metadata: authors: 0: author: Lau, Lawrence J.
1: author: Jamison, Dean T.
2: author: Louat, Frederi
docna: 0: docna: Education and productivity in developing
            countries : an aggregate production function approach
docty: Policy Research Working Paper
subtopic: Demographics,Primary Education,Secondary Education,Economics of Education,Educational Sciences
teratopic: Education
abstracts: cdata!: The estimated rates of return to
            education are typically (often considerably) above 10
            percent a year in real terms - a respectable rate of return.
            The rates of return are highest for primary education, and
            higher in countries where educated manpower is scarcer, and
            the durability of educational capital can be as high as 50
            years.  The effect of education on real output has not been
            well documented.  The authors have pooled data on 58
            developing countries, from 1960 through 1986, to estimate an
            aggregate production function using as independent variables
            the quantities of capital, labor, land, average educational
            attainment of the labor force, and chronological time.  They
            measured the percentage change in a region's real GDP
            in response to an increase of one year in the average
            educational attainment of the working age population in
            1985.  The estimated effects range from negative to more
            than 5 percent a year.  The results suggest : a) a positive
            relationship between the level of primary schooling achieved
            and the size of its effect; b) a threshold of four years of
            schooling before primary school has an effect; and c) the
            effect of secondary education seems to be independent of the
            level of secondary schooling attained, although local
            factors may predominate here.  The authors conclude that
            education is an important determinant of aggregate real
            output and productivity but that its effect varies
            considerably across countries and regions.
repnme: repnme: Education and productivity in developing
            countries : an aggregate production function approach
display_title: Education and productivity in
            developing countries : an aggregate production function approach
listing_relative_url: /research/1991/03/700043/education-productivity-developing-countries-aggregate-production-function-approach
topicv3: Primary Education m1326139 480,Education m1327048 470,Secondary Education m1327058 481,Economics of Education m1327511 1540,Population Projections m1504366 3662
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Education
origu: Policy, Research & Ect Affairs
no_of_pages: 38
model_extractions: **Policy, Rerorh, and Extwnal Aftfir**

**World Development Report**

WPS 612

- This paper a product of the Wclfare and Human Resources Division, Population and Human Resources Department - was prepared **as** a background paper for the _1990 World Developmeni Report_ on poverty. Copies are available free from the Woild Bank, 1818 H Street NW, Washington DC 20433. Please contact the World Development Report office, room SI 3-060, extension 31393 (33 pages, with tables).

The estimated rates of return to education are typically (often considerably) above 10 percent a - year in real terms a respectable rate of retum. The rates of return are highest for primary education, and higher in countries where educated manpower is scarcer. And the durabili of educational capital can be as high as 50 years.

But the effect of education on real output has not been well documented. In particular, few published studies of aggregate production functions establish a statistically significant link between real GDP and the labor force's educational attainment. Lau, Jamison, and Louat found that education has had littile effect on the aggregate real GDPs of a sample of Sub-Saharan African countries.

Now Lau, Jamison, and Louat have pooled data on 58 developing countries, from 1960 through 1986, to estimate an aggregate production function usinig as independent variables the quantities of capital, labor, land, average educational attainment ol' thC labor force, and chronological time.

They measured the percentage change in a region's real GDP in response to an increase of one year in the average educational attainment of the working age population in 1985. The estimated effects range from negative to more than 5 percent a year.

# The results suggest:

> * A positive relationship between the level of primary schooling achieved and the size of its effect.

* A threshold of four years of schooling before primary school has an effect.

c The e'flect of' secondary education seeCIms to be independent of the level of secondary schiooling attained, although local factors may predomiiinate here - wittess the negative eli'ect estimated for South Asia.

They conclude that educatioln is an important determinant of aggregate real output and productivity but that its eff'ect varies considerably across countries and regions.

More research is needed to explain why education varies in its ef'fectiveness, especially where the ef'f'ect appears to be n1egaltivc. TIlcy speculate that certain f'actors mazy inlIuence the e'ffect of primrary and secondary education on aggregate real output - among them, a country's institutions, its organizations lor production and distribution, the compositioni and skill requirements of its industries, the stiucture of education, and the incidence of war anid pestilence.

The PRE Working Paper Scries disseminatcs thc findings of work under **way** in **the** Bank's Policy, Research. an(l Extcmal AffairsComplex. Anobjectiveofthcscries is togetthcscfindingsoutquickly,even if prcsentations arc less thain fullylpolished. The flndings, interpretations, and conclusions in these papers do not necessarily represent official Bank polic .

P'rd,z&ei ds thl< I'Kl R I) ..eimI.ti;Ktn _(.entcr_
# Table of Contents

|Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .<br>1|
|---|
|The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .<br>4|
|The Data<br>.<br>. . . . . . . . . . . . . . . . . . .<br>. .<br>. . . . .I<br>. .<br>8|
|The Estimation Results<br>. . . . . . . . . . . . . . . . . . . . . . . . . . 16|
|Concluding Remarks<br>. . . . . . . . . . . . . . . . . . . . . . . . . . . . 22|
|References<br>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25|
|Tables|
|Table 1 Average Years of Primary Education, by Region . . . . . . . . . . 13|
|Table 2 Average Years of Secondary Education,<br>by Region . . . . . . . . . 13|
|Table 3 Average Years of Total Education, by Region . . . . . . . . . . . 13|
|Table 4 Ratio of Primary Education Attainment to|
|Secondary Education Attainment . . . . . . . . . . . . . . . . . . . . . . 14|
|Table<br>5Alternative Specifications<br>of the Aggregate|
|Production Function with Region-specific<br>Effects of<br>education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17|
|Table 6 Alternative<br>Specifications<br>of Aggregate|
|Production<br>Function<br>without<br>Region-specific|
|Effects<br>of Education<br>. . . . . . . . . . . . . . . . . . . . .18|
|Table<br>7 Tests<br>of Hypotheses<br>. . . . . . . . . . . . . . . . .19|
|Table 8 Percentage Change in Real GDP in Response to an<br>Additional Year of Education per person of Working Age<br>in 1985 . . . . . . . . . . . . .<br>. . . . . . . . . . . . .20|

