State of the “life span revolution” between 1980 and 2000

Journal of Development Economics 80 (2006) 518–526

www.elsevier.com/locate/econbase

State of the blife span revolutionQ between1980 and 2000

Rati Ram *

Economics Department, Illinois State University Normal, IL 61790-4200, USA

Received 23 January 2004; received in revised form 28 January 2005; accepted 22 February 2005

Abstract

Using data for 163 countries, state of the blife span revolutionQ over the period 1980–2000 is

studied in terms of measures of cross-country inequality and through least-squares and quantile-

regression estimation of simple convergence models. Four main points are noted. First, dynamics of

the cross-country distribution of life expectancy during these 20 years seem markedly different from

those for the preceding decades: instead of the sharp bconvergenceQ noted until the 1980s, there is

lack of convergence and an indication of bdivergenceQ. Second, the divergence is particularly marked

during the 1990s. Third, spread of HIV/AIDS has probably been a significant factor in generating

divergence during the 1990s. Fourth, besides the sizable temporal heterogeneity, quantile-regression

estimates of convergence models reveal a substantial heterogeneity across the top and the bottom

quartiles within each period.

D 2005 Elsevier B.V. All rights reserved.

JEL classification: O1; I1

Keywords: Life expectancy; Inequality; Convergence; Quantile regression

1. Introduction

Life expectancy is often considered to be a prime indicator of human well-being.

For instance, besides numerous other scholars, Maddison (2001, p. 29) noted that

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R. Ram / Journal of Development Economics 80 (2006) 518–526 519

bIncreases in life expectation are an important manifestation of improvement in

human welfareQ. The large increases in life expectancy after the Second World War,

notably in less-developed countries, were heralded by Ram and Schultz (1979) as the

blife span revolutionQ.The global improvement in life expectancy during the 1960s and the 1970s and the

cross-country bconvergenceQ in this prime indicator of well-being have been

extensively documented by several researchers. However, the course of this revolution

over the 1980s and 1990s has not been as well researched and is thus less well

known1. The few scholars who have included in their studies the life-expectancy scenario

for the 1980s (or early 1990s) are almost unanimous in reporting bconvergenceQ. Forexample, based on data for 1980 and 1985 (along with those for 1960 and 1970), Ingram

(1994, pp. 322–323) stated that bConvergence is quite marked for life expectancyQ andthat there is bsharp convergence in life expectancyQ. Similarly, Sab and Smith (2002,

p. 205), who considered convergence in health and education on the basis of 84-

country data for the period 1970–1990, stated that there is bunconditional convergenceQin life expectancy, bthat countries are converging to a common steady stateQ, and that

the common speed of convergence is about .010 or 1% per year. Also, considering

data for 49 countries covering the period 1965–1995, Becker et al. (2003) concluded

that bThe absence of income convergence noticed in the growth literature is in stark

contrast with the reduction in inequality after incorporating recent gains in longevityQ.This study is motivated mainly by four considerations. First, since the 1990s and

even the 1980s have not been adequately covered in the research on life expectancy, it

is useful to study these periods with the largest possible number of countries. Second,

most studies seem to have either looked at some measures of cross-country inequality

or estimated a convergence model. It appears useful to consider measures of cross-

country inequality along with estimates of convergence models. Third, it is perhaps

important to take a look at the possible impact of HIV/AIDS on cross-country

distribution of life expectancy. Fourth, while almost every estimation of convergence

models has been premised on the postulate of a common convergence coefficient, it

should be instructive to explore variations across the countries by using quantile-

regression methodology.

Several conclusions seem interesting. First, the period 1980–2000 presents a contrast

from 1960–1980 in terms of the magnitude of improvement in life expectancy as well

as in cross-country distribution of the improvement. Second, the 1990s appear

particularly dismal and there is an indication of bdivergenceQ in life expectancy. One

thus notes large differences across the decades. Third, the role of HIV/AIDS in the

observed divergence during the 1990s appears strong. Last, within each period,

quantile-regression estimates of convergence models reveal large differences in the

coefficients for the top and bottom quartiles.

