Income & Educational Expenditure/Student Interaction -1.56623 -1.75 0.081

Low Income & Educational Expenditure/Student Interaction -0.81441 -0.69 0.493

(Natural Logarithm) of GDP per Capita -11.1044 -1.68 0.095

Government Expenditures 0.249755 0.36 0.718 0.106717

Investment 1.816117 2.99 0.003 1.085942

Inflation -0.0197 -0.60 0.552 -0.02579

Population Growth -19.6244 -4.75 0.000 -0.79954

Terms of Trade Index -0.04555 -1.80 0.074 -0.0271

Gini Index 0.443618 0.97 0.334 0.45001

Democracy Index -4.44404 -1.37 0.173 -0.41304

Rule of Law Index -21.9528 -2.74 0.007 0.02412

_cons 106.7999 1.96 0.052

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Gini Index Omitted 2

Number of observations 277

R-squared 0.4717

Adjusted R-squared 0.4477

Independent Variables Coef. t-stat p Elasticity

Educational Expenditures Per Student 0.84809 1.11 0.268 0.43010

Upper Middle Income & Educational Expenditure/Student Interaction -1.15155 -2.18 0.030

Lower Middle Income & Educational Expenditure/Student Interaction -1.77220 -2.59 0.010

Low Income & Educational Expenditure/Student Interaction -1.36513 -1.41 0.159

(Natural Logarithm) of GDP per Capita -0.21610 -0.04 0.969

Government Expenditures 0.06799 0.10 0.918 0.02905

Investment 3.31986 13.38 0.000 1.98510

Inflation -0.02593 -0.71 0.477 -0.03396

Population Growth -6.71604 -2.76 0.006 -0.27362

Terms of Trade Index -0.04419 -1.56 0.120 -0.02629

Gini Index

Democracy Index -3.89285 -1.52 0.129 -0.36181

Rule of Law Index -37.25643 -5.14 0.000 0.04093

_cons -0.80196 -0.02 0.986

Rule of Law Index Omitted 3

Number of observations 281

R-squared 0.269

Adjusted R-squared 0.2363

Independent Variables Coef. t-stat p Elasticity

Educational Expenditures Per Student 1.96062 2.59 0.010 0.99431

Upper Middle Income & Educational Expenditure/Student Interaction -1.61516 -2.75 0.006

Lower Middle Income & Educational Expenditure/Student Interaction -2.70099 -3.97 0.000

Low Income & Educational Expenditure/Student Interaction -3.39249 -3.78 0.000

(Natural Logarithm) of GDP per Capita -33.94797 -6.59 0.000

Government Expenditures 0.26638 0.45 0.656 0.11382

Investment 1.38405 2.9 0.004 0.82759

Inflation 0.04684 2.44 0.015 0.06134

Population Growth -20.35060 -5.63 0.000 -0.82912

Terms of Trade Index -0.04287 -1.64 0.101 -0.02551

Gini Index 0.69786 1.74 0.083 0.70792

Democracy Index -6.14787 -2.49 0.013 -0.57140

Rule of Law Index

_cons 294.11510 6.72 0.000

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Both Rule of Law and Democracy Index Omitted 4

Number of observations 394

R-squared 0.3573

Adjusted R-squared 0.3388

Independent Variables Coef t-stat p Elasticity

Educational Expenditures Per Student 0.78520 1.46 0.144 0.39821

Upper Middle Income & Educational Expenditure/Student Interaction -1.03060 -2.28 0.023

Lower Middle Income & Educational Expenditure/Student Interaction -2.12089 -4.39 0.000

Low Income & Educational Expenditure/Student Interaction -2.70344 -3.92 0.000

(Natural Logarithm of) Starting GDP per Capita -22.12370 -5.56 0.000 -4.36234

Government Expenditures 0.11185 0.2 0.845 0.04779

Investment 3.00415 12.01 0.000 1.79632

Inflation -0.00603 -0.53 0.599 -0.00790

Population Growth -7.30047 -3.09 0.002 -0.29744

Terms of Trade Index -0.02863 -0.95 0.340 -0.01704

Gini Index

Democracy Index -2.12586 -1.06 0.288 -0.19758

Rule of Law Index

_cons 181.65910 5.4 0.000

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Table 3 - Final Regression Results

