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The economic effects of lowering HIV incidence in South Africa:
A CGE analysis
E.L. Roos ⁎, J.A. Giesecke
Centre of Policy Studies, Victoria University, Melbourne, Australia
abstractarticle info
Article history:
Accepted 20 February 2014
Available online 22 March 2014
JEL classification:
C68
I190
O55
Keywords:
Computable general equilibrium (CGE)
Africa
HIV prevention
South Africa has the highest UNAIDS HIV severity rating: “generalised pandemic”. A country with this classifica-
tion requires public health interventions aimed at the general population. This paper investigates the efficacy of
one such policy, examining the national economic effects of an increase in condom use. We use an epidemiolog-
ical model to estimate the impact of condom use on HIV infections distinguished by age, gender and race. The
epidemiological model's outputs are input to an economy-wide dynamic general equilibrium model that distin-
guishes labour market participants by age, gender, race, labour market status and HIV status. We find that the
programme generates gains in real consumption with a present value of approximately USD $30 billion, or
USD $2000 per household.
© 2014 Elsevier B.V. All rights reserved.
1. Introduction
South Africa is defined by the Joint United Nations Programme
on HIV/AIDS (UNAIDS) as experiencing a hyper-endemic HIV epi-
demic, with epidemiological data showing HIV prevalence among
adults aged 15–49 at more than 15% (Department of Health, 2011;
Shisana et al., 2009; UNAIDS, 2008). Heterosexual transmission re-
mains the dominant mode of HIV transmission in South Africa, followed
by mother-to-child transmission. An important factor contributing to
South Africa's high HIV prevalence is the existence of multiple hetero-
sexual concurrent relationships, with low and inconsistent condom
use, especially in long-term relationships (Department of Health,
2010:10).
Epidemiological data shows that HIV prevalence and incidence
rates
1
vary across subgroups within the South African population. The
Human Science Research Council conducted national household-based
population surveys in 2002, 2005 and 2008. Results from these surveys
show that the epidemic has a disproportional impact on the working
age population (Shisana et al., 2009: 31). Gender variation in HIV
prevalence is especially evident in younger age groups, with women
aged between 20 and 24 four times more likely to be HIV positive
than males in the same age group (Department of Health, 2011: 18).
More broadly, females aged 15 and older show disproportionally high
levels of HIV infection (13.6%) relative to men in the same age group
(7.9%) (Shisana et al., 2009: 79). On average, younger females are infect-
ed about 5 years earlier than males. For young females, the prevalence
rate peaks at 32.7% in the age group 25–29. For males, the peak age
group is 30–34, with a prevalence rate of 25.8% (Shisana et al., 2009:
30). Within South Africa, there is also significant racial variation in HIV
prevalence, with the prevalence rate for Africans substantially higher
than that of other racial groups. HIV prevalence for Africans is 13.6%,
compared with 1.7% for Coloureds, and 0.3% for Indians and Whites
(Shisana et al., 2009:79).
2
Many studies suggest that there is an inverse
relationship between HIV prevalence and educational attainment, with
higher levels of educational attainment associated with lower HIV prev-
alence rates. This is consistent with findings from the 2002 HIV house-
hold survey which suggested that the prevalence of HIV among those
with tertiary degrees was lower than those with no school, primary or
high school attainment (Shisana and Simbayi, 2002: 54). Historical
imbalances in terms of educational attainment and employment
discrimination are reflected in the current race and gender profiles of
Economic Modelling 39 (2014) 123–137
⁎Corresponding author. Tel.: +61 3 9919 1491.
E-mail address: louise.roos@vu.edu.au (E.L. Roos).
1
HIV prevalence is defined as the total number of infections at a given point in
time. HIV incidence is defined as the number of people or percentage of a population
who become newly infected over a period of time, traditionally a given year (UNAIDS,
2008:31).
2
See Shisana et al. (2009 ) for a detailed figure showing HIV prevalence by gender and
age (p.31) and a detailed table of HIV prevalence by gender, age, population group and
province (p.79).
http://dx.doi.org/10.1016/j.econmod.2014.02.028
0264-9993/© 2014 Elsevier B.V. All rights reserved.