1 For the 1990s, Ram (2005) provides a short description of the contrast between changes in cross-country

dispersions of income and life expectancy.

R. Ram / Journal of Development Economics 80 (2006) 518–526520

2. Data, methodology, and the main results

2.1. Data

All information is taken from World Bank’s (2002) World Development Indicators

on CD-ROM.2 Although data for 1960 and 1970 are also considered in a quick manner,

the primary focus is on the numbers for 1980, 1990 and 2000 so as to study the period

1980–2000. Every country for which data could be found on the CD-ROM has been

included. There are 163 countries for which information for all the 5 years (1960, 1970,

1980, 1990 and 2000) is available. This is perhaps the largest cross-country dataset used in

any such study.

Besides considering the full dataset, a smaller subset is also studied after excluding

countries that have been severely affected by HIV/AIDS. Although incidence of AIDS

is an important component of the global picture of human health, life expectancy and

well-being, it is of interest to consider the role of AIDS as an explanatory factor in the

observed changes during the 1980s and 1990s.

2.2. Methodology

Two measures of cross-country inequality in life expectancy are computed. One is

the well-known standard deviation (SD) and the other is an adaptation of the

population-weighted index (L) proposed by Theil (1979) for income. The measure L is

well known in the literature on income inequality and has also been used by Ram

(1982, 1992) and others for life expectancy and several indicators of basic-needs

fulfillment. Bourguignon (1979) has shown, in the context of income inequality, that

the measure possesses many desirable properties.3

These indexes (SD and L), along with coefficient of variation (CV), enable one to

track the course of cross-country inequality in life expectancy and to judge

convergence or its absence. A decline (increase) in inequality may be interpreted as

indicating sigma-convergence (divergence) for life expectancy.

Besides construction of inequality indexes, standard (unconditional) convergence-

models are also estimated. Following Sab and Smith (2002, p. 206) and other scholars,

such a model may be written as

ln Eit=Ei0ð Þ ¼ aþ b ln Ei0ð Þ þ ui ð1Þ

where Ei0 and Eit denote ith country’s life expectancy in period 0 (bbaseQ period) andperiod t, respectively, and u is the standard error term. A significantly negative sign on b

indicates convergence during the period. Also, as noted by Sab and Smith (2002, p. 205),

2 One exception is China for whom life expectancy in 1960 is incorrectly given as 36.3 years in the CD-ROM.

The author’s correspondence with the World Bank indicated that the correct number is 47.0, which has been used

in this study.3 The expressions for both SD and L are given in the notes below Table 1. Bourguignon (1979) defined L as

ln (A /G) where A and G are the (weighted) arithmetic and geometric means. However, it can be shown that ln (A /

G) is exactly the same as the expression given in Table 1.


the (annual) speed of convergence is given by � ln (1+b) / t. Eq. (1) is estimated by the

ordinary least-squares (OLS) procedure for the periods 1980–2000 and 1990–2000.

As already stated, a significant dimension of this study is to consider whether the

nearly universal postulate of a common global coefficient in models of convergence is

reasonable. One way to do that is to estimate quantile regressions for different segments

of conditional distribution of the relative increase in life expectancy. Such estimates for

Eq. (1) would indicate the effect of initial life expectancy on different parts of the

(predicted) distribution of the proportionate increase in life expectancy during the period.

The two segments on which this study focuses are the top and bottom quartiles of the

distribution. Technical details about quantile-regression methodology are omitted here. As

explained by Chamberlain (1994, p. 181), Deaton (1997, pp. 83–84), Arias et al. (2001,

p. 21), and other scholars, the estimation procedure involves minimizations that are

similar to minimizing the sum of absolute deviations (berrorsQ) in a median-regression

context. The minimization problem can be solved by linear programming. However, as

Deaton (1997) and other scholars have pointed out, estimation of the covariance matrix of

the parameter estimates and hence hypothesis tests can become difficult in the presence

of departures like heteroscedasticity. One way to attenuate these difficulties is to obtain

standard error estimates by the bbootstrapQ methodology. A procedure in STATA employs

the bootstrap to generate fairly robust standard errors, which have been used in this paper.