Dependent Variable: Change In Real GDP per Capita After Log(GDP/Capita) Omission I

Number of observations 277

R-squared 0.4717

Adjusted R-squared 0.4498

Independent Variable Coef. t-stat P>t Elasticity

Educational Expenditures Per Student, All Levels 0.83582 1.20 0.231 0.423874

Upper Middle Income & Educational Expenditure/Student Interaction -1.14571 -2.26 0.024

Lower Middle Income & Educational Expenditure/Student Interaction -1.75671 -3.15 0.002

Low Income & Educational Expenditure/Student Interaction -1.33550 -2.22 0.027

Government Expenditure, G/Y 0.06288 0.10 0.922 0.026867

Investment, I/Y 3.32083 13.47 0.000 1.98568

Inflation -0.02587 -0.71 0.477 -0.03388

Population Growth -6.71978 -2.77 0.006 -0.27378

(Net Barter) Terms of Trade Index -0.04418 -1.56 0.119 -0.02629

Democracy Index -3.89397 -1.53 0.128 -0.36192

Rule of Law Index -

37.36597 -5.59 0.000 0.041055

_cons -2.46043 -0.19 0.851

After Government Expenditure Omission II

Number of observations 277

R-squared 0.4717

Adjusted R-squared 0.4518

Independent Variable Coef. t-stat P>t Elasticity

Educational Expenditures Per Student, All Levels 0.86581 1.39 0.166 0.43909

Upper Middle Income & Educational Expenditure/Student Interaction -1.14504 -2.27 0.024

Lower Middle Income & Educational Expenditure/Student Interaction -1.75876 -3.17 0.002

Low Income & Educational Expenditure/Student Interaction -1.34282 -2.26 0.025

Government Expenditure, G/Y

Investment, I/Y 3.32154 13.51 0.000 1.98611

Inflation -0.02457 -0.73 0.467 -0.03218

Population Growth -6.73860 -2.79 0.006 -0.27454

(Net Barter) Terms of Trade Index -0.04399 -1.56 0.119 -0.02617

Democracy Index -3.83730 -1.55 0.123 -0.35665

Rule of Law Index -37.24890 -5.68 0.000 0.04093

_cons -2.19157 -0.17 0.864

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After Inflation Omission III

Number of observations 277

R-squared 0.4706

Adjusted R-squared 0.4528

Independent Variable Coef. t P>t Elasticity

Educational Expenditures Per Student, All Levels 0.83620 1.35 0.180 0.42407

Upper Middle Income & Educational Expenditure/Student Interaction -1.12577 -2.23 0.026

Lower Middle Income & Educational Expenditure/Student Interaction -1.72110 -3.11 0.002

Low Income & Educational Expenditure/Student Interaction -1.31694 -2.22 0.027

Government Expenditure, G/Y

Investment, I/Y 3.31847 13.51 0.000 1.98427

Inflation

Population Growth -6.70086 -2.78 0.006 -0.27301

(Net Barter) Terms of Trade Index -0.04341 -1.54 0.124 -0.02583

Democracy Index -3.87491 -1.56 0.119 -0.36015

Rule of Law Index -36.69837 -5.64 0.000 0.04032

_cons -2.26684 -0.18 0.859

As one can see in the Table 3, I continued refining the model, and the log(GDP) per

capita) was the next variable that had to be dropped, followed by Government Expenditures, as

both were insignificant by any reasonable level, with P-values over .9. This suggests the

aforementioned mixed effects of government spending in terms of efficiency, and that growth

does not depend on the development or income of a country. In Regression II, all remaining

variables would pass at the planned 50% significance level. But, the model had more potential;

after dropping the next most insignificant variable, Inflation, with the highest p-value of the lot at

.467 and its possible mixed effects, the final Regression III was produced, and all of its variables

pass at a 20% significance level. The same relationship in the key independent variables remains;

High income countries’ educational expenditures have a positive relationship with growth, and is

the second most elastic variable in the equation (though inelastic in general terms). For every

percentage point increase of these expenditures, economic growth increases by .83 of a

percentage point; for every 1% increase in educational expenditures, economic growth increases

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by .43%. This refined model explains 47.06% of the variation in growth, or 45.28% if one

accounts for the number of variables. But, one can see there is a significantly negative difference

between High Income countries and the other classes, and since their coefficients have absolute

values greater than that of the bare variable, one can conclude they in fact possess negative

growth.