Contents lists available at ScienceDirect
Economic Modelling
journal homepage: www.elsevier.com/locate/ecmod
occupational employment. Unskilled labour tends to be poorly educated
and mainly performed by Africans.
3
People employed in skilled occupa-
tions report higher levels of education and are predominantly per-
formed by the White population group (Statistics South Africa, 2009).
With HIV prevalence and incidence rates varying along the dimensions
of age, gender, race, education and employment status, it is important
that our economic model embodies this detail.
HIV prevention at a population level requires a combination of pre-
vention measures to be most effective (UNAIDS, 2010). This concept
of combined prevention rests on three pillars: biomedical, behavioural
and structural changes. The combined intervention strategy depends
on the interdependent and mutually reinforcing attributes of individual
interventions. For example, the effectiveness of a biomedical interven-
tion (such as condom distribution) is likely to be enhanced when
accompanied by a behavioural intervention (such as an instruction
programme in correct condom use). This would in turn require a
structural intervention (such as government funding and policy
formation).
The South African Minister of Health has recently reaffirmed the im-
portance of combined prevention, and the role of condom distribution
within this prevention programme, with the national HIV Counselling
and Testing (HCT) campaign launched in 2010 (Motsoaledi, 2010). To
our knowledge, no study has focused on the economic evaluation of
condom distribution programmes in South Africa. For a developing
country such as South Africa, understanding the economic contribution
of the programme is important, particularly in the context of the signif-
icant economic damage caused by AIDS as reported by Booysen et al.
(2003),Haacker (2002) and United Nations (2004). In this paper we in-
vestigate the economic consequences of a change in the number of sex
acts protected by condoms. The aim is to provide insights into the pos-
sible economic consequences of public condom distribution. Results of
3
In this paper Africans refers to the Black population group.
Fig. 1. Flows between categories at the start of year tand activities during year t.
124 E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
this type can be useful for evaluating the net benefits of such
programmes.
Since the early 2000's, public condom distribution in South Africa has
expanded from approximately 267 million units in 2001 to 445 million
units in 2010 (Marumo, 2011). Despite this increase, the number of
condoms per male remains low. On average, 14.5 male condoms were
distributed per male 15 years and older in 2010/11 (Day et al., 2012).
A number of studies have shown that condoms play a key role if it is
part of a wider prevention programme in reducing HIV infections. For
example, for South Africa, Rehle and colleagues use the Human Science
Research Council surveys to estimate changes in incidence between
2002 and 2005 and between 2005 and 2008. Among the results, they
find that incidence decreased for women between the ages of 15 and
24. Behavioural trends were analysed, finding both an increase in
condom use at last sex, and a rise in the propensity to be tested for
HIV (Rehle et al., 2010). The rise in condom use for women may also
point to thefact that females are becoming more empowered to negoti-
ate condom use. The 2008 survey finds that not only has there been a
shift in negotiating skills towards women, but communities are becom-
ing more open to discussing topics such as sex and condom use (Shisana
et al., 2009). The increase in reported condom use is consistent
with findings of a panel data study among South African youth by
Dinkelman et al. (2007). Dinkelman et al. examined recent trends in
adolescent sexual behaviour in Cape Town to determine whether house-
hold and community poverty and negative economic shocks predict
risky behaviour. Their study found that sexual behaviour between
2002 and 2005 shifted towards safer practices. They found a statistically
significant increase in condom use and a decrease in the incidence of
multiple sexual partners for women aged 17 to 22. Results from the
2006 national HIV/AIDS communication survey for South Africa shows
that education and information have led to an increase in condom use
and HIV testing among young adults (Parker et al., 2007). The survey
further showed that, although other risky behaviours, such as multiple,
concurrent and intergenerational partnerships may have increased
over time, condom use has also increased. However, while the evidence
suggests that there has been an increase in condom use, consistent con-
dom use, especially among youth, is still not optimal (Parker et al.,
2007).
