Quality-adjusted human capital and productivity growth.
Islam, Rabiul ; Ang, James B. ; Madsen, Jakob B. 等
I. INTRODUCTION
Although endogenous growth models predict that human capital is one
of the most important sources of economic growth, the macrolevel
empirical evidence is at best mixed. (1) So far, most studies have
concentrated on educational attainment and hence the ambiguous findings
may be due to measurement errors as well as large variations in the
quality of schooling across countries. The quality of teaching, as
measured by internationally comparable test scores, shows staggering
cross-country variations among eighth-grade students. While Qatar and
Ghana achieve scores in mathematics and science close to 300 in the 2007
Trends in International Mathematics and Science Study (TIMSS), the
Western countries score close to 500, indicating large differences
between developed and developing countries. The quality of schooling is
often inadequate in developing countries due to high teacher and student
absentee rates, fewer teaching days a year, rote learning, insufficient
teacher qualifications, and the lack of basic resources such as school
books, clean classrooms with chairs and tables, and stationery
(Pritchett 2004). Furthermore, the high burden of diseases among
students in developing countries reduces their attention and
concentration in the classroom (Sachs 2001). Thus, even if educational
attainment is not that low in many developing countries it may not
deliver the desired growth effects because of the poor quality of
teaching and the learning environment.
In response to the huge gap in schooling quality, some studies have
examined the impact of human capital quality on growth. Using science
and mathematics scores on internationally comparable tests as measures
of human capital quality, Hanushek and Kimko (2000), Barro (2001), and
Hanushek and Woessmann (2008, 2012) find that educational attainment
loses significance once educational quality is controlled for in the
regressions. However, despite the concern that educational attainment
may be endogenous, as highlighted by Bils and Klenow (2000),
Vandenbussche, Aghion, and Meghir (2006), and Hanushek and Woessmann
(2012), none of these studies have catered for potential feedback
effects from productivity growth to the quality as well as the quantity
of schooling, due to the difficulties associated with finding good
instruments. Furthermore, Hanushek and Kimko (2000), Barro (2001), and
Hanushek and Woessmann (2008, 2012) have not allowed for the interaction
between human capital quality and distance to the frontier--a
potentially important issue since human capital is likely to have played
a role in facilitating the transfer of technology from the frontier.
Here we argue in favor of using quality-adjusted educational
attainment over either the quantity or the quality of education as
measures of human capital in growth regressions. Educational attainment
measures the number of years of schooling among the adult population,
whereas educational quality captures how much they have actually learned
in school. Using a nonparametric estimation strategy, Delgado,
Henderson, and Parmeter (2013) show that educational attainment is
largely ineffective in predicting per capita gross domestic product
(GDP) growth rates, suggesting that educational attainment may not
adequately measure human capital if the quality dimension of education
is omitted in the regressions.
This article contributes to the literature as the first paper that,
to the best of our knowledge, explicitly examines the productivity
growth effects of quality-adjusted human capital. Furthermore, we
investigate the growth effects of the interaction between distance to
the frontier and quality-adjusted educational attainment of the adult
population under the assumption that human capital enables nonfrontier
countries to absorb the technology that is developed at the frontier, in
the spirit of Nelson and Phelps (1966) and Vandenbussche et al. (2006).
Finally, and most importantly, we introduce a new set of instruments to
cater for measurement errors and endogeneity of the quality and quantity
of educational attainment. While variables such as public educational
expenditures and lagged educational attainment have been used as
instruments for educational attainment in the literature (see, e.g.,
Vandenbussche et al. 2006), they may well be an outcome of growth, and
public educational expenditure is more likely to influence the quality
than the quantity of teaching since all countries considered here have
compulsory schooling. In light of this, we use outcomes of pathogen
stress as instruments. As shown below, they are highly correlated with
our measure of quality-adjusted educational attainment but uncorrelated
with the error term, suggesting that they are strong and valid
instruments that satisfy the exclusion restriction assumption.
The next section sets out the theoretical framework and Section III
discusses the data, measurement issues, and the instruments used. The
empirical results are presented in Section IV and extensions and
robustness checks are carried out in Section V. The last section
concludes.
II. THEORETICAL FRAMEWORK
The model estimated in this paper is based on the following Nelson
and Phelps (1966) model extended by the level of human capital by
Benhabib and Spiegel (1994):
(1)
([[??].sub.t]/[A.sub.t]) = [psi][h.sub.t] + [phi][h.sub.t]
[([[bar.A].sub.t] - [A.sub.t])/[A.sub.t]], [phi](0) = 0,
where A is technology, [bar.A] is the technological frontier, and h
is human capital. Nelson and Phelps (1966) define [bar.A] as the
theoretical level of technology, i.e., "the best-practice level of
technology that would prevail if technological diffusion were completely
instantaneous" (p. 71). The philosophy behind the Nelson-Phelps
model is intuitive: the further a country is behind the technological
frontier, the higher is its growth potential provided that it has a
sufficiently high level of human capital, or absorptive capacity, to
take advantage of its backwardness.
The importance of education and technological catch-up for growth
has also been emphasized in the studies of Henderson and Russell (2005)
and Vandenbussche et al. (2006). In particular, using a sophisticated
growth accounting approach, Henderson and Russell (2005) decompose
productivity growth into technological change, technological catch-up,
and capital accumulation. They find that human capital is a significant
contributor to productivity growth and that "convergence
clubs" formation is induced mainly by efficiency changes associated
with technological catch-up. In the theoretical model developed by
Vandenbussche et al. (2006), unskilled human capital facilitates
imitation or diffusion of existing technology whereas skilled human
capital promotes the innovation of new technology. Hence, their model
predicts that tertiary education should become increasingly important
but primary and secondary education less important for growth as a
country moves closer to the technology frontier (see also Ang, Madsen,
and Islam 2011). The benefits of technology transfer for growth from the
rich to the poor countries, however, have been questioned by Caselli and
Coleman (2006). They argue that skilled and unskilled labor are not
perfect substitutes and find evidence supporting their proposition that
skill premiums play an important part in driving cross-country
technological differences. These results imply that poor countries are
more efficient than rich countries at using unskilled workers since they
have a larger supply of unskilled labor. The presence of a skill
premium, therefore, acts as a barrier deterring technology transfer from
technologically sophisticated countries to technological laggards.
Benhabib and Spiegel (1994) extend the Nelson-Phelps model to allow
for the separate growth effects of human capital since the model has the
unwarranted property that it does not account for factors that are
responsible for growth in the frontier countries and does not allow
human capital to have productivity growth effects independent of the
technology adopted from the frontier countries. Note that human capital,
h, is unlogged following the Mincerian approach in which an additional
year of schooling has the same growth effects regardless of the level of
education, under the assumption that the returns to an additional year
of education are independent of the number of years of education. That
is, the growth effects of extending schooling by one year are the same
for populations with 1 or 12 years of education. The predictions of this
extended model have been supported by the empirical findings of
Griffith, Redding, and van Reenen (2004), Benhabib and Spiegel (2005),
Vandenbussche et al. (2006), and Madsen, Islam, and Ang (2010), among
others.
Although previous attempts have had some success in estimating the
extended Nelson-Phelps models, these are not without problems. First, it
is not easy to measure human capital and previous studies have
predominantly focused on number of years of schooling without accounting
for the fact that the quality of schooling varies substantially across
countries, as discussed in Section I. Second, the reference frontier
country may differ across countries. Most poor countries use production
technology that is not developed at the technology frontier (Sachs
2001), and thus the United States may not be the sole technology
frontier, as is often assumed in empirical studies. Different advanced
countries specialize in different technologies in different sectors.
Thus, it is likely that the frontier, in addition to the United States,
comprises other technologically sophisticated countries such as other G7
members. For poor countries the reference technology frontier is likely
to be found among middle-income countries that have developed
technologies particularly suitable for production in low-income
countries, as discussed in the following section.
III. EMPIRICAL FRAMEWORK
Extending the model given by Equation (1) to allow for control
variables yields the following specification that will be estimated for
a panel of 60 countries in the period 1970-2010:
(2)
[g.sup.A.sub.i] = [alpha] + [[beta].sub.1] [([PHI]x H).sub.i], +
[[beta].sub.2][([PHI]x H).sub.i] x [DTF.sub.i,1970] +
[gamma]'[C.sub.i] + [[epsilon].sub.i],
where [g.sup.A] is total factor productivity (TFP) growth; [PHI] is
the quality of education measured in various ways as discussed below; H
is educational attainment among adults aged 25 years and above; DTF is
distance to the frontier, which is measured at the start of the sample
period in 1970, following the literature (see, e.g., Benhabib and
Spiegel 1994); C is a vector of control variables; and e is a stochastic
error term.
The following control variables are included in the regressions:
trade openness (exports plus imports divided by GDP), the ratio of
foreign direct investment inflow to GDP, the rates of consumer price
inflation, and the investment ratio (gross capital formation over GDP).
Trade openness is assumed to influence growth positively in the
literature under the assumption that open economies have a more
outward-oriented policy. (2) Foreign direct investment is assumed to be
growth-enhancing because it embodies new technology, know-how, and
knowledge. Inflation retards growth because it is often an indication of
macroeconomic mismanagement.
The investment ratio is included in the regression as it is found
by Levine and Renelt (1992) to be the most robust determinant of growth
among a large set of growth variables. The investment ratio can
influence growth through the production function or through productivity
externalities. In the neoclassical growth model, the investment ratio
has growth effects as long as the economy is on its transitional growth
trajectory, as is often assumed in empirical studies. Investment has
permanent growth effects if there are positive externalities to
investment and provided that there are scale effects in ideas
production. Scale effects in ideas production are implicitly assumed in
Equation (2) in the sense that human capital is assumed to have
permanent as opposed to temporary growth effects.
A. Estimation Method and Instruments
The instrumental variable technique is used to deal with potential
endogeneity and measurement errors for the quality-adjusted educational
attainment measure and its interaction with distance to the frontier.
(3) Educational attainment is measured with errors since it does not
allow for differences in student and teacher attendance rates and the
number of school days per year across countries and time periods, in
addition to the usual errors associated with census surveys, on which
most of the educational attainment data are based, de la Fuente and
Domenech (2006), for example, find large errors in the census data on
educational attainment for OECD countries that, supposedly, have data of
much better quality than developing countries. Moreover, the quality of
schooling is subject to measurement errors because most of the measures
used here do not allow for the fact that the average cognitive abilities
among children entering the schooling system differ across countries
(Eppig, Fincher, and Thornhill 2010).
Bils and Klenow (2000) argue that schooling is endogenous because
the returns to investment in schooling depend positively on the expected
productivity growth rates, which in turn depend on the contemporaneous
and historical growth rates. The quality of education may also be
endogenous since the resources available for teaching are likely to
depend positively on economic growth. Governments are likely to cut
budgets for education expenditure in periods of low or negative growth
following the shrinking growth or direct reductions in tax revenues.
However, since it is hard to reduce school enrolment numbers due to the
provision of free-of-charge education and compulsory schooling
requirements, the resources available to each student are likely to
shrink during periods of low, decreasing, or negative growth.
