Human Resource Development and
Economic Growth in Developing Countries:
A Simultaneous Model
SWP407
World Bank Staff Working Paper No. 407
July 1980
Prepared by: David Wheeler, Consultant
Development Policy Staff
sht (c) 1980                                     | 
orld Bank
, Street, N.W.
igton, D.C. 20433, U.S.A.
.ws and interpretations in this document are those of the autr
ana snould not be attributed to the World Bank, to its affiliated
organizations, or to any individual acting in their behalf.






The views and interpretations in this document are those of the author and
should not be attributed to the World Bank, to its affiliated organizations,
or to any individual acting on their behalf.
SusAt i '0 .L
WORLD BANK                         4 Joi  t I  i
iVrNreoni, D C  21Z f
Staff Working Paper No. 407
July 1980                    '-      -
HUMAN RESOURCE DEVELOPMENT AND ECONOMIC GROWTH
cl
IN DEVELOPING COUNTRIES: A SIMULTANEOUS MODEL
A Background Study for World Development Report, 1980
This paper is a cross-country statistical analysis
of the relationships among economic growth, human resource
development (improvements in education, health and nutrition),
and population growth in developing countries. It applies
simultaneous equation techniques to a large set of data
recently assembled by the World Bank in ways that reduce some
of the difficulties and-ambiguities that beset earlier work in
this field.
As well as confirming that economic growth promotes
human resource development, the analysis indicates that human
resource development contributes substantially to growth --
by increasing labor productivity and physical investment, and
by reducing fertility. Education appears to be particularly
important. Family planning programs are also shown to have an
independent effect on fertility, although their strength is
affected by other social and economic variables.
The estimated model is used to simulate the effects
of alternative policies over long periods of time. This permits,
among other things, an examination of the tradeoffs between
increased physical investment and increased spending on human
resource development.
Prepared by: David Wheeler
Consultant,
Development Policy Staff
Copyright Q 1980
The World Bank
1818 H Street, N.W.
Washington, D.C. 20433
U.S.A.






FOREWORD
"'his report has been subdivided in a minaer which may seem peculiar
at first glance. Chapters I, II, and III devote most of their attention
to a general discussion of research hypotheses and the results of the
study. Technical detail has been relegated to the numerous appendices
wherever possible. Readers who are accustomed to having their methodology
served up as the first course in a research presentation may find this
approach quite troublesome. I sincerely hope that they are not
inconvenienced.
-his rather broad-ranging study may be read by people who have
general or highly specialized interests in several development-related
fields. The mode of organization whizh I have chosen represents my own
attempt to strike a balance among these rather diverse interests.
Hopefully, non-specialists can absorb the maLn themes of the study by
reading only the first three chapters. At the same time, I have provided
signposts throughout which direct specialists to the relevant technical
appendices.






TABLE OF CONTENTS
Page
I.   INTRODUCTION AND SUMMARY OF RESULTS ................   .. 1
II.   MODELING OUTPUT GROWTH ................................ 12
An Open Economy Variant              ...... 29
The Investment Rate ................................... 34
III.   MODELING POPULATION GROWTH              .     ... 40
Fertility Change ...................................... 41
Changes in the Death Rate               ..               50
IV.   STIMULATING SOCIO-ECONOMIC DEVELOPMENT ................ 52
The Model ............................................. 56
APPENDIX A (Output Equations) ......................... 74
APPENDIX B (Output Equations) .......................... 83
APPENDIX C (Demographic Equations) .................... 87
APPENDIX D (Demographic Equations) .................... 96
APPENDIX E (Simulation Model) ......................... 101
APPENDIX F (Simulation Model) ......................... 109
APPENDIX G (Unsuccessful Experiments) ................. 116
APPENDIX H (Sample Countries) ......................... 124
BIBLIOGRAPHY .......................................... 130



4



page 1
I. INTRODUCTION AND SUMMARY OF RESULTS
During the past two decades, many poor countries have, exper-
ienced improvements in per capita income and human resource
variables such as education, health, and nutrition. Empirical
analyses of the development process have generally assigned a purely
causal role to income expansion, although a few have identified the
human resource variables as possible "sources of growth." This
study attempts to incorporate both views by examining the growth
process as a set of dynamic relations linking output, population,
and human resources. Extensive use has therefore been made of
insights provided by both economists and demographers. Prior work
by economists has been helpful in the definition of an output growth
model which is explicitly simultaneous in output and human resource
changes. The associated model of population growth owes much to
prior work by demographers.
The full dynamic model developed in this report contains both
recursive and simultaneous elements. Within growth periods, income,
population, and human resource variables change in response to pre-
vailing rates of birth, death, capital accumulation, and labor force
growth. These rates are i.n turn influenced by the full set of induced
changes. Because the four crucial stock-adjustment rates are re-
garded as fixed in the short run, it is convenient to refer to them
collectively as "accumulation parameters." By the same logic, the,
human resource measures will join income and population as "response
variables" when a composite reference is required.
In the determination of output growth, the role of human resource
variables has been considered in the context of both accumulation and
response. In the direct determination of output, the argument that human
resource variables have an important role is so plausible as to be beyond



page 2
argument, at least in a general sense.    The Western empiri-al literature
on growth has discerned an important role for education in the growth
process, whether its contribution is taken to be labor-augmenting,
capital-augmenting, or factor-neutral (1). Few would doubt that the
process of education can have a positive impact on workers' earnings,
although there is disagreement about the degree to which the pure role of
"learning" can be divorced from the behavioral effects of "szhooling" and
the impact of credentialism (2).
-he case could also be made that health and nutrition are
potentially-important contributors to productivity in LD_'s. Both of these
(1) Fconometric work on factor-augmentation in industrial societies has
generally used time series to measure the contribution of education (see
Intriligator (1965), Denison (1967), and Barger (19691). Econometric work
on the sources of growth in I.DC's has tended t3 compensate for data
scarcity by adopting a cross-sectional approach (Robinson (1971)). Fallon
and rayard (1975) have estimated the degree of complementarity between
skills and physical capital in productivity letermination across
countries. Other recent papers (Correa (197)), Hicks (1979), Wheeler
(1980)) have attempted to extend the study of sources of growth in LDC's
to include health and nutrition, as well as education.
(2) "he debate concerning social returns to education has been long and
heated. Fields (1980) notes that most work suffers from a failure to take
simultaneity into account in analyzing the intertemporal association
between change in income and change in education. Among those who have
done empirical work on the relationship between educatioa and productivity
change, conclusions are very mixed.  A study of agricultaral productivity
by Hayami and Puttan (1970) suggests an important role for technical and
general education in explaining the differential between rich and poor
countries. rhis conclusion is supported by the extensive comparative work
of Psacharopoulos (1973), who has calculated a substantial average social
rate of return across countries. Among the skeptics, contrary evidence is
cited by Nadiri (1972), who concludes from a survey of the literature that
eduation has generally been unimportant as a determinant of differentials
across countries, although within-country contributions often appear
significant. Blaug (1973,1978) and others have explainel this seeming
paradox with a "credentialist" interpretation of within--ountry
differentials.
Micro-level studies seem to have been no more successful in
resolving this controversy than their macro-level counterparts. In an
excellent study of labor absorption in the Japanese zotton-spinning
industry, Saxonhouse (1977) finds very strong evidence to support the
hypothesis of complementarity between capital and educated labor. On the
other hand, some direct studies of the relationship between education and
the industrial performance of workers have failed to discern any such
association (see, for example, Fuller (1975)).



page 3
factDrs are undoubtedly characterized by thresholds beyoad which their
effects on output are negligible. In countries whose populations must
endure widespread epidemic illness and nutritional deficiency, however, it
is plausible to suppose that productivity is below its potential level
with existing stocks of capital and effective labor. The evidence,
although relatively scanty, certainly does not suggest a rejection of the
hypothesis that these factors can make a difference (3).
If it is possible to entertain the hypothesis that education,
health, and nutrition have an impact on productivity in poor countries, it
is of course certain that the opposite is true. Wealthier societies enjoy
substantially higher levels of all three variables. In part, this is
because higher levels of public investment in health and education are
possible in societies which can mobilize more revenue. In addition,
increased disposable income allows families to purchase more
welfare-enhancing goods and services.
Obviously, it is impossible to evaluate hypotheses concerning the
impact of human resource improvements on growth without taking
simultaneity explicitly into account. We can therefore characterize a
plausible model of the "response" system as a multi-equation model in
which levels of output, education, nutrition, and health are
simultaneously determined. In such a system of equations, the stocks of
capital and labor would be joined by existing institutional capacity for
education and health promotion and other policy variables as exogenous
elements in any particular (short) growth period.
While a "response" role for human resource variables may be
important, they may also have a significant effect on investment behavior.
(3) A few micro-level studies of the relationship between nutrition and
productivity have been attempted. See Basta and Churchill (1974).



page 4
Tn this study, both literacy and life expectancy have been hypothesized to
join per capita income as determinants of the investment rate. The role
of life expectancy was taken to be potentially significant because of
life-cycle effects on consumption and savings behavior. In the case of
literacy, a potentially important role can be traced to studies which
attribute significant shifts in econamic behavior to the effect of
education on attitude formation and economic calculation (4). For LDC's,
it also seems plausible to expect a positive relationship between per
capita income and the rate of capital formation, ceteris paribus. This
hypothesized relationship would follow from the observable decline in
marginal propensity to consume as societies shift away from the
subsistence margin toward a condition in which some discretionary income
is available.
Tn the preceding brief discussion, attention has been focused on
hypothesized relations which tie human resource variables to the process
of accumulation and response in output determination. Another plausible
set of hypotheses links these variables to demographic changes. The death
rate in any society is linked to the existing institutional and technical
capacity for preventive and curative medicine, as well as the prevailing
levels of education and income. Several persuasive arguments also tie
human resource variables to the birth rate, although an appropriate model
of causation is somewhat more complex than in the case of death rate
determination. ¶he birth rate itself is determined by the population
proportion of childbearing women and their total fertility. Since the
number of women is exogenous during any growth period, it is really
differences in total fertility rates which must be explained.
(4) Support for this hypothesis has been found by Koh (1977) in the case
of entrepreneurial behavior in Japan.



page 5
Fithin the relevant age cohort, the fertility rate can plausibly be
related to a set of human resource and other variables. The perceived
opportunity cost of children seems to rise with income, so that
fertile-age women bear fewer children, ceteris paribus. At the same time,
the relationship between child-bearing and marriage would seem to dictate
some relationship between age at marriage and total fertility. It is
plausible to suppose that age at marriage is, in turn, a function of
education, income, and life expectancy. In addition, appropriate education
should have an effect on fertility once women accept the notion that fewer
children are desirable, as would the cost anl availability of
contraceptives (5). Finally, since it is arguably the expected number of
surviving children which should be the ultimate object of fertility
decisions, the infant mortality rate should have some effect.
Certainly, the arguments which have been posed in the preceding
paragraphs would be acceptable to many students of partisular aspects of
the development process. As previously mentioned, micro-level studies
have examined at least some of them in considerable detail. Until fairly
recently, however, the data available for cross-country 2xamination of the
major hypotheses have simply been insufficient for econometric work. An
additional problem has been posed by the degree to which macro-level
cross-section results are believable. Cross-country comparisons of
value-based data such as GDP statistics are suspect in many ways, and
problems of data scarcity have prevented the application of some
compensatory techniques in the past. In cross-section work, there is also
the problem of masked correlations, so that even results which seem to
(5) Fxisting cross-sectional evidence concerning the relationship between
education and fertility has been summarized in Cochrane (1979). Dyson, et.
al. (1978) have recently published work on the long-run dynamic links
joining fertility, mortality, and income.



page 6
corroborate maintained hypotheses about causal relations can frequently be-
explained with reference to other, unobserved variables. Finally, the
evident presence of simultaneity in the determination of socio-economic
outcomes has always presented a major stumbling block to the pursuit of
consistent and believable research efforts in this domain.
In the project whose results are being reported in this paper, all
of these problems were evident from the beginning. A major part of the
research effort has therefore been devoted ta overcoming them, insofar as
this has been perceived to be possible. In all cases, an attempt has been
made to move toward believability in results by estimating regression
equations with cross-country changes rather than levels. This use of
change relations has yielded one additional advantage: Among plausible
models of output determination, several have an intertemporal
specification in percent change form. In a cross-section of time series,
the calculation of percent changes within countries avoids the index
number problems which plague many cross-country studies.
Even when a cross section of time series is employed, of course, it
is not possible to give an unambiguous interpretation to econometric
results in most cases.   Masked correlations may still be present, and it
would be rare to find a case in which at least one alternative explanation
for observed results could not be imagined. In addition, the use of
relatively scanty data and the necessity for some experimentation in the
evaluation of alternative functional forms and the testing of variables
which seem plausible a priori increase the risk that any single set of
regression results is simply a sampling accident.
For this reason, considerable time and effort have been expended in/
the attempt to cross-check the data in a variety of ways. Identical
models of behavior for the 1960's and the 1970's have been estimated
separately for the output response eguations, since this part of the model



page 7
is most subject to the difficulties associated with the simultaneity
problem and the possible effect of intervening variables. This same set of
equations has been re-estimated with whole world regions excluded, to test
for the possibility that apparently "general" phenomena are in fact
traceable to the characteristics of a particular region. Finally, a
substantial set of plausible intervening variable effects has been
hypothesized, and the fundamental equations have been re-run to see
whether the originally specified relations seemed to remain once other
factors were accounted for.
Pith all this as prelude, it is undoubtedly fitting to conclude the
introduction with a summary of the principal findings of the research
project. In the response component of the output equations, simultaneous
equation estimating techniques have been employed throughout. The results
have suggested the confirmation of some prior hypotheses and the rejection
of others. As anticipated, changes in per capita income across countries
seem to have a significant, positive impact on changes in literacy and
life expectancy. In addition, a positive impact is suggested for calorie
consumption, which can be interpreted as the best single available measure
of general nutritional status. None of the direct links from per capita
income to social indicator variables is particularly surprising, although
the results have the advantage of being based on changes rather than
levels.
Of more potential interest in the simultaneous estimates is the
evaluation of hypotheses concerning the impact of the so=ial indicator
variables on output growth. In each case, as previously mentioned, there
is a plausible argument for some contribution to productivity.
After an exhaustive series of tests over different time periods,
with various regional exclusions, and with the use of many plausible
intervening variables to test for continued significance, a relatively



page 8
clear set of conclusions has emerged. The impact of literacy change on
output change is apparent in all the tests which have been run. When life
expectancy change is used as a proxy for health improvement, however, no
consistent results are obtained. In simultaneous estimates for the 1960's,
changes in life expectancy appear to contribute significantly to changes
in output. In the 1970's, however, the effect is reversel: This variable
loses significance and in fact exhibits a negative relationship with
output change in the simultaneous estimates. It seems appropriate to con-
clude that the results for the 1960's may have been a sampling accident,
and that life expectancy as a proxy for health cannot be identified as a
significant contributor to productivity growth (6).
Although education and health are really at the fo_us of attention
here, it is certainly of interest to examine the hypothesized impact of
nutrition on productivity. The results of all the econometric exercises
certainly lend support to this hypothesis, if the available index of
nutrition is acceptable as a proxy. After simultaneity has been
explicitly accounted for, changes in calorie consumption appear to have a
significant impact on output changes across countries. It must be noted,
however, that the calorie variable may be serving as a proxy for relative
changes in agricultural productivity. Some development economists have
maintained that agricultural growth has a differential impact on output
growth, and the observed result may be in part an indire-t confirmation of
this hypothesis. At the present time, there does not seem to be any good
way of separating the two effects.
As previously noted, plausible hypotheses link human resource
(6). "his is not to say, of course, that health has no effect on
productivity in poor countries. The results simply suggest that the
available measure is not very helpful in gauging the marginal effect of
health improvements at the macro level.



page 9
variables with accumulation parameters as well as response variables in
the growth system. in the case of output growth, an association can be
hypothesized between levels of education and life expectancy and the
investment rate in LDC's. Such a link, if established, would suggest an
indirect role for the available health measure in the generation of
productivity change, as well as an additional role for education.
Again, econometric work on the relationship between the investment
rate and various causal variables has yielded mixed conclusions. Time
series work in this particular context has not been plentiful in the past,
and in this project it was hypothesized that the effects which were being
tested might show up over relatively long periods if at all, given the
substantial measurement problems which exist. In the case of the
investment rate, regression equations were fitted to data on changes in
the investment rate across LDC's during the period 1960-1977. The results
suggest relatively strong roles for per capita income and literacy in the
determination of this rate. The result for life expectanzy is extremely
weak when it is used along with literacy in the investment rate equation,
although the coefficient of the life expectancy term satisfies the usual
statistical criteria when literacy is excluded. At best, any hypothesized
role for life expectancy in the determination of relative investment rates
is certainly cast into doubt by thesa results.
In the demographic component of the modeling exercise, the results
are similarly mixed. As previously mentioned, part of the variation in
birth rates across countries can be attributed to differing proportions of
young women in their populations. There is obviously a component of the
death rate which is sensitive to age structure differentials as well. Once
this deterministic component is accounted for, both rates can plausibly be
related to several human resource and policy variables. rechnical and
institutional capacity should have an effect on the death rate, as should



page 10
changes in the level of health-promoting consumption at higher income        /
levels. Other variables such as nutrition and education might be supposed;
to have some effect, as well. In the case of fertility rates, income,
infant mortality rates, and appropriate family planning efforts could
certainly be suggested as causal variables. A potential _omplication is
raised by the possibility that family planning activity will occur
differentially in countries which have alreaay exhibited some decline in
fertility rates, because of encouragement effects.
Tn econometric work on birth and death rate determination,
regression equations were fitted to seventeen-year changes to allow for
periods of time sufficient to overcome the effects of measurement error.
In both cases, the data allowed for explicit testing of the hypothesis
that the causal variables had differential effects in different age
cohorts. In the case of fertility rates, estimation was further
complicated by the necessity of allowing for explicitly simultaneous
determination of fertility rates and family planning activity, as well.
Among the variables which might plausibly have been related to
changes in death and fertility rates, those mentioned above all appear to
play a significant role. In the case of death rate changes, only the
availability of medical personnel as indexed by doctors per capita appear
to account for effects beyond those attributable to changes in per capita
income and a strong autonomous technical change component.
In the simultaneous equation estimates, an important role in
fertility rate determination is suggested for per capita income, the death
rate (which is a proxy for unavailable infant mortality rate data), the
literacy rate of the population, and the level of family planning
activity. '"he latter, in turn, seems well explained by contemporaneous
declines in the fertility rate and the institutional capacity of the
society in question (as proxied by the secondary school enrollment ratio).



page 11
the results certainly do not refute the hypothesis that fertility decline
contributes significantly to the initiation 3f family planning activity
across countries, for whatever reason. In addition, the fertility results
suggest that the marginal effects of causal variables across age cohorts
cannot be differentiated from one another at a high level of statistical
confidence, although cohort-specific constant terms appear to differ
significantly.
Although the impact of singulate age at marriage on fertility rates
coulA not be measured in the time-change equation because data were
insufficient, this variable was tested in a set of separate equations
fitted to the combined pool of data for the years 1960 and 1977 in order
to maximize degrees of freedom. These results suggest that age at marriage
is well accounted for by literacy and life expectancy. Rhen all three
variables are included in a cross-section regression, the residual
component of age at marriage seems to account for no additional variance
in the fertility rate.
In the aftermath of a relatively complex set of econometric
estimation exercises, it is always of interest to examine the dynamic
behavior implied by the full set of equations. As previously mentioned,
the equation system whose parameters have been estimated is too complex
for the calculation of fixed multipliers. Simulation is thus the relevant
tool for analysis and prediction. In a later section of this report, the
econometric results are translated into a simulation model which is used
to examine growth dynamics under alternative policy assumptions for a set
of "representative" LDC's. Full hypothetical data sets to be used as
initial conditions for these simulations have been assembled for
Sub-Saharan Africa, South Asia, and South America. In addition, data for
the full set of LDC's has been employed in constructing a "representative"
LDC case.



page 12
II. MODELING OUTPUT GROWTH
In this chapter, particular attention will be paid to the portion of
the modeling exercise which links human resource development to output
growth. The first section will be devoted to a discussion of results for a
basic growth model which treats the national economy as if it were closed.
In the second part, an open-economy model will be used to test the first
results for the effects of certain important intervening variables.
Briefly, the model of responses which is the basis for the
econometric exercise in this section is designed to overcome several
serious methodological problems. First, it is explicitly simultaneous in
the relevant variables. Improved nutrition, health, and education can make
a contribution to productivity in poor countries, but it is also evident
that growth in national income can produce positive increments in these
same variables. The structural equations used for the growth model contain
sufficient numbers of exogenous variables to allow the disentangling of
joint causal effects (that is, they are just- or over-identified in the
parlance of econometrics).
In the specification of the growth response equations, it has been
necessary to address another problem which is complementary with the
first. nluch of the criticism of cross-section work in the past has
centered on the use of relative variable levels across-countries. M¶any
socio-economic variables are highly correlated with one another, and in
running cross-section regressions the researcher always faces the
intervening variable problem in interpreting results. It would be better
to incorporate time series on individual national experiences into such
work if possible, and fortunately the available data are now sufficient to
allow for this. rThus, all of the econometric work reported here has been
done on cross-sections of changes rather than levels across countries.



