In recent years, economists have placedgreat emphasis on the importance of the"residual factor" or "technical change" inaccounting for observed increases in out-

* The Population Council and the Universityof Michigan, respectively. The authors grate­fully acknowledge the assistance of Lincoln T.Polissar, who computed the population projec­tion for this study, and the comments of WaiterB. Watson and John F. Kantner.

THE EFFECTS OF DIFFERING TRENDS IN FERTILITY AND OFEDUCATIONAL ADVANCE ON THE GROWTH, QUALITY,

AND TURNOVER OF THE LABOR FORCE

GAVIN JONES AND PAUL GINGRICH*

RESUMEN

Relativamente, pocos intentos se han hecho para investigar el efecto de diferentes tendencias dela fecundidad sobre el subsiguiente crecimiento, la composici6n por edades y el cambio en la fuerzade trabajo en los paises subdesarrollados. Aun menor atencWn se le ha prestado a la interrelaci6nentre tendencias alternativas de fecundidad y trayectorias alternativas de avance educacional, en ladeterminacWn de la "calidad" y cambio de la fuerza de trabajo en anos subsiguientes.

El presente trabajo es un madesto intento de rectificar esta deficiencia. Una poblaci6n con unaestructura por edades, tasas vitales, y tasas de registro escolar, representativas de muchos paises delAsia del Sur, Medio Este, y Africa, fue proyectada por sesenta anos, de acuerdo a los siguientesgrupos de condiciones: (a) fecundidad constante-tasas de registro educacional constantes; (b) fecun­didad constante-tasas mejoradas de registro educacional; (c) fecundidad descendente-tasas de regis­tro educacional constantes; (d) fecundidad descendente-tasas mejoradas de registro educacional.

El crecimiento, la estructura por edades, y las tasas de reemplazo y de logro educacional de lafuerza del trabajo, resultantes de las varias proyecciones, fueron sometidas a examen. Los resultadosindican que, en contra de una argumentaci6n comun, el mantenimiento de una fecundidad elevadano dO, coma resultado un reemplazo mds rdpido de la [uerza de trabajo inicial, pobremente educada,por trabajadores mejor educados. La fuerza de trabajo original es reemplazada en forma algo mdsrdpida cuando la fecundidad permanece alta y cuando las tasas de asistencia a las escuelas no seelevan. Pero controlando las tasas de asistencia a las escuelas, las tendencias en el loqro educacionalde la fuerza del trabajo, durante un periodo de sesenta anos, permanecen casi identicas en las pro­yecciones constante y descendente de la fecundidad.

SUMMARY

There have been relatively few attempts to investigate the effect of different trends in fertility onthe subsequent growth, age composition, and turnover of the labor force in underdeveloped countries.Even less attention has been given to the interrelationship between alternative fertility trends andalternative paths of educational advance in determining the "quality" and turnover of the laborforce in subsequent years.

The present paper is a modest attempt to rectify this deficiency. A population with an age struc­ture, vital rates, and school enrollment rates representative of many countries in South Asia, theMiddle East, and Africa was projectedfor sixty years, according to the following sets of conditions:(a) constant fertility-constant educational enrollment rates, (b) constant fertility-improving edu­cational enrollment rates, (c) declining fertility-constant educational enrollment rates, and (d)declining fertility-improving educational enrollment rates.

The growth, age structure, replacement, and educational attainment rates of the labor force re­sulting from the various projections were examined. The results indicate that, contrary to a commonline of argument, maintenance of high fertility does not result in a more rapid replacement of theoriginal poorly educated labor force by better educated workers. The original labor force is replacedsomewhat more rapidly when fertility remains high and when rates of school attendance are notraised. But controlling for school attendance rates, trends in the educational attainment of the laborforce over a sixty-year period are almost identical in the constant and declining fertility projections.

put in various countries. These economistsdefine technical change very broadly.R. M. Solow, for example, takes it to in­clude all factors, other than an increasein capital, that increase or decrease out-put per head.' It is widely agreed that

! R. M. Solow, "Technical Change and theAggregate Production Function," Review ofEconomics and Statistics, XXXIX (August,1957), 312-20.

226

Differing Trends in Fertility of the Labor Force 227

improvements in the quality of the laborforce (principally improvements in itshealth, education, and skills) are an im­portant component of this broadly definedtechnical change.2

Attempts to define their precise contri­bution run up against very difficult prob­lems, but, in a recent article, David C.McClelland has shown that, within groupsof countries starting at approximately thesame level of economic or technologicaldevelopment, countries that invest moreheavily in education have tended to de­velop more rapidly than the other coun­tries. 3

Despite the difficulties of measuringthe precise contribution of education toeconomic development, few would dis­agree with the Secretary-General of theUnited Nations when he states that "theunutilized talents of their people consti­tute the chief present waste and the chieffuture hope of the developing countries."!The educational attainment of the laborforce is presently extremely low in mostcountries of Asia, Africa, and Latin Amer­ica. In Latin America, for example, lessthan five percent of the labor force has asecondary education and less than one­fourth has completed six grades of elemen­tary school." The situation in Africa isstill worse.

The importance of improving the edu-

2 For references to a number of importantarticles on the subject, see Frederick Harbisonand Charles A. Myers, Education, Manpower andEconomic Growth (New York: McGraw-Hill,1964), pp. 3-11; and OECD Study Group in theEconomics of Education, The Residual Factorand Economic Growth (Paris: Organization forEconomic Cooperation and Development, 1964).

3 David C. McClelland, "Does Education Ac­celerate Economic Growth?" Economic Develop­ment and Cultural Change, XIV, 3 (April, 1966).

4 Quoted in H. W. Singer, "The Notion of Hu­man Investment," Review of Social Economy,XXIV, 1 (March, 1966), 2.

5 David Ladin, "Population Policy and Meth­odology" (paper presented to the PreparatorySeminar for the Meeting on Population Policiesin Relation to Development in Latin America,Pan American Union [Washington, D.C., Feb­ruary, 1967, cyclostyledJ), p. 17.

cational level of the labor force in orderto achieve a rapid growth in output, andrapid economic development generally,implies that the sooner this poorly edu­cated labor force is replaced by a better­educated group of workers, the better.Under what circumstances can these coun­tries maximize the rate at which theirlabor force is replaced by better-educatedworkers? Is such a goal appropriate any­way?

In this paper, we will present the resultsof a model designed to provide some par­tial answers to these questions by investi­gating the replacement of the labor forceand its changing "quality" according toalternative trends in fertility and educa­tion. Because the factors that affect thereplacement rate of the female labor forceare very complex, our paper is confined tothe male labor force.

Assuming that trends in mortality ratesand in labor-foree activity rates? at theolder ages are given, the variables thatwill determine the replacement rate of themale labor-force in a closed population are(1) trends in fertility, and (2) trends in ac­tivity rates at the younger ages. The sec­ond variable is largely a function of trendsin the proportions of young people inschool.7 Because the labor force in a high­fertility country is so heavily weighted byyoung workers, changes in activity ratesat the older ages, even if they do occur,will have very little effect on the replace­ment rate.

The model will use an initial populationstructure, activity rates, and educationallevel of the labor force that are represen­tative of the less advanced of the develop­ing areas. Table 1 sets out some basic

8 Labor-force activity rates (hereafter calledactivity rates) for any group in the populationcan be defined as the number economically activeas a percentage of the total number in the group.

7 Trends in activity rates at the younger agesare also closely correlated with urbanization andthe percentage of economically active males innon-agricultural employment. For the sake ofsimplicity, however, trends in activity rates inour model are related solely to trends in educa­tional enrollment ratios.

