metadata: authors: 0: author: Patrinos,Harry Anthony
1: author: Psacharopoulos,George
count: World
docna: 0: docna: Education : past, present and future global challenges
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Industrial Economics,Primary Education,Economics of Education,Educational Sciences,Educational Policy and Planning,Educational Institutions & Facilities,Economic Growth,Educational Policy and Planning -
            Ministry of Education,Educational Policy and Planning -
            Institutional Development
teratopic: Macroeconomics and Economic Growth,Poverty Reduction,Education
abstracts: cdata!: Progress in educational development in
            the world since 1900 has been slow and uneven between
            countries. Providing basic education for all children in
            developing countries has been and remains an unmet challenge
            of governments and international organizations alike. This
            is in sharp contrast to recent findings in the economics
            literature on the catalytic role of human capital for
            economic growth and social development in general. Using a
            newly constructed matched data set on education and national
            accounts in the 1950 to 2010 period, this paper estimates
            the loss of income and equity associated with not having a
            faster rate of human capital accumulation, using alternative
            methodologies and specific country examples. Such loss is
            projected backward (1900-1950) and forward (2010-2050) using
            plausible assumptions regarding what countries could have
            done in the past or may do in the future to accelerate human
            capital formation. The findings suggest that the welfare
            loss in terms of per capita income conservatively ranges
            from about 7 to 10 percent. Improved educational attainment
            is also shown to have an effect in reducing income inequality.
repnme: repnme: Education : past, present and future global challenges
display_title: Education : past, present and future
            global challenges
listing_relative_url: /research/2011/03/13978852/education-past-present-future-global-challenges
topicv3: Primary Education m1326139 480,Economic Growth m1326241 471,Education Policy and Planning m1326781 1513,Education m1327048 470,Returns to Education m1327513 2174
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Poverty Reduction,Education
no_of_pages: 35
author_keys: 0: author_key: 95903
1: author_key: 91401
model_extractions: WPS5616 Policy Research Working Paper 5616

# Education

Past, Present and Future Global Challenges _Harry Anthony Patrinos George Psacharopoulos_ The World Bank Human Development Network Education Team March 2011
Policy Research Working Paper 5616

# **Abstract**

Progress in educational development in the world since 1900 has been slow and uneven between countries. Providing basic education for all children in developing countries has been and remains an unmet challenge of governments and international organizations alike. This is in sharp contrast to recent findings in the economics literature on the catalytic role of human capital for economic growth and social development in general. Using a newly constructed matched data set on education and national accounts in the 1950 to 2010 period, this paper estimates the loss of income and equity associated with not having a faster rate of human capital accumulation, using alternative methodologies and specific country examples. Such loss is projected backward (1900–1950) and forward (2010–2050) using plausible assumptions regarding what countries could have done in the past or may do in the future to accelerate human capital formation. The findings suggest that the welfare loss in terms of per capita income conservatively ranges from about 7 to 10 percent. Improved educational attainment is also shown to have an effect in reducing income inequality.

This paper is a product of the the Education Team, Human Development Network. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at hpatrinos@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Education: Past, Present and Future Global Challenges**<sup>**1**</sup>

Harry Anthony Patrinos and George Psacharopoulos<sup>2</sup>

> 1 Education chapter commissioned for the forthcoming Copenhagen Consensus on Human Challenges, “The Way the World is: Past, Present and Future Global Challenges,” edited by Bjørn Lomborg, forthcoming Cambridge University Press.  We thank Emilio Porta, Kevin Macdonald and Martin Schlotter for assisting us in constructing the database, and two anonymous reviewers whose comments on a draft of this paper led to significant improvements in content and exposition.  We thank two anonymous reviewers, Kasper Thede Anderskov and Bjørn Lomborg for useful questions and guidance.  All errors remain our own and the views expressed here are those of the authors and should not be attributed to the World Bank Group.

> 2 Lead Education Economist, World Bank; and formerly London School of Economics and World Bank.
2

# **Contents**

|1. Introduction ................................................................................................................ 3|
|---|
|2. Historical perspective ................................................................................................. 4|
|3. Defining the challenge ................................................................................................ 7|
|4. Review of the analytical literature ............................................................................... 8|
|5. Estimating the challenge .......................................................................................... 13|
|6. The welfare loss of illiteracy ..................................................................................... 25|
|7. Equity links ............................................................................................................... 25|
|8. Caveats .................................................................................................................... 26|
|9. Conclusion ............................................................................................................... 28|
3

# **1.  Introduction**

Formal education is a relatively recent institution in the history of mankind dating a mere two centuries. The recognition that education relates to the country‘s development is even more recent, dating back just a few decades. Non-formal education of course existed since time immemorial in the form of philosopher/student or master/apprentice relationship, and some European universities date back to the 13<sup>th</sup> century. But organized schooling where children of a certain age were obliged to attend school started as late as the nineteenth century in England.

The link between education and economic development was instigated by the so-called human capital school originating at the University of Chicago in the early 1960s (Schultz 1961a; Becker 1964). According to early versions of human capital theory, expenditure on education is an investment with many similarities to investment in machines. National resources are used while the student is in school, in the form of direct outlays to education and foregone labor earnings. But later in life more educated workers contribute to national output more than less educated workers. The discounted difference between the cost and benefit flows related to education can lead to estimates of the profitability of investment in human capital.

This basic idea was expanded in the 1980s and 1990s to include predictions of the socalled new growth theory postulating that education, beyond enhancing an individual‘s productivity, also has an efficiency boosting ―external‖ effect on others, thus further enhancing national output (Lucas 1988; Romer 1986, 1990). A flood of empirical research has followed attempting to estimate the effect of education on economic growth (see, for example, Barro 1991; Mankiw, Romer and Weil 1992; McMahon 1999; Benhabib and Spiegel 1994, 2005).