page 13
This creates a much more stringent test of hypotheses concerning the
behavior of individual variables than would otherwise be possible.
Combined vith the need for explicit simultaneity and the
desirability of time changes in this sort of madel, there is an additional
requirement of theoretical credibility. In econometric work, any
specification of relationships beteen variables will automatically impose
behavioral hypotheses on the data. For models which relate output to
factors of production, this point is of particular significance. Unless we
believe that factors of production are always perfect substitutes for one
another (so that diminishing returns do not apply), then we should not be
interested in a simple linear regression model of the production process.
Similarly, if we believe that factors of production cannot be substituted
for one another at all, we should have no interest in putting all of them
together in a regression equation. Fe could simply calculate their
relations to final output one at a time. For all intermediate cases (and
almost all believable cases are intermediate, especially at the aggregate
level), it is obviously desirable to have an appropriate specification.
The simplest intermediate specification in common use in economics
is the Cobb-Douglas, which is linear in the logarithms of inputs rather
than in their original levels. It is easy to show that this specification
implies diminishing returns while still allowing for a substantial degree
of substitutability among inputs (In fact, it imposes the assumption that
the elasticity of substitution is unitary, which might well be overly
liberal in many cases). A slightly more supple specification is provided
by the CES ("constant elasticity of substitution") form, which can be
approximated by a regression equation which is linear in the logarithms
and the squares of differences in logarithms of inputs. The CES
specification does the Cobb-Douglas specification one better by continuing
the assumption of diminishing returns and constant elasticity of



page 14
substitution while allowing the latter to take on other-than-unitary
values if these are suggested by the available data.
Finally, to summarize a complex subject with heroic brevity, it
should be noted that even more general specifications are currently
available. "hese forms allow, among other things, for the measurement of
variable elasticities of substitution among inputs. Several have been
extensively studied and applied, but the specification which seems to be
most convenient has been christened the "translog" (after transcendental
logarithmic) function. This function is linear in the first powers,
squares, and cross-products of the logarithms of inputs. Clearly, its
flexibility is balanced by a rather disagreeable proliferation of
right-hand side terms, many of which may be subject to the familiar curse
of multicollinearity.   Where data are relatively scarce, the associated
loss of degrees of freedom is likely to present statistical problems, as
well.
Hopefully, this brief discussion has provided some evidence in favor
of the argument that it is never sufficient to throw variables into a
linear regression unless there is good reason to believe that "infinite
substitutability" is as good an assumption as any other a priori. Since
this is not likely to be the case in an output equation, we are forced to
shop among the other candidates. In this study, the shopping has been
confined to a comparison of th7e Cobb-Douglas and CES specifications. The
need for simulaneous equations estimation, the use of variables in
time-change form, and the requirement of a plausible specification of the
relationship of inputs to outputs simply precluded the use of the translog
specification. As it turned out, these same conditions produced
circumstances under which the necessary linear approximation of the CES
specification also performed very badly. Thus, the output equation work
which is reported in this study has been heavily dependent on



page 15
specifications which are derived from the basic Cobb-Douglas form.
Having briefly surveyed the theoretical terrain, we can pass to the
equation set which has actually been estimated. As noted, the output
equation is basically derived from the Cobb-Douglas function. This
log-linear specification, when translated to time-change form, is linear
in percent changes in model variables. Thus, a specification of the
input-output relationship suggested by our basic hypotheses concerning the
contribution of human resources to growth at the macro-level would look
like the following (7):
<dq>   aO + al*Cdk> + a2*<dl> + a3*<dh> + a4*<dn> + a5*<de> + u
where
<dq> = Change in output
<dk> = Change in capital
<dl> = Change in the labor force
<dh> = Change in health status
<dn> = Change in nutrition status
<de> = Change in education
u = A random error term
Tn the output equations which have actually been estimated for this
study, data problems have necessitated some aepartures from the pure
Cobb-Douglas form. Capital stock data across countries are simply
unavailable, and the variable actually employed in the equations is the
intraperiod change in capital (investment), divided by the initial level
of output. o"he consequences of this assumption are discussed in Appendix
(A) apologies are offered for the expression of relatively complex
symbolic equations on single lines in this report. The writing, editing,
and 'rinal production of the paper have been greatly facilitated by the use
of word-processing software which, unfortunately, makes no provision for
mathematical symbols. Hopefully, this form :f "technical progress"' will
not prove too inconvenient for the reader.



page 16
A. For the moment, it should suffice to say that they may not be overly
damaging in work at this level of aggregation.
The second major departure from the form implied by the Cobb-Douglas
specification is the substitution of the intraperiod change in literacy
for the intraperiod percent change as the measure of basic educational
improvement. -his substitution is intended to solve a significant
measurement problem. During a period in which many countries have moved
from extremely low literacy to somewhat higher levels, modest absolute
gains translate to huge percent changes. The result for econometrics is
that a relatively small number of countries which began at very low
literacy levels in 1960 can dominate the entire sample numerically. It has
therefore been deemed desirable to use absolute differences for literacy
change. In theoretical terms, this translates to a model which is very
similar to the Cobb-Doublas except that the effect of education enters as
a multiplicative exponential rather than a multiplicative power of
education itself.
'he other equations of the output model have been specified in a way
which dovetails with the specification of the output equation. For the
available measures of nutrition and health, percent changes have been
employed. In addition, the nutrition change eguation incorporates a term
which captures some delay in the adjustment of current consumption to per
capita income, while the life expectancy change equation incorporates
terms to capture the effects of nutrition, education, and the availability
of medical personnel.
Because the contribution of literacy to output change has been
modeled using absolute changes, the literacy change equation has been
specified in compatible form.   Its exact mathematical derivation is
presented in Appendix A. This equation measures the marginal effect of
per capita income growth on the growth of literacy as well as the actual



page 17
effect of schooling on the age cohort which passes to adulthood in each
period. In the regression equation, the coefficient of the
appropriately-modified schooling variable can be interpreted as the
measured probability that a student who attended primary school during the
period in question actually became literate in the process. Tn the life
expectancy equation, an index of medical personnel availability is used to
capture the effect of public health efforts on life expectancy change.
Both of the availability indices mentioned above represent service
intensity levels which make contributions to changes in endogenous
variables. At first glance this may seem inappropriate, since an adequate
causal model must in the final analysis relate changes to changes. rhis
remains true for the current exercise, but service levels are crucial
intermediaries. In the literacy equation, for example, the change in
adult literacy is mainly due to the result of a "throughput" process.
Children have passed through primary education facilities (whose capacity
is represented by the primary enrollment ratio), and some have emerged
literate. "hus, an automous flow (children) through service institutions
whose capacity is defined results in a changed condition of literacy for
the adult population.
"his same "throughput" notion applies to all equations in the
response model except the output equation. In the life expectancy
equation, the flow in question is health technology. For a poor country,
the degree to which a constantly-improving technology can be applied
depends upon the availability of appropriate channels. One channel is
clearly the set of potential services defined by available medical
personnel and facilities. Another is associated with the means for
effectively transferring public health information. Undoubtedly, primary
schooling is important in this process, as are various printed media.
Thus, both the primary school enrollment ratio and the adult literacy rate



page 18
are defensible indices of information-transfer capacity.
A look at the global evidence for the past two decades also suggests
that there has been a sizable and near-univecsal up-shift in life
expectancy which has been due to the widespread employment of mass
vaccinations and other internationally-subsidized technologies. For any
country, then, there should be a substantial component of life expectancy
change which is simply "autonomous." Since countries may well differ with
respect to their ability to implement such universally-available health
measures, it makes sense to suppose that life expectancy change in the
1970's should exhibit some lagged relationship with the change in the
19FO's for a particular country. A lagged adjustment term has therefore
been included in the life expectancy equation.
Tn the interest of completeness, three sets of basic regression
results are presented here. As a fairly stringent test of the underlying
hypothesis concerning the direct contribution of human resource variables
to growth, the same model was run on data for the 1960's, data for the
1970's, and a set which pooled data for both periods. The initial results
made it clear that life expectancy as a measure of health has no
consistent impact on output growth, although the reverse phemenon is
apparent. Because the exclusion of life expectancy change from the output
equation and the consequent decoupling of the life expectancy change
equation from the simultaneous system allowed for a significant saving in
degrees of freedom in estimation, the basic model presented here is in
three-equation simultaneous form (8).
(8) In the growth model as specified, all of the equations are
over-identified. A series of dummy variables for major sub-regions were
introduced in the second stage to aid in absorbing unexplained variance,
since it was clear that local culture and natural conditions could have
have an important influence on the processes being observed. The
sub-regions defined for this work were the Caribbean, Central America, the
Andean countries, the rest of South America, North Africa, the Sahel, West



page 19
Figure 1
OUTPUT EQUATION PESULTS -- CLOSED ECONOMY MODEL (*)
1960 - 1970
N    R**2
<dq> = .052 + .142*<dk> + .301*<dl> + .869*<dn>                           39   .39
(.124) (.034)       (.319)        (.440)
+ .016*[Ett]-Ett-1) 
(.005)
<dn> = -.057 + [4.215-.868*lnN]*[<dq>-<dp>]                               39   .38
(.022) (1.031)(.222)
+ .038*ln[ (Q/P)/N]
(.020)
EEt)-7tt-1]*[1/(1+<da>)   = -2.423 + .988*S*[<da>/(1+<da>)]               39   .56
(2.259) (.137
+ 8.313*[<dq>-<dp>]
(3.697)
1970-1977
<dq> = -.109 + .182*<dk> + .592*<dl> + .557*(dn>                          43   .51
(.079) (.036)       (.337)       (.390)
+ .0080*(E[T)-E[t-1)]
(.0037)
<dn> = -.033 + [4.450-.948lnN]*[<dq>-<dp>]                                43   .31
(.016) (1.370)(.292)
+ .051*ln[ (Q/")/N]
(.014)
tt) - Eft-1)*[1./(1+<da>) I = 2.985 + .639*S*C<da>/(1+<da>)]             43   .43
(2.045) (.174)
+ 14.485*[<dq>-<dp>]
(5.248)
Africa, Central Africa, East Africa, Rest Asia, South Asia, Southeast
Asia, East Asia.
(*) Standard errors in parentheses beneath coefficients.



page 20
Pooled Data
N    R**2
<dq> = [.012 - .087*D70] + .146*<dk> + .565*(dl> + 1.011*<dn>           82   .50
(.088) (.048)       (.025)      (.239)      (.417)
+ .0096*[Ett)-EEt-1)]
(.0037)
<dn>   [-.040 + .00q*D701 + [3.259-.674lnN]*'<dq>-<dp>]                 82   .35
(.017) (.016)        (.894)(.191)
+ .04?*ln[(Q/P)/F]
(. 0 12?)
E(t) - Ett-1)*[1/(1+<da>)] = [-.996 + 3.986*D70)                        82   .31
(2.265) (1.810)
+ .755*S*[<da>/(1+<da>)] + 12.291*[<dq-<dp>j
(.138)                     (4.188)
Life Expectancy Change, 1970-1977
<dh> = -.124 + 6.948*(1/H) + [.573-.144lnH]*[<dq>-<dp>]                 52   .63
(.038) (1.570)         (.290)(.072)
+ .142*<dh(t-1]> + .077*<dn(t-1)> + .027*[E/H]
(.082)           (.027)            (.012)
- 1.10E-5*[fl/FF * .010*[S/S]
(.70r-5)        (.006)
'ariable Definitions
<dq>,<dl>,<dh>,<dn>,<dp>,<da> = Percent changes in real GDP, labor, life
expectancy, nutrition, population, and
adult population, respectively.
<dk> = [Change in capital]/initial GDP (See Appendix A)
E[t-1],E[t) = Literacy rate in initial and final years of estimation period,
respectively.
ln T = Logarithm of initial nutrition level
QfP = Initial level of per capita income
S = Previous primary school enrollment ratio relevant for the newest
adult age cohort.
Dn0 = Dummy variable with values [0=1960-1970, 1=1970-1977]
H = initial life expectancy level
I = Initial availability of medical personnel
E (In life expectancy equation) = Initial literacy rate



page 21
,the three sets of estimates presented above seem to tell a
consistent story (9). Capital, labor, literacy, and the measure of
nutritional adequacy all show up in the output equation in both periods
with the expected sign, reasonable magnitudes, and a general pattern of
adequacy by an appropriate one-tailed criterion. An exception is posed by
the labor coefficient in the period (1960-70). Since it loes not seem
plausible to suppose that labor has no effect on output in any case,
attention should be focused on the magnitude of the estimated coefficient
itself.
In interpreting the results for the output equation, it is important
to note that the capital stock change variable is really the total change
in capital during the estimation period divided by the initial output
level. Bor reasons which are explained in detail in Appendix A,
interpretation of the resulting coefficient depends upon an independent
estimate of the capital-output ratio. Generally, the estimation results
seem consistent with a capital-output ratio of about 3 and constant
returns to scale. '"he implied capital and labor shares are not radically
different from those found in econometric estimates for the industrial
societies (10).
As mentioned in the introduction, some ambiguity attaches to the
"nutrition" coefficient which accompanies the percent change in calorie
consumption. In part, this result may represent the beneficial impact of
rapid agricultural growth, which has been pointed to by numerous
development economists as a potential source of differential productivity
(9) clearly, the intersection samples used for estimation of the change
equations are much smaller than the full set of countries. In limited
samples, the risk of systematic bias is always present, but the country
observations represented in the preceding estimates look remarkably like a
random draw. See Appendix H for a complete list.
(10) See for example Barger (1969).



page 22
in TDC's. It might well be overly optimistic to attribute all of the
measured impact to nutrition, although it is certainly plausible to
suppose that some of the effect is due to this variable (11).
In summary, the simultaneously-estimated response equations do not
refute two of the basic hypotheses which were of interest to this study --
that basic nutrition and education make a contribution to the explanation
of output growth patterns when changes in the basic factors of production
(capital and labor) and simultaneity are taken into account. The same
pattern appears in the 1960's, the 1970's, and in the pooled sample, with
observable differences in estimated coefficients no greater than might be
expected from normal sampling variation. As always in statistical inquiry,
these results do not "prove" anything. They simply show that an
appropriately-specified model yields rather robust results which are
consistent with the hypothesis that human resource improvements are
productivity-augmenting at the aggregate level (12).
Tn the other two equations, the measured impact of per capita income
growth shows up as expected. A log-interaction term has been included in
the nutrition equation to control for a declining calorie demand
elasticity as the general nutrition level rises (13). Note that the
endogenous variable in these equations is output growth itself, while
population growth enters exogenously. In the system being modeled,
(11) For the reader who leans toward the agricultural interpretation of
this result, the nutrition component has been excluded and the resulting
two-equation output model estimated by 3SLS in a subsidiary exercise. The
results are reported in Appendix B. Except for a reduction in explained
variance as a result of the exclusion, they are very similar to the full
output equation results.
(12) The oil-producing states have been excluded from all regressions in
this study except for the open economy variant of the output response
model. Tn this version, the inclusion of import growth on the right-hand
side allowed for the introduction of oil producers without horrendous
outlier effects.
(13) A complete discussion of this issue can be found in Reutlinger and
Selowsky (1975).



page 23
percent change in population is the difference between birth and death
rates, both defined as "accumulation parameters." For the short periods
used in estimation, these parameters are assumed to be fixed (determined
by the initial levels of several variables, including some of the human
resource variables), although it is clear that they can change between
periods in a way which makes the model fundamentally recursive.
In the nutrition change equation, the importance of the coefficient
of the initial income/nutrition ratio suggests that delayed adjustment is
not negligible in explaining current changes in nutrition in LDC's. No
major differences in the nutrition equation results for the two decades
seem evident. In the literacy equations, however, one important
difference is obvious. If the estimates for the 1960's and 1970's are to
he believed, they suggest that attempts to move rapidly to mass primary
education with limited material and human resources has resulted in a
substantial decline in the marginal efficiency of the schooling process in
many LDC's. For the 1960's, the estimated probability that any student who
actually attended primary school would become literate is quite close to
one. For the 1970's, however, the probability is apparently lower (14).
this is not to say that rapid expansion has not had a beneficial impact,
since seventy percent of a large number is clearly preferable to
ninety-eight percent of a much smaller number (15).
(14) Some studies of educational performance in LDC's support the
implication of this finding. Inkeles (1974) has found a significant
performance gap between students from LDC's and industrial economies on
equivalent examinations in recent years.
(15) Although the distribution of literacy growth data in the 1960's is
relatively smooth, some unfortunate tendencies in national self-reporting
seem to have cropped up in the 1970's. Reported literacy gains for
Tanzania and Somalia are gross outliers in the distribution, and it seems
probable that measurement and enthusiasm for adult literacy campaigns have
become intertwined in the reporting for these two countries. They have
been excluded from the response model because of a strong feeling on the
part of the author that the kind of literacy growth which is meaningful
for productivity cannot be divorced from the process of schooling. If the



page 24
'"here are, of course, numerous possible explanations for this
downshift in probability. Its existence seems entirely plausible,
however, given the circumstances under which rapid expansion has taken
place. In passing, it should be noted that attention was given to the
possibility that the literacy probability parameter would itself vary
across countries as a function of relative capacity indices such as
initial literacy and per capita income. In several trials, no apparent
sensitivity emerged, and the assumption of constancy across countries
cannot be refuted using the kinds of data which were available for this
study.
In summary, it seems fair to conclude that hypothesized impacts for
basic education and nutrition on productivity change are consistent with
the available data. The growth model performs about equally well for the
1960's and the 1970's. It should be emphasized here that the result for
the 1960's lacks one note of ambiguity which is unavoidably present in the
second set. "he available World Bank estimates for nutritional adequacy
and literacy are "mid-seventies" observations, which can realistically be
regarded as random draws from the period 1974-1976. Under the assumption
that the change registered during the observation period could be
extrapolated directly through 1977, these data can be used in an output
equation along with measured labor, capital, and output changes for the
entire 7-year period. Nevertheless, it is comforting to note the strength
of the results for the 1960's.
"he results for the life expectancy regression are satisfactory,
although this particular equation was subjected to more experimentation
than any other in the study (16). Both lagged life expectancy change and
two countries are included in the sample, the output equation results are
unaffected but the proportion of variance accounted for by the literacy
equation drops by about .10.



page 25
lagged nutrition change have an apparent impact, along with
contemporaneous per capita income change. All of the throughput variables
previously mentioned appear to make a contribution, as well (17).
Although the reported econometric estimates are the best which could
be produced under the circumstances, the reader may feel justified in
retaining a certain skepticism concerning the degree to which they
actually reflect the hypothesized interactions. At least two bases for
such skepticism can readily be imagined. Although regression coefficients
always purportedly measure "representative" impacts across data sets which
can be characterized by smooth frequency distributions, they may in fact
be quite sensitive to the impact of a few outliers in the data. If the
term "outlier" is used rather loosely, it can also represent cases in
which purportedly general results are actually reflections of experience
in one or two relatively homogenous subsets of the data. In the current
context, for example, it might be imagined that measured human resource
impacts were in fact due to particular circumstances in single regions.
Fast Asia has recently been celebrated as an exemplar of both educational
and economic progress, and the informed skeptic might well wonder whether
the measured impact of literacy on output were not in fact a reflection of
a peculiar set of dominating circumstances in East Asia alone.
It is impossible to control for all sources of such skepticism in
exercises like the current one. It does seem reasonable, however, to
attempt some obvious further tests of the numbers. A simple device is an
examination of the scatter diagrams which are associated with the measured
(16) nost plausible variables simply made no contribution to explained
variance in the change equation. See Appendix G for amplification.
(17) It should be borne in mind that the index for medical personnel has
been entered as population/doctor, so that the expected value of the
associated coefficient is negative in the case of life expectancy and
positive in the case of the death rate.



page 26
partial coefficients in the output equations. In order to produce such
scatters, a variable of interest such as literacy change is plotted
against "residualized" output change, where the estimated regression
coefficients are used as a means of introducing statistical control for
the presence of other variables in the equation. In the following
figures, the relevant scatter diagrams are reptoduced for literacy and
nutrition change for the pooled data. They do not suggest that the
measured results have been produced by one or two outliers in any case.
Figure 2
-20.          O. .      20.         40.     -0.25      . 0.00        0.25       0.50
0.70 '             .                         0.60,              E
I.      ..    ,       ,              'I      ,
,  .   E                  [      ~       ~      ~~~~~~~I  C 
K                         1         AK    A
0.40'             A                      .       .A                A
Ali J                        S.         H A HE    B
|  .   CK         . . 0.20 1            2 J    E
I             .  n                        ,  I,        C22EK  F         E
AKK    B         F              I        DB2J     C   a
H34EE2   .A H            ..                J22  2 C
0.10 :       A   H2H  F2.                      .  :     .2 OGH3 2222 C
H G3G  C               .   .        I      D63A4     C
I         E323DF DE                                    D :  nD  H A
I           C2C2GC                      .    I   F    B       B
.1       ~~F2 G. -0.201                                  E
: .        H C EA 2        H                 :          G
-0.20 :A         CBB 0                   .       :B                   H.
.9                              *             ~~~~~~~~~~~~~~~~~H
1.    *.,    H
I    . ,                                      S . . .
-0.50 1                                       -0.60 1
:====== I=====          ======    = I         :…      --   -I=======|=====|===,=
-20.          0.        20.         40.      -0.25       0.00        0.25        0.50
Literacy vs. Output, Pooled                 Nutrition vs. Output, Pooled
As an additional test for regional dominance in the regression
equations, entire regions were excluded from the pooled sample and the
system re-estimated in a series of experiments. The results are reported
in Figure 3.



