• TABLE OF CONTENTS
HIDE
 Title Page
 Abstract
 Introduction
 Mathematics of life expectancy
 Literature review
 Life expectancy model
 Data used
 Estimated model
 Econometric results
 Uses of the estimated model
 Conclusion
 Notes
 Reference






Title: Econometric analysis of life expectancy
CITATION PDF VIEWER THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00096193/00001
 Material Information
Title: Econometric analysis of life expectancy
Physical Description: Book
Language: English
Creator: Jones-Hendrickson, S. B.
Publisher: Caribbean Research Institute
Place of Publication: St. Thomas, U.S. Virgin Islands
Publication Date: 1982
Copyright Date: 1982
 Record Information
Bibliographic ID: UF00096193
Volume ID: VID00001
Source Institution: University of the Virgin Islands
Holding Location: University of the Virgin Islands
Rights Management: All rights reserved by the source institution and holding location.

Downloads

This item has the following downloads:

PDF ( 2 MBs ) ( PDF )


Table of Contents
    Title Page
        Title Page
    Abstract
        Page 1
    Introduction
        Page 2
        Page 3
    Mathematics of life expectancy
        Page 4
        Page 5
        Page 6
        Page 7
    Literature review
        Page 8
        Page 9
        Page 10
    Life expectancy model
        Page 11
        Page 12
        Page 13
    Data used
        Page 14
    Estimated model
        Page 15
    Econometric results
        Page 16
        Page 17
    Uses of the estimated model
        Page 18
        Page 19
    Conclusion
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
    Notes
        Page 25
    Reference
        Page 26
        Page 27
        Page 28
Full Text







AN ECONOMETRIC ANALYSIS OF LIFE EXPECTANCY








by



S.B. JONES-HENDRICKSON


Social Research Center
Caribbean Research Institute
College of the Virgin Islands
January, 198Z












An Econometric Analysis Of Life Expectancy


Abstract
This work develops u model which seeks to determine

the dependence of life expectancy on birth race, death rate,
infant mortality and per capital Gross National Product. The
estimates are based on a single equation regression analysis
for sixty-seven "developed" and "developing" countries. The
cross sectional data are drawn from a World Bank Publication
The Assault on Poverty (1975, Annex 2 pp. 414-415).
All of the estimates parameters are significant at tcie
conventional 1 and 5 percent level of significance, except
infant mortality. Ninety-seven percent of the variation
is explained, and two-thirds of the observed values of the
dependent variable, life expectancy, are within 1 1.74 of
their respective values as estimated by the regression.
This work is a first analysis of data from which we
will subsequently discuss the issues in developing countries
and specifically Microstate Economies.








I. Introduction


The essential qualities or features of this work emanate

from our concern with the quality of life, the nature of

life and the factors which impinge on health care delivery.
In 1946, when the World Health Organization's (WHO) constitu-
tion was signed, one key point was very clear: "health," the
constitution stated, "is a state of complete physical and social
well-being, and not merely the absence of diseases and infirmity."
The WHO definition is useful. But, we are cognizant of the
point developed by Stewart and Siddayao (1973) that the
demand for health services is a function of the
individual, and the health of the individual
could at some income levels be directly related
to his income. (Furthermore), the lowest
income groups are more likely to have poor nutri-
tion and inappropriate health habits, and may
require health attention more frequently than
higher income groups (p.8).
On reflecting on this passage, and when it was placed in
the context of nations, it began to shed some light on the
nature of length of life in the so-called developed and develop-
ing countries. Fundamentally, we began to recast the demand-for-
health scenario along the lines of a length-of-life point of
view. Our concern was to determine what causal factors may
be linked, operationally, to the length of living experienced

by individuals in both economically demarcated groups of
countries.
Several approaches were considered in order to establish
our first approximation to long life differences between de-
veloped and developing countries. At first, ratios such as








doctors to population, nurses to population, hospital beds to

population, and the rest, were considered. These were not con-

sidered in a direct sense. They were considered in a derived

sense. Once again, Stewart and Siddayao (1975) provided the

line of departure in the development of our approach.

The demand for health services note Stewart and
Siddayao (1973) is, in effect, a demand for good
health. Yet, it cannot be assumed that the amount
of expenditures on medical care has a direct rela-
tionship with achieving the level desired, just as
it cannot be assumed that the number of physicians
relative to the population is indicative of the
level of health of any segment of the population
(p.57).

Spurred on by this thought, it occurred to us that the

length of life one lives must be related to other factors beside

the conventionally accepted high level health manpower ratios.

