Technical Companion to Chapter II¹

A. Introduction

This appendix serves as a technical companion to Chapter II. It provides a fuller description of the economic theory and supporting empirical evidence on why educating children is a profitable investment. It begins with a discussion of individual benefits and costs of education, including how individuals make school-work decisions and assessments of rates of return as a measure of investment profitability. Evidence on the rates of return to education in over 90 countries is examined. Next, the relationship between education, macroeconomic performance and the social benefits and costs of education is considered. The discussion of the empirical “social rates of return” that follows from this line of research concludes that while education appears to have a positive affect on economic growth, the channel through which it works is not known with certainty. There is also some uncertainty on whether the social rate of return from education implies profits to society as a whole that exceed the sum of those accruing to individuals in the society. That is, whether society can profit by investing in education beyond what individuals invest is a somewhat open question. The strongest evidence that societies profit from investments in education comes from the studies that find large positive individual rates of return, supplemented by the fact that extra profits may accrue to society as a whole and some evidence that these profits take the form of specific types of spillover benefits.

B. The Benefits and Costs of Education

1. Human Capital Theory

The underpinning of the theory of human capital stems from the work in the 1950s and 1960s of Nobel Laureate Gary Becker, T.W. Schultz and Jacob Mincer. This work and its subsequent extensions are known as human capital theory because they consider choices to forgo work in favor of education that are made by, or on the behalf of, individuals to be investments in the individual’s personal stock of income producing assets. Individuals choose education and training to build capital in the form of enhanced skills and competencies that they believe will bring them future rewards in the form of higher earnings in the workplace when they complete their education and training.

In deciding whether to pursue education, an individual—or typically in the case of children, their parents—must evaluate whether what is given up today is justified by the rewards received in the future. If a child goes to school instead of working,² the family must give up the child’s income or the goods and services that the child would have produced for the family. These are the “opportunity costs” of going to school. In addition, the family may also have to pay out of pocket expenses for tuition, for text books, school uniforms and a number of other incidental costs.

When deciding between work or school for their children, families consider as the cost of education the sum of the opportunity and out of pocket costs, and weigh them against the benefits education brings for the child.³ In the human capital model, the benefits accrue from higher earnings over the lifetime of the child as an adult educated worker compared to the earnings as an uneducated child worker who would continue to forgo these benefits as an uneducated adult worker. The difference between the educated and uneducated worker’s earnings is the payoff to education. By comparing this payoff or benefit to the costs of education, and factoring in the effects of time and impatience,⁴ families can decide whether education is a profitable investment for their children.

Clearly, most families do not construct ledgers or make explicit calculations about the value of education for their children. But it is reasonable to expect that they at least loosely consider the costs and benefits described above, and that analyses of their choices should confirm whether families are behaving as rational investors would in seeking out profitable investments on behalf of their children.

2. The Rate of Return and Investment Profitability

The main tool to evaluate the profitability of an investment is its rate of return. A rate of return is similar to an interest rate on a savings account. In fact, the interest rate on a savings account is a rate of return. At some early date, money—the principal—is deposited into the account, and it grows at some rate of interest. Eventually, that interest is returned, along with the principal, to the holder of the savings account. Similarly, money may be invested in other assets whose value will grow or decline. That growth or decline is the investment’s “rate of return.” If the rate of return is positive, more money is returned to the investor than was initially invested; if the rate of return is negative, the investor gets back less.

The rate of return to an investment is a useful measure because it reveals in a single number the benefits of an investment. The rate of return also allows for the evaluation of one investment against other investment options. This comparison is a key element in assessing an investment’s profitability.

In determining if a child’s time and other monetary resources are best allocated to schooling, it is important to consider the alternative investment options. If the return on some other opportunity is greater than the return to education, an investor with limited resources would be better off—at least from a financial perspective—choosing to invest in the alternative opportunity. For example, suppose that the rate of return to the education of a farm family’s child was nine percent, but alternatively the family could send the child to work and use the proceeds from the child’s labor to invest in, say, a tractor which would yield a return of 11 percent. If the family’s resources are so limited that it can only take on one investment or the other, investing in the tractor is the financially more sound investment.