Between where the model started and ended, from Regression 2 in Table 2 and

Regression III in Table 3, the control variables that remained all had the same signs, and roughly

the same values.

This amount of negative growth was unanticipated. To briefly test if education/human

capital promotes growth in the most general terms, I reran the regression model with just the

single, bare variable. The variables dropped out of insignificance remained the same. At the 20%

significance level, one surprisingly finds that education expenditures per student for all countries

exert a significantly negative influence on economic growth.

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Table 4 - Regressions Without Interaction Variables Dependent: GDP Growth

All Variables i

Number of obs 277

R-squared 0.4514

Adj R-squared 0.4329

Independent Variables Coef. t P>t Elasticity

Educational Expenditures Per Student -0.42610 -0.87 0.385 -0.21609

Log(GDP per capita) 3.05645 0.92 0.360

Inflation -0.01360 -0.37 0.711 -0.0178

Population Growth -4.99814 -2.13 0.034 -0.20363

(Net Barter) Terms of Trade Index -0.04151 -1.45 0.149 -0.0247

Democracy Index -4.35716 -1.7 0.091 -0.40497

Rule of Law Index -28.29824 -4.21 0.000 0.031092

Government Expenditure, G/Y -0.08326 -0.13 0.901 -0.03558

Investment, I/Y 3.30173 13.15 0.000 1.974263

_cons -21.14646 -0.7 0.485

Government Expenditure Omitted ii

Number of obs 277

R-squared 0.4514

Adj R-squared 0.435

Independent Variables Coef. t P>t Elasticity

Educational Expenditures Per Student -0.46295 -1.18 0.237 -0.23478

Log(GDP per capita) 2.955369 0.92 0.361

Inflation -0.01527 -0.45 0.655 -0.01999

Population Growth -4.96986 -2.13 0.034 -0.20248

(Net Barter) Terms of Trade Index -0.04175 -1.46 0.145 -0.02484

Democracy Index -4.42996 -1.78 0.077 -0.41173

Rule of Law Index -28.3578 -4.24 0.000 0.031158

Government Expenditure, G/Y [Omitted]

Investment, I/Y 3.30024 13.19 0.000 1.97337

_cons -20.7001 -0.69 0.490

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Inflation Omitted iii

Number of obs 277

R-squared 0.451

Adj R-squared 0.4367

Independent Variables Coef. t P>t Elasticity

Educational Expenditures Per Student -0.46464 -1.19 0.235 -0.23564

Log(GDP per capita) 2.893934 0.9 0.369

Inflation [Omitted]

Population Growth -4.9748 -2.14 0.033 -0.20268

(Net Barter) Terms of Trade Index -0.04141 -1.45 0.148 -0.02464

Democracy Index -4.44211 -1.78 0.076 -0.41286

Rule of Law Index -28.0903 -4.22 0.000 0.030864

Government Expenditure, G/Y [Omitted]

Investment, I/Y 3.298431 13.2 0.000 1.972288

_cons -20.33 -0.68 0.497

Log(GDP per capita) omitted iv

Number of obs 277

R-squared 0.4493

Adj R-squared 0.4371

Independent Variables Coef. t P>t Elasticity

Educational Expenditures Per Student -0.54191 -1.42 0.156 -0.27482

Log(GDP per capita) [Omitted]

Inflation [Omitted]

Population Growth -5.2243 -2.26 0.024 -0.21285

(Net Barter) Terms of Trade Index -0.04113 -1.44 0.150 -0.02447

Democracy Index -4.31366 -1.74 0.084 -0.40092

Rule of Law Index -23.6814 -5.26 0.000 0.026019

Government Expenditure, G/Y [Omitted]