Furthermore, we thought that length of life is critical to the

perspectives of countries, particularly developing countries

notably low income Microstate Economies). Length of life and

planning for the people who live long lives are of vital import

in developing countries. What really turned the thought into

substantive action was a passage from Chiang (1972) who con-

tends that

in planning health services for a nation, or
for a community, we need some objective
criteria on which to base our judgement, to
guide our decision, and to evaluate the accom-
plishments of our performance. A planning
(sic) without a model is futile, a health
service program without a measure of the out-
come is ineffective (p.19).

To us, the concept of long life provides some criterion

on which a country could be assessed. The single equation model








which we develop in Section IV follows the Mathematics of Life

Expectancy in Section II and a review of the Literature in Sec-

tion III. In terms of the structural analysis of the model,

we believe that hypotheses could be tested to determine concrete

empirical links between life expectancy and per capital income,

for example. The model also could provide some useful measures

for forecasting given the death rates, infant mortality, and

per capital gross national product of nations. From a policy

point of view, these microanalytic features could be fed back

into the overall macroeconomic systems provided the model stands
replication, and provided accurate data are readily available.

The fifth section presents the data in a descriptive frame

of reference. This section is followed by the estimated model

in Section VI, the econometric results in section VII, uses of

the estimated model in section VIII and the overall conclusions

in section IX.

II. Mathematics of Life Expectancy

Life expectancy at a given age is a summary of the mortal-

ity conditions at that age plus all subsequent ages.
Life expectancy calculations depend, to a large extent, on

age-specific mortality rates. Consequently, reliable data, as

they pertain to the mortality and distribution of populations
by age and sex, are of tremendous importance.1 From a simple

example, we can illustrate the concept of life expectancy.

Life expectancy at age thirty, for instance, summarizes
mortality conditions at age thirty and the years beyond age

thirty. The mortality rate at any given age is a measure which









indicates that a person selected at random will die at the given

age.
Let us consider the following:

Four persons have age characteristics such that A lives

for one week; 8 lives for 28 years; C lives for 72 years and

D lives for 90 years. All four individuals lived a total of

190 years. Life expectancy at birth is approximately 47.5 years.

Messrs B,C,D reached the age of one year. From that age they

lived for a total of 187 years, hence their life expectancy at

age one is 62.3 years. Messrs C and D reached the ages of 30

and 60. Mr. C. lived until 72 and Mr. D. lived until 90. Thus,

life expectancy of Mr. C at ages 30 and 60 is 42 and 12, respec-

tively. Likewise, life expectancy for Mr. D at those samac ear-

marked ages is 60 and 30, respectively. What should be clear

is this: life expectancy at a given age is not the same thing
as expected age at death.

Our illustration is simplistic. Life expectancy is more

complex than our simple illustration above. Let us first start

with life tables. Life tables are developed in the framework

of probabilities for individuals. For the entire population,
life tables are, technically viewed, deterministic models of

mortality and survivorship.2
The substantive features of life tables, as far as we are

concerned, center on the answers we can derive from them. We

can derive answers pertaining to the probability of Mr. B, age

50, surviving until he reaches age 70, or what is the probabil-

ity that he will outlive Mr. B junior, who is currently age 20.










From the point of view of groups born at a given time, we can

determine what proportion will survive to reach some age in the

future. Finally, we could also get answers from the life tables

which would tell us what proportion of a population will be at

retirement age, given certain set-specific conditions of birth
rate and death rate.

For developing countries which depend on their human re-

sources, as a critical input in the production process, these

answers from the life tables are of tremendous import. They

will not eliminate the problems of barriers to development. The
answers, however, can be useful in the long run planning strat-

egies of the countries. For developing countries, and particu-

larly Microstate Economies, therefore, some accurate knowledge

of life expectancy of their people and what affects the life

expectancy are crucial.
How is life expectancy derived, mathematically? Following

Keyfijz (1972,pp.34-35) we note that the probability of one
surviving from birth to some age may be defined as

s(a) ........................................... (1.0)
for a continuous function of a, and

sa ................. ........................ (2.0)

for a discrete case. The change in the number of people who
survive between sa and sa +1 is designated da. In the general

case, if the people live until y years in the future,

sa say+y = yda ............................. (3.0)
The probability of Mr. A dying during the succeeding y years
given that he is age a is obtained by our dividing (3.0) by











(2.0). Hence we obtain
sa sa+y= 1 +y

aa a

= yda
Sa (4.0)

If we wish to determine the cumulative number of years lived

for y years in the future for a cohort which is currently age
a, we simply write

y a = /5a+y s(x) d x (5.0)



Expression (5.0) represents the number of people aged, precisely,

a to a+y in the "stationary" population. If we let y equalA, where

A is the maximum age of any body in the society, we obtain

Sa a R fa s (x)dx (6.0)

R represents the cumulative remaining years for the group of

individuals who have reached age a, one of whom will survive
to age A. The expected proportion for an individual in the

cumulative proportion is obtained by our dividing expression

(6.0) by the probability of someone surviving from birth to
age a, say. In other words we can divide Ra by sa.

