Educational Policy and Labour Productivity: An Output Accounting Exercise

Author(s): J. B. Knight and R. H. Sabot

Source: The Economic Journal, Vol. 97, No. 385 (Mar., 1987), pp. 199-214
Published by: Wiley on behalf of the Royal Economic Society
Stable URL: http://www.jstor.org/stable/2233331
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TheEconomicJournal,97 (March1987), 199-2 I4

Printedin GreatBritain

EDUCATIONAL POLICY AND LABOUR

PRODUCTIVITY: AN OUTPUT ACCOUNTING
EXERCISE*

J. B. KnightandR. H. Sabot

What is the contribution of education to output, productivity or their growth?

Economists have tried to answer this question using output accounting or
growth accounting - by the decomposing of output or its growth into the
contributions of various factors, including education.
The approach in this paper is output accounting, of which Krueger (I968)
provides an early example. Using crude aggregate census data on some
20- mostly developing - countries, Krueger posed the question: how much do
differencesin educational endowments lead to differencesin per capita income?
She estimated the effect on per capita income in the United States of assuming
not the U.S. educational distribution but the distributionin each other country.
then related to the differences in per capita income.
The size of this effect xw}as
Krueger explained more than half the difference in per capita income by
differences in human capital, and so concluded that human capital (defined
more broadly than educational attainment) contributed more than all other
factors combined. Another version of the same exercise, but using a three-factor
production function, was conducted by Fallon and Layard (I 975), with similar
data sources but for a different set of countries. They found the contribution
of their index of human capital to be lower than Krueger's estimate and
generally lower than that of physical capital.
Output and growth accounting both sufferfrom well-known drawbacks (see,
for instance, Bowman, I980 and Nelson, I98I). First, failing to take account
of the other determinants of income can bias estimates of the difference
in income and productivity attributable to education. Secondly, in simply
assuming that the (standardised) earnings difference between the educated
and uneducated measures the productivity of education, output and growth
accountants attribute causation to what may at least in part be a non-causal
correlation. The relation between education and earnings may reflect payment
for unmeasured 'natural ability' or for educational qualifications irrespective
of their economic value, i.e. 'credentialism'. This effective equating of the
marginal products of factors to their remuneration has led some practitioners
to treat growth accounting as no more than 'a first step' that 'cannot be relied
upon to give answers to counterfactual questions' (Matthews et al. I 982, p. I 5) .
Adjustments to the earnings difference to estimate the marginal product of
education have in general simply attributed an arbitrary proportion of the
* This article is the result of research supported by the World Bank. Its findings, interpretations and
conclusions do not necessarilyrepresent official policy of the Bank and are the responsibilityof the authors.
Two referees and an editor provided helpful comments and suggestions.
[ I991

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200 THE ECONOMIC JOURNAL [MARCH

difference in earnings to ability or other correlates of education (see, for

instance, Denison, I967, pp. 82-7).
Thirdly, these accounting exercises are generally conducted over time periods
or across economies that differ much in the relative supply of and the relative
demand for educated labour. Differences in the structure of factor prices or their
marginal products according to factor endowments and the characteristics of
production functions make the answers to the counterfactual questions being
posed unreliable.' Krueger (I968, pp. 643-5) argued that her estimated
contribution of education would give a minimum estimate, essentially because
the marginal product of human capital in the United States would be relatively
low if the United States was well endowed with human capital. But her estimate
would not be low if the U.S. economy had a greater relative demand for human
capital.
In this paper we minimise these three drawbacks by examining a 'natural
experiment' in Kenya and Tanzania. These countries differ in their educational
policies, but they are sufficiently similar in relevant respects other than the
supply of educated labour. In particular there is evidence that the relative
demand functions for different categories of educated labour are very similar
in the two economies (Knight and Sabot, I983, I984). The analysis here is
based on two, strictly comparable, sets of microeconomic data. Earnings
functions can therefore be used in place of mean earnings by educational level.
The data sets provide information on the educational attainment of workers
and on their cognitive skills and reasoning abilities. The measures of cognitive
skill and reasoning ability enable us to isolate human capital from the screening
and credentialist effects of education, thereby improving on conventional
estimates of the marginal product of education. The measures make possible
an estimate of the effects on output of the difference between the two countries
not only in the quantity but also, by means of educational production functions,
in the quality of education.
Section I contains a brief account of the data and the setting for the analysis.
Section II presents estimates of a recursive model of cognitive skill acquisition
and earnings determination. Section III examines how much the divergent
educational policies in the two countries have generated measurable differences
in the quality of education provided. In Section IV a method is developed for
estimating the effect of education on the cognitive skills of workers and on their
earnings and productivity. In Section V we conduct policy simulation exercises
which show the effect in one country of adopting the other's policies relating
to the quantity and quality of education. This permits an estimate of the
contribution of educational policies to the productivity of workers. Section VI
sums things up.

1 Attempts in growth accounting to allow for non-marginal educational expansion have used assumed
or estimated elasticities of substitution between education and other factors to measure the effect on factor
prices and factor weights (see, for instance, Dougherty, I 97I and Selowsky, 197 I); attempts to allow for the
changing structure of factor prices have involved the use of a chain-linked Divisia index (see, for instance,
Jorgenson and Griliches, I967).