Throughout the short history of formal education it has been a perennial challenge as to how to provide the quantity and type of education that would maximize social welfare. In this paper we define the welfare loss related to education in terms of efficiency and equity. Given the lack of a global utility function, welfare loss in this paper really means loss of income. The efficiency component is estimated as a counterfactual of higher per capita income or its growth had educational development proceeded faster than indicated in the historical data. The equity component is estimated by the change in the Gini inequality index had countries followed more expansive education policies.

Our estimates of the loss associated with education spanning 1900 to 2050 are based on a comparison of two scenarios: (1) An inertia scenario where countries follow existing education policies and (2) a challenge scenario where countries would have followed more efficiency- and equity-oriented education policies.

Backward and forward extrapolation of the welfare loss is based on coefficients regarding the contribution of education to economic growth and equity in the ―actual‖ or ―data-known‖ period 1950 to 2000 from new estimates and the empirical literature on the subjects and, of course, assumptions regarding the application of such coefficients beyond the range of actual data. Given the highly aggregate nature of this exercise, high and low estimates are given.

The coefficients linking education to economic growth are derived from two subsets of the economics of education literature: (1) Micro estimates of the social rates of return to
<!-- Start of picture text --> 100<br>308 —<br>70<br>60<br>50 ——Feypt<br>2 —| inland<br>2 40 === Portugal<br>5 30<br>~ 20<br>10<br>1900 1910 1920 1930 1940<br>Census year<br><!-- End of picture text -->
5

**Table 1.  Mean years** **<u>of schooling and illiteracy rates (%), 1870-2000</u>**

||Africa|Japan<br>Korea<br>Taiwa<br>n|Latin<br>Ameri<br>ca|Easter<br>n<br>Europ<br>e|Europ<br>e &<br>offsho<br>ots|China|<sup>South</sup><br>Asia|Other<br>Asia|World<br>mean|
|---|---|---|---|---|---|---|---|---|---|
|1870||||||||||
|School<br>years|0.13|0.63|0.59|0.83|3.02|1.00|0.03|0.25|<br>1.0|
|<br>Illiteracy|96.5|82.9|86.0|79.1|37.2|82.3|99.3|94.6|78.9|
|<br>1910||||||||||
|School<br>years|0.27|2.41|1.28|1.61|5.00|1.26|0.27|0.50|<br>1.8|
|<br>Illiteracy|93.8|46.2|71.8|67.8|16.1|78.6|94.6|89.6|67.0|
|1950||||||||||
|School<br>years|0.79|6.31|2.81|5.05|7.22|1.65|0.88|1.43|<br>3.2|
|<br>Illiteracy|85.2|13.2|44.7|12.1|4.5|73.8|83.9|73.4|51.2|
|1970||||||||||
|School<br>years|1.71|8.78|4.13|7.65|9.06|3.33|2.25|3.35|<br>4.7|
|<br>Illiteracy|70.5|4.1|32.7|7.0|1.7|50.9|66.9|46.4|39.1|
|1980||||||||||
|School<br>years|2.37|9.58|4.89|8.02|9.83|4.55|2.91|4.35|<br>5.3|
|Illiteracy|60.4|2.0|26.6|6.6|1.6|37.1|60.1|34.5|33.3|
|1990||||||||||
|School<br>years|3.18|10.29|6.22|9.47|10.50|5.66|3.31|5.57|<br>6.1|
|<br>Illiteracy|50.2|1.2|18.4|6.9|1.7|26.0|54.3|21.1|27.7|
|2000||||||||||
|School<br>years<br>Illiteracy|4.02<br>39.5|10.98<br>1.3|6.94<br>14.5|9.86<br>5.5|10.99<br>1.8|6.64<br>19.7|4.02<br>48.3|6.52<br>15.3|<br>6.7<br>23.6|

Source: Based on Morrisson and Murtin (2007: Table 2) The pattern in Table 1 shows that between 1970 and 2000, average years of schooling rose by similar amounts across all regions at about 2-3 years of schooling. The biggest increases are in China and the smallest in South Asia. Other than China and Other Asia, there is only modest convergence in average years of schooling between developed and developing worlds. The pace of world growth in human capital accelerated in the second half of the 20th century. Since 1950, world years of schooling have increased relatively steadily at a rate of 0.6 to 0.7 years per decade. Before 1950, only Europe, North America and the OECD countries of Asia maintained that pace of schooling increase. That means that the current developing countries are adding human capital at a pace comparable to that of the current developed countries. The recent acceleration of world human capital development is due to developing countries investing at the pace of developed economies. The developed economies have not slowed their pace, adding about 0.7 years of schooling per decade for the last 130 years.
<!-- Start of picture text --> 14<br>12<br>2 10 //<br>8/<br>88 Western countries a .<br>G / wt<br>- 6 Japan Russia / ‘ “uropeodthern V4Y<br>4 ; a MEN<br>/ Latin Ameri /<br>2 °<br>-_ a Eastemasia Sub-Sahara<br>ne re Africa<br>fheo 1880oo1900 1920 1940 1960 1980 2000<br><!-- End of picture text -->
<!-- Start of picture text --> 12<br>10 a<br>. Latin America, ~~ EastAsia<br>3 Advanced a .<br>=<br>: ~ East Europe Uae<br>a;<br>o<br>26 cwwe 7-<br>c aw ~ 2<br>: ae |<br>= we" ) ;<br>- Middle East<br>- ae<br>| _-wore<br>2<br>0<br>e €§% F&§ F© EF© CF. F F F F| SF F | |<br><!-- End of picture text -->
<!-- Start of picture text --> 120<br>105 million<br>100<br>5 8 72 million<br>=<br>5<br>zg=2 60 i ae - TT eee a-=56 million<br>: -=— eine<br>~ 40 wee<br>& i ee =<.<br>8 million<br>20<br>0<br>1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015<br><!-- End of picture text -->
9 public expenditure on schooling, plus the forgone earnings of those who are in school rather than working.