Now suppose that credit is available so that resources need not be limited to those currently available to the family. Further, suppose that the interest rate on a loan taken out to finance the direct and indirect costs of education is less than the rate of return expected for the investment in education. Then borrowing to finance education would be a wise course of action because the returns to education would be expected to be large enough to allow the loan to be repaid and still leave something for the investor. This logic applies to any investment: it is profitable to pursue any investment for which the rate of return exceeds the rate of interest for borrowing. Continuing with the example of the previous paragraph, if the rate of interest for borrowing for any project is, say, seven percent, then the family should borrow to invest both in the tractor and the child’s education since both are expected to yield rates of return that imply that the family can more than cover the costs of borrowing.

On the assumption that credit is available for financing investments in education, the forgoing discussion suggests that these investments can be gauged by comparing their rates of return against market interest rates for borrowing. If the rate of return to education exceeds the market interest rate, then the investment is profitable. The main problem with this evaluation rule is that it is usually difficult to determine the market interest rate for borrowing. And particularly when it comes to financing education in less developed countries, this is largely because credit markets may not exist.⁵ The choice of a benchmark against which to compare rates of return to education to assess education’s profitability then comes down to an educated guess. This report uses a benchmark of seven percent because this is the most commonly assumed estimate of a long term interest rate.⁶ Thus, an investment in education on behalf of a child is considered to be profitable if its expected rate of return exceeds seven percent.

3. Measuring Rates of Return to Education

There are basically two methodologies to estimate individual rates of return to education from data on individual earnings.⁷ In the first, known as the “full discounting” (or “full”) method, individuals are grouped by age and educational attainment, and average earnings are calculated within each age education group, so that an average age based “salary history” can be constructed for individuals with a given level of education. The return to the additional level of schooling is found by comparing the costs and earnings streams of adjacent education groups. For example, in the case of primary education, the rate of return is calculated as that rate which makes the stream of earnings of the typical primary educated worker equal to the  earnings of a typical uneducated workers plus the costs of education.⁸ In the second approach, known as the “Mincerian” or “earnings function” method, statistical techniques are used to control for individual characteristics, and the rate of return is derived based on the difference in earnings of persons who are “statistically similar” except for their differences in years of educational attainment.⁹

The choice of methodology is often dictated by data availability. The earnings function approach has the advantage of not being as demanding in terms of the amount of data needed to implement it. It can provide a good ballpark estimate of the rate of return to education. In principle, the full method can provide even better estimates; however, the full complement of data needed to implement it is often unavailable. Thus, the rates of return generated by the two methods are not exactly comparable. Some of the more important reasons for this follow.

One problem with studies that use the earnings function method is that technically it yields a rate of return to the highest year of schooling received by the typical person in the sample. If the rate of return to each year of schooling is not the same, the earnings function estimate will not be an accurate estimate of the return to individuals who vary in some way from the typical person in the sample. It is generally believed that each additional year of education returns less than the one before it,¹⁰ so that individuals with fewer years of education than the average person will have a higher rate of return than that estimated using the Mincerian method. In considering child labor versus education, interest is most focused on the rate of return to primary education. If the years of education of the typical person in the sample exceed primary levels, the estimated rate of return is likely to be too low an estimate of the returns to primary education.

A second drawback to the earnings function method is that it assumes implicitly that individuals forgo earnings at all points during their education. In most countries, even those where child labor is prevalent, the youngest children are least likely to work, or work for pay, so that their costs of forgoing work and pursuing education are almost always overstated by the earnings function method. The concern with which this consideration should be accorded depends on the average level of education in the economy under study. If educational attainment is high, the forgone earnings of young children are a small consideration relative to the total forgone earnings resulting from investments in education, and the rate of return calculation is not likely to be much lower than it should be. But if average educational attainment is low, then the forgone earnings assumed to young children are likely to make up a large portion of the costs of schooling and therefore the rate of return measured may quite substantially underestimate the true rate of return.

On the other hand, the earnings function method tends overestimate the individual rate of return to education if the direct costs of education are borne by the individual receiving it, particularly if these costs are high. This is because the methodology does not factor these costs into the calculation of the rate of return. Since the rate of return is an indication of the degree to which the benefits of education exceed the costs, and the costs are underestimated, the degree to which the benefits exceed the costs tends to be overestimated.