In this paper, we examine the labour market and economy-wide
effects of an increase in condom use and decrease in HIV incidence.
There are many channels through which HIV affects the economy
(Arndt and Lewis, 2000).At the level of the AIDS-affected household, re-
searchers have identified the potential for reductions in labour supply,
through ill-health, absenteeism, care-giving and death (Booysen et al.,
2003; International Labour Organization, ILO, 2005; International
Monetary Fund, 2004; Jefferis et al., 2006; Jefferis et al., 2007). Expendi-
ture switching can take place, towards medical treatment and funeral
costs (Booysen et al., 2003; Steinberg et al., 2002; United Nations,
2004). The impact that these factors have on individual household
budgets can result in reduced spending on education, and thus lower
the educational attainment of the children of AIDS-affected households
(Steinberg et al., 2002). At the firm level, productivity can be affected
by absenteeism, employment of temporary staff, loss of expertise,
retraining costs and poor morale (Rosen et al., 2003; United Nations,
2004; USAID, 2001). At the government level, HIV/AIDS-related spend-
ing can increase, which may have implications for other elements
of public spending such as welfare and education (International
Monetary Fund, 2004). Of these many channels, we focus on labour
supply.
The remainder of the paper is structured as follows. In Section 2 we
describe the theoretical structure of our economic model, SAGE-H.
Section 3 outlines the model's database. In Section 4, we describe a
simple “back-of-the-envelope”representation of the main economic
relationships in SAGE-H that will prove important in understanding
our simulation results. Section 5 describes how we translate a hypothet-
ical condom distribution policy into a set of exogenous shocks to an in-
dependent epidemiological model and our economic model. Section 6
discusses the simulation results, and Section 7 concludes the paper.
2. Description of the Sage-H model of the South African economy
SAGE-H is a large-scale dynamic computable general equilibrium
(CGE) model of the South African economy. SAGE-H consists of two
inter-dependent modules. The first module describes the behaviour of
industries, investors, households, government and exporters at the na-
tional level, and is based on the theoretical structure of the MONASH
Table 1
BOTE: stylised representation of selected relationships in SAGE-H⁎.
Equations holding within any given year of the year-on-year base-case and policy simulations
(1) Short-run closure⁎(2) “Effective”long-run closure⁎
Y=C+I+G+(X−M)Y=C+I+G+(X−M)(B.1)
Y¼1
Af1 K;LDðÞ Y¼1
Af1 K;LDðÞ (B.2)
C+G=APC ×GNP C +G=APC ×GNP (B.3)
G/C=ΓG/C=Γ(B.4)
GNP =Y×f2(TOT)−FDATT ×RGNP =Y×f2(TOT)−FDATT ×R(B.5)
M=f3(Y,TOT)M=f3(Y,TOT)(B.6)
TOT =PX/PM TOT =PX/PM (B.7)
PX =f4(1/X,F
d
)PX =f4(1/X,F
d
)(B.8)
I=f5(ROR/F
inv
)I=f5(ROR/F
inv
)(B.9)
Ψ=I/KΨ=I/K(B.10)
(K/LD)=f6(ROR,A,TOT)(K/LD)=f6(ROR,A,TOT)(B.11)
W=f7(K/LD,A,TOT)W=f7(K/LD,A,TOT)(B.12)
LD =LS ×ER LD =LS ×ER (B.13)
LS =LF
HIVn
×OR
HIVn
+LF
HIVp
×OR
HIVp
LS =LF
HIVn
×OR
HIVn
+LF
HIVp
×OR
HIVp
(B.14)
Equations determining start-of-the-year variables in year-on-year base-case and policy simulations
T
HIVn,HIVn
=1−T
HIVn,HIVp
−DRT
HIVn
(B.15)
LF
HIVn
=LF
t−1
HIVn
×T
HIVn,HIVn
+NEW
HIVn
(B.16)
LF
HIVp
=LF
t−1
HIVp
(1−DRT
HIVp
)+HIV
new
+NEW
HIVp
(B.17)
HIV
new
=LF
t‐1
HIVn
×T
HIVn,HIVp
(B.18)
K=K
t‐1
×(1‐Depr)+I
t‐1
(B.19)
FDATT =FDATT
t‐1
+I
t‐1
−(1−APC
t‐1
)GNP
t‐1
(B.20)
Lagged wage adjustment in the policy simulations
W
Wbase ¼Wt−1
Wbase
t−1
þαLD
LDbase −LS
LSbase
hi (B.21)
⁎Bold denotes exogenous. Remaining variables are endogenous. Table 2 includes a description of the variables in Table 1.