page 27
Figure 3
CLOSED ECONOMY MODEL WITH REGIONAL EXCLUSIONS
MODEL EQUATIONS
(1) <dq> = [al + a2*D70] + a3*<dk> + a4*<dl> + a5*<dn> + a6*[Ett)-Ett-1)]
(2) <dn> = bl + [b2 + b3*1nN]*[<dg>-<dp>] + b4*ln[(Q/P)/N]
(3) E[tt-E[t-1)*r1/(1+<da>)] = cl + c2*S*r<da>/(1+<da>)] + c3*[<dq>-<dp>]
3SLS RESULTS WITH SPECIFIED REGIONS EXCLUDED (*)
AFRICA          S. AMERICA      E.,S.E. ASIA    S.,S.E. ASIA
al              .0376           .0149           -.0043         -.0420
(.0999)         (.1044)         (.0903)         (.0949)
a2              -.0574          -.0554          -.0746         -.0594
(.0465)         (.0547)         (.0444)         (.0480)
a3              .1393           .1678           .1706          .1737
(.0271)         (.0285)         (.0258)         (.0267)
a4              .3472           .3957           .4078          .4446
(.2994)         (.2922)         (.2334)         (.2557)
af;             .5474           .5838           .4800          .5934
(.4775)         (.3971)         (.3429)         (.3671)
a6              .0207           .0105           .0099          .0135
(.0056)         (.0045)         (.0038)         (.0041)
bl              -.0514          -.0395          -.0373         -.0427
(.0201)         (.0131)         (.0144)        (.0163)
b2              3.1732          5.6945          3.7803         4.1827
(.8997)         (.9562)         (1.000)         (.9799)
b3              -.6529          -1.2072         -.7965         -.8744
(.1919)         (.2064)         (.2146)         (.2104)
b4              .0419            0685           .0568           .0481
(.0137)         (.0169)         (.0131)         (.0147)
(continued on next page)
(*) Standard errors in parentheses beneath coefficients



page 28
AFFICA         S. ANERICA      E.,S.E. ASIA   S.,S.E. ASIA
cl              .6151         '.3658          1.'2819    i    .9534
(1.7385)       (1.7556)        (1.6770)       (1.7035)
c2              .8481          .'85-15        .8387           .8552
(.1009)        (.1544)         (.1267)        (.1317)
c3              9.3233         8.2971         5-.7916         7.5153
(2.9056)       (3.7554)        (3.6345)       (3.4090)
R **2
(1)            .52            .57             .58            .56
(2)            .35            .56             .37            .38
(3)            .56           ' .47            .4,3           .46
F               58             58             71              69



page 29
Although the exclusion procedure resulted in a substantial loss of
degrees of freedom in the cases of Africa and Southern America, the
resulting estimates seem to diverge by no more than would be expected from
sampling variability. A possible exception is the greater responsiveness
of output change to literacy change when Africa is excluded from the
sample. In any case, there is certainly nothing in these results to
suggest that the estimates for the full pooled sample have been spuriously
generated by a dominating association in one region.
One additional source of doubt must be confronted in evaluating the
reliability of the results. It is possible to propose explanations for
differential growth performance which go considerably beyond those offered
by the basic model. It could plausibly be argued that variables such as
literacy and nutrition change are in fact rough proxies for other forces
whose impact, if directly measured, would render negligible the
coefficients of the human resource variables themselves.
Since several extended views of the growth process were of
independent interest to the production of this report, an attempt has been
made to expand the basic model to incorporate them. The roles of exp3rts
and capital inflows in the process of growth have been given particular
attention by many development theorists, and a model which attempted to
take these phenomena explicitly into account would certainly be of
interest as a complement to the current exercise.
An Open Economy variant
It has been suggested by many development theorists that
"extraverted" LDC's could be expected to grow more quickly than others.
nany reasons for this have been offered. Countries which subject
themselves to the rigors of international competition are quite likely to



page 30
be forced toward relatively efficient resource allocations, with
consequent productivity benefits. At the same time, such economies are
the most likely to attract foreign investment, so that the easing of the
domestic capital constraint might serve a growth-promoting role.
Complementary reasons for supposing that extraversion would have a
growth-promoting role are easy to imagine. The importing of associated
management skills or recent capital vintages could make a measureable
difference in aggregate productivity. Similarly, the employment of local
labor in efficiently-operated export industries might, under normal
conditions of turnover, be supposed to have a training impact which would
produce more general benefits through spread effects.
All of these arguments are plausible, and many of them have been
reinforced by the performance of several LDC's which have focused on
export promotion policies in recent years. East Asian societies such as
South Forea, Hong Tong, Taiwan, and Singapore are particularly notable in
this regard, of course, although cases in Africa and Latin America can
also be cited. In this subsection, a relatively simple extension of the
previous modeling exercise will be used to measure the apparent impact of
the kinds of factors mentioned above, as well as the degree to which the
statistical results for the human resource variables survive the
translation to a more complete model.
Again, the specification of the output equation is in growth rates,
with the exception of the literacy change variable. In the revised output
equation, the relative severity of the foreign exchange constraint will be
indexed by the contemporaneous growth rate of imports, while a test for
any differential effect of manufacturing export performance on
productivity will be attempted using the growth rate of manufacturing
exports. The latter variable has been explicitly endogenized in the
expanded model.



page 31
The manufacturing export equation itself has been specified to
reflect some obvious, simple principles of comparative advantage, as well
as the simultaneous impact of output growth. Capital is more mobile than
labor in the world, and the relative attractiveness of labor as a
complement to capital across LDC's must be systematically related to
relative quality and price, appropriately measured. In the expanded
model, relative wage levels have been proxied by per capita incomes, and
the available measures of basic education (the literacy rate) and health
(life expectancy) have been used as quality indices (18).
Tn the open economy model, then, the manufacturing export growth
rate in a particular period is specified as a function of the total output
growth rate during the period, the initial level of per capita income, and
initial levels of literacy and life expectancy. The growth rate of
imports is left exogenous. The results for the 1960's and 1970's are
reported in the following figures.
(18) This approach to the role of human resources in comparative advantage
owes much to Balassa (1979).



page 32
Figure 4
OPEN ECONOMY MODEL - 3SLS RESULTS ()
Pooled Data
N    R**2
<dq> = .2298 * .0366*<dk> + .2441*<dl> + .6194*(dn>                      71    .65
(.0963) (.0302)       (.2120)       (.4276)
+ .0091*[EEt)-E[t-1)] + .7257*dmx + .1.6080*dim
(.0041)                (.3429)       (.4538)
dmx = -.1221 + .0012*E + .0024*! - .00022*(Q/P) + .1955*<dq>             71    .36
(.0951) (.00078)   (.0026)   (.00007)        (.0434)
1960-1970
<dq> = .1863 + .0060*<dk> + .2476*<dl> + 1.5196*<dn>                     32   .23
(.1492) (.0472)       (.3217)       (.4286)
+ .0112*[Eft)-E(t-1)] * .6808*dmx + 2.6754*dim
(.0045)                (.4137)      (.9017)
dmx = .1312 + .0016*E - .0048*H + .00016*(Q/P) + .1951*<dq>              32    .15
(.1493) (.0013)    (.0044)   (.00014)         (.0616)
1970-1977
<dq> = .0170 * .0780*<dk> + .4255*<dl> + .1584*Cdn>                      41    .69
(.0583) (.0343)       (.2540)       (.3256)
+ .00S9*[Ett)-E[t-1lf + .7661*dmx + 1.000*dim
(.0031)                (.1745)      (.3362)
dmx = -.3011 + .0014*E + .0064*H - .00038*(Q/P) + .1672*<dq>             41    .62
(.0924) (.00074)   (.0024)   (.00006)        (.0523)
Variables Not Previously Defined
dmx = Growth rate of manufacturing exports
dim =                 imports
(*) Standard errors in parentheses beneath coefficients. The estimates for the,
nutrition and literacy equations are effectively identical to those obtained for
the closed economy model. These results have been excluded from the Figure for
the sake of readability.



page 33
Several interesting patterns are suggested by these results.
Certainly, the apparent role of literacy in the growth process is not
called into question. Literacy change retains essentially the same
magnitude, the appropriate sign, and a high degree of statistical
significance in all three sets of regression results. The role of
nutrition, on the other hand, is made more ambiguous by the poor result
for the 1970's. The use of the import terms in the output equation
substantially reduces the directly-estimated contribution of capital. The
fact that much capital has been imported by the sample countries makes
this result unsurprising. With the exception of the nutrition result for
the 1970's, then, the use of the open economy model appears to add
explanatory power without neutralizing human resource effects on output.
Fven a cursory examination of the manufacturing equation results
reveals that the fit is much better for the 1970's than for the previous
decade. As always, two alternative explanations for this result are
possible. The first might suggest that one of the two sets of results is
simply a sampling accident, and that the export equation is: (a)
irrelevant or (b) acceptable, depending upon the predisposition of the
observer. A second plausible interpretation of the result might be that
the world has changed, and that the international market is now
sufficiently articulated that these simple measures of comparative
advantage in labor resources capture an important source of differential
competitiveness for LDC's.
If the optimistic interpretation of the mixed result is accepted, an
interesting implication for human resource policy follows immediately. If
it is really true that manufacturing export activity is a source of
differential productivity gain, for whatever reason, and if it is also
true that part of comparative advantage is attributable to basic human
resources such as literacy, then it follows that countries which pay



page 34
little attention to these factors will suffer a double penalty. They will
lose part of the output differential which is apparent in both sets of
results on "closed economy" grounds alone. rn addition, they will
experience more difficulty in export promotion, with attendant benefits,
than their counterparts which have focused on human resources. If the
pooled results are regarded as the best summary of the evidence from both
decades, the role of education in this domain certainly shows up more
convincingly than the role of health (insofar as health is indexed by life
expectancy, that is).
Obviously, this sort of argument is only partial, however. Funds
for human resource investments and the support of heavy associated
recurrent costs may well come from surpluses which could be allocated to
physical investments.   To say that human resource investments can have
benefits is not, therefore, the same thing as claiming that the
productivity impact of these investments is necessarily superior to that
of physical investment. At this point, an explicit consideration of the
trade-off question would be premature. After the entire socio-economic
growth model has been specified and fitted to the available data, the
resulting equations will be combined into a simulation model which will
provide a vehicle for trade-off exercises.
rhe Investment Rate
Before moving from a consideration of output components in the
growth model to the demographic side, some attention must be paid to the
investment rate. A recursive specification of its relationship with the
rest of the output equations seems justifiable. It is the level of the
investment rate which determines the change in the capital stock and
subsequent change in the output growth rate. Since the investment rate is



page 35
itself hypothesized to be a function of several variables which represent
initial conditions in any growth period, the investment equation has been
estimated separately by ordinary least squares.
In many ways, the investment relation represents the most limited
part of this study. It is obvious that the observable aggregate
investment rate in any society results from the interplay of many public
and private resource allocation decisions. In addition, both domestic and
international factors can play a role. No attempt has been made to handle
these complexities in a structural model. Rather, the equation which is
fitted to the data is a reduced form with some rather heroic
presuppositions built in.
"he basic investment equation has three components. These components
are all determinants of the supply of investible funds, and an implicit
assumption is made that this supply is actually translated into investment
activity through the intermediation of public or private institutions. As
any analyst of financial affairs in LDC's can affirm, this view is an
oversimplification at best. At least, however, one would expect a
substantial degree of correlation between the supply of investible funds
and investment activity across countries.
-he supply-side components which are incorporated into the
investment equation for this exercise are three in number. Per capita
income is included, since it is to be anticipated that the rate of
personal savings will rise as a society moves away from the subsistence
margin. In addition, two human resource variables are incorporated in the
specification. Life expectancy is employed because of an hypothesized
link between expected lifespan and savings behavior on the part of
individuals in a particular society. In effect this represents nothing
more than an extension of the life cycle approach to savings behavior.
-he literacy rate is included to test the hypothesis that higher levels of



page 36
basic education promote a fundamental change in attitude toward economic
calculation and long-range planning. In the view of some, this effect may
be particularly pronounced in rural areas.
Again, then, all the incorporated variables are really supply-side
factors, and the explicit connection between the associated forces and the
ultimate realized investment rate is left obscure in the specification.
It should be noted in passing that both basic education and health could
be regarded as human capital variables, in the spirit of the manufacturing
export equations, and that an alternative interpretation of any perceived
effect on the investment rate would pass through the impact of differences
in human capital for the international flow of investment. Whether the
hypothesized effect is foreign, domestic, or some combination, however,
the investment equation remains entirely a supply-side construct.
rith all this as precautionary introduction, we now pass to a brief
consideration of specification and estimation. In this zase, as in the
others, the regression equation has been fitted to changes in the
investment rate rather than to levels. The right-hand side has been made
explicitly nonlinear in an attempt to control for a presumed decrease in
the marginal impact of the included supply factors as the investment rate
rises. -hus, changes in life expectancy and the literacy rate are divided
by the initial investment rate in the complete specification, while shifts
in per capita income are specified as percent changes rather than absolute
differences.
The estimation results, as produced by least-squares regression, are
reproduced below (19). The initial investment rate was also incorporated
(19) For reasons explained in Chapter II, Somalia and Tanzania have been
excluded from the sample used to estimate the investment equation. In
addition, Argentina and Mauritania have been excluded. The reported
investment increase for Argentina is obviously in error -- it is absurdly
large. The reported increase for Mauritania is also so large as to be an



page 37
as a means of controlling for any sensitivity of autonomous shift factors
to initial conditions. Indeed, as the following scatter diagram of the
investment level in 1960 and changes in investment from 1960 to 1977 makes
clear, the phenomenon of regression toward the mean seems to have operated
quite powerfully in this domain. The scatter shows that (ceteris
paribus), countries with unusually high investment rates exhibited a
decline over the period, while countries with unusually low rates
exhibited an increase.
0.        15.       30.       45.
*        t========== =========== : ===2========|
25. 
,1, C
I     J
I    C K
I      A
I      E  - G
1       2 J
10.I    D K   F2E
1       2 2KA
I       EF  A
I   B HC D2 JF 2
t       B BF A
I   J     HG   B
I       2C     G     A
B   D
-5.1       E   F  GE F
I                   H
:             ~~~~~~C
I    .C
-20. 1
I         I =--==t=,=.=.=  =~===-==== I
0.        15.       30.       45.
Tnvestment Pate (1960) (X) vs Investment Rate Changes (1960-77) (Y)
she regression equation in this case has been fitted to
seventeen-year changes in order to reduce the effect of measurement error
and sluggish responsiveness on the overall measure of error variance. The
results are presented in the following Figure:
extreme outlier in the distribution, which is otherwise guite regular.



page 38
Figure 5
INVESTMENT RATE CHANGES, 1960-1977 (*)
N    R**2
Irt) - ITt-1) = 11.0502 - .7842*I[t-1)                                      39    .63
(2.4479)    (.1351)
+ 5.3056*[Q/Pft]-Q/P[t-1) ]/fQ/P(t-1)]
(1.6174)
• 3.1372*[TE{,tl-?[t-1] J/1(t-1)
(1.3612)
I(t] - ITt-1) = 8.1247 - .5321*I{t-1)                                       58    .59
(3.3318)  (.1524)
+ 6.2889*[Q/PEt)-Q/P(t-1)/[Q/P(t-1) I
(1.1106)
+ 3.6924*[Htt)-HIt-1) ]/I(t-11
(1.7719)
S{t} - I(t-1  = 8.3445 - .6939*I[t-1)                                      39    .62
(6.9651) (.2568)
* 5.3017*[Q/P(t)-Q/P[t-1) )]/Q/P(t-1)]
(1.6369)
+ 2. 1829*[ ft) -REt-1) /1 (t-1) + 3.0705*[ E (t -E(t-i -}/I (t-1)
(5.2518)                       (1.3869)
Variables Not Previously Defined
I = Investment rate
__taadeosiprnhe_eeh____         t
(    Standard errors in parentheses beneath coefficients



page 39
'he results suggest an important role for income change in the
generation of investment rate change, and changes in the literacy rate
have apparently had an impact as well. Although its effect is not
statistically significant when it is incorporated along with literacy
change in the equation, life expectancy change emerges impressively when
literacy change is excluded. "'he literacy data are relatively sparse, and
it should he noted that twenty degrees of freedom have been gained in the
second equation. A fundamental ambiguity therefore remains. It is
possible that multicollinearity is the culprit, but it also entirely
possible that life expectancy change has no independent explanatory power.
As a conclusion to this section, it is worth noting that the use of
seventeen-year changes in estimation throws the recursive assumption into
doubt. Over this long a period, an upward-shifting investment rate would
undoubtedly promote upward shifts in human resource variables, so that
simultaneous causation (in a rather complex, second-order form) would
create difficulties for the interpretation of regression coefficients.
Although the long-period results will be used in subsequent simulation
exercises, the possibility of some simultaneity bias in the coefficients
of this particular equation must be borne in mind. Hopefully, future work
can cast further light on this entire subject by recasting investment rate
determination into explicitly structural form with allowances made for the
contributions of public and private decision makers (both domestic and
foreign), as well as the supply-side variables which have been utilized in
this report.