2.3. Main results

Column (1) in Table 1 provides a quick view of mean life expectancy in 1960, 1970,

1980, 1990 and 2000. It is easy to see that the pace of increase has become much slower

since the 1980s. Although some slowdown in the increase is to be expected, there seems to

be a watershed during the 1980s. While the mean increased by 6.5 years in the 1960s and

about 4.0 years in the 1970s and more than 10 years during 1960–1980, the improvement

during the 1980s was about 2.5 years and that during the 1990s was less than 1.5 years.

The absolute increase over the 1990s is thus less than one-fourth of that during the 1960s.

In percentage terms, the drop is even bigger since the increase was about 12.5% in the

1960s but only around 2.0% over the 1990s.

While changes in the mean are of interest, it is more important to study the patterns

of cross-country dispersion or inequality. Columns (2), (3) and (4) in Table 1 give an

indication of global inequality in life expectancy for 1960, 1970, 1980, 1990 and 2000.

For all measures, one can clearly discern a big drop in inequality during the 1960s and

a modest fall during the 1970s. The drop over the 1980s is also fair. This is the scenario

that is most familiar and has been noted by numerous scholars. However, there is an

increase in inequality during the 1990s and the inequality in 2000 has risen to the 1980

level (or even higher in terms of SD). The numbers indicate that convergence is likely

to have ended during the late 1980s or the 1990s and divergence seems to have begun.

A pessimist would thus say that the blife span revolutionQ is already over despite the

fact that levels of life expectancy are quite low in many developing countries. Of

course, Table 1 shows that one is still likely to observe significant convergence by

looking at a period other than 1980–2000 and 1990–2000, which is what almost all

scholars have done.

Table 1

Cross-country mean and inequality in life expectancy for selected years

Year Full sample (weighted)

mean (N =163)

Full-sample index of inequality

(N =163)

Inequality index after excluding

high-AIDS cases (N =124)

(1) (2) (3) (4) (5) (6)

L SD CV L SD

1960 52.1 .023 11.56 0.22 .0224 11.49

1970 58.6 .014 9.60 0.16 .0118 8.99

1980 62.3 .011 8.98 0.14 .0085 8.08

1990 65.0 .009 8.25 0.13 .0057 6.91

2000 66.4 .011 9.19 0.14 .0045 6.31

The weighted means are obtained by using population shares as weights. L stands for a slight adaptation of Theil’s

(1979) population-weighted inequality index and is expressed as

L ¼Xni¼1

pi ln pi=yið Þ

where pi is the population-share of country i, ln denotes natural logarithm, and yi is the share of the country in

aggregate global life expectancy and, writing Pi for the ith country’s population and Ei for its life expectancy, is

defined as

yi ¼ PiEið Þ=Xni¼1

PiEi:

SD denotes standard deviation and has the following well-known expression

SD ¼Xni¼1

pi Ei � Eð Þ2#:5"

where Ei is life expectancy in country i (for a given year), pi is the population share of the country, E is the

weighted global mean defined as

Xni¼1

piEi

and n is the number of countries. CV denotes coefficient of variation and equals the ratio of SD to mean. All

information is derived from 2002 edition of World Development Indicators on CD-ROM. Life expectancy refers

to life expectancy at birth. Computations have been done on SAS for Windows (version 8).


The picture since 1980 can also be studied in terms of the simple model of

convergence specified in Eq. (1). The full-sample column in section A of Table 2, which

contains a summary of the OLS and quantile-regression estimates for the periods 1980–

2000 and 1990–2000 for the entire sample, suggests several points.

First, the OLS estimates indicate a tiny and insignificant convergence coefficient

for 1980–2000, but there is a highly significant divergence during the 1990s

(1990–2000).

Second, for the period 1980–2000, quantile-regression estimates reveal strong

contrasts between the top and bottom quartiles (of the conditional distribution of life-

expectancy changes). While one observes convergence within the top quartile, there is

an insignificant divergence in the bottom quartile.