125E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
model (Dixon and Rimmer, 2002). The second module describes labour
supply, and is based on the theory described in Dixon and Rimmer
(2010) and Dixon et al. (2011). While the complete model is too large
to describe in detail in a journal-sized paper, we render such a descrip-
tion unnecessary by presenting a back-of-the-envelope model (hereaf-
ter, BOTE) that describes the key economic relationships in SAGE-H
that are relevant to our simulation of a fall in the number of new HIV in-
fections. Use of miniature models such as BOTE to describe the results
from a full-scale applied economic model has a long tradition in CGE
modelling.
4
Before describing BOTE, we first provide a brief overview
of SAGE-H.
SAGE-H models production of 28 commodities by 28 industries.
Three primary factors are identified: land, capital and labour. Labour is
further distinguished by 11 occupational types. The model has one
representative household and one central government. Optimising
behaviour governs decision-making by the household and firms. Indus-
tries minimise costs subject togiven input prices and a constant returns
to scale production function. The household is assumed to be a budget-
constrained utility maximiser. Units of new industry-specific capital are
cost minimising combinations of South African and foreign commodi-
ties. We assume that domestic and imported varieties of commodities
are imperfect substitutes for each other, with this modelled via constant
elasticity of substitution (CES) functions. The export demand for any
South African commodity is inversely related to its foreign-currency
price. SAGE-H models the consumption of commodities by government
as well as direct and indirect taxes. All sectors are competitive and
all commodity markets clear. SAGE-H recognises five main types of
dynamic adjustment: capital accumulation, net foreign liability accu-
mulation, public sector debt accumulation, labour force movements be-
tween labour market states via transition matrices and labour market
offers, and short-run stickiness in wage adjustment. Capital accumula-
tion is industry-specific and linked to industry-specific net investment.
Changes in industry-specific investment are linked to changes in
industry-specific rates of return. Changes in net foreign liabilities are
linked to changes in the current account balance, and changes in public
sector net debt are linked to changes in the government deficit.
The model's HIV detail is expressed in the labour supply theory.
This theory imposes a stock/flow dynamic on labour market groups dis-
tinguished by labour market activity, age, gender, race, and HIV status
and, if positive, HIV stage. Broadly, the theory specifies that at the start
of year t, people aged 15–65 (the working age population, hereafter
the WAP) are divided into categories based on common characteristics.
These characteristics are age, gender, race, HIV status/stage and labour-
market activity in year t −1. People in categories offer their labour
services to activities performed during year t. Although most people in
year t remain within the same employment status they held during
year t −1, a person may offer (and be accepted) into a different em-
ployment statuses. At the end of year t, people still part of the WAP
progress one year in age and may change their HIV status/stage. Some
people leave the WAP due to retirement or death. After this transition,
people are again grouped into categories, based on common character-
istics. The process of labour supply from a category to an activity is then
repeated.
The following equations explain the operation of the labour supply
module. Eq. (E.1a), allocates people of gender g,racer, at the start
of year tto categories based on their labour market activities in year
t−1, while also ensuring that people move between age groups and
HIV statuses via the mediation of a transition matrix.
