The impact of AIDS on income and human capital.
Ferreira, Pedro Cavalcanti ; Pessoa, Samuel ; Dos Santos, Marcelo Rodrigues 等
I. INTRODUCTION
In the time it takes to read this paper, more than 1600 people will
become infected by the HIV virus worldwide and 960 will die due to AIDS.
Seventy-one percent of the deaths will occur in Africa, by far the
worst-affected region. Out of the 39 million persons estimated to be
living with HIV/AIDS in the world, almost 65% live in Sub-Saharan
Africa. (1) Worse still, of the 5 million adults and children newly
infected with HIV, 4 million are Africans, an indication that the
epidemic may not yet have reached its peak. In some countries, such as
Swaziland, one out of three adults is infected, and the figures for
Lesotho, Botswana, and Zimbabwe are not much different. By the end of
2005, there were ten countries in Africa in which more than 10% of the
adult population was infected with HIV, and another five countries with
infection rates between 6% and 8%.
It is clear today that AIDS is not only a health disaster, but a
major development crisis. There is now a large array of papers, books,
and newspaper articles dedicated to the study of the economic
consequences of AIDS in Africa (and elsewhere). The majority of them are
case studies from household or hospital surveys, from firm or plant
level evidence, and from government reports.
The present paper explores two channels on how HIV/AIDS affects
long-run income that have not been sufficiently stressed by the
literature: the reduction of the incentives to stay in shool due to
shorter expected lifespan and the reduction in productivity of
experienced workers. According to the World Population Prospects (United
Nations 2001), life expectancy at birth in the 35 highly affected
countries of Africa was estimated to be, in 1995-2000, 6.5 yr less than
it would have been without AIDS. In Botswana, life expectancy went from
60 yr in 1985 to less than 40 in 1999 while in countries such as
Swaziland, Zimbabwe, Zambia, and South Africa it decreased in the same
period by more than 10 yr. When comparing to 2015 projections (U.S.
Census Bureau 2004) the picture is even more dramatic, as life
expectancy with AIDS in Botswana, 34.7 yr, is less than half of what it
would be in a scenario without the epidemic.
The impact of longevity on development and education has been,
recently, the object of a large number of studies. In the studies of
Soares (2005), Khakemi-Ozacan, Ryder, and Weil (2000), Boucekkine, de la
Croix, and Licandro (2002), and Ferreira and Pessoa (2007), we see that
in one way or another, longer lives allow for extension of the
population working life and, consequently, an increase in the present
value of the flow of wages of a given investment in education. Higher
returns to education in turn induce individuals to stay in school
longer, increasing average human capital of the population, with a
potential effect.
The reduction in productivity of infected workers attracted
considerably more attention. That is so not only because workers in poor
health are unable to perform at usual levels, but also because of
absenteeism due to illness. A case study in Burkina Faso, for instance,
found that net revenues from agriculture production in AIDS-affected
households usually decrease by 25%-50% (Guinness and Alban 2000). This
study also has evidence of reduction in agriculture output in
AIDS-affected households in Zimbabwe, which goes from 61% in the case of
maize to 29% in the case of cattle.
We use these facts to motivate an artificial economy where
individuals live for three periods, may get infected in the second
period, and with some probability die of AIDS before reaching the third
period of their lives. Parents care for the welfare of the future
generations (and their longevity), so that they will maximize lifetime
utility of all future generations in their dynasty. Those with the HIV
virus may or may not receive medical treatment, and infected-treated
individuals are more productive than those who receive no medical
attention (but less so than healthy agents) and have a larger chance to
survive to the third period of their life. Motivated by the empirical
studies of Neal and Johnson (1996) and Keane and Wolpin (1997), we
assume that the children's education depends on the parental human
capital investments. The reduction in longevity due to AIDS decreases
total funds--there are less intergenerational transfers, for
instance--available for education, saving, and consumption. Parents
spend less time helping the education of their children, so that
schooling falls when compared to a non-AIDS situation. Moreover, if the
life expectation along the dynasty decreases, incentives to invest in
the future generations will also fall.
All of this will have a direct impact on output, as human capital
is a factor of production. Moreover, the marginal productivity of
capital decreases with the reduction of education, a complementary
input. As savings and physical capital investment are endogenous in this
model, they will both fall in equilibrium, further reducing output.
Additionally, AIDS also has a direct impact on aggregate output as HIV
positive workers are less productive and also because many workers die
at their productive peak, increasing the proportion of less efficient
workers in the labor force.
This model is used to simulate the long-run impact of the HIV/AIDS
epidemics in Africa. (2) The model predicts that a country with an adult
infection rate of 20% such as South Africa will be 18% less productive
than it would be without HIV/AIDS. The most affected countries will be
in the future, on average, a quarter poorer than they would be without
AIDS. This estimated decrease in per capita output is well above
previous estimates. The model also finds that, in the long run, human
capital could fall, in some cases, to two-thirds of the levels observed
before the epidemic. On a positive note, simulations show that the
overall impact on incomes and education could be significantly reduced
if medical treatment is extended to most of the infected population.