Ra =a s (x)dxtsa = eoa (7.0)
sa

From a probability frame of reference, ea which is "the mean

of the distribution of years to death for persons age (a) is

called the expectation of life" (Keyfitz, 1972, p.35).









III. Literature Review

One would have imagined that with all of this instruc-

tive demographic information at hand, that analyses of life

expectancy would have been integral to theories of development,
or at least that the subject matter would have occupied the

attention of many economists. Unfortunately, the previous

literature of life expectancy, as it pertains to economic de-

velopment, is sparse.
Some articles have explored features closely related to

life expectancy and some of the intrinsic factors that we are

attempting to identify in this work.
Weintraub (1962) believes that the "relationship between

the birth rate and per capital income (is) negative"3 (pp.812-817).

Adelman (1963) argues that there is a "homogeneity" in the re-

sponse of population pressure in both "developed" and "less
developed countries" (pp. 315-339). Simon (1969) claims that

the birth rate falls in "less developed countries" as the average

income rises (pp.327-341). Gregory and Campbell (1973) dismiss

Adelman (1963) homogeneity assumptions and argue that "popula-

tion planning at the aggregate level must proceed differently

in developed and developing countries" (pp.233-241).

In the Caribbean, Roberts (1957, pp.264-265), Roberts
(1968) and Sinclair (1974) are concerned with demographic
issues, and specifically fertility patterns. Even though
they have a full grasp of the fertility situation in the region,

their concerns, like their metropolitan counterparts, are not

with life expectancy per se.5 In our view, none of the previously









mentioned literature dealt explicitly with life expectancy.

But, there are some inchoate references to life expectancy

and economic developmental issues in the liLerature.6

In the World Bank Report (1975, pp. 348:50), life ex-

pectancy is given a brief treatment. It is discussed in rela-

tionship to wealth and infant mortality. The life expectancies

of developing countries are discussed. However, there is no

profound treatment of the subject matter. The discussion on
the "health conditions of developing countries" recognizes

that "life expectancy at birth and at selected ages is the most

reliable measure of health status available" (World Bank,

1975:348).

Michael Todaro (1977:171-172) discusses "fertility and

mortality trends" comparing in passing, birth rate, in develop-

ing and developed countries and the relationship of the birth
rates to life expectancy. Coale and Hoover (1972, p.34 and

pp.376-377), briefly discuss life expectancy at birth under

two general topics: (a) prospective changes in Indian Popula-

tion during a 30-year period (1956-1986), and (b) 'recent
trends in Mexican fertility and mortality.' In the case of

the latter, mortality rates are compared with life expectancy.

But the thrust of the section centers on the "typical associa-
tion between the level of life expectancy and the annual in-

crements to life expectancy" (Coale & Hoover, 1972, p.377).
The simple correlation analysis developed by Coale and

Hoover (1972) has a conclusion which states that there is a

correlation between the average annual increase in life expec-









tancy and its level of .91 for males, and .85 for females.

The relationship was obtained from observations over a twenty-

year period for 20 countries.8 The authors were interested in

pointing out that a "linear association between level of expec-

tation of life implies a typical pattern to estimate the course
of improving chances of survival in Mexico until 1985"(p.377).

In the Caribbean, Harewood (1974, pp.31-42) compares life

expectancies of females with males presenting data from 1901-

1970. His focus was on Trinidad and Tobago, but he also makes

some references to the rest of the Caribbean. Here, too, the

emphasis is a static view of life expectancy. No causal links

are established. It is purely a demographic exercise.
By and large, most of the literature which touched on

life expectancy did not come to grips with the fundamentals of

why life expectancy differed among nations. In a scathing

attack, Salas (1978,pp.276-282) points out the gap between

life expectancies in the developing world and the developed
world. The figures ranged from 42-54 years in the developing

world to between 65 and 71 years in the developed world. Salas

points out that the figures hide the distributional problem
because there were some life expectancies from 38 to 73 years.

Latin America was represented by an average of 62 years, Asia

by 56 years, and Africa by 45 years. These rates have increased

by one or two years since the mid-nineteen seventies data which

Salas used. However, he makes an important point when he says

(Salas, 1978)









that a gap of 26 years in life expectancy should
exist between Africa and the developed world is
a tragic comment on the latter's inability to give
substance to the rhetoric of global independency
(p.278).
This disparity in data requires some explanation. Our

paper is a first step towards that explanation. We will first

consider what are the links between life expectancy, on the one

hand, and some well established demographic and economic vari-

ables on the other. We now turn to the model in section three.