CATt
o;a;g;r;hðÞ
¼X
aa∈AGE X
hh∈STG
ACT t−1
o;aa;g;r;hhðÞ
To;aa;g;r;hh;a;hðÞ ðE:1aÞ
CATt
N;a;g;r;hðÞ
¼Exogenous ðE:1bÞ
where
To;aa;g;r;hh;a;hðÞ
¼F1o;aa;g;r;hh;a;hðÞ
F2aa;g;r;HivN;a;Stage1ðÞ ðE:2Þ
and
HIVNEW t
a;g;rðÞ
¼X
o
ACTt−1
o;aa;g;r;HivNegðÞ
To;aa;g;r;HivNeg;a;Stage1ðÞ
ðE:3Þ
for o∈EUP;a∈AGE;g∈GEN;r∈RACE;h∈STG;aa ∈AGE;hh ∈STG
where
4
See Dixon et al., (1984) fo r an early example.
-2.4
-2
-1.6
-1.2
-0.8
-0.4
0
0.4
0.8
2006
2008
2010
2012
2014
2016
2018
2020
2022
2024
2026
2028
2030
2032
2034
2036
2038
2040
2042
2044
HIV negative
Stage 1
Stage 2
Stage 3
Stage 4
Fig. 2. Number of persons by HIV negative and HIV positive category at the start of each year(percentage deviation from baseline).
126 E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
CAT
(o,a,g,r,h)
t
is the number of adults with employment status owho
are of age a,genderg, race rand HIV status hat the start of year t.
CAT
(N,a,g,r,h)
t
is the number of new entrants to the WAP who areof age
a,genderg, race rand HIV status h.Theyaredefined as people who
were not part of the WAP in year t−1, but will be 15 in year t.New
entrants are exogenously added at the start of each year.
ACT
(o,aa,g,r,hh)
t−1
is the number of people with employment status o,of
age aa,genderg,racerand HIV stage hh in year t−1.Thisarray
describes the detail of South Africa's highly differentiated labour
market.
HIVNEW t
a;g;rðÞ
is the number of new HIV cases by age a, gender gand
race rof people already part of the WAP.
T
(o,aa,g,r,hh,a,h)
is a transition matrix recording the proportion of peo-
ple in each labour market activity oby gender gand race r,surviving
from age aa to aand moving from HIV stage hh to h.
F1
(o,aa,g,r,hh,a,h)
is a shift variable on the proportion of people in each
employment status oby gender gand race r, surviving from age aa
to aand moving from HIV stage hh to h.
F2
(aa,g,r,HivN,a,Stage1)
is a shift variable on the proportion of people by
gender gand race rmoving from age aa to aand from the negative
HIV stage to Stage 1.
EUP is the set of all employment statuses comprising: (i) 11 occupa-
tions, (ii) two unemployment statuses and (iii) “permanently de-
parted from the labour force”(PDL) status. The 11 occupations are
Legislators, Professionals, Technicians, Clerks, Service workers,
Skilled agricultural workers, Craft workers, Plant and equipment op-
erators, Elementary workers, Domestic workers and an Unspecified
occupation. Unemployment statuses are short-term and long-term.
Short-term unemployment is where a person is unemployed in
year t −1 but employed in year t −2. Long-term unemployment
is where a person is unemployed in year t −1 and year t −2. PDL
refers to people who are either not economically active or who are
in HIV Stage 4.
5
AGE is the set of all age groups defining the working age population,
namely: 15–24, 25–34, 35–44, 45–54 and 55–65.
GEN is a set defining males and females.
RACE is a set defining two race groups namely; African and “Other”.
The “Other”group refers to the sum of the Coloured, Indian and
White population groups.
STG is a set containing all HIV stages, namely: HIV negative, HIV
Stage 1, HIV Stage 2, HIV Stage 3 and HIV Stage 4. The HIV positive
stages are based on the World Health Organisation's (WHO) clinical
classification of HIV/AIDS for adults and adolescents with confirmed
HIV infection (World Health Organisation, 2007: 12, 15–16).
6
Eq. (E.1a) models two transitions; (i) people moving from one age
group to the next and (ii) people changing their HIV status/stage. Nor-
mally the transition matrix is treated as exogenous. However, in formu-
lating the policy shocks for this paper, it was helpful to endogenise
elements of the transition matrix to accommodate independent infor-
mation on the number of new HIV cases. This is the purpose of
Eqs. (E.2) and (E.3). Eq. (E.2) sets the transition variable equal to two
shift variables. Eq. (E.3) calculates the number of new HIV cases as peo-
ple who were part of the HIV negative WAP in year t −1 and become
HIV positive (Stage 1) in year t. We expand on the operation of
Eqs. (E.2) and (E.3) in Section 5 where we explain the calculation of
our policy shocks.