page 40
ITI. MODELING POPULATION GROWTH
Tn the demographic part of this modeling exercise, the focus will be
on the determination of two accumulation parameters -- the birth rate and
the death rate -- whose difference is the population growth rate. Since
these parameters join the investment rate as initial conditions in the
determination of growth dynamics during a particular period, they are to
be incorporated into the full model recursively. our interest here will
be in specifying a set of linear demographic models whose validity across
countries will be tested in time difference form. In this case there are
persuasive arguments for the use of the full seventeen-year period which
is available for the measurement of time changes.
Appropriate models of birth and death rate determination should both
allow for the representation of different age cohorts in the population.
At the same time, their behavioral underpinnings differ in some important
ways. 7he promotion of death rate decline is primarily a problem of
education and institutional capacity, since the idea of a longer life span
has undeniable universal appeal. Fertility, on the other hand, is
significantly affected by explicit personal decisions. Once women have
decided to bear fewer children, it is true that appropriate contraceptive
supplies and institutional capacity can help in the translation of intent
into result. -he fact remains, however, that the decision (in most
societies, at least) is essentially a family matter.
Thus, two sets of variables are necessary for a complete approach to
the analysis of fertility rate changes. Some can plausibly be related to
fertility decisions, while others have more to do with the provision of
appropriate supplies and institutional capacity. Admittedly, some
variables could be said to have effects which transcend this kind of
dichotomy. "Appropriate" education, for example, can certainly aid women



page 41
who have decided to have fewer children; it can also be organized to play
a persuasive role. In the specification which will be employed in this
study, a variable is introduced which attempts to capture both effects.
nodeling Fertility Change
Obviously, the focus here must be on the fertility rate of women in
the appropriate age cohorts rather than on the crude birth rate. It is
only in the context of fertility rates that estimated behavioral
coefficients can be readily interpreted. Fortunately, the available data
permit the calculation of rough fertility measures across countries. For
the years 1960, 1970, and 1977, age cohort estimates by sex have been
taken from the UNESCO data file available to the World Bank. When the
Bank's own estimated crude birth rates are divided by the proportions of
women aged 15 to 49 in national populations, rough but serviceable
national fertility rates are generated.
Once the translation from crude birth rates to fertility rates has
been effected, some unavoidable complexities in modeling present
themselves. As a prelude to their consideration, it is appropriate to
begin with the variables which will be used to represent the inducement of
attitudinal change and the role of institutional capacity in changing
fertility rates. Since decisions concerning family size must be affected
by survival expectations, the infant mortality rate or some proxy must be
included. "his "statistic" must vary with individual circumstances, so
that no single family could be expected to have a very precise estimate of
survival probability for its children. For the entire society, however,
it would be reasonable to expect some intertemporal responsiveness,
however sluggish, of the total fertility rate to measured life chances.
In the fertility model to be estimated in this section, the crude



page 42
death rate is used as the appropriate index-of these life chances. The
"dual" of the death rate is, of course, life expectancy. Because it is
relatively unaffected by age cohort effects which could be removed from
death rates in a multivariate analysis, the life expectancy measure is
preferable for a simple illustration of nonlinearity in this context.
Consider the following scatter diagram, which portrays the relationship
between life expectancy and the fertility rate in a pooled sample for the
years 1960,1970, and 1977.
Figure 6
30.    45.     60.    75.
I t ======== . ======== 
260. I
H 4A R2 G
X B42244G84F 5FGK B
I  A74A7 t'44U4  2JC
1 2 2 5;p22FF22 2 B
193.  A A 3D456 6KEA3 232 2  E
1  2 22C 3 HJJ2 2 JFJ FF
I  A 2C 2FFDKDJ2 JFJ2F
I          lD BFK2C2J
.        K K G  J G
0 KKK F 2
127. I            G 2 D K
F F CJK
K F
2 2 30J
I               K 3F23
.2                222 G
60.I I
I ='''''''= '''''. …   ''' .'=
30.    45.     60.    75.
LIFE EXPECTANCY (X), VS. FERTILITY (Y), POOLED DATA
There is an evident threshold effect in these data, with the
marginal relationship between life expectancy and total fertility becoming
much steeper as the former moves above 50 years. Of course, this scatter
may simply be masking a "true" relationship between the total fertility
rate and some variable correlated with life expectancy such as per capita
income. -his possibility is, of course, the whole reason for doing
multivariate analysis.
Nevertheless, the scatter diagram illustrates the kind of
relationship which can only be captured by a nonlinear specification. This
impression is enhanced if we look at the scatters for 1960, 1970, and 1977
as three "snapshots" of a process at work:



page 43
Figure 7
LIFE EXPECTANCY (X) VS FERTILITY (Y)
30.         45*         60.         75.      30.         45.         60.         75.
260.                                         260.
A
3A Er.                                            C
t 14 2JJ 4          E                          2 23.JCJF SH
t   ElB6EC   22EG     C3                     t    B2 3 C     r;
t  2 2   El      26   F                      t       5   IIFG
193.     B E12 2 B     A    r3 H F           193.t         242 K E 2 G3E F       E
2 2EH        JK                                 B   E     A     G  GF
t  B  CH     K F     K                 t         sB 2HHB    A   H  F
K   F  H(32                                      (3 F
K
H
127, t                           K           127.                        J
*                              H             j                       F   (
2 F                 t                            3j
2                                             6 (3A
A              *A A
60. t                                       60, t
t ==.-. .. _=-: t=rr::==t - - ==r  I  -  ................................... .=-a-=.:rt: r=r= t=._.--.==-....~- - I ~.-... ............................. 
30.         45.         60.         75.     30.         45.         60,         75.
1960                                          1970
30.         45.         600.        75.
260.
*        cEl C:   CA
t        x'l 33     AH
I      B 4   22 2   2F
t         E12DE   E 2
193. t         J2 4K    F
t            2 CEG   E G E
H (3  E GFr
K    G
t             J H B      F
A   KKH    2
127.                           2    K
EH
H
tK      (
J   F 22
2K A
60. t                                  A
t r:rr:=:=:r:==r .. t~ ~ ~ ~~I - ..~ .-r:== -==::=  -r-::r.-=:=- :r:=
30.         45.         60.         75.
1977



page 44
In considering this sequence of pictures, it is difficult to avoid
the feeling that all the societies are flowing over the same waterfall as
time passes (20). Note that as the minimum'life expectancy in the set
increases during the two decades, fewer and fewer countries are upstream
from the falls, and the point at which the plunge is taken remains
relatively constant.   Pith this as additional evidence, it would seem
perfectly sensible to model the relationship between national changes in
life expectancies and fertility rates nonlinearly.    Although the simple
bivariate relationship between death rates and fertility rates is not
quite as clear because of complicating age cohort effects in older
populations, the same principle obviously applies when these two variables
are linked in a multivariate analysis.
If the infant mortality rate is the appropriate
expectations-adjustment variable, other variables can be expected to play
a role in the decision process itself.. The negative relationship between
per capita income and fertility across countries is well known. Numerous
explanations for this phenomenon have been offered, but at some risk of
oversimplification they might be summarized in the statement that the
perceived opportunity cost of children seems to rise as family income
increases. Part of this undoubtedly has to do with rising human resource
investment costs, part with family fragmentation in association with
urbanization and industrialization, and part may have to do with the
related tendency of societies to shift the burden of retirement assurance
from families to government as national wealth increases. Thus, per capita
income serves as an index of a set of associated phenomena. It is useful
to measure income change in scale-free form, so percent change in per
(20) It may be this "waterfall" effect which was identified in Kirk (1974)
with the attendant observation that the pace of fertility decline seems to
have accelerated in poor countries during the past decade.



page 45
capita income is adopted as the appropriate measure.
If possible, it is desirable to complement the effects of the death
rate and income with some measure of family planning effort in the
fertility equation. The level of family planning activity is proxied with
an index devised by nauldin and Berelson after a detailed study of the
experiences of many I.DC's (21).. Besides paying considerable attention to
"appropriate education", this index is designed to give weight to
institutional capacity, public support, and the provision of
contraceptives. Although its scoring system is undoubtedly rather
arbitrary in some respects, it is at least an attempt to quantify a
complex phenomenon.
It should be noted that the !Lauldin-Berelson index is not immune to
the danger associated with the construction of any such performance index:
It is difficult to be objective about relative effort when observations on
performance have already been made. Thus, there is some risk that the
!auldin-Perelson index is actually a "residual."   In addition, this index
may measure a phenomenon which is determined simultaneously with the
fertility rate. If it is true that enhanced family planning effort should
yield some observable benefits over time, it may also be true that such
efforts are only likely to become important in countries where the
circumstances appear encouraging on other grounds. An explicitly
simultaneous specification therefore seems advisable, and a separate
equation explaining variations in planning activity must be specified as
well.
Since it is desirable to estimate the fertility equation in
time-difference form, the Mauldin-Berelson index introduces an additional
complication. Tt is reasonable to suppose that all countries in the set
(21) See nauldin and Berelson (1977).



*                         page 46
would have received a score near zero on this-index in 1960. However, the
:same assumption-would)-by no means be justified for 1970. Thus, the use off
the tl-B.index forces a.seventeen-year specification in changes. This form
may well be reasonable on other grounds, since adjustments to changes in
other model variables will certainly not be instantaneous. In addition,
.the use.:of a relatively.long time interval should aid in reducing the
relative effect of mieasurement.error on regression results.
As noted in the introduction to this report, any consideration of
fertility rates would be incomplete without an attempt to incorporate the
impact of differential age cohort proportions across countries. In this
study, three alternative specifications of cohort-specific variability
have;-been evaluated econometrically.  Although the mathematical details
.and.the extended discussion of result's have been relegated to Appendix C,
.the-:¢e.ssence of the modeling approach' and the final estimation results will
be p^resented and discussed here.
-     !. ti can be argued that all of the factors mentioned above' should have
some impact-on the fertility rate of any female age cohort in a particular
'9'ociety.. '-he scarcity of appropriate data, however, has prevented
detailed econometric work on the degree to which the impacts differ across
cohorts. In this study, an attem'pt has been made to approach this question
as a set*of specific hypotheses which can be tested econometrically.
Basica.lly, the statistical "foil" employed is a model which allows
varia-bles to have-different marginal impacts on the behavior of different
age cohorts.  Fith limited degrees of freedom it is difficult to
incorporate more than a few such cohorts, and here the relevant female age
group (taken to'be-in the range 15-49) has been divided into three
subgroup's (15-24, 25-34, and 35-49). The model in which all marginal
impacts are allowed to vary by age cohort has been used as the basis for
testing a substantially constrained model in which marginal impacts are



page 47
identical across cohorts but cohort-specific rates themselves are allowed
to differ by a constant term. The test establishes that the equality
constraints cannot be rejected, and Occam's razor has been employed in the
choice of fertility rate model. In the final specification, the
imposition of the marginal equality constraints generates a model in which
simple differences in age cohort percentages enter additively along with
the variables previously mentioned. The resulting equation fits the data
on seventeen-year changes quite well, with all model variables passing the
conventional test of significance (one-tailed).
As a complement to the fertility rate change equation, it has been
necessary to introduce a second equation to explain the change in family
planning activity across countries during the same period. one variable in
this equation must be the change in the planning index itself (which is
the same as the level in the mid-1970's under the assumption that all
national scores were effectively zero in 1960). Another logical candidate
would he some index of relevant institutional capacity. Among the
available variables the secondary school enrollment ratio has been chosen
as the most appropriate instrument, since it simultaneously measures a
society's training of potential cadres and the sophistication of the
institutional resources available.
Tn the following Figure, estimates for the final two-equation model
of simultaneous determination are presented (22). As in the case of the
output response equations, the technique of three-stage least squares has
been employed in estimation. The econometric results are quite strong.
Only changes in the female age cohort 25-34 had any apparent impact on the
total fertility rate during the seventeen-year period, perhaps reflecting
(22) A full list of intersection sample countries for the demographic
equations is presented in Appendix H.



page 48
a world-wide upshift in age at marriage (23). This result has been
cross-checked in several ways using alternative time-change and
cross-section specifications, and the basic conclusion seems to hold up.
-herefore, the only age-specific component which shows up in the final
estimate for the fertility rate equation is the change in the percent
representation of the age cohort previously mentioned.
(23) The available data on age at marriage are simply too scanty to make
their inclusion feasible in time-change regressions of the sort reported
here. It is, however, possible to draw some conclusions about the direct
impact of age at marriage on fertility using cross-section data. See
Appendix D for a full discussion and cross-section results which
incorporate age at marriage.



page 49
Figure 8
FERTIT,ITY RATE CHANGE, 1960-1977 (4)
3SLS RESULTS
N    R**2
FEtt  - Ftt-1) = 187.338*[ p2534t) -W2534[t-1)                           62   .76
(98.439)
+ 9.6361*[D[tt-D(t-1)   - .2470*[D(t)**2 - D(t-1)**2]
(2A309)                 (.0665)
- 19.4159*[Q/PEt)-Q/PEt-1) /[Q/PEt-1))- 1.3122*PL
(5.868)                                 (.7308)
PL = .3245*SEC - .1218*[FEt)-F(t-1)]                                     62   .73
(.0764)     (.0205)
Variables Not Previously Defined
W2534 = Women in age cohort 25-34 as a percentage of all women
in age cohort 15-49
D = Crude death rate
PI = nauldin-Berelson index of family planning activity
SEC = Secondary school enrollment ratio
(*) Standard errors in parentheses beneath coefficients



page 50
rlodeling Changes in the Death Rate
As in the case of fertility rates, the death rate is a weighted
average of age-specific effects. Again, the problem of degrees of freedom
has intervened to force the use of a relatively limited number of age
groups in the econometric work. For the present purposes it was decided
that division into three groups (0-14,15-49,50+) would be sufficient.
Alternative impact specifications were evaluated, and again the
constrained model with equal marginal cohort impacts was compatible with
the data.
it proved rather difficult to identify "non-deterministic" factors
which seem to have had a significant impact on death rate changes. Only
the availability of medical personnel as indexed by doctors per capita,
among several plausible indices (See Appendix G for amplification), has a
significant multivariate association with death rate changes between 1960
and 1977. A model which explicitly recognizes the presence of an
autonomous component akin to "technical progress," along with changes in
the population percentages of children and older people, accounts for
about 72 percent of the variation in death rate changes in the sample for
the period 1960-1977. The final equation estimate is presented below.
tmhe age cohort coefficients can be interpreted to mean that the constant
additive component in the death rate attributable to these two vulnerable
groups is about the same across the sample countries. As previously
mentioned, the full set of results in the death rate equation suggests
that the marginal impact of medical personnel is not significantly
different across cohorts.



page 51
Figure 9
CPIDE DEATH PATE CRANGES, 1960-1977 (*)
N    P**2
Dft) - Dft-1] = 6.6523 - 1.06705*Dft-1) + .0193*D[t-1l**2            64  .72
(1.6247) (.1949)         (.0055)
+ 2.4956E-5*M ft-1) + 19.3986*[Y{t)-Y t-1i j
(1.1442E-5)         (8.37428)
+ 19.8577*[Oft]-Oft-1) )
(7.5606)
Variables Not Previously Defined
Y = Children (1-15) as a percentage of the total population
0 = Persons aged 50+ "
(*) Standard errors in parentheses beneath coefficients



page 52
IV. SIIULAt"ING SOCIO-ECONOMIC DEVELOPMENT
In the first three sections of this report, a set of dynamic
relations among output, population, and human resource variables has been
specified and estimated econometrically. The results are useful in at
least two ways. In the first place, they cast some light on the validity
of certain hypotheses concerning the links between human resource
development and the growth of per capita income. Secondly, they provide a
measure of the relative impact of right-hand side variables in the
structural equations. Such a measure is appropriate for policy discussion,
since it is clear that response sensitivities vary consilerably.
Although individual parameter estimates provide the essential
foundation for empirical analysis in cases such as this one, the
complexity of the system being modeled precludes any reduction of the
dynamic equations to a simple set of multipliers. In such complex cases
simulation is a natural tool for analysis. Estimated coefficients provide
the measures of mean responsiveness which can be used for a simulation of
dynamic behavior. It is unrealistic to expect that the future evolution of
poor T!DC's will exactly reflect the evolution of their slightly
better-endowed counterparts in the immediate past. To the extent that the
fitted equations account fairly well for observed behavior under
reasonable causal hypotheses, however, they provide a more accurate and
consistent basis for projection than casual observation.
Fe will begin our consideration of simulation in this context with
an examination of the essential components of the model and the role which
they will have to play in a whole-system exercise. The most fundamental
distinction which must be drawn is between the elements which are
ultimately endogenous and those which are exogenous. Endogenous variables
are those whose future values will in the final analysis be determined by



page 53
the interaction of model equations. Exogenous variables, on the other
hand, are those whose complete future time paths must be specified as a
prerequisite for running the model at all.
Fhile this distinction between variable types is certainly the most
important one in the modeling exercise, there is another which is also
quite significant. rot all variables which are "ultimately endogenous" in
the sense defined above have been treated as endogenous in the econometric
estimations reported in Chapters II and III. Recall that in many of the
fitted equations, initial values of certain variables join lagged changes
as "predetermined" variables in the identification of system coefficients.
'he use of the two-block structure (accumulation-response) reflects a
recursive view of the growth process which has already been explained.
I"hus, many of the variables which are predetermined in the
econometric estimates will themselves change intertemporally as a
simulation exercise joins the two equation blocks in dynamic interaction.
7ith the distinction among "endogenous," "exogenous," and "predetermined"
now firmly in mind, we can proceed to a discussion of the roles played by
particular model variables in the simulation process.
-he separation of model variables into categories corresponding to
the terms used above depends upon a fundamental view of the world which
has been built into the equation system. Basically, this view can be
summarized as follows: It may be reasonable to regard public policy
instruments as independent levers for influencing the future of a
particular system. However, it is unreasonable to suppose that those
instruments can be applied in any kind of a vacuum. History counts in the
sense that the conditions prevailing in a society at any point in time
will have important consequences for the future evolutionary possibilities
of the system. A model which aspires to serious consideration must build
in these initial conditions in a plausible way.



page 54
For convenience of exposition, all of the predetermined variables in.
the present model are presented along with the endogenous variables in
Figure 10.
Figure 10
Predetermined Variables
Policy Variables                         Initial Conditions
nedical Personnel                        Birth Rate
Schooling                                Death Rate
Population
Adult Population
Investment Rate
Nutrition Level
Life Expectancy
Literacy
Per Capita Income
Endogenous Variables
Accumulation              Response
Population Change         Output Change
Capital Stock Change      Nutrition Change
Age Cohort Change         Literacy Change
Labor Force Change        Life Expectancy Change
Family Planning



page 55
A glance at Figure 10 makes it obvious that our estimation exercise
has produced a model whose data requirements are substantial. When the
equations are fitted together, the resulting system requires initial
values for a large number of variables as well as hypothesized future time
paths for several policy variables. Although the list of variables is
useful in separating them into intellectual categories, the precise way in
which they will fit into the simulation model still warrants discussion.
A look back at the estimated equations will aid consilerably here in
determining the role played by different variables in the system. Perhaps
the most useful way in which to discuss alternative roles is to identify
the data which must be specified before a simulation model based on the
estimated equations can even be run. Obviously, all of the truly exogenous
variables such as policy instruments must be known. As for the rest, the
best vehicle for organization may again be sequential consideration of
blocks and equations.
In the response block, output growth determination depends on prior
knowledge of the labor force growth rate and the growth of the capital
stock. Evaluation of the nutrition equation depends upon prior knowledge
of the initial level of nutrition, along with the growth rate of
population. In the literacy equation, additional information requirements
are imposed by the need for data on primary school enrollment ratios
during the relevant period for the most recent adult age cohort. The
growth rate of the adult population is also required for the evaluation of
this equation. Finally, the life expectancy change equation depends upon
the initial level of life expectancy, change in life expectancy during the
preceding period, change in nutrition during the preceding period, and the
initial levels of literacy, schooling, and medical personnel availability.
If all of these data are known, then the response equations will generate
contemporaneous changes in output, nutrition, and litera-y. In addition,



page 56
life expectancy change can be calculated.
It is obvious that some of the prerequisite data for the response
block are immediate products of the accumulation block. In this block, for
example, the determination of the investment rate leads immediately to the
capital stock change variable (capital stock change/initial output) which
is used in the output change equation. This new investment rate, in turn,
aepends upon the investment rate in the preceding period and recent
changes in per capita income and literacy.
The accumulation block is also the locus for the calculation of the
population growth rate, which is the difference between the crude birth
rate and the crude death rate. The crude birth rate can be calculated
once we know the appropriate female age cohort percentage and recent
changes in the death rate, per capita income, and family planning
activities. Calculation of the death rate in turn depends upon the prior
death rate, age cohort changes, and the-availability of medical personnel.
The nodel
Fith all this as prelude, it is now time to turn to the simulation
equations themselves. Hopefully, the preceding discussion will have
cleared the methodological thickets sufficiently to allow for a relatively
clear view of the process being described. The "Closed Economy" model has
been used as the foundation for the response block here.
The behavior of the model will be illustrated using data for a
"typical" poor country and for hypothetical countries in Sub-Saharan
Africa, South Asia, and South America. A series of experiments has been
designed to gauge apparent trade-offs between physical and human resource
investments. This section will describe the experiments and their



page 57
results, while a full description of the model and the sDlution technique
has been included in Appendix E. The model in its current form is built
around 10 estimated equations. Many additional equations have been
necessary for appropriate variable definitions, the tracking of age cohort
groups from birth to death, and other "housekeeping" functions.
Such a model-building effort can be justified if the result holds
some promise of providing information which could not be gained by
inspection of individual econometric results. In this case, there are
simply too many such results for their total implication to be grasped
through separate consideration. Rather than calculating a set of fixed
multipliers, we are forced to conduct policy experiments with the
knowledge that outcomes will be sensitive to initial conlitions as well as
on-going levels of public activity. Since the notion thaLt "history
matters" seems eminently sensible in any case, this indeterminacy should
probably be regarded as a strength of the simulation approach.
obviously, believable policy experiments must be founded on
believable initial conditions in this case. Although it is certainly
possible to construct a "typical" LDC from central tendencies in
distributions of socio-economic data, it also seems advisable to allow for
major regional differences by experimenting with typical poor-country data
for different regions. For the present purposes, four sets of initial
conditions have therefore been constructed. The numbers are broadly
representative of the recent historical experiences of poor countries in
the areas specified.



page 58
Figure 11
INITIAL CONDITIONS -- TYPICAL LDC CASES
AFPICA       SOUTH AMERICA   SOUTH ASIA      "TYPICAL LDC"
Per Capita Income
1960                    50              210             60              180
1970                    57.5            268.8           91.4            207
1977                    63.8            330.4           96             *227
literacy Rate
1t60                    10              39              15              29
1970                    15              50              20              40
1977                    20              63              21              55
Life Expectancy
1960                    37              43              44              46
1970                    40              48              48              50
1977                    42              52              51              54.5
Calorie Sufficiency
19hO                    85              69              84              80
1970                    78              76              94              82
1977                    78              77              93              84.5
Rirth Pate
1960                    49              48              49              47
1970                    48              47              47              45
1977                    44.5            40              44              39.1
Death Pate
1960                    27              23              23              20
19'0                    24              19        -     18              17
197'                    20.2            16.6            16.5            13.8
Investment Rate
1960                    13              12.4            12.5            15.3
19X0                    14              18.8            19              18.4
1977                    17.7            22.8            18              20.8
Primary School Enrollment Ratio
1960                    10              64              52              65
1970                    40              80              69              76
1977                    55              93              71              89
Population per Doctor
1960                    37706           8978            31076           8370
1970                    32788           7014            20718           7600
1977                    29220           5361            19299           7956



page 59
Some of the historical indices presented in Figure 11 above are
quite different, while others (such as initial birth rates) are similar.
Phile it might have been desirable to incorporate more variance into
initial conditions for the sake of comparison, the interest here has been
focused on an attempt to use numbers which are representative of regional
conditions. With these numbers (and a large additional set of observations
on other variables such as the GDP growth rate) as initial conditions, the
full 43-equation simulation model has been run, through a sequence of
7-year periods to the year 2026. The resulting baseline simulation has
been used for comparison with the results of some policy experiments.
Priefly, it can be said that five illustrative simulations have been
run for each IDC type. Two are intended to illustrate the consequences of
educational policies which differ significantly from those represented by
the baseline runs. The other three are an attempt to examine the
implications of policies which allocate equivalent resources at the margin
to physical investment, education, and family planning. No heroic claims
of significance are made for any of these illustrative runs. Although an
attempt has been made to use actual cost estimates wherever possible, the
numbers are extremely rough (24).
The main purpose of the three trade-off experiments is to confront
the central cost-benefit question: Granted that any physical or human
resource investment is a "good", what can be said about relative marginal
net benefits? In the generation of an appropriate response to this
question, nothing less than a consideration of full system dynamics will
do. the combination of econometrics and simulation attempted here, with
all of its evident simplifications and weaknesses, is intended to provide
(24) The cost estimates used in these trade-off exercises have been drawn
from Burki and Voorhoeve (1977).



page 60
the foundation for a consistent answer. The results of the two simulation
exercises are presented in the following Figures.
Tn the first set, the predicted consequences of three different
approaches to education are examined. The LOW results reflect the
predicted evolution of the hypothetical African and South Asian societies
under the assumption that the primary school enrollment ratio is frozen at
.'0 and no family planning activity is undertaken. The schooling
assumption is quite pessimistic, of course, since both societies have
primary enrollment considerably above .20 at the present time. The intent
is to examine the sensitivity of the model to sharp shifts in important
policy variables as well as to predict the implication of a specific
policy alternative.
rhe n1EDIuN simulation reflects the "normal" case which has been
built into the model.   Family planning is determined endogenously in this
case.  In each period, the primary school enrollment ratio is predicted
using the results of a simple asymptotic regression fitted to
cross-country data for the year 1977. In the HIGH simulation, the same
model is employed, but the literacy rate is given an exogenous boost of 30
percent for the period 1977-1984.
In order for the impacts of these alternative assumptions to be
clearly demonstrated, the three education simulations have been run
through 12 simulation periods (or 84 hypothetical years). It would
obviously be wrong to attach any significance to the final numbers
produced by such long runs. Their advantage lies in the pattern of
non-linear responses which they clearly illustrate. The excessive length
of the simulations is useful in revealing some of the behavioral dynamics
implied by the current structure of the model itself.



fA,Z.L
Figure 12                                             [     Oo B ti|
.             .           _ t ~~~~~~~~C K%cfA 
ALTERNATIVE EDUCATIONAL AND FAMILY PLANNING POLICIES:
SOME PREDICTED OUTCOMES
AVR.3CA                                                       SSo&   AsiA
0.        200.        400.       600.        800.       1000       50     200.    350.    500.    650.    800.   950.   1100.
0.~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~=== 200                      ====a= '00  ====== ' ===='==== '====     ====
3= 3                                                                313
2 C                                                                2 C
2 2     C                                                           .   2 C                                  feL CAPITA
*    AB   C                           'L*,Ct                            AB    C
I     AB    C                                                     8WacA.  A B   C
a       A B     C                                                   8      A   B    C
- A   B      C                                                      A     B     C
A     B      C                                                    A        B     C
A       B       C                                                 A           B      C
13      A          B        C                                       *     A               B      C
131         A              B          C                             13        A                    B     C
A                     B          C                         *      A                         B       C
:   =    =   =   =    =    =   =    =    =   =    ==A  B  C         :       A                                B        C
0.        200.        400.       600.        800.       1000.      50.    200.    350.    500.    650.    800.    950.  1100.
40.0    45.0    50.0    55.0   60.0    65,0    70.0    75.0      50.0        55.0        60.0        65.0        70.0       75.0
:===-==:===…3=:--  ===… I======:============= =                3 ; 
313                                                                :     A2
ABC                             Lwa                   '                A     B C
AD A CB  C  ~   ~    Lt-aA                                     B     C
AB C~~~~~~~~~~~~~~~~ 
-1-                A     B      C                                '1              A        B       C
91                   A      A  - B      C                      ,13 |                   AA               C 
*                      A           B     C                                          a                   B       CA
1  A      B      C                                             ~~~~                     ~~~~~~~~~~~~~~A  B  C
A      B       C                                              A               B       C
A  B  C~   ~   ~  ~~~~~~~~~ 
131                   A             B     C                131                    A                    B       C
A               BBCC                                        A                        B     C
*40.0    45.0   50.0   -55.0    60.0    65.0    70.0    75.0     ,50.0        55.0        60.0       65.0        70.0        75.0
,10.0   20.0    30.0    40.0    50.-0   60.0 , 70.0     80.0
10.0    20.0    30.0    40.0   50.0    60.0    70.0    90.0     ;      ====   =======-==-==   …====-======     ========
…====       =======    I=ew  ======n 1=-==  ==== ======= I   
3     23                         C                              *tthc     2                            C 8Lc E&ACIW
A B  ccA   B                c
8 '  AAA  B                 C       C                     8 'AA                     B                 c     C
A            B                 C                                   A                      B          C A
A          B'                  C    cA                                                               B       C
81 A             B                CA  B   C                               A                              B      C
*  A                        B            C                     13    A                                B        C
13*   A                             B         C,                         A                                  B       C
A-                               B        C,                      A                                      B     C
A                                   B       C              13    === A  ===    B===   C===     ===     ===     ===
A    B    C~~~~~~~~~ 
:=======:=======:=======:======  ======= ======= =======   t10.0  20.0  30.0  40.0  50.0  60.0   70.0    80.0
10.0    20.0    30.0    40.0    50.0   60.0    70.0    80.0



8ii
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SO@ATm As#A
0.250        0.300       0.350        0.400       0.450        0.500               0.325     0.350      0.375     0.400      0.425     0.450      0.475
3 :                                                           3                       ========= . ========= ========= : ========= : ========= : X===.=== :
3 -  3A
c-is                           C2                   ~,o                    PPiM#J                               C BA
° - IX C BA                                 0- o S                          C      C B  A
*  8:                                                                           C     B    A BA
*                          C     B       A                                      8                  C       B                       AA
A                                                                                       A
C3    B C  B    A                                          *3 |        C             B               A
B           A                                                                                    A
;3:        C      B                  A                                             :        C B                             A
===== ===                          ====         === * == == C                               B                            A
0.250       0.300        0.350        0.400       0.450        0.500               0.325     0.350      0.375     0.400      0.425     0.450      0.475
0.080   0.100    0.120   0.140   0.160    0.180   0.200    0.220               0.080        0.100        0.120       0.140        0.160       0.180
3                                       3                                                               3
3                          so                                                                A2                    O F &emuevea.i
A2                                                                                        ABC
2C                           IQ) +                                                   AB C
ABC                                                                       :         A  B C
8:     A B C                                                                   8:         A   B  C
:   A B  C                                                           :            A      B   C
A   B     C                                                                          A         a     C
A  B  c                                                        ~~~~                  ~~~~~~~~~~~~~A  B  C
A     B       C                                                  :                   A             B       C
:          ~     ~~A  B  .    C                                            :A                                     *B       C
13:                  A           B         C                                   13:                       A                      B      C
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0.000   0.100    0.120   0.140   0.160    0.180   0.200    0.220               0.080        0.100        0.120       0.140        0.160       0.180



page 64
-he time plots of simulation outcomes in Figure 12 reveal some of
the implications of such drastically differing approaches to education.
The dominant impression in both the African and South Asian cases is the
persistent contrast between relative stagnation in the LOW cases and
relatively rapid progress in the other two. The impact of the exogenous
one-period boost in literacy is also quite striking. The model equations
predict that this one shift will generate a time path which diverges
substantially from that of the !EDII! case for most of the crucial model
variables.    An interesting variation on this theme is provided by the
growth of literacy, where inherently asymptotic behavior produces an
apparent convergence for time paths in the MEDIUM and HIGH cases.
One advantage of the relatively complex approach to modeling taken
in this report is that it allows for a comparison of outcomes along
dimensions other than that provided by per capita income. The simulation
plots also allow for a comparison of long-run outcomes in three other
important determinants of the physical quality of life -- literacy, life
expectancy, and nutrition. In the education simulation runs, relative
stagnation in the tO1 case is also apparent.
Given a basic understanding of the econometric equations which form
the core of the model, it is not difficult to trace the reasons for the
behavior predicted in these three cases.. A sudden surge in literacy has
three mutually-reinforcing effects. There are immediate responses
predicted for the output growth rate and the investment rate. These
reinforce one another in producing income gains, which in turn join with
other variables in inducing gains in nutrition, health, and education. At
the same time, the induced up-shift in the per capita income level
produces a response in death rates and fertility rates. Although the
effect of the death rate decline is perverse in the sense that the
sluggish responsiveness of fertility to infant mortality changes yields a



page 65
positive impact on population growth, the direct impact of income change
on the fertility rate has an additional important effect. The net effect
of all these forces is a simultaneous upshift in the growth rate of output
and a downshift in the growth rate of population. The advantage produced
by the initial surge tends to persist through time, as indicated by the
comparison with the MEDIUM case.
"'he relative stagnation apparent in the LOW case can be explained
with reference to many of the phenomena mentioned above. with primary
schooling frozen at a very low level, successive age cohorts arrive at
adulthood with very low literacy rates. At the same time, no outlet is
provided for family planning activity as an additional instrument for
lowering the fertility rate. The cumulative impact of these two lapses is
seen in a birth rate which is so persistently high as to overwhelm the
prevailing death rate. In addition, the absence of the self-reinforcing
dynamic interaction between output and education growth leaves the economy
dependent on the increment provided by changes in the capital stock and
the physical quantity of labor, rather than the quality of labor.
'"he final result of this relative stagnation in per capita income
and human resource indices is a country whose population is much larger
and much poorer (in per capita terms) than that predicted by the MEDIUM
and HIGH cases. The exponential nature of the accumulation parameters
produces a long-run aggregate GDP which is larger for the MEDIUM and HIGH
cases.
Since the simulation model which has been used to produce these
results is quite detailed, it produces time paths for many more variables
than those which have been mentioned in this illustrative discussion. As
one further example of the workings of the model, it may be useful to
consider the evolution of population age structure predicted by its
demographic component. For this reason additional simulation plots have



page 66
been produced for the population proportions of the groups aged (1-15) and
(FO+). Fere again the apparent evolution is a logical result of the
economic and demographic dynamics previously described. As fertility
rates and death rates both decline, the population gets relatively older.
This phenomenon is reflected, both in the plunge in the proportion of
children in the population and in the relatively rapid rise in the oldest
age cohort. Some additional complexities are introduced by a mild
reversal of the death rate as the older age cohort becomes more dominant
in the population and by a mild inflection in the progressive decline of
the fertility rate as the relative size of the cohort aged (25-34)
increases and then decreases again.
The contrasting simulations reported here are not intended to
provide a full illustration of the behavioral dynamics of the model, nor
do they provide more than a very partial view of the kinis of behavior
predicted by the model under alternative assumptions about initial
conditions and public policies. They do suggest that the model as
specified and estimated accords a very powerful role to both education and
family planning activities in the determination of long-run social and
economic outcomes.
From the perspective of public policy analysis, it is of course
insufficient to use an apparently powerful impact to justify increased
investment in schooling or family planning activities. A consideration of
the significance of simulation outcomes must depend on some consideration
of relative marginal net benefits, whenever this is possible. A logical
alternative to the use of public resources for the promotion of human
resources would be their diversion to physical investment. Since an
augmented investment rate would increase the growth rate of output, with
subsequent impacts on income, human resources, and fertility, it might
well be argued that the best approach to the human resource problem is an



page 67
augmented growth rate of the capital stock (25).
It is apparent that this kind of debate can be resolved only through
a modeling approach which is at least akin to that taken in this project.
Recause initial conditions clearly count, the way in which
resource-equivalent policy interventions occur should have consequences
for final outcomes. At the same time, a consideration of marginal net
benefits must take dynamic relations explicitly into account.    A policy
which moves resources directly into physical investment will have an
immediate impact on per capita income and visible short-run impacts on
other socio-economic variables as the effect of enhanced family income
spreads through the system.
Investments in human resources, by contrast, will have general
impacts which become apparent over longer periods of time. An expansion
of primary enrollments in the 1980's will begin to have a visible impact
on socio-economic outcomes during the succeeding decade, as more literate
adults join the labor force and make decisions about optimal family size.
An intensification of family planning activity might well take even longer
to demonstrate its full effect, since the impact of a permanently-lowered
(29) Discussions of the trade-off between equity and efficiency in this
context have encountered difficulty in drawing a precise line between
"consumption" and "investment." If the social objective function is
expanded to include literacy, health, and nutrition, of course, the very
notion of "investment" probably has to be overhauled. Some earlier
studies have attempted to examine the question of trade-offs at the
aggregate level in a dynamic context. Among economists, notable efforts
are due to Ahluwalia and Chenery (1974) and Adelman and Morris (1973). In
work which preceded the current effort (Wheeler, 1980), I attempted a
simpler set of simultaneous estimates for the 1960's with some attendant
benefit-cost analysis.
As could be expected, the work by economists has tended to give
short shrift to demographic problems. Among demographers, the opposite
tendency has prevailed. Several efforts to model long-run demographic
reactions to economic change have been attempted, with little explicit
attention given to the economic growth model. The first major work of
this 'type was attempted by Coale and Hoover (1958). For a more recent
effort see Dyson, et. al. (1978).



page 68
fertility rate on the evolution of per capita income would only become
apparent after a succession of smaller age cohort groups had passed into
the system.
For all of the reasons just cited, it is difficult to consider
policy experiments in this context without the introduction of much
disagreeable complexity. Different policies will generate different time
paths, not just for per capita incomes but for other variables which are
important in determining the physical quality of life (PQLI). Some
investments have longer gestation periods than others as well, and again
this fact applies to the evolution of PQLI variables as well as per capita
income. 7hus, trade-off experiments of the type proposed here cannot
yield unambiguous conclusions unless the results of one policy dominate
the results of others absolutely and at every future point in time.
pith this fundamental point in mind, the trade-off simulation
results presented in the following Figure are specified as relative
rankings at the end of each '-year simulation period (26). It is clear
that relative rankings can shift through time, and that slow starters do
not necessarily lose the race. In such long-run processes, of course,
entire lives can be lived as the race proceeds and the question of an
appropriate discount rate must intrude. If, as some have argued, the
long-run social discount rate for an entire society should be zero in such
cases, then endurance should always be given precedence over speed in the
judgment of final outcomes.
(26) It is, of course, difficult to evaluate the simulation experiment
without some knowledge of the calculations which have been employed to
produce value-equivalent activities. A complete accounting of these
calculations is given in Appendix F.



page 69
Figure 13
TRADE-OFF RESULTS
AFRICA
Investment      School         Planning
Income
1984                           1             2                2
1991                           1             2                3
1998                           2             1                3
2005                            2            1                3
2012                           3             1                2
2019                           3             2                1
2026                           2             3                1
Iiteracy
1984                           1             2                2
1991                           2             1                3
1908                           2             1                3
2005                           2             1                3
2012                           2             1                3
2019                           2             1                3
20?6                           2             1                3
*Iife Expectancy
1984                           1             2                3
1998                           2             1                3
200S                           2             1                3
2012                           2             1                3
2019                           2             1                3
2026                           2             1                3
Futrition
1984                           1             2                2
1 901                           1            2                3
1998                           3             1                2
?005                           3             1                2
2012                           3             1                2
2019                           3             2                1
2026                           3             2                1



page 70
South America
Investment      School         Planning
Income
1984                            1            2                2
19¶'1                          2             1                3
1998                           2             1                3
2o005                           2            1                3
2012                           2             1                3
2019                           2             1                3
2026                            3            1                2
literacy
1984                            1            2                2
1991                           2             1                3
1998                           2             1                3
2005                           2             1                3
2012                           3             1                2
2019                           3             1                2
2026                            3            1                2
Life "xpectancy
1984                           2             1                3
1991                           2             1                3
1998                           2             1                3
2005'                          2            1                3
2012                           2             1                3
2019                            2            1                3
2026                            2            1                3
'utrition
1984                            1            2                2
1 91                           2             1                3
1°98                           2             1                3
2005                            2            1                3
2012                            2            1                3
2019                           2             1                3
2026                           2             1                3



page 71
Figure 13 presents the trade-off simulation results for the African
and South American cases. These two have been employed as contrasts,
since a glance back at initial conditions will reveal that the two cases
are in most respects quite different. An intertemporal time path of
relative ranking is provided for per capita income, literacy, life
expectancy, and nutrition. For each case, the same basic experiment has
been run. In the Investment simulation, the investment rate has been
autonomously increased by 1 percent of GDP for one 7-year simulation
period. For School, equivalent resources are devoted to increasing the
primary school enrollment ratio during the same 7-year period, using World
Bank estimates of recurrent cost for personnel, materials, and overhead by
world region.
Since cost estimates for typical family planning programs are
unavailable, the Planning simulation is based on a different approach.
From Forld Bank estimates of the cost of training basic zommunity health
teams, the number of teams has been calculated for an expenditure equal to
the original investment increment. The resulting number has then been
divided into the number of females of child-bearing age in each
hypothetical country to produce ratios of "target" females to community
health personnel. In no case was the result greater than 200 fertile-age
women per 3-person team.
Under these assumptions, it seems reasonable to suppose that such an
expansion of community health workers would represent an effort equivalent
to a Mauldin-Berelson score of at least 3 (their maximum index score is
30). In the African case, a one-period increase of 3 in the N-B index is
sufficient to produce a per capita income higher than that produced by the
one-period direct investment alternative. In the South Amerian case, an
increase of only 2 is sufficient to produce the same effect. The
simulation results reported have been generated by these "lower bound"



page 72
increases. In view of the apparent possibilities for population coverage
associated with resource increments of the magnitude considered, it is
entirely possible that the suggested one-period impacts on the family
planning index are conservative. In any case, the intertemporal results
for per capita income and the PQLI variables have been included.
7"he pattern of intertemporal fluctuation in rankings for Africa
makes it obvious that any policy conclusions cannot be divorced from
explicit valuation of PQLI outcomes, as well as a discount rate. Except
for an intermediate period in which the School variant dominates
absolutely, there are no clear winners in this experiment. During the
first periods, the results of the Investment and School simulations
exhibit approximate parity, while the balance shifts from Investment to
Planning in later periods. Since the assumptions underlying the Planning
simulation may well be overly conservative, the balance might be expected
to shift sooner than this particular experiment would indicate.
In the South American case, the final judgment can be made with more
certainty. In all but the first period, the School result dominates
absolutely. Again, however, the same evolutionary pattern is evident in
the rankings for the other variants. During the first periods, Investment
clearly dominates, but Planning has overtaken it in two categories by the
final period.
Certainly, the set of illustrations presented here provides no
conclusive evidence concerning the trade-offs which would be confronted by
policy-makers in actual cases. Although careful attempts have been made
to estimate the parameters of all model equations in appropriate ways, the
simulation results are inevitably sensitive to the specifications which
have been adopted. In the final analysis, the conclusion which emerges
from the simulation seems sensible, however. In brief summary, this
conclusion might be stated as follows.



page 73
There can be no definitive statements about which of a set of
hypothetical resource allocations is absolutely superior. Initial
conditions will create different short-run marginal productivities, and
the long-run consequences of alternative policies may well be quite
different than their short-run results. In its current form, the
simulation model illustrates these lessons without necessarily providing a
definite basis for analysis in particular national cases. It is true that
the initial conditions for a particular society could be used along with
alternative policies for specific predictions. Since the non-availability
of appropriate data has greatly handicapped the construction of such
models in the past, the predictions yielded by this model could provide a
useful basis for discussion concerning apparent future trends. In the
final analysis, however, the model in its current form still contains too
many simplifications for any great confidence to be placed in its
predictions.



page 74
APPEMDIX A
SINULTANEOUS ESTIMATION OF THE RESPONSE EQUATIONS:
PPRBLENM OF SPECIFICArION AND MEASUREMENT
1) Data Scarcity and nodel Specification
't would be incorrect to assert that no empirical work has focused
on the effects of basic human resource development on productivity across
countries in the 1970's. Some analysts have done cross-section studies of
the intercorrelation among measures of economic performance, public policy
decisions, and basic social indicators. Most of the published studies,
however, are actually static exercises.     That is, they attempt to draw
inferences about causality within countries from data which have only been
taken across countries. Since many socio-economic indices are roughly
correlated, it is relatively easy to obtain good cross-section results
which tempt the researcher to draw broad policy conclusions.
As any practicing econometrician who has worked in this area can
affirm, unfortunately, cross-country correlation and within-country
causality are definitely two different things. Characteristically,
regression exercises which suggest high degrees of intercorrelation in
cross-section lose most of their "explanatory power" when within-country
changes are considered (27). And yet, this type of modeling exercise must
in the final analysis be concerned with changes. Most professional
(27) Recent work by Norawetz (1977) illustrates this phenomenon. Morawetz
presents results for a large number of regressions relating indices of
basic needs fulfillment to levels of per capita GNP. For 30 of 32
regressions run using levels for 1960 and 1970, a statistically
significant relationship is evident. When changes (1960-1970) in basic
needs indicators are regressed on changes in per capita GNP, however, only
5 of 16 regressions exhibit a significant relationship.



page 75
economists are unlikely to be persuaded by cross-section regressions
estimated on levels alone.
It is precisely this necessary juxtaposition of simultaneity in
modeling and time-changes in the data which makes the econometric problem
so difficult in the present context. At the very least, for example, an
appropriate growth model should be explicitly simultaneous in changes in
output, nutrition, and education. Such a model would include indices for
these three endogenous variables, as well as a relatively large set of
predetermined variables. If all the data for all of the variables in
question were available, there would be no problem. Unbiased, efficient
estimates for the parameters of simultaneous equations can be obtained
with the aid of systems estimation techniques such as three-stage least
squares (28). Tlnfortunately, the spottiness of the data presents a severe
problem.
,he available Porld Bank data for 88 countries are focused on
measured levels of various socio-economic indices at three points in time:
1960, 1970, and "the mid-70's" (1974 through 1977 in various individual
cases). "he most recent data are fairly plentiful, but there are still
many gaps in the full 88-country matrix for the mid-1970's. As the data
move back in time, they get spottier. The result is that measurable
changes in key indices are rarer than corresponding levels. In a
simultaneous model, many of the crucial changes must be taken from the
same set of countries. Only the intersection of available measures
counts. The size of this intersection diminishes steadily as the number
of simultaneously-measured changes mounts, and the result can be
disastrous for system-modeling techniques such as three-stage least
(28) The classic discussions of three-stage least squares estimation can
be found in Zellner and Theil (1962) and Madansky (1964).



page 76
squares.
mlhus, reality once again presents the econometrician with a
situation which has not been anticipated in the textbooks. The need for a
simultaneous model and the need to measure model variables in changes are
-in clear conflict with one another here. For equations which are not
explicitly part of the simultaneous system, simple linear equation
techniques will suffice, and each equation can be fitted using the data
which are needed only for it. To the extent that simultaneity is
abandoned, degrees of freedom in estimation will be maximized for
individual equations in the model. At the.same time, the artificial
decoupling of truly simultaneous relations will result in inconsistent
parameter estimates in the equations in question. Since the spottiness of
the data cannot be remedied, this problem cannot be avoided. Some
compromise has therefore been unavoidable in model specification.
2) leasurement Problems
-he data for this study have been drawn from 88 poor countries in
Africa, Asia, Southern America, and Southern Europe. In most cases, the
variables employed for estimation can only be defended as the best
available. -he input and output measures in the three human resource
response equations are all national averages, so that substantial
differences in distribution are masked by the data. This problem is apt
to be more severe for the measurement of availability of medical personnel
than for the other indices. Aggregative measures of population per doctor
say nothing about differences in the length or efficacy of training
programs or the geographical distribution of medical personnel within
countries. thus, this measure is not very satisfactory as an index of
generalized access to medical care.



page 77
"he measures of nutrition and education, on the other hand, may not
be too had. As a measure of nutritional status per capita calorie
availability is a reasonable approximation. It is now generally accepted
that calorie sufficiency is much more likely to indicate nutritional
adequacy than any other index. At the same time, available microeconomic
studies always show a rapid drop in the income elasticity of calorie
consumption across income classes within countries, so that it is
reasonable to link expansion in calorie consumption with increases in the
nutritional status of the poor as per capita income rises (29). Among
measures of the change in embodied basic education, the shange in the
adult literacy rate is undoubtedly the best available index.
",he conventional economic indices in the study are subject to many
of the usual strengths and weaknesses. The measured change in gross
domestic product seems acceptable, aside from the usual index number
problems. similarly, the change in total population presents no
particular problem. 11he way in which <dk> and <dl> are employed in the
simple production model is unfortunately much less satisfactory. The use
of percent changes in capital and labor in a production model incorporates
the assumption of constant utilization of the available services. This is
obviously wrong (and particularly so for labor in poor countries), but
nothing can be done about it because reliable information on capacity
utilization rates and unemployment rates for these countries simply does
not exist.
In addition, the available labor force data seem to be very
unreliable. As a result, the growth rate in the labor force in this report
is indexed by the growth rate in the adult population. Although admittedly
(29) Complete discussions of these and related issues can be found in
Peutlinger and Selowsky (1975).



page 78
crude, this index at least is based on data which have been gathered with
relative accuracy. Tt would be difficult to argue that it does not
capture the dominating age cohort effect in labor force growth. At the
same time, the use of percent changes in the model makes the implicit
exclusion of the labor force participation rate much less damaging, since
it is likely to remain relatively constant over short periods and
therefore washes out of a percent change measure.
An additional complication is introduced by the complete -
non-availability of reliable and comparable capital stock figures for
these countries, so that it is impossible to obtain direct measures of
percent changes for the period 1970-1977. Available data on yearly
investment and output do allow for estimation under the assumption
(admittedly heroic) that the    general capital-output ratio for the
countries in question did not change significantly during the estimation
periods. Some manipulation of the production model yiells:
[dQ/dt]/Q(o) = [dA/dt]/{[oJ + g1*[ Q(o fIK (o) ]*[ (dwdt)/Q[o) ]
+ g12*[dL'/dt ]/L' (o]
or
(2)  <dq> = <dA> + gll*[(Q/K)*<dk>] + gl2*<dl'>
where
Q = Output
A = An appropriate index of technical progress
K = Capital
I = Labor
<dq>,<dk>= As previously defined
<dA> = Percent change in technical progress index
<dl'> = Percent change in effective (augmented) labor
{o) = Initial period
Since we can observe [(dK/dt)/Q[o) , estimation with some unknown
degree of bias is possible. It is comforting to note that the mean



page 79
capital output ratio must be somewhere in the range (2-5) and the combined
output elasticities for capital and effective labor can be somewhat
greater than one at most, so the econometric results must conform to
certain obvious restrictions.
3) output nodeling in a Simultaneous Context
In modeling the production process, it is necessary to give
simultaneous attention to the roles of factor-augmenting inputs and to the
roles of effective capital and labor in determining output. In the
determination of effective labor, the contribution of nutrition is assumed
to be characterized by unitary elasticity of substitution. The
contribution of education, on the other hand, is specified log-linearly.
The partial equation for augmented labor is as follows (30).
(3)  L'{ t) = L{t) * (N (t **b1) * exp (E (t) *b2)
where L = Labor
L' = Augmented Labor
N = An appropriate measure of nutrition per worker
E = An appropriate measure of basic education
per worker
{t} = Time subscript
Two alternative specifications of the production function have been
(30) The symbol ** denotes exponentiation in this report.



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considered:
(4a) Augmented CES:
Q{tt  = Aft) * [a*(Ktt)**p) + (1-a)*(LI (t)**p) ]**(1p)
where A = An index of technical progress
K = Capital
a,p = CES parameters
Q = Output
(t4b) Augmented Cobb-Douglas:
Q It) = A t] *(K (t) **g1) * (1I (t) **g2)
Empirical testing has yielded the conclusion that (4a) is not
significantly better than (4b) as a representation of production in this
case. t"hus, production is assumed to exhibit the following behavior
throughout:
(5) Q[t) = Alt) * (Kft1**g1)
*  [   t} *(N ft)**b1) * exp(E{t}*b2) ]**g2
Fere gl and g2 can be interpreted as the output elasticities of capital
and effective labor, while the b's are labor-augmenting parameters for
nutrition and education.
Equation (5) would be appropriate for estimation if time series for a
single country were being considered. In this case, however, only two
primary observations (for 1970 and the mid-'70's) are available for each



page 81
country in the sample, along with one additional set of past observations
(for 1960).  The model must therefore be specified to reflect the
consequences of single-period changes across countries. The time
derivative of (5) is used as the production eguation.
(6) <dq> = <dA> + gl*<dk> + g2*<dl> + g2*bl*<dn> + g2*b2*<de>
where <dx> = [dXtt)/dt]/X[t)
"his equation is linear in percent changes, with the exception of the
literacy component (which is linear in changes). For compatibility,
id.entical change specifications have been imposed on the social indicator
equations (31). The health and nutrition equations are relatively
self-explanatory. Since the literacy equation has been specified
appropriately in absolute changes, however, it requires a little more
attention. The functional form employed here follows directly from an
explicit specification of the process of "literacy produztion."
"'he variable which is basically of interest in this context is the
number of literate adult labor force members. Some of these adults may
well educate themselves, and we would expect the demand for self-education
(or for commercial forms of adult instruction) to be positively related to
per capita income. For the vast majority of adults, however, literacy
will have come about as a result of primary schooling.
For two time periods ([t) and (t-1)), then, we can model the
(31) It should be noted that although factors have been identified as
capital- or labor-augmenting in the discussion of specification, they are
indistinguishable from "neutral" sources of technical change in the
Cobb-Douglas specification.



page 82
increase in the number of literate adults as:
(7) J.AD{t} - LAD [t-1} = Pr (E) *S*[ AD Eti - AD{t-11]
where
LAD = Number of Literate adults
AD = Number of Adults
S = Primary school enrollment ratio
during the period when the adult age
cohort received primary schooling
Pr(E) = Probability that some experience of
schooling results in literacy
Fe know that the adult literacy rate is equal to the ratio (LAD/AD). Some
mathematical manipulation therefore gives us the following relationship:
(8) N,t3 - Ett-1)*[1/(1+<da>) = Pr(E)*S*[<da>/(l+<da>)]
where
E = The adult literacy rate
<da> = Percent change in the adult population
from {t-1} to t



page 83
APPENDIX B
LITERACY AND PRODUCTIVITY: A TWO-EQUATION MODEL
'The response equations estimated for this report have all
incorporated the change in calories consumed as a conplement to literacy
change in the determination of intraperiod output change. As noted in
Chapter 'I, the nutrition results are rendered ambiguous by the
possibility that they measure the efficiency impact of differential
agricultural growth as well as the impact of nutritional improvement.
One possible response to this ambiguity could be an arbitrary
rejection of the calorie consumption measure as a valid component of the
output equation. If nutrition were excluded, the resulting growth model
would identify basic education as the only contributor to productivity
growth. Tn the following Figure, results for an education-augmenting
growth model are presented. Although only the output equation results are
presented, all three-stage estimates have been produced in association
with a literacy change equation identical to the one employed previously.
It is clear that the exclusion of nutrition change from the output
equation has no real consequence for the remaining estimates. Again, the
estimated effect of literacy change in the output equation exhibits an
apparent decline between the first and second decades. Although the 95
percent confidence intervals for the two estimates overlap slightly, it
may well be that the impact of reported literacy change has declined.
It is not clear, of course, that the true impact of literacy has
declined. During the decade of the seventies, a general enthusiasm for
rapid human resource development may have led to widespread optimism in
national self-evaluation of educational performance. As previously



page 84
mentioned, -anzania and Somalia have been excluded from all estimates
because the reported impacts of their adult literacy campaigns seem
neither plausible nor appropriate as measures of the kind of educational
achievement which is of interest here. In any case, the results in all
three sets of estimates are again consistent with the hypothesis that
basic education has a significant impact on productivity.



page 85
Figure 15
LITERACY AND PRODUCTIVITY CHANGE:
A TrO-EQUATION MODEL (*)
1960-1970 (**)
N    R**2
<dq> = .0147 + .161*<dk> + .222*<dl> + .0254*[[(t)-E(t-1j]               40    .37
(.1278) (.030)       (.341)      (.0055)
1970-1977
<dq> = -.0855 + .187*<dk> + .498*<dl> + .0080*[E(t)-E(t-1)]              44    .47
(.0798) (.037)       (.342)      (.0041)
Pooled Data
<dq> = [.006 - .069*D70] + .168*<dk> + .346*<dl> + .018*[E(t)-E(t-1)] 82       .54
(.087) (.044)       (.022)      (.237)       (.0041)
(*) Standard errors in parentheses beneath coefficients
(*) Erach of the three equations presented below has been estimated by
three-stage least squares along with the literacy change equation whose
specification has been seen several times. Since the results for the second
equations are essentially identical with those for previous models, they have
not been included here.



I
I



page 87
APPENDIX C
AGE COHORTS IN DEMOGRAPHIC CHANGE EQUATIONS
In the discussion of fertility and death rate determination which absorbed
Chapter ITT of this report, a relatively simple model of age-cohort impact was
specified and estimated. Although mention was made of more intricate models, a
full discussion was deferred to this Appendix in the interest of readability.
At first, it may seem illusory to suppose that the differential impacts of
causal variables across age cohorts can be estimated without cohort-specific
data. While it is true that the absence of such data prevents the specification
and estimation of completely general models, it is certainly possible to use the
available numbers to good effect. The key to this possibility lies in the fact
that the total fertility rate and the crude death rate are weighted averages of
age-specific rates. A brief mathematical development can be used to show that
zohort-specific sensitivities can be measured once a model of responsiveness has
been imposed. Although either accumulation parameter could be employed for the
demonstration, the. fertility rate will be used here.
Fe will define the total fertility rate as:
(9) F = (VI/W)*fl + (W2/W)*f2 + ... + (Wn/W)*fn
where
F = Total fertility rate
Fk= Number of women in fertile age cohort k
N = Total women of child-bearing age
fk = Fertility rate of women in age cohort k
Fe are in possession of crude birth rates from world Bank data and age
cohort estimates from United Nations data, but we lack cohort-specific fertility
rates. This sort of problem is not uncommon in econometrics. The standard



page 88
response is to replace the unknown with its known determinants in a
mathematically-specified relationship whose parameters can be estimated.
In order to develop some plausible fertility determination models, we will
suppose initially that fertility in each age cohort responds to one variable, X.
In addition, we will lend flexibility to the model by supposing that the
marginal effect of X differs across cohorts. Thus, for the kth cohort, we would
have a simple linear model of fertility determination:
(10) fk = akl + ak2 * X + uk
where uk is a random, additive error term and
the ak's are parameters
If we substitute into the expression for the total fertility rate, we
obtain:
(11)      (TTl/F)*[a1l + a12*X + ul] + (W2/W)*[a21 + a22*X + u2]
+ ... + (Wn/W)*[anl + an2*X + un]
= all*(W1/W) + a12*(W1l/T)*X + a21*(W2/W) + a22*(W2/W)*X
+ ... + anl*(Vn/V) + an2*(Wn/W)*X
+ [ul*(W1/7) + ... + un*(Wn/W)]
Since it is clear that W = R1 + ... + Wn, the above reduces to:
(12) F = (all-an1)*(W1/W) + (a12-an2)*(W1/W)*X
+ (a21-anl)*(W2IW) + (a22-an2)*(W2/W)X + .
+ anl.+ an2*X + e
where e = the additive sum of weighted error terms
previously specified
An unconstrained linear model which allows X to have a differential impact



page 89
across age cohorts will be specified as (12) above. This model can usefully be
contrasted with a simpler version, which constrains all marginal impacts of X to
be equal:
(13a) a12 = a22 = ... = an2
All difference coefficients of X-terms in the former equation become zero
in this constrained specification, and we have:
(13b) v = (all-an1)*(W1/W) + (a21-anl)*(W2/W) +
+ anl + an2*X + e
"'he constrained and unconstrained versions of the linear model can be
compared statistically. Fith multiple age cohorts and several causal variables,
it is clear that the number of right-hand terms in the unconstrained version of
this model is likely to be burdensome. A statistical test on the multiple
coefficient constraints implied by the simple version of the model is therefore
appealing. If the simple linear model cannot be rejected statistically, we are
bound to gain precision in estimation by adopting it.
-he two models of cohort-specific determination proposed thus far
incorporate assumptions about responsiveness which are at opposite extremes. In
the unconstrained version, estimated marginal impacts are left completely free
to vary as the data dictate. In the constrained version, they are all forced to
equality. It is also possible to specify an intermediate alternative which
accords some flexibility to coefficient estimates without sacrificing degrees of
freedom. Instead of constraining all marginal coefficients to be equal, this
intermediate form imposes a constant multiplicative relationship across cohorts.
"'hus:



page 90
(14) F = (V1/F)*f1 + (V2/W)*f2 + ... + (Wn/W)*fn
= (W1/T7)*f1 + (W2/7)*c2*f1 + .. + (Un/W)*cn*fl
where the c's are taken to be
unvarying multiplicative constants
Pith age cohort relationships specified in stochastic form as before (and
noting that the female age cohort ratios sum ta 1), we have:
(15) F =   (l/F)*tal1 +al2*!] + ... + (Vn/F)*cn*[al1 + a12*X] + e
= [cn + (1-cn)*(W1/W) + (c2-cn)*(W2/W) +        * [a11 + a12*X1
+ e
This intermediate model is nonlinear in the parameters, but it can be estimated
using maximum likelihood methods.
Some Comparative Estimates
The discussion in the first part of this Appendix was focused on the
problem of estimating differential marginal impacts across age cohort groups for
fertility rates. It is clear that exactly the same reasoning could be applied
to the design of cohort-sensitive death rate models. In this section, the
models developed previously will be compared statistically for fertility rates
and aeath rates, using cross-section data for 1977. In each case, the variables
employed are those which are already familiar from the difference equations
presented in Chapter III.
Fertility Estimates
In the fertility equations, the total fertility rate (F) across countries



page 91
is related to data on family planning activity.(PL), the crude death rate (D),
per capita income (Q/P), and three age cohorts for childbearing females
(T1524,72534,W3549).   Since the three age cohort percentages sum to one, W3549
has been selected as the residual percentage.
All three models developed in the previous section have been estimated
using the same data. The results are presented in the following Figure:



page 92
Figure 16
COMPARATIVE RESULTS - FERTILITY EQUATIONS (*)
Linear Unconstrained Model
F = -942.688 - 8.2886*PL - 4.9425*D + 2.2174*D**2 + .83249*(Q/P)
(1833.27)(25.0729)    (221.7)     (7.20)         (.8099)
+ 2192.44*W1524 + 8.9219*PL*W1524 - 57.985*D*W1524 - .3824*D**2*W1524
(2397.65)          (32.62)          (270.2)             (8.34)
- 1.5604*(Q/P)*N1524 + 227.466*W2534 + 9.6382*PL*W2534 + 159.22*D*R2534
(1.369)               (4060.1)        (55.18)             (497.8)
- 8.501*D**2*72534 - .6227*(Q/P)*W2534
(16.40)             (1.162)
E = 65   R**2 = .85    SSR = 13613.2   F(14/50) = 26.1
Constrained Linear nodel
F = -560.866 + 982.780*W1524 + 706.839*W2534 - 1.7762*PL
(108.718) (131.328)        (217.582)          (.4713)
+ 15.9139*D - .3897*D**2 - .01402*(Q/P)
(3. 017)   (.0919)       (. 0114)
N = 65   R**2 = .86    SSR = 14431.7   F(6/58) = 66.1
Nonlinear Model
F = [ -1.520 + 3.555*W1524 + 2.576*W2534 ]
(.597)  (1.212)        (1.212)
* t 98.312 - 2.4192*PL + 19.963*D - .4824*D**2 - .0216*(Q/P) ]
(.7322)  (.6268)       (10.418)  (.2723)        (.0134)
N = 65   R**2 = .84    SSR = 15857.8
(*) Standard errors in parentheses beneath coefficients



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The results in Figure 16 indicate that the more complex models do
not make a significant marginal contribution to the explanation of
fertility rate differentials. The unconstrained linear model is obviously
plagued by multicollinearity, and individual estimates seem to wander
randomly. An application of the standard F-test yields the conclusion
that the full set of constraints implied by the hypothesis of equal
marginal impacts cannot be rejected (The small increase in the sum of
squared residuals makes this an obvious result). At the same time, all
available measures of goodness of fit (R**2, SSR) suggest that the
constrained linear model fits better than,its nonlinear counterpart.
Certainly, the experiments undertaken here do not exhaust the
econometric possibilities which could be considered if actual
cohort-specific fertility data were available. In the absence of such
data, it has still been possible to compare three different models of
responsiveness. -he statistical evidence points toward the provisional
acceptance of the simplest model, which imposes equal marginal impacts of
causal variables on cohort-specific fertility rates. It should be noted
that the results still suggest constant cohort-specific differences.
Death Rate Estimates
""he crude death rate and the total fertility rate for a population
are similar in the sense that both are weighted averages of
cohort-specific rates. Thus, the theoretical development of three
comparative models of fertility rate determination can be essentially
replicated in the case of the death rate. Again, cross-section data for
1977 have been employed in the comparative analysis. The regression
equations have been fitted using the variables which proved to have a
significant association with death rate changes in a cross section of time



page 94
differences. The results are presented in the following Figure.
Figure 17
COMPARATIVE RESULTS - DEATH RATE EQUATIONS (*)
linear Unconstrained Model
D = -16.692 + 6.782E-4*M + 53.512*Y - 7.99E-4*Y*M + 46.735*0 - .0010*0*$
(14. 159) (.0015)      (24.84)    (.0027)         (32.85)    (.0029)
I = 68   R**2 = .56    SSR = 805.8   F(5/62) = 18.0
Linear Constrained Model
D = -14.085 + 2.203E-4*1 + 49.009*Y + 40.624*0
t11.736) (2.670*E-5)   (20.583)   (27.240)
N = 68   P**2 = .57    SSR = 807.4   F(3/64) = 30.8
Nonlinear Model
D = [-1.0184 + 3.9832*Y + 3.1664*0] * [10.9809 + .00021*M]
(.81-4)   (1.244)     (1.803)      (1.085)   (3.72E-5)
N = 68   R**2 = .56    SSR = 810.7
(*) Standard errors in parentheses beneath coefficients



page 95
Once again, the evidence suggests provisional acceptance of the
constrained linear model.   The F-test on the multiple coefficient
constraints fails resounding to reject the hypothesis of equal marginal
impacts. At the same time, the nonlinear fixed-ratio alternative seems
inferior by the standard measures of goodness-of-fit. On the basis of the
evidence currently available, it seems appropriate to conclude that
cohort-specific death rates across countries differ significantly only by
a constant term. The hypothesis that medical personnel affect all cohorts
equally at the margin certainly cannot be rejected at any reasonable level
of statistical confidence.