IV. Life Expectancy Model

A model is an attempt to come to grips with the links
between reality and manageability. But modeling could, con-

ceivably, be located in the framework of an art and a science

(Intriligator, 1978, p.14-15). The model we offer below is our

attempt to determine the impact of birth rate (BR), death rate
(DR) Infant Mortality (IM), and per capital Gross National

Product (PY) on life expectancy.

LE = LE(BR,DR,IM.PY) (8.0)

The behavioral conditions that we have attached to the equation
are:

&LE < 0; SLE 0; SLE 4 0; 6LE > 0 (9.0)
6BR 6DR SIM SPY
Essentially, we are arguii.g from (9.0) that there is on

the one hand a positive relationship between life expectancy

and per capital income. On the other hand there is an inverse

or negative relationship between life expectancy and birth rate,

death rate, and infant mortality. We have defined life expec-









tancy before. We define the other variables as follows:

Birth rate

(BR) is the number of births per year per thousand popu-

lation in a given state, country, district or group.

Death rate
(DR) is the percentage of deaths, normally counted at

per thousand among the population of a country or some other
geographical or political entity, over a given period.

Infant Mortality Rate

(IM) is the number of deaths of persons from age one and
below relative to the number of live births in a country, and

so on, over a period of time.

Per Capita Gross National Product
Per Capita Gross National Product is the Gross National

Product of a country divided by the population. This datum is

traditionally thought of as a measure of economic growth, and
sometimes, of the level of living in a country. Linearizing

equation (8.0) we have
LE- a+bBR+b DR+b3 IM+b4PY+U (10.0)
where (1) the variables are the same from earlier definitions,

(2) the behavioral characteristics are now illustrated by b's
and U is the stochastic disturbance term. LE is the dependent

or endogeneous variable, BR,DR,IM,PY are the independent or

exogenous variables. These variables, along with the assump-

tions regarding the distribution of the stochastic term, U,

represent the basic linear regression model.

The stochastic assumptions concerning the disturbance









term U, namely the "disturbance assumption," the "assumption

of hoLoskedasLicity," the heteroskedasticity and the "absence

of serial correlation" are all well known and well developed
in the literature. Some basic references include Christ (1966),

Malinvaud (1970), Theil (1971), Schmidt (1976), and Intriligator

(1978). Consequently, we need not reproduce those assumptions
here.

In all econometric problems, we need to bear in mind the

problems of multicollinearity, heteroskedasticity serial corre-

lation, qualitative dependent variables, specification errors

in variables, structural breaks, among other econometric short-

comings. The most important issues in the case of single-

equation econometric studies are multicollinearity, hetero-

skedasticity and serial correlation.
Multicollinearity could occur as a result of several

factors: (a) a constant across sample variable; (b) one explan-

atory variable as a combination of other variables; (c) a dummy
variable which is all inclusive of other dummy variables, and

so on. In all cases, the normal equations of the least squares

will not be solved. It should be aoted, however, that multi-
collinearity is not a major problem if forecasting is the objec-

tive of the analysis. Good fo ecasts can be obtained from
estimates even though multicollinearity is present. In our

case, structural analysis is of greater importance than fore-
casting. An evaluation of the separate effects of the individ-

ual variables is our task. Multicollinearity is a serious

problem in this case; however, we did not detect any evidence









of multiple collinearity in our equation.

Heteroskedasticity develops when there is a breakdown in

the assumption of homoskedasticity: in other words, when the

variances of the stochastic disturbance term are not finite
and constant over the sample, homoskedasticity will be present.

When this problem exists, the least-squares estimates will not

be efficient and not be the best estimations--even though they

may still be linear. In addition, a certain degree of bias

will be built in the estimates, hence the conventional t and F

tests will not be valid tests of statistical significance.9

Here, too, we did not detect any instance of heteroskedasticity.

Finally, we turn to serial or autocorrelation. This common

problem in applied econometrics refers to the situation wherein

the disturbance terms are not independent of one another. When

serial correlation exists, its inadequacies are similar to

those which obtain in the presence of heteroskedasticity. The

Durbin-Watson test provides the kind of "prescription" to accept

or reject serial correlation. Once again, our equation has

passed the test. Let us now turn to the data.