228 DEMOGRAPHY

properties of this initial population. It ischaracterized by high fertility, moderate­ly high mortality, and the youthful agestructure that goes with a history of highfertility. The vital rates and populationstructure are roughly equivalent to thoseof South and South-West Asia (includingIndia and Pakistan), Indonesia, much ofAfrica, and the poorest Latin Americancountries. The proportions in school atages 10-14, 15-19, and 20-24 years canhardly be typical of all these countries,because there is so much inter-countryvariation. In Indonesia in 1961 for exam­ple (if the figures are to be trusted), pro­portions in school were somewhat higherthan the 50, 20, and 5 we have used;whereas in Pakistan in the same year theywere still substantially lower. However,from the available data, it seems that arelatively small fraction of the world'schildren (about one-fourth) now live incountries that have school attendancerates lower than those we have taken forour base year. 8

Starting with this base population andprojecting it ahead for 60 years, we will

8 This is on the assumption that school en­rollment rates in mainland China are a littlehigher than those we have adopted. This appearsto be the case. If we look only at school attend­ance rates at ages 15-19 and 20-24 years, ahigher proportion (perhaps 30 percent) of chil­dren live in countries with school attendanceratios lower than our base year rates.

Table l.-DEMOGRAPHIC AND EDUCATIONAL

CHARACTERISTICS OF THE

BASE POPULATION

CHARACTERIST.ICS

Population

Birthrate ( per 1,000 )................... 44.3Deathrate ( per 1,000 )................. 19.3Growth rate ( per 1,000 ).................... ..... 25.0Expectation of life at hirth (years).... 45.0Percentage of males under 15 years. ••••• 43.8

~

Percentage in school

)Isles aged 10..14 years........................... 50Males aged 15-.19 ye.ars................................ 20Males aged 20..24 years, ...... 4...................... 5

compare the length of time taken to re­place various proportions of the laborforce under four sets of conditions: (1)constant fertility-constant educationalenrolIment rates; (2) constant fertility­improving educational enrollment rates;(3) declining fertility-constant education­al enrollment rates; and (4) declining fer­tility-improving educational enrolImentrates.

The model will show us, moreover, theabsolute size and age composition of thelabor force and the dependency ratiosunder the alternative conditions. The nextstep will be to show the educational com­position of the labor force at variouspoints of time under these four sets ofconditions. Some of the implications ofthe results will then be discussed.

ASSUMPTIONS AND METHODS

A summary of the basic assumptionsand methods used in the projections isgiven here. A more detailed discussion ofsome aspects is contained in the Appendix.

POPULATION PROJECTION

The initial population of 1 million wasprojected for 60 years by the componentmethod, utilizing Coale and Demeny,"Regional Model Life Tables and StablePopulations," Model West. Two projec­tions were computed. The same mortalityassumptions were adopted for both name­ly, that the expectation of life at birthwould rise from 45 years in the first five­year period to 70 years forty years later,the decline being more rapid in the firstten-year period." But one projection (theconstant-fertilityprojection) assumed thatthe ratio of female births to women aged15-44 years remained constant through­out the sixty-year period," whereas the

• Mortality level 11 was assumed to apply tothe mid-point of the t - t + 5 period. Mortalitywas assumed to decline linearly to level 15 in thenext ten years; thereafter the rate of mortalitydecline was halved, so that one new mortalitylevel was reached in each five-year period. Mor­tality was assumed to level off after level 21 wasreached during the t + 40 - t + 45 period.

10 At 0.103.

DijflRing Trends in Fertility of the Labor Force 229

other (the declining-fertility projection)assumed that this ratio fell linearly byone-half in the first thirty years and re­mained constant thereafter.

IMPROVING EDUCATION PROJECTION

School attendance.-As shown in Ta­ble 1, it was assumed that of the malesaged 10-14, 15-19, and 20-24 years inyear t, the percentages who attendedschool were 50, 20, and 5 percent, respec­tively. A fairly rapid rise in school attend­ance rates was postulated, so that by yeart + 30 the attendance rates for the sameage groups were 97, 60, and 15 percent,respectively." These last rates are higherthan those recorded in nearly all advancedcountries at the present time. Only therates in the United States exceed them inall three age groups, although a few othercountries exceed them in one age grouponly. The rates attained in year t + 30were assumed to hold for all subsequentyears. For years t - 10 through t, thesame rate of educational advance as foryears t through t + 30 was assumed."This is in line with the rapid educationaladvances achieved by most countries dur­ing the last decade.

The projected school attendance ratesprovided the basis for projecting bothactivity rates and educational attainmentrates. It should be noted that, in using

11 These increases are by no means unrealis­tically rapid. We have assumed, for example,that the attendance rate at age 15-19 yearstrebles (from 20 percent to 60 percent) in thirtyyears. Somewhat similar data in the UNESCOStatistical Yearbook for 1965, giving secondaryschool enrollment as a ratio of the populationaged 15-19 years, show that, in the thirteen-yearperiod 1950-63, this ratio more than doubled ineight of the thirteen countries which started theperiod at levels between 10 percent and 30 per­cent. See Philip J. Idenburg, "Educational Con­sequences and Determinants of PopulationTrends" (paper [A.6/25/E/495] presented to theUnited Nations World Population Conference[Belgrade, 1965, mimeographed]), Chap. 2.

12 The rates for years t - 10 through t + 30were derived from the rates selected for years tand t + 30 by linear interpolation and extrapo­lation.

these rates to project both activity ratesand educational attainment rates, weused cross-sectional data'" showing therelationship between the different vari­ables in a number of countries in order toproject changes in one country over time.

Activity rates.-There is normally arather close inverse relationship betweenschool attendance rates and activity ratesin any age group.v Therefore, activityrates at ages 10-24 years were derivedfrom school attendance rates at the sameages by means of regression equations.

For ages 25 years and over the activityrates used were simply an average of ratesfor all countries with available data." Nochange was made after year t for the ratesof ages 25-49 years, but, for ages 50 yearsand over, the rates were assumed to fallover a period of fifty years from the levelobserved in agricultural countries to thatof the industrialized countries. The sameholds for all projections. The complete setof rates is given in Table A-3.

Educational attainment of the laborforce.-One would expect a fairly closerelationship to exist between the schoolattendance ratios of any cohort as itpasses from 10 to 24 years of age and theeducational attainment ratios of the samecohort in subsequent years. More specifi­cally, one would expect the proportion inschool when the cohort was aged 10-14years to bear a fairly close relation to theproportion who, in later years, have com­pleted four years of primary school; simi­larly, the proportion in school when thecohort was aged 15-19 years should beara fairly close relationship to the propor­tion who, in subsequent years, have com-

11 This is to say that we used data from anumber of coantries at approximately the sametime or, inthe case of educational attainmentrates, over approximately the same ten-yearperiod.

14 This is not to deny that in many less de­veloped countries a surprisingly high proportionof young people are neither in school nor in thelabor force, and that in such situations risingschool attendance rates might sometimes beachieved by lowering this proportion.

16 See the Appendix.

230 DEMOGRAPHY

pleted four years of secondary school edu­cation; and similarly for the proportion inschool at ages 20-24 years and the propor­tion who have completed three years ofcollege. It was on the basis of this generalreasoning that we calculated our educa­tional attainment ratios, linking them bymeans of regression equations to schoolattendance rates of the same cohort inearlier years.

The detailed methodology is set outin the Appendix. Using the regressionsgiven in Table A-4 and the school attend­ance rates already calculated, educationalattainment rates were calculated for malesaged 25-29 years. It was assumed that thesame rates applied to economically activemales in this age group. It was also as­sumed that the educational attainmentrates for each cohort did not change oncethat cohort had reached age 25-29 years,that is, mortality and retirement rateswere assumed to be independent of edu­cational attainment. These assumptionsare probably not correct but are satisfac­tory for the purpose. It would be unreal­istic to refine them further in view of thewide margin for error in other parts ofthe model.

Since school attendance rates were notavailable for years prior to t - 10, theinitial distribution of educational attain­ment for the entire labor force could notbe obtained in this manner. It would havebeen invalid to assume that educationalattainment levels in the base year werethe same in all age groups above age 25years, because the levels of education inmost countries have been improving, atleast slowly, over a long period. Instead,we examined educational attainment ratesabove this age for all underdevelopedcountries with relevant data, and we usedthe ratios of the rates for each 5-year agegroup above age 30 years to the rates atage 25-29 years to calculate the educa­tional attainment of those aged 30 yearsand over in year t.

The educational attainment rates forages 10-24 years presented special prob­lems because it was necessary to allow for

the likely differences in educational at­tainment between those who had alreadyentered the labor force and those whowere still in school. Educational attain­ment rates for all males at these ages wereagain derived from school attendancerates, and then weighted by the ratio ofthese rates to rates for males in the laborforce, as calculated from the limited inter­national data on the subject. (See theAppendix.)

CONSTANT EDUCATION PROJECTION

The "base" labor force, the "base"educational attainment rates, and theschool attendance rates in years t - 10,t - 5, and t were the same for both con­stant and improving education projec­tions. For the constant education projec­tion, schoolattendance rates were assumedto remain at the level of year t for allyears thereafter. The activity rates andeducational attainment rates were thencalculated in exactly the same manner asin the improving-education projection.

It might be thought that the educa­tional attainment of the labor force wouldremain constant in the constant-educationprojection. But because of the assumptionthat educational levels had been improv­ing in the past, this is not so. In fact, itis not until year t + 55, when all thosein the original labor force have been re­placed, that educational attainment ratesare the same at all ages 25 years and overand do not change from year to year.

RESULTS

Growth and Age Structure.-Table 2summarizes various aspects of the popu­lation and labor force projections. Fur­ther details of the labor force projectionare contained in Appendix Table A-I. Ittakes some time, on the one hand, beforealternative trends in fertility are reflectedin differences in the size of the labor force,because children born after year t do notbegin to enter the labor force in sizeablenumbers for about fifteen years. In fact,even by year t + 25 the difference in thesize of the work force between constant-

Dijfering:Trends in Fertility of the Labor Force 231

and declining-fertility projections is only1.6 percent (in the improving-educationcase), although it grows to 15.7 percentby year t + 40.16 On the other hand, dif­ferences in the size of the workforce be­tween the constant- and improving-edu­cation projections begin to show upimmediately. In the declining-fertilityprojection, the workforce according tothe constant-education assumption is al­ready 9.1 percent higher in year t + 15than it is according to the improving-

16 The differences are somewhat larger (3.4percent and 23.7 percent, respectively) if we usethe constant education assumption.

education assumption, and, by year t +25, the difference has reached 15.0 per­cent.

The youthful segment (aged 10-24years) grows more rapidly than the re­mainder of the workforce only in theconstant-fertility-constant-education pro­jection. In the three other projections, theworkforce ages appreciably over the sixty­year period. The youthful componentgrows most slowly in the declining-fertil­ity-improving-education projection, be­cause the decline in fertility slows therate of growth of the population at ages10-24 years (after a lag of ten years), and

Table 2.-PROJECTIONS OF THE TOTAL POPULATION, TOTAL MALE POPULATION, ECONOMICALLY

ACTIVE MALES, MALE ACTIVITY RATES, AND PERCENTAGE OF THE LABOR FORCE AGED

10-24 YEARS, UNDER CONDITIONS OF CONSTANT AND DECLINING FERTILITY AND

CONSTANT AND IMPROVING EDUCATION, BY YEAR, YEAR t TO t + 60

YearFertility condition

and projectiont t+15 t+30 t+45 t+60

CONSTANT FERTILITY

Total males •••••••••••••• 501.2 763.0 1245.7 2124.7 3673.6

Total population ••••••••• 1000.0 1520.0 2474.8 4212.1 7272.0

Economically active males:1. Constant education •••••• 275.7 409.9 652.0 1090.7 1877 .32. Improving education .•••• 275.7 375.4 537.0 894.6 1534.0

Activity rates:percent ofmales economically active:1. Constant education •••••• 55.0 53.7 52.3 51.3 51.12. Improving education••••• 55.0 49.2 43.1 42.1 41.8

Percentage of 1abor forceaged 10-24 years:1. Constant education •••••• 37.1 37.0 38.5 39.2 39.92. Improving education ••••• 37.1 31.2 25.4 25.9 26.4

DECLINING FERTILITY

Total males •••••••••••••• 501.2 723.1 965.4 1262.1 1596.2

Total population••••••••• 1000.1 1441.1 1921.9 2512.7 3180.3

Economically active males:1. Constant education ••.••• 275.7 409.4 605.1 804.7 .1017.22. Improving education ••••• 275.7 375.2 517.3 711.2 896.0

Activity rates: percent ofmales economically active:1. Constant education ••.••. 55.0 56.6 62.7 63.8 63.72. Improving education ••••• 55.0 51.9 53.6 56.3 56.1

Percentage of 1abor forceaged 10- 24 years:1. Constant education ••..•• 37.1 36.9 34.0 27.5 27.72. Improving education •••.• 37.1 31.1 22.8 18.0 18.0

232 DEMOGRAPHY

improving education accentuates thiseffect by reducing the proportions that areeconomically active at these ages.

LABOR FORCE REPLACEMENT

Several methods were used to examinethe replacement of the labor force accord­ing to the various projections. One was tocalculate the ratio of entries into thelabor force to withdrawals from the laborforce (resulting from death and retire­ment) during each time period." From

17 The number of deaths occurring to the eco­nomically active population of time t1 in anysubsequent five-year period were calculated byapplying the same mortality rates used in thepopulation projection. This assumes that mor­tality is the same for the active and the inactivepopulation. Next, for each five-year cohort, thesurvivors from the labor force of t1, so calculated,were subtracted from the actual labor force attime t + 5. If positive, this difference was as­sumed to be the number of withdrawals by re­tirement. This method gives only the net entryor withdrawal owing to retirement of each agegroup, because the underlying assumption is thatthere is only one entry and one withdrawal perworker.

Table 3 it can be seen that the ratio ofentries to withdrawals grows significantlyin the constant-fertility-constant-educa­tion projection. This reflects the declinein mortality rates, which slows down theincrease in deaths at a time when entriesinto the labor force continue to grow rap­idly. In fact, in both constant-fertilityprojections, entries grow by over sixtimes, while deaths only double. Retire­ments grow much faster than deaths, butthe total number of retirements is rela­tively small. In the improving-educationprojection, the ratios do not rise as fastas in the constant-education projectionbecause rising school-attendance ratesslow entry to the labor force.

Differences in fertility have practicallyno effect on the ratios for the first fifteenyears and very little effect for aboutthirty years. But for the next thirty yearsthe differences become very pronounced,and by year t + 60 the ratio of entries towithdrawals is more than twice as highin the constant- as in the declining-fertil-

Table 3.-RATIO OF ENTRIES TO WITHDRAWALS IN THE LABOR FORCE, UNDER CONDITIONS OF

CONSTANT AND DECLINING FERTILITY AND CONSTANT AND IMPROVING EDUCATION FOR

THE TOTAL MALE LABOR FORCE AND FOR THE MALE LABOR FORCE HAVING COMPLETED

FOUR YEARS OF SECONDARY SCHOOL, BY PERIOD, H + 5 TO t + 55-t + 60

PeriodFertility and educational

conditions 1;- t+lO_ t+25- t+40_ t+55-t+5 t+15 t+30 t+45 t+60

A. Total male labor forceConstant fertility:

Constant education••••••••••••• 2.6 3.3 4.0 4.9 5.3Constant fertility: ,

Improving educatioU •••••••••••• 2.2 2.7 3.0 4.2 4.6Declining fertility:

Constant education.............. 2 •.6 3.2 3.1 2.5 2.1Declining fertiitty: ••.•.

Improving education•••••••••••• 2.2. 2.7 2.6 2.4 2.0

B. Male labor force havingcompleted four years ofsecondary school:

Constant fertility:Constant education ••••••••••••• 13.5 10.0 7.5 5.9 4.3

Constant fertility:Improving education •••••••••••. 12.9 15.6 14.9 11.9 6.5

Declining fertility:Constant education••••••••••••• 13.5 10.0 6.9 3.7 1.9

Declining fertility:Improving education ••••••••••.• 12.9 15.6 13.6 7.6 3.1

Differing Trends in Fertility of the Labor Force 233

ity projection. The effects over the longperiod are striking: in the declining-fer­tility projections, entries grow by lessthan three times in sixty years as opposedto the sixfold growth in the constant­fertility projections.

Given the ratios in Table 3, one mightexpect the labor force to be replaced muchmore quickly when fertility remainedhigh than when it declined. To deter­mine how many years it takes to replacethe labor force of the base year, the re­maining members of the original laborforce were traced through time until allhad disappeared. This rate was the samefor all projections (Table 4, part 1).Thus differences in rates of replacementof this originallabor force arise solely fromdifferences in the rate at which new work­ers enter.

Beginning with the labor force at timet and controlling for education, Part 2of Table 4 shows that the effect of differ-

ential fertility in replacing the originallabor force is very small. With constanteducational levels, for example, the highfertility projection takes twenty-eightyears to yield a labor force in which newworkers constitute 75 percent-only oneyear less than it takes the lower fertilityprojection. With improving educationallevels, the difference is again only oneyear. The reason is that the fertility changetakes time significantly to affect the num­ber of labor-force entrants, and by thetime it has a large effect, the originallabor force is rather small owing to retire­ments and mortality.

In order to discover whether or notfertility does have a larger effect after atime, we looked at the replacement of thelabor force existing at year t + 15. (Whenwe control for education, this labor forceis almost identical in both constant- anddeclining-fertility projections.) In thiscase, because the base year has been ad-

Table 4.-REPLACEMENT OF THE INITIAL MALE LABOR FORCE

Part 1.__Males labor force of time t: Percentage still in the labor force after.10, 20, 30, 40 years

Year

All projections ••••••••••••••••••••••

t+IO t+20 t+30 t+40

84.3 69.0 51.5 31.6

Part 2.--The increasing share of new workers in the male labor force. Number ofyears required for workers who are not present in the base year and in year t+15to consitute various proportions of the male labor force.

New workers as percent of the malelabor force

50 75 90percent percent percent

A. Beginning with the male laborforce of time t

Constant fertility-constant education •• 16 28 40Constant fertility_improving education. 18 31 42Declining fertility_constant education. 16 29 42Declining fertility_improving education 18 32 43

B. Beginning with the male laborforce of time t+15

Constant fertility-constant education•• 15 27 39Constant fertility-improving education. 17 28 39Declining fertility_constant education. 17 32 44Declining fertility_improving education 18 32 43

234 DEMOGRAPHY

vanced to the time when differences infertility begin significantly to affect thenumber of entrants to the labor force, thereplacement time varies more sharplyaccording to fertility. The high-fertilitypopulation takes five years less than thedeclining-fertility population to reach thepoint at which new members constitutethree-fourths of its labor force, assumingconstant educational levels. As the rateat which the original workers disappeardiffers infinitesimally according to fertil­ity, the difference in replacement timeagain results solely from the larger num­ber of new entrants in the constant-fer­tility population.

By contrast, educational trends makelittle difference to the rate at which thelabor force of year t + 15 is replaced,when we control for fertility. In the im­proving-education projection, the initiallabor force disappears more rapidly thanin the constant-education projection, but,at the same time, new workers enter moreslowly. The more rapid removal and theslower entry approximately offset eachother.

To sum up: if the aim is to have thelabor force composed of larger percent­ages of new workers at any given time,there is an advantage in higher fertility.But it is a very small advantage if westart with the labor force of year t. More­over, in replacing the labor force of year t,the advantages of quicker entry to thelabor force in the case of high fertility areoffset by slower entry if educational levelsimprove. Once the different fertilitytrends have been in operation for tenyears or longer, the higher-fertility pro­jection has a substantial, but not spec­tacular, advantage in replacing the result­ing labor force.

EDUCATIONAL ATTAINMENT OF

THE LAB OR FORCE

Table 5 shows the growth of numbersin the various educational attainmentcategories according to the different pro­jections. In the base year, the labor forcecomprises primarily very poorly educated

workers. There are 195,000 workers withless than four years of primary school(most of whom could be classed as func­tional illiterates);" compared with only10,000 with more than four years of sec­ondary school. However, the number ofbetter-educated entrants grows rapidly inall projections, far exceeding the numberof better-educated withdrawals. (See Ta­ble 3, Part B.) Thus, the number of better­educated workers grows rapidly, especial­ly in the improving-education projections:in these projections, the number of work­ers in the lowest educational categorystarts to decline after year t + 15 and isactually surpassed by the number withfour years of secondary school by yeart + 35.

Table 6 shows the trends in the educa­tional attainment rates for the labor forceaccording to the various projections. Thefirst row of the table shows that whenschool attendance rates remain constant,educational attainment rates are lowerfor the constant-fertility projection thanfor the declining-fertility projection. Theexplanation is somewhat involved. Withconstant educational levels, once the orig­inallabor force has disappeared, the sameeducational attainment rates are appliedto each age group which has completed itseducation; that is, to each age groupabove age 25 years. The only way differ­ences can arise over time in the education­al attainment of the constant-educationpopulation is if the educational attain­ment rates at young ages, 10-24 years,are different from those applied at ages25 years and above.

It is logical to expect these rate to bedifferent. Suppose that 50 percent of themembers of each cohort have receivedfour years of secondary education by thetime they are aged 25 years. Now whenthese same cohorts are aged 15-19 years,it is unlikely that more than, say, 20 per-

18 Some experts, in fact, consider a minimumof five years of schooling necessary to insurepermanent functional literacy. See United Na­tions, Economic Survey of Asia and the Far East,1965 (Bangkok: 1966), p. 85.

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Differing Trends in Fertility of the Labor Force 237

cent will have completed four years ofsecondary school. Almost none of thoseaged 15 or 16 years, for example, will havecompleted this level. Thus, the education­al attainment rates will be much lowerfor the age group 10-24 years, and thesame argument holds when it is appliedto the economically active rather than tototal, males. Indeed, educational attain­ment rates for economically active malesaged 10-24 years will be still lower thanthose for all males at these ages, becausefor some years at least (according to ourassumptions) those who enter the laborforce at these ages will have lower educa­tional attainment rates than the totalmales in the cohort."

When these age-specific rates are ap­plied to two populations, the populationwith the larger percentage of young people(those aged 10-24 years) in the labor forcewill have lower rates of educational at­tainment for the labor force as a whole.Since the constant fertility population haslarger proportions of its members at young

IV Data from three less-developed countriesindicated, on the one hand, that for males aged10-24 years, educational attainment rates wereconsiderably lower for lab or-force members thanfor total males. Educational attainment rates forlabor-force members were about one-third of therates for total males in these age groups. On theother hand, in the United States, the rates forlabor-force members aged 10-24 years were ap­proximately the same as the rates for all malesin these age groups. We assumed that the ratioof educational attainment rates for labor-forcemembers aged 10-24 years to those for all malesin these age groups would rise linearly from theratio for the underdeveloped countries ratio tothe ratio for the United States over a period ofthirty years. See the Appendix for further details.

ages, its educational attainments are be­low those for the declining-fertility popu­lation when educational levels are con­stant. But this difference is not very large.By year t + 60 our projections show adifference of 2.3 percentage points fornumbers who have completed four yearsof primary education. Even if it were as­sumed that the educational attainmentrates for ages 10-24 years were zerofor allthree levels of schooling, the differencewould rise to only 6.8 percentage points.For the other two levels of educationalattainment, the differences are even less.

From part B of Table 6 it can be seenthat improving educational levels act tolessen or even to reverse the foregoingdifferentials. The constant-fertility popu­lation again has a larger proportion ofyoung workers. But, as the educationallevels rise, only the younger cohorts aredirectly affected. The improving educa­tionallevel of each succeeding cohort pass­ing through these ages partly counterbal­ances the fact that not all those at youngages have completed as high a level ofschooling as they eventually will, and thatthe educational attainment of those whoenter the labor force at these ages is lowerthan that of the young people who remainin school.

How important is this counterbalanc­ing effect? Surprisingly, it is not very im­portant at all. As shown in Table 7, it isstrong enough to reverse the tendency foreducational attainment to be higher inthe declining-fertility population only inthe case of the percentage who have com­pleted four years of primary school. For

Table 7.-DIFFERENCES IN EDUCATIONAL ATTAINMENT, BY YEARS OF SCHOOLCOMPLETED, WHEN EDUCATIONAL LEVELS ARE IMPROVING (CONSTANT FERTILITY

PROJECTION MINUS DECLINING FERTILITY PROJECTION), THE MALELABOR FORCE, BY YEAR, YEAR t 'to t + 60

Difference in Year

percentage completed t 1+15 t+30 t+45 t+60

4 years of primary school ••• ° ° 0.6 2.8 2.24 years of secondary school. ° ° ° 0.2 _0.53 years of college •••••••••• ° 0 _0.1 -9.25 -0.5

238 DEMOGRAPHY

the other two levels of education, itmerely moderates the amount by whichthe educational attainment of the declin­ing-fertility population exceeds that ofthe constant-fertility population.

This finding is of considerable interestin view of the claim made by a numberof writers that a high-fertility population,with its young age structure, is more fa­vorably situated than a low-fertility pop­ulation to replace the labor force withhigher-quality workers." Our study dem­onstrates the fallacy of this claim. The av­erage educational level of the labor forceis not raised more quickly in a high-fer­tility than in a declining-fertility popula­tion when both experience the same rateof educational advance. To be more pre­cise, it can be raised more quickly only ifthe rate of educational advance is veryfast indeed (faster than we have assumed),so that it can overcome the tendency foryounger workers to have lower education­al attainment rates than the rest of thelabor force. And, even then, the differ­ences are not great, as the following ex­ample demonstrates.

To discover the maximum effect on theeducational attainment of the labor forcethat could be produced by a combinationof high fertility and very rapid advancesin educational levels at the young ages, weassumed that there had been a suddenjump in school enrollment ratios, from thestarting ratio to the maximum ratio inone five-year period. This assumptionimplied that in subsequent years, alllabor-force members above age x wouldhave reached the old educational attain­ment rates, while all those below age xwould have attained the maximum rate.

20 Easterlin (following Keyfitz and Lieben­stein), for example, states that "If the educa­tional system is steadily raising years of school­ing, then the replacement of less by better edu­cated persons in the work force will occur morerapidly if the age distribution is characterizedby a higher proportion of young to old." RichardA. Easterlin, "Effects of Population Growth onthe Economic Development of Developing Coun­tries," Annals of the American Academy of Po­litical and Social Science (January, 1967), p. 105.

In year t + 60, the maximum effect wasproduced when x equalled 40 (implyingthat 55.6 percent of those aged 40 yearsand over had completed four years of pri­mary school, compared with 97 percentof those aged under 40 years).

According to the foregoing assump­tions, under conditions of constant fer­tility, 83.1 percent of the labor force inyear t + 60 had received four years ofprimary education. Under conditions ofdeclining fertility, only 77.2 percent ofthe labor force had received the sameamount of education. The difference is5.9 percentage points as compared to adifference of 2.2 percentage points in thesame year under assumptions of steadilyimproving educational levels,"

Finally, it is worthwhile to isolate theeffect of improving educational levels onthe educational attainment of the "ma­ture" labor force by considering only thelabor force aged 20 years and over. Withconstant educational levels, educationalattainment rates for this group do notdiffer according to fertility. Table 8 givesthe differences between the alternativefertility projections that result from im­proving educational levels. As can beseen, these are not large--never morethan 2.6 percentage points in the case ofthose who completed four years of pri­mary school and even less for the otherlevels.

It should be noted that, once educa­tionallevels have stopped improving (thatis, once even the oldest cohorts in thelabor force have achieved the maximumrates of school attendance), the high-fer­tility population no longer has any ad­vantage in terms of educational attain­ment. At this time, the younger-age groupsagain have lower educational attainmentrates than do older-age groups becausemany of their members have not yet com­pleted their schooling. When the maxi­mum educational attainment rates areapplied to each age group, the educational

1 The maximum difference under assumptionsof steadily improving educational levels is 3.0percentage points in year t + 50.

Differing Trends in Fertility of the Labor Force 239

attainment of the labor force turns out tobe practically identical for the two popu­lations. When the percentage who havecompleted four years of primary schoolis 97 percent for ages 25 years and over(and slightly lower for younger groups),for example, the percentage of the laborforce who have completed four years ofprimary school is 96.6 percent in yeart + 60 in the declining-fertility case and96.5 percent in the constant-fertility case.

DISCUSSION

If we control for fertility, the existinglabor force is replaced more rapidly byyoung workers when school attendancerates are prevented from rising. Few peo­ple, of course, would argue the desirabilityof this situation. We have shown, more­over, that the existing labor force tendsto be replaced somewhat more rapidly byyoung workers when fertility remainshigh. However, assuming the same rateof advance in raising school attendanceratios, the average educational level ofthe labor force rises at virtually the samerate in a high-fertility as in a declining­fertility population. In other words, theargument that high fertility enables theexisting, unskilled labor force to be re­placed more rapidly by younger, better­educated workers than if fertility declineddoes not hold water, even on the heroicassumption that school enrollment ratios

can be raised as rapidly in a high-fertilityas in a declining-fertility population.

It is now time to drop the assumption,implicit in the discussion thus far, thatthe proportion of the school-age popula­tion attending school can be raised just asrapidly in a high-fertility as in a declining­fertility population. It can be demonstrat­ed that a high-fertility population willfind it more difficult to achieve a givenrise in school enrollment ratios than apopulation in which fertility is rapidlydeclining.

Table 9 shows the tremendous increasein the number of males attending schoolthat would be needed to raise educationallevels in the constant-fertility population,compared with the more modest rise nec­essary to achieve the same result in thedeclining-fertility population. To raisethe educational level as rapidly as postu­lated in the improving-education projec­tions, the number of males in school wouldhave to more than double within the firstfifteen years according to both fertilityassumptions. By the year t + 30 the num­ber of males in school would need to haveincreased 5.2 times in the high-fertilitypopulation, compared with 3.6 times inthe declining-fertility population, and thedifference between the two projectionsthereafter would continue to widen rap­idly.

The ratio of males in school to males

Table 8.-PERCENTAGE OF THE MALE LABOR FORCE AGED 20 YEARS AND OVER,BY YEARS OF SCHOOL COMPLETED, ASSUMING IMPROVING EDUCATIONAL

LEVELS, UNDER CONDITIONS OF CONSTANT AND DECLINING FERTll.ITY,

BY YEAR, YEAR t TO t + 60

Fertility conditions andYear

years of school completedt t+15 t+30 t+45 t+60

A. Constant fertility4 years of primary school •• 30.4 44.2 62.3 82.2 92.74 years of secondary school 4.3 14.2 29.6 45.4 52.53 years of college ••••••••• 0.4 2.5 6.5 10.4 12.3

B. Declining fertility4 years of primary school ••. 30.4 44.2 61.9 79.6 92.34 years of secondary school 4.3 14.2 29.4 43.9 52.73 years of college •••••••••. 0.4 2.5 6.5 10.3 12.&

240 DEMOGRAPHY

in the labor force given in Table 10 is onemeasure of the relative burden of educa­tion according to the different projections.Naturally enough, this ratio is much high­er in the improving-education projectionsthan in the constant-education projec­tions. But, controlling for educationallevel, it becomes much higher in thehigh-fertility population by about yeart + 25, and the gap between the ratio forhigh- and declining fertility populationsbecomes very wide indeed by about yeart + 35.

Another measure of the "educationalburden" is the percentage of the GNPthat would have to be devoted to educa-

tion if educational levels were to be raisedas postulated. This percentage rises morerapidly in the high-fertility populationtoo. If we assume that per capita incomesand the amount spent per school enrolleebegin at the same level and rise at thesame rate" in both high- and declining-fer­tility populations, then to achieve theprojected rise in educational levels, theproportion of the GNP devoted to educa­tion would have to be 2 percent higherin the high-fertility than in the declining­fertility population after twenty years,12 percent higher after 30 years, and 30

22 Fifteen percent every ten years in this ex­ample.

Table 9.-INDEX OF THE NUMBER OF MALES IN SCHOOL, UNDER CONDITIONSOF CONSTANT AND DECLINING FERTILITY AND CONSTANT AND

IMPROVING EDUCATION, BY YEAR, YEAR t TO t + 60

Fertili ty and educationalYear

conditionst t+15 t+30 t+45 t+60

Constant fertility-constanteducation ................. 100 152 257 442 772

Constant fertility-improvingeducation .................. 100 230 522 897 1565

Declining fertility-constanteducation •••••••••••••••••• 100 145 174 197 246

Declining fertility-improving education ••••.••• 100 221 361 404 508

Table IO.-RATIO OF MALES IN SCHOOL TO MALES IN THE LABOR FORCE,UNDER CONDITIONS OF CONSTANT AND DECLINING FERTILITY AND

CONSTANT AND IMPROVING EDUCATION, BY YEAR, .~

YEAR t TO t + 60

Fertility and educationalYear

conditionst t+15 t+30 t+45 t+60

Constant fertility-eonstanteducation ................. 0.27 0.27 0.29 0.30 0.30

Const~nt fertility-improvingeducation•••••••••••••••••• 0.27 0.45 0.72 0.74 0.76

Declining fertility-constanteducation ................•• 0.27 0.26 0.21 0.18 0.18

Declining fertility_improving education•••••••• 0.27 0.44 0.52 0.42 0.42

Differing Trends in Fertility of the Labor Force 241

percent higher after forty years." Thesedifferences may not seem particularly im­pressive, at least up to year t + 30. How­ever, if we make the more realistic assump­tion that per capita incomes would notrise as rapidly when fertility remainedhigh as when it declined." we come upwith a higher figure for the percentage ofGNP needed for education in the high­fertility population and a greater discrep­ancy between this figure and the figurefor the declining-fertility population.

It is possible, of course, that the gov­ernment in the high-fertility country willplace such strong emphasis on educatingits children that it will raise its school en­rollment ratios just as rapidly as will thegovernment of a declining-fertility coun­try which does not set as much store bythis goal. But the important point is thatany given rise in school enrollment ratioswill be easier to achieve in a declining­fertility than a high-fertility population,and, since there is no obvious reason whythe former would place less emphasis onraising the educational levels of its popu­lation than the latter, it is realistic toassume that countries with declining fer­tility will normally raise their school en­rollment ratios (and consequently, in time,

23 These figures appear to hold for all realisticinitial levels of per capita incomes and amountsspent per school enrollee. The school enrollmentfigures used in the calculations included childrenaged 6-9 years. For age 6 years it was assumedthat the enrollment rate increases linearly from40 percent in year t to 90 percent in year t + 30,and for ages 7-9 years from 60 percent in year tto 97 percent in year t + 30. The rates were notchanged after year t + 30.

24 There are a number of studies which supportthe contention that per capita incomes would notrise as rapidly for the population of an under­developed country if its fertility remained highas if its fertility declined. Important ones areAnsley J. Coale and Edgar M. Hoover, Popu­lation Growth and Economic Development in Low­Income Countries (Princeton: Princeton Univer­sity Press, 1958); Paul Demeny, "InvestmentAllocation and Population Growth," Demogra­phy, II (1965); and T. K. Ruprecht, "Populationand Economic Growth in the Philippines,"(mimeo), Paper presented to the Midwest Con­ference on Asian Affairs, Lawrence, Kansas City,Nov. 11, 1967.

the average educational attainment oftheir labor force) more rapidly than coun­tries where fertility remains high.

Another important element of realismthat must be introduced into the discus­sion is the fact that, at the present time,rates of unemployment and general under­utilization of the available labor force arevery high in most underdeveloped coun­tries, and the problems of absorbing eachyear's entrants into productive employ­ment are acute. To achieve rapid econom­ic growth, most underdeveloped countriesbadly need a better-educated labor force,butnot one that is doubling every twenty ortwenty-five years. Therefore, in a typicalunderdeveloped country, the declining­fertility-rising-education situation is dis­tinctly preferable to the constant-fertil­ity-rising-education condition, because itachieves much the same increase in theeducational level of the labor force with­out adding as many prospective workers.

The serious unemployment problemsof the less-developed countries providean additional reason why such countriesshould try to raise school enrollment ra­tios as rapidly as possible. There are, ofcourse, very important noneconomic argu­ments for raising these ratios, and theimprovement in the quality of the laborforce which rising enrollment ratios fore­shadows is economic reason enough. Butanother major "fringe benefit" is that arise in enrollment ratios results immedi­ately in a slackening rate of growth ofthe labor force, and this can be expectedto ameliorate the unemployment situationsomewhat. It is unlikely that governmentshave given the latter effect much weightin their decision to step up educationalexpenditures, but it is an important effectnonetheless.

Finally, it should be noted that wehave so far ignored the possibility of rais­ing the educational level and productivityof the existing Iabor force through variouskinds of in-service training schemes, nightcourses, and so on. Such schemes could bean important supplementary method ofraising the educational attainment of thelabor force, although in view of young

242 DEMOGRAPHY

people's greater receptivity to educationand the rapidity with which the laborforce is replaced even in the declining-fer­tility projection, it seems doubtful whetherit would normally be economically justi­fiable to divert substantial funds fromexpanding the school system to providingin-service training programs.

CONCLUSIONS

The model discussed in this paper is along-term one, and its practical relevancemight appear to be small. Most modelswhich seek to demonstrate the effect offertility changes on economic developmentignore their effect on the labor force. Thisis reasonable: it takes twenty years forfertility changes to register any substan­tial effect on the size of the labor force,and most economic planners are forced towork within a shorter time horizon thanthis. But this does not mean that studiesof the long-term effects of fertility changeon the labor force are useless. The timelag between shifts in educational policyand their impact on the growth and qualityof the labor force is much shorter and lies

well within the "practical" time horizonof the economic planners.

In all four projections employed in thispaper, massive increments to the laborforce occur over the sixty-year period.Even when steadily declining fertility andsteadily improving education is assumed,the labor force more than trebles; if fer­tility remains high, it grows by five or sixtimes. The contrast, then, is not betweenslow growth and rapid growth, but ratherbetween rapid growth and extremely rap­id growth.

The basic conclusion of the study isthat, given the rate of advance in raisingschool enrollment rates, it makes very littledifference to the time taken to replace thepoorly educated labor force with a groupof better-educated workers whether fertil­ity remains high or declines. The qualify­ing phrase in this sentence is very impor­tant. Since a high fertility population willfind it more difficult to achieve a givenrise in school enrollment ratios than willpopulations in which fertility is decliningrapidly, the educational standard of thelabor force could normally be raised to agiven level more rapidly if fertility wereto decline.

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years

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-44

years

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do

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nan

dfertil

ity

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ns

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yea

rs

of

sch

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mp

lete

dt

t+5

t+1

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15

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vels

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29

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rs

of

seco

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1.3

12

.01

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13

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13

.51

3.4

13

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years

of

co

lleg

e..

,.....................

0,3

0.5

1.0

1.4

1.7

1.9

2.1

2.3

2.4

2.4

2.5

2.5

2.5

Decli

nin

gferti

lity

4y

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of

pri

ma

rysc

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..~.........

29

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5.5

47

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9.0

50

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1.0

51

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64

ye

a;r

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fse

con

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....

....

....

..3

.65

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.69

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0.5

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.61

2.7

13

.61

4.4

15

.01

5.1

15

.11

5.1

3y

ea

rs

of

co

lleg

e........................

0.3

0.5

1.0

1,4

1.7

2.0

2.2

2.5

2.7

2.9

2.9

2.f

t2

9

Imp

rovi

ng

edu

cati

on

al

lev

els

Co

nst

an

tfertil

ity

4y

ea

rs

of

pri

ma

rysc

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ol.

................

29

.43

3.7

38

.84

4.4

50

.45

6.8

63

.57

0.5

77

.98

3.1

87

.39

0.4

92

.64

yea

rso

fse

con

da

rysc

ho

ol...............

3.6

5.8

8,9

12

.71

7.2

22

.32

8.2

33

.83

8.7

42

,44

5.3

47

.44

8.8

3y

ears

of

co

lleg

e........................

0.3

0.7

1.3

2.1

3.2

4.4

5.9

7.1

8.4

9.4

10

.21

0.1

11

.1

Decli

nin

gferti

lity

4y

ears

of

pri

ma

rysc

ho

ol•

....

....

....

....

29

.43

3.7

'3

8.8

44

.45

0.4

56

.66

2.9

69

.97

5.7

80

.38

4.3

117.

79

0.4

4y

ears

of

seco

nd

ary

sch

oo

l•..

....

....

....

3.6

5.8

8.9

12

.71

7.2

22

.52

8.2

33

.73

8.3

42

.24

5.2

47

.44

9.3

3y

ears

of

co

lleg

e••••••••..

....

....

..•..

•0

.30

.71

.32

.13

.24

.26

.07

.28

.59

.71

0.5

11

.11

1.6

Differing Trends in Fertility of the Labor Force 245

ASSUMPTIONS AND METHODS: IMPROVING

EDUCATION PROJECTION

Ages 10-24 years.-Activity rates forages 10-24 years were calculated from theprojected school attendance rates, usingthe following regressions, which were cal­culated from data for all available coun­tries in the United Nations DemographicYearbook, (1963 and 1964). The first re­gression utilizes data from sixteen coun­tries; the second, from 36 countries; andthe third, from 33 countries. Differencesin definition of "economically active"were ignored.

rates for ages 25-49 years were not varied.For ages 50 years and over it was assumedthat the rates would drop from the levelof those in agricultural countries to thelevel of those in industrialized countriesover a period of fifty years from time t.This assumption was adopted for all pro­jections.

CALCULATION OF EDUCATIONAL ATTAIN­

MENTS OF THE LABOR FORCE

I. Year t.A. The age group 10-14 years. The per­

centage completing four years of pri­mary school was obtained by the meth-

Percentage ofmales in school

aged:

10-14 years

15-19 years

20-24 years

'J

Percentage ofmales eco­nomically

active aged:

10-14 years... ... . .... y = 71.23 - 0.742 x(rI = 0.97)

15-19 years.. . . . . . . . .. y = 94.10 - 0.947 x(rI = 0.83)

20-24 years " y = 97.75 - 1.110 x(rI = 0.36)

The reason for the rather poor fit inthe age group 20-24 years appears to bethat for several countries, some of thepersons attending school were also classi­fied as economically active. In the ab­sence of further information the regres­sion was used as calculated.

Ages 25 years and over.-Age-specificactivity rates for males for ten-year agegroups (given in United Nations, Depart­ment of Economic and Social Affairs,Population Studies, No. 33, DemographicAspects of Manpower. Report I: Sex andAge Patterns of Partidpation in EconomicActivities [New York: 1962], Table 3.2),are average rates for agricultural and in­dustrialized countries. The percentageseconomically active for each five-year agegroup were derived by interpolation froma smooth curve plotted through the givenrates.

At time t it was assumed that the ac­tivity rates of the agricultural countriesapply to the base population. Activity

od described under "Special Problems"below. It was assumed that no maleaged 10-14 years had completed fouryears of secondary school or three yearsof college.

B. The age group 15-19 years.1. Table A-4 gives the percentage of

males aged 20-24 years who com­pleted four years of primary schoolin year t + 5. This same percentagewas used as the percentage of totalmales aged 15-19 years who com­pleted four years of primary schoolin year t, To find the correspondingpercentage for the labor force, it wasassumed that all males in school atages 15--19 years had completedfour years of primary school. Thisnumber was subtracted from thetotal number aged 15-19 years whohad completed four years of primaryschool to obtain the number of malesnot in school who completed fouryears of primary school. This per­centage was applied to those in thelabor force.

246 DEMOGRAPHY

2. The percentage who completed fouryears of secondary school was ob­tained by the method describedunder "Special Problems."

3. It was assumed that no males aged15-19 years had completed threeyears of college.

C. The age group 20-24 years.1. Table A-4 gives the percentage of

total males aged 20-24 years whocompleted four years of primaryschool. The method described in1. B. 1., for the age group 15-19

years was used to obtain the corre­sponding percentage for the laborforce.

2. Table A-4 gives the percentage ofmales aged 25-29 years who com­pleted four years of secondary schoolin year t + 5. This figure was alsotaken as the percentage of totalmales aged 20-24 years who hadcompleted four years of secondaryeducation in year t. The same meth­od as in 1. B. 1., for the ages 15-19years was used to derive the per-

Table A-3.-PERCENTAGES OF MALES WHO ARE ECONOMICALLY ACTNE ACCORDING TO IMPROVING

EDUCATION PROJECTION, BY YEAR, YEAR t TO t + 60

YearAge

(years) t+25 t+35 t+40 t+40t+50 to

t t+5 ·t+10 t+15 t+20 t+30 t+60

11)_14 ........... 34.1 28.3 22.5 16.7 10.9 5.1 0 0 0 0 0

15-19 ........... 75.2 68.8 62.5 56.2 49.9 43.6 37.3 37.33 37.3 37.3 37.3

20_24 ........... 92.2 90.3 88.5 86.6 84.8 82.9 81.1 8 .• 1 81.1 81.1 81.1

25-29 ........... 95.7(8) .... .... . ... .... .... .... .... . ... .... . ...30-34........... 97.0(8) .... .... .... .... .... .... . ... .... . ... . ...35_39........... 97.5(8) .... .... .... .... .... .... .... .... . ... . ...40_44 ........... 97.5(a) .... .... .... .... .... . ... .... .... . ... . ...45-49 ........... 96.9(01 .... .... .... . ... .... .... .... .... .... . ...50-54 ••••••••••• 95.6(a) 95.5 95.4 95.3 95.2 95.1 95.0 94.9 94.8 94.7 94.6

55-59 ........... 93.5 93.1 92.7 92.3 91.9 91.5 91.1 90.7 90.3 89.9 89.5

60-64 ........... 89.0 88.1 87.2 86.3 85.4 84.5 83.6 82.7 81.8 80.9 80,0

65 and over...... 70.1 66.9 63.6 60.4 57.1 53.9 50.7 47.4 44.2 40.9 37.7

(a)Rates for. ages 25-49 years remain constant at the level of year t ,

Table A-4.-EDUCATIONAL ATTAINMENT RATES, BY YEARS OF SCHOOL COMPLETED, FOR ALL

MALES IN SPECIFIC AGE GROUPS, BY YEAR, YEAR t TO t + 40 AND AFTER

YearAge group and

t+40educational attainment

t t+5 t+l0 t+15 t+20 t+25 t"30 t+35 andover

Percentage of males aged 20_24years who completed four yearsof primary school ............... 41.8 48.7 55.6 62.5 69.4 76.3 83.2 90.1 97.0

Percentage of males aged 25-29years who completed fouryears of secondary school ....... 5.7 11.8 18.3 24.6 30,9 37.3 43.6' 49.9 56.2

Percentage of males aged 25-29years who completed threeyears of college .............•.. 0.5 2.2 4.0 5.7 7.4 9.1 10.8 12.6 14.3

Source: Assumed and projected school enrollment ratios, and the following r-eg re s s ron equa t Ion s calculatedon the basis of data from sixteen countries.

~

Percentage of males in schoolyear t, aged:

10_14 years •.•.•....•...••

15_·19 years ..••......••...

15-19 years ....••..........

tPercentage of males in year t + 10

who completed:

FOurs years of primary school (aged20_24 years)........................ y 0= 11.47 + 0.882 x

(r2 = 0.790)

Four years of secondary school (aged25_29 years)..... y = 0.652 + 0.948 x

(r' = 0.818)

Three years of college (aged 25-29years............................... y 0= 1.20 + O.2f18 x

(r' = 0.806)

sPECIAL PROBLEMS

In calculating three rates-the per­centageof the labor force aged 10-14,15-19, and 20-24 years, who completedfour years of primary school, four yearsof secondary school, and three years ofcollege, respectively-it was necessary tofind (1) the percentage of all males in theage group who had completed the level

Table A-S.-RATIOS OF EDUCATIONAL

ATTAINMENT, BY AGE GROUP

1. The percentage of total males aged20-24 years who had completed fouryears of primary school in year twas obtained from Table A-4. Toobtain the same percentage of malesaged 25--29 years, it was assumedthat the ratio of the percentage ofmales aged 25--29 years who hadcompleted four years of primaryschool to the percentage of malesaged 20-24 years who had com­pleted four years of primary schoolequals the ratio of the percentageaged 30-34 years who had com­pleted four years of primary schoolto the percentage aged 25--29 yearswho had completed four years ofprimary school. This ratio is thefirst entry in Table A-5.

2. The percentage of males aged 25-29years who had completed four yearsof secondary school and three yearsof college is given in Table A-4.

E. Ages 30 years and over. For each of thefive-year age groups at ages 30 yearsand over, the ratios given in Table A-5

Differing Trends in Fertility of the Labor Force 247

centage of the labor force aged 20-24 were used to derive rates from thoseyears who had completed four years already calculated for the ages 25--29of secondary school. years.

3. The percentage who completed three F. Explanation. It was important to de-years of college was obtained by the rive a realistic distribution of educa-method described under "Special tional attainments in the base year.Problems." Educational levels, we assumed, had

D. The age group 25--29 years. For ages been improving over the years prior toover 25 years, it was assumed that the year t, To find the typical pattern ofpercentage who completed the various educational advance in the past in de-educational levels is the same for the veloping countries, ratios were ealcu-total male population as for the labor lated as in Table A-5 for every develop-force. ing country for which data could be

found (that is, for ten countries for thefirst two columns and six countries forthe third column). The ratios in TableA-5 are averages of these individualcountry ratios. Each row gives thefactor by which the 25-29 year agegroup's educational attainment ratemust be multiplied to give the educa­tional attainment for the older-agegroup. Those rates apply only to year t,

H. Years after t.A. Ages 10-24 years. The same method

used for these ages as in year t,B. Ages 25-29 years. The method here

was the same as for year t, except thatthe percentage who completed fouryears of primary school was taken fromTable A-4 and equals the percentageof the age group 20-24 years who hadcompleted four years of primary schoolfive years earlier.

B. Ages 30 years and over. For any cohortaged 3'0 years and over, the percent­ages who had attained the variouslevels of education were taken from theeducational attainment of that cohortwhen it was aged 25--29 years. In otherwords, it was assumed that as eachcohort advanced past the 25--29-yearage range, the percentages who hadattained the various levels remainedthe same.

._.. ". .- -

PercentagePercentage

Percentagewho

whocompleted

who

Age g-roupcompleted

4 yearscompleted

4 yearsof

3 yearsof primary

secondaryof

educationeducation

college

30_34/25_29 ••••••• 0.89 0.79 0.8935_39/25_29 ••••••• 0.82 0.66 0.7340_44/:!5_29 ••••••• 0.73 0.56 0.5945-49/25_29 ••••••• 0.65 0.48 0.4850_ 54/25- 29 ••••••. 0.57 o."a 0.4055- 59/25_ 29 .•••••• 0.50 0.35 0.3460_ 64/25- 29 .•••••• 0.42 0.29 0.2865 +/ 25- 29 ••••••• 0.38 0.24 0.18

248 DEMOGRAPHY

of education in question and (2) the rela­tion of the rate for all males to that ofthose in the labor force only. Both of thesecould be expected to vary as the educa­tional structure changed.

In order to find (1), we used the regres­sions (based on the data from seventeencountries for the first regression and fromtwenty countries for the second and thirdregressions) shown in the accompanyingtabulation.

into the required rates for the labor force.

Percentage of the economically active who have finishedsome secondary school divided by the percentage of thetotal population who have finished some secondary school

Columbia, males aged 15-19 years. . .. 0.46Ecuador, both sexes aged 15-19 years.. 0.28Korea, males aged 15-25 years. . . . . .. 0.36

Average................. 0.36

At time t, this average was used for allthree groups. At time t + 30, it was as-

Educational attainment rates for allmales at base ages were obtained fromthe projected school attendance rates bymeans of the foregoing regressions. Em­pirical data relating the educational at­tainment of all males at ages 10-24 yearsto the educational attainment of those inthe labor force at these ages were difficultto come by. The data shown in the ac­companying tabulation were used to ob­tain factors by which to convert the edu­cational attainment rates for all males

Four years of secondary school(aged 15-19 years) .

Three years of college(aged 20-24 years) .

Percentage of males in year twho had completed:

Four years of primary school(aged 10-14 years) . 'Y = 56.7 + 1.485 x

(,-I = 0.828)

'Y = 1.083 + 0.248 x(r2 = 0.565)

'Y = 1.450 + 0.566 x(r2 = 0.531)

surned that the educational attainmentsfor the labor force and the total popula­tion in these groups were identical. Thiswas on the basis of data from the 1960Census of the United States, which wasassumed to be representative of the de­veloped countries. For years between timet and t + 30, the ratio was increasedlinearly from 0.36 to 1.00. The threeschedules of educational attainment ratesfor the labor force, obtained in this man­ner, are set out in Table A-6.

20-24 years

xPercentage of

males in schoolin year t, aged:

10-14 years

15-19 years

Table A-6.-EDUCATIONAL ATTAINMENT OF MALES IN THE LABOR FORCE, BY AGE GROUPAND YEARS OF SCHOOL COMPLETED, BY YEARS, YEAR t TO t + 30: IMPROVING EDU­

CATION PROJECTION

YearAge group and educational

level t t+5 t+lO t+15 t+20 t+25 t+30

Percentage aged 10_14 years ~ho

completed 4 years of primaryschooL, ••••••••••••••••••••••••• 6.3 13.7 23.3 35.6 50.6 68.1 87.3

Percentage aged 15_19 years whocompleted 4 years of secondaryschool .....•..................•• 1.4 2.6 4.1 6.0 8.3 10.9 13.8

Percentage aged 20_24 years whocompleted 3 years of college •••• 0.5 11.1 1.9 2.9 4.1 5.5 7.0