page 96
APPENDIX D
AGE AT MARRIAGE AND FERTILITY:
SOME CROSS-SECTION RESULTS
At the present time, data on age at marriage across countries are
quite scarce (32). Since this study focuses on changes cather than
levels, the scarcity problem is compounded. It has not been possible to
incorporate age at marriage into the fertility change equation without
reducing degrees of freedom to absurdly low levels. Rowever, the possible
effect of this variable on fertility has been considered sufficiently
important to warrant an independent look in cross-section. The following
Figure reports a set of regression results which have been used to
evaluate the apparent impact of age at marriage. Again, the particular
nature of the Mauldin-Berelson index has allowed data pooling only for the
years 1960 and 1977. In all regression equations, the constrained linear
specification of age cohort impact has been employed.
(32) The data on singulate age at marriage used for econometric work in
this report have been supplied by the World Bank.



page 97
Figure 18
CROSS-SECTION RESULTS:
SIFGUT.ATE AGE AT MARRIAGE, HUMAN RESOURCE VARIABLES,
AND FERTILITY RATE DIFFERENTIALS (*)
(Pooled Data, 1960 and 1977)
N    R**2
F = -941.83 + 525.407*W1524 + 1083.72*W2534                              40   .66
(245.58) (153.37)          (298.51)
+ 69.1413*SAM - 1.93422*SAM**2
(22.549)         (.571)
F = -629.80 + 588.41*W1524 + 732.64*W2534                                40   .74
(230.85) (1314.35)       (277.63)
- 3.079*PLAN + 44.012*SAli - 1.249*SAM**2
(.873)      (20.833)        (.532)
F = -648.51 + 476.11*W1524 + 689.22*f2534                                40   .76
(221.98) (138.00)         (267.16)
- 2.4274*PLAN + 26.710*SAM - .767*SAM**2 + 9.761*8 - .102*H**2
(.892)       (22.51)        (.569)          (5.740)    (.054)
(Including Oil-Producers) (**)
= -593.21 + 366.76*W1524 + 525.26*W2534 - 2.613*PLAN                     44   .80
(1P9.03) (123.78)        (235.51)       (.775)
+ 12.447*SAM - .351*SAM**2 + 16.145*H - .157*H**2 - .525*E
(20.643)      (.528)           (5.580)    (.052)       (.226)
SAI = 8.756 + .210*H + .011*E                                            45   .641
(1.298) (.025)    (.008)
Variables Not Formerly Defined
SAM = Singulate Age at Marriage
(*) Standard errors in parentheses beneath coefficients
(**) For the sake of consistency, all econometric work for this study has
avoided the use of the major oil-producing countries. With both literacy and
SAM in the same equation, however, degrees of freedom are at a premium.     In this
case, an exception to the general rule seems warranted.



page 98
Tt is apparent from the first set of regression results that
singulate age at marriage (SAM) has a strong effect on the total fertility
rate when it is used along with age cohorts in a simple equation.
Inspection of the scatter associating SAM with fertility makes it clear
that the marginal impact rises at higher marriage ages. An exponential
term has been employed to capture the impact of this increasing negative
association. ¶hen the lauldin-Berelson index is added to the equation,
the SAn terms are still highly significant by the classical criteria.
these two variables alone appear to account for much of the observed
variation in the total fertility rate across countries.
It is not sufficient, of course, to introduce only SAM and the
planning index into the cross-section equation. In Chapter III, a major
role in fertility changes was discerned for changes in infant life
chances. Unfortunately, the introduction of life chances into the
fertility equation leads to a fundamental ambiguity in measuring the
impact of age at marriage. As previously noted, the crude death rate and
life expectancy are essentially dual measures which can be used
interchangeably in the fertility rate equation. However, there is also
good reason to suppose that life expectancy is an important determinant of
age at marriage.
It is quite plausible to suppose that people will zhoose to marry
later if they can expect to live longer. The reasoning underlying this
hypothesis resembles the life-cycle interpretation of consumption and
savings behavior. The experience of more advanced economies suggests a
significant tendency to defer marriage for investment in education,
coupled with an apparent desire to postpone family responsibilities until
later in life. -he last regression equation, which attempts to account for
variations in age at marriage, is resoundingly consistent with this
hypothesis. The estimated coefficient for life expectancy suggests a high



page 99
degree of responsiveness, and the confidence bound around the estimate is
obviously quite narrow. Since it was supposed that education might play a''
role which could be distinguished from that of life expectancy, literacy
was also included as an explanatory variable. The literacy result is
considerably weaker, although the suggested level of responsiveness is
again fairly high. ?hen per capita income is considered along with
literacy and life expectancy, it explains no additional variance in age at
marriage. Both literacy and life expectancy, on the other hand, retain
the approximate levels of association suggested by the two-variable
regression result.
Obviously, the pattern of association suggested by the SA!
regression implies a serious multicollinearity problem in the fertility
regressions. The last two fertility equations confirm the existence of
this problem. When life expectancy and literacy are included with SAM in
the fertility equation, the apparent contribution of SAM becomes
negligible.  Two alternative explanations for this result are plausible.
it might be argued that literacy and life expectancy are the two
systematic determinants of age at marriage, so that nothing but a random
relationship could be expected between fertility and the residual
component of SATT (that is, the part which is not collinear with the
combined effect of literacy and life expectancy). On the other hand, it
might be argued that life expectancy is the dual of the death rate and
that the apparent impact of literacy on fertility operates directly
through attitudinal change (As we have seen, this apparent impact of
literacy does not hold up in the more demanding fertility change
specification). If this viewpoint were adopted, then the evidence would
be consistent with the hypothesis that age at marriage has no impact on
fertility.
In the final analysis, this second viewpoint seems unreasonable.



page 100
Both casual observation and common sense suggest that people who marry
later do have fewer children, on average. Even if a role for SAM is
accepted, however, the available evidence suggests that it can be
identified only to the extent that age at marriage operates as an
intermediary for the effects of life expectancy (primarily) and education
(possibly).



page 101
APPENDIX E
SIMULATION
1) A Perspective on Simulation l9odeling
In policy research, a simulation model generally serves three main
purposes: It forces the analyst to think comprehensively; it enforces
consistency; and it facilitates detailed intellectual experiments with
public policy instruments. In the initial phase of a project, it forces
the researcher to consider carefully which features of a particular system
seem to be understood and which require further study before the total
behavior of the system can be explained. It is an unfortunate tendency of
the human imagination to leave difficult issues in the realm of the
implicit whenever possible. Then the growth process, for example, is
studied in partial academic exercises, the researcher can focus on a few
aspects and ignore the degree to which the results are sensible when
viewed from the perspective of the whole system.
rhen a simulation model is being designed, this luxury is no longer
available. "he full set of relations among endogenous and predetermined
variables must be worked out. If the model is to have any credibility at
all, all of the hypothesized relations must be estimated econometrically
under conditions in which the standard strictures dictated by statistical
theory are respected.
Once the equations of a simulation model have been estimated and
fitted together, the second major role of simulation comes into play. No
matter how rigorous and comprehensive the intellect of the analyst, any
first attempt to design equations which explain the operation of a
particular system will suffer from conceptual errors. Most of these will



page 102
be due to the fact that the mind is best suited for the consideration of
problems in partial form. In considering the aggregate implication of an
assembled set of partial views, the computer-driven simulation model is a
singularly unforgiving associate. Inconsistent reasoning and incompatible
specification of different relations in the model are quickly exposed,
since attempted simulation exercises yield absurd results. St is in the
tracking down of these absurdities and subsequent reconsideration of
partial relations from a systemic perspective that the utility of the
simulation model as an intellectual tool becomes most apparent.
Finally, once both of the preceding steps have been completed
successfully, the simulation model can be employed for policy experiments.
Since the computer does most of the work in this stage, it is in most
respects the easiest and most enjoyable part of the process. At this point
the full implications of the modeling exercise become clear. Generally,
policy simulation models are designed under the assumption that public
policy instruments are exogenous to the system being considered. This
specification leaves the analyst free to examine the hypothetical
evolution of the system under alternative assumptions concerning the time
paths of the policy variables. At this stage, attention usually focuses
on "sensitivity analysis," in which one policy instrument is changed while
the others are held constant.
Implicitly, sensitivity analysis is a form of cost-benefit analysis.
Policy research is usually undertaken because public administrators are
interested in effective approaches to the governance of systems in
environments where several competing goals are valued and resources are
limited. One important notion underlying the design and use of dynamic
simulation models is that complex, interactive systems have behavior
patterns characterized by marked nonlinearities and discontinuities. If
this is the case, then all cost-equivalent policy packages are very



page 103
unlikely to have the same consequences for the attainment of valued goals.
It is easy to see that some approaches will be superior to others if they
give relative weight to outcomes which have relative priority in the minds
of administrators. Fhat may be less immediately obvious is that in highly
nonlinear systems some cost-equivalent policy approaches can dominate
others absolutely (that is, they can yield superior results along all of
the valued dimensions).
It is this latter possibility which is undoubtedly the ultimate
source of the evident allure of simulation models. Unfortunately, too
much can be made of this. It is all too easy for public administrators to
throw up their hands in the face of daily pressures and leave the design
and interpretation of models of the complex systems which they must
confront to the "experts." "his "black box" syndrome has become quite
common, and it can be the only possible explanation for the widespread
acclamation and acceptance given to the conclusions of such
evidently-flawed models as the Urban Dynamics and World Dynamics systems
used by the Systems Dynamics Group at MIT to justify sweeping conclusions
concerning problems as diverse as urban renewal and the philosophy of
limited growth for the world as a whole (33).
In fact, simulation models can only be valuable to the extent that
they are not "black boxes." "Counterintuitive" results are useful results
only if they can be shown to be intuitive once the structure of the system
is clearly seen. In order for this to be possible, over-complexity in the
(33) -his group has been the source of such notable recent exercises as
Urban Dynamics, by Jay Forrester, and The Limits to Growth, by Dennis
neadows, et. al. Anyone who thinks that these models truly produce
"answers" to the world's problems has only to examine them closely.
Unfortunately, their equation systems are lengthy if not particularly
complex, and few have taken the trouble. Such exercises are frequently
ballyhooe.d as yielding "counterintuitive" results, but this always turns
out to be far from the case if the time is simply taken to consider the
equation systems closely.



page 104
design of model equation systems is best avoided. The true value of
simulation exercises lies in their ability to test the internal
consistency of a set of ideas about a particular process. If
seemingly-plausible sets of estimated relations yield peculiar results
when they are fitted together into a model, then two conclusions are
possible: First, the thinking of the researcher may suffer from some
important inconsistency which must be corrected. Secondly, it may be that
the peculiar results are themselves reasonable when the behavior of the
entire system is considered.
In either case, it is obvious that no conclusions can be drawn from
simulation exercises if the equations on which they are based are too
complex to be sorted out retrospectively. In a good simulation model, the
source of any peculiar results can be traced down and analyzed. At this
level, the model becomes tremendously valuable as an aid to learning
because it uses the speed of the computer to augment the analytical
capabilities of the policy analyst. Hopefully, however, this argument
will help to persuade the reader that any simulation experiment should be
considered carefully in the context of model design and the potential role
of factors which have been excluded from the model altogether.
2) Simulation flodel Equations and Solution Techniques
'n the simulation model equations the symbols are precisely those
which have been employed in the estimation section, so that redefinition
does not seem to be necessary. Wherever possible, the estimation results
reported in Chapters II and III have been transfered exactly into the
simulation. Some adjustments have been necessary for the completion of
the model, however. Most of these are designed to compensate for the fact
that the "period" used for modeling here is 7 years. Thus, the projected



page 105
capital growth variable is produced by multiplying the anticipated yearly
investment rate by 7 (recall that the capital growth measure in the fitted
output equation is defined as (capital change)/(initial output), so that
the simulation equation is tailored to the econometric approach).
resides the adjustment for 7-year periods and some necessary
divisions by 100 or 1000 to produce appropriately scaled rates, the
equations are either definitions, year-to-year adjustments of initial
conditions, or directly transcribed econometric results. Three
improvisations have been necessary for the replication of "normal"
performance in schooling and family planning over long simulation runs.
Fquations 2 (primary schooling) and 3 (population per doctor) have been
generated by asymptotic regression models fitted to cross-country data for
1977. For the prediction of "normal" progress in secondary schooling, a
log-linear model has been fitted to 1977 cross-section data to produce
simulation equation 31.



page 106
Figure 19
SIMULATION MODEL EQUATIONS
(1) Q/P   Q/P(-1) * (1 + DQ-1) - DP(-1))
(2) S = 102.53 - 3030.69/(Q/P)
(3) 1. =-346.02+1885320/(Q/P)
(4) PM1   1 - D(-l)/1000
(5) PM2 = (1 - D(-1)/1000)**7
(6) P1' = P(-1) * 1l(-1)/1000 * (1 + PM1 + PM1**2 + PM1**3 + PM1**4 + PN1**5
+ PlTl**6)
(7) P814 = °17(-1) * PM2
(8) P1521 = P814(-1) * PM2
(9) P2228 = P1521(-1) $ PM2
(10) P2935 = P2228(-1) * PM2
(11) P3642 = P2935(-1) * P112
(12) P4349 = P3642(-1) * PM2
(13) P5056 = P4349(-1) * PM2
(14) P5763 = P5056(-l) * PM2
(15) P6470 = PS763(-1) * PM2
(16) P7177 = P6470(-1) * PM2
(17) P = P17 + P814 + P1521 + P2228 + P2935 . P3642 + P4349 * P5056 * P5763
+ P6470 + P7177
(18) Y = (P17 + P814)/P
(19) 0 = (P5056 + P5763 + P6470 + P7177)/P
(20) PFT = .5 * (P1521 + P2228 + P2935 + P3642 + P4349)
(21) PW2534 = .5 * (4/7*P2228 + 6/7*P2935) / PWT
(22) DP = (P - P(-1))/P(-1)
(23) A = P - P17 - P814
('4) DA = (A - A(-1))/A(-1)



page 107
(25) D = 6.1121 + .01746*D(-1)**2 + 2.6041E-5*M(-2) + 18.8983*(Y-Y(-2))
+ 20.2856*(O-D(-2))
(26) DFP = 187.338*(PV2534 - PW2534(-2)) + 9.63614*(D-D(-2))
- .2470*(D**2 - D(-2)**2) - 15.4159*[Q/P - Q/P(-2)]/QfP(-2)
- 1.3122*PL
(?7) PPL = PPL(-1) + PL(-1)
(?8) PL = IF PPL GE 30 TREN 0 ELSE .3245*SEC(-2) - .1218*DFR
(29) FR = FPE(-2) + DFR
(30) E = FE * (P¶T/P)
(31) SEC = PXP(-2.4124)*(Q/P)**.9348
(32) N = N(-1) * (1+DN(-1))
(33) LN = LOG (N)
(34) E = SE(-1)
(3 ) H =   (-1) * (1 + DH(-1))
(36) IR = LOG(H)
(3') I = 11.0502 + .2158*I(-2) + 5.3056*[Q/P - Q/P(-2)]/Q,P(-2)]
+ 3.1372*[E - E(-2) ]/I(-2)
(38) DL = DA
(39) DR = 7 * I
(40) DQ = .012 + .146*DK + .565*DL + 1.011*DN + .0096*(SE - E)
(41) DF = -.04 + (3.25? - .674t*LN)*(DQ - DP) + .042*LOG[(QfP)/N]
(42) SE = E*[1/(1+DA) ] -.996 + .755*[S(-1) + S(-2) ]/2*[DA/(1+DA)]
+ 12.291*(DQ - DP)
(43) DR = -.124 + 6.948*1/H + .142*DH(-1) + (.573-.144*LH)*(DQ - DP)
+ .077*DN(-1) + .027*E/H + 1.10E-5*M/H + .01*S/H



page 108
-he simulation model reflects the dynamic, block-recursive structure
of the original model. Thus, initial levels of accumulation parameters
join with exogenous and lagged endogenous variables to determine output
and human resource variable responses in each period. The induced changes
in the response variables in turn generate new accumulation parameter
levels.
Since the model is a combination of simultaneous and recursive
components, the simulation problem is not trivial. Fortunately, the work
for this project was done using the TROLL system at MIT. The simulation
routine in TPOLL automatically structures model equations into
simultaneous blocks and iterates to a convergent solution in each period
using a variant of the Gauss-Seidel method. Since all model equations are
inherently linear, no convergence problems were encountered in the
simulation exercises.



page 109
APPENDIX F
TFE CAICULATION OF EQUIVALENT PHYSICAL
AND HUMAN RESOURCE EXPENDITURES
In Chapter Is, the results of several trade-off experiments were
presented and discussed. Although reference was made to World Bank cost
estimates, detail was suppressed in the interest of readability. In this
Appendix, the estimates themselves will be considered. Pll of the
representative numbers have been drawn from Burki and Voorhoeve (1977), as
previously mentioned.
The methodology underlying the equivalent cost estimates in the
trade-off experiments is not at all elaborate. The criterion for judgment
has been "essential equivalence," given the approximate, aggregative
nature of the data. Across investment categories, only performance at a
considerably higher level should really be judged "superior" in any
meaningful sense. Even in the case of superior performance, the results
must be judged in the context of the simplifying assumptions which have
been made. Finally, as previously mentioned, judgments about relative
performance cannot escape value weightings. The responses of income and
the PQII variables differ by investment category, and the intertemporal
response paths vary as well, so that some discount rate (explicit or
implicit) is inevitable in the formation of final judgments.
necause of the relative simplicity of the calculations which have
been made for the trade-off exercises, it seems sufficient to explain the
methods employed in a general way. Once the methodology has been
presented, the numbers for specific regional cases will be presented in
tabular form.
The "foil" for comparison in these experiments is the 50-year



page 110
behavior of the baseline model for each regional case, under the
assumption that the investment rate is raised by one percent only for the
seven-year period from 1977 to 1984. The calculation of this increment is
perfectly straightforward. Given the measured national income and
investment rate in any particular year, the value of a one-percent
increment in the investment rate can be obtained by simple multiplication.
Fhile per capita income levels in this study have been measured in
1960 U.S. dollars, the world Bank cost estimates are denominated in 1975
U.S. dollars. Since the U.S. price index went up by somewhat more than 100
percent between 1960 and 1975, all cost estimates have simply been halved
to reflect 1960 equivalents. Given the index number problems which plague
this sort of calculation and a common preference for currency
overvaluation, this deflator may be quite conservative. Once the cost
corrections have been made, the generation of equivalent activity numbers
is quite simple. Since the assumptions underlying comparisons for
schooling and family planning are quite different, it undoubtedly makes
sense to discuss them separately.
In the case of schooling, the World Bank data are divided (by
region) into four cost categories -- teachers' salaries, materials,
administrative overhead, and capital costs. The appropriate unit for cost
measurement is a little difficult to define in this context, but the Bank
estimates are standardized per student-place. Since multiple-shifting is
quite common in schools, there can obviously be more students than
student-places in the system at any one time. Teachers' salaries are
calculated per 50 student-places; materials costs are simply set at 7
percent of salaries, and overhead is calculated as an additional 3 percent
of salaries. Separate figures for capital costs per student-place have
been included in the Bank estimates.
The need for rough comparability between the investment experiment