V. Data Used

The data used were obtained from a World Bank Publication,

The Assault on World Poverty (1975). As presented in the ap-

pendix, the data are from annex two (1975, pp.414-415). The

original sources for the variables are for (i) per capital GNP,

World Bank Atlas (1973, pp.6-14); (ii) crude birth, death

rates, and life expectancies, United Nations projections, un-

published data; averages for 1970-1975; (iii) infant mortality









rates, World Health Organization (1979). Infant mortality in

some countries such as Albania, Burundi, Indonesia, Dahomey,

Uganda, Senegal, Ghana, Syrian Arab Republic, Honduras, Ivory

Coast, Japan, Zambia, and Trinidad and Tobago were obtained

from the United Nations Statistical Yearbook 1972 (1973).

In some other cases as in Nigeria and Ecuador, infant mortal-

ity rates were estimated by the World Bank.

Given the variety of sources from which these data were

put together by the World Bank, it is quite possible that the

data are afflicted with the usual problems. However, a cross

checking of the relevant data did not show too many deviations

from those generally in use in some of the countries checked.

We believe, therefore, that any inaccuracies or biases in the

data used, are on the order of small.

The means of the variables are:
Life Expectancy ................... 55.0433

Birth Rate ........................ 39.2731

Death Rate ........................ 14.2985

Infant Mortality .................. 169.6269
Gross National Product ............ 498.2091

VI. Estimated Model
The estimated model and its relevant test statistics are

given below, where the standard errors are in parentheses be-

low the estimated coeficients:

LE = 82.7413 0.2445BR 1.2440DR 0.0090IM + 0.001OPY
(1.1816) (0.0336) (0.0004) (0.0636) (0.0058)









R2 = 0.9763

F (4,62) =637.4561

D-W (Adjusted for 0 gaps)= 1.9606

Number of Observations = 67

Sum of Squares =186.8849

Standard Error of the Regression 1.7362

Birth rate, death rate, and per capital gross national
product are all statistically significant at the one percent

level of statistical significance, using a two-tail test.

The R2 indicates an explanation of over 97 per cent of
the variation in the variables; and with the Durbin-Watson

statistic hovering around two, there is no indication of

serial or autocorrelation. With a standard deviation of 1.7362,
our results indicate that the estimates of the standard devia-

tion of the coefficients fall within 1.7362 standard deviation

of their respect values.

VII. Econometric Results
The signs of the estimated coefficients are in accordance

with the predicted or theoretical signs which we outlined in

equation nine. In the cases of Infant Mortality (IM) and Per
Capita Gross National Product (PY), their magnitudes are smaller

than we anticipated. Particularly in the case of the latter,

we thought, apriori, that it would have been of the order of

the coefficient of the death rate.

Our concern in this paper is to get a first approximation

of the relationship between life expectancy and the right hand

side variables of death rate, infant mortality, per capital








gross national product, and birth rate. For the future, how-

ever, the model could be reformulated to come to grips with

future implications as they impact on otheL variables. In

this respect the single equation model may be reformulated to

account for a simultaneous equation system. Here we may wish

to have life expectancy as a function of the present set of

variables. In turn, each of the independent variables could

themselves depend on other variables.
For illustration, birth rate could be a function of health

expenditures per capital; the health budget relative to Gross

National Product, and so on. Death rate could also be a func-

tion of these variables. Likewise, infant mortality could be

a function of health expenditures devoted to prevention of

diseases; the population per bed ratio; the population pez

physician ratio; the support services per physician; and the

rest. In essence, there are several other instances wherein
we can reformulate our model to capture more explanatory power

in the choice of variables.

In addition to the reformulation of the model, we could

also develop alternative structural prescription in future

work. We may wish to use log analyses as well as disaggrega-
tion of the data according to income strata among the countries

in question. From the log analyses we could interpret the

parameters estimates, directly, as elasticities. Disaggrega-
tion of the data according to income strata would filter out

some noise in the results. Suffice to say, that our single

equation system is merely a first attempt at coming to grips
with some of the underpinning features of life expectancy as

it relates to birth rate, death rate, infant mortality, and









per capital gross national product.

VIII. Uses of the Estimated Model

In considering the uses of the estimated model, we will

focus on the structural analysis of the model. Here the

relevant multipliers, the elasticities, forecasting and policy

evaluation are crucial for us.

The Impact Multipliers are given in Table I.

Table I: Impact Multipliers

Exogeneoui-- Endogeneous
Variable variable Life Expectancy

Birth Rate .2445

Death Rate 1.2440

Infant Mortality 0.0089

Per Capita GNP 0.0010


The first line indicates that if the birth rate is in-

creased by 1 per thousand, life expectancy will decline by

.2445 years or a little over three months. The second line
suggests that if death rate increases by 1 per thousand, life

expectancy will decline by 1.2440 year or about 15 months.
Line three implies that if infant mortality increases by 1

relative to the population, life expectancy will decline by

three days. Finally, if per capital income increases by one

dollar, life expectancy will increase by less than a day.