The findings of this study are, to say the least, extremely
worrisome. It indicates that the current catastrophic situation in
Sub-Saharan Africa, or in any country where HIV/AIDS reaches similar
levels, is not yet at its peak. We are already observing a decline in
school enrollment in affected areas. According to the 2002 Report on the
Global HIV/AIDS Epidemic (UNAIDS 2002), in Central African Republic and
Swaziland it fell by 20-36%, and in parts of KwaZulu-Natal Province in
South Africa, the number of pupils attending the first year of primary
school was 20% lower in 2001 than in 1998, and economic hardship was the
major factor. In Kenya and Tanzania, the gross primary enrollment rate
fell, between 1980 and 1997, from 115% to 85% and from 93% to 67%,
respectively (UNAIDS 2000). This is consistent with the channel stressed
by our model. Moreover, Hamoudi and Birdsall (2004) provide econometric evidence, using Sub-Saharan African countries data, that a fall of life
expectancy at birth of 10 yr is associated with a reduction of 0.6 yr of
education. On the same topic, Soares (2006) presents micro-level
evidence on the effect of adult longevity on schooling. Using data from
the 1996 Brazilian Demographic and Health Survey, he shows that higher
longevity is systematically related to higher education attainment.
There is currently a small but active literature on the economic
impact of HIV/AIDS at more aggregated levels. Cuddington (1993) and
Cuddington and Hancock (1994) use modified versions of the Solow model
in which fractions of the annual AIDS-related medical costs are financed
out of savings. Haacker (2002) simulates a similar model for nine of the
most affected African economies. In all these papers, the estimated
impact of the epidemic on per capita GDP was found to be very modest, a
long-run decline of 0%-3% in most cases. Arndt and Lewis (2000) simulate
a CGE model in which AIDS affects TFP, labor productivity, and public
expenditures. They estimate that income per capita in South Africa will
fall by 8% until 2010, and, not surprisingly, half this fall will be
caused by reduced savings due to the assumption that infected
individuals do not save. (3)
Three recent contributions related to our study are Young (2005),
Bell, Devarajan, and Gersbach (2006), and Corrigan, Glomm, and Mendez
(2005). The first paper finds very little impact of AIDS/HIV. This is so
because the population decrease offsets the detrimental impact on the
human capital accumulation of orphaned children, so that the AIDS
epidemic enhances future consumption prospects in South Africa. Note,
however, that by working with a Solow model of capital accumulation the
article forces a large impact of fertility decreases, as long-run income
is a negative function of population growth rate. In a more complete
general equilibrium model such as the neoclassical growth model (or our
simple OLG model), where saving is endogenous, income in the long-run is
a function of the capital-labor ratio, so that decreases in population
bring about an adjustment in the capital stock. Furthermore, AIDS
epidemic affects age-population distribution in an unequal way. It is
true that AIDS brings about a reduction in population, but individuals
at advanced ages tend to be more affected than young ones. In some
countries in Africa, in which life expectancy is very low, individuals
do not reach the more productive and experienced stage of their lives.
(4) Thus, in a life-cycle model, in which age-population distribution
tends to play an important role, the increase of the marginal
productivity of labor due to the reduction of population tends to be
offset by the fall of the share of experienced workers. This is the
reason that in our model changes in the population growth rate have a
very small impact on output.
Bell and coauthors also focus on the impact of the disease
environment on human capital transmission mechanisms from parents to
children in a model calibrated to South Africa. Parents may die,
affecting the amount and quality of child rearing and also the funds
necessary to pay for formal education, which is the only form of
investment. Results are such that the economy could shrink to half its
current size in four generations. A similar model is also found in
Corrigan, Glomm, and Mendez (2005), which adds physical capital
accumulation. In this model, parents care for the consumption of their
children (and not welfare as in ours) and HIV-infected individuals die
for sure in the third period of life and are less productive in the
second. They find an impact much smaller than that in Bell, Devarajan,
and Gersbach (2006).
The remainder of the paper is organized in four sections. In the
next section the theoretical model is presented, and in Section III we
discuss the calibration and measurement procedures. In Section IV, the
results are presented while Section V concludes.
II. ECONOMIC ENVIRONMENT
This economy is populated by overlapping generations of people who
live for three periods and are altruistic toward their descendants. In
the first period of life, "children," individuals spend all
their time in school. In the second period, "young adult,"
they work, save, and decide the human capital of their kids, by choosing
the number of hours they will dedicate to their education. In the last
period of life, "experienced adult," individuals only work and
choose optimally a bequest, which is received by the young adults.
A fraction n of young adults find out in the beginning of this
period of their lives that they are infected by the HIV virus. These
individuals then decide if they will start treatment or not, whose costs
are exogenously given and may be partially or totally subsided by the
government. The probability of surviving to the third period of life
increases with the treatment. The productivity decreases if workers get
infected and decreases even further if they are not getting any medical
care. If their parents die of AIDS (or by any other reason) young adults
do not receive the voluntary bequest.
All decisions in this economy are made by the parents, who care
about the welfare of their children. Formally, this means that they will
maximize lifetime utility of all future generations in their dynasty.
Hence, parents will take into account expected utility of future
members of their dynasty when deciding bequest. In this case, the larger
the bequest, the more time young adults could dedicate to the education
of their children. If parents die prematurely, leaving no bequest, the
disposable income of their young adults, son/daughter, decreases, so
they will spend more time in the labor market and less at home helping
the education of the kids. (5) Hence, the higher the infection rate and
consequently the lower life expectancy, the lower will be the education
of the next generations, everything else being equal. Formally, we
assume that human capital of an individual of the next generation,
h', follows:
(1) h' = [OMEGA][(nh).sup.[theta]],
where [OMEGA] and [theta] are constants, n is the time parents
spend with their children, and h is the human capital of parents.