Estimates of social returns to education, as commonly found in the literature, ignore nonincome benefits of education (for example, improved health) and the possibility of positive externalities from education, such as productivity spillovers, lower crime, reduced use of social services, increased civic participation, and so on.

The private rate of return to an investment in a given level of education in such a case can be estimated by finding the rate of discount ( _r_ ) that equalizes the stream of discounted benefits to the stream of costs at a given point in time. In the case of university education lasting five years, for example, the formula is: where ( _Wu_ - _Ws_ ) is the earnings differential between a university graduate (subscript _u_ ) and a secondary school graduate (subscript _s_ , the control group). _Cu_ represents the direct costs of university education (tuition, fees, books), and _Ws_ denotes the student's foregone earnings or indirect costs.

Typical results of rate of return applications are reported in Table 3 showing that the returns are higher when investment takes place at the lower level of education, especially in low income countries. This well documented pattern is due to diminishing returns as investment in human capital ascends by level of education, similar to the diminishing returns on investment in physical capital. In addition, the returns to education are higher in developing countries because of the scarcity of human capital in those countries relative to industrial countries.

**Table 3.  Social returns to investment in education by level and** **<u>per capita income group (%)</u>**

||E|ducational leve<br>|l|
|---|---|---|---|
|Per capita income group|Primary|Secondary|Higher|
|Low income|21.3|15.7|11.2|
|Middle income|18.8|12.9|11.3|
|High income|13.4|10.3|9.5|
|World average|18.9|13.1|10.8|

Source: Based on Psacharopoulos and Patrinos (2004: table 2) An alternative methodology is the so-called ―Mincerian earnings function‖ used mainly to estimate the private returns to education (Mincer 1974): (2) _Ln_ ( _Yi_ ) = _f_ ( _Si_ , _<u>Zi</u>_<sup>)</sup> where _Y_ refers to the earnings of person _i_ , _S_ to the number of years of schooling and _Z_ to a battery of other individual characteristics. The property of this semi-logarithmic expression is that the regression coefficient of the years of schooling can be interpreted as the rate of return to investment in education.
10

|**Table 4. Macro-estimated returns to one additional ye**|**ar of schooling**|
|---|---|
|Effect|Source|
|No significant effect of years of schooling on economic growth|Benhabib and<br>Spiegel(1994)|
|Each additional year of schooling attainment in a country is<br>associatedwithabout 30%higherGDPpercapita|Heckman and<br>Klenow(1997)|
|A one-year increase in the average years of schooling of the<br>labor forceraises output per workerbetween5% and15%|Topel (1999)|
|A one year increase of years of schooling associated with<br>0.30% peryear fastergrowth|Bils and Klenow<br>(2000)|
|Macro-estimated rate of return to schooling between 18% and<br>30%|Krueger and Lindahl<br>(2001)|
|A one-year increase in average education raises per capita<br>income between3% to 6%|Bassanini and<br>Scarpetta (2001)|
|A one year increase in the mean years of schooling is<br>associated with a rise in per capita income by 3%-6%, or a<br>higher growth rate of one percentage point|Sianesi and van<br>Reenen (2003)|
|No evidence of wide social returns to education based on<br>cross-county regressions|Pritchett (2006)|
|Macro-estimated rate of return to schooling 27%|de la Fuente and<br>Domenech (2006)|
|Macro-estimated rate of return to schooling between 9.0 and<br>12.3%|Cohen and Soto<br>(2007)|
|Macro returns to years of schooling 36.9%, or each year of<br>schooling is statistically significantly associated with a long-run<br>growth rate thatis 0.58 percentage pointshigher|Hanushek and<br>Woessmann (2008)|
|Controlling for physical capital stock, the rate of return to the<br>average year of schooling is 12.1%|Barro and Lee (2010)|

Such a function has also been applied in a macro context where _Y_ refers per capita income or output per worker in country _i_ and _S_ to the mean years of schooling of the population or the work force. The enrolment ratio at different levels of education has also been used in lieu of years of schooling as an independent variable. Table 4 gives typical results of application of such function fitted to pooled cross-country-time data.

Another methodological line of estimating the contribution of education to economic growth has been instigated by the work of Solow (1956, 1957) who added technical change ( _T_ ) as an independent variable in an aggregate production function, along with the traditional factors of production physical capital ( _Kp_ ) and labor input ( _L_ ) in order to explain output ( _Y_ ). Omitting time subscripts for expository simplicity, the Solow function takes the form (3) _Y = f (Kp, L, T)_ Schultz (1961a,b) challenged Solow‘s formulation and added education as a determining factor of income. A stream of empirical research followed along two alternative measures of the education input: "Schultz-type" and "Denison-type" growth accounting.
11 In Schultz-type accounting, human capital ( _Kh_ ) is added as an independent variable in the production function, along with physical capital ( _Kp_ ) and the number of people employed: Differentiating with respect to time as to get the growth rate of output ( _gy_ ), and making elementary substitutions, one gets the estimating expression: where s _l_ is the share of labor in national income, _gl_ the rate of growth of the labor force _, I_ is the investment in physical ( _p_ ) or human ( _h_ ) capital, and _r_ the rate of return on the respective investment. Therefore, _rp_ and _rh_ correspond to the return on physical and human capital. Note that _rh_ corresponds to the coefficient of schooling in our estimates, namely equation (2), though _<u>rh</u>_ in Schultz‘s model corresponds to the social rate of return while the coefficient on _S_ gives the private rate of return.