Investment, I/Y 3.276567 13.18 0.000 1.959215

_cons 4.228695 0.35 0.728

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In terms of channels of effect, the P-value of the bare Educational Expenditures variable

decreased from Regression I to Regression II, from .231 to .166, meaning that controlling for

Government Expenditures renders educational expenditure less significant. One could speculate

that Government Expenditures, previously containing a positive coefficient, efficiently

contributes to growth only if it comes under the control of people who are more educated and

skilled. The P-value for all four key variables decreased from Regression 1 to 2, upon the

omission of the Gini Index. This would suggest the view that human capital thoroughly drives

inequality within a country. The P-value also decreased from Regression 2 to Regression I, from

.268 to .231, upon the omission of the natural logarithmic form of starting GDP per capita. This

could illustrate having a more educated, skilled society will provide for a higher standard of

living.

7. Conclusion:

I predicted a positive relationship between educational expenditures per student and

economic growth in the form of GDP per capita, and that this relationship would be stronger for

countries in lesser developed states. My hypothesis was mostly disproven. At 20% significance,

there is enough sample evidence to suggest that educational expenditures per student, expressed

as a percentage of GDP per capita, does beneficially influence economic growth, but only in the

case of High Income countries. Surprisingly, the theory of diminishing marginal returns did not

apply, as Upper Middle, Lower Middle, and Low Income countries displayed no clear trend

except all their expenditures negatively influence growth. Upon further investigation of this

unanticipated finding, I found that the overall trend, for all countries, is significantly negative.

However, in light of all the current theory and the sole confirming case for High Income

countries, one can deduce that it might be an appropriate policy to spend more on education in

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inducing growth, but one should be extremely wary of inefficiency, depending on developmental

status and education level.

This study opens doors for further investigation. After much difficulty in data collection,

there was a tradeoff in choosing to omit the Gini Index in determining a starting point for this

study. Dropping it produced a slight increase in observations and a large boost in the R-squared

terms. But, at an individual level, in each of the early regressions in which it was used, its

coefficient was significant by any reasonable standard. One might like to revisit this study with

the Gini Index included. Furthermore, I had to make a compromise in the use of key independent

variables, choosing educational expenditures per student aggregated for all levels, rather than

separate variables for the primary, secondary, and tertiary levels. The aggregated indicator has

more data available via UNESCO, provides a “package deal” policy perspective on how the

spending at each level combine, and allows one to simplify the model - if one were to have used

the three separate variables in interaction with the four developmental classes, this would

complicate the model into 12 key independent variables. On the other hand, this would have

been insightful, as it allows one to isolate which level is the most efficient/effective for each

developmental class. Lastly, there is a wealth of alternate measures of education briefly touched

upon in the literature review and worth exploring, such as sex composition, teacher-pupil ratio,

enrollment, and literacy rates.

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4. Reference List

Barro, R. J. 1992. “Human Capital and Economic Growth.” Policies for Long-Term Economic

Growth (Federal Reserve Bank of Kansas City). Accessed February 27, 2015.

Many theoretical models of economic growth, such as those of Nelson and Phelps (1966); Lucas

(1988); Becker, Murphy, and Tamura (1990); Rebelo (1992); and Mulligan and Sala-i-Martin

(1992), have emphasized the role of human capital in the form of educational attainment.

Empirical studies of growth for a broad cross section of countries, such as those by Romer

(1990a), Barro (1991), Kyriacou (1 991), and Benhabib and Spiegel (1992), have used proxies

for human capital. These studies have, however, been hampered by the limited educational data

that were available on a consistent basis for a large number of countries. Recent research by

Barro and Lee (1992) through the World Bank has provided better estimates of educational

attainment for a large number of countries over the period 1960 to 1985. Hence, these data make

it possible to use a broad sample of experience across countries and over time to assess the

interplay between human capital and economic growth. This paper summarizes preliminary

empirical results that use these data. These results provide empirical support for economic

theories that emphasize the role of human capital in the growth process.