Human capital accumulation occurs outside the labor market.
However, in order to obtain a realistic wage profile, we assume that
productivity increases along the life cycle, so that productivity of
young adults, [[upsilon].sub.2], is smaller than that of experienced
adults, [[upsilon].sub.3]. We also posit that a HIV-positive worker is
less productive than otherwise, but that medical expenses enhance the
productivity of infected workers.
We assume that parents also care about how long each child will
live, in such a way that the discount factor applied to children's
welfare is a function of their expected life expectancy. This captures
the idea that parents are altruistic but the parental human capital
investment may be influenced by the offspring's expected life
expectancy since it may affect the expected return on that investment.
The model, hence, emphasizes two channels from HIV/AIDS to long-run
income, the reduction of longevity, and the reduction of productivity.
Moreover, the fact that infected individuals die in the peak of their
productivity will also impact aggregate output.
The key difference among individuals is whether they were infected
or not in the second period of life and, finding themselves with the HIV
virus, if they receive medical care or not. The probability of surviving
to the third period of life of a healthy individual, [[PHI].sub.H], is
larger than that of an infected-treated individual, [[PHI].sub.IT],
which, in its turn, is larger than that of an infected non-treated
individual, [[PHI].sub.IN]. These exogenous probabilities will allow the
model to match the observed life expectancy of different countries.
A. Decision Problem of Households
(Pa) Healthy Individuals. The problem of a healthy individual is to
optimally pick savings, a, bequest, b', human capital of their
children, h', and the fraction of the time they dedicate to their
children learning, n, in order to maximize
(2) [V.sub.H](h, b) = u([c.sub.2]) +
[beta]{[[PHI].sub.H][u([c.sub.3) + [gamma]EV(h', b')] + (1 -
[[PHI].sub.H])[gamma]EV(h', 0)},
subject to his/her second-period budget constraint
[c.sub.2] + a = (1 - [tau])(1 - n)wh[[[upsilon].sub.2] + (1 + r)b +
[xi], (3)
third-period budget constraint
[c.sub.3] + b' = (1 - [tau])wh[[upsilon].sub.3] + (1 + r)a +
[xi], (4)
and the law of motion of human capital h' =
[OMEGA][(nh).sup.[theta]], where [beta] is the discount rate with
respect to his/her own future and [gamma] is the discount factor applied
to children's welfare.
In the second period of life net income from labor, (1 - [tau])(1 -
n)wh[[upsilon].sub.2], and voluntary and involuntary bequest (b and
[xi], respectively) are split between consumption, [c.sub.2], and
savings, while total time is divided between work and child rearing. In
the third period of life, income is divided between consumption,
[c.sub.3], and voluntary bequest. We assumed that govemment taxes labor
income to finance the subsidy to AIDS treatment. The expected welfare of
the children is:
(5) [[PHI].sub.H]EV(h', b') + (1 -
[[PHI].sub.H])EV(h', 0),
given by the sum of the utility EV(h', b') in the case
that the parent survive to the third period of life and so leaves a
bequest b'--multiplied by the survival probability
[[PHI].sub.H]--and the utility EV (h',O) in the case that the
parent dies prematurely (and so the son/daughter gets no bequest)
multiplied by (1 - [[PHI].sub.H]), the mortality risk of a healthy
individual.
The first component, EV(h', b'), is given by:
(6) EV(h', b') = (1 - [pi])[V.sub.H](h', b') +
[pi] max{[V.sub.IT](h', b'), [V.sub.IN](h', b')}.
The first term to the right-hand side is the probability of the
son/daughter not getting infected multiplied by his/her welfare in this
case. The second term is the product of the probability [pi] of getting
infected and the best option, in terms of welfare, between choosing to
be treated or not.
The second component of the expected welfare of the children,
EV(h',O), follows exactly the same logic of EV (h',b'),
only that no bequest is left to the son because the parent died (from
other causes than AIDS).
(Pb) HIV-Positive Individuals, "Treated." The problem of
HIV-positive individuals is similar. However, he/she will first choose
to be treated or not, depending on [V.sub.IT](h',b') being
larger or smaller than [V.sub.IN](h',b').
If individuals are receiving medical care, their problem is such
that they chose h',b',n, and a in order to maximize:
(7) [V.sub.IT](h, b) = U([c.sub.2]) + [beta]
{[[PHI].sub.IT][u([c.sub.3]) + [gamma]EV(h', b')] + (1 -
[[PHI].sub.IT])[gamma]EV(h', 0)},
subject to:
[c.sub.2] + a = (1 - [tau])w(1 - n)wh[[upsilon].sub.2T] + (1 + r)b
+ [xi] - (1 - s)m
(8) [c.sub.3] + b' = (1 - [tau])wh[[upsilon].sub.2T] + (1 +
r)a + [xi] - (1 - s)m h' = [OMEGA][(nh).sup.[theta],
where [[upsilon].sub.2T]([[upsilon].sub.3T]) is the productivity of
the young (experienced) adult in this case, m is the cost of the medical
treatment and s is the government subsidy. The relevant difference in
the budget constraint with respect to healthy agents is that in this
case agents spend in the second and third period of life a fixed amount
of their income in medication. The government may pay for a fraction s
of the treatment costs.
As just said, HIV-positive individuals will choose between
receiving or not receiving medical care by comparing [V.sub.IT] to
[V.sub.IN]. If the former is larger than the latter, they will choose to
be treated. In contrast, if m is too large with respect to his/her
income or if s is too small, infected individuals may prefer not to pay
for any medical treatment, even if this increases the chance of dying
before the third period of life and decreases effective labor.
(Pc) HIV-Positive Individuals, "Non-treated." In the case
in which HIV-positive individuals do not receive medical attention, the
problem is similar to that of a treated individual, but now the (1 - s)m
component is not present in the budget constraint and productivity will
be [[upsilon].sub.2N] and [[upsilon].sub.3N], assumed to be smaller than
[[upsilon].sub.2T] and [[upsilon].sub.3T], respectively. Of course,
survival probabilities are also different (and smaller).
Finally, we assume, for simplicity, that the intergenerationtal
discount factor [gamma] depends linearly on the offspring's
expected life expectancy:
(9) [gamma] = (1 - [pi])[[PHI].sub.H] [pi][[psi][[PHI].sub.IT] +
(1 - [psi])[[PHI].sub.IT]]
The first term on the right-hand side is the product of the
probability of not getting infected, (1- [pi]), and the survival
probability [[PHI].sub.H], which governs the life expectancy of healthy
individuals. The term in brackets gives the life expectancy of an
infected individual: the fraction of treated-infected individuals,
[psi], times their survival probability, [[PHI].sub.IT], plus the
fraction of non-treated individuals, (1 - [psi]), times their survival
probability [[PHI].sub.IN]. (6)
This formulation is adopted here in order to capture the idea that
parents care about the welfare of their children but the parental human
capital investment may be influenced by the offspring's expected
life expectancy since it may affect the expected return on that
investment. (7)
B. Technology
Output is produced with a constant return to scale Cobb-Douglas
technology:
(10) Y = [ZK.sup.[alpha]][H.sup.1-[alpha]]
where Y represents output, K denotes physical capital services, H
represents the aggregate human capital services, and Z is total factor
productivity. The problem of the firms is standard. They pick capital
and human capital optimally and the first-order conditions are given by:
(11) w = (1 - [alpha]) [ZK.sup.[alpha]][H.sup.1-[alpha]],
(12) r = [alpha][ZK.sup.-[alpha]-1][H.sup.1-[alpha]] - [delta].
C. Equilibrium
Our analysis focuses on stationary equilibria. (8) Let [omega] =
{h, b} and [[lambda].sub.H]([omega]) and [[lambda].sub.I](omega), with
[integral] d[[lambda].sub.H]([omega]) = [integral]
d[[lambda].sub.I]([omega]) = 1, denote the share of healthy and infected
agents at state [omega]. (9) Given the policy parameter s, an
equilibrium for this economy consists of value functions
{[V.sub.H](omega]), [V.sub.IT] ([omega]), [V.sub.IN] ([omega])}, policy
functions {[c.sub.2] ([omega]), [c.sub.3] ([omega]), a([omega]),
n([omega]), b'([omega])}, (10) a share of treated-infected
individuals [psi], time-invariant measures of agents
{[[lambda].sub.H]([omega]), [[lambda].sub.I]([omega])}, accidental
bequest distribution [xi], a labor income tax [tau] and prices {w, r},
such that:
1) {[c.sub.2] ([omega]), [c.sub.3] ([omega]), a([omega]),
n([omega]), b '([omega])} solve the dynamic problems Pa, Pb, and
Pc.
7. This idea is developed by Soares (2005) who provides rationality
for that based on arguments from evolutionary biology literature.
8. In some experiments, we will also analyze the behavior of the
economy during the transition from an equilibrium to another.
9. Of course, the share of healthy and infected agents in the
population is (1- [pi]) [integral] d[[lambda].sub.H]([omega]) and [pi]
[integral] d[[lambda].sub.I]([omega]), respectively.
10. Note that for mature adults, the state variable is actually
given by {h,a,h'}, so that we should write [c.sub.3](h,a,h')
and b'(h,a,h'). However, given a(h,b) and h'(h, b), we
can write the policy functions of mature adults as [c.sub.3]([omega])
and b'([omega]).
2) The individual and aggregate behavior are consistent:
(13) K = [pi] [integral] [[mu].sub.A][b.sub.1]([omega] +
[[mu].sub.o][a.sub.I]([omega])]d[[lambda].sub.I]([omega]) + (1 - [pi])
[integral] [[mu].sub.A][b.sub.H]([omega]) +
[[mu].sub.o][a.sub.H]([omega])]d[[lambda].sub.H]([omega]),
(14) H = [pi] [integral] [[mu].sub.A][1 -
n.sub.I]([omega]][h.sub.I]([omega])[[upsilon].sub.2I] +
[[mu].sub.o][h.sub.I]([omega])[[upsilon].sub.3I]}d[[lambda].sub.I]([omega]) + (1 - [pi]) [integral] [[mu].sub.A][1 -
n.sub.H]([omega]][h.sub.H]([omega])[[upsilon].sub.2H]
[[mu].sub.o][h.sub.H]([omega])[[upsilon].sub.3H}
d[[lambda].sub.H]([omega]),
where [[mu].sub.A] and [[mu].sub.o] are the shares of young adults
and experienced adults in the population, respectively.
3) Factors' prices are such that they satisfy the optimum
conditions (11) and (12).
4) The share of treated-infected individuals is given by:
(15) [psi] = [integral] [I.sub.d]
([omega])d[[lambda].sub.I]([omega]),
where [I.sub.d]([omega]) = 1[for all][omega] such that
[V.sub.IT}([omega]) > [V.sub.IN]([omega]), [I.sub.d]([omega]) = 0
otherwise.
5) The distribution of accidental bequests is given by: ~to [~ f
al(co)d~.i(co) (16) ~-- I.to+bta
(16) [xi] = [[mu].sub.o]/[[mu].sub.o] + [[mu].sub.A] [[pi]
[integral] [a.sub.I]([omega])d[[lambda].sub.I]([omega])].
6) The government budget constraint is satisfied every period:
(17) [tau] = [pi][psi]sm/[omega]H
7) The measure of agents in equilibrium is obtained by iterating on
the distribution until it converges to the invariant distribution.
III. CALIBRATION
We calibrate our economy to some benchmark African nations. These
countries were picked in order to have a broad distribution of infection
rates, life expectancy, and medical expenditures. Some parameters,
however, will be common to all economies.
The period in our economic model has 21 yr. We assume that there is
a continuum of individuals with mass one, which are split into
childhood, young, and experienced adults. The mass of children and young
adults are the same since it is assumed, for simplicity, that every
child reaches adulthood. Thus, the shares of young and experienced
adults in the population are, respectively, given by:
(18) [[mu].sub.A] = 1/2 + (1 - [pi])[[PHI].sub.H] +
[pi])[[PHI].sub.I]
and
(19) [[mu].sub.o] = (1 - [pi])[[PHI].sub.H] + [pi][[PHI].sub.I]/ 2
+ (1 - [pi])[[PHI].sub.H] + [pi][[PHI].sub.I]
where [[PHI].sub.I] = [integral]
{I.sub.d]([omega])[pi][[PHI].sub.IT] + [1 -
[I.sub.d]([omega])][[PHI].sub.IN]}d[[lambda].sub.I]([omega])
One can see that as [pi] goes up [[mu].sub.A] increases and
[[mu].sub.o] decreases, so that this formulation entails that as the
AIDS epidemic gets worse, the share of young and less productive
individuals increases and the average labor productivity in the economy
falls. This variation can be influenced by how many infected individuals
are receiving treatment since it affects the value of [[PSI]sub.I].
Capital share is set to 0.37, in line with Gollin (2002), and the
annual depreciation rate to 5%. The scale parameter Z of the production
function was chosen in order to normalize the wage rate w. Thus, we set
Z = 1.75.
We set the relative risk aversion parameter [sigma] to 4.0. This
value was picked because when using smaller [sigma], a large number of
infected individuals would choose not to be treated even with the
subsidy close to 1. This is so because with lower [sigma], and high
intertemporal elasticity of substitution, individuals do not care for
smoothing consumption and would rather consume more today than spend
money on treatment, even at increasing their risk of dying. However in
countries where treatment is entirely funded by the government (such as
Brazil) the number of HIV-positive individuals that choose not to be
treated is extremely small, close to zero. With [sigma] = 4.0, all
infected individuals will receive medical care.
We used an interest rate slightly above the U.S. annual interest
rate--taking into account the higher risk of African economies--as a
target to calibrate the discount factor. Thus, the annual discount
factor was taken to be 0.98, corresponding to an annual interest rate in
the model without AIDS of about 7%.
Survival probabilities [[PHI].sub.H], [[PHI].sub.T], and
[[PHI].sub.IN] were chosen in order to match the life expectancy of each
type of individual in the model with those observed on data. (11) To
calibrate [[PHI].sub.H], we used the life expectancy observed in each
country before the appearance of the AIDS/HIV epidemic. In general, it
means the life expectancy in 1980-1985. In contrast, life expectancy in
2000-2005 was taken into account to calibrate [[PHI].sub.IN]. This
procedure might overestimate the life expectancy mainly in countries in
which the coverage of AIDS treatment is high. However, if we take into
consideration that AIDS treatment started being carried out only
recently in most African countries, then our assumption works because it
takes time for the effects of AIDS treatment to be felt by infected
individuals. Finally, based on empirical evidence from Soloway (2008),
life expectancy increases, on average, about 13 yr for those who start
getting medication at the first stage of the disease. Thus, we added
this estimation to life expectancy in 2000-2005 to obtain a value for
[[PHI].sub.IT]. In Table 1, we present the values of {([[PHI].sub.H],
[[PHI].sub.IN], [[PHI].sub.IT]} and the life expectancy (inside
parentheses) that was used in their calibration.
We also show in the last row of Table 1 the infection rate used for
each country in our simulations. These values are based on the
percentage of adults estimated to be living with HIV/AIDS according to
UNAIDS (2003).
The parameters of the human capital production function are more
difficult to calibrate since
there is very diverse empirical evidence regarding them. (12) We
follow Kapicha (2006) and set [OMEGA] = 1.0 and [theta] = 0.45.
It is very difficult to find reliable estimates of the medical cost
of AIDS/HIV treatment for different countries. The price of the same
medication, for instance, may change from country to country and labor
cost also varies considerably. In 1999, the Brazilian Ministry of Health
(Ministerio da Saude do Brasil 1999) financed a very comprehensive study
on the subject. It estimated the direct and indirect costs of various
types of treatment (e.g., at home or in health centers), at different
hospitals and cities. As one could expect, costs vary a lot across
hospitals and locations, and in some cases the same type of treatment
would be twice as expensive from one place to another.
Given that there was information on the number of persons receiving
each type of treatment in each location, we used these estimates to
calculate the annual average cost of AIDS/HIV treatment per patient. We
then divided this estimate by the Brazilian income per capita of the
same period. We found that, on average, total treatment cost represented
23% of the latter. Hence, we set m to be 0.23 in every country of our
sample, almost a quarter of income in the non-AIDS scenario. (13)
Finally, to calibrate productivity we set first [[upsilon].sub.3]
to be 50% larger than [[upsilon].sub.2], which was normalized to one.
Remember that a period in the model represents 21 yr, so that we are
assuming that productivity increases by 1.8% every year. The second step
is to determine the reduction m productivity due to AIDS when
individuals do or do not receive treatment. There are not many estimates
in these cases. Part of the evidence on production and productivity
reduction due to AIDS comes from case studies. For instance, in Burkina
Faso, net revenues from agriculture production in AIDS-affected
households usually decrease by 25%-50% (Guinness and Alban 2000). This
study also has evidence of reduction in agricultural output in
AIDS-affected households in Zimbabwe, going from 61% in the case of
maize to 29% in the case of cattle.
There is also evidence from company level studies. One such paper
is Aventin and Huard (2000), who studied companies in Ivory Coast and
found that for an HIV prevalence of 10% among these firms' workers,
costs related to HIV/AIDS could be as high as 10% of the total labor
cost.
Haacker (2002) uses these studies to calibrate the productivity
reduction due to AIDS. In this paper, it is assumed that an AIDS
incidence rate among the workforce of 1% reduces total factor
productivity by 0.5%. This is the same as in the studies of Arndt and
Lewis (2000) and Cuddington and Hancock (1994), where productivity of
workers with AIDS is reduced by one half. From some of the evidence in
the case studies, we find these values too high so we decided for more
conservative parameters. We set the loss of productivity to be 15% when
individuals are under medical care and 30% otherwise.
IV. RESULTS
The economic impact of the AIDS epidemic depends on whether or not
the treatment of infected individuals is subsidized. Table 2 presents
simulations for our sample of African countries, in the cases of no
subsidy (s = 0), full subsidy (s = 1), and when half of the expenses are
paid by the government (s = 0.5). Without subsidy, no individual chooses
to receive treatment (as they cannot afford it) and the estimated
long-run decrease of output per capita (with respect to the non-AIDS/HIV
scenario) caused by the epidemic ranges from 42% in Swaziland, the most
affected country in Africa, to 18% in South Africa.
[FIGURE 1 OMITTED]
These losses can be significantly reduced as long as infected
individuals get medical attention. However, given that people cannot
afford all the cost of medication by themselves, nobody will get
treatment unless the government decides to subsidize it. In fact, when s
= 1, all infected individuals receive medication and the fall in output
per capita ranges from 23.67% to 6.11%, which is much smaller than that
obtained when s = 0. Hence, instead of a fall of almost one-third in
human capital accumulation in Botswana, we would observe a decrease of
about 8% (and less than half the reduction of output). Likewise, in
Lesotho output losses are halved when full subsidy is provided, and a
major reason is that human capital jumps from 73% to 93% of the non-AIDS
scenario.
In Figure 1, we present the behavior of output (Figure 1A) and of
the share of infected individuals that receive medical care (Figure 1B)
as we vary the amount of subsidy s provided by government. As the
results are similar, we only present those of Botswana and South Africa.
Output behavior is closely related to the number of infected individuals
getting treatment, which, in turn, depends on s. In fact, the greater
the subsidy for HIV treatment, the number of people receiving medical
attention rises and the fall in output per capita due to the AIDS
epidemic decreases.
The reason for the results described above is that treated
individuals are more productive and have a smaller probability of dying.
This has a direct impact on output, but also induces more human capital
investment, boosting long-run income even more. Once again, we find that
the impact of the disease can be significantly reduced by government
policy. Note that in these two relatively well-off nations, full subsidy
is not necessary to induce medical treatment for the entire infected
population. The results in Figure 1 hints that governments should
provide full HIV treatment since it not only relieves the suffering of
infected individuals, but also improves the performance of the economy.
In Table 3, we investigate the isolated effect on output of the
fall in life expectancy and of the reduction of labor productivity. The
experiments were carried out by taking into account only Botswana and
South Africa data and by setting s = 1. As can be seen in Table 3, the
fall in output due to life expectancy is higher in Botswana than in
South Africa. This is so because the reduction in life expectancy in the
former is greater than in the latter. Moreover, in South Africa the
reduction in labor productivity accounts for most output reduction and
the "pure life-expectancy effect" is small, although this is
not the case for many countries. In any case, as previous studies have
indicated, the reduction of effective labor due to AIDS has very
important aggregate economic implications.
[FIGURE 2 OMITTED]
In Figure 2, we show the transition path of output per capita of
Botswana between different steady states. First is presented the
transition from a steady state without AIDS to one in which there is
AIDS and government does not pay for the treatment. Once the steady
state with AIDS and s = 0 is reached, we assume that government starts
providing full subsidy for infected individuals.
Note that it takes a very long time for the full impact of the
epidemic to be felt, more than 200 yr, although most output losses are
observed in the first 4 periods, around 80 yr. This is possibly the
reason for which in some countries such as Botswana the observed income
reduction up until now is not as drastic as the long-run figures we
found in Table 2. In fact, with the AIDS/HIV epidemic just starting its
third decade, our model estimates a GDP loss of less than 10%. In the
same fashion, output expansion after the introduction of public
treatment is also very slow. Hence, the timing of government
intervention is key to minimize the losses caused by the disease.
As a robustness check, we show in Table 4 the results when [gamma]
is constant. In this case, the intergenerational discount does not
depend on the offspring's life expectancy and, as a result, the
AIDS epidemic tends to have a smaller impact on human capital
accumulation and on the intergenerational transfer of wealth. Now,
especially in the cases in which public subsidy is low, the loss of
output is smaller. It is only 25.48% in Swaziland, compared to 42%
observed in the previous case, when s = 0. Still it is a very relevant
number, but smaller than that in our benchmark calibration.
Note, however, that a larger number of infected individuals,
especially in more affluent economies are able to pay for medical care.
This is so because economies are richer now as compared to the [gamma]
endogenous case. One can see that even when s = 0.0, nearly 44% of
infected individuals in Botswana and 34% in South Africa would receive
HIV treatment. This is a counter factual result, as even in developed
countries the proportion of individuals obtaining medical care becomes
significant only after governments start paying for the treatment. In
fact, people in most sub-Saharan countries are very poor and medication
is so expensive that almost nobody would be able to get treatment
without government's help. Therefore, the model in which [gamma]
depends on the offspring's life expectancy seems to describe better
individuals' decision on medical care.
In Table 5, we carry out a sensibility analysis in regards to the
relative risk aversion parameter [sigma], for the case of Botswana. (14)
The output fall is now stronger; it goes from 13.5% to 18%. This result
is mostly due to the changes caused by the fall in life expectancy,
since the isolated impact of labor productivity is nearly the same. In
fact, as opposed to the case of [sigma] = 4.0, in the model with [sigma]
= 3.0 when we modify the parameters of life expectancy (holding
productivity constant) only 68.7% of the infected individuals get
medical treatment, so that the fall in output is greater than that
obtained with the benchmark calibration.
Note, however, that since s = 1.0 in both cases, everyone should
get treatment. A reason for this finding is that when the intertemporal
substitution rate (1/[sigma]) increases, individuals care less about the
period of their lives in which they consume, so they are not willing to
spend even small amounts of their income on medication. Thus, given that
the probability of dying early is higher for non-treated infected
individuals, they may prefer not to take medication and consume as much
as they can at early stages of their lives, something they will not want
to do if the intertemporal substitution rate is low. (15) As said
before, we find this result at odds with data (people do get treatment
when they do not have to pay for it), but in any case the fall in output
is not too distant from that of [sigma] = 4.0.
V. CONCLUSION
In this paper, we use an overlapping generation's model with
the education decision made by parents to study the long-run impact of
the HIV/AIDS epidemic. Our results show that the life-expectancy and
productivity effects are very strong and apparently dominate other
channels that the literature has examined. Smaller expected productive
life by future members of the dynasty represents a reduction of the
return to education investment and so also of the long-run level of
human capital. HIV-positive individuals are also less productive, so
that the spread of the disease has a direct impact on output. This, in
turn, decreases the return and consequently the equilibrium level of
physical capital stock and savings. The final result is a strong decline
in output per capita.
The introduction of these general equilibrium effects is the main
theoretical contribution of this paper to the study of the economic
consequences of the HIV/AIDS epidemic. Once they are taken into account,
their estimated impact on per capita income is away above previous
estimates. The model predicts that, on average, the group of countries
where the epidemic is stronger will be, in the long run, a quarter
poorer than they would be without AIDS. The simulations for Swaziland
and Zimbabwe are even more dramatic.
Most of the countries where AIDS has spread dramatically are
already extremely poor, so their development prospects are even more
pessimistic, especially if the current situation persists. Moreover,
HIV/AIDS is expanding rapidly in Eastern Europe and Central Asia,
reaching some of the most populous regions and countries in the world,
such as China and India. In the latter, close to 4 million people live
with HIV. Hence, if the tragedy in Africa serves as a leading indicator,
in the near future there will be an economic, social, and health
disaster of unheard dimensions in modern times, unless a much stronger
prevention effort at the global level is launched.
However, our findings are not entirely pessimistic. Medical
treatment can have a very positive impact on income and education, by
reducing the chance of dying from the disease and by boosting the
productivity of HIV-positive workers. In some cases, such as South
Africa, the income difference between the full coverage scenario and one
of no treatment at all--not too distant from the current situation--is
above 10% points. This result hints that if not only for purely
humanitarian reasons (e.g., decreasing the chance of dying as well as
the pain and suffering of large populations) the investment in
widespread medical programs should be considered also due to their large
income return.
ABBREVIATIONS
RHS: Right-Hand Side
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(1.) All the figures in this paragraph are from UNAIDS (2006).
(2.) Erosa, Koreshkova, and Restuccia (2007) use a similar model to
investigate the impact of human capital investment on cross-country
differences in total factor productivity and in the variation in per
capita incomes across countries.
(3.) Other noteworthy references are Bloom and Mahal (1997), Bonnel
(2000), and Dixon, McDonald, and Roberts (2000).
(4.) Also, the death of experienced workers, especially teachers,
affects the intergenerational transmission of knowledge.
(5.) We assume that assets left by parents who die of AIDS are
distributed equally as involuntary bequest across all living
individuals. This will simplify considerably calculations and
simulations, but in most cases the assets of HIV-positive individuals
are very small, so that results are not affected decisively.
(6.) Thus, in the case of non-HIV/AIDS epidemic y is equal to
[[PHI].sub.H]. For larger infection rates [pi], [gamma] gets smaller.
(11.) Data about life expectancy was taken from UNAIDS (2006).
(12.) See some empirical evidence in Browning, Hansen, and Heckman
(1999) and Trostel (1993).
(13.) Of course, some components of total cost do not change
proportionally with income, so that we may be underestimating m,
although wages and drug prices are certainly smaller in most African
countries than in Brazil. However, as we will see later, even in this
case no agent chooses to acquire treatment without subsidy, so that
larger m would not significantly change people's behavior in the
model.
(14.) Each entry in Table 5 is such that (.;.) = (output in terms
of AIDS free case; infected individuals treated).
(15.) Another way to think about this result is to take the
probability of dying as a determinant of the intertemporal substitution
rate that an agent faces. Infected individuals who do not get medication
face a lower intertemporal substitution rate than those receiving
medical attention. Thus, if the intertemporal substitution rate derived
from their preferences (l/[sigma]) is low, which entails that they do
not want to substitute consumption intertemporally, some of them may
prefer not to get treatment, even when they do not need to pay for that.
PEDRO CAVALCANTI FERREIRA, SAMUEL PESSOA and MARCELO RODRIGUES DOS
SANTOS *
* A first version of this paper was partially written when P.C.F.
was visiting the University of Illinois at Urbana-Champaign. He would
like to thank the hospitality of the Department of Economics and Steve
Parente, Werner Baer, Frank Shupp, the editor, and two anonymous
referees for their helpful comments. The authors acknowledge the
financial support of CNPq-Brazil and FAPERJ. M.R.D.S also acknowledges
the financial support of CAPES.
Ferreira: Graduate School of Economics, Fundacao Getulio Vargas,
Praia de Botafogo 190, 1125, Rio de Janeiro, RJ 22253-900. Brazil. Phone
55-21-37995840, Fax 55-21-25538821, E-mail ferreira@fgv.br
Pessoa: Graduate School of Economics, Fundacao Getulio Vargas,
Praia de Botafogo 190, 1125, Rio de Janeiro, RJ 22253-900, Brazil. Phone
55-21-37995840, Fax 55-21-25538821, E-mail pessoa@fgv.br
Dos Santos: Graduate School of Economics, Fundacao Getulio Vargas,
Praia de Botafogo 190, 1125, Rio de Janeiro, RJ 22253-900, Brazil. Phone
55-21-37995840, Fax 55-21-25538821, E-mail msantos@fgvmail.
doi: 10.1111/j.1465-7295.2010.00273.x
TABLE 1
Life-Expectancy Parameters and Infection Rate
Botswana Zimbabwe Lesotho Swaziland
[[PHI].sub.H] 1.00 (63.00) 0.87 (60.40) 0.80 (59.0) 0.69 (58.50)
[[PHI].sub.IN] 0.18 (46.00) 0.07 (43.50) 0.02 (42.6) 0.00 (42.00)
[[PHI].sub.IT] 0.77 (59.00) 0.69 (56.50) 0.61 (55.6) 0.42 (51.00)
[pi] 0.37 0.27 0.285 0.388
South Africa
[[PHI].sub.H] 0.95 (62.20)
[[PHI].sub.IN] 0.28 (47.55)
[[PHI].sub.IT] 0.89 (60.55)
[pi] 0.215
TABLE 2
Output, Human Capital, and Infected Individuals Treated
Output Human Capital
s=0.0 s=0.5 s=1.0 s=0.0 s=0.5 s=1.0
Botswana 66.65 79.06 86.50 69.49 84.12 92.37
Zimbabwe 71.22 85.30 90.55 73.84 89.10 94.86
Lesotho 70.49 67.68 87.01 72.88 71.09 92.31
Swaziland 58.10 56.92 76.34 64.27 63.42 84.96
South Africa 81.85 86.46 93.89 83.48 89.56 97.17
Infected Individuals
Treated
s=0.0 s=0.5 s=1.0
Botswana 0.0 64.85 100.0
Zimbabwe 0.0 59.71 100.0
Lesotho 0.0 0.0 100.0
Swaziland 0.0 0.0 100.0
South Africa 0.0 52.68 100.0
TABLE 3
Output Per Capita (% of AIDS Free Case)
Life Labor
Expectancy Productivity Total
Botswana 93.22 92.07 86.50
South Africa 98.74 94.91 93.89
TABLE 4
Output, Human Capital, and Infected Individuals Treated with y = 1
Output Human Capital
s=0.0 s=0.5 s=1.0 s=0.0 s=0.5 s=1.0
Botswana 82.40 85.98 88.77 88.65 92.62 94.93
Zimbabwe 83.29 88.44 93.15 86.02 93.18 97.98
Lesotho 82.84 88.53 92.70 87.91 91.87 97.39
Swaziland 74.52 84.84 89.12 86.91 92.81 95.15
South Africa 87.44 91.21 94.87 92.85 95.82 98.01
Infected Individuals
Treated
s=0.0 s=0.5 s=1.0
Botswana 44.12 88.69 100.0
Zimbabwe 0.487 68.61 100.0
Lesotho 0.339 70.18 100.0
Swaziland 0.0 85.56 100.0
South Africa 34.05 77.81 100.0
TABLE 5
Sensibility Analysis
Life Labor
Expectancy Productivity Total
[sigma] = 3.0 76.65; 68.72 92.83; 100.0 82.11: 100.0
[sigma] = 4.0 93.22; 100.0 92.02; 100.0 86.50; 100.0