A final drawback—although this is actually related to the way results from earnings function studies are normally presented rather than a problem with the methodology per se—is that returns based on earnings function are usually not available by the educational groupings that are standard in international education data, i.e., “primary,” “secondary,” and “tertiary” or “university.”

4. Empirical Evidence

Tables A-1 and A-2 at the end of this appendix present estimated rates of return to education for many countries around the world. The estimates in Table A-1 were derived using the full method, while those in Table A-2 correspond to the earnings function methodology.

Turning first to Table A-1, the estimates in the panel labeled “Private Returns” indicate that only two out of the 53 studies that reported rates of return to primary education found rates of return less than the baseline figure of seven percent. Forty-six studies found returns well in excess of seven percent ( ten percent or higher), and several studies reported returns of more than double the seven percent benchmark. Returns to secondary and higher education also tend to exceed the benchmark.

The earnings function method used in Table A-2 similarly indicates strong rates of return to investments in education. As shown in the column labeled “coefficient,” 88 of the 109 studies in the table show rates of return to education exceeding the seven percent benchmark. The estimated private returns in Table A-2 tend to be lower than in Table A-1, which may be expected for the reasons noted above. However, the message from Table A-2 remains the same as the message from Table A-1: investment in education is a profitable choice for individuals and households.

One criticism of the individual rate of return is that while it takes into account the costs of education borne by individuals, it does not take into account the costs of education that are borne by society, such as the cost of providing free public schooling. Similarly, some benefits of education do not accrue exclusively to individuals, but also benefit society at large. For reasons discussed in Chapter II, it is relatively easy to adjust private rates of returns to reflect social costs but not for social benefits.

In Table A-1, the panel entitled “Social Returns” presents “narrow” social returns that adjust private returns to take account of social costs (but not social benefits). Even with this downward adjustment, the narrow social rates of return are nearly always higher than the seven percent benchmark, reinforcing the proposition that education is a worthwhile investment. The correct interpretation of this evidence is as follows: if the social costs were shifted back to the families whose children are educated, this shift could be done in a manner so that the families would pay all the costs of their children’s education and still conclude that education is a profitable investment. At the very least then, it is safe to conclude that societal decisions to subsidize education do not divert children to school when working would be a socially preferable use of their time.

Finally, recall from the previous section that the ideal way to assess the profitability of education would be to compare rates of return against applicable market interest rates. But this is generally not possible because market interest rates are not available, and therefore a benchmark of seven percent has been used as a proxy. See Table A-3 which compares rates of return to education and estimates of market interest rates for a set of 15 countries.¹¹ For 12 out of the 15 countries, the rate of return to education exceeds the market interest rate, offering more evidence that education is a profitable investment.

5. Education or Ability?

There is little controversy in the economics literature over the finding that more educated individuals earn more than less educated ones, or the methodology that yields this finding. There is, however, some controversy over the interpretation that the higher earnings of educated workers represent returns to investments in education.

Some economists have suggested that individuals pursue education as a way to signal their innate level of ability.¹² They posit that since the payoff to education is only forthcoming to individuals who demonstrate their ability on the job, low ability individuals choose to forgo education, and the costs it entails, because they expect that education will not affect their earnings. According to this view, since only innate ability matters ultimately it makes sense for an individual to save on the costs of education, unless the individual is a high ability worker. Notice that education does nothing more in this theory than reveal abilities; the payoff in the form of higher wages rewards those abilities, and education itself does not confer any extra benefit. If this were true, then education should not be viewed as an investment in future productivity enhancements and there should be no special efforts to encourage education.

Most attempts to portion out higher earnings of educated individuals between ability and education have shown that, even if ability does matter some, there is still a specific payoff to education per se.¹³ Perhaps the most convincing studies have been those which measure the returns to education of identical twins. Because identical twins are genetically equivalent, so are their ability levels; therefore, identical twins should receive the same earnings regardless of educational attainment. After accounting for a number of other factors that might cause differences in the earnings of identical twins, studies generally show that the more educated twin earns more,¹⁴ demonstrating that education itself does matter.

C. The Relationship Between Education and Economic

Growth

At the country level, a question that is often asked is does education affect economic growth? Research suggests that education makes individuals more productive, and rewards them for this enhanced productivity, suggesting that education should be related to better macroeconomic performance. If education makes individual citizens more productive and leads to growth in their individual income prospects, the average level of productivity and growth of income in a nation’s economy should also be higher.