The following instruments are used for quality-adjusted educational
attainment and its interaction with DTF: (1) disability-adjusted life
years lost per 100,000 population (DALY) due to communicable, maternal,
perinatal, and nutritional diseases and (2) estimated death rates due to
communicable, maternal, perinatal, and nutritional diseases per 100,000
population (EDR).
DALY measures the number of years lost due to ill-health,
disability, or early death and is calculated as the sum of reduced life
expectancy relative to the Japanese life expectancy and the years of
quality life lost due to disability and poor health. We use DALY due to
communicable, maternal, perinatal, and nutritional diseases as an
instrument, thus excluding DALY due to noncommunicable diseases such as
cancer, cardiovascular diseases, and injuries--factors that are unlikely
to influence school performance since they most often happen much later
in life. DALY due to communicable, maternal, perinatal, and nutritional
diseases serves as a good instrument for the quality of learning and
teaching because infectious and parasitic diseases impair the ability to
learn, reduce students' attention and concentration in the
classroom, and increase student and teaching absenteeism. Moreover, DALY
is a good instrument for educational attainment because it is
influential for life expectancy and individuals who are expected to live
longer are likely to invest more in schooling than those with a shorter
life expectancy because the returns from investment in schooling are
spread over a longer life span. Bils and Klenow (2000) show formally
that there is a one-to-one relationship between the optimal years of
schooling and years of expected life.
DALY due to communicable, maternal, perinatal, and nutritional
diseases is not likely to be influenced by growth because they are,
essentially, driven by pathogen stress. Guernier, Hochberg, and Guegan
(2004) show that pathogen stress is determined by ecology and that
parasitic and infectious diseases are particularly widespread in the
tropics. Helminth (all kinds of parasitic worms) and vector-borne
diseases, for example, are much more widespread in the tropics than the
temperate zones and these diseases are responsible for the high DALY in
the tropical countries (Sachs 2001).
Finally, deaths due to communicable, maternal, perinatal, and
nutritional diseases are used as instruments for quality-adjusted
educational attainment for the same reasons as DALY. These two
instruments are highly correlated since they have a large overlap. The
main difference between them is that nonfatal diseases, such as helminth
morbidity, affect DALY but are rarely fatal. Malaria, as a major
parasitic disease, is not always terminal for infected people who have
gained immunity (Sachs 2001). Thus, malaria and helminth are two major
diseases that show up more strongly in DALYs than in EDRs and, at the
same time, are influential for school children's and school
teachers' attendance rates and concentration at school (Sachs
2001). Finally, EDR has the advantage over DALY in that it is not
measured with nearly as large an error as DALY since there is a large
judgmental component associated with the measurement of DALY.
B. Data and Measurement Issues
The variables used to estimate Equation (2) are constructed as
follows. (4) TFP is recovered from the following aggregate production
function: Y = [AK.sup.[alpha]][(HL).sup.1-[alpha]], where Y is the real
GDP: K, the real physical capital stock; L. the total labor force; H,
the quantity of schooling; and [alpha], the share of capital in total
output. TFP (A) is thus measured as y/[k.sup.[alpha]] [H.sup.1-[alpha]],
where y is the output per worker (Y/L), and k is the capital per worker
(K/L). Quantity of schooling, H is computed as: exp([theta] x SCH),
where SCH is the educational attainment, defined as the average years of
schooling among the population aged 15 years and above, and [theta] is
the returns to schooling, which is usually set at 0.07 in the literature
(see, e.g., Jones 2002). However, in light of the previous findings of
Psacharopoulos and Patrinos (2004) and Henderson, Polachek, and Wang
(2011) that these returns vary significantly across countries, we follow
their approach and allow the returns to schooling to vary across
countries using the estimates of Bils and Klenow (2000) and
Psacharopoulos and Patrinos (2004). The dataset of Barro and Lee (2010)
is used for educational attainment because it has the broadest coverage
for the available data on educational attainment, noting that this
latest version of their dataset has accommodated the problems in their
previous one (i.e., Barro and Lee 2001) highlighted by Cohen and Soto
(2007). The results are almost identical if alternative datasets are
used (see Appendix A).
Capital's income share ([alpha]) is allowed to vary across
countries. Most of our estimates for a are extracted from Gollin (2002)
and Caselli and Feyrer (2007), where preference is given to the latter
for overlapping countries. The missing values of [alpha] are measured as
the predicted values from regressing capital income shares on real per
capita GDP for available countries. (5) Capital stock is constructed
using the perpetual inventory method with a 5% rate of depreciation,
following Bosworth and Collins (2003). The initial capital stock is
estimated as [I.sub.0]/([delta] + g), where [I.sub.0] is the initial
real investment, [delta], the rate of depreciation, and g, the
steady-state rate of investment growth.
Two educational quality composite indicators, namely output and
input, are derived based on the method of principal component analysis.
The results presented throughout the article are based on the
educational quality output measure. Analyses that involve the
educational quality input measure are relegated to the robustness
section. The principal component analysis is an approach that is often
used to reduce a large set of correlated variables into a smaller set of
uncorrelated variables, known as principal components. The first
principal component is chosen as it is able to account for most of the
variation in the data and, therefore, captures most of the information
from the different measures capturing various aspects of educational
quality.
The output indicator of the quality of education consists of the
following indicators: nonrepetition rates at the primary and secondary
levels, test scores in mathematics, science and reading at the primary
and secondary levels, and the number of universities per worker listed
in the ARWU's top 500 rankings. Nonrepetition rates capture the
quality of teaching in the sense that students who do not meet the
national standards will be required to repeat classes. Test scores
capture the quality of teaching directly by measuring student
capabilities. Hanushek and Kimko (2000) and Hanushek and Woessmann
(2008) advocate test scores as the preferred measures over other quality
indicators of education such as teacher-pupil ratio and per capita
expenditure on education. The shortcoming of the scoring measures is
that the cognitive abilities of students entering school are influenced
by parents' stimulation of children during their upbringing, which
in turn is likely to vary substantially across countries (Hanushek and
Woessmann 2012). It is well known that parents with fewer children spend
more resources on stimulating children than parents with more children
(Galor and Weil 2000).
University ranking is used as a proxy for the quality of teaching
because high ranking universities require high entrance qualification
scores, which can only be satisfied in countries with good quality
teaching. Furthermore, countries with good universities tend to produce
high quality teachers. The Shanghai Jiao Tong University's Academic
Ranking of World Universities is used here. By ranking the top 500
universities it provides information for a substantially larger sample
of countries than any other international university ranking system. Its
ranking indicators include alumni and staff winning Nobel Prizes and
Field Medals, highly cited researchers, articles published in Nature and
Science, articles indexed in major citation indices (e.g., the Science
Citation Index-Expanded and Social Science Citation Index), and the per
capita academic performance of an institution.
Following Card and Krueger (1992), Lee and Barro (2001), and
Sequeira and Robalo (2008), we use the teacher-pupil ratio at the
primary and secondary levels and the ratio of real public educational
expenditure per student to real per capita GDP at the primary,
secondary, and tertiary levels as the input measures of educational
quality. These indicators reflect the quality of schooling through
resources allocated to each student. They vary substantially across
countries and, as expected, their values appear to be low in many
developing countries. The shortcoming of these measures is that they do
not measure some important dimensions of the quality of teaching, such
as learning to think independently, problem solving, lateral and
creative thinking, and the caliber of teachers.
The scatter plots for the quality-adjusted human capital measure
([PHI]x H) against the growth rate and level of TFP are presented in
Figures 1 and 2, respectively. The graphs show that the level as well as
the growth in TFP is positively related to [PHI]x H. The relationship
between level of TFP and ([PHI]x H) is particularly strong.
In Figure 1, Togo, Zimbabwe and, to some extent, China appear to be
outliers. It is, however, well known that Zimbabwe's recent poor
growth performance has been affected by macroeconomic mismanagement and,
thus, is unrelated to ([PHI]x H). China's TFP growth has been
higher than justified by ([PHI]x H) because the surge in innovative
activity and savings has been highly influential for its growth
experience (Young 2003; Ang and Madsen 2011, 2013). Togo's decline,
which started around 1977, has predominantly been caused by plummeting
prices of its main earnings: cotton (50%), coffee (87%), and cocoa (72%)
where the numbers in parentheses are the decline in the real market
prices of these commodities over the period from 1977 to 2010 (see
Harvey et al. 2010). Thus, the outlier status of Togo, Zimbabwe, and
China is not evidence against the human capital hypothesis, but rather a
reflection of the fact that other factors have also had a forceful
influence on growth rates for these countries. Overall, the figures
suggest a strong positive relationship between productivity and ([PHI]x
H).
DTF for country i is measured as ([TFP.sup.leaders]- [TFP.sup.i])/
[TFP.sup.leaders] in 1970. In contrast to most other empirical studies,
we do not use the United States as the sole technology leader because
many rich countries also adopt technologies developed in frontier
countries outside the United States. Furthermore, poor countries
generally do not make use of the frontier technology, but rather often
adopt lower level technologies that are developed and used in
middle-income countries (Masters and McMillan 2001; Quah 1996; Sachs
2001). In this context, it is important to note that agriculture is the
most significant production sector in many developing countries and,
therefore, that the transfer of agricultural technology such as
agricultural machinery and new plant varieties are more important for
aggregate economic outcomes than transfers of manufacturing technology
for these countries. Since high-yielding crops developed in the
temperate zones cannot generally be adapted to tropical climates, and
vice versa (Sachs 2001), the technology leader among developing tropical
countries is more likely to be located in the tropical or sub-tropical
zone.
[FIGURE 1 OMITTED]
The approach used here to differentiate the reference technology
leader is consistent with the "twin peaks" proposition of Quah
(1996), who argues that countries tend to polarize into twin peaks of
rich and poor, thus converging toward their own convergence clubs. Using
advanced econometric techniques Bianchi (1997), Henderson, Parmeter, and
Russell (2008), and Pittau, Zelli, and Johnson (2010) find evidence in
favor of the presence of polarization and clubs formation in the
distribution of income across countries as hypothesized by Quah (1996).
Moreover, Masters and McMillan (2001) find that temperate countries have
converged to high levels of income while tropical countries have
converged toward income levels associated with economic scale and the
extent of the market.
Following this discussion, the total sample of 60 countries is
split into two groups of 30, one with the higher and the other the lower
per capita GDPs in 2010, under the assumption that the two have
different technology leaders. An alternative classification based on
income data in 1970 is used as a sensitivity check in Section V. The
technological leaders for the high income group consist of the G7
countries (Canada, France, Germany, Italy, Japan, the United Kingdom,
and the United States), which are the major technology-producing
countries in the world. Brazil, Bulgaria, the Dominican Republic,
Mexico, and Turkey, which are all in the low-income group in per capita
GDP terms, are used as the reference technology frontier group for the
low-income countries. These five nonoil and noncommodity-based countries
are also those with the highest TFP levels over the entire sample period
(using the latest TFP data yields the same ranking) in the low-income
group.