# Figures

|Figure 1 Effect of one Additional Year of Primary|
|---|
|Education per person on Real GDP (%) . . . . . . . . . . . . . . .23|
|Figure 2 Effect of one Additional Year of Secondary|
|Education per person on Real GDP (%) . . . . . . . . . . . . . . .23|
|Figure 3 Effect of one Additional Year of Total|
|Education per person on Real GDP (%) . . . . . . . . . . . . . . . . . . . 24|
|ADpendices|
|Appendix 1 List of Countries in the Sample, by Region . . . . . . . . . . 27|
|Appendix 2 Comparison of Estimates of Educational|
|Capital Stocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28|
|Appendix 3 Estimation Results under|
|Constant Returns to Scale . . . . . . . . . . . . . . . . . . . . . . . . 32|
|Appendix-Table 1 Alternative Estimates of Mean Years<br>of Schooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30|
|Appendix-Table 2 Corrleation between the Estimates|
|of Total Years of Schooling . . . . . . . . . . . . . . . . . . . . . . . 31|
|Appendix-Table 3 Alternative Specifications of the|
|Aggregate Production Function with Region-specific|
|Effects of Education, Under Constant Returns to Scale . . . . . . . . . . 33|

The authors are respectively Professor of Economics, Stanford University, Professor of Education and Professor of Public Health, University of California at Los Angeles, and Researcher at the World Bank. They are grateful to Bela Balassa, John Ham and Jacques van der Gaag for helpful comments and ShuCheng Liu and Regie Stites for competent research assistance.
Education and Productivity in Developing Countries: An Aggregate Production Function Approach Lawrence J. Lau, Dean T. Jamison and Fr6deric F. Louat

# 1. Introduction

Education is well known to have a direct and positive effect on economic development,<sup>economic</sup> growth and productivity. For examples: Denison (1967, 1979), using a growth-accounting framework, found that between ten and fifteen percent of the growth in the real national income of the United<sup>States</sup> can be attributed to education'; Jamison and Lau (1982), summarizing more than thirty<sup>studies of the</sup> relationship between agricultural output and education around the world, estimated that<sup>each additional</sup> year of education achieved by the head of an agricultural household increases its annual<sup>agricultural</sup> output, holding the agricultural inputs constant, by an average of slightly less than two percene;<sup>Lau and</sup> - Yotopoulos (1989), on the basis of three years of intercountry data<sup>-</sup> 1960, 1970 and 1980 assembled and constructed by Hayami and Ruttan (1985), estimated that every increase in the<sup>number of</sup> agricultural college and university graduates per ten thousand of the agricultural population of<sup>a country</sup> 'Denison also attributed similar, but somewhat smaller, percentages of the growth in real national income to education in other countries. See also Bowman (1980).

'See Jamison and Lau (1982), pp. 35-38.
increases annual agric'i. tiral output, holding the agricJltural inputs constant, by approximately ten percent'. While the magnitudes of Lhese effects are not exceptional!y large, they can be economically significant because of the durability of educational capital which can be as high as fifty years.

There have also been numerous studies in which the economic benefit of education is measured in terms of its effect on the lifetime earnings of individual workers. The implied rate of return to the education is then estimated. This is the so-called 'Human Capital' approach, pioneered by Schultz (1961). PsacharopoLulos (1985) has summarized the many rate of return to education studies around the world. He found that the estimated rates of return to education arr .ypically above, and sometimes considerably above, ten percent per annum in real terms, which is generally considered a very respectable rate of return. The rates of return are higher for lower levels of education, that is, they are the highest for primary education, followed, in descending order, by respectively secondary and higher education. They are also higher in countries where educated manpower is more scarce.

What are some of the channels through which education affects economic growth, productivity and development in general? First, education enhances the ability of an individual to perform standard taskc and to learn to perform new tasks. Second, education enhances the ability of an individual to receive and process new information. Third, education enhances the ability of individuals to communicate and therefore to coordinate activities with one another. Fourth, education enhances the ability of an individual to evaluate and adjust to changed circumstances. Fifth, education helps to reduce subjective uncertainty and unnecessary anxiety as well as fatalistic acceptance of the status quo and thereby enhances the probability of adoption of new technologies or practices by an individual. Finally, at higher levels, education also helps to bring about innovations in the production technology.

Moreover, there is evidence from the experience of many countries that education, by enabling the acquisition of the necessary skills by the workers, is in fact a complementary input to physical capital 'See Lau and Yotopoulos (1989).

2
and technology. Having physical and financial capital as well as access to technology is not enough: there must be the skilled manpower to make use of these resources. For example, the successes of South Korea and Taiwan in developing their resnective economies and the failure of Thailand, until recently, to develop hers, may be partially attributed to the relatively lower level of educational development in Thailand in the 1960's and 1970's. By the late 1980's, however, Thailand has finally caught up with the level of educational development achieved by South Korea and Taiwan in the early 1960's and is now well on her way to becoming the fifth "Newly Industrialized Economy' (NIE).

Despite the abundance of microeconomic level empirical evidence on the positive effect of , .. 1;aon on productivity, at the aggregate, macroeconomic level, the effect of education on real output has not been well documented.' In particular, there are very few published studies of aggregate production functions that succeed in establishing a statistically significant direct link between real GDP and the educational attainment of the labor force. One reason why the effect of education is frequently found to be statistically insignificant in aggregate production function studies for individual countries is multicollinearity of the data on the inputs: capital stock, labor force (less so for employment), and educational attainment of the labor force. (The land input generally does not vary much.) The capital stock and labor force are usually heavily trended. Similarly, the average level of educational attainment of the working-age population typically shows slow and smooth increases over time. The consequence is that it is difficult if not impossible to identify the effects of capital and labor, let alone those of education and technical progress, separately, using time-series data from a single country. Moreover, the effects of scale are often confounded with those of technical change, especially if all the inputs have been increasing over time. Thus, additional rastrictive assumptions (such as constant returns to scale in the physical inputs) frequently have to be made in order to obtain meaningful estimates.

'Aggregate production function studies for the agricultural sector have found statistically significant positive effects of education on output. See, for example, Lau and Yotopoulos (1989).

3
The muil.collinearity and the resulting r.on-identification of the key parameters of the aggregate product n function c be overcoir. by pooling the time-series data of several countries and by standardizing the measurements of the inputs. Such an attempt was made by Jamison and Lau<sup>in an</sup> unpublished study of the aggregate real outputs of the countries of sub-Saharan Africa for the period 1960-1985. They found, contrary to expectation, that education has had little effect on the aggregate real **GDPs** of **these** countries. **This** finding **may,** however, **be** attributed to the unfavorable local conditions, the lack of complementary inputs, insufficient institutional capability, or failure to reach a critical threshold, rather than the general ineffectiveness of education per **se.** It is t!erefore of both academic and practical interest to ascertain whether the finding for subSaharan Africa is applicable elsewhere. In this study, the data of 58 developing countries from 1960 through 1986 are pooled to estimate an aggregate production function with the quantities of capital, labor and land, average educational attainment of the labor force, and chronological time as the independent variables.

# 2. The Model

Aggregate real output, the dependent variable of the production function, is measured as the real GDP in constant 1980 U.S. dollars. The independent variables consist of the quantity of the capital stock at the end of the previous year, also in 1980 U.S. dollars, multiplied by an estimated country-specific rate of utilization for the current year, and the quantities of labor force ar.d arable land for the current year. In addition, there is a vdriable measuring the average nun ber of years of schooling, both separately and together for primary and secondary education, per person of working age, defined to be 15-64. Tertiary education was omitted because data are available for very few countries.

The basic maintained hypothesis of the study is that all countries have the same underlying production function in terms ef standardized inputs. However, countries may differ in terms of the 4
definitions and qualities of their measured inputs and in their levels of technical efficiencies in production Thus,

# (2.1) Yi, = Ajo(t) F(KWj, L%, T'j, E'i)

where **Yh** is the quantity of real output of the **ith** country in period **t,** AjO(t) is an index of technical efficiency (the ability of producing output from given inputs) of the **ith** country in period **t,** and **K,,** L', T%, **E',** are the standardized (or efficiency equivalent) quantities of physical capital, labor, land and educational capital of the ith country in period t respectively. Note that the production function, F(.), is the same for all countries.

However, the quantities of standardized inputs can not be directly observed. It is assumed that the quantities of measured inputs may be converted into standardized inputs through mult.plicative factors called augmentation factors. Specifically, Note that the augmentation factors are country as well as input specific. For one reference country, Aix may be set equal to one for all X. This is equivalent to standardizing all inputs in terms of the inputs of that country. For example, if China is selected to be the reference country and Indian physical capital is fifty percent more effective than Chinese capital, then **ACK=** I and **AIK=** 1.5 where the subscripts C and I refer to China and India respectively. These augmentation factois are also not directly observable.' lit turns out that country and input-specific standardization or conversion factors can in fact be separately identitfied and estimated from the data under some circumstances. See Lau and Yotopoulos (1989) and Boskin and Lau (1990).

5
In this study, the aggregate production function is assumed to have the Cobb-Douglas form, so that: (2.3) InYj, = lnAjO(t) + £ OXa 1nXit X-K. **LT, B** It is further assumed that the technical efi1ciency factors take the form

# (2.4) Ajo(t) = Ajo **exp(OR** DjR.t)

where DIR is a dummy variable which takes the value one if the ith country is in the **Rth** region and ia may be interpreted as the rate of growth of totil factor productivity (or equivalently technical change) in the Rth region. Under these assumptions, the production function in equation (2.3) may be rewritten as: Equation (2.5) relates the quantity of measured real output to the quantit.es of measured inputs and chronological time. Note that all the augmentation factors collapse into single country-specific multiplicative factors, which, upon the taking of natural logarithms, become country-specific intercept terms in the regression equation. Thus, the augmentation factors themselves cannot be separately 6
identified in this case.' In this study, the aggregate Cobb-Douglas production function is represented in the natural logarithmic form, with all the variables, except chronological time, expressed in terms of their natural logarithms. Thus, the parameters may be interpreted as production elasticities. The elasticity of educational capital is, however, allowed to differ across geographic regions. Five regions are distinguished: Sub-Saharan Africa, East Asia, Latin America, Middle Ea, +-North Africa, and South Asia. - Three different measures of edu'cational capital are used primary education, secondary education, and primary and secondary education together. In addition, the trend rates of growth of total factor productivity, or equivalently the trend rates of growth of output net of the growth of inputs, are also allowed to differ across regions as well as between pre- and post-1980. These trends reflect not only the influence of technical progress, but also other regional or worldwide factors, for example, the macroclimatic change in Sub-Saharan Africa, the slowdown of world trade and the drying-up of credit and aid flows to the developing world in the 1980s, depletion of natural resources, the rising public concern for the environment in the newly industrialized economies, and the decline in the average length of the workweek, etc.

The aggregate Cobb-Douglas production function is estimated, after the natural logarithmic transformation, in the first-differenced form, by ordinary least-squares. The rationale for using the firstdifferenced form lies in our assumption concerning the stochastic disturbance term in the production function. We a.sume that the stochastic disturhance te- -i represents mostly technical change, which, while unpredictable, has persistent effects on current as well as future outputs once it has occurred. This may be contrasted to the case in which the stochastic disturbance term represents mostly weather, the 'The non-identification of input-specific augmentation factors is well-known for the Cobb-Douglas case. With other production functions, such as the transcendental logarithmic production function introduced by Christensen, Jorgenson and Lau (1973), the augmentation factors can in fact be separately identified and estimated.

7
effect of which is transitory and confined to the output of the current period. The use ef ordinary leastsquares may be justified by the fact that the c2pital stock of the previous year, the labor torce and land are either pre-determined or exogenous and that whatever country-specific effect there may be have been taken into account. In principle, however, the rate of utilization is endogenous, and one may wish to use the method of instrumental variables. Finding a set of country-specific instrumental variables that work for the entire sample is no **easy task. Limited experimentaion suggests that the resul rf the instrumental** variables estimation will not be qualitatively different from those of oruinary least-squares **as long as the chosen set of instrumental variables** can explain the rate of utilization adequately.

# 3. **The Data**

The principal source of data used in this study is the Bank Economic and Social Database (BESD) of the World Bank, which consists of a compilation of various databases from different sources (including the International Labour Office (ILO), the International Monetary Fund (IMF), the United Nations Educational, Scientific and Cultural Organization (UNESCO) and the World Bank itself).

The sample analyzed in this study consists of a set of 58 developing countries from five regions of the world. 26 corintries are located in Sub-Saharan Africa, 7 in East Asia, 15 in Latin America, 6 in the Middle East-North Africa region (MENA) and 4 in South Asia. Other developing countries have been excluded from the sample solely on the basis of data unavailability, with the exception of four European countries (Hungary, Malta, Portugal and Yugoslavia) which have been excluded because their historical development experiences, both economic and educational, were not directly comparable with those of the more typical developing countries. The complete list of c-rntries in the sample is presented in Appendix 1.

The aggregate real output of each country is measured by its real GDP in constant 1980 U.S. dollars, data on which are taken directly from BESD. The aggregate level of labor input is measured by 8
its labor force. The aggregate level of land input is measured by its quantity of arable land. All of these variables are taken directly from BESD. Data on another possible measure of aggregate labor input, employment, are unfortunately not generally available for the countries and the time period under study.

The construction of the physical and the educational capital stocks deserves so,..e explanation. The estimation of a time series of physical capital stocks for each country begins with the compilation and/or estimation of a time series of gross domestic investments (or gross domestic **fixed** investments whenever available) for each cotintry for as long a time period as possible.<sup>t</sup> Once such a time series is available, the time series of physical capital stocks can be estimated by the perpetual inventory method given the capital stock of any benchmark year, assuming an annual depreciation rate of, say, S percent.<sup>2</sup> Unfortunately, benchmark year capital stocks are not generally available for the countries in the sample. It has therefore been necessary to estimate a benchmark year capital stock for each country.

Tle procedure use-d in this study Is as follows. Both the ca; tal stocks and gross domestic (fixed) investments of all coult-ies in the sample are assumed to be zero in 1945. Linear interpolation is used to fill out Ehe missing years of data on gross domestic (fixed) investments in 1980 U.S. dollars up to 1960 or the l,rst vear for which data are available. On the basis of the ;;aal series of investments so obtained, the perpetual inventory method is used to generate the time series of capital stocks, assuming that they 'Gross domestic investment is the sum of gross domestic fixed investment and net change in stocks (inventory). It is generally larger than gross fixed investment, though not necessarily so. Tbkuis a time series of capital stocks constructed with a gross domestic investment series is likely to be different from that constructed with a gross domestic fixed investment series. However, as long as the ratio of gross domestic fixed investmen **t** o gross domestic investment is approximately constant for each country within the sample period, the estimation results for the aggregate production function will not be materially affected.

MThe formula used to construct the capital stock is: K, = 0.95 -,., + 1, 9
wer: zero in 1945 and a rate of depreciation of 5 percent per annum.' One may object to the realism of our assumption of a<sup>zero capital stock in 1945 for all the</sup> develuping countries. Obviously not all of the physical capital<sup>Ftock vanished during World War 11.</sup> However, with a rate of depreciation of 5 percent per annum, physical<sup>capital stock depreciates totally</sup> in approximately twenty years. The error introduced by assuming<sup>a zero capital stock in 1945 is likely</sup> to be small in the early 1960s 2nd immaterial thereafter. In<sup>any case, given the presence of country-</sup> specific constant terms in the aggregate production function (prior<sup>to first-differencing), only the</sup><sup>**rates**</sup> of growth of the physical capital stocks matter, the absolute values<sup>do not. Thus, our estimation results</sup> are unlikely to be sensitive to (reasonable) alternative estimates of<sup>the benchmark year capital stocks.</sup> Finally, a time series of annual rates of utilization of the capital<sup>stock is estimated for each</sup> country as the ratios of actual real GDP to potential real GDP.<sup>The potential real GDP series is</sup> constructed with the "convex hull" method, a variant of the "peak-to-peak"<sup>method. Starting with a plot</sup> of the time series of actual real GDP against chronological time, the<sup>time series of potential real GDP</sup> is given by the lowest concave (with cespect to time) curve the value<sup>of which in each period is greater</sup> than or equal to the actual real GDP for that period. The rate of utilization<sup>is then estimated as the ratio</sup> of actual real GDP to potential real GDP: its value is therefore always<sup>between zero and one. The time-</sup> series of utilization rates thus obtained for each country is multiplied<sup>to the estimated time series of</sup> capital stocks to generate a time-series of "utilized capital stocks' which<sup>are used in the actual estimation</sup> oi the aggregate production function.

'Other alternative methods can be used to provide estimates of the benchmark<sup>year capital stocks.</sup> For example, it is possible to use the average rate of growth of investment<sup>during the 1960s in each</sup> country to generate estimates of investments for years prior to 1960. The<sup>estimated time series of</sup> investments will reach zero not necessarily in 1945 and certainly not at<sup>the same time for all the</sup> countries. However, this method generates meaningful results only<sup>if the average rate of growth of</sup> investment during the 1960s is similar to the average rate prior to 1960. In certain countries<sup>with high</sup> rate-s of investment in the early 1960s, especially those which won independence at about<sup>the same time,</sup> this assumption is obviously unreasonable.

10
In the case of the educational capital stocks,<sup>the difference between stocks and flows is even more</sup> important because of the time lag between investment<sup>(school enrollment) and addition to the human</sup> capital stock (entry into the labor<sup>force) and because of the much longer durability of human capital</sup> compared to physical capital. The<sup>educational capital stock is defined as the total number of person-</sup> school years among the working age population<sup>(those aged 15-64). The estimation of a time series of</sup> educational capital stocks for each country<sup>begins, analogous to the case of the estimation of physical</sup> capital stocks, with the compilation and/or estimation<sup>of a time series of annual school enrollment figures</sup> separately for primary and secondary general<sup>education for each country for as long a time period as</sup> possible. Once such a time series is available,<sup>the time series of educational capital stocks can be</sup> estimated by the perpetual inventory method,<sup>assuming</sup><sup>**no**depreciation, no mortality and no migration</sup> during the working lives of individuals. For<sup>the period 1900-1960 (which is generally the first year of</sup> availability of the data), annual school enrollments<sup>are separately estimated for primary and secondary</sup> general education, based on backward trend<sup>extrapolation from the available actual data. Ordinary least-</sup> squares regressions are used to estimate these<sup>country-specific trends. However, if any backcasted annual</sup> enrollment figure is negative, it is automatically<sup>set equal to zero. With the estimated time series of</sup> annual school enrollments, the total number of<sup>person-school-years in the population of working age (15-</sup> 64 years), which is the total number of years<sup>of schooling completed by all individuals belonging to this</sup> age group, can be calculated.' The average<sup>number of years of schooling completed per person of</sup> working age is obtained by dividing the total stock<sup>of person-school-years by the size of the working age</sup> population in each period. Mortality during<sup>the working life is ignored in the estimation of the</sup> educational capital stock because of lack of<sup>data. Taking mortality into account would require age-</sup> specific mortality rates as a time-series for each<sup>country; in addition one would need to assume that they</sup> 'Unfortunately, the data available consist of only<sup>gross annual school enrollments at the primary and</sup> secondary levels and do not distinguish repeaters<sup>separately. Thus, the number of completed school years</sup> does not necessarily correspond to and in general<sup>will overstate the educationa</sup><sup>**l**evels attained.</sup> I1
do not differ across levels of educational attainment. Because mortality is ignored, our estimates of both the educational capital stock and the average number of years of schooling completed per person of working age are likely to be biased upward.' In the following tables we present the average years of schooling completed per person in the labor force, for primary, secondary, and total education, by region. The ratio of completed years of primary education to completed years of secondary education is also presented in Table 4.

'There are undoubtedly many other ways of estimating the annual enrollment figures for the pre-1960 period. It is our belief that short of attempting to collect actual school enrollment data on a country-bycountry basis it is unlikely that there will be an unequivocally better method.

12
Table 1 Average years of primary education.<sup>by region</sup>

||Africa|East<br>Asia|Mena|Latin<br>America|South<br>Asia|
|---|---|---|---|---|---|
|1965|0.85|2.26|1.51|1.78|2.47|
|1975|1.79|3.79|2.83|3.29|3.38|
|1985|2.91|4.80|4.01|4.79|3.81|

Table 2 Average years of secondary education, by region

||Africa|East<br>Asia|Mena|Latin<br>America|South<br>Asia|
|---|---|---|---|---|---|
|1965|0.03|0.13|0.16|0.17|0.12|
|1975|0.12|0.56|0.49|0.52|0.46|
|1985|0.34|1.18|0.99|0.98|0.96|

Table 3 Average Years of total education,<sup>by region</sup>

||Africa|East<br>Asia|Mena|Latin<br>America|South<br>Asia|
|---|---|---|---|---|---|
|1965|0.88|2.38|1.67|1.95|2.59|
|1975|1.91|4.34|3.32|3.81|3.84|
|1985|3.25|5.98|5.00|5.77|4.77|

13
Table 4 Ratio of primary education attainment to secondarv education attainment

||**Africa**|**East**<br>**Asia**|**Mena**|**| Latin**<br>**| America**|**South**<br>**Asia**|
|---|---|---|---|---|---|
|1965|31.72|18.02|9.28|10.52|21.00|
|1975|14.72|6.81|5.74|6.31|7.29|
|1985|8.60|4.08|4.07|4.89|3.99|

14
We note that the ranking of educational attainment by regions has changed over time. For primar) education, South Asia has apparently stagnated. East Asia has pulled ahead in both primary and secondar\ eduLCition. We also note that the educational structure of Africa is quite ditterent from those of the other regions: Africa :eems to have a much smaller ratio of secondary to primary educated individuals in its labor force.

Psacharopoulos and Arriagada (1986) have estimated mean years of schooling attained by the labor torce fo. different countries around the world that can conceivably be used as a substitute for our estimated educational capital stocks.' However, they only provide **data** for isolated points in time for each country and not a time-series. It has not been possible to generate, from their data, a meaningful time-series for the countries and period covered in this study. Nor has it been possible to apply their methodology to fill in the data gaps, principally because census data are not available for many countries, especially for the early years. In Appendix 2 we present a more detailed comparison between the estimates of Psacharopoulos and Arriagada (1986) and ours.

For almost all of the countries in the sample", data are avalable for all of the variables from 1960 to 1987 and that is the period used for the estimation of the aggregate production function.

'They use attainment rates provided by Kaneko (1986), who utilizes data from reports of the censuses undertaken worldwide from 1975 to 1984.

zThe only exceptions are Hong Kong and Singapore, the education data for which are not available for 1987 at the time of the study.

15
# 4. The Estimation Results

The results for four alternative specifications of the educational capital stoek variablesprimary education, secondary education, the sum of primary and secondary education, and primary and - secondary education separately are presented in Tables 5 and 6, We first test the hypothesis that the educational effects are the same for all regions. This hypothesis can be rejected for all four specifications at the 0.01 percent level of significance. Similarly, the hypothesis of no educational effects can also be rejected. **The** hypotheses that tlie growth trends are independent of the regions and that there **is no break in the trend between pre-1980 and post-1980 can also be rejected at the 0.01 percent level of significance (See Table 7).** 16
Alentie cifictns of the aggregate production ftaul.tin With region-spt,ific effects of Aducio

# Table **_5_** Alentie

|trmebt|t<br>**_fiftg_**<br>.K."a<br>Ian|sciadry<br>twtf"t<br>Ia|tol4<br>(ti<br>m|both<br>tais<br>of o.utlar|
|---|---|---|---|---|
|**Cap"**«<br>ti<br>_orw_|.601<br>(.9.8)<br>**.04**<br>(2.11)<br>.191<br>_0(1.6)_|.oO8<br>(51.2)<br>**.04**<br>(2.01)<br>.2Z60<br>12.61)|.62<br>(50.1)<br>**.09**<br>_12.20)_<br>_223_<br>(2.la)|.^a<br>_2)_<br>(.Z)<br>12.15)<br>.Z24<br>_(2.20)_|
|Prim<br>**lag.**<br>(Africa)<br>Primrv<br>Eciuc.<br>(East**Asia)**<br>**_Pr_mry_ld.**<br>PCt_r=**gig.**<br>(Let.<br>**Mric)**<br>Priai<br>Eelu.<br>**(IowAt Asia)**|**-. 009**<br>(0.67)<br>**.226**<br>(5.10)<br>*021<br>**.120**<br>(0.29)<br>**.003**<br>**(0.0?)**|-<br>-<br>-<br>-<br>-|-<br>-<br>-<br>-<br>-|**.U18**<br>(2.06)<br>.144<br>(2.740<br>**-.O**S<br>.OS;<br>(1.07)<br>**.501**<br>**01.30)**|
|**Swd.**<br>**Elx.**<br>**(Af**<br>**Xri**<br>_SWA._<br>**_E&._**<br>**lint Lala)**<br>l<br>.<br>mmk -<br>**_(PAoW)_**|-<br>**_a)**<br>**-.**<br>-|.01Z<br>**(244**<br>**061**<br>**(5.33)**<br>**.081**<br>**(4.09)**|-<br>-<br>_-_|.OZO<br>**(3,20)**<br>**.039**<br>**(2.80)**<br>**_.us_**<br>**(4.311)**|
|Sam"~<br>**lix.**<br>(Let:**_A aic)_**<br>**$aw.**<br>**lix.**<br>**(SWA Asia)**|-<br>-|**.037**<br>**(3.42)**<br>***.073**<br>(2.92)|-0|**(1.82)**<br>_-. 087_<br>**(3.23)**|
|**_*att_**<br>**_Ei._**<br>**(Africa)**<br>**latat**<br>**Ei.**<br>**(lit Asia)**<br>(NOW)<br>tat<br>**Ea**e .<br>'Lt<br>17b<br>**Total****_lixO._**<br>**(Ia*AhAt'a)**|-<br>-<br>-<br>i0cU<br>-|_-tO._<br>-<br>-|**(.0**<br>.1e7<br>**(_.05)**<br>(1.72)<br>**.13S**<br>OM5)<br>0.7<br>**.07**<br>(1.05)|-<br><|
|umisy**119-9**<br>(Afri4s)<br>**(EintAsiA)**<br>|**.004**<br>**(OK )**|**Ut03**<br>**(0.M)**|**.008**<br>**(0.97)**|**.0**<br> <br>**01.11)**|
|**0ou0a**ltf<br>**(lint**<br>**"isa)**|-|-|--||
|<br><br>_<br>r**1%0-19**<br>**_(IOU)_**<br>_<br>196<br>(NOW)<br>19f0-P|**.014**<br>(2.33)<br>.029<br>(4.24)<br>*007|-. 001<br>(0.14)<br>.024<br>(3.)<br>-004|**.008**<br>(0.69)<br>.027<br>(3.79)<br>-0|.00W<br>(1.40)<br>.021<br>(4.07)<br>003|
|_<br>(Let.<br>Assrkl<br>O_.<br>19Ca<br>(Let.<br>A_rie)<br>_.<br>1960-29<br>**(South Asi**<br>Oqr<br>19801<br>(bAt<br>Asia)|.<br>_0l.2)_<br>.016<br>(2.69)<br>.013<br>(0.50)<br>.031<br>(3.95)|.<br>01.3)<br>.017<br>(3.08}<br>.016<br>(2.19)<br>.034<br>(4.53)|. <br>0l.30)<br>.016<br>(2.72)<br>.001<br>(0.16)<br>.03i1<br>(3.96)|.<br>(0.59)<br>.018<br>(3.10)<br>.018<br>(2.39)<br>.US5<br>(4,62)|
|_m 160-79<br>_<br>tWOs|.009<br>0.S9)<br>..031<br>**(6.73)**|..0<br>_(O.n)_<br>.039<br>(7.24)|-.010<br>( 1.60)<br>.. 040<br>(7.03)|.. 013<br>(2.41)<br>**_-040_**<br>(.31)|
|**_masbr of_**<br>Marvtr,<br>**AdiAtatd**<br>I<br>**-a ar0.75**<br>,|15,1|1477<br>**S.7C**|**1506**<br>**_0.7_**|**1427**<br>**0.796**|

- I **All variables except dummy variables are in the form of first-differences of ratural loganitms.**

- **2 East Asia is chosen as the base region. Its dummy variables are therefore omitted from the** regressiorl equation.

- **3 Numbers in parentheses are t-ratios.**

17
Alternative specifications of aggregate<sup>production function</sup> without reciion-specific effects of<sup>education</sup> Table 6

|Variable|**Modet**with<br>primry<br>e.kwat ion|Model with<br>**secondary**<br>education|**Model**with<br>total<br>education|**Model**with<br>both<br>levelc<br>of educat.v|
|---|---|---|---|---|
|Capital<br>1<br>iLand<br>**Labor**|<br>.596<br>(49.4)<br>.046<br>(2.05)<br>.210<br>(2.04)|.600<br>(50.4)<br>.0OU<br>(2.16)<br>.297<br>(2.96)|.596<br>(49.4)<br>.047<br>(2.08)<br>.223<br>(2.18)|.600<br>(50.3)<br>.047<br>!<br>(2.14)<br>**_.275_**<br>(2.70)|
|Primry<br>Ed&w.<br>Secord. Educ.<br>**Total**<br>Edue.|.008<br>(0.81)<br>-<br>_|-<br>.023-<br>(5.74)<br>-|-<br>.016<br>(1.60)|-.019<br>**(1.35)**<br>**.026**<br>(5.54)<br>-|
|**0u**Y1960-79<br>(Africa)<br>**Dtuv**<br>**1980.**<br>(Africa)<br>**DtUV**1960-79<br>**(East Asia)**<br>**Du y 1980s**<br>(East Asia)<br>**Dutmv**1960-79<br>(Nena)<br>Du0**y 1980**<br>(Mena)<br>Du y1960-79<br>(Let.Aric)<br>DIu<br>1980s<br>(Lat.<br>Aieric)<br>Duiy 1960-79<br>(South Asia)<br>**DuO**y1980s<br>(South Asia)|-. 015<br>(4.48)<br>**.024**<br>(4.46)<br>_<br>-<br>-. 006<br>(1.34)<br>.023<br>(3.35)<br>-. 014<br>(4.16)<br>.014<br>(2.51)<br>-.013<br>(2.84)<br>.025<br>(3.30)|-.01S<br>(4.58)<br>**.024**<br>(4.58)<br>_<br>-<br>-. 004<br>(0.92)<br>.023<br>(3.43)<br>-. 013<br>(3.77)<br>.015<br>(2.65)<br>-.011<br>(2.44)<br>.026<br>(3.47)|**-. 015**<br>(4.60)<br>**.024**<br>(4.44)<br>_<br>_<br>**-. 005**<br>(1.32)<br>.023<br>(3.34)<br>-. 014<br>(4.14)<br>.014<br>(2.51)<br>-. 013<br>(2.82)<br>.025<br>(3.31)|-. 014<br>(4.35)<br>**.024**<br>(4.64)<br>-. 003<br>(0.75)<br>.023<br>(3.47)<br>-. 012<br>(3.72)<br>**.015**<br>(2.68)<br>-. 011<br>(2.42)<br>.026<br>(3.47)|
|**Dumy**1960-79<br>Duiy 1980s|.008<br>(1.74)<br>-.032<br>(5.86)|-. 000<br>(0.01)<br>-.037<br>(6.74)|-.007<br>(1.49)<br>-.033<br>(5.98)|.001<br>(0.30)<br>-.036<br>(6.54)|
|Numberof<br>observations|<br>1506|1477|1506|1477|
|Adjusted<br>R-square|0.781|0.790|0.781|0.790|

Notes

- I All variables except dummy variabLes<sup>are in the form of first-differences</sup> of naturaL logaritms.

- 2 East Asia is chosen as the<sup>base region. Its durmyvariables</sup> are therefore omitted from the regression equation.

- 3 Numbers in parentheses are t-ratios.

18
# Table 7 Tests of hyxxtheses

|||**Modelwith**<br>**primary**<br>**education**|**Modelwith**<br>**secondary**<br>**education**|**Modelwith**<br>**total**<br>**aducation**|**modelwith**<br>**both levels**<br>**of education**|
|---|---|---|---|---|---|
|**Hypothesis**|**(1)**|||||
|**D.F.**||**4**|**4**|**4**|**a**|
|F Value||**9.42**|**9.33**|**9.32**|**6.60**|
|Prob>F||0.0001|0.0001|0.0001|0.0001|
|**Hypothesis**|**(2)**|||||
|<br>**D.F.**||**S**|**S**|**5**|**10**|
|**F Value**||**7.67**|**14.20**|**7.76**|**5.86**|
|Prob>F||**0.0001**|0.0001|0.0001|0.0001|
|Hypothesis|**(3)**|||||
|D.F.||8|8|8||
|F Value||6.34|**5.82**|**5.73**|6.11|
|Prob>F||**0.0001**|0.0001|0.0001|0.0001|
|Hypothesis|**(4)**|||||
|D.F.||5|5|5|5|
|F Value||6.67|7.46|6.15|**5.S9**|
|Prob > F||0.0001|0.0001|0.0001|**0.0001**|
|**Hypothesis**|(5)|||||
|<br>D.F.||I|I|1|1|
|F Value||**2.26**|**0.72**|**1.43**|**1.28**|
|Prob>F||0.133|0.395|0.233|0.259|

Note: D F. are degrees of freedom of the constraint. Hypothesis (I) Educational effects are the same for all regions.

Hypothesis (2) Educational effects are zero.

Hypothesis (3) Growth trends are independent of region.

Hypothesis (4) Growth trends are the same between pre-1980 and post-1980.

Hypothesis (5) Constant returns to scale in capital, labor and land.

19
Table 8 Percentage change in real GDP in response to an additional year of education per person of working age in 1985

|||**Africa**|**East**<br>**Asia**|**Mena**|**Latin**<br>**America**|**South**<br>**Asia**|
|---|---|---|---|---|---|---|
|Primary|(1)|<br>-0.31|4.71|-0.52|2.67|0.08|
|Secondary|**(2)**|<br>3.55|5.17|5.13|3.82|-7.67|
|Total|(3)|<br>-0.26|3.32|1.51|2.34|0.77|
|Primary<br>Secondary|(4)|-1.32<br>5.79|3.01<br>3.28|-1.12<br>5.65|1.29<br>2.52|1.64<br>-9.09|

(1) Calculated from Table 5, column 1.

(2) Calculated from Table 5, column 2.

(3) Calculated from Table 5, column 3.

(4) Calculated from Table 5, column 4.

20
- The estimated capital, labor and land elasticities respectively 0.6, 0.2 and 0 05 - approximately are quite stable across the different specifications and rather reasonable for developing countries. (For developed countries, the capital elasticity would have been<sup>expected to be</sup> much lower (0.4) and the labor elasticity much higher (0.6).) The land<sup>elasticity is low, but not</sup> unreasonably so, considering that the non-agricultural part of real<sup>GDP does not depend on the quantity</sup> of arable land.

The sum of the estimated production elasticities of the physical inputs, capital,<sup>labor and land,</sup> is **_0.85,_** suggesting that there are perhaps decreasing returns to scale in the physical<sup>production inputs.</sup> However, the hypothesis of constant returns to scale cannot be rejected in all four<sup>of the spec;fications</sup> at the 10 percent level of significance.' Finally, the estimated regional trends of growth,<sup>net of the</sup> growth in inputs (or equivalently, the rates of technical progress) range between -4 and -1 percent<sup>per</sup> annum. They appear quite reasonable in light of what is known about the economic<sup>development of the</sup> different regions. For example, there was a significant slowdown in the growth of total<sup>world imports</sup> in the 1980's which affected adversely the rates of growth of the countries of the East Asian<sup>region.</sup> The estimated educational elasticities vary significantly across regions. For East Asia and Latin America, they are almost always consistently statistically significant and positive. For both<sup>Africa and</sup> Middle East and North Africa, primary education appears to have negative, but mostly<sup>statistically</sup> insignificant effects whereas secondary education has consistently statistically significant positive<sup>effects.</sup> For South Asia, primary education is generally statistically insignificant whereas secondary education<sup>has</sup> a statistically significant negative effect. It is interesting to note from Table 6 that if the<sup>educational</sup> elasticities are constrained to be the same across regions, [.,imary education is not statistically<sup>significant</sup> whereas secondary education is positive and statistically significant.

'The estimation results do not change materially when the restrictions implied by the hypothesis of constant returns to scale in the physical inputs are imposed on the aggregate production function.<sup>These</sup> results are presented in Appendix 3.

21
# S. Concluding Remarks

What do these educational elasticities mean? In Table 8 the estimated mean percentage change in the real GDP of the region in response to an increase of one year in the average educational attainmnent of the working age population in 1985 are presented for each category of education. The estimated effects range from negative to over 5 percent per annum. The estimated effects are plotted against the average educational attainments in Figures I through 3. The results are suggestive of a positive relationship **between** the size of the effect of primary education and the level of its attainment, indicating the possible existence of a threshold of 4 years for primary education to have a significant impact. Similar thresholds for the effectiveness of primary education have been found in microeconomic level studies. The effect of secondary education appears to be independent of the level of secondary educational attainment, although here local factors may predominate, as witnessed by the large negative estimated effect for South Asia.

We conclude that education is an important determinant of aggregate real output and productivity but that its effect varies considerably across countries and regions. Further research is necessary in order to explain the variability of its effectiveness, especially where the effect appears to be negative. It is speculated that the institutions, the organizations for production and distribution, the industrial compositioii and its skill requirements, the structure of education', and war and pestilence may all have played a role in determining the effect of primary and secondary education on aggregate real output.

'This includes the composition of the educational capital stock by primary, secondary and tertiary as well as the rate of progression through the educational process. For example, students who continue to advance educationally are effectively removed from the labor force for the duration. The educational system may also select out the best students to continue. All of these considerations tend to lower the effective educational capital stock in the short to intermediate term.

22
## Figure I

# Effect of one Additional Year of Primary Education per Person on Real GDP (%)

<!-- Start of picture text --> Percentage change in real GDP<br><!-- End of picture text --> <!-- Start of picture text --> East 4Asm<br>3% Latin<br>2%<br>1%<br>0% - South Asia<br>Africa<br>Atnas<br>-1%- . I . I<br>2.5 3 3.5 4 4.5 5<br>Average years of primary education<br><!-- End of picture text -->

# Figure 2 Effect of one Additional Year of Secondary Education per Person on Real GDP (%)

<!-- Start of picture text --> Percentage change in real GDP<br>6% -<br>Man& East Asia<br>4% Africa Latin America<br>2%<br>0% -<br>-2%<br>- 4%<br>- 6%<br>South AJ/J<br>8% -<br>0.3 0.6 0.9 1.2<br>Average years of secondary education<br><!-- End of picture text --> 23
Figure 3

# Effect of one Additional Year of Total Education per Person on Real GDP (%)

## Percentage change in real GDP

<!-- Start of picture text --> East Asia<br>3% 1<br>Lat/n America<br>2%-<br>Mene<br>1% t<br>South Asia<br>0%<br>Afr/ca<br>3 4 5 6<br>Average years of total education<br><!-- End of picture text --> 24
# Refe!rences

Boskin, M.J. and L.J Lau (1990), "International and<sup>Intertemporal Comparisons of</sup> Productive Efficiencies: An Application of the Meta-Production<sup>Function," Working Paper,</sup> Department of Economics,Stanford University.

Bowman, M.J. (1980), "Education and Economic Growth<sup>An Overview," in T. King,</sup> ed., Education and Income: A Background Study for World Development<sup>Report. 1980, World</sup> Bank Staff Working Paper No. 402, Washington, D.C., 1-71.

Bowman, M.J. (1987), "The Relevance of Education," in G.<sup>Psacharopoulos, ed.,</sup> Economics of Education: Research and Studies, Oxford:<sup>Pergamon Press, 305-307.</sup> Christensen, L.R., D.W. Jorgenson and L.J. Lau (1973),<sup>"Transcendental Logarithmic</sup> Production Frontiers," Review of Economics and Statistics, 55: 2845.

Denison, E.F. (1967), Why Growth Rates Differ. Post-War<sup>Experience in Nine Western</sup> Countries, Washington, D.C.: Brookings Institution.

Denison, E.F. (1979), Accounting for Slower Economic Growth:<sup>The United States in</sup> the 1970's, Washington, D.C.: Brookings Institution.

Griliches, Z. and D.W. Jorgenson (1966), "Sources of Measured<sup>Productivity Change:</sup> Capital Input," American Economic Review, 56: 50-61.

Hayami, Y. and V.W. Ruttan (1985), Agricultural Development:<sup>An International</sup> PersDective, revised and expanded ed., Baltimore: Johns Hopkins University<sup>Press.</sup> Hicks, N.L. (1980), "Is There a Trade-Off between Growth<sup>and Basic Needs?" Finance</sup> and Development, 17: 17-20.

Hicks, N.L. (1987), "Education and Economic Growth,"<sup>in G. Psacharopoulos, ed.,</sup> Economics of Education: Research and Studies, Oxford: Pergamon Press,<sup>101-107.</sup> Jamison, D.T. and L.J. Lau (1982), Farmer Education and Farm Efficiency,<sup>Baltimore:</sup> The Johns Hopkins University Press.

Jorgenson, D.W. and Z. Griliches (1967), "The Explanation of<sup>Productivity Change,"</sup> Review of Economic Studies, 34: 249-283.

Kaneko, M. (1986), The Educational Composition of<sup>the World's Population: A</sup> Database, Discussion Paper 29, Education and Training<sup>Series, Washington, D.C.: The World</sup> Bank.

Lau, L.J. and P.A. Yotopoulos (1989), "The Meta-Production<sup>Function Approach to</sup> Technological Change in World Agriculture," Journal of Development<sup>Economics, 31: 241-269.</sup> 25
Lockheed, M.E., D.T. Jamison and L.J. Lau (1980), "Farmer Education and Farm Efficiency: A Survey," Economic DeveloDment and Cultural Chanoe, 29: 37-76.

McMahon, W.W. (1987), "Expected Rates of Returns to Education," in G. Psacharopoulos, ed., Economics of Education: Research and Studies, Oxford: Pergamon Press, 187-196. McMahon, W.W. (1984), "The Relation of Education and R & D to Productivity Growth," Economics of Education Review, 3: 299-313.

Mincer, J. (1974), Schooling. ExDerience and Earnings, New York: Columbia University Press.

Mincer, **J.** (1979), 'Human Capital and Earnings," in D. M. Windham, ed., Economic Dimensions of Education, Washington, D.C.: National Academy of Education, 1-31.

Psacharopoulos, G. (1985), "Returns to Education: A Further International Update and Implications," The Journal of Human Resources, 20: 584-604.

Psacharopoulos, G. (1987), "Earnings Functions," in G. Psacharopoulos, ed., Economics of Education: Research and Studies, Oxford: Pergamon Piess, 218-223.

Psacharopoulos, G. and A.M. Arriagada (1986), The Educational Attainznent of the Lao Force: An International ComDarison, Discussion Paper No. 38, Education and Training Series, Washington, D.C.: The World Bank.

Schultz, T.W. (1961), "Investment in Human Capital," American Economic Review, 51: 1-17.

Schultz, T.W. (1975), "The Value of the Ability to Deal with Disequilibria," Journal of Economic Literature, 13: 872-876.

26