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 + 𝑠 𝑐,𝑡(𝛽1 + 𝛽2 𝑢 𝑐,𝑡, + 𝛽3 𝑙 𝑐,𝑡 + 𝛽4 𝑏 𝑐,𝑡) + 𝛽5 𝑦𝑐,𝑡 + ∑ 𝛽𝑖 𝑥𝑖 + 𝜀𝑖
Where:
𝑔 = Rate of change in Real GDP per capita

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𝑠 𝑐,𝑡 = Total public educational expenditure per student for all levels, expressed as a percentage
of real GDP per capita
𝑢 𝑐,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
𝑙 𝑐,𝑡 = Interacting Dummy variable likewise indicating Lower Middle Income classification
𝑏 𝑐,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,𝑡 𝑐,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 𝑡 𝑐,𝑡, Upper Middle Income countries are
assigned a 1 in the dummy variable 𝑢 𝑐,𝑡, Lower middle Income a 1 in 𝑙 𝑐,𝑡, and Low(est) Income a
1 in 𝑏 𝑐,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
R-squared 0.4717
Independent Variables Coef. t-stat p Elasticity
Investment 3.31986 13.38 0.000 1.98510
Inflation -0.02593 -0.71 0.477 -0.03396
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
R-squared 0.269
Independent Variables Coef. t-stat p Elasticity
Investment 1.38405 2.9 0.004 0.82759
Inflation 0.04684 2.44 0.015 0.06134
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
R-squared 0.3573
Independent Variables Coef t-stat p Elasticity
(Natural Logarithm of) Starting GDP per Capita -22.12370 -5.56 0.000 -4.36234
Investment 3.00415 12.01 0.000 1.79632
Inflation -0.00603 -0.53 0.599 -0.00790
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
R-squared 0.4717
Independent Variable Coef. t-stat P>t Elasticity
Educational Expenditures Per Student, All Levels 0.83582 1.20 0.231 0.423874
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
(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
R-squared 0.4717
Independent Variable Coef. t-stat P>t Elasticity
Government Expenditure, G/Y
Investment, I/Y 3.32154 13.51 0.000 1.98611
Inflation -0.02457 -0.73 0.467 -0.03218
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
R-squared 0.4706
Independent Variable Coef. t P>t Elasticity
Government Expenditure, G/Y
Investment, I/Y 3.31847 13.51 0.000 1.98427
Inflation
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
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
Inflation -0.01527 -0.45 0.655 -0.01999
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
Inflation [Omitted]
Democracy Index -4.44211 -1.78 0.076 -0.41286
Rule of Law Index -28.0903 -4.22 0.000 0.030864
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
Log(GDP per capita) [Omitted]
Inflation [Omitted]
Democracy Index -4.31366 -1.74 0.084 -0.40092
Rule of Law Index -23.6814 -5.26 0.000 0.026019
Investment, I/Y 3.276567 13.18 0.000 1.959215
_cons 4.228695 0.35 0.728

Rosete 22
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

Rosete 23
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.

Rosete 24
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

Rosete 25
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.

Rosete 26
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.

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