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 1987] EDUCATION AND PRODUCTIVITY 20I

I. THE SETTING AND THE DATA

The natural experiment has been in progress in East Africa over the last twenty
years. Kenya and Tanzania are similar in size, colonial heritage, resource
endowment, structure of production and employment, and level of develop-
ment. Nor do technical conditions or physical capital intensity differ much for
their urban wage economies. The countries differ markedly, however, in one
key dimension of the supply of educated labour, the dimension we are interested
in: the emphasis on secondary education. Kenya and Tanzania achieved
political independence in the early I 96os with administratively similar but very
undeveloped educational systems and negligible stocks of indigenous educated
manpower. In I962 primary enrolment (standards I-VIII) as a proportion of
the relevant age group was 47 % in Kenya and 23 % in Tanzania, and
secondary enrolment (forms I-IV) was 3 % in (25,000) Kenya and 2%
(I4,000) in Tanzania. Both countries have now come close to the objective of
universal primary education, with a primary enrolment ratio in I980 of more
than i00% in Kenya and of 88% in Tanzania. And university enrolments
remain at less than I % of the relevant age group. It is with secondary education
that the main policy issue arises in East Africa.
Enrolments in secondary education have diverged: in Kenya, with a slightly
smaller population, the secondary-school enrolment ratio was 25 % (400,000
pupils) in I 980, and in Tanzania it was 4 % (6o,ooo pupils). Secondary
education is tightly rationed in Tanzania for reasons of financial and manpower
planning, whereas both the public and private sectors have been more
responsive to demand in Kenya. The Tanzania government started with a
smaller system, accepted that post-primary education should not be expanded
beyond the requirements of the economy as gauged by existing input-output
relationships, and gave budgetary priority to primary education and literacy.
These differences in supply are reflected in the educational composition of the
wage-labour forces in the two countries. Differences may also have grown in
the quality of secondary education. The private and self-help system burgeoned
in Kenya, and Tanzania adopted an egalitarian approach to secondary schools
and stressed Kiswahili rather than English as the medium of instruction
in primary schools.
-To subject this experiment to quantitative analysis we required rigorously
comparable data. Two surveys were therefore administered within a few
months of each other in I980 by a team including the authors. The samples,
each containing nearly 2,000 employees, were randomly selected on an
establishment basis, using a two-stage procedure, from among the wage-labour
forces of Nairobi and of Dar es Salaam.' The surveys were confined to the
1 The sampling frame was the full list of establishments in the capital city, provided by the government
statistical service in each country. All employing establishments with fixed addresses were covered in
principle, but very small firms were likely to be under-representedin the frame. The sample was stratified
on the basis of sector (manufacturing, government, other non-manufacturing). The non-government
establishments were also stratified according to size measured by the number of employees. Roughly 70
establishments were selected in each country. Within each establishment, employees were sampled on a
random basis, the sampling fraction ensuring stratification of employees by establishment size. Non-response
by firms and employees was negligible.

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202 THE ECONOMIC JOURNAL [MARCH

capital cities because of the high concentration of employed secondary-school

leavers in urban areas and because previous labour market survey work had
suggested that a capital was not unrepresentative of urban areas in respect of
relevant wage-employment characteristics.' The surveys provide information
on the earnings, education, employment experience and other characteristics
of respondents.
We also have information on the worker's cognitive skill and reasoning
ability - two measures not previously found in studies of developing countries
and only rarely found in studies of the education-wage relationship in
developed countries. Our measure of cognitive skill is the combined score in
the tests of literacy and numeracy designed by the Educational Testing Service
of Princeton specifically for use in these surveys. The designs were based on
questions in language comprehension and mathematics from the national
primary school-leaving and secondary school-leaving examinations and on
other guides to the content of the academic curriculum, which is much the same
in the two countries. The major difference is that the use of Kiswahili is stressed
more in Tanzania; questions were therefore set in both English and Kiswahili
for respondents to choose the language they preferred. Reasoning ability was
tested with 'Raven's Progressive Matrices' (Raven, I956). Widely used in
developing countries, this test involved matching pictorial patterns, for which
literacy and numeracy provide no advantage (see, for example, Klingelhofer,
I967, Sinha, I968 and Wober, I969). All three tests appear to have been
appropriate for the target groups: the frequency distributions of test scores
reveal considerable variance on each test but very few perfect scores and no
zero score.
Not all respondents were given the tests which yielded our measures of
reasoning ability, literacy and numeracy: testing was confined to a subsample
of primary school and secondary school completers. The primary school
completers left school after standard VII (standard VIII before the withdrawal
of the eighth standard in each country) and the secondary school completers
after form IV. From the primary- and secondary-completers in the two samples
(just over goo in each country), two subsamples of about 200 were randomly
selected for testing.2 The size of the subsamples was determined by time and
cost constraints,3 and the educational stratification was chosen because of policy
interest in the economic value of the four-year course of secondary education.
In each educational stratum the subsamples were found to be well represent-
ative of the larger samples. The analysis of this paper is necessarily based entirely
on the tested subsamples.
1 See Sabot (I 979), which compared Dar es Salaam with other towns in Tanzania. In relation to the urban
areas in general the capital cities may have an over-representationof government services (20 and 25 % of
employees in Nairobi and Dar es Salaam respectively) and manufacturing (20 and 23 %) and an
under-representationof small firms (9 % in establishments with fewer than 20 employees in both cities).
2 The subsample was stratified into primary- and secondary-completers (roughly ioo of each) in order