A few observations seem pertinent at this stage relative

to the impact multipliers. The estimate of the death rate has









largest impact on life expectancy. The small impact of life

expectancy derivable from infant mortality changes may be due to
some integrative effects between infant mortality and death

rate. Likewise, the very miniscule impact of per capital in-

come on life expectancy, positive though the coefficient is,

may be due to the wide variability in data, aggregation prob-

lems, and poor measure of GNP variable. In this case, a gini-

coefficient may have been more appropriately used. Gini-

coefficients are not readily available for all of the countries.

Let us now turn to the elasticities evaluated at the

means. In Table 2 we present the results.

Table 2: Elasticities for Birth and Death Rate, Infant
Mortality, and Per Capita GNP

Elasticities Value


'LE, BR 0.1744

qLE, DR 0.3232

LE, IM 0.0274

"LE, Q 0.0091



From Table 2 we note that line one suggests that the

relationship between life expectancy and birth rate is negative,
and furthermore it could be characterized as inelastic. Speci-

fically, for every 1 percent increase in birth rate, life ex-
pectancy will fall by over 17 percent. Lines two and three

are similarly characterized as line one. In these two cases,









for every 1 percent increase in death rate, life expectancy

will fall by over 32 percent. For every one percent increase

in infant mortality, life expectancy will fall by two percent.

Finally, for every 1 percent increase in GNP, life expectancy

will increase by .91 percent.

IX. Conclusion

In the final analysis, in this paper we were concerned
with beginning a systematic analysis of the relationship of

life expectancy to birth rate, death rate, infant mortality,

and per capital gross national product. All of the variables

except infant mortality are statistically significant at the

1 percent level. From the point of view of the impact multi-

pliers, the order of impact is death rate, birth rate, infant

mortality and per capital GNP. And zrom the view of the elas-

ticities, the impact order is death rate, birth rate, infant
mortality, and per capital GNP.

The results are indicative of a first approximation to

work which is critical to developing or Third World Countires.

We have some reservations with regards to the impact multiplier
and elasticity of per capital GNP. Our concern also centers on

infant mortality from the point of view of its impact multiplier.

Nevertheless, for the policy maker, it seems that we may state,

with some caveats, that a reduction in death rate will have a
positive impact on life expectancy. This may create a long-run

problem of an aged non-productive problem, in a dynamic framework.

A second point could be made, namely, per capital income has a

positive relationship with life expectancy. This is really









stretching the imagination a bit. It is important to note,

again, that the disparate sources of income data may have

caused some problems in the results. All things being equal,

however, the results are a beginning. Perhaps we are antici-

pating large parameter estimates when in fact what we have

obtained are the best linear estimates.

Future work in this area, may be usefully tackled by

evaluating the data in logs, eliminating infant mortality, or

merely considering a difference of birth and death rate. In

addition, other variables could be incorporated. Some, such

as nurses per population, health expenditures per capital and

so on, may make the results of the life expectancy model more

precise in all variables. Nonetheless, we believe that the

results offer a beginning in this vital area of life expectancy.

Since the area seems to be inadequately discussed in the litera-

ture, there is a great deal of work to be done. For us, we

plan to disaggregate the data in "developed" and "developing"

countries, as well as make some other structural changes in

our basic life expectancy equation. In our future work, too,

we will focus on the policy implications to be derived from

the study from the point of view of the decision-maker in

Microstate Economies.






Appendix

Measures of Health Status by Level of Per Capita
Gross National Product (GNP) in Selected Countries


Per Capita Crude Crude Infant Life
Countries GNP birth rate death rate Mortality expectancy

Burundi 60 41.8 24.9 150 39.0
Upper Volta 70 48.5 24.9 180 39.0
Ethiopia 80 49.5 23.8 162 40.0
Indonesia 80 44.8 18.9 125 45.4
Yeman Arab Republic 90 49.5 20.0 160 45.5
Malawi 90 47.7 23.7 148 41.0
Guinea 90 46.6 22.8 240 41.0
Sri Lanka 100 28.6 6.3 50 67.8
Dahomey 100 49.9 23.0 110 41.0
Tanzania 110 50.1 23.4 122 44.5
India 110 41.1 16.3 139 49.z
Sudan 120 47.8 18.5 130 47.2
Yemen, People's Democratic
Republic of 120 50.0 22.7 160 45.3
Uganda 130 46.9 15.7 160 50.0
Pakistan 130 47.6 16.8 130 49.4
Nigeria 140 49.3 22.7 150 41.0
Central African Republic 150 43.2 22.5 190 41.0
Mauritania 170 48.8 23.4 187 41.0
Bolivia 190 43.7 18.0 60 46.7
Liberia 210 50.7 22.3 159 43.5
Sierra Leone 210 41.9 20.2 197 43.5