In Denison's formulation, instead of adding human capital in monetary terms, the labor force ( _L_ ) is split up by level of education, say _L0, L1, L_ 2, and _L3_ , to denote those whose highest qualification is no schooling, primary, secondary and higher education: Differentiating with respect to time, growth accounting takes the form: where _si_ stands for the wage share of labor with the _i_<sup>_th_</sup> qualification in national income, and g _i_ for the rate of growth of workers with that qualification.

Typical results from the early literature on the macro contribution of education to economic growth based on "Schultz-type" and "Denison-type" growth accounting are presented in Table 5. The results show consistency with the micro literature in the sense that the effect of education on growth is substantial.
12

**Table 5.  The contribution of education to economic growth in the** **<u>early literature</u>**

|Country|Contribution of education to the<br>economic growth rate (%)|
|---|---|
|Belgium|14.0|
|Canada|25.0|
|Korea|16.0|
|UK|12.0|
|USA|15.0|

Source: Psacharopoulos (1984) Note: Estimates are based on within-country growth accounting using Schultz (1961b) and Denison (1967) methodologies The 1980s experienced the appearance of endogenous growth theory (Lucas 1988; Romer 1990). In their formulation, beyond a measure of human capital that is actually used by different firms in the economy ( _Kh_ ), _S_ years output also depends on the average level of human capital ( _K h_ ). In addition, human capital is endogenous, rather than exogenous, in the system; that is, human capital is produced by using resources: The dramatic theoretical implications of endogenous growth theories is that output is no longer constrained by the constant-returns-to-scale property of the Solow production

> function, and that ―knowledge‖ (proxied by _K h_ ) becomes a kind of public good that spills over the economy as an externality, allowing output to grow beyond the measurable inputs.  Another, equally important implication of this model is that, by virtue of the average stock of human capital being a public good, there might be social underinvestment in human capital formation.  This implication is very relevant to the education challenge topic of this paper.

Empirical applications of the new growth theory are relatively recent, diverse, and not easily summarized. Although some studies have reported a high impact of education on growth, others have argued that there is little or nothing to be learned from the empirical growth literature (for example, Topel 1999; Pritchett 2006; Banerjee and Dufflo 2005; Durlauf, Johnson and Temple 2005).

The inconsistency between micro and newer macro evidence on the returns to education has occupied the literature for a long time (for example, Krueger and Lindahl 2001; Sianesi and van Reenen 2003). The main reason for such inconsistency is that countries differ in many other respects that cannot easily be measured and controlled for in cross-country regressions, whereas within-country micro data automatically control for such factors.
13

# **5.  Estimating the challenge**

―Growth with equity‖ is a contemporary development goal espoused by governments and international organizations (for example, World Bank 2005). In theoretical terms one can assume that social welfare ( _SW_ ) consists of two components: efficiency ( _EF_ ) and equity ( _EQ_ ), as in the following social welfare function:

# (10) _SW = f (EF, EQ)_

This function could be specified as:

# (11) _SW = (Y/P)_<sup>_α_</sup> _(1- GINI)_<sup>_β_</sup>

where ( _Y_ / _P_ ) is per capita income, _GINI_ is the common inequality index and α and β the value of the weights one puts at the efficiency and equity components. Assigning such weights implies a value judgment that is best left to voters and politicians. The education challenge in this framework is how particular education policies (for example, greater coverage of primary education) are conducive or not to changing the values of per capita income and income distribution in a way that promotes social welfare.<sup>4</sup>

# **Data and sources**

The following data were used in our simulations:

- Historical national accounts data from Maddison (2010)

- Investment in education data from the World Bank on line indicators (EdStats)

- Education data from Barro and Lee (2010) and World Bank indicators

- Micro returns to education from Psacharopoulos and Patrinos (2004)

- Gini coefficients from the Word Bank indicators

Although all measures of education are used in this paper, our central education variable is the average years of schooling of the population aged 15-plus. This choice is dictated both by the availability of a solid comparable database spanning 60 years (1950-2010), and the fact this measure is a summary of educational development encompassing all levels (Barro and Lee 2010). This measure of education also links to an extensive body of recent theoretical and empirical economic growth literature from which we can borrow parameters or compare our estimates. It also happens that the educational level of the population, rather than the work force, is more appropriate in a macro analysis of this kind in order to catch the wider or external effects of education on per capita income, for example, by lowering fertility or improving health conditions of the population at large.

It should be mentioned at the outset that years of schooling sometimes or often masks the quality of schooling; for example, four years of education in Finland does not equal four years of schooling in Colombia. Hanushek and Woessmann (2008) have shown that education quality affects economic growth. Increases in wages from a one standard deviation increase in cognitive test scores range from a low 5 percent in Ghana (Jolliffe 1998) to a high of 48 percent in South Africa (Moll 1998). In South Arica, Gustafsson, van der Berg, Shepherd and Burger (2011) using a grade- and race-specific educational 4 For an application of this framework to an actual country case, see Psacharopoulos (1977).
14 quality measure in a Mincerian earnings function, find that an improvement of 1.07 standard deviations in the quality measure for adults aged 20 to 29 results in an income improvement of 30 percent. Hanushek and Kimko (2000) found that a one-standard deviation change in labor force quality is associated with a nearly 1 percentage point higher economic growth rate. Coulombe et al. (2004) report that a 1 percent higher literacy score raises labor productivity by 2.5 percent. However, there are no historical data back to 1900 on education quality to use in our analysis.

In addition to the spottiness of the historical data, there are many new countries in the known data period that did not exist before 1950 (for example, breakups of colonial territories), and many others that did not exist before 1990 (for example, the offshoots of the former Soviet Union), thus limiting the number of education-income observations. For all the above reason we opted to work with regional averages in the simulations and projections. Of course we report illustrative individual country stories when sufficient data are available.

# **Efficiency and equity links**

Figure 5 plots 1,596 pairs of observations of per capita income and years of schooling in 146 countries between 1950 and 2010. Treating the oil-rich countries in the upper left quadrant as outliers, the shape of the income-education relationship seems to illustrate a threshold level of 6 years of schooling as a necessary condition for the returns to schooling to manifest. In the new growth literature Azariadis and Drazen (1990) were the first to suggest what educators (Anderson and Bowman 1963) and economic historians (Easterlin 1981) had been saying for a long time: that there might be a threshold in terms of human capital accumulation before a country can reap growth benefits. In their words: _"once ... the stock of knowledge surpass[es] certain critical values, aggregate production possibilities may expand especially rapidly"_ (Azariadis and Drazen 1990).

Benhabib and Spiegel (2005) identified an even lower threshold of human capital. Unless nations had a critical value of about 2 years of schooling in 1960 they achieved lower growth rates over the next 35 years relative to the comparators. Sala-I-Martin, Doppelhofer and Ronald Miller (2004) found that a 10-percentage-point increase of the primary school enrollment rate is associated with a 0.27-percentage-point increase of the growth rate.
Ype <!-- Start of picture text --> 40000<br>35000 .<br>30000 so. ae<br>25000 "ett - _oFeet<br>. = &8e eos.<br>20000 . a Sans<br>15000 . » eas? ys<br>| ~ wef le ER Oe<br>10000 oteot Segae:Se paxaeee ee<a<br>0 aaiees eo aerate =<br>0.00 5.00 10.00 15.00<br><!-- End of picture text -->

<!-- Start of picture text --> $<br><!-- End of picture text --> $ P _ o(a+b3)
16

# **Data periods**

There are three distinct data periods in the 150 years time span considered in this paper, as shown in Figure 6:

1. The 1950 to 2010 period refers to actual data on income and education available in our database.

2. The 1900 to 1950 period contains a mix of actual data and estimated data, as for example, many countries in the data set did not exist in the that period.

3. The 2010 to 2050 period contains only assumed or estimated data based on the known trends in the 1950 to 2010 period or assumptions.

**Figure 6.  Actual and estimated data periods**

<!-- Start of picture text --> Y, S<br>Some values estimated All values actual All values estimated<br>1900 1950 2010 2050<br><!-- End of picture text -->

# **An illustrative case**

Before applying our methodology on a world scale, it should be useful to illustrate it by comparing only two countries‘ record regarding education and economic growth: South Korea and Pakistan. Table 6 contrasts the educational and economic history of the two countries in the ―known‖ 1950-2010 period. Both countries started with more or less the same per capita income in 1950, but Korea had a considerable advantage in years of schooling relative to Pakistan. By 2010 Korea‘s level of educational development reached nearly 12 years of schooling, equivalent to the average adult having completed secondary schooling, whereas Pakistan‘s educational development has not yet reached 6 years of schooling – a minimum for literacy. Since 1950 the income difference grew dramatically in favor of Korea. In constant prices Korea‘s per capita income grew 23fold versus Pakistan‘s 3-fold growth, corresponding to a 5.2 percent versus 1.8 percent rate of economic growth. Many analysts have attributed much of the differential economic performance of Korea and Pakistan to the difference in the countries‘ educational development (Easterlin 1981; World Bank 1993).
17

|Country/|**Table 6**<br>Years of<br>(15+ ye|**.Comparin**<br>schooling<br>ars old)|**g Korea an**<br>Per capi<br>(1990 co|**d Pakistan **<br>ta income<br>nstant $)|Economic<br>growth rate|
|---|---|---|---|---|---|
|Year|1950|2010|1950|2010|(%)|
|Pakistan|1.0|5.6|643|2,239|1.8|
|S. Korea|4.5|11.8|854|19,614|5.2|

Source: Years of schooling from Barro-Lee (2010); per capita income from Maddison (2010) It may take a decade for a country to increase the mean level of education attainment of the population by one year, as shown in Figure 7. It also depicts the _S_ -shaped path countries follow in their educational development history. That is, slow progress is made in the beginning, then accelerating and eventually slowing down.

**Figure 7.  Mean years of schooling of the adult population, Korea and Pakistan**

<!-- Start of picture text --> S<br><!-- End of picture text --> <!-- Start of picture text --> 14.0<br>12.0<br>Korea<br>10.0<br>8.0<br>6.0<br>4.0 Pakistan<br>2.0<br>0.0<br>1940 1950 1960 1970 1980 1990 2000 2010 2020<br><!-- End of picture text --> In order to establish what Pakistan‘s per capita income would have been in the period 1900 to 2050 had it followed a different education policy, we must first establish a relationship between education and income. In this illustrative example such a relationship is obtained by fitting a Mincerian function using per capita income ( _Y_ ) and years of schooling ( _S_ ) circa 2009 in 128 countries:
18 (15) Ln _Y_ = 5.805 + 0.351 _S_ , R<sup>2</sup> = 0.62, N = 128 ( _t_ =14.4) Variants of the above Mincer-macro function using per capita income as the dependent variable in cross-country data have been fitted by Krueger and Lindahl (2001), Heckman and Klenow (1997) and Hanushek and Woessmann (2008). Our estimate of a 35 percent ―return‖ to one additional year of schooling is nearly identical to theirs. After fitting such a function, Heckman and Klenow (1997) concluded that: _“each additional year of schooling attainment in a country is associated with about 30% higher GDP per capita, whether one looks at 1990, 1985 or 1960..... The macro-Mincer coefficients....are consistent with large positive external productivity gains to economy-wide schooling attainment.”_ Barro and Lee (2010), among many others, have fitted the same function using output per worker (rather than per capita income) as the dependent variable and adding a measure of physical capital stock as an independent variable. Since their estimate of the _b_ coefficient is about one-half of ours, we adopted a 50 percent reduction of our estimated welfare loss as a lower bound. Table 7 and Figure 8 present estimates the welfare loss in terms of potentially higher per capita income had Pakistan a higher level of educational attainment as indicated in Col. 2, Table 7.

**Table 7.  Pakistan: Welfare loss** **<u>as percent of per capita income</u>**

|Year<br>(1)|Enhanced<br>years of<br>schooling<br>(2)|Per capit<br>(constan<br>Actual<br>(3)|a income<br>t 1990 $ )<br>Simulated<br>(4)|Welfa<br>(<br>Lower<br>bound<br>(5)|re loss<br>%)<br>Upper<br>bound<br>(6)|
|---|---|---|---|---|---|
|1900|0.2|264|354|17.1|34.2|
|1950|3.0|643|947|23.6|47.2|
|2010|6.0|2,239|2,714|10.6|21.2|
|2050|8.0|4,570|5,475|9.9|19.8|

Source: Based on equation (15), Table 6 and assumed enhanced years of schooling Notes: Col. 2, hypothetical years of schooling used in the simulation Col. 3, Actual or projected per capita income given the 1950-2010 growth rate Col. 4, Estimate value based on equation (15) and Col. 2 Col. 5 = (Col. 6) / 2 Col. 6 = ( (Col. 4 – Col. 3) / Col 3)100
19

# **Figure 8.  Welfare loss associated with not having one additional year of schooling, Pakistan (upper bound)**

<!-- Start of picture text --> 60<br>50<br>40<br>% 30<br>20<br>10<br>0<br><!-- End of picture text -->

# **Alternative Pakistan simulation**

The Mincerian function was fitted to just the time-series observations for Pakistan, 19502010. The number of observations is only 13 because the education data are available in 5-year periods (see Table 8): (16) Ln _Y_ = 6.319 + 0.290 _S_ , R<sup>2</sup> = 0.89, N = 13 (t = 9.41)

**Table** **<u>8.  Alternative Pakistan simulation using time series</u>**

|Schooling/loss|1900|1950|2010|2050|
|---|---|---|---|---|
|Inertia_S_|0.1|0.9|5.6|7.0|
|Enhanced_S_|1.3|1.9|6.6|7.8|
|Upper bound loss (%)|42.0|34.0|34.0|26.0|
|Loss lower bound (%)|21.0|17.0|17.0|13.0|

The results are largely consistent with the 13 percent micro-estimated social rate of return to investment in primary education in Pakistan in 1975 (Psacharopoulos 1985: table A-1).
<!-- Start of picture text --> 10<br>9<br>8<br>7<br>6<br>5<br>4<br>3<br>2<br>1<br>0<br>1900 1950 2000 2050<br><!-- End of picture text -->
21

**Table 9.  Welfare loss associated with not having one additional** **<u>year of schooling, World</u>**

|Year|Inertia S|Enhanced S|Welfare<br>Lower bound|loss (%)<br>Upper bound|
|---|---|---|---|---|
|1900|0.5|1.5|17.5|35.0|
|1950|2.7|3.7|14.7|29.4|
|2010|8.0|9.0|14.7|29.4|
|2050|10.0|11.0|11.1|22.1|

Note: Enhanced S = Inertia S + 1

# **Regional estimates**

The years of schooling coefficient of fitting the basic Mincerian function (equation 12) within regional groups of countries is reported in Table 10. This is the upper bound of what countries might have lost in the period of known actual data by not having one more year of schooling. East Asia and the Pacific that includes many dynamic economies in the period 1950-2010 exhibit the highest loss, whereas Latin America and Sub-Saharan Africa the least. Such pattern might be due to two reasons. First, it is a well know fact that the Mincerian function underestimates the returns to primary education; that is, the level of education most relevant to these countries (Psacharopoulos 1994). Second, the inferior education quality in Latin America and Sub-Saharan Africa relative to other countries could be depressing returns in those regions. Also, it could be due to the fact that education is worth so much more in East Asia, especially the fast growing ―tigers‖, that any deviation from the optimum shows larger relative losses. The fact that income loss differs between regions could be due to differences regarding economic institutions or access to capital.

**Table 10.  The welfare loss of not having one more year of schooling,** **<u>by region, 1950-2010</u>**

|Country group|Welfare loss<br>(% per capita income)|
|---|---|
|Advanced economies|20.2|
|East Asia and Pacific|34.3|
|Europe and Central Asia|22.8|
|Latin America and Carr.|16.1|
|Middle East and N. Africa|14.5|
|South Asia|21.0|
|Sub-Saharan Africa|17.0|
|**World**|**25.8**|

Source: Equation (12) fitted within regional groups of countries Note: When multiplied by 100 the education coefficient measures the percent increase of per capita income associated with one extra year of schooling; all coefficients are statistically significant at the 1% probability level or better
22

# **Yearly estimates**

Mincerian macro regressions were fitted within each year. As shown in Table 11 and Figure 10 the macro returns to schooling seem to increase over time, a trend that might be counter-intuitive given expected diminishing returns to investment in education as the stock of human capital rises. But the new growth theory provides some clues for this pattern. According to Azariadis and Drazen (1991) cited earlier, there is a threshold level of schooling after which returns increase significantly. As more and more people achieve higher levels of schooling, and since schooling attainment is not infinite (see _S_ - shape above), relative earnings tend to decline, and the individual rate of return will decrease, as predicted by classical economic theory. The point here is that increased schooling does not increase inequality, and may in fact contribute to its decline. The steady increase in schooling demonstrated in Table 1 should result in falling inequality in the world over time, but not necessarily a falling gap between developed and developing countries because of the lack of convergence in schooling across rich and poor countries, as demonstrated in the recent growth literature.

However, at the country level, higher levels of schooling for a larger proportion of the population lead to spillover effects, as more people are able to learn and share knowledge. Thus it is not odd to see declining individual returns to schooling while social returns continue to rise. Individual returns to schooling at early stages of development, when only a fraction of the population is educated, could reflect ―rents‖ as educated individuals are able to extract surplus earnings. As education rises, rents are eliminated and returns seem to decrease, while for society the more educated population contributes to more social learning and thus higher social returns.

**Table 11.  Over time trend of the returns to** **<u>education</u>**

|Year|Returns (%)|
|---|---|
|1950|24.9|
|1955|25.6|
|1960|25.7|
|1965|27.3|
|1970|27.0|
|1975|27.3|
|1980|27.9|
|1985|30.7|
|1990|31.8|
|1995|30.9|
|2000|32.8|
|2005|34.4|
|2010|36.3|
|**Overall**|**25.8**|
<!-- Start of picture text --> 36.0<br>34.0<br>32.0<br>30.0<br>28.0<br>26.0<br>24.0<br>1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010<br><!-- End of picture text -->
24

**Table 12. Growth accounting** **<u>simulation of the welfare loss</u>**

|Country<br>(1)|r<br>Overall<br>social r,<br>full<br>method<br>average<br>(%)<br>(2)|(Ie/Y)<br>inertia<br>ed. exp.<br>as % of<br>GDP<br>(%)<br>(3)|r*(Ie/Y)<br>Inertia<br>educ.<br>contrib.<br>growth<br>points<br>(4)|Enhanced<br>education<br>contri-<br>bution<br>growth<br>points if<br>(Ie/Y) + 1<br>(5)|Enhanced<br>-inertia<br>difference<br>in growth<br>points<br>(6)|Actual<br>inertia<br>Growt<br>h rate<br>(7)|Enhanced<br>to inertia<br>growth rate<br>(%)<br>(8)|
|---|---|---|---|---|---|---|---|
|Argentina|7.7|4.6|0.35|0.43|0.08|4.1|1.9|
|Brazil|20.7|4.0|0.83|1.04|0.21|2.9|7.1|
|Chile|11.1|3.9|0.43|0.54|0.11|5.3|2.1|
|China|12.9|2.5|0.32|0.45|0.13|8.0|1.6|
|Colombia|15.1|3.1|0.47|0.62|0.15|3.2|4.7|
|Ecuador|12.4|1.3|0.16|0.29|0.12|2.0|6.2|
|Ethiopia|13.7|3.9|0.54|0.67|0.14|5.3|2.6|
|Ghana|15.8|4.7|0.74|0.90|0.16|4.8|3.3|
|Israel|10.0|6.6|0.66|0.76|0.10|4.3|2.3|
|Japan|8.4|3.7|0.31|0.39|0.08|1.2|7.0|
|Malawi|13.8|4.1|0.57|0.70|0.14|3.9|3.5|
|Mexico|12.5|4.9|0.61|0.74|0.13|2.9|4.3|
|Nepal|11.0|3.0|0.33|0.44|0.11|4.0|2.7|
|Paraguay|14.6|5.3|0.77|0.92|0.15|2.7|5.4|
|Philippines|10.9|3.5|0.38|0.49|0.11|3.8|2.9|
|Singapore|13.6|3.1|0.42|0.56|0.14|6.1|2.2|
|Spain|9.8|4.3|0.42|0.52|0.10|2.9|3.4|
|Uganda|35.5|2.5|0.89|1.24|0.36|6.3|5.6|
|UK|7.5|4.6|0.35|0.42|0.08|2.4|3.1|
|Venezuela|13.3|3.0|0.40|0.53|0.13|3.1|4.3|
|Vietnam|8.1|2.9|0.23|0.31|0.08|7.3|1.1|
|**World**<br>**mean **|**13.9**|**4.0**|**0.55**|**0.69**|**0.14**|**4.0**|**3.3**|

Source: Based on the estimated education term of equation (5) Notes: Col.2 from Psacharopoulos and Patrinos (2004), average of social rates of return, full method Col. 3 from World Bank indicators Col. 4 = (Col. 2) * (Col. 3)/100 Col. 5 re-estimation based on a 1 percentage point increase in education expenditure Col. 6 = (Col. 5 - Col. 4) Col. 7 from Maddison (2010) Col. 8 = (Col. 6 / Col. 7) * 100
25

# **6.  The welfare loss of illiteracy**

The simulations presented above were based on one extra year of schooling relative to the counties‘ historical and inertia-projected educational attainment. We now ask the question: What is the welfare cost of illiteracy? This is estimated as the effect of some countries at some point in their history having less than 5 years of schooling on average.<sup>5</sup> In order to do this simulation we assigned to countries in this category 5 years of schooling and fitted again the main Mincerian function (equation 17, above): The 38.1 percent return to years of schooling in the above function is of course exaggerated because of the artificial assignment of extra human capital to countries in the past were below the literacy level. Subtracting from this coefficient the 25.8 percent return of the base equation (17), above, we obtain a net return of 15.3 percent due to literacy. Or, the welfare loss associated with illiteracy is equivalent to a 15.3 percent drop in per capita income. Note that this result is especially robust in the sense that, by comparing the base to the ―literacy-for-all‖ function we net out or hold constant differences between counties in the physical capital stock and many other unobservables that affect per capita income. Gustafsson, van der Berg, Shepherd and Burger (2011) report that in South Africa an increase of literacy from 21 to 50 percent on the PIRLS scale, GDP per capita would be around 23% higher.

# **7.  Equity links**

In our database we could match Gini coefficients and mean years of schooling for 114 country cases in the 1985 to 2005 period. Figure 11 shows that income inequality declines with increasing levels of schooling. One extra year of schooling is associated with a reduction of the Gini by 1.4 points (on the Word Bank scale measuring the Gini from 0-100, rather than 0-1): 5 About one half of the observations belong to this category.
Gini <!-- Start of picture text --> 70.00<br>*> *<br>60.00 o* 22 °.<br>;<br>* a t+.<br>50.00 o * See” oS<br>> oer % &<br>* % o« *<br>40.00 oo te te °<br>. ° ~ *<br>° ; *- ~ “Fe *<br>30.00 ° oe ee<br>*. °<br>20.00<br>0.00 5.00 10.00 15.00<br><!-- End of picture text -->
27 Countries also differ in many other aspects than those measured by the physical and human capital stock, for example, a different culture and discipline towards study and work; quality of schooling; quality of institutions; quality of policymaking; openness of economy; democracy; civil rights; economic freedoms. There are many other ―causal‖ variables that are likely to have a positive effect on growth and also likely to be positively correlated with the error term, such as investment rates, trade policies, colonial history, monetary policies, restrictions on markets. Such omitted variables can lead to large margins of error in accounting for differences in the economic growth path between countries.

Even if other inputs in production are held fixed, countries that limit the scope for using human capital should generate low estimates of the social returns to schooling. There will only be a return to human capital when there is disequilibrium due to shocks caused by technology, prices, or other factors that require a reallocation of resources (Schultz 1975). Countries that limit shocks by setting input or output prices centrally, or countries that use traditional technologies that do not change, will have limited returns to human capital. The former reason is why returns to schooling doubled following the transition to market (Fleisher et al. 2005), while the second is why returns to schooling are larger offfarm than on farm in countries with traditional agricultural methods (Fafschamps and Quisumbing 1999; Godoy et al. 2005). Countries with bad institutions that create returns to corrupt actions will have human capital diverted to nonproductive expropriation of the returns of entrepreneurs rather than productive innovation (Murphy et al. 1991, 1993). That suggests that the economic environment is critical to the return to an additional year of schooling.

One possibility running in the opposite direction that might be that our estimates are underestimates of the real impact of education is the existence of externalities. However, there is no clear evidence in the literature on the existence or magnitude of such externalities (Banerjee and Duflo 2005; Lange and Topel 2006; Pritchett 2006).

The most plausible argument for large positive social returns is from agglomeration economies where all firms in a locality become more productive because of an atypically high density of educated. This argument makes the most sense in an industrialized economy rather than in the developing economies that have been our focus.

Because of liquidity constraints in developing poor children spend less time in school when their families get an unforecastable negative income shock from weather, unemployment due to national business cycles or localized job loss, or currency crises. However, it is unclear if transitory shocks that reduce current schooling result in a permanently lower level of schooling completed.

Another issue is the resource cost of ―fixing‖ the challenge. In the case of education, a very large amount of resources would have to be used to provide an additional 1-2 years of schooling or, alternatively, ensure that everyone has enough years of schooling to be literate, and this cost needs to be subtracted from the welfare gains associated with such an increase in the years of schooling of the population. Put another way, the welfare loss of having low levels of schooling is offset, at least to some extent, by the actual uses made of the resources that would have to be devoted to avoid those low levels of schooling.
28 If, as is likely, the marginal cost of schooling is increasing in years of schooling, then the cost of adding an additional year of schooling will be greater than the average cost of attaining the current level of schooling. Rising marginal cost of schooling mean that estimates of current marginal returns to schooling will overstate the returns to further increases in schooling attainment.

# **9.  Conclusion**

In order to provide a best and conservative indication of the welfare loss associated with one extra year of schooling we adjusted the lower bound estimates presented in Table 9, above, by 41 percent. This adjustment is based on the difference between private and social returns to primary education, as in Psacharopoulos and Patrinos (2004, Table 2). Making a similar adjustment to the gross loss associated with literacy we obtain a 9 percent net loss on overage during the 1950-2010 period on which this estimate is based. As indicated in the last column of Table 1, World illiteracy has been falling by about three percentage points per decade. Based on linear interpolation and extrapolation of the historical data, the 9 percent central loss estimate has been adjusted upwards and downwards to obtain values for 1900 and 2050, respectively. Table 13 shows our best estimates of the welfare loss associated with a lower level of educational attainment over one and a half century.

Our lower bound estimate of the global loss in terms of a lower or potentially higher per capita income, had countries a higher level of educational attainment by one schooling year, is depicted in Figure 12. Such losses range from 7 to 10 percent over the 150 year period. The loss from illiteracy ranges from about 4 to 12 percent.

**Table 13.  Welfare loss in terms of lower per capita income because of low educational attainment**

||Percent GDP|loss from:|
|---|---|---|
|Year|One school year<br>deficiency|Illiteracy|
|1900|10.3|12.3|
|1950|8.7|9.0|
|2010|8.7|9.0|
|2050|6.5|3.8|

Based on our growth accounting results, the welfare or income loss amounts to about 1 percentage point of the average country‘s growth rate had the countries invested one percentage point more of their GDP on education. In addition to the above efficiency effects, one additional year of schooling is associated with a reduction of inequality by 1.4 points on the Gini scale.
29

**Figure 12.   Global welfare loss from the World’s education challenge**

Loss as % of GDP <!-- Start of picture text --> 14<br>12<br>One year of schooling<br>10 Literacy<br>8<br>6<br>4<br>2<br>1900 1950 2010 2050<br><!-- End of picture text --> Investments in the health, knowledge and skills of the people—human capital—are as important as investments in the more visible, physical capital of the country. Every country that sustained high growth for long periods put substantial effort into schooling its citizens and deepening its human capital. Conversely, considerable evidence suggests that other developing countries are not doing enough (Commission on Growth and Human Development 2008) **.** This is the remaining challenge.