to ensure that there would be adequate numbers in each educational stratum. The regressionanalysis based
on the subsample uses the unweighted data, but for mean values of the dependent and independent variables
(required in the simulation analysis) the subsample is weighted according to the ratio of primary- to
secondary-completersin the full sample. Non-response to the tests was negligible.
3 It took half an hour per respondent to complete the questionnaire and an hour per respondent to

administer the tests.

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 I987] EDUCATION AND PRODUCTIVITY 203

II. A MODEL OF COGNITIVE SKILL ACQUISITION AND EARNINGS

DETERMINATION

We posit a recursivemodel representedin the followingtwo equations:

H= ao+a1R+a2S+a3T+a4B+a5G+U (I)
where ln W= bo+b1R+b2S+b3H+b4L+b5L2+ V (2)
H = cognitiveskillscore
R = reasoningabilityscore
S = a dummyvariableindicatingcompletionof secondaryschooling,the
omittedsubcategorybeing completionof primaryschooling
T = yearssinceleavingschool
B = a dummyvariableindicatingbirthin an urbanarea, birthin a rural
area being the omittedsubcategory
G = a dummyvariabletakinga value of I if the secondaryschoolattended
by a secondary-completer, and the primaryschool attended by a
primary-completer, was a governmentschool,and o otherwise
W= earningsper month
L = yearsof employmentexperience,directlymeasured
U, V = disturbanceterms,with U assumedto be uncorrelatedwith V.
Equation (I) is an educationalproductionfunction,similarin form to those
used in most such studies (surveyedby Hanushek, I979 and Lau, I979);
estimatesarepresentedin Table I. In eachcountrycognitiveskillbearsa highly
significantpositiverelationshipto educationallevel and to ability. In Kenya,
secondary education raises cognitive skill by II -75 points or by 35 % at the
means;similarresultsare obtainedin Tanzania.The elasticityof responseof
cognitiveskillto reasoningabilityat the meansis roughlyo04in bothcountries.
Becausethe numberof yearsthat have elapsedsincethe respondentleft school
is a proxyfor changein the qualityof schoolingover time and for gain or loss
of cognitive skill after leaving school, the sign of its coefficientcannot be
predicted.In neithercountrywas the coefficienton T significantlydifferent
fromzero, and the termwas thereforedeletedfromthe estimatedequation.In
both countriesthe coefficienton B is almostsignificantlynegative,suggesting
that urbanbirth,and by implicationurbaneducation,reducescognitiveskill.
Thiscounter-intuitive resultmayreflectgreaterselectivityin accessto schooling
and to the urban labour market among the rural-born,who face stiffer
competition,ratherthanbetterqualityof ruralschools.In Kenyathecoefficient
on G is significantlypositive,in accordwith our expectationthat government
schoolsare on averageof higherquality than privateschoolsin Kenya.
In our modelfor the determinationof inputsin the educationalproduction,
reasoningability is exogenousand secondary-schoolattendanceis influenced
by reasoningabilityand by the availabilityof secondaryschoolplaces,which
is exogenous.Educationalattainmentfunctionshave been estimatedfor the
samplesby meansof probitanalysis(Boissiereet al. I985).1 In both countries
1 Tests of recursivenessrelating this equation to our equations (i) and (2) failed to reject the null hypothesis
that the equation system is recursive.

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204 THE ECONOMIC JOURNAL [MARCH

Table I
Kenyaand Tanzania:EducationalProduction
Functions
Pooled
Variable Kenya Tanzania sample

S Secondary schooling I I'754 I0-939 II-6II

(8-50) (8-84) (I2-07)
G Government school 3-366 O-995 2.475

(2-49) (0-76) (2-53)

B Urban birth - 3-567 -2-65I - 2-868
(I-78) (I.82) (2-31)
R Reasoning ability 0-570 0-487 0-5I9

(5-55) (5-58) (7-47)

K Kenya 7.7I2

(8'45)
Constant I 5'49 I2-34 9'903
R2 0042 0-44 o056
Standard error of H 8.77 7'76 8'45
Percentage standard error of H 2I'I 26-2 23.5
N 205 I 79 379

Notes
(i) The dependent variable is H, cognitive skill.
(2) The figure in parentheses beneath a coefficient is its t statistic.
(3) The H variable was marked out of 6I, there being a maximum of 28 in the literacy test and 33 in
the numeracy test; the maximum score for R was 36.
(4) The dummy variable K represents membership of the Kenya sample, the base subcategory being
membership of the Tanzania sample.
(5) A log-linear specification (ln H, ln R and ln Treplacing H, R and T) was also estimated but was inferior
in terms of the percentage standard error of H (29 % in Kenya and 3 I % in Tanzania), and the significance
of some coefficients.
(6) The White heteroskedasticitytest (White, 1980) cannot reject the null hypothesis of homoskedasticity
of the errors. The White standard errors, i.e. standard errors which are consistent even in the presence of
unknown heteroskedasticity,are very similar to the reportedstandard errors,and in no case does a coefficient
cease to be significant when the White standard error is substituted.

the probability of going to secondary school increases significantly with

reasoning ability and with the size of the secondary relative to the primary
system at the time that primary schooling was completed. Ability thus
influences the acquisition of cognitive skillsboth directly and indirectly through
access to secondary education. The main difference in educational attainment
between the two countries is due to the difference in the size of their secondary
school systems, which in turn can be attributed to differences in government
policies. The findings are consistent with the views that in Kenya, with its large
private as well as government system, the market for secondary education is
in equilibrium, whereas in Tanzania there is excess demand for secondary
school places. Estimates of private rates of return to secondary education and
subjective responsesto survey questions also suggest excess demand in Tanzania
(Knight and Sabot, I986).
Equation (2), the semi-logarithmic earnings function, includes H, R and S
among the independent variables to separate the positive effects on earnings
of cognitive skill acquisition and reasoning ability from that of secondary school
attendance. The first can be taken to representthe effect of human capital, and

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I987] EDUCATION AND PRODUCTIVITY 205

Table 2
Functions
KenyaandTanzania:Earnings
Variable Kenya Tanzania

R Reasoning ability o-oo6 o-ooo8

(I-I50) (OI45)
S Secondary schooling 0 I92 0-II2

(2-469) (I*4I7)
H Cognitive skill 0-020 0O0I3
(6- I 77) (3-2I8)
L Employmentexperience 0-045 0-055

(9-842) (io-o6o)
Constant 5.476 5.726
R2 0-440 0-425
Standarderrorof ln W 0-405 0-4I9
N 205 I 79

Notes
(i) The dependent variable is ln W, the natural logarithm of earnings.
(2) The figure in parentheses beneath a coefficient is its t statistic.
(3) The L2 term in the specification was deleted from the estimated regressionbecause its coefficient was
not significant in either case.
(4) The White heteroskedasticitytest (White, I980) rejects the null hypothesis of homoskedasticityof the
errors in the case of Kenya but fails to do so in the case of Tanzania. However, the White standard errors
are very similar to the reported standard errors in both countries, and in no case does a coefficient cease
to be significant when the White standard error is substituted.

the secondthe effectof individualability on earnings.The coefficienton S is

a ragbag that could represent'credentialism',i.e. payment for secondary
educationirrespectiveof its productiveeffects, or the use of schoolingas a
statisticalscreeningdevicefor unobservedcharacteristics, or preschoolhuman
capital formation,or non-cognitivehuman capital traits acquiredin school.
Employmentexperienceis a proxyforpost-schoolskillacquisition,the normal
expectationbeingthatthe earnings-experience profilehasan inverted-Ushape,
namely b4> o and b5< o.
Estimatesof equation (2) are reportedin Table 2. The coefficienton the
experienceterm is positive and highly significant.School attendancehas a
positiveeffecton earnings,thiseffectbeingstatisticallysignificantin Kenyabut
not in Tanzania.The coefficienton reasoningability is not at all significant
in either country: reasoningability has only an indirecteffect on earnings
throughthe accessto, and the skillsacquiredin, secondaryschool.By contrast,
the coefficienton cognitiveskill is positiveand significantat the I 0 level in
both countries.An extrapoint scoredin the cognitiveskilltest raisesearnings
by 2 0 ?0 in Kenyaand by I 3 %0in Tanzania.The importanceof cognitiveskill
in explainingearningsprovidessupportfor the humancapitalexplanationof
the correlationbetweenschoolingand earnings.It alsosuggeststhat the higher
earnings of the more educated largely representhigher productivity- a
conclusionalso reached from the more detailed analysisin Boissiereet al.
(I985) .
A Chowtestindicatesthat the earningsfunctionsdiffersignificantlybetween

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206 THE ECONOMIC JOURNAL [MARCH

the two countries. In particular, the return to cognitive skill is lower in Tanzania
than in Kenya (Table 2), despite Kenya's greater endowment of cognitive skill.
This finding suggests that the production function is more efficient in Kenya,
that such other factors as physical capital are relatively more abundant in
Kenya, or that government pay policy depresses the return to cognitive skill
in Tanzania.
Each type of explanation is plausible; each is examined in Knight and Sabot
(i984). The Kenya economy is commonly thought to be more efficient owing
to advantages in management, market size, capacity utilisation and availability
of inputs. This efficiency could have implications for the marginal product of
educated relative to uneducated labour. The structure of the urban economy
might also raise the relative demand for educated labour in Kenya. But
evidence from the surveys does not confirm this hypothesis: we find a close
similarity in skill-based occupational composition of the two full samples. The
percentages of employees in the main occupational groups in Kenya and
Tanzania respectively are: managerial and supervisory io09, I2 3; clerical
3I7, 33.4; skilled manual 23-I, 2I-3; semiskilled manual I6-3, I6-3; unskilled
manual i8&o, i6.6.1 The similarity of occupational structure suggests that the
demand for cognitive skill in relation to unskilled labour does not differ between
the two urban economies on account of their structural characteristics.
Moreover, simulations with complex earnings functions, estimated using the full
samples, fail to reject the null hypothesis that the relative demand functions are
the same in the two countries. In support of the second explanation, there is
institutional evidence and evidence from the full samples of an egalitarian pay
policy in the public sector - both government and parastatal organisations - of
Tanzania. However, using the tested subsamples, the introduction in equation
(2) of a dummy variable representing employment in the public sector (P) and
a ' public sector x cognitive skill' interaction term (P H) does not produce the
hypothesised significant negative coefficient on the interaction term.2 Whatever
the reason for the difference in the return to cognitive skill, the important
consideration is that the qualitative conclusions from the simulation analysis
conducted below do not depend on whether the Kenya or Tanzania coefficient
is used in the simulation.
Before combining the two functions, we test whether the estimated model is
recursive - that is, whether the estimates are consistent and not subject to
simultaneous equations bias. If some unmeasured characteristics, such as drive
and determination, contributed both to cognitive achievement and to earnings,
the error terms U and V would be correlated, as would cognitive skill and V.
Applying a method developed by Hausman (I978), we added the predicted
value of cognitive skill (H) as an independent variable in (2).3 In showing that,
1 The criterion for occupational classification was the level of vocational skills of various kinds likely to
be involved in ajob. Classificationwas done by the researcherson the basis ofjob-description questionnaires
completed during interview.
2 Their introduction for Tanzania has negligible effects on the explanatory power of equation (2) and
on the coefficientsof the other variables, and yields the coefficients + o-o36P and + o-002P *H (their respective
t values being O I58 and 0-03 I). When interaction terms are added for all the independent variables (P-R.
P-S, P-H and P-L), the coefficient on P-H remains insignificant at +o-oo6 (0-528).
3 H is generated using (i) plus the other exogenous variables in the system.

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 i987] EDUCATION AND PRODUCTIVITY 207

for both countries, the coefficient is not significantly different from zero, we
cannot reject the assumption that our equation system is recursive.1
III. EDUCATIONAL POLICY AND DIFFERENCES IN COGNITIVE
ACHIEVEMENT
The average level of reasoning ability is much the same in the two countries:
Rk = 27-8 and Rt = 26-4. Levels of cognitive skill are, by contrast, significantly

higher in Kenya than in Tanzania. Kenya's mean scores are 23 % higher on

the literacy test and 44 % higher on the numeracy test. With Hk = 40o? and
Ht = 30-3, the absolute difference in mean cognitive skill scores is 9.7. The
regression results from the pooled sample in Table I indicate that, even after
standardising for differences in characteristics, the mean cognitive skill score
of Kenyans exceeds that of Tanzanians by 7-7. However, a Chow test rejected
the null hypothesis that the educational production functions of the two
countries are the same. This is therefore not the best estimate of the part of the
difference in cognitive skill due to differences in educational production
functions. We measure this difference by means of decomposition analysis.
Given that the mean cognitive skill of Kenyans is determined by the linear
educational production function Hk =fk(xk) - where ik are the mean values
of the set of independent variables - the mean value of cognitive skill that
Tanzanians would achieve if the Kenya production function were to apply
would be fk(xt). The gross difference between the two countries is then
decomposed as follows:

Hk Ht =fk (xk jt) + [fk (Xt) -ft (Xt) ] (3)

or
Hk-Ht = ft(-k 6t) + fkk) -ft(jk)] (3')

The former term shows the component explained by differences in the

proportion of workers with secondary education and in the mean values of the
other explanatory variables. The latter term - the residual - can be interpreted
as a measure of the difference in the 'quality' of education, in the sense that
output per unit of inputs is higher in one country than in the other.
As expected, inter-country differences in the explanatory variables other
than educational attainment contribute little to the explanation. According to
whether the Kenya or Tanzania educational production function is used,
differences in the quantity of secondary education account for I5 or I400 of
the gross difference respectively. This reflects the fact that the proportion of
secondary-completers in the full sample total of primary- and secondary-
completers is greater in Kenya (Sk = o0532) than in Tanzania (St = 0.4I4).
However, the residual accounts for no less than 75 or 78%. For given mean
values of the explanatory variables, the predicted cognitive skill score using the
Kenya educational production function greatly exceeds that using the Tanzania
function as predictor.
This result suggests that country differences in the quality of education are

1 The coefficients on H are -O-OI2 and +O-OI2, and their t statistics o-86i and 0o970, in Kenya and
Tanzania respectively.

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208 THE ECONOMIC JOURNAL [MARCH

an important determinant of cognitive achievement. We equate the residual

with differences in quality, although we recognise that differences in the
incentive systems in the two countries could produce different drive and family
support, and that these might contribute to the residual. The lower quality
of education in Tanzania could stem from divergences in educational policy.
For example, although expenditures per pupil are roughly the same in the
two countries, greater stress has been placed on curriculum diversification
in Tanzania, perhaps at the cost of time spent on general academic skills, and
on Kiswahili at primary school, perhaps at the cost of efficient learning in
English at secondary school (Cooksey and Ishumi, I986).

IV. THE SIMULATION METHODOLOGY

The two functions can be used together for simulation purposes to answer the
following counterfactual questions. First, what is the effect on the average
cognitive skill of the Tanzania labour force of increasing the quantity of
education to the Kenya level? Secondly, what is the effect on the average
cognitive skill of the Tanzania labour force of increasing the quality of education
to the Kenya level?
To answer the first question, we substitute the Kenya for the Tanzania (full
sample) mean value of the secondary school dummy variable, and predict the
cognitive skill score using the Tanzania educational production function:
Ht = aOt+altRt+a2tsk+a4tBt+a5tGt (4)
To answer the second question, we substitute the Kenya for the Tanzania
educational production function and predict the cognitive skill score using the
Tanzania mean values of the independent variables:
Ht = aOk+alk Rt +a2kSt + a4k t+a5kG. (5)

Further counterfactual questions can then be posed: what is the effect on

average earnings in Tanzania if, in turn, the quantity, the quality, and the
quantity and quality of education in Tanzania are increased to the Kenya level?
The answer requires that the mean cognitive skill score resulting from each of
these counterfactual changes in educational policy be substituted for actual
cognitive skill in the Tanzania earnings function to predict the consequent
change in mean earnings:
ln Wt = bot+bltSt,k+b2tRt+b3tHt+b4tLt, (6)
with the subscript to S being either k or t, as will be explained below.
The assumptions implicit in these exercises should be recognised explicitly.
The simulations assume that the policy changes do not affect the coefficients
of the functions nor the mean values of the other independent variables. It is
also assumed that, reflecting the rationing of secondary places in Tanzania,
there would be an effective demand for the simulated increases in the supply
of secondary places.

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 I987] EDUCATION AND PRODUCTIVITY 209

V. CROSS-COUNTRY POLICY SIMULATIONS

Our results suggest that more literate and numerate workers are more
productive. Tanzania may thus have paid a price in output foregone by
restraining the growth of secondary education and reducing the quality of
education for the sake of other goals. Our next exercise is to quantify this price
by simulating the effect on wages, and thus on productivity, of differences
between the two countries in the quantity and quality of education.
The results of our simulation exercises are presented in Table 3. The base
runs use the actual values of both variables and coefficients; the predicted and
actual mean levels of cognitive skill and of earnings are therefore the same.
Simulation I shows the effect of the difference in quantity, simulation 2 the
effect of the difference in quality, and simulation 3 the effect of simultaneous
changes in quantity and quality. The Tanzania simulations introduce par-
ameters from Kenya, and the Kenya simulations parameters from Tanzania.
An increase in the quantity of secondary education in Tanzania to the Kenya
level would, on the basis of equations (I) and (2), increase the mean cognitive
skill of the wage-labour force by 4 % and mean earnings by 3 % (simulation
I). An increase in the quality of education would increase cognitive skill by
24 % and earnings by I0 % (simulation 2). And a simultaneous increase in
quantity and quality would increase cognitive skill by 29 % and earnings by
I 3 % (simulation 3).
Do these increases in predicted earnings also measure the increase in the
productivity of employees? They are thAeresult of assuming increases in the
predicted mean value of cognitive skill (H) and in the proportion of secondary-
completers (8). The effect on earnings of the rise in H can only be interpreted
as representing a productivity relationship. Although the coefficients on S could
reflect unmeasured human capital acquired in secondary school, it might
instead reflect credentialism, screening for ability, or pre-school human capital.
If so, the rise in S would make no contribution to productivity. Simulations I a
and 3 a differ from simulations I and 3 only in that the value of S in the other
country is not substituted in the earnings function. They therefore show the
lower-bound estimate of the effect on productivity of expanding secondary
education in Tanzania to the Kenya level, assuming that the coefficient on S
contains no productivity element. The quantity effect on productivity falls by
less than half (compare simulations I and I a) and the combined quantity and
quality effect falls by I-5 percentage points to I2 % (3 and 3a). The
interpretation of the coefficient on secondary education in the earnings function
has little influence on the predicted change in productivity which results from
introducing Kenya educational policy in Tanzania.
These simulations suggest that the opportunity costs to Tanzania of con-
straining the quantity and quality of education are substantial. The mean wage
of the Kenya subsample was 4I % higher than that of Tanzania, when
converted at the official exchange rate; it would be higher if calculated on the
basis of purchasing power parity. In I97I, before the effects of the divergent
educational policies were manifested in the labour market, the mean urban

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 THE ECONOMIC JOURNAL [MARCH
2IO

G B R S G B R S
H L R S H L R S Mean
Mean
Constant
Predicted ChangePredicted
Coefficients Constant
Urban Coefficients
Urban values
Mean(W) in Mean(H)
values Percentage
Percentage
Cognitive
Changeinmean Reasoning Cognitive
Secondary Reasoning
Secondary
birth
Secondary
Secondary Reasoning
Reasoning Kenya
Employment Employment birth
Government Government
skill mean cognitive
earningst
skill
changeA
ability ability
change
skill schoolability ability and
in (AW) in
(AH) school schooling
schooling schooling schooling

mean experience experience mean

A (AH)A
(AW)
t * Tanzani
I
IOI4 39 I5
Since - - - runBase The
Figure 39-562
9-026 0-532
27-8i6 562 490 3-366-3567
0-570I754 O0532
0-7000-IIO27-8i6
0-0448
O-OI97
5-4757 o-oo58
O-I924
theas
for - Effect
-48 966 * * 38- * * * * * I
* * * * I
base -4-8
38-I75
-3'5
I'39
75 0-44
of
dependent 0-4I4

run. *

variable
-2-7
27 987
* * * * * *
-3-5
38-
I * * * * *
Ia Varying
in 38-175
-I-39
75 0-44
the *
the
Kenya
-138876 * * * * * * * * * 2
-13-6 -I8-8
earnings 32-II -7'45
32-III -2-65I
0487IO-938
I 12-340
O0995
Simulation Quantity
*

function
Educational Policy
is -I79 835 * * * * * * * 3
and
-17-6
* Earnings
-22-I
-8-74
30-820 0-44 30-820 52-340 -2-65I
O0995 0487IO0939 Tab
*
production
3
function Quality
-2
logarithmic,-i6o854
-I5-8
* * * * * -22-I
* * * *-4I4 3a Simulation
of
-8-74 65I 0o487IO-938
30-820 32-820 12-340
O0995 044 function

'predicted
7I7 I2 -2
- - runBase
mean
- -

7-I6326434
29-964 *04I4 29-964 65I 0487IO0939
340 O0995 07300-I9026-434
04I4
Educatio
5-726I 00550o-ooo8
OOI29 0II25
on
2I 738 4 * I
earnings' 29 * * * * * * *
3
* * * * *

is 3I-255 o532
I-29
3I5255 0-532
a
Cognitiv
II 728 * * * * * * *
* * * * * ia
4-3
geometrici-6 I-29
3I-255 3I5255 0o532

mean.
Tanzania
70 787
* * * * *
I
* * * 2
Achieve
97 24-2
7-24
37-202 37-202 -3567
3366
15'490 0570I*754
Simulation and
on
I
95 8i2 O
* * * * * * * * 3
13-2 28-8
*0532 8-63
38-589 38-589 15'490 -3567
3366 0570I-754 532

I Earning
84 8oi * * * * * * *
*
28-8 3a
II-7 8-63
38-589 0-4I4 38-259 I5-4903.366-3567
0570I-754 0-532

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 I987] EDUCATION AND PRODUCTIVITY 2II
wage in Kenya was only some IO % higher. A third of the current difference
in predicted mean wages converted at the official exchange rate (95 in relation
to 297 shillings) can be explained by the lower mean cognitive skill of Tanzania
employees.
It is reassuring that similar results are obtained when the simulations are
conducted on the Kenya subsample (Table 3). The quantity effect on
productivity is 500, the quality effect I40%, and the combined effect I80%.
Reinterpretation of the coefficient on secondary education in the Kenya
earnings function reduces the change in productivity by less that 2 percentage
points. The main contrast is that an even higher proportion of the difference
in predicted mean wages (60o0) can be explained by the higher mean cognitive
skill of the Kenya workers. Even if the use of a purchasing-power-parity
conversion factor were to reduce these percentages, the difference in cognitive
skills would remain important.
As a guide to the potential gains from improving the quantity and quality
of education in Tanzania, these estimates are liable to be biased in various
respects. First, they take no account of diminishing returns to large increases
in the supply of cognitive skills relative to other inputs. We have used the Kenya
and Tanzania surveys to estimate the elasticity of relative earnings with respect
to relative educational expansion, the inverse of the elasticity of substitution
between educational levels (Knight and Sabot, 1984). Our estimate is that an
increase in the Tanzania ratio of secondary- to primary-school leavers in the
wage-labour force to the Kenya level reduces the ratio of their earnings by some
io%: the predicted gain in labour productivity would be little affected by
diminishing returns. This result squares with our finding that the returns to
cognitive achievement are not significantly lower in the manual occupations,
which would absorb much of the additional supply of high cognitive achievers,
than in the white-collar occupations, where they are now concentrated in
Tanzania (Boissiere et al. I985). Secondly, the fact that access to secondary
schooling is fairly meritocratic implies that the expansion of secondary enrol-
ment in Tanzania would reduce the qualifications of entrants to the secondary
system. It also implies that our simulations overestimate the increase in
productivity from educational expansion.
Thirdly, any upward bias in the estimate resulting from the above con-
siderations may be offset by the downward bias that would result if our
specifications had failed to capture the depressing effect of pay policy on the
return to cognitive skill in Tanzania. Although the relative supply of cognitive
skills is greater in Kenya, the return to them is higher. As a consequence, when
the Kenya earnings function instead of the Tanzania one is used to measure
the effect of changing the quantity and quality of education, it produces a
change in earnings which is over 4 % greater (Table 3). A further reason for
expecting downward bias in the estimate of productivity increase stems from
the way of selecting the subsample. Those who acquired most cognitive skill in
secondary school were most likely to have continued their education beyond
form IV - and would therefore be excluded from the tested subsample.
Finally, although it is very plausible that higher cognitive skill commands