Per Capita Crude Crude Infant Life
Countries GNP birth rate death rate Mortality expectancy

Thailand 210 43.7 10.4 23 58.6
Egypt, Arab Republic of 220 37.8 15.0 120 50.7
Viet-Nam, Republic of 230 41.8 23.6 100 40.5
Philippines 240 43.6 10.5 62 58.4
Senegal 250 47.3 22.2 93 42.0
Ghana 250 48.8 21.9 156 43.5
Congo 270 45.1 20.8 180 43.5
Paraguay 280 42.2 8.6 39 61.3
Syrian Arab Republic 290 46.9 14.4 24 53.8
Hunduras 300 49.3 14.6 37 53.5
Ecuador 310 41.8 9.5 87 59.6
Tunisia 320 41.0 13.9 76 54.1
El Salvador 320 42.2 11.1 58 57.8 c
Ivory Coast 330 45.6 20.6 138 43.5
Turkey 340 39.4 12.7 153 56.4
Algeria 360 49.4 16.6 86 51.5
Iraq 370 49.2 14.8 26 52.6
Columbia 370 40.6 8.8 81 60.9
Zambia 380 51.5 20.3 259 44.5
Guatemala 390 42.8 13.7 83 52.9
Malaysia 400 39.0 9.8 38 59.4
Dominican Republic 430 45.8 11.0 49 57.8
China, Republic of 430 26.7 10.2 18 61.6
Iran 450 45.3 15.6 160 51.0








Per Capita Crude Crude Infant Life
Countries GNP birth rate death rate Mortality expectancy


Nicaragua
Brazil
Peru
Albania
Cuba
Costa Rica
Mexico
Jamaica
Portugal
Yugoslavia
Romania
Chile
Panama
Bulgaria
Hong Kong
Trinidad & Tobago
Venezuela
Singapore
U.S.S.R
Japan
Israel
United States


450
460
480
480
510
590
700
720
730
730
740
760
820
820
900
940
1,060
1,200
1,400
2,130
2,190
5,160


Source: The Assault on World Poverty,

1975, pp. 414-415 (Annex 2).


Baltimore; Johns Hopkins University Press,









Notes

1. For a discussion on these, see Health Condition in the
Americas (1978).

2. For a discussion of life tables and the mathematical
analysis used in this section, see Keyfitz (1972).
3. For another point of view, see (Jones: 1975: 215).

4. For a recent analysis of fertility and development, see
Repetto (1979). Repetto argues that intranational and
international income redistribution is a feasible mecha-
nism of development to reduce fertility. He tests the
hypothesis that, at any stage of economic development,
the birth rate will be lower the more equal the distribu-
tion of income. See Repetto's earlier work (1978).

5. Other discussions of "fertility" decline can be found in
Jay Weinstein (1978). Michael E. Conroy (1974) and
Nancy R. Folbre (1976) are concerned with pointing out
that there is no direct relationship between fertility
decline and public expenditure.

6. Some quasi-linked references to our topic may be squeezed
from the fertility development nexus which are found in
Alvin J. Harman (1970); John D. Kasarda (1971); Harvey
Leicenstein (1974). By and large these authors, and
numerous others, are concerned with fertility decline and
their impact on economic development. All of them tend
to concur with Leibenstein (1974:470-71) that the "deter-
minants of fertility decline are manifold." History,
socio-cultural factors, cultural forces all play critical
roles.

7. For another view which addresses the question 'what in-
fluence do human made conditions have on fertility rate'
see JoAnn Kropp Glittenberg (1979).

8. This linearity/non-linearity discussion as it relates to
fertility (and indirectly to life expectancy) has been
discussed by: T. Paul Schultz (1974). He notes that the
character of family size suggests that linear demand
models are too restrictive for the study of fertility.
Both theoretical and empirical evidence have been presented
for non-linearity between explanatory variables and fer-
tility.
Empirical analyses using Microeconomics Data, vis-A-vis
fertility; See Robert Willis (1973): Eva Bernhardt (1972);
Julian Simon (1974); W. Sanderson and R. Willis (1971).
All of these authors havys made the claim for non-linearity
between fertility and the various variables used.

9. See Goldfield and Quandt (1965) for a discussion of some
tests of heteroskedasticity.









REFERENCES

Adelman, I. An econometric analysis of population growth,
American Economic Review. 1963, 53, 315-399.