1. Growth Accounting

Gross domestic product (GDP) measures a country’s output, i.e., the sum of all goods and services produced in the country in a given time period. Output is produced using inputs, or factors of production, such as land, labor, and capital. Each of these inputs makes a contribution to GDP, its growth, or both.

In the 1950s, Nobel Laureate Robert Solow proposed “technical change” as an additional input to which some portion of GDP should be attributed. This insight acknowledged that something other than land, capital, and “head count” labor could affect GDP and its growth rate. Initially, technical change was a catch-all category that accounted for any portion of output that could not be attributed to land, labor, or capital. However, in the 1960s, economists established that embedded in technical change could be the effect of education on the GDP and its growth.¹⁵ Rather than treating “labor” as homogeneous units, it should be differentiated by educational attainment. Making this adjustment reduced the amount of GDP and its growth attributed to the catch-all technical change by allotting more to more educated types of labor.

These insights spawned a number of growth accounting studies in which GDP growth in an individual country was attributed to growth in the factors of production. Results from a number of these studies have been collected in Table A-4. The figures presented cover varying time periods and have not been derived in ways that are strictly comparable; therefore, comparisons across countries should be avoided. The figures have been included only to emphasize the big picture: in nearly all cases, a significant portion of GDP growth is attributed to education.

2. Cross-Country Analyses

An alternative approach to assessing the macroeconomic impact of education is to use statistical techniques on cross-country data to assess whether countries with higher levels of, or larger changes in, educational attainment grow faster than other countries. In these exercises, a variety of other variables that might affect growth rates are factored out statistically, so that the impact of education is not confused with the impact of other variables, such as population growth.¹⁶

Table A-5 summarizes 27 studies which analyze cross-country data to assess the relationship of education to growth. Unlike the individual level results, which are clear on the point that education is a profitable investment, and the growth accounting results, which tend to suggest that education contributes positively to growth, cross- country studies present a more clouded picture. Among the inconsistencies are the findings of some studies that education affects growth negatively; and, the differences in the mechanisms through which education spurs growth, e.g., the level versus growth in education, primary versus secondary education, education of males as opposed to females, and the existence of a threshold level of education that must be passed before a positive relationship is discovered.

The inconclusiveness of the cross-country literature on the relationship of education to growth results in part from data and methodological shortcomings. Another shortcoming is that cross-country studies have generally ignored the question of whether the relationship between education and growth implies social rates of return to education that exceed private rates of return. As explained in Chapter II, this is a very important issue from a policy perspective. If the social returns to education exceed the private returns, then additional returns to society can be secured if society invests in education beyond the investments made by its individual members.

Comparable measures of schooling or educational attainment in a cross-country context are hard to establish. Data are typically reported by level of education, e.g., primary, secondary or tertiary, or by years of education completed. Both of these measures are affected by the fact that the quality of education in one country may not be the same as in another. For example, the educational attainment associated with five years of schooling in one country may not be equivalent to five years of schooling in another if there are vast differences in the quality of schooling. Yet cross-country data would report only the number or proportion of individuals with five years of schooling in each country, as if each group of individuals was equally well educated. Another manifestation of the quality issue is the fact that hold back rates may differ from country to country, so that in a country where holding back students is relatively common, more years of schooling may not signal the actual attainment of more skills and competencies. Finally, there are vast differences in the quality of data collection efforts across countries, suggesting that errors of measurement–e.g., different years of schooling recorded than actually experienced—could contaminate the underlying data. These errors of measurement could be particularly problematic in data sets where some of the education data are imputed based on past or related data.