Table 2

OLS and quantile-regression estimates of coefficient b in convergence models of life expectancy

A. Unconditional convergence model: Eq. (1) of the text

Full sample Excluding high-AIDS cases

(N =163) (N =124)

1980–2000

OLS �0.025 (�0.63) �0.191* (�6.90)Quantile-regression:

Top quartile �0.233* (�4.61) �0.363* (�11.17)Bottom quartile 0.104 (1.31) �0.117* (�2.95)

1990–2000

OLS 0.069* (2.20) �0.062* (�3.76)Quantile-regression:

Top quartile �0.100* (�4.89) �0.161* (�6.74)Bottom quartile 0.160* (3.58) �0.016 (�0.49)

B. Illustrative comparisons of OLS estimates of convergence coefficients in unconditional and simple

conditional convergence models of life expectancy

Full sample Excluding high-AIDS countries

Unconditional Conditional Unconditional Conditional

1980–2000 (N =125) (N =93)

0.033 (0.69) 0.026 (0.30) �0.215* (�6.85) �0.214* (�4.36)1990–2000 (N =145) (N =108)

0.095* (2.76) 0.143* (2.40) �0.051* (�3.02) �0.012 (�0.45)The simple conditional model is obtained by adding the logarithm of initial-period real GDP per capita to the

unconditional model and may be written as

ln Et=E0ð Þ ¼ a1 þ b1 ln E0ð Þ þ c ln Y0ð Þ þ u1:

Quantile-regression estimates (of section A) are obtained on STATA (version 7). The numbers in parentheses are

t-statistics and are based on bootstrap standard errors for quantile regressions with 1000 replications. OLS

estimates are obtained on SAS for Windows (version 8). An asterisk indicates significance at least at the 5% level.

Additional regression details are omitted to keep the table compact. In particular, differences between quantile-

regression estimates for top and bottom quartiles show high statistical significance in all cases. ln( Y0) denotes

logarithm of real GDP per capita in international dollars in 1980 for 1980–2000 regressions and in 1990 for 1990–

2000 regressions. The underlying samples for part B are exactly the same as in part A, but the number of

observations is depleted due to missing data on real GDP per capita.


Third, the contrast shown by quantile-regression estimates is even more dramatic for

1990–2000. There is a highly significant convergence within the top quartile, but a highly

significant divergence in the bottom quartile. These contrasts seem to be among the most

informative aspects of the study.

Fourth, it is useful to compare the global picture revealed by OLS estimates of the

convergence model with that suggested by the inequality indexes in Table 1. Over the

period 1980–2000, L and CV are unchanged while there is a slight increase in SD, but

OLS estimate of the convergence model shows an insignificant convergence in life

expectancy. For 1990–2000, inequality indexes increased and the OLS estimates show


divergence. Thus, despite the thought that sigma- and beta-convergence are not identical

concepts, the global (full sample) scenarios indicated by Table 1 and section A of Table 2

seem largely consistent.

3. Search for an explanation and some further reflections

When considering possible reasons for lack of (or slow) convergence in life expectancy

during the 1980s and divergence during the 1990s, the role of HIV/AIDS easily comes to

mind. Although prevalence of AIDS is an integral part of the health and life-expectancy

status of the international community, it is useful to consider how the global scenario looks if

countries with a significant incidence of AIDS are excluded. A reasonable procedure to do

that is to treat a prevalence rate of 2% or higher among the adult population (age 15–49) at

the end of 2001 as a case of bhighQ incidence. That is almost the same as the criterion of 1.9%

adopted for 1999 incidence byUnited Nations (2002, p. 103).4 Following that criterion, and

using the incidence information contained in UNAIDS (2002), 39 of the 163 countries

fall in the high-prevalence category. Columns (5) and (6) in Table 1 and the last column

in section A of Table 2 report indexes of inequality and estimates of convergence

models after excluding the high-AIDS countries. Four points are indicated by these

numbers. First, in contrast to the full-sample scenario, the inequality indexes show a

decline during the 1990s. However, the decline is much smaller than during the earlier

decades. Second, again in contrast to the full-sample estimates, OLS estimates after

exclusion of the high-AIDS cases show significant convergence during 1990–2000 as

well as during 1980–2000; but the speed of convergence implied by the OLS estimate

for 1990–2000 is about 0.6%, which is nearly half of that reported by Sab and Smith

(2002, p. 205) and also about half of that implied by the estimate for 1980–2000. Third,

therefore, one may say that prevalence of HIV/AIDS is a major factor in the global

patterns observed for 1980–2000 and 1990–2000. However, considering the magnitudes

of decline in the inequality indexes from 1990 to 2000 and of the convergence

coefficient for 1990–2000 after excluding the high-AIDS countries, HIV/AIDS might

not be the entire story. Fourth, as for the full sample, quantile-regression estimates

indicate huge heterogeneity across the top and bottom quartiles. For the bottom quartile,

no significant convergence is observed during the 1990s even after excluding countries

with high incidence of HIV/AIDS. Also, speeds of convergence are very different for the

two quartiles in both periods.

Although unconditional convergence models seem appropriate for life expectancy and

have been used by Sab and Smith (2002) and other scholars, it may be of interest to

consider estimates from simple models of conditional convergence that include (initial)

real GDP per capita as a conditioning variable. Section B in Table 2 provides an

illustrative comparison of OLS estimates of convergence-coefficients from conditional

and unconditional models with and without the high HIV/AIDS countries. Although the

underlying sample is identical with that on which Table 1 and section A of Table 2 are

4 United Nations (2002) included Brazil and India also in the high-AIDS group despite low prevalence rates in

these countries.


based, missing data on real GDP per capita reduces the effective sample sizes. It may be

seen that the full-sample picture is similar in both models and is broadly consistent with

that in section A. After excluding the high HIV/AIDS countries also, the two models

yield almost identical estimates for 1980–2000. However, the convergence coefficient in

the conditional model for 1990–2000 is weak.

Despite the fact that most high HIV/AIDS countries are located in Sub-Saharan Africa

(SSA), one might have interest in looking at the position if all SSA countries are excluded.

Unreported OLS estimates of convergence models indicate that exclusion of SSA

generates a scenario that is similar to that in the last column of section A of Table 2. One

could, therefore, perceive the observed divergence in life expectancy as largely a SSA

phenomenon.

Three additional observations seem relevant. First, despite the divergence in life

expectancy during the 1990s, which seems largely due to HIV/AIDS, it is possible that

global convergence may be observed in later decades. Estimates complied by United

Nations (2002) and more recent documents indicate that there might be a cessation and

reversal of the demographic consequences of AIDS in or around the year 2020 in most

countries. Second, since bconvergenceQ and bdivergenceQ are essentially long-term

concepts, their application to a period of 10 or even 20 years should be interpreted with

caution. Third, some Barro-type growth models have been estimated by using instrumental

variables (IVs). However, IVs seem more useful for income-growth regressions that

contain several potentially endogenous variables. In convergence models of life

expectancy, typically the only regressor is initial life expectancy, which is predetermined.

The initial-income variable in simple conditional models of the kind shown in section B of

Table 2 may also be reasonably treated as predetermined.

4. Concluding observations

Using data for 163 countries, this study considers the course of the life span revolution

during the relatively under-researched 1980s and 1990s. Four main points seem to stand

out. First, in sharp contrast to the earlier decades, there is lack of cross-country

convergence in life expectancy during 1980–2000 and a marked divergence during the

1990s. Second, however, the AIDS epidemic seems to be a major factor behind the

observed patterns. Third, sigma-convergence measures, represented in cross-country

inequality indexes, and beta-convergence regression coefficients indicate similar

scenarios. Fourth, along with a substantial temporal heterogeneity across the decades,

quantile-regression estimates of convergence models reveal large differences in the

coefficients for the top and the bottom quartiles within each period.

Acknowledgements

Useful comments from Lant Pritchett and two perceptive referees are gratefully

acknowledged. The usual disclaimer, of course, applies. Helpful research assistance was

provided by V. Cristina Iliuta.


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State of the “life span revolution” between 1980 and 2000