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2I2 THE ECONOMIC JOURNAL [MARCH

higher earnings because it raises the productivity of labour, only under the
rigorous assumptions required for marginal product to equal wage will the
increase in productivity equal the increase in earnings. However, there may be
a direct proportional relationship. For instance, monopoly in the product
market may depress the wage below marginal product, or marginal product
may fall short of the wage if public sector employment exceeds the most
profitable level. We cannot therefore claim that the predicted absolute increase
in average earnings in Tanzania precisely measures the absolute increase in
average labour productivity, but the percentage increases are likely to be
similar.

VI. CONCLUSIONS
The project design has been comparative - first, to establish what relationships
are robust, secondly, to explain such differences in relationships as are to be
found between the two countries, and thirdly, to illuminate an issue on which
policies in otherwise similar countries have differed greatly. Two findings,
significant not only because they pass the usual statistical tests but also because
they hold in both countries, are the positive effect of secondary education on
cognitive skills and the positive effect of cognitive skills on earnings. They
support the interpretation of the relation between secondary education and
earnings as showing the effect of human capital acquisition in school on pro-
ductivity at work. The observed differences in relationships and in parameters
also assist the analysis. The difference in educational production functions
permits identification of the effects of educational quality; the difference in
mean secondary school attendance, the effects of educational quantity. The
recursive model, estimated in the same way in the two countries, makes possible
cross-country productivity-accounting analysis of the effects of education.
Kenya and Tanzania differ considerably in the quality of (secondary and
pre-secondary) education and the quantity of secondary education. The
cognitive skill of urban wage-employees with the same ability and school
attendance is substantially higher in Kenya. Secondary enrolment rates and
the level of education of the urban wage-labour force are also higher in Kenya.
Consequently, the mean level of cognitive skill per urban wage-employee - and
therefore mean earnings and productivity - is far higher in Kenya. Our
simulations suggest that if the quantity and quality of education in Tanzania
were raised to that of Kenya, the mean earnings of Tanzania urban wage-
employees would be I 3 % higher. Since their productivity is likely to rise by
a similar percentage, the economic benefits to Tanzania from pursuing such
a policy would be substantial. The differences between the two countries in
educational policy regimes appear to have been an important factor in their
diverging mean wage and productivity of urban labour.
The difference in labour productivity attributable to the difference in policies
for secondary education is likely to grow over time. The educational composi-
tion of the urban wage-labour force in I 980 did not fully reflect the divergence
in policies which emerged in the I970s. The proportion that secondary-

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 I987] EDUCATION AND PRODUCTIVITY 213

completersconstitutedof the combined group of primary-and secondary-

completersforthe sampleas a wholewasstillonly moderatelyhigherin Kenya
(where it was 0.53) than in Tanzania (0.41). For this reason the effect of
simulatinga rise in the quantityof secondaryeducationin Tanzania to the
Kenya level was modest,raisinglabourproductivityin the urbanwage sector
by 3 %. However,the differencein the proportion(o027) for the cohortwhich
had enteredthe marketwithin the previoussix yearswas more marked(the
proportionbeingo-65 in Kenya and o038in Tanzania).If the presentpolicies
continue,the ensuingchangein the educationalcompositionof urbanwage-
employmentwill increase the differencein the proportionof secondary-
completersin the relevantlabourforceand so increasethe differencein labour
productivityattributableto secondaryeducation.
There are limits to the policy implicationsof resultsobtained for urban
wage-employeesin countrieswith predominantlyruraleconomies.Neverthe-
less, since additionalsecondaryschool graduateswould almost certainlybe
employedin the urbanwagesector,it wouldseemthat Tanzaniacouldbenefit
substantiallyfroman improvementin the qualityof its educationand quantity
of its secondaryeducationtowardsthe Kenyalevel. Thereare reasonswhy the
estimatesmade in the simulationanalysismay be biasedand why our results
mustthereforebe regardedas suggestiveratherthan conclusive.Nevertheless,
they have beenobtainedwhilstavoidingsomeof the drawbacksthat normally
underlieoutputaccountingor growthaccountinganalysesof the contribution
of education.The greatersimilarityof the two urbanwage economiesand the
greatercomparabilityof our data have permittedsomewhatmore realistic
simulationexercisesthan are normallyfeasiblein cross-countryoutput ac-
countingstudies.And throughthe introductionand measurementof cognitive
skillsas a link betweeneducationand earnings,it has been possibleto answer
questionsof causalitythat othershave simplyhad to beg.
of Economics
Institute andStatistics,OxfordUniversity
WilliamsCollege,
andDevelopment
Research TheWorldBank
Department,
Date of receiptoffinal typescript:AugustI986

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