A recent study¹⁷ assesses the influence of errors in education data on the results of studies that attempt to measure the relationship between education and growth. It compares different data sources and uses statistical techniques that to some extent fix errors in the data. The study finds that once these errors are dealt with to the extent possible, the results from studies that show a negative relationship between changes in education and economic growth tend to be reversed. The study further concludes that there are certain inherent and unfixable problems in education data that make them unsuited to conclusively address the question of whether the social returns to education exceed the private returns. Finally, the study points to the credible theoretical arguments describing spillover benefits as the strongest case for public involvement in educational investments.¹⁸

Another recent study¹⁹ evaluates methodological approaches to analyzing the relationship between education and growth and finds them to be disappointing. For example, one influential approach could yield either a negative or a positive relation- ship between education and growth and either result could be consistent with the hypothesis that education encourages growth or with the hypothesis that education retards growth. In other words, the methodology allows no firm conclusion about the causal relationship between education and growth. When the methodological approach is more consistent with the earnings function methodology used to analyze individual data, the results have the unambiguous interpretation of being social rates of return to education. Moreover, they are positive and sometimes larger than comparable individual rates of return.²⁰ However, given the methodological and data problems in  this line of research, the author of this study suggests that the strongest evidence that education enhances human capital and productivity still comes from the studies using individual level data.²¹

D. Conclusion

The details reviewed in this appendix support the conclusion in Chapter II that the most convincing evidence about the profitability of education as an investment comes from the studies that work with data on the experience of individuals. These studies clearly suggest that education is a profitable investment made on behalf of an individual child. Research that aims to assess how education translates directly into macroeconomic outcomes (such as growth in GDP) is not as conclusive with regard to the value of education as a social investment. This inconclusiveness appears to stem mainly from data and methodological problems. Theory suggests that there are a number of ways that education should benefit society beyond the sum total of the benefits to the members of society. While there is not enough confidence among economists in existing evidence to conclude the theory has been proved, there appears to be less confidence that the evidence disproves the theory.²²

• Table A-1: Returns to Investment in Education by Level
• Table A-2: Coefficient on Years of Schooling: Mincerian Rate of Return
• Table A-3: Returns to Investment in Education and Bank Deposits (percent)
• Table A-4: Percentage of Economic Growth Rate Attributed to Education
• Table A-5: Education and Growth: Evidence from cross-country Studies

¹ This appendix draws heavily on a background paper, available on request, prepared under contract for this report: George Psacharopoulos, “The Opportunity Cost of Child Labor: A Review of the Benefits of Education” (Washington, D.C: Bureau of International Labor Affairs, U.S. Department of Labor, June 1999).

² This could mean that the child goes to school instead of working at all, or it could mean that the child works fewer hours so that the child can also go to school.

³ Recall from Chapter II that families do not consider (fully) benefits that accrue beyond the child or family when deciding whether a child should go to school, so that many of the benefits that education brings from a social perspective are not considered in the context of private family decisions.

⁴ Inflation matters because the higher the rate of inflation the higher future earnings have to be to compensate for giving up current earnings. Patience matters because more impatient, or perhaps desperate because of poverty, individuals would rather have money and the things it can buy today rather than waiting for some higher standard of living and consumption in the future.

⁵ Lars Ljungvist, “Economic Underdevleopment: The Case for Missing Markets for Human Capital,” Journal of Development Economics, 40(2) (April 1993) 220. See also, M. Woodhall, “Designing a Student Loan Program for a Developing Country: The Relevance of International Experience,” Economics of Education Review, 7 (1)1 (1988): 160.

⁶ “Deep Discount,” The Economist, 351 (8125) (June 26, 1999) 90.

⁷ This is a synthesis of a more detailed discussion of methodological issues that may be found in George Psacharopoulos, “Returns to Investments in Education: A Global Update,” World Development, 22(9) (September 1994): 1325-26.

⁸ Using the full method, the rate of return for primary education is calculated by solving for r the following formula

where r is the (internal) rate of return, (Y_p - Y_u)_t is the difference in earnings between a primary educated worker and an uneducated worker at some point in time t, and Y_u + C_u is the sum of the foregone earnings (Y_u) and out of pocket costs (C_u) that are incurred if someone goes to school. Note that the costs are incurred before date m, while the benefits accrue from date m+1 and beyond. Rates of return for higher levels of education are calculated analogously.

⁹ The basic earnings function takes the form:

where Y_i is the earnings of individual i, S_i is the number of years of schooling accumulated by that individual, EX_i measures the individual’s of experience in the labor market, and Z_i may contains other information about the individual such as gender, race, ethnic background, industry or occupation in which the individual works. The equation is fit using statistical techniques to data on a number of individuals to get an average or expected earnings function. Since b = ¶lny/¶S is approximately the percentage change in earnings that comes from one additional year of schooling, the coefficient b is interpreted as the rate of return to the last year of schooling. This method is also referred to as the “Mincerian” method after the economist, Jacob Mincer, who first proposed it.