Barro, R. J. (1999). “Human Capital and Growth in Cross-country Regressions.” Swedish

Economic Policy Review 6(2), 237-277. Accessed February 17, 2015.

The determinants of economic growth and investment are analyzed in a panel of around 100

countries observed from 1960 to 1995. The data reveal a pattern of conditional convergence in

the sense that the growth rate of per capita GDP is inversely related to the starting level of per

capita GDP, holding fixed measures of government policies and institutions and the character of

the national population. For given values of these variables, growth is positively related to the

starting level of average years of school attainment of adult males at the secondary and higher

levels. Growth is insignificantly related to years of school attainment of females at these levels or

to years of primary attainment by either sex. The strong effect of secondary and higher schooling

suggests a paramount role for the diffusion of technology. The weak effect of female schooling

suggests that women’s human capital is not well exploited in the labor markets of many

countries. Data on students’ scores on internationally comparable examinations are used to

measure the quality of schooling. Scores on science tests have a particularly strong positive

relation with economic growth. If science scores are held fixed, then results on reading

examinations are insignificantly related to growth. (The results on mathematics scores could not

be reliably disentangled from those of science scores.) Given the quality of education, as

represented by the test scores, the quantity of schooling—measured by average years of

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attainment of adult males at the secondary and higher levels—is still positively and significantly

related to subsequent growth. The results on test scores also hold if the estimation is by

instrumental variables, where the instrument list includes variables that have significant

explanatory power for test scores—prior values of total years of schooling in the adult population

(a proxy for the education of parents), pupil teacher ratios, and school dropout rates.

Hanushek, Eric and Dongwoook Kim. 1995. “Schooling, Labor Force Quality, and Economic

Growth.” National Bureau of Economic Research Working Paper Series 5399. Accessed

Accessed February 17, 2015.

Human capital is almost always identified as a crucial ingredient for growing economies, but

empirical investigations of cross-national growth have done little to clarify the dimensions of

relevant human capital or any implications for policy. This paper concentrates on the importance

of labor force quality, measured by cognitive skills in mathematics and science. By linking

international test scores across countries, a direct measure of quality is developed, and this

proves to have a strong and robust influence on growth. One standard deviation in measured

cognitive skills translates into one percent difference in average annual real growth ratesþan

effect much stronger than changes in average years of schooling, the more standard quantity

measure of labor force skills. Further, the estimated growth effects of improved labor force

quality are very robust to the precise specification of the regressions. The use of measures of

quality significantly improves the predictions of growth rates, particularly at the high and low

ends of the distribution. The importance of quality implies a policy dilemma, because production

function estimates indicate that simple resource approaches to improving cognitive skills appear

generally ineffective.

Keller, Katarina R.I. 2006a. “Investment in Primary, Secondary, and Higher Education and the

Effects on Economic Growth.” Contemporary Economic Policy. 24(1), 18-34.

Accessed February 27, 2015.

This author analyzes the effects of primary, secondary, and higher education on per

capita growth for flow measures of education: enrollment rates, public expenditures, and

expenditures per student. Worldwide panels since 1960 and developing and developed country

subsamples are examined. Secondary and higher education enrollment rates and expenditures per

student in lower education stages and primary overall demonstrate significance. Public higher

education expenditures overall and per student are disadvantageous. This study recommends

raising enrollment rates and prioritizing public expenditures toward lower education stages,

while ensuring that expenditures per student keep up with increases in student cohorts. Indirect

effects of education are explored.

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Keller, Katarina R.I. 2006b. “Education Expansion, Expenditures Per Student and the Effects on

Growth in Asia.” Global Economic Review, 35 (1), 21-42. Accessed February 25, 2015.

This article estimates the separate effects of primary, secondary and higher education on

economic growth in Asia since 1960. Enrollment rates, public expenditures and public

expenditures per student are used as measures of education in an empirical panel data analysis.

Expenditures toward primary education and expenditures per student in this education stage have

contributed highly significantly to economic growth, while expenditures toward the higher stages

seem more inefficiently utilized. Enrollment rates in secondary education especially play an

important role in increasing growth rates. Enrollment rates, in particular, display significant

indirect effects.