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and the re-allocation to schooling introduces a problem in the appropriate
treatment of capital cost in this context. Since the seven-year boost
should be regarded as a one-time increase for the sake of equivalence, it
does not seem appropriate to allocate all capital cost per new student to
the expansion. For simplicity, the following compromise has been adopted:
Only recurrent costs have been employed in the schooling calculations, but
student-places have been adopted as the basic unit for cost estimation.
The use of a conservative deflator along with student-places should
approximately balance the suppression of capital costs from the
calculation, since recurrent costs are heavily dominant in the
determination of total education costs and capital costs would have to be
spread over several student generations in a full intertemporal
calculation.
In the case of family planning, the determination of "essential
equivalence" has been even rougher. Although use has been made of the
lauldin-Berelson index of family planning activity in the econometric
work, no apparent basis exists for converting M-B scores into cost
estimates. For the present purposes, therefore, the opposite tack has
been taken. Under the assumption that family planning teams in rural
areas would be in many ways comparable to community health workers, the
Forld Rank cost estimates for health teams were used for the conversion of
investment values to team-equivalents. These team-equivalents were then
compared with the female population in fertile-age cohorts to determine
the capacity for coverage provided by such an expenditure. In no case was
the ratio higher than 200 females per three-person team -- seemingly quite
a modest ratio.
'ith these relatively low ratios in hand, I proceeled to the second
part of the family planning exercise. Some experimentation with the
simulation model by region was used to determine the minimum value of an



page 112
exogenous boost to the M-B index which would generate a final (50-year)
per capita income growth higher than that achieved by the investment
increment. In most cases, the requisite boost was only 2 (out of a total
possible t-B score of 30); in one case, it was 3.    My own conclusion is
that family planning investment at the margin is at least equivalent to
physical investment if long-run outcomes are most highly valued. In fact,
the awarding of an M-B score of only 2 to such a drastic expansion of
family planning personnel seems quite conservative.
Since the family planning experiment involved the prior calculation
of nearly-equivalent income outcomes, it may seem unnecessary to include
any simulation runs which can be compared with those for schooling and
investment. The family planning simulations do seem to be of interest,
however, for two reasons: First, they reveal the extent to which
"essential equivalence" in income outcomes is matched by relative
performance for the valued PQII variables. Secondly, they facilitate a
clearer perception of the different pattern of relative outcomes at
different points in time.
All relevant calculations are presented in the following Figure. In
the Schooling set, per capita income and population are combined to yield
total national income. one percent of this figure is taken as the
hypothetical investment increment. Total recurrent cost per student-place
is then calculated using the indicated estimates for teachers' salaries
and mark-ups for materials and overhead. Division of the increment by the
unit recurrent cost yields the number of new students supported by the
additional revenue (under the heroic assumption, of course, that no
constraint exists in teaching capacity). Finally, the new students can be
combined with total children in the primary-age population to produce the
one-period boost in the primary enrollment ratio. In two cases (South
America and typical), the resulting estimates are much greater than 1.00.



page 113
rumbers larger than one are quite common in LDC's, because older
uneducated children are attracted to primary schools as capacity expands.
"he basis for the family planning numbers in the following Figure
should be relatively clear. The indicated investment increment has simply
been divided by the cost per three-person team to yield the number of
team-equivalents. -his result is in turn divided into the number of
fertile-age females to produce a ratio of females to teams.



page 114
Figure 20
COnPARATIVE COST ESTIMATES - SIMULATION EXPERIMENTS
(1) Recurrent Education Cost Estimates
Region              Salary         Materials (a)  Overhead
Africa               1146/50        .07 x (a)      .03 X (a)
S.America            1334/50         "   "          "    "
S.Asia               899/50          "   "          i
-ypical              1044/50         n   "           1
CALCULATION OF EQUIVALENT SCHOOLING EFFORT
Pegion               Income/Capita  Population     Increment
(mill.)       (mill.)
Africa               63.77          6.866          4.379
S.America            330.36         5.734          18.944
S.Asia               95.97          69.376          66.580
Typical              227.08         6.929           15.733
Primary-Age    Primary         New Students   Increment
Population     School             (mill).     to Primary
(mill.)      Enrollment                     Enrollment
Ratio                          Ratio
Africa               1.474         5S.00           .175            11.85
S.America            1.112          93.36          .649            58.41
S.Asia               14.074         70.95          3.387           24.05
Typical              1-331          89.18          .685            51.48
(2) Family Planning Calculations
Region               Increment      Cost/Team      No. of Teams
Africa               4.379          599.5          7304
S.America            18.944         599.5          31,600
S.Asia               66.580         599.5          111,059
Typical              15.733         599.5           26,244
Fertile-Age ?omen/Team         M-B Score for Equivalency
Africa                     193                               3
S.America                   39                               2
S.Asia                     127                               2
Typical                     57                               2



page 116
APPENDIX G
UNSUCCESSFUL EXPERIMENTS
No econometric study ever proceeds from start to finish in the
clean, precise way suggested by textbooks in the field. In the
consideration of behavior in any socio-economic system, there are always
many hypotheses which compete in the mind of the researcher. When the
research effort involves substantial discussion with others who can
themselves suggest many plausible and ingenious ideas (and this was
certainly the case in the current effort), the competitive field becomes
crowded indeed.
Under these circumstances, the econometrician must contend with two
substantial sources of uncertainty in the research process. The first is
the problem of equation specification. While standard economic production
functions have been much studied, and the properties of contending
specifications are pretty well understood, the same cannot be said of the
functions which "produce" life expectancy or literacy in a society. For
that matter, the simultaneous specification of output and social
indicators is itself relatively unconventional, and existing work provides
little prior guidance concerning the appropriate specification of combined
production functions.
Thus, experimentation with alternative functional forms becomes an
inevitable part of undertakings like the present one. Much
experimentation of this kind lies behind the results which are presented
in this report, although occam's razor was applied in most cases when the
temptation to venture into truly exotic specifications became strong.
Basically, my concern has been to work with cross-section changes rather
than cross-section levels, for reasons which have been discussed in detail



page 117
in the report. In most cases, then, attention has been confined to the
competition between percent changes and absolute changes. There are
problems with either measure, but consistent specification moved the
proceedings toward percent changes in the response block. In the
accumulation block no such constraint applied, and absolute changes seemed
to do quite nicely.
It should be re-emphasized that the main difference between percent
and absolute change specifications lies in the underlying assumption
concerning the degree to which right-hand side variables are substitutable
for one another in determining outcomes. A specification in absolute
changes asserts that right-hand side variables are perfect substitutes in
the process, while the use of percent changes is equivalent to asserting
that the variables are "very good" (unit-elastic) but not perfect
substitutes.
It is, of course, entirely possible that neither assumption is
appropriate. In using asymptote-modified forms of relations in the
accumulation and response specifications, I have moved away from these
simple forms, but toward specifications whose properties have not been
completely thought through at this point. This kind of thinking needs to
be done, but it is a separate research project in itself. It certainly
deserves entry in the category "Priority for Future Research."
There,is, of course, a second source of uncertainty in this kind of
study which interacts with the first one. In each of the processes which
were examined in the preparation for this report, the explanatory power of
many seemingly-plausible variables turned out to be negligible.
"Negligible" is a loaded term in econometrics, of course, since some
variable which theoretically has a role to play should not be excluded
from an equation just because the standard error of its coefficient is
relatively large in a particular sample result. Econometric art



page 118
definitely merges with science in this particular domain, since the
intersection of available data shrinks with the inclusion of more and more
variables in a model. In cross-section work on a relatively limited
sample, the fundamental discipline imposed by the degrees-of-freedom
problem is severe.
Although the final results represent equations fitted-using
variables which seem to "work," therefore, it is certainly important to
mention the also-rans as well. Sherlock Holmes' dictum concerning the dog
which didn't bark is as important in this kind of detective work as in any
other. In the interest of comprehensibility, our gallery of failures will
be presented sequentially.
In the output equation, there has actually been remarkably little
evolution as the project has proceeded. The one major exception is
provided by a series of experiments with life expectancy, all of which
failed to provide any evidence of a direct link between contemporaneous
life expectancy change and output change. This was somewhat surprising,
since previous work on the 1960's which I had undertaken did suggest an
important role for life expectancy change. For the seventies, this
materialized neither in percent nor in absolute change specifications. It
is true, of course, that the initial level of life expectancy seems to
have an impact through its effect on manufacturing export growth (in the
1970's, at least), but no change relation can be discerned. This presents
one of the more interesting puzzles to emerge from the modeling exercise.
since the model results for the 1960's and 1970's are similar in many
other respects, why not in this one? Perhaps the result for the 1960's
was spurious, and perhaps not. in any case, this question remains to be
resolved..-
The other major set of experiments performed on the output equation
involved the comparison of the performance of published labor force growth



page 119
data with the performance of adult population change as a proxy. As
mentioned in the body of the report, few would argue with the contention
that the adult data are more carefully collected. Over short periods,
labor force participation and unemployment rates must come very close to
being constant multipliers, and they should therefore wash out when
percent changes are employed. In any case, the experiments certainly
seemed to go in favor of the adult data. Estimates based on the labor
force data were very unstable from sample to sample, and they frequently
yielded estimated elasticities so large as to be very unreasonable. The
estimates obtained with the adult population growth rate, on the other
hand, are quite stable from sample to sample and very reasonable.
T.ike the output equation, the nutrition equation has not been the
object of a tremendous amount of experimenation. Absolute changes have
been tried, but they do worse than percent changes (This is also true for
the contribution of nutrition change in the output change equation, so the
percent change specification had no competition in this case).
-he literacy equation has been subjected to two experiments which
were not fruitful. there is a plausible argument which asserts that
self-education should be positively related to life expectancy as well as
per capita income, and various specifications of life expectancy change
were duly tried. Bone worked. In addition, it seemed plausible to
suppose that the literacy-production-probability coefficient would be
sensitive to existing levels of per capita income, health, and literacy in
different societies. The appropriate experiments with interaction terms
were undertaken, and all the results were robustly insignificant.
In the case of the health equation,, the present product is the
result of very substantial experimentation. When life expectancy change
is measured in percent terms, it is necessary to introduce some control
for asymptotic behavior on the right-hand side of the equation. If such a



page 120
term is not included, sadly enough, an absolutely beautiful life
expectancy change equation emerges. In this fragile but exquisite
construct, seemingly important roles emerge for almost every variable
which might plausibly be supposed to have an impact on life expectancy
change. Present and lagged changes in medical personnel, present and
lagged changes in nutrition, present and lagged changes in schooling--all
show up strongly, with seeming significance, and with correctly descending
lag weights in every case. Unfortunately, the whole thing is totally
non-robust. Pith the common-sense introduction of a simple hyperbolic
term (1/F) to control for asymptotic behavior, the whole thing collapses
and only lagged nutrition emerges from the rubble.
Now, there are two possible responses to a situation such as the one
just described. one plausible argument would hold that structural
explanations are better than non-structural explanations, and that if the
choice is between a set of plausible explanatory variables and a simple
hyperbolic term the former should be chosen. On the other hand, when this
simple term "explains" as much variation in the data as a whole host of
contenders, Occam's razor comes readily to mind. In this case, the flowery
construct has been suppressed because it is so non-robust. The variables
which remain in the equation, on the other hand, are very resistant to
specification change, and their presence has been justified in detail in
the text. Jn passing,it should also be noted that several other plausible
variables were tried in the life expectancy equation, and none of them had
any apparent impact. Present and past changes in population per hospital
bed and' population per "nursing person" (a vaguely-defined concept at
best) failed to produce any meaningful results, as did the initial levels
of the same variables. In addition, the available measure of "safe water"
availability had no effect.
In the manufacturing export equation, very little experimentation



page 121
has been done. All of the variables in the equation seemed plausible,
given the argument about human resources which formed the basis for this
exercise and the evident importance of relative wages in a competitive
environment. The bad result for the 1960's introduces a major ambiguity,
of course.
Fe now pass to the chronicle of experiments with the accumulation
block equations, where the number of attempts again varied considerably
from problem to problem. The investment rate change equation was not the
subject of many experiments other than those already reported in the text.
The one exception involved a plausible argument about the role of
"extraversion" of the economy in the determination of the investment rate.
Tt was hypothesized that a change in the ratio of exports to GDP should
elicit some response in the investment rate, on the theory that large
enterprises (public or private) are disproportionately involved in trading
activities and find it easier to mobilize savings. Although the
export-ratio term generally had the correct sign in the investment rate
change equations when it was included, the associated standard error was
always quite large. This variable was therefore excluded from the final
estimates.
rork on fertility rate determination in this report was guided by
the extensive previous work of demographers, so it was relatively easy to
choose appropriate right-hand variables. A major exception was provided by
the literacy rate, which generally does quite well in cross-section
studies of fertility rate determination. When time changes are employed,
the direct contribution of this variable to changes in fertility
apparently vanishes. Since literacy change contributes to output change,
of course, the effect of this variable is still indirectly present.
As previously noted, the approach to fertility function estimation
taken in this study may draw some claim to novelty from the use of time



page 122
changes, age cohort effects, and a simultaneous specification of the
relationship between family planning activity and fertility change. The
obviously nonlinear relationship between the death rate (a proxy for the
infant mortality rate) and the fertility rate was incorporated in the
final equation specification. In passing, it should be noted that the
relatively superior performance of the constrained linear fertility model
(see Appendix C) suggests that the crude death rate is a good proxy for
the infant mortality rate. If the data had suggested a differential
pattern of marginal impacts across cohorts, this would not have been the
case.
Before passing on to the death rate experiments, it should be noted
that the near-duality of life expectancy and the death rate applies to the
role of the associated infant mortality factor in the fertility rate
equation, as well. When life expectancy change is used in the fertility
rate equation in place of the change in the death rate, it performs
equally well. since the death rate is a more direct index of the
phenomenon being modeled (the response of fertility decisions to the
survival probability for children), it has been used in this study. The
death rate coefficient has the advantage of ready interpretation, as well.
Both the model results and the scatter diagrams displayed in Chapter III
demonstrate the strong nonlinearity in this. coefficient. The coefficient
which measures response to expected infant survival moves rapidly toward
unity as the death rate declines.
Finally, we arrive at the death rate change equation. In this
modeling exercise, the utility of this equation lies principally in its
necessity for a complete specification of the population growth rate in
the simulation model. For all other purposes, the life expectancy
equation does as well or better. In any case, the guiding principle in
experiments with the death rate change equation was the theoretical



page 123
necessity of' near-parity with the specification of the life expectancy
change equation. The variables which remain in the reported equation are
those which "worked." Only age cohort changes and changes in the
availability of medical personnel seem to have had significant impacts on
observed death rate changes across countries. Among the large set of
other possibly-relevant present and lagged changes and initial levels, no
other variables emerged unscathed. Obviously, death rate changes as
measured are not the easiest things in the world to explain. A large
portion of the "explanation" in my equation is provided by the asmymptotic
term and the lagged endogenous term which represents the continuity of
peculiar local patterns of death rate decline. A major problem may well be
presented by errors in measurement in this case.



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APPENDIX H
SAMPLE COUNTRIES
In Appendix A, considerable attention is paid to the pr6blem of data
scarcity when time-change equations are estimated in this context. Each
intersection of variables contains a different subset of observations from
the full 88-country group. Under such circumstances, it is unwise to
ignore the risk that a particular intersection sample may be entirely
unrepresentative of the full set. In this Appendix, the intersection
samples for the principal output and demographic models are listed. It
might have been supposed a priori that data availability was positively
associated with per capita income. Fortunately, this does not seem to have
been the case. The smaller samples bear a surprising resemblance to
random draws, with no detectable bias in favor of a particular region or
income level.



page 125
Figure 21
CLOSED ECONOMY SAMPLE COUNTRIES
1960                 1970
PORTUGAL             PORTUGAL
GREECE               TURKEY
SPAIN               YUGOSLAVIA
TURKEY               MOROCCO
YUGOSLAVIA          TUNISIA
nOROCCO             CHAD
TUNISIA              ETHIOPIA
CAMEROON             GHANA
ZAIRE                IVORY COAST
GHANA                KENYA
IVORY COAST          MADAGASCAR
KENYA                MALAWI
LIBERIA              MAURITANIA
SENEGAL              SENEGAL
SOMALIA              SIERRA LEONE
SUDAN                SUDAN
vANZANIA             TOGO
TOGO                 UPPER VOLTA
DOMINICAN REPUBLIC   ZAMBIA
EL SAIVADOR          DOMINICAN REPUBLIC
JAMAICA              EL SALVADOR
MEXICO               JAMAICA
PANAMA               MEXICO
ARGENTINA           NTCARAGUA
BOLIVIA              PANAMA
BRAZIL               ARGENTINA
CHILE                BOLIVIA
COLOMBIA             BRAZIL
PARAGUAY            CHILE
SYRIA                COLOMBIA
AFGHANISTAN          PARAGUAY
SRI LANKA            URUGUAY
INDIA                SYRIA
PAKISTAN             AFGHANISTAN
HONG KONG            SRI LANKA
SOUTH KOREA         INDIA
MALAYSIA             PAKISTAN
PHILIPPINES          HONG KONG
THAILAND             SOUTH KOREA
MALAYSIA
PHILIPPINES
SINGAPORE
THAILAND



page 126
Figure 22
LIFE EXPECTANCY EQUATION
PORTUGAL             BOLIVIA
GREECE               BRAZIL
SPAIN                CHILE
T'URKEY              COLOMBIA
YUGOSLAVIA           PARAGUAY
MOROCCO              URUGUAY
TUNISIA              ISRAEL
CAMEROON             SYRIA
CHAD                 AFGHANISTAN
ZAIPE                INDIA
ETHIOPIA             NEPAL
GHANA                PAKISTAN
GUINEA               HONG KONG
IVORY COAST          SOUTH KOREA
KENYA                MALAYSIA
LIBERIA              SINGAPORE
MADAGASCAR           THAILAND
NALAWI
MAURITANIA
SENEGAL
SIEPRA LEONE
SOMALIA
SUDAN
TANZANIA
TOGO
UPPER VOLTA
ZAMBIA
DOM. REP.
EL SALVADOR
HAITI
JAMAICA
MEXICO
NICARAGUA
PANAMA
ARGENTINA



page 127
Figure 23
SAMPLE COUNTRIES - FULL INVESTMENT EQUATION
TURKEY
YUGOSLAVIA
MOROCCO
TUNISIA
EGYPT
BURUNDI
BENIN
GHANA
IVORY COAST
KEIYA
RWANDA
SENEGAL
TOGO
DOMINICAN REPUBLIC
EL SALVADOR
GUATEMALA
HONDURAS
JAMAICA
NEXICO
PANA N A
BOLIVIA
BP A ZIL
CHILE
COLONBIA
PARAGUAY
PERU
AFGHANISTAN
BURNA
SRI LANKA
INDIA
PAKISTAN
BANGLADESH
TAIWAN
HONG KONG
SOUTH KOREA
NALAYSIA
PHILIPPINES
THAILAND
PAPUA NEW GUINEA



page 128
Figure 24
SAMPLE COUNTRIES - FERTILITY CHANGE MODEL
TURKEY               DOMINICAN REPUBLIC
MOROCCO             EL SALVADOR
TUNITSIA             GUATEMALA
EGYPT                HAITI
CAMEROON             HONDURAS
CENTRAL AFR. REP.    JAMAICA
ZAIPE                MEXICO
ETHIOPIA             NICARAGUA
GHANIA               PANAMA
GUINEA               BOLIVIA
IVORY COAST          BRAZIL
KENYA                CHILE
IESOTHO              COLOMBIA
LTBERIA              PARAGUAY
MADAGASCAR           PERU
MAT,AWI             JORDAN
nALI                LEBANON
MAURITANIA          SYRIA
RIGER                AFGHANISTAN
RPAITDA              BTRMA
SENEGAL             SRI LANFA
SIERRA LEONE         INDIA
SOMALIA             NEPAL
SUDANl              PAKISTAN
TANZANIA             BANGLADESH
TOGO                 HONG KONG
UGANDA              SOUTH KOREA
UPPER VOLTA         LAOS
ZAMBIA               MALAYSIA
COSTA RICA           PHILIPPINES
SINGAPORE
THAILAND



page 129
SAMPLE COUNTRIES - DEATH RATE EQUATION
PORTUGAL             UPPER VOLTA
GREECE               ZAMBIA
SPAIN               COSTA RICA
"URFEY               EL SALVADOR
YUGOSLAVIA           GUATEMALA
MOROCCO              HAITI
TUNISIA              JAMAICA
EGYPT                MEXICO
BURUNDI              NICARAGUA
CAMEROON             PANAMA
CENTRAL AFR. REP.    ARGENTINA
CHAD                 BOLIVIA
ZAIRE                BRAZIL
BENIN               CHILE
ETHIOPIA            COLOMBIA
GRANA                PARAGUAY
GUINEA               PERU
IVORY COAST          URUGUAY
KENYA               JORDAN
LIBERIA              SYRIA
MADAGASCAR           AFGHANISTAN
MALAWI               BURMA
HALT                SRI LANKA
MAURI'T'ANIA        INDIA
NIGER                NEPAL
PEANDA               PAKISTAN
SENEGAL              HONG KONG
STERRA LEONE         SOUTH KOREA
SOMALIA             LAOS
SUDAN                MALAYSIA
TAN7ANIA             SINGAPORE
TOGO                 THAILAND
PAPUA NEW GUINEA



page 130
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HG 3881.5 .W57 W67 NO.407
c.2
F WHEELER, DAVID, 1946-
- HUMAN RESOURCE DEVELOPMENT
I AND ECONOMIC GROWTH IN