¹⁰ That is, there are diminishing returns to education.

¹¹ George Psacharopoulos, “The Opportunity Cost of Child Labor: A Review of the Benefits of Education” (Washington, D.C: Bureau of International Labor Affairs, U.S. Department of Labor, June 1999) 25-26. The market interest rate used is the real bank deposit rate which is the nominal interest rate on a variety of bank deposits less the rate of inflation.

¹² See, for example, Michael Spense, “Job Market Signaling,” Quarterly Journal of Economics 87 (3) (August 1973) 355-374.

¹³ See, e.g., Zvi Griliches and William M. Mason, “Education, Income and Ability,” Journal of Political Economy 80(3), Part II (May-June 1972): S99; and J. Bound, Z. Griliches and B.H. Hall, “Wages, Schooling and IQ of Brothers and Sisters: Do the Family Factors Differ?” International Economic Review 27(1) (February 1986) 77; and, Colm Harmon and Ian Walker, “Estimates of the Economic Return to Schooling for the United Kingdom,” American Economic Review 85(5) (December 1995) 1284.

¹⁴ Orley Ashenfelter and Alan Krueger, “Estimates of the Economic Return of Schooling from a New Sample of Twins.” American Economic Review, 84(5) (December 1994) 1157; Cecilia E. Rouse “Further Estimates of the Economic Return to Schooling from a New Sample of Twins,” Economics of Education Review, 18(2) (1999) 149-157; Paul Miller, Charles Mulvey and Nick Martin, “What do Twins Studies Reveal About the economic Returns to Education? A Comparison of Australian and U.S. Findings,” American Economic Review 85(3) (June 1995) 597.

¹⁵ For example, T.W. Schultz, “Investment in Human Capital,” American Economic Review, (March 1961); and, Edward F. Denison, Why growth rates differ; postwar experience in nine western countries, (Washington: Brookings Institution, 1967).

¹⁶ This list of variables factored out, or “controlled for,” can be quite long. In one of the more parsimonious exercises, N. Gregory Mankiw, David Romer and David M. Weil, “A Contribution to the Empirics of Economic Growth,” Quarterly Journal of Economics 107(2) (May 1992) 420, data on the log of per capita GDP (GDP*) is fit to data on the fraction of 12 to 17 year olds enrolled in secondary education multiplied by the fraction of the working age population that is of school age (ED), the ratio of physical investment to GDP (I/GDP), the rate of population growth (n), the rate of growth of technology (g), and the rate of physical capital depreciation (d). The result is:

GDP* = 7.81 + 0.73 log(ED) + 0.70 log(I/GDP) - 1.50 log (n + g + d),

which implies that after controlling for I/GDP, n, g and d, a one percent change in ED raises per capita GDP by 0.73 percent.

¹⁷ Alan B. Krueger and Mikael Lindahl, “Education for Growth: Why and For Whom?” (Princeton, NJ: Princeton University Department of Economics, February 1999).

¹⁸ Alan B. Krueger and Mikael Lindahl, “Education for Growth: Why and For Whom?” (Princeton, NJ: Princeton University Department of Economics, February 1999) 44-45.

¹⁹ Robert Topel “Labor Markets and Economic Growth” paper presented to the Society of Labor Economists (1998, http://gsbmxn.uchicago.edu/SOLE/1998.htm) 31-32. Forthcoming in Orley Ashenfelter and David Card (eds.) Handbook of Labor Economics, vol. III.

²⁰ Robert Topel “Labor Markets and Economic Growth” paper presented to the Society of Labor Economists (1998, http://gsbmxn.uchicago.edu/SOLE/1998.htm) 46. Forthcoming in Orley Ashenfelter and David Card (eds.) Handbook of Labor Economics, vol. III.

²¹ Ibid. at 48.

²² George Psacharopoulos, “The Opportunity Cost of Child Labor: A Review of the Benefits of Education” (Washington, D.C: Bureau of International Labor Affairs, U.S. Department of Labor, June 1999) 41-49.