IV. EMPIRICAL RESULTS
Table 1 presents the estimates of Equation (2) where the quality of
education is measured by the first principal component of our output
measures, teaching quality. Consider first the ordinary least squares
(OLS) estimates in column (1). Consistent with the predictions of the
extended Nelson and Phelps (1966) model, the coefficients of
quality-adjusted human capital ([PHI]x H) and its interaction with the
technology gap ([PHI]x H x DTF) are both found to be highly significant
and have the right sign. Consequently, quality-adjusted educational
attainment has both direct growth effects through the [PHI]x H -term and
indirect growth effects through facilitating the adoption of
technologies developed by the reference frontier countries. A
nonfrontier country will continue to benefit from the technologies
developed by the frontier countries until it eventually catches up. In
steady state, a nonfrontier country will grow at a rate that is
determined by the weighted average of quality-adjusted educational
attainment and the productivity growth rate of the frontier countries.
[FIGURE 2 OMITTED]
The parameter estimates are almost unaltered when control variables
are included in the regressions (column (2)). Among them, the investment
ratio and the inflation rate are statistically significant and of the
right signs and these results prevail in all remaining regressions in
Table 1. Since the output effects of capital accumulation are already
accounted for in the TFP estimates, the significance of the investment
ratio suggests that there are positive productivity externalities to
investment or that the economies have not yet converged to their steady
state following a shock to the investment ratio. Inflation suppresses
productivity growth, indicating that macroeconomic mismanagement is
growth abating. Finally, the effects of foreign direct investment inflow
and openness to international trade are insignificant in all
regressions.
Different combinations of instruments are used for quality-adjusted
educational attainment and its interaction with the initial DTF in the
regressions in columns (3)-(5). The Wu-Hausman tests reject the null
hypothesis of exogeneity of quality-adjusted human capital at
conventional significance levels, suggesting that the instrumental
variable technique is appropriate. The F-tests of excluded instruments
in the first-round regressions exceed 18 in all cases, suggesting that
the instruments are sufficiently correlated with quality-adjusted
educational attainment and its interaction with DTF to serve as good
instruments.
Consider the regression in column (3) in which quality-adjusted
educational attainment and its interaction with DTF are instrumented
using EDR and their interactions with DTF as instruments. In line with
the OLS results, quality-adjusted educational attainment and its
interaction with DTF are found to be significantly positive determinants
of productivity growth. This finding remains unchanged when EDR is
replaced with DALY (column (4)) or when DALY is added as an additional
instrument (column (5)). Finally, the estimated coefficients are higher
in the IV than the OLS estimates, pointing toward an attenuation bias
introduced by measurement errors.
Overall, our results are largely consistent with the results of
Hanushek and Woessmann (2012), who find that the quality of education is
a significant contributor to GDP growth. A remarkable feature of our
results is that quality-adjusted educational attainment has permanent
growth effects; that is, the economies will keep growing as long as
quality-adjusted human capital exceeds a certain level that is
determined by the negative constant term. This implies that there are
scale effects in ideas production and that knowledge creation overcomes
the force of diminishing returns to the factors of production. Economies
will experience permanent growth effects from investment in
quality-adjusted educational attainment. These results go beyond the
predictions of the human capital-based extended Solow growth model and
semi-endogenous growth models in which human capital has only transitory
growth effects.
One drawback of the parameter estimates presented in Table 1 is
that one cannot read the economic significance of the coefficients of
quality-adjusted educational attainment and its interaction with DTF. To
ease the interpretation of the parameter estimates, Table 2 shows the
implied growth effects of changes in the quality or quantity of human
capital from the baseline regression (column (5) of Table 1). Note that
H and [PHI] are each normalized to be in the interval between 0 and 1.
Consider column (1), which shows the partial derivatives of TFP growth
with respect to quality ([PHI]) or quantity (H) of education without
considering their absorptive capacity (i.e., DTF is set to zero).
Suppose an average country that has accumulated 0.6 units of educational
attainment (H = 0.6) experiences an improvement in the quality of
teaching ([DELTA][PHI]) by 0.5 units, then its TFP growth rate is
predicted to increase by 0.39% points. The same result applies to a
country with [PHI] = 0.6 that experiences an increase in H by 0.5 units.
These results are plausible in the sense that a marked increase in the
quality or quantity of human capital is required to gain a permanently
higher productivity growth rate of 0.39% points.
The growth effects of the interaction between quality-adjusted
educational attainment and DTF are displayed in the next three columns
in Table 2. For the average country (H or [PHI] = 0.6) that has half of
the TFP of the reference leader country, its productivity growth rate
will increase by 0.47% points following an increase in [PHI] or H by
0.5. This growth effect is plausible. However, for a poor country that
is very distant from the frontier (DTF = 0.9) and which has an H or
[PHI] of 0.2, the effects of increasing [PHI] or H by 0.5 is a mere
0.18% points gain in growth, which shows that being distant from the
reference frontier is not a sufficient condition for benefitting from
transfers of technologies developed at the frontier.
Finally, following from the multiplicative nature of H and [PHI] in
the computation of quality adjusted educational attainment and its
interaction with DTF, the growth effects of increases in either H or
[PHI] are increasing functions of [PHI] and H, respectively. Thus, the
returns from enhancing human capital are highest in highly educated
societies--an issue we will elaborate on in the extensions and
robustness tests in the next section. This result may not seem plausible
in light of the standard assumption of diminishing returns to factors of
production. However, looking at the test scores across countries, these
results do make sense. Since test scores are progressive in design it is
much harder to improve the scores from 500 to 600 than from 100 to 200
in the PISA tests. Similarly, lower grade teaching is much less
intensive than higher grade teaching. Hence, the results following from
the multiplicative nature of H and [PHI] are quite plausible.
V. EXTENSIONS AND ROBUSTNESS TESTS
Thus far the results have been based on certain output-related
measures of quality of teaching, growth rates over a relatively short
time span, the extended Nelson-Phelps model, cross-sectional data, a
certain technology frontier reference group, and a multiplicative
relationship between H and [PHI]. Furthermore, innovations and
institutional quality and unobserved regional heterogeneity have not
been controlled for in the regressions. These considerations are catered
for in this section. Following the benchmark model in the last column of
Table 1. DALY and EDR are used as instruments in all regressions below.
Moreover, except for the regression based on the Mankiw-Romer-Weil
model, all control variables are included in the regression.
A. Using Input Measures of Quality
To ensure that our results are not driven by the choice of
educational quality measures, the quality of human capital is also
measured as the first principal component of two input measures, namely
the teacher-pupil ratio at the primary and secondary levels and the
ratio of real public educational expenditure per student to real per
capita GDP at the primary, secondary, and tertiary levels, to provide a
sensitivity check of the results. As shown in column (1) in Table 3, the
coefficients of quality-adjusted educational attainment and its
interaction with DTF are both significant and of the right sign. These
results are consistent with our baseline results.
B. Alternative Measures of Educational Quality
The regressions in columns (2) and (3) in Table 3 use the data of
Hanushek and Kimko (2000) and Hanushek and Woessmann (2012) as
alternative measures of educational quality. Their data are constructed
using test scores in mathematics and science. The coefficients of
quality-adjusted educational attainment and its interaction with DTF
remain significant--a result that reinforces the findings above that the
results are not very sensitive to the measurement of schooling quality
and that quality-adjusted educational attainment is a good measure of
human capital.
C. Functional Relationship Between Quality and Quantity
A multiplicative relationship between the quality and quantity of
schooling has been assumed in the previous analyses. This implies that
the growth effect of [PHI] is positively related to H and, hence, that
the highest growth effect of quality will be achieved for high values of
educational attainment. Measuring the interaction between quality and
quantity, instead, by ln([PHI]x H) yields insignificant coefficients of
quality-adjusted human capital (results are not shown), suggesting that
the growth effects of a change in [PHI] are not inversely related to H
or vice versa. The following alternative functional forms are considered
in columns (4)-(6) in Table 3: [PHI][e.sup.H], [e.sup.[PHI]]H, and
[e.sup.[PHI]][e.sup.H]. The coefficients of quality-adjusted educational
attainment are all significant at conventional levels. From the baseline
regressions and the results in this subsection, it can be concluded that
the growth effects of [PHI] (H) are unambiguously increasing functions
of H ([PHI]). What the best exact functional form is, however, cannot be
determined from the relatively small sample used here.
D. Individual Effect of Education Quantity
To assess the importance of adjusting for its quality, human
capital is measured as the quantity of human capital (H). The results,
which are reported in column (7) in Table 3, show that in this case the
coefficient of human capital quantity is only significant at the 10%
level; thus much less precisely estimated than the case where it is
adjusted for educational quality. Moreover, its interaction with
distance to the frontier loses significance at conventional significance
levels. These results give support to our approach that it is essential
to account for the quality of education in the assessment of the effects
of human capital on productivity growth.
E. The Mankiw-Romer-Weil Model
The estimates have so far been based on the extended Nelson-Phelps
model. We consider below a slightly modified model of Mankiw, Romer, and
Weil (1992) to investigate whether the results are robust to the
neoclassical specification. Specifically, production is given as:
[Y.sub.it] = [[K.sup.[alpha]].sub.it][e.sup.[beta][PHI]H.sub.it][(AL).sup.1-[alpha]-[beta].sub.it] (3)
The above equation differs from the production function of Mankiw
et al. (1992) only to the extent that we adjust human capital for
quality and assume that the returns to one additional year of schooling
is independent of the existing years of schooling. Incorporating
Equation (3) into the model of Mankiw et al. (1992) yields the following
dynamic growth model:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
where [lambda] is the sjteed of convergence toward steady state;
[g.sup.Y/L.sub.i], the average growth rate of real GDP per worker over
the period 1970-2010; [(Y/L).sub.1970], the initial income per worker;
(I/Y), the investment ratio; ", the population growth rate; g, the
rate of technological progress; and [delta], the rate of depreciation.
Equation (4) is the standard dynamic Solow model in which growth is
positively related to investment and human capital in the transitional
path from one steady state to the other while population growth hampers
economic growth through capital dilution.
Allowing for the interaction between human capital and DTF (note
that the results are almost unaltered if the interaction term is omitted
from the regressions) yields the following unrestricted counterpart of
Equation (4)
(5)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where (g + [delta]) is assumed to be 5%, following Mankiw et al.
(1992).
Column (8) in Table 3 presents the results for regressing the above
equation without imposing any restrictions. It is evident that the
estimates are consistent with the extended Nelson-Phelps growth model in
which quality-adjusted educational attainment and its interaction with
DTF are the important drivers of growth. Furthermore, the coefficients
of the investment ratio and initial income are both significant and of
the right sign, indicating that income is converging toward its steady
state and that the variations in investment have positive growth
effects.
A problem associated with the unrestricted regression of Equation
(5), however, is that the coefficients cannot be held up against the
theoretical predictions of Equation (4) because the model is not
identified. To identify the parameters of the Solow growth model we need
to impose the restriction of constant returns to scale. Doing so yields
the results in the last column of Table 3. Unfortunately, the
restriction of constant returns to scale (i.e., [b.sub.1] + [b.sub.4], =
[b.sub.5]) is strongly rejected at the conventional significance levels
(F (1, 52) = 12.53, p = .0009). Thus, the parameter estimates of the
restricted model need to be taken with a pinch of salt. Recovering the
scale coefficients from the estimates in the last column of Table 3
using Equation (4) yields [alpha] = .21 and [beta] = .79, which are
quite plausible, thus giving support to the Solow growth model extended
to allow for quality-adjusted human capital and its interaction with
DTF.
F. Panel Data Estimates
So far we have only exploited the crosssectional variations in the
data, following the common practice in the literature. Consequently, the
variations identified are only between countries but not across time. To
address this concern, the model is also estimated in 20-year differences
using a fixed effect panel estimator, and an IV-GMM panel estimator as
well as the system GMM dynamic panel estimator. The results reported in
columns (1)--(3) in Table 4 suggest that our previous findings prevail,
in that both quality-adjusted human capital and its interaction with the
technology gap are significant determinants of productivity growth.
G. Long Historical Growth Rates
An issue that plagues almost all cross-country growth regressions
is that the growth rates typically span a period of 30-40 years from
1960, but such a short period may not be representative of the growth
histories of the countries involved in the regressions. Countries go
through long phases of low and high growth. Many South American nations
and the Philippines, for example, had comparatively high growth rates
before World War II, but lost momentum thereafter. Most of the Asian
miracle economies, by contrast, experienced dismal growth rates up until
the mid-20th century and subsequently experienced spectacular growth
rates. Unfortunately, we cannot overcome this problem by measuring the
dependent variable in levels since the theory says that quality-adjusted
educational attainment influences growth rates and not the level of
income. To overcome this problem, the per capita growth rates over the
period 1820-2008 are used as the dependent variable--a variable that
captures the essentials of modern growth history, noting that per capita
income was close to the subsistence level for almost all the countries
in the world around 1820. Although quality-adjusted educational
attainment in the period 1970-2008 may not have been representative for
the entire period 1820-2008, a lot of the variation in the regressors is
driven by DALY and EDR as instruments and it is not unreasonable to
assume that the ranking of these variables between countries has been
relatively constant over time.
The estimation results of these long regressions are displayed in
column (4) in Table 4. The coefficients of quality-adjusted human
capital and its interaction with DTF are remarkably significant,
suggesting that per capita income growth in the poor countries over the
past two centuries has been impaired by insufficient quality-adjusted
educational attainment. Since education in turn has been influenced by
pathogen stress that has resulted in a large number of years lost due to
ill-health, disability, and early death, the results here give insight
into a potential channel through which geography influences growth and
why tropical countries tend to be the poorest in the world.
H. Controlling for Institutional Quality and Innovations
The quality of institutions and per worker publications of
scientific and technical journal articles are included as additional
control variables in the regressions in columns (5) and (6),
respectively, to address the critique of Bosworth and Collins (2003) and
Chen and Luoh (2010). They find that the quality of teaching becomes
insignificant for growth once institutions and scientific journal
publications are allowed for. The quality of institutions is measured by
the POLITY index, which consists of a number of authority characteristic
component variables, including regulation of chief executive
recruitment, competitiveness of executive recruitment, openness of
executive recruitment, executive constraints, regulation of
participation, and competitiveness of participation. The POLITY index,
which has a scale ranging between -10 (strongly autocratic) and +10
(strongly democratic), differs from the index used by Bosworth and
Collins (2003), who use the International Country Risk Guide (ICRG)
institutional quality data. These data are not used here because they
are only available from 1984 (see Knack and Keefer 1995), whereas the
POLITY data cover the whole sample period considered here. However, the
principal results remain unaltered if data from the ICRG are used (the
results are not shown). Scientific journal publications are measured as
the number of scientific and engineering articles published in physics,
biology, chemistry, mathematics, clinical medicine, biomedical research,
engineering and technology, and earth and space sciences.
As is evident from the regressions in columns (5) and (6), the
principal findings in this article are robust to the inclusion of POLITY
and scientific or technical journals per worker, thus overcoming the
Bosworth and Collins (2003) and Chen and Luoh (2010) critique. The
results prevail if both variables are included in the same
specification. The coefficients of quality-adjusted educational
attainment and its interaction with DTF are statistically significant in
both cases. The coefficients of POLITY and scientific journals per
worker are insignificant. This need not mean that these variables are
unimportant for prosperity. The quality of institutions has been found
to be an important determinant of the level of per capita income and is
rarely used in growth regressions (see, e.g., Acemoglu, Johnson, and
Robinson 2001; Hall and Jones 1999). Thus, the quality of institutions
may have been important for historical growth rates but not the growth
rates in the period 1970-2010. The insignificance of the coefficient of
scientific journals may reflect the fact that (1) scientific journals
may not be good proxies for innovative activity because they do not
measure the research activity that is undertaken in the private sector
and (2) scientific journals are predominantly published in the
Anglo-Saxon countries.
I. Using an Alternative Distance to the Frontier Measure
Our results may be sensitive to the selection of leaders and to the
classification of countries between the two groups. For example, it is
possible that Brazil, Bulgaria, the Dominican Republic, Mexico, and
Turkey that we chose as leaders for the low-income group, could have
been converging to the G7 leaders. To ensure that the results are not
driven by the classifying of the countries using income data in 2010, we
reclassify the countries based on income in 1970 and select only five
leaders. In this case, the chosen leader countries in the developing
group are Brazil, Chile, the Dominican Republic, Malaysia, and Turkey.
Column (7) in Table 4 shows that our results still hold even if this
alternative classification based on initial income is used.
J. Including Regional Dummies
Next, we include several regional dummies to ensure that the
relationship between quality adjusted education and TFP growth that we
have found so far is not affected by the correlation between education
and some unobserved heterogeneous effects. Following the approach of
Temple (1998) and Temple and Woessmann (2006), regional dummies for
sub-Saharan Africa, non-OECD East Asia and the Pacific, Latin America
and the Caribbean, and the high-income OECD countries are included in
the regression in column (8) in Table 4. The results we have obtained so
far remain largely unchanged when these regional dummies are included in
the regression. This result is more robust than that found by Hanushek
and Woessmann (2012) in which the size of their schooling quality
coefficient reduces somewhat when regional dummies are added to the
specification. Thus, our results are not subject to the critique of
Temple (1998), who shows that the positive effect of schooling on growth
found in Mankiw et al. (1992) disappears once regional fixed effects are
controlled for. Instead, our results are consistent with Temple and
Woessmann (2006), whose results are also robust to the inclusion of
regional dummies.
K. Considering Alternative Measures of TFP
The quality of schooling has so far not been used as an input in
our calculation of the TFP measure since we do not have estimated
returns for educational quality. The omission of education quality may
affect the measurement of TFP and the distance to the frontier variable
and therefore bias our results. To cater for the role of schooling
quality we assume that the returns to T are the same as the returns to
H. Furthermore, it is also assumed that the returns to [PHI] and H are
constant across countries. Columns (9) and (10) in Table 4 report the
estimates. As is evident, our principal results are not driven by these
considerations.
L. Effects of Each Level of Educational Attainment on Growth
Thus far we have used total educational attainment and one
composite measure of the quality of teaching. Educational attainment is
disaggregated into primary, secondary, and tertiary education in the
regressions in Table 5. The test scores at grade 4 are used as teaching
quality measures for primary education, the test scores at grade 8 are
used for secondary schooling, and university rankings are used for the
quality of teaching at the tertiary level. Each level of education is
entered separately into each individual regression because the common
sample in some cases is only 20 observations when mathematics, science,
and reading are considered jointly.
The regressions show that quality-adjusted educational attainment
and its interaction with DTF at any educational level are statistically
significant determinants of growth. Considering the different dimensions
of teaching quality it is notable that the growth effects of reading
skill scores are no lower than the growth effects of scores in
mathematics and science. This result is remarkable because scores in
mathematics and science are often considered to be essential for growth
(Hanushek and Kimko 2000; Hanushek and Woessmann 2008), presumably
because productivity growth, in steady state, is driven by product and
process innovations that are outcomes of R&D activities done by
researchers with a background in science or engineering. There are two
reasons why reading skills are influential for growth. First, scores in
science, mathematics, and reading are highly correlated. Thus, we would
expect the growth outcome to be quite similar for the three score
dimensions.
Second, reading scores are essential for communication and
coordination. Poor reading skills may result in a breakdown of
coordination and the more people involved in an interlinked production
process with bad reading and communication skills, the more likely it is
that a production breakdown will occur. As shown by Kremer (1993), skill
complementarities are important in producing O-Ring forms of fragile,
delicate output. Small differences in worker skills may cause marked
differences in cross country productivities because weak links in the
production process can have large macro effects. Kremer (1993) begins
with a seemingly obvious point: looking around at common forms of rich
country economic output, he notes that often one small error in the
production process can drastically destroy the value of the final
output. After all, in an O-Ring world, lower worker quality means
multiplicative increases in errors across the spectrum of production.
Considering the coefficients of quality adjusted primary,
secondary, and tertiary education, the coefficients are approximately
the same across levels of education, thus supporting the Mincerian-type
earning functions in which the returns to education are the same for all
its levels. Hence, it is not the logs but the levels of education that
are relevant in growth regressions. The coefficients of the interaction
terms are 0.001-0.002 for primary education, 0.002-0.007 for secondary
education, and 0.042 for tertiary education, implying that they are
increasing functions of the levels of quality adjusted education. This
result is intuitive in the sense that workers with better quality and
higher levels of education are more able to use and develop the
technology that is developed at the frontier countries than otherwise.
VI. CONCLUDING REMARKS
Empirically it has been difficult to find a positive relationship
between educational attainment and growth (Delgado et al. 2013). In this
article, we argue that one reason for the absence of a robust
relationship between growth and educational attainment is that
educational attainment measures only the quantity dimension of human
capital and, as such, suppresses the quality dimension of educational
attainment. To overcome this deficiency, we measure human capital as
quality-adjusted educational attainment. Furthermore, in contrast to
almost all other studies, we use instruments for quality-adjusted
schooling, acknowledging that educational attainment is likely to be
particularly endogenous in cross-sectional studies since the resources
that are available for the quality as well as the quantity of schooling
depend on past and current growth rates. Furthermore, the returns to
education depend on expected growth rates. Deaths and life years lost
due to communicable diseases were used as instruments because they were
highly correlated with quality-adjusted educational attainment and
because they were likely to satisfy the identifying restriction that the
disease environment influences growth through quality-adjusted
education.
The results gave consistent support for the hypothesis that
quality-adjusted human capital and its interaction with the technology
gap are essential for growth. The results are robust to different
combinations of instruments, different measures of the quantity and
quality of human capital, inclusion of control variables, alternative
estimation periods, inclusion of regional dummies, alternative measures
of productivity, and different model specifications. Furthermore, we
found that the social returns to the quality (quantity) of schooling are
increasing functions of the quantity (quality) of schooling and this
relationship is robust to variations in the functional relationship
between quality and quantity in the regressions. The significance of
this result is that the returns to investing in quality teaching are
highest in the countries with the longest years of education, thus
suggesting that it is difficult for countries with low education to
overcome their development trap.
ABBREVIATIONS
DALY: Disability-Adjusted Life Year
DTF: Distance to the Frontier
EDR: Estimated Death Rate
GDP: Gross Domestic Product
GMM: Generalized Method of Moments
ICRG: International Country Risk Guide
OLS: Ordinary Least Squares
PCA: Principal Component Analysis
PWT: Penn World Table
TFP: Total Factor Productivity
TIMSS: Trends in International Mathematics and Science Study
doi:10.1111/e.cin 12052
APPENDIX A
Alternative Measures of Educational Attainment
The results in the main body of the paper are based on the
educational attainment data of Barro and Lee (2010). The results in
Table Al are based on the following alternative data sources on
educational attainment: Baier, Dwyer, and Tamura (2006), Cohen and Soto
(2007) and Lutz et al. (2007). Furthermore, Barro and Lee's (2010)
data on educational attainment for the population aged 25 years and
above are considered, noting that the data used in the main text refer
to the population aged 15 years and above. In terms of significance and
the size of the coefficients, the results are very similar to the
baseline results in column (5) of Table 1. These results reinforce the
results in the main text that quality-adjusted educational attainment
and its interaction with distance to the frontier are significant
determinants of productivity growth.
APPENDIX B
Sources of Data
TFP: K, L, and Y are calculated from the 7.0 version of the Penn
World Table (see http://pwt.econ.upenn.edu/php_site/pwt_index.php).
Capital stock is computed using the perpetual inventory method with a 5%
rate of depreciation. The initial capital stock is estimated as
[I.sub.0]/([delta] + g), where [I.sub.0] is the initial real investment
and g the steady-state rate of investment growth. PWT 7.0 data are
available till 2009 and therefore, required data for final year (2010)
have been spliced with available data in the 2011 World Development
Indicators online database
(see http://databank.worldbank.org/ddp/home.do?Step=
12&id=4&CNO=2).
H: "Quantity of human capital (H)" is measured by the
average years of schooling for the population aged 15 or 25 years and
above. It is compiled from four different sources: (1) Barro and Lee
(2010) (see http://www.barrolee.com/), (2) Cohen and Soto (2007) (see
http://soto.iae-csic.org/Data.htm), (3) Lutz et al. (2007) (see
http://www.iiasa.ac.at/Research/POP/edu07/index.html7sbs 11), and (4)
Baier et al. (2006) (see http://www.jerrydwyer.com/growth/index.html).
Lutz et al. (2007) and Baier et al. (2006) school attainment data are
available till 2000 and hence those schooling data are extrapolated from
2001 to 2010.
[PHI]: "Quality of human capital ([PHI])" is measured by
two schooling input and five schooling output variables. The input
variables include: (1) teacher-pupil ratio and (2) real public
educational expenditure per student/real per capita GDP. The output
variables consist of (1) the rates of nonrepetition, (2) test scores in
mathematics, (3) test scores in science, (4) test scores in reading, and
(5) number of universities per million workers listed in ARWU's top
500 ranking. Data on educational input and output variables except
university ranking are compiled from Lee and Barro (2001) for 1970-1990.
Those data have been extended by Altinok and Murseli (2007) from 1991 to
1999. Data from 2000 to 2010 have been compiled from UNESCO Institute
for Statistics (see http://stats.uis.unesco.org/unesco/tableviewer/document.aspx?ReportId=143); Institute of Education Sciences for TIMSS (see
http://nces.ed.gov/timss/); and PISA database (see
http://pisa2009.acer.edu.au/multidim.php). ARWU's top 500 ranking
universities' data are obtained from "Academic Ranking of
World Universities (ARWU)" (2003-2010) published by the Shanghai
Iiao Tong University (see http://www.arwu.org).
Control Variables: Data on "the rate of inflation"
(measured as the growth rate of CPI), "trade openness"
(measured as the sum of total exports and imports over GDP), "the
ratio of FD1 inflows to GDP," and "scientific and technical
journal articles" from 1970 to 2010 are taken from the 2011 World
Development Indicators online database (see
http://databank.worldbank.org/ddp/home.do?Step=12&id= 4&CNO=2).
Data on "the ratio of investment to GDP" are compiled from the
7.0 version of the Penn World Table (PWT 7.0) (see
http://pwt.econ.upenn.edu/php_site/pwt_index.php). POLITY data are
obtained from the "Polity IV project" of the University of
Maryland (see http://www.systemicpeace.org/polity/polity4.htm).
Instrumental Variables: Data on "the estimated death rates per
100,000 population (EDR)" and "the disability-adjusted life
years per 100,000 population (DALY)" have been collected from the
World Health Organization's Global Health Observatory Data
Repository (see http://apps.who.int/ghodata/). These data are available
for 2002 and 2004 and thus their average values have been considered in
the empirical estimation.
Other Variables: Data on "Per Capita GDP" (1990
International Geary-Khamis dollars) over the period 1820-2008 are
collected from Statistics on World Population, GDP and Per Capita GDP,
1-2008 AD available at Angus Maddison's homepage (see
http://www.ggdc.net/MADDISON/oriindex.htm).
TABLE A1
Alternative Measures of Educational Attainment
(1) Barro
and Lee (2010), (2) Cohen and
[greater than Soto (2007),
H is measured using or equal to] [greater than or
sources from: 25 years equal to] 15 years
[PHI] x H 0.013 *** 0.007 ***
(6.299) (3.543)
[PHI] x H x DTF 0.005 *** 0.005 ***
(3.168) (3.080)
No. of observations 60 55
R-squared 0.403 0.469
Diagnostic Tests
Hansen test (p value) 0.246 0.149
C-test ([PHI] x H) 0.882 0.369
instruments (p value)
C-test ([PHI] x H x DTF) 0.193 0.172
instruments (p value)
Endogeneity-test (p value) 0.028 0.077
1st-stage F-statistic 23.331 46.034
1st-stage F-statistic 32.660 31.871
([PHI] x F x DTF)
1st-stage [R.sup.2] 0.839 0.880
([PHI] x H)
1st-stage [R.sup.2] 0.896 0.896
([PHI] x H x DTF)
(3) Cohen and (4) Lutz et al.
Soto (2007), (2007), [greater
H is measured using [greater than or than or equal
sources from: equal to] 25 years to] 15 years
[PHI] x H 0.007 *** 0.013 ***
(3.500) (5.419)
[PHI] x H x DTF 0.005 *** 0.005 ***
(2.938) (3.074)
No. of observations 55 54
R-squared 0.463 0.388
Diagnostic Tests
Hansen test (p value) 0.145 0.253
C-test ([PHI] x H) 0.393 0.636
instruments (p value)
C-test ([PHI] x H x DTF) 0.163 0.140
instruments (p value)
Endogeneity-test (p value) 0.093 0.047
1st-stage F-statistic 46.711 22.682
1st-stage F-statistic 24.720 53.490
([PHI] x F x DTF)
1st-stage [R.sup.2] 0.881 0.793
([PHI] x H)
1st-stage [R.sup.2] 0.890 0.899
([PHI] x H x DTF)
(5) Lutz et al. (6) Baier et al.
(2007), [greater (2006), [greater
H is measured using than or equal than or equal
sources from: to] 25 years to] 15 years
[PHI] x H 0.013 *** 0.013 ***
(5.390) (7.523)
[PHI] x H x DTF 0.005 *** 0.007 ***
(2.961) (3.552)
No. of observations 54 59
R-squared 0.381 0.447
Diagnostic Tests
Hansen test (p value) 0.246 0.256
C-test ([PHI] x H) 0.637 0.483
instruments (p value)
C-test ([PHI] x H x DTF) 0.125 0.112
instruments (p value)
Endogeneity-test (p value) 0.042 0.028
1st-stage F-statistic 20.101 29.861
1st-stage F-statistic 40.310 58.170
([PHI] x F x DTF)
1st-stage [R.sup.2] 0.784 0.859
([PHI] x H)
1st-stage [R.sup.2] 0.890 0.896
([PHI] x H x DTF)
Note: Baier et al. (2006) do not provide data on average years of
schooling for population aged 15 years and over. [PHI] is the
quality of human capital measured by PCA extracted educational
output. DALY and EDR are used as instruments for quality-adjusted
educational attainment and its interaction with DTF. All
regressions include trade openness, FDI inflows/GDP. inflation rate
and investment ratio as control variables.
* Significant at 10%; ** Significant at 5%; and *** Significant at
1%. See also notes in Table 1.
REFERENCES
Acemoglu, D., S. Johnson, and J. A. Robinson. "The Colonial
Origins of Comparative Development: An Empirical Investigation."
American Economic Review, 91, 2001, 1369-401.
Altinok, N.. and H. Murseli. "International Database on Human
Capital Quality." Economics Letters, 96, 2007, 237-44.
Ang, J. B., and J. B. Madsen. "Can Second-Generation
Endogenous Growth Models Explain Productivity Trends and Knowledge
Production In the Asian Miracle Economies?" Review of Economics and
Statistics, 93, 2011, 1360-73.
--. "International R&D Spillovers and Productivity Trends
in the Asian Miracle Economies." Economic Inquiry, 51, 2013,
1523-41.
Ang, J. B., J. B. Madsen, and M. R. Islam. "The Effects of
Human Capital Composition on Technological Convergence." Journal of
Macroeconomics, 33, 2011, 465-76.
Baier, S. L., G. P. Dwyer, and R. Tamura. "How Important Are
Capital and Total Factor Productivity for Economic Growth?"
Economic Inquiry, 44, 2006, 23-49.
Barro, R. J. "Economic Growth in a Cross Section of
Countries." Quarterly Journal of Economics, 106, 1991, 407-43.
--. "Human Capital and Growth." American Economic Review,
91, 2001, 12-7.
Barro, R. J., and J. W. Lee. "International Data on
Educational Attainment: Updates and Implications." Oxford Economic
Papers, 53, 2001, 541-63.
--. "A New DataSet of Educational Attainment in the World,
1950-2010." NBER Working Paper No. 15902, 2010.
Baum, C. F., M. E. Schaffer, and S. Stillman. "Instrumental
Variables and GMM: Estimation and Testing." The Stata Journal, 3,
2003, 1-31.
Benhabib, J., and M. M. Spiegel. "The Role of Human Capital in
Economic Development: Evidence from Aggregate Cross-country Data."
Journal of Monetary Economics, 34, 1994, 143-73.
--. "Human Capital and Technology Diffusion," in Handbook
of Economic Growth, edited by P. Aghion and S. Durlauf. Amsterdam, The
Netherlands: Elsevier, 2005, 935-66.
Bianchi, M. "Testing for Convergence: Evidence from
Nonparametric Multimodality Tests." Journal of Applied
Econometrics, 12, 1997, 393-409.
Bits, M., and P. J. Klenow. "Does Schooling Cause
Growth?" American Economic Review, 90, 2000 1160-83.
Bosworth, B., and S. M. Collins. "The Empirics of Growth: An
Update." Brookings Papers on Economic Activity, 2, 2003, 180-200.
Card, D., and A. B. Krueger. "Does School Quality Matter?
Returns to Education and the Characteristics of Public Schools in the
United States." Journal of Political Economy, 100, 1992, 1-40.
Caselli, F., and W. J. Coleman. "The World Technology
Frontier." American Economic Review, 96, 2006, 499-522.
Caselli, F., and J. D. Feyrer. "The Marginal Product of
Capital." Quarterly Journal of Economics, 122, 2007, 535-68.
Caselli, F., G. Esquivel, and F. Lefort. "Reopening the
Convergence Debate: A New Look at Cross-Country Growth Empirics."
Journal of Economic Growth, 1, 1996, 363-89.
Chen, S.-S., and M.-C. Luoh. "Are Mathematics and Science Test
Scores Good Indicators of Labor-Force Quality?" Social Indicators
Research, 96, 2010, 133-43.
Cohen, D., and M. Soto. "Growth and Human Capital: Good Data,
Good Results." Journal of Economic Growth, 12, 2007, 51-76.
de la Fuente, A., and R. Domenech. "Human Capital In Growth
Regressions: How Much Difference Does Data Quality Make?" Journal
of the European Economic Association, 4, 2006, 1-36.
Delgado, M. S., D. J. Henderson, and C. F. Parmeter. "Does
Education Matter for Economic Growth?" Oxford Bulletin of Economics
and Statistics, 2013. doi: 10.1111/obes.12025.
Engelbrecht, H. -J. "Human Capital and International Knowledge
Spillovers in TFP Growth of a Sample of Developing Countries: An
Exploration of Alternative Approaches." Applied Economics, 34,
2002, 831-41.
Eppig, C., C. L. Fincher, and R. Thornhill. "Parasite
Prevalence and the Worldwide Distribution of Cognitive Ability."
Proceedings of the Royal Society B: Biological Sciences, 77, 2010,
3801-08.
Galor, O., and D. N. Weil. "Population, Technology, and
Growth: From Malthusian Stagnation to the Demographic Transition and
Beyond." American Economic Review, 90, 2000, 806-28.
Gemmell, N. "Evaluating the Impacts of Human Capital Stocks
and Accumulation on Economic Growth: Some New Evidence." Oxford
Bulletin of Economics and Statistics, 58, 1996, 9-28.
Gollin, D. "Getting Income Shares Right." Journal of
Political Economy, 110, 2002, 458-74.
Griffith, R., S. Redding, and J. V. Reenen. "Mapping the Two
Faces of R&D: Productivity Growth in a Panel of OECD
Industries." Review of Economics and Statistics, 86, 2004, 883-95.
Guernier, V., M. E. Hochberg, and J.-F. Guegan. "Ecology
Drives the Worldwide Distribution of Human Diseases." PLOS Biology,
2, 2004, 740-46.
Hall. R. E., and C. I. Jones. "Why Do Some Countries Produce
So Much More Output Per Worker Than Others?" Quarterly Journal of
Economics, 114, 1999, 83-116.
Hanushek, E. A., and D. D. Kimko. "Schooling, Labor-Force
Quality, and the Growth of Nations." American Economic Review, 90,
2000, 1184-208.
Hanushek, E. A., and L. Woessmann. "The Role of Cognitive
Skills in Economic Development." Journal of Economic Literature,
46, 2008, 607-68.
--. "Do Better Schools Lead to More Growth? Cognitive Skills,
Economic Outcomes, and Causation." Journal of Economic Growth, 17,
2012, 267-321.
Harvey, D. I., N. M. Kellard, J. B. Madsen, and M. E. Wohar.
"The Prebisch-Singer Hypothesis: Four Centuries of Evidence."
Review of Economics and Statistics, 92, 2010, 367-77.
Henderson, D. J., and R. R. Russell. "Human Capital and
Convergence: A Production-Frontier Approach." International
Economic Review, 46, 2005, 1167-205.
Henderson, D. J., C. Parmeter, and R. R. Russell. "Modes,
Weighted Modes, and Calibrated Modes: Evidence of Clustering Using
Modality Tests." Journal of Applied Econometrics, 23, 2008, 607-38.
Henderson, D. J., S. W. Polachek, and L. Wang. "Heterogeneity
in Schooling Rates of Return." Economics of Education Review, 30,
2011, 1202-14.
Henderson, D. J., C. Papageorgiou, and C. F. Parmeter. "Growth
Empirics without Parameters." Economic Journal, 122, 2012, 125-54.
Jones, C. "Sources of U.S. Economic Growth in a World of
Ideas." American Economic Review, 92, 2002, 220-39.
Kalaitzidakis, P., T. P. Mamuneas, A. Savvides, and T. Stengos.
"Measures of Human Capital and Nonlinearities in Economic
Growth." Journal of Economic Growth, 6, 2001, 229-54.
Knack, S., and P. Keefer. "Institutions and Economic
Performance: Cross-Country Tests Using Alternative Institutional
Measures." Economics and Politics, 7, 1995, 207-27.
Knowles, S., and P. D. Owen. "Health Capital and Cross-Country
Variation in Income Per Capita in Mankiw-Romer-Weil Model."
Economics Letters, 48, 1995, 99-106.
Kremer, M. "Population Growth and Technological Change: One
Million B.C. to 1990." Quarterly Journal of Economics, 108, 1993,
681-716.
Krueger, A. O. "Factor Endowments and Per Capita Income
Differences among Countries." Economic Journal, 78, 1968, 641-59.
Lee, J. -W., and R. J. Barro. "Schooling Quality in a Cross
Section of Countries." Economica, 68, 2001, 465-88.
Levine, R.. and D. Renelt. "A Sensitivity Analysis of
Cross-Country Growth Regressions." American Economic Review, 82,
1992, 942-63.
Lutz, W., A. Goujon, K. C. Samir, and W. Sanderson.
"Reconstruction of Populations by Age, Sex and Level of Educational
Attainment for 120 Countries for 1970-2000." Vienna Yearbook of
Population Research 2007, 2007, 193-235.
Madsen, J. B. "The Anatomy of Growth in the OECD since
1870." Journal of Monetary Economics, 57, 2010, 753-67.
Madsen, J. B., M. R. Islam, and J. B. Ang. "Catching Up to the
Technology Frontier: The Dichotomy between Innovation and
Imitation." Canadian Journal of Economics, 43, 2010, 1389-411.
Mankiw, G., D. Romer, and D. N. Weil. "A Contribution to the
Empirics of Economic Growth." Quarterly Journal of Economics, 107,
1992, 407-37.
Masters, W. A., and M. S. McMillan. "Climate and Scale in
Economic Growth." Journal of Economic Growth, 6, 2001, 167-86.
Nelson, R. R., and E. S. Phelps. "Investment in Humans,
Technological Diffusion, and Economic Growth." American Economic
Review, 56, 1966, 69-75.
Pittau, M. G., R. Zelli, and P. A. Johnson. "Mixture Models,
Convergence Clubs, and Polarization." Review of Income and Wealth,
56, 2010, 102-22.
Pritchett, L. "Measuring Outward Orientation in Developing
Countries: Can It Be Done?" Journal of Development Economics, 49,
1996, 307-35.
--. "Where Has All the Education Gone?" The World Bank
Economic Review, 15, 2001, 367-91.
--. "Towards a New Consensus for Addressing the Global
Challenge of the Lack of Education." Center for Global Development
Working Paper No. 43, 2004.
Psacharopoulos, G., and H. A. Patrinos. "Returns to Investment
in Education: A Further Update." Education Economics, 12, 2004,
111-34.
Quah, D. T. "Twin Peaks: Growth and Convergence in Models of
Distribution Dynamics." Economic Journal, 106, 1996, 1045-55.
Radelet, S., J. Sachs, and J.-W. Lee. "The Determinants and
Prospects of Economic Growth in Asia." International Economic
Journal, 15, 2001, 1-29.
Romer, P. M. "Endogenous Technological Change." Journal
of Political Economy, 98, 1990, S71-102.
Sachs, J. D. "Tropical Underdevelopment." NBER Working
Paper 8119, 2001.
Sequeira, T., and P. Robalo. "Schooling Quality in a Cross
Section of Countries: A Replication Exercise and Additional
Results." Economics Bulletin, 9, 2008, 1-7.
Temple, J. "Robustness Tests of the Augmented Solow
Model." Journal of Applied Econometrics, 13, 1998, 361-75.
Temple, J., and L. Woessmann. "Dualism and Cross-country
Growth Regressions." Journal of Economic Growth, 11, 2006. 187-228.
Vandenbussche, J., P. Aghion, and C. Meghir. "Growth, Distance
to Frontier and Composition of Human Capital." Journal of Economic
Growth, 11, 2006, 97-127.
Young, A. "Gold into Base Metals: Productivity Growth in the
People's Republic of China during the Reform Period." Journal
of Political Economy, 111, 2003, 1220-61.
(1.) A series of empirical studies find either significantly
positive (Barro 1991; Mankiw et al. 1992; Gemmell 1996; Engelbrecht
2002; Madsen 2010), significantly negative (Caselli, Esquivel, and
Lefort 1996), insignificant (Knowles and Owen 1995; Pritchett 2001;
Radelet et al. 2001; Henderson, Papageorgiou, and Parmeter 2012) or even
nonlinear relationships between education levels and growth
(Kalaitzidakis et al. 2001). In some studies, the growth rate of human
capital is found to have a significant impact on output growth (Krueger
1968; Barro 1991; Mankiw et al. 1992), whereas others cast doubt on this
channel and propose that the stock of human capital can better explain
variations in output growth (Romer 1990; Benhabib and Spiegel 1994,
2005; Hall and Jones 1999). See Delgado et al. (2013) for an overview of
the literature.
(2.) Pritchett (1996) finds that different measures of outward
orientation capture different dimensions of the trade regime and,
therefore, sometimes give conflicting results. Since trade regime is not
the focus of this article, we do not investigate this matter further.
(3.) We use the generalized method of moments (GMM) in the
instrumental variable estimation. A key advantage of the IV-GMM
estimator over the commonly used IV2SLS approach is that the former is
more efficient in the presence of heteroskedasticity. This is our
preferred method since under the strict assumption of no
heteroskedasticity, the IV-GMM estimator is asymptotically no worse than
the IV-2SLS estimator (Baum, Schaffer, and Stillman 2003).
(4.) These data can be downloaded at
http://jakobmadsen.net/data-archive-6/.
(5.) Regressing capital income share on real per capita income
across countries gave a constant coefficient of 0.297367 and a slope
coefficient of -0.0000071. The correlation coefficient is -0.72. Income
shares for the following countries are estimated using per capita
income: Argentina, Brazil, Bulgaria, Cameroon, China, Cyprus, the
Dominican Republic, Germany, Iceland, Indonesia, Iran, Kenya, Malawi,
Mali, Mauritania, Senegal, Syria, Thailand, Togo, Turkey, Uganda, and
Zimbabwe.
MD. RABIUL ISLAM, JAMES B, ANG and JAKOB B. MADSEN *
* Helpful comments and suggestions from Hans-Jurgen Engelbrecht,
Dorian Owen, participants at the 39th Australian Conference for
Economists and, particularly, two referees are gratefully acknowledged.
Md. R.I. acknowledges financial support received from the Monash
University Postgraduate Publications Award. J.B.A. and J.B.M. gratefully
acknowledge financial support from the Australian Research Council (ARC
Discovery Grant no. DP120103026). We also thank Nadir Altinok for
providing the educational quality database.
Islam: Alfred Deakin Postdoctoral Research Fellow, Alfred Deakin
Research Institute, Deakin University, Burwood, VIC 3125, Australia.
Phone +613 92517818, E-mail rabi.islam@deakin.edu.au
Ang: Associate Professor, Division of Economics, Nanyang
Technological University, Singapore 637332. Phone +65 65927534, Fax +65
67946303, E-mail james.ang@ntu. edu.sg
Madsen: Professor, Department of Economics, Monash University,
Caulfield East, VIC 3145, Australia. Phone +613 99032134, Fax +613
99031128, E-mail Jakob.Madsen@monash.edu
TABLE 1
TFP Growth and Quality-Adjusted Human Capital
(1) Basic (2) Add (3) IV =
model (OLS) controls (OLS) EDR (IV-GMM)
[[PHI].sub.i] 0.010 *** 0.007 ** 0.018 ***
x [H.sub.i] (3.375) (2.587) (7.123)
[[PHI].sub.i] x 0.004 ** 0.005 *** 0.005 ***
[H.sub.i], 1970 (2.497) (2.738) (3.077)
[Investment.sub.i] 0.031 0.035 **
/[GDP.sub.i] (1.296) (2.489)
[Inflation.sub.i] -0.005 *** -0.003 **
(-4.242) (-2.657)
FDI [Inflows.sub.i] 0.241 ** 0.108
/[GDP.sub.i] (2.049) (1.239)
Trade openness, -0.007 -0.004
(-1.245) (-0.840)
No. of 60 60 60
observations
[R.sup.2] 0.199 0.461 0.308
(4) IV = (5) IV = EDR,
DALY (IV-GMM) DALY (IV-GMM)
[[PHI].sub.i] 0.015 *** 0.013 ***
x [H.sub.i] (5.592) (6.372)
[[PHI].sub.i] x 0.011 *** 0.005 ***
[H.sub.i], 1970 (3.938) (3.305)
[Investment.sub.i] 0.035 ** 0.034 ***
/[GDP.sub.i] (2.579) (3.294)
[Inflation.sub.i] -0.005 *** -0.004 ***
(-3.757) (-3.429)
FDI [Inflows.sub.i] 0.166 * 0.112
/[GDP.sub.i] (1.826) (1.386)
Trade openness, -0.005 -0.002
(-1.116) (-0.544)
No. of 60 60
observations
[R.sup.2] 0.274 0.407
Diagnostic tests for
IV-GMM (columns (3)-(5))
Hansen test (p value) 0.207 0.170 0.251
C-test ([[PHI].sub.i] x [H.sub.i]) 0.363 0.366 0.879
instruments (p value)
C-test ([[PHI].sub.i] x [H.sub.i] x 0.400 0.338 0.202
[DTF.sub.i], 1970) instruments
(p value)
Endogeneity-test (p value) 0.010 0.009 0.027
1st-stage E-statistic ([[PHI].sub.i] 21.961 19.560 29.662
x [H.sub.i])
1st-stage F-statistic ([[PHI].sub.i] 24.430 12.061 45.430
x [H.sub.i] x [DTF.sub.i],1970)
1st-stage [R.sup.2] ([[PHI].sub.i] 0.671 0.678 0.838
x [H.sub.i])
1st-stage [R.sup.2] ([[PHI].sub.i] 0.837 0.700 0.904
x [H.sub.i] x [DTF.sub.i], 1970)
Notes: The dependent variable is the average growth rate of TFP
over the period 1970-2010. H is the quantity of schooling measured
by average years of schooling for the population aged 15 and over
and <t>, the quality of schooling measured by the first principal
component of the rates of nonrepetition at the primary and
secondary levels; test scores in mathematics, science, and reading
at the primary and secondary levels; and the number of universities
listed in the ARWU's top 500 rankings per million workers. Initial
distance to frontier ([DTF.sub.1970]) is the TFP gap in 1970
between the technological leaders and the country under
consideration. The G7 countries are the technology leaders for the
30 countries with the higher income levels, whereas Brazil,
Bulgaria, the Dominican Republic, Mexico, and Turkey are the
technology leaders for the 30 countries with the lower incomes in
2010. The IV-GMM estimates in columns (3)-(5) use the estimated
death rates per 100,000 population by causes (communicable,
maternal, perinatal, and nutritional conditions) (EDR). the
estimated disability- adjusted life years per 100,000 population by
causes (communicable, maternal, perinatal, and nutritional
conditions) (DALY), and their interaction with DTF1970 as
instruments. The Hansen test is a test of overidentifying
restrictions that checks the validity of the instruments where the
null hypothesis is that the instruments are not correlated with the
residuals from the structural estimates. The C- test is the
difference-in-Hansen test that examines the exogeneity of the
instrument subsets under the null hypothesis that the subsets of
instruments are exogenous. The null hypothesis under the
endogeneity test is that the specified endogenous variables can be
treated as exogenous. An intercept is included in the regressions
but not reported. The numbers in parentheses are f-statistics and
are based on robust standard errors.
* Significant at 10%; ** significant at 5%; and *** significant at
1%.
TABLE 2
Partial Derivatives of TFP Growth with Respect to
Quality or Quantity of Education
([[partial derivative].sup.A] /
[partial derivative][PHI]) or DTF = DTF = DTF = DTF =
([[partial derivative].sup.A] / 0 0.30 0.50 0.90
[partial derivative]H) (1) (2) (3) (4)
[PHI] or H = 0.2 0.26 0.29 0.31 0.35
[PHI] or H = 0.4 0.52 0.58 0.62 0.70
[PHI] or H = 0.6 0.78 0.87 0.93 1.05
[PHI] or H = 0.8 1.04 1.16 1.24 1.40
[PHI] or H = 1.0 1.30 1.45 1.55 1.75
Notes: Column (1) shows only the estimated direct effects (i.e.,
DTF = 0) on TFP growth for a change in [PHI] or H, whereas the
remaining columns report both the estimated direct and indirect
effects of [PHI] or H on TFP growth. The partial derivatives in
column (1) are obtained by multiplying [[??].sub.1] by the assumed
values of H or [PHI]. Columns (2)-(4) add these direct effects to
the indirect ones, which are obtained by multiplying [[??].sub.2]
by the assumed values of H or [PHI] and DTF. [[??].sub.1] and
[[??].sub.2] are estimated parameters for quality-adjusted human
capital and its interaction with the technology gap, respectively,
obtained from our benchmark regression in column (5) of Table 1. H
and [PHI] are scaled to a range between 0 and 1 to ease
interpretation. DTF = 0.30 refers to a country with a TFP that is
70% of the reference frontier country, DTF = 0.50 refers to a
country with a TFP of half the reference frontier country, and DFT
= 0.90 refers to the country that has a TFP that is 10% of the
reference frontier country.
TABLE 3
Alternative Human Capital Measures and Specifications
(1) (2)
h = [PHI] x H,
where is
labor force
h = [PHI] x H, quality
where is input (Hanushek
measures and Kimko 2000)
h 0.049 *** 0.031 ***
(6.013) (6.311)
h - ln(n+g +[delta])
h x DTF 0.019 *** 0.012 ***
(3.199) (3.753)
ln[(I/Y).sub.1970]
ln(I/Y)
ln(I/Y) - ln(n+g+[delta])
ln(n+g+[delta])
No. of observations 60 53
[R.sup.2] Diagnostic Tests 0.344 0.472
Hansen test (p value) 0.172 0.225
C-test (h) (p value) 0.569 0.825
C-test (hxDTF) (p value) 0.502 0.484
Endogeneity-test (p value) 0.039 0.083
1st-stage E-statistic (h) 11.362 24.910
1st-stage E-statistic 28.260 25.672
(hxDTF)
1st-stage [R.sup.2] (h) 0.665 0.834
1st-stage [R.sup.2] 0.903 0.904
(hxDTF)
(3) (4)
h = [PHI] x H,
where [PHI] is
cognitive data
(Hanushek and h = [PHI]
Woessmann 2012) x [e.sup.H]
h 0.028 *** 0.006 ***
(5.303) (7.105)
h - ln(n+g +[delta])
h x DTF 0.009 *** 0.002 ***
(3.675) (3.163)
ln[(I/Y).sub.1970]
ln(I/Y)
ln(I/Y) - ln(n+g+[delta])
ln(n+g+[delta])
No. of observations 47 60
[R.sup.2] Diagnostic Tests 0.485 0.465
Hansen test (p value) 0.279 0.172
C-test (h) (p value) 0.578 0.215
C-test (hxDTF) (p value) 0.268 0.134
Endogeneity-test (p value) 0.095 0.021
1st-stage E-statistic (h) 13.249 13.742
1st-stage E-statistic 96.590 87.971
(hxDTF)
1st-stage [R.sup.2] (h) 0.776 0.745
1st-stage [R.sup.2] 0.937 0.917
(hxDTF)
(5) (6)
h = [PHI] h = [e.sup.[PHI]]
x [e.sup.H] x [e.sup.H]
h 0.003 *** 0.002 ***
(6.308) (6 793)
h - ln(n+g +[delta])
h x DTF 0.001 *** 0.001 ***
(3.043) (2.854)
ln[(I/Y).sub.1970]
ln(I/Y)
ln(I/Y) - ln(n+g+[delta])
ln(n+g+[delta])
No. of observations 60 60
[R.sup.2] Diagnostic Tests 0.380 0.391
Hansen test (p value) 0.303 0.264
C-test (h) (p value) 0.880 0.584
C-test (hxDTF) (p value) 0.277 0.320
Endogeneity-test (p value) 0.017 0.013
1st-stage E-statistic (h) 20.351 17.045
1st-stage E-statistic 29.443 50.391
(hxDTF)
1st-stage [R.sup.2] (h) 0.812 0.794
1st-stage [R.sup.2] 0.881 0.900
(hxDTF)
(7) (8) (9)
Mankiw-
Mankiw- Romer-Weil
Romer-Weil model
h = H model (restricted)
h 0.013 * 0.008 **
(1.909) (2.474)
h - ln(n+g +[delta]) 0.006 **
(2.400)
h x DTF 0.006 0.006 *** 0.004 **
(1.587) (4.759) (2.307)
ln[(I/Y).sub.1970] -0.005 *** -0.008 ***
(-2.884) (-4.890)
ln(I/Y) 0.021 ***
(5.476)
ln(I/Y) - ln(n+g+[delta]) 0.003
(0.918)
ln(n+g+[delta]) -0.006 ***
(-4.122)
No. of observations 60 58 58
[R.sup.2] Diagnostic Tests 0.484 0.338 0.184
Hansen test (p value) 0.112 0.195 0.151
C-test (h) (p value) 0.450 0.429 0.578
C-test (hxDTF) (p value) 0.388 0.225 0.272
Endogeneity-test (p value) 0.094 0.886 0.160
1st-stage E-statistic (h) 26.039 14.012 13.041
1st-stage E-statistic 8.667 43.341 26.234
(hxDTF)
1st-stage [R.sup.2] (h) 0.768 0.846 0.835
1st-stage [R.sup.2] 0.787 0.917 0.930
(hxDTF)
Notes: DALY and EDR are used as instruments for quality-adjusted
educational attainment (h) and its interaction with DTF. Except for
columns (8) and (9) where the Mankiw et al. (1992) model is used,
all regressions include trade openness, FDI inflows/GDP, the
inflation rate and the investment ratio as control variables. For
columns (8) and (9), n is the population growth rate; g, the rate
of technological progress, [delta], the depreciation rate, and (g+
[delta]) is assumed to be 5%, following Mankiw et al. (1992).
* Significant at 10%; ** significant at 5%; and *** significant at
1%.
TABLE 4
Further Robustness Checks
(1) (2) (3)
Panel fixed Panel System
effects IV-GMM GMM
(20-year (20-year (20-year
interval) interval) interval)
h 0.146 ** 0.276 *** 0.263 ***
h x DTF (2.323) (5.365) (3.468)
0.085 ** 0.118 *** 0.114 ***
(2.080) (3.396) (2.714)
Non-OECD East Asia
& the Pacific
Latin America & the
Caribbean
Sub-Saharan Africa
High income OECD
POLITY
Scientific journals/labor
No. of observations 120 120 120
[R.sup.2] 0.489 0.295 --
Diagnostic Tests
Hansen test (p value) -- 0.417 0.165
C-test (h) (p value) -- 0.861 0.141
C-test (hxDTF) 0.452 0.277
(p value)
Endogeneity-test -- 0.000 --
(p value)
1st-stage E-statistic (h) -- 31.624 --
1st-stage F-statistic 26.581 --
(h x DTF)
1st-stage [R.sup.2] (h) -- 0.812 --
1st-stage [R.sup.2] -- 0.864 --
(hxDTF)
(4) (5) (6)
y = GDP Add
growth rate Add scientific
(1820-2008) POLITY journals
h 0.007 *** 0.013 *** 0.016 ***
h x DTF (4.283) (3.010) (3.910)
0.002 ** 0.005 *** 0.006 **
(2.068) (3.062) (2.540)
Non-OECD East Asia
& the Pacific
Latin America & the
Caribbean
Sub-Saharan Africa
High income OECD
POLITY -0.001
(-0.186)
Scientific journals/labor -0.005
(-1.315)
No. of observations 58 60 60
[R.sup.2] 0.310 0.405 0.433
Diagnostic Tests
Hansen test (p value) 0.615 0.192 0.196
C-test (h) (p value) 0.295 0.786 0.179
C-test (hxDTF) 0.777 0.151 0.112
(p value)
Endogeneity-test 0.073 0.061 0.063
(p value)
1st-stage E-statistic (h) 26.572 15.182 11.420
1st-stage F-statistic 7.603 32.061 20.953
(h x DTF)
1st-stage [R.sup.2] (h) 0.838 0.853 0.844
1st-stage [R.sup.2] 0.874 0.904 0.852
(hxDTF)
(7) (8)
Alternative
DTF (based Include
on 1970 regional
income data) dummies
h 0.015 *** 0.011 ***
h x DTF (5.232) (2.811)
0.005 *** 0.003 **
(2.830) -2.067
Non-OECD East Asia 0.012 ***
& the Pacific (2.744)
Latin America & the -0.004
Caribbean (-0.893)
Sub-Saharan Africa -0.012 ***
(-3.931)
High income OECD -0.006
(-1.495)
POLITY
Scientific journals/labor
No. of observations 60 60
[R.sup.2] 0.303 0.581
Diagnostic Tests
Hansen test (p value) 0.235 0.322
C-test (h) (p value) 0.158 0.725
C-test (hxDTF) 0.299 0.368
(p value)
Endogeneity-test 0.021 0.0921
(p value)
1st-stage E-statistic (h) 24.601 18.601
1st-stage F-statistic 16.035 27.280
(h x DTF)
1st-stage [R.sup.2] (h) 0.700 0.876
1st-stage [R.sup.2] 0.801 0.943
(hxDTF)
(9) (10)
TFP calculated
using [PHI] x H TFP calculated
as an input using [PHI] x H as
(return from an input (return
H is used) from H is NOT used)
h 0.011 *** 0.010 ***
h x DTF (5.411) (5.121)
0.006 *** 0.009 ***
(3.408) (4.629)
Non-OECD East Asia
& the Pacific
Latin America & the
Caribbean
Sub-Saharan Africa
High income OECD
POLITY
Scientific journals/labor
No. of observations 60 60
[R.sup.2] 0.391 0.526
Diagnostic Tests
Hansen test (p value) 0.246 0.282
C-test (h) (p value) 0.849 0 775
C-test (hxDTF) 0.180 0.149
(p value)
Endogeneity-test 0.023 0.092
(p value)
1st-stage E-statistic (h) 24.321 28.290
1st-stage F-statistic 38.330 38.353
(h x DTF)
1st-stage [R.sup.2] (h) 0.828 0.828
1st-stage [R.sup.2] 0.893 0.859
(hxDTF)
Notes: DALY and EDR are used as instruments for quality-adjusted
educational attainment (h) and its interaction with DTF. All
regressions include trade openness, FDI inflows/GDP the inflation
rate, and the investment ratio as control variables. In column (7),
Brazil, Chile, the Dominican Republic, Malaysia, and Turkey are
chosen to be the technology leaders for the 30 countries with the
lower incomes in 1970 in our sample. The number of instruments used
in the system GMM estimation is 34 (column (3))
* Significant at 10%; ** significant at 5%; and *** significant at
1%.
TABLE 5
The Composition of Quality-Adjusted Human Capital
(1a) (1b) (1c)
PRI PRI PRI
Mathematics Science
[PHI] = PCA score score
[PHI] x H 0.003 *** 0.006 *** 0.005 ***
(6.076) (9.605) (5.251)
[PHI] x H x [DTF.sub.1970] 0.001 ** 0.001 ** 0.002 **
(2.569) (2.646) (2.303)
No. of observations 60 46 37
[R.sup.2] 0.413 0.380 0.293
Diagnostic Tests
Hansen test (p value) 0.201 0.549 0.420
C-test ([PHI] x H) 0.776 0.782 0.435
(p value)
C-test ([PHI] x H x DTF) 0.271 0.318 0.627
(p value)
Endogeneity-test (p value) 0.042 0.015 0.053
1st-stage F-statistic 10.211 84.113 36.301
([PHI] x H)
1st-stage F-statistic 76.460 92.531 19.120
([PHI] x H x DTF)
1st-stage [R.sup.2] 0.771 0.823 0.753
([PHI] x H)
1st-stage [R.sup.2] 0.902 0.876 0.774
([PHI] x H x DTF)
(1d) (1e) (2a)
PRI PRI SEC
Reading Nonrepetition
[PHI] = score rate PCA
[PHI] x H 0.006 *** 0.004 *** 0.003 ***
(7.862) (5.796) (5.724)
[PHI] x H x [DTF.sub.1970] 0.001 ** 0.001 *** 0.002 ***
(2.249) (3.177) (3.620)
No. of observations 47 60 60
[R.sup.2] 0.593 0.462 0.324
Diagnostic Tests
Hansen test (p value) 0.205 0.132 0.182
C-test ([PHI] x H) 0.283 0.607 0.822
(p value)
C-test ([PHI] x H x DTF) 0.226 0.203 0.480
(p value)
Endogeneity-test (p value) 0.074 0.295 0.002
1st-stage F-statistic 46.302 24.731 21.881
([PHI] x H)
1st-stage F-statistic 9.462 110.123 24.211
([PHI] x H x DTF)
1st-stage [R.sup.2] 0.774 0.745 0.781
([PHI] x H)
1st-stage [R.sup.2] 0.795 0.915 0.854
([PHI] x H x DTF)
(2b) (2c) (2d)
SEC SEC SEC
Mathematics Science Reading
[PHI] = score score score
[PHI] x H 0.005 *** 0.006 *** 0.003 **
(2.795) (3.270) (2.246)
[PHI] x H x [DTF.sub.1970] 0.004 *** 0.007 *** 0.002 ***
(3.212) (3.819) (2.844)
No. of observations 46 46 40
[R.sup.2] 0.376 0.251 0.554
Diagnostic Tests
Hansen test (p value) 0.216 0.192 0.380
C-test ([PHI] x H) 0.572 0.312 0.495
(p value)
C-test ([PHI] x H x DTF) 0.405 0.226 0.322
(p value)
Endogeneity-test (p value) 0.083 0.097 0.017
1st-stage F-statistic 14.021 11.141 15.720
([PHI] x H)
1st-stage F-statistic 31.240 10.074 31.282
([PHI] x H x DTF)
1st-stage [R.sup.2] 0.625 0.655 0.777
([PHI] x H)
1st-stage [R.sup.2] 0.828 0.775 0.892
([PHI] x H x DTF)
(2e) (3)
SEC TER
Nonrepetition
[PHI] = rate Uni rank
[PHI] x H 0.005 *** 0.048 ***
(5.290) (3.951)
[PHI] x H x [DTF.sub.1970] 0.003 *** 0.042 **
(3.835) (2.157)
No. of observations 60 60
[R.sup.2] 0.325 0.107
Diagnostic Tests
Hansen test (p value) 0.228 0.155
C-test ([PHI] x H) 0.861 0.530
(p value)
C-test ([PHI] x H x DTF) 0.166 0.177
(p value)
Endogeneity-test (p value) 0.004 0.020
1st-stage F-statistic 24.932 14.850
([PHI] x H)
1st-stage F-statistic 36.001 11.051
([PHI] x H x DTF)
1st-stage [R.sup.2] 0.755 0.404
([PHI] x H)
1st-stage [R.sup.2] 0.883 0.559
([PHI] x H x DTF)
Notes: PRI, SEC, and TER indicate primary, secondary, and tertiary
level of education, respectively. DALY and EDR are used as
instruments for quality-adjusted educational attainment and its
interaction with DTF. The human capital variables are normalized to
the range of 0 and 1. All regressions include trade openness, FDI
inflows/GDP, the inflation rate, and the investment ratio as control
variables.
* Significant at 10%; ** significant at 5%; and *** significant at
1%. See also notes to Table 1.