Bernhardt, E. Fertility and economic status in Sweden: some
recent findings on differentials in Sweden. Population
Studies, 1972, 26, 2.
Chiang, C.L. A stochastic model for health service planning,
Systems Analysis Applied Health Services, PAHO Advisory
Committee on Medical Research, Washington, D.C. 1972.

Christ, C. Econometric models and methods, New York: John
Wiley and Sons, 1966.

Coale, A. Hoover, E.M. Population and economic development in
low-income countries, New Jersey: Princeton University
Press, 1972.

Conroy, M.E. Recent research in economic demography related
to Latin America and the Agenda Latin American Research
Review, 1979, 9 3-27.
Conroy, M. and Folbre, N.R. Population growth as a deterrent
to economic growth: A repraisal of the evidence, Institute
of Society Ethics and Life Sciences, February, 1976.

Glittenberg, J.K. A comparative study of fertility in highland
Guatemala: A Ladino and Indian town Caribbean Studies
Association Fourth Annual Meeting, Martinique 1979.

Goldfield, S.M. and Quandt, R.E. Some tests for homoskedasticity,
Journal of the American Statistical Association, 60 539-547.
Gregory, P. et al. Differences in fertility: development and
developing countries, Journal of Development Studies,
1973, 9, 233-241.
Harewood, J. The population of Trinidad and Tobago, CICRED
Series, Institute of Social and Economic Research,
St. Augustine: Trinidad, University of the West Indies,
1974.
Harman, A.J. Fertility and economic behaviour in the Philipines.
Santa Monica, California: Rand Corporation, 1970, (Mimeograph)
Intriligator, M.D. Econometric models, techniques and applications.
New Jersey: Prentice-Hail, 1978.

Jones, G. Population growth and educational planning in
developing nations, New York: John Wiley and Sons, Inc.,
1975.









Kasarda, J.D. Economic structure and fertility: a comparative
analysis, Demography 1971, 8 307-317.

Keyfitz, N. Applied mathematical demography, New York: John
Wiley and Sons, 1972.

Leibenstein, H. An interpretation of the economic theory of
fertility: promising path or blind alley Journal of
Economic Literature, 1974, 12 457-479.

Nalinvaud, E. Statistical methods in econometrics (2nd Rev.
Ed). Amsterdam: North-Holland Publishing Co., 1970.

Pan American Health Organization (PAHO), Health conditions in
the Americas, 1973-1976, Scientific Publication (No.364)
Washington, D.C., 1978.

Roberts, G.W. Some demographic considerations of federation,
Social and Economic Studies, 1957, 6, (2), 264-265.

Roberts, G.W. The present fertility position of Jamaica, in
Egon Szabody (Ed), World Views of Population Problems,
Budapest: 1968.

Repetto, R. The interaction of fertility and the size distribu-
tion of income, Journal of Development Studies, 1978, 14,
22-39.

Repetto, R. Economic equality and fertility in developing countries,
Baltimore: Johns Hopkins Press, 1979.

Sanderson, W. and Willis, R. Economic models of fertility:
some examples and implications Annual Report, National
Bureau of Economic Research, 1971.

Salas, R.M. World population growth: hopeful signs of a slow
down. The Futurist, October 197& XII, (5) 276-282.

Schutz, T.P. fertility determinants: a theory, evidence and an
application to policy evaluation, Santa Monica: Rand
Corporation, 1974.

Schmidt, P. Econometrics, New York: Marcel Dekker, 1976.

Simon, J. The effects of income on fertility, Population
Studies, 1969, 23, 327-341.

Simon, J. The effects of income on fertility, Chapel Hill:
Population Center, University of North Carolina, Monograph
19, 1974.

Sinclair, S. A fertility analysis of Jamaica: recent trends
with reference to the parish of St. Ann, Social and
Economic Studies. 1974, 23, (4) 588-636.









Stewart, C.T. (Jr.) and Siddayao, C.M. Increasing the supply of
medical manpower, Washington D.C.: American Enterprise
Institute, 1973.
Theil, H. Principles of Econometrics, New York: John Wiley and
Sons, 1971.
Todaro, M.P. Economics for a developing world, London: Longmans
Group, 1970.
Weinstein, J. Fertility decline and social services access:
reconciling behavioral and medical models, Comparative
International Development, Spring, 1978, XIII, (1), 71-99.
Weinstraub, R. The birth rate and economic development: an
empirical study, Econometrica, 1962, 30. (4) 812-817.

Willis, R. An econometric analysis of fertility in Sweden,
1870-1965, Econometrica, 1973, 41.

World Bank, The assault on poverty, Baltimore: John Hopkins
Press, 1975.
World Health Organization (WHO), National Health Plannning in
Developing Countries, Technical Reports Series, No. 350,
Geneva, 1967.




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs