Auburn University Montgomery AIDS Crisis and Growth Questions The questions below refer to paper ‘AIDS crisis and growth” 1. Using a simple language and an

Auburn University Montgomery AIDS Crisis and Growth Questions The questions below refer to paper ‘AIDS crisis and growth” 1. Using a simple language and an example tell a story that lays out the intuition for the effects of AIDS pandemic on accumulation of physical and human capital in the baseline model with productive medical expenditures.2. Why does lowering child wage in the model make the crisis more severe (see Table 4)?3. List three or four important ideas on which the analysis is built and which are related to the papers linked below. Discuss how implementation of these ideas differs between the AIDS paper and the related papers. 4. Based on the discussion in question 3, propose one model extension and explain why it would be important for this analysis. Journal of Development Economics 77 (2005) 107 – 124
www.elsevier.com/locate/econbase
AIDS crisis and growth
Paul Corrigana, Gerhard Glommb,*, Fabio Mendezc
a
Michigan State University, United States
Department of Economics, Wylie Hall, Indiana University, Bloomington, IN 47405, United States
c
Department of Economics, Business Building 402, University of Arkansas, Fayetteville, AR 72701, United States
b
Received 1 May 2000; accepted 1 February 2004
Abstract
We investigate an OLG economy where an AIDS epidemic influences human capital
accumulation and growth through the creation of large numbers of orphans. We study how intrafamily allocations regarding school and work time of children are adjusted in the face of AIDS
within a family, and how, in turn, these adjustments influence accumulation of physical and human
capital. We compute the aggregate effects of an AIDS epidemic on human and physical capital
accumulation and growth. We find that growth effects of an AIDS epidemic are large. Some policies
such as subsidization of AIDS medication have relatively small effects.
D 2004 Elsevier B.V. All rights reserved.
JEL classification: O11; I12
Keywords: AIDS; Orphans; Human capital; Growth
1. Introduction
This paper addresses the question: What is the effect of the massive AIDS crisis in subSaharan Africa on economic growth? Answers to this question matter for two reasons:
First, even moderate growth effects can have a sizeable impact on the welfare of future
generations. Second, neither is there any cure, nor is there any chance of controlling the
* Corresponding author. Tel.: +1 812 855 7256; fax: +1 812 855 3736.
E-mail address: gglomm@indiana.edu (G. Glomm).
0304-3878/$ – see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.jdeveco.2004.02.005
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P. Corrigan et al. / Journal of Development Economics 77 (2005) 107–124
epidemic in the near future. Predicting the effects of the AIDS crisis, and evaluating the
usefulness of proposed policies to mitigate its economic effects (such as subsidizing AIDS
medications) are hence of great importance.
Just what those effects might be, however, seem rather dependent on the techniques and
model used. Early empirical evidence gathered in the 1990s surprisingly pointed to small
or unimportant growth effects of the AIDS epidemic. Regressing growth rates on AIDS
incidence for a cross-section of countries, Bloom and Mahal (1997) found small or
insignificant coefficients. The World Bank report Confronting AIDS: Public Priorities in a
Global Epidemic (1997) came to a similar conclusion and argues that growth effects of the
AIDS crisis are likely to be small.
In contrast, many of the theoretical contributions that concentrate on the potential longrun (future) effects predict that the AIDS crisis will have a much larger impact. Kambou et
al. (1992), for example, used a simulation model of the economy of Cameroon and
conclude that AIDS can cut the rate of GDP growth by up to 50%. Cuddington and
Hancock (1994) used a Solow type growth model to study the growth effects of AIDS in
Malawi. This model was extended in Cuddington and Hancock (1995) to allow a dualistic
labor surplus economy and in Cuddington et al. (1994) to include demographic and
epidemic equations that can be used to study how AIDS related policies impact the
macroeconomy. Similar conclusions concerning sizeable aggregate effects have been
reported by Arndt and Lewis (2000). The potential for large effects of the AIDS epidemic
on macroeconomic outcomes is confirmed in more disaggregated frameworks in Arndt
and Lewis (2001) and Arndt (2003).
There are several channels through which the AIDS epidemic can potentially influence
economic growth:
1. AIDS decreases life expectancy and hence the incentive to invest.
2. The AIDS epidemic creates a huge number of orphans. In all likelihood human capital
accumulation by orphans faces more obstacles than if parents were present.
3. Potentially large medical costs associated with treatment of AIDS patients can divert
public resources from productivity enhancing public expenditures such as education or
infrastructure investments.
4. Firms might be reluctant to hire and invest in training of workers if there is a high
likelihood of workers dying because of AIDS.
5. To the extent that AIDS is more prevalent among highly skilled workers and that highly
skilled labor is complementary to capital, the AIDS epidemic can influence the rate of
return on investment and, in turn, savings and capital accumulation.
In this paper we concentrate on the first two channels, viz. the effect of the drop in life
expectancy on investment and the large generation of orphans produced by AIDS. In a
recent paper, Ferreira and Pessoa (2003) consider how the AIDS-induced decrease in life
expectancy decreases the incentive to invest in human capital. They find that in the face of
an AIDS epidemic schooling time can decline by half; the potential for large growth
effects as a result is obvious.
The large generation of AIDS orphans and their potential impact on African economies
has received much less attention. In some countries HIV/AIDS infection rates now exceed
P. Corrigan et al. / Journal of Development Economics 77 (2005) 107–124
109
20% of the adult population; in Swaziland, for example, the adult infection rate for 2001
was over 33% (UNAIDS (2002a,b)/WHO Epidemiological Fact Sheet). With no cure
being available now (or likely to be in the near future), and treatments used in the
developed world being prohibitively costly, adults facing early deaths are leaving behind
large numbers of orphans. According to some estimates there are already over 13 million
orphans due to AIDS. By 2010 the number of orphans is expected to increase to levels
exceeding 25 million (see Hunter and Williamson (2002)). For Mozambique, Arndt (2003)
estimates that by 2010 roughly every fourth child will have lost at least one parent.
Orphans typically have fewer opportunities to obtain human capital than if parents were
alive. Available evidence points to significant reallocations of resources within families
where AIDS is present. Often, upon the death of a parent, children’s time is allocated away
from schooling to work in order to supplement family income. According to UNAIDS
(2000) children are often pulled from school when a parent contracts AIDS. Moreover, the
presence of AIDS in a family requires additional expenditures both in terms of time and in
terms of financial expenditures for the (medical) care of the AIDS patient, so that fewer
resources are available for schooling and other investments.
In Section 2 we present a model in which the AIDS epidemic can influence long-run
growth. This model is an OLG economy where individuals live potentially for three
periods: youth, adulthood and old age. In each period a fraction of the adult population
contracts AIDS, which implies certain death before the third period, old age. There are two
augmentable factors in the model, physical capital (which is accumulated in the standard
fashion from savings of the young) and human capital. Our approach differs from earlier
theoretical research on this issue (e.g. Kambou et al., 1992; Cuddington and Hancock,
1994) inasmuch as earlier papers in this vein did not explicitly model intertemporal choice.
The accumulation of human capital follows Lucas (1988) in the sense that the two
inputs in future human capital are time and parental human capital. Each child is endowed
with one unit of time, which can be allocated to learning or to working so that family
income may be supplemented. Parents make time allocation decisions for their children;
hence each individual makes decisions only in the two periods adulthood and old age.
If there is AIDS in the family, the parents also decide how to allocate family income
between standard consumption goods such as food, clothing and shelter and medical
expenses for the AIDS patient. The related medical expenditures are modeled as utility
enhancing goods only. The definition of equilibrium for this simple version of model is
given in Section 3; we derive the equilibrium solution in Section 4.
In Section 5, we present and solve a modified version of our model in which AIDS
related medical expenditures can enhance labor productivity of the AIDS infected worker.
This modification is motivated by the lower labor productivity exhibited by AIDS infected
workers (see, for example, Guinness and Alban, 2000) and the effect that medications may
have upon their productivity. This modification also allows us to better study the effects of
public and international subsidies of AIDS medications, as well as the effects of
international laws that control the distribution of generic-version drugs that sell at a
fraction of the standard price. The idea behind such policy recommendations is to make
AIDS patients well enough to live more or less normal and productive lives, which would
include being better able to care for their children (who themselves could perhaps return to
school).
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P. Corrigan et al. / Journal of Development Economics 77 (2005) 107–124
In Section 6 we solve both versions of the model numerically and present the main
results. We calibrate this model to sub-Saharan economies and run the model through
some potential AIDS epidemics scenarios. Finally, Section 7 provides our conclusions.
2. The simple model
Each individual in the economy belongs to a dynasty indexed by xaX, where X spans
the entire population in each generation. We normalize the size of the young population
each period to one. Each individual of each generation t lives for, at most, three periods. In
the first period of life (hereafter byouthQ) the individual either works or learns. Learning,
here, is either formal schooling or receiving informal education from parents. What
matters is that learning is associated with an opportunity cost, foregone wage income.
In the second period of life (badulthoodQ), the individual inelastically supplies labor to
the firm. At the beginning of adulthood an individual learns if he has HIV/AIDS; he faces
a probability p t of remaining healthy and a probability of 1p t of being infected with
HIV/AIDS. HIV/AIDS infection implies a loss of health, which lowers labor income in the
second period of life. Infection also implies certain death at the end of period two. Our
modeling of mortality risk as purely exogenous is similar to the way it is modeled in
Pecchenino and Utendorf (1999).
As a consequence, only individuals who remain uninfected save a portion of their
income for the third period (bold ageQ). In contrast, an individual who is ill does not save at
all in the second period; but in addition to the busualQ consumption expenses, an HIV/
AIDS infected individual faces medical expenditures. We think of these medical expenses
only as those associated only with HIV/AIDS.
In our model, adults make all schooling/working decisions for the family, including
their children. We assume that effective labor of HIV/AIDS infected individuals is a
fraction Wb1 of effective labor of healthy individuals. We also assume that effective labor
of children is a fraction Db1 of effective labor of the healthy adults.
There is a government that taxes labor income of all adults. In our model labor income
of children is not taxed; this assumption captures children working in the household or in
the informal sector. The tax revenue is used to finance government consumption or
investment in some non-productive kind of capital. This tax is introduced to mirror one of
the many distortions in African economies described in Collier and Gunning (1999). Our
interpretation of government investment in non-productive capital is consistent with
Devarajan et al. (2000). The only other item in the government budget is a potential
subsidy to AIDS related health care. We assume that the government’s budget constraint is
balanced in each period.
The preferences of a healthy individual are given by
a1 lnct þ a2 lnft þ a3 lnctþ1 þ a4 lnhtþ1 ;
where c t is the individual’s own consumption in adulthood, f t is the consumption of his
children, c t+1 is the individual’s consumption in old age and h t+1 is his children’s human
capital. We have introduced this type of intergenerational altruism into the model to ensure
that investment in children’s human capital is positive.
P. Corrigan et al. / Journal of Development Economics 77 (2005) 107–124
111
An individual who is HIV/AIDS infected knows that he will not survive to period three,
and thus does not derive utility from old-age consumption. However, HIV infection does
bring about medical expenses, which enter the individual’s preferences. Thus, a HIV
positive individual’s preference function is
a1 1=q ln½cqt þ hmqt þ a2 lnft þ a4 lnhtþ1 ;
where m t is AIDS related medical expenditures and where q and h are preference
parameters, with q measuring the elasticity of substitution and h the share of medical
expenses in the budget.
The technology is described by a standard Cobb–Douglas production function
Yt ¼ A Kta L1a
;
t
where Y t is aggregate output, K t is the aggregate capital stock and L t is the aggregate stock
of effective labor in the economy.
In this model there are three different kinds of labor: labor by healthy adults; labor by
HIV/AIDS infected adults; and labor by children. We assume that all three types of labor
are perfect substitutes so that effective labor is simply the weighted average of the three
kinds of labor, which can be written as

Lt ¼ pt 1 þ 1 nht D þ ð1 pt Þ W þ 1 nst D Ht ;
where H t represents aggregate human capital at time t and n represents the fraction of the
children’s time that is devoted to learning, both when parents are healthy (n h) and when
parents are sick (n s).
Human capital of each child is produced using human capital of the parent and the
child’s own time as an input. For simplicity we assume, that the learning technology is
linear in the time input. This production function is given by
htþ1 ¼ Bnt ht ;
where B L takes on the value B H when the parent is healthy and B S when the parent is sick.
We assume B HzB S, as a child’s return to schooling will be lower if he has no parent
present to devote time to his development. In our base case scenario we let B H=B S=B and
then we conduct sensitivity analysis for the case B HNB S.
3. Equilibrium
In this section, we state the household’s maximization problems and we define a
competitive equilibrium for our economy. A healthy middle-aged adult solves the
problem
max
fct ;ft ;ctþ1 ;nt g
a1 lnct þ a2 lnft þ a3 lnctþ1 þ a4 lnhtþ1
s:t: ct þ ft þ st ¼ ð1 st Þwt ht þ ð1 nt Þwt ht D
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P. Corrigan et al. / Journal of Development Economics 77 (2005) 107–124
ctþ1 ¼ ð1 þ rtþ1 Þst
htþ1 ¼ Bnt ht ;
where w t is the wage rate per effective unit of labor, r t+1 is the net real interest rate and
s is the labor income tax rate imposed by the government. We will refer to this as
problem P H.
An HIV/AIDS infected person solves the problem
max
fct ;ft ;mt ;nt g
a1 1=q ln½cqt þ hmqt þ a2 lnft þ a4 lnhtþ1
s:t: ct þ ft þ rt pt mt ¼ ð1 st Þwt ht W þ ð1 nt Þwt ht D
htþ1 ¼ Bnt ht ;
where p t is the pre-subsidy price of medical care and r t expresses the subsidy rate so that
r t p t is the post-subsidy price of medical care relative to consumption. We will refer to this
as problem P S.
We are now in a position to define an equilibrium for this economy.
Definition. A competitive equilibrium for this economy is a collection of sequences of
h
s
s
distributions of individual household decisions {cht , c t+1
, f t h, nht }l
tN0 when healthy, {c t , f t ,
s
s l
l
m t , n t }t=0 when sick, sequences of aggregate stocks of physical capital {K t }t=0 and
effective labor {L t } and sequences of prices {w t , r t+1, p t }l
t=0 satisfying
h
, f th, nht } solve problem P H,
(i) the decisions {cht , c t+1
s
s
(ii) the decisions {c t , f t , mst , nst } solve problem P S,
(iii) capital markets clear so that
Z
Ktþ1 ¼
st ðxÞdlðxÞ;
X
(iv) human capital follows the law of motion
htþ1 ¼ Bs nst ht or htþ1 ¼ Bh nht ht
depending on health status,
(v) factor markets are competitive so that factor prices are determined by
wt ¼ ð1 aÞYt =Lt ;
rt ¼ aYt =Kt
(vi) the government budget constraint is satisfied every period, that is
Gt þ ð1 rt Þpt Mt ¼ ðpt þ ð1 pt ÞWÞst wt H:
Note that only factor prices are determined endogenously in the model; the price of
medical care is taken to be exogenous. What we have in mind is that the price of the AIDS
medications is determined in a world market and the small African country takes this price
P. Corrigan et al. / Journal of Development Economics 77 (2005) 107–124
113
as given. Alternatively we can think of a constant returns to scale production function
which transforms one unit of output into 1/p t units of medical services. If medical services
are supplied in a competitive market the price of medical services will be equal to its
marginal cost p t .
4. Solving the model
We can now solve the model. After some algebra, the first order conditions for problem
P H of a healthy individual yield
cht ¼
a1
ð1 þ D st Þwt ht ;
a1 þ a2 þ a3 þ a4
ð1Þ
fth ¼
a2
ð1 þ D st Þwt ht ;
a1 þ a2 þ a3 þ a4
ð2Þ
st ¼
a3
ð1 þ D st Þwt ht ;
a1 þ a2 þ a3 þ a4
ð3Þ
chtþ1 ¼ ð1 þ rtþ1 Þ
nht
a3
ð1 þ D st Þwt ht
a1 þ a2 þ a3 þ a 4

a4 1 þ D s t
:
¼
D ð a1 þ a2 þ a3 þ a4 Þ
ð4Þ
ð5Þ
As only the proportion of healthy individuals p t are doing any saving, and health is
independent of human capital level, Eq. (3) implies that
Ktþ1 ¼
pt a3
ð1 þ D st Þwt Ht :
a1 þ a2 þ a3 þ a4
ð6Þ
The first order conditions of problem P S of an HIV/AIDS infected individual yield
cst ¼
a1
1
q ðD þ Wð1 st ÞÞwt ht ;
1
a1 þ a2 þ a4 1 þ h 1q
rt pt 1q
ð7Þ
fts ¼
a2
ðD þ Wð1 st ÞÞwt ht ;
a1 þ a2 þ a4
ð8Þ
1
mst
1
1
a1
h 1q rt1q pt1q
¼
q ðD þ Wð1 st ÞÞwt ht ;
1
a1 þ a2 þ a4 1 þ h 1q
rt pt 1q
ð9Þ
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P. Corrigan et al. / Journal of Development Economics 77 (2005) 107–124
implying that
1
pt mst
1
q
a1
h 1q rt1q pt1q
¼
q ðD þ Wð1 st ÞÞwt ht :
1
a1 þ a2 þ a4 1 þ h 1q
rt pt 1q
ð10Þ
Economy-wide spending on medical services then is given by

p t Mt ¼ 1 p t
1
1
q
a1
h 1q rt1q pt1q
q ðD þ Wð1 st ÞÞwt Ht
1
a1 þ a2 þ a4 1 þ h 1q
rt pt 1q
ð11Þ
and individual schooling time is
nst ¼
a4 ð D þ W ð 1 s t Þ Þ
:
D ð a1 þ a2 þ a4 Þ
ð12Þ
Notice that schooling time when parents are infected nst is smaller than schooling
time when parents are healthy nht only when W, the productivity of ill parents, is
sufficiently small. If infected parents were as productive as healthy parents, schooling
time with infected parents would be higher than with healthy parents. This is because
with healthy parents there are more demands for income from child labor, i.e.
consumption for old age. Thus, in order to ensure that nht Nnst , we assume that W is
sufficiently low.
Conditions (5) and (12) give an economy-wide rate of growth of human capital and the
corresponding labor input as
Htþ1 ¼

BH pt
a4 ð D þ 1 s t Þ
a4 ð D þ W ð 1 s t Þ Þ
þ B S ð1 p t Þ
Ht
Dða1 þ a2 þ a3 þ a4 Þ
Dða1 þ a2 þ a4 Þ

Lt ¼ pt 1 þ D 1 nht þ 1 pt Þ W þ D 1 nst Ht

D ð a1 þ a2 þ a3 Þ a4 ð 1 s t Þ
¼ pt 1 þ
þ ð1 pt Þ
ða1 þ a2 þ a3 þ a4 Þ

Dða1 þ a2 Þ a4 Wð1 st Þ
1þ
Ht :
ða1 þ a2 þ a4 Þ
ð13Þ
ð14Þ
The budget-balance condition gives us
ðpt þ Wð1 pt ÞÞwt Ht st ¼ Gt þ ð1 rt Þpt Mt :
ð15Þ
According to Eq. (15) any fixed tax rate and any fixed level of (wasteful)
government expenditures G t un…
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