Eq. (E.4) describes planned labour supply to specificlabourmarket
activities in year tby people distinguished by start-of-year labour
market categories. These offers are guided by changes in the relative
returns available across different labour market activities.
Lt
oo;a;g;r;h;oðÞ
¼CATt
oo;a;g;r;hðÞ
Boo;a;g;r;h;oðÞ
ATW oðÞ
X
p
Boo;a;g;r;h;pðÞ
ATW pðÞ
0
B
B
@
1
C
C
A
η
ðE:4Þ
for oo ∈EUPN;a∈AGE;g∈GEN;r∈RACE;h∈STG;o∈EUP
where
5
As describedin WH O,( 2007), people with Stage4 HIV have severe symptomssuch as
HIV wasting syndrome and pneumonia (WHO, 2007:16).
6
WHO clinical staging of established HIV infection is: Asymptomatic (Stage 1), mild
symptoms (Stage 2), Advanced symptoms (Stage 3) and Severe symptoms (Sta ge 4)
(WHO, 2007: 12).
-0.21
-0.16
-0.11
-0.06
-0.01
0.04
0.09
0.14
0.19
0.24
2006
2008
2010
2012
2014
2016
2018
2020
2022
2024
2026
2028
2030
2032
2034
2036
2038
2040
2042
2044
Labour supply (Persons)
Employment (Persons)
Real wage
Labour force (Persons)
Fig. 3. Aggregated labour demand, supply, real wage and labour force (percentage deviation from baseline).
127E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
L
(oo,a,g,r,h,o)
t
is the planned labour supply (offers) from all employ-
ment statuses oo of age a,genderg,racerand HIV stage h, to all
employment statuses o.
CAT
(oo,a,g,r,h)
t
is the number of adults in each employment status oo
who are of age a,genderg,racerand HIV status hat the start of
year t.
B
(oo,a,g,r,h,o)
captures exogenous non-wage factors (such as prefer-
ences) that may motivate people of age a,genderg,racer, HIV status
hand labour market status oo to offer their labour to activity o.
ATW
(o)
is the occupation-specific real after-tax wage rate.
ηis a parameter that reflects the ease with which adults can shift
between activities. Following Dixon and Rimmer (2010),wesetηat 2.
EUPN is a set of all employment statuses defined at the start of year t.
They include employment, unemployment, PDL and new entrants.
Eq. (E.5) describes the wage adjustment mechanism which is oper-
ational during policy simulations (Dixon and Rimmer, 2010).
Wpolicy
toðÞ
Wbase
toðÞ
−
Wpolicy
t−1oðÞ
Wbase
t−1oðÞ
¼αLDpolicy
toðÞ
LDbase
toðÞ
−
LSpolicy
toðÞ
LSbase
toðÞ
2
43
5for ο∈OCC ðE:5Þ
where
W
t(o)
base
and Wpolicy
toðÞ are the wage in the baseline and policy simulation
in year t, respectively;
W
t−1(o)
base
and Wpolicy
t−1oðÞ are the wage in the baseline and policy simula-
tion in year t−1, respectively;
LD
t(o)
base
and LDpolicy
toðÞ are the demand for labour in the baseline and
policy simulation in year t, respectively; and
LS
t(o)
base
and LSpolicy
toðÞ are labour supply in the baseline and policy simula-
tion in year t, respectively.
In the policy simulation, W
t(o)
base
,LD
t(o)
base
and LS
t(o)
base
are exogenously de-
termined and equal to their baseline values. Wpolicy
toðÞ ,LDpolicy
toðÞ and LSpolicy
toðÞ
evolve endogenously. Eq. (E.5) states that if, for example, a policy causes
a larger percentage deviation in labour supply than labour demand,
then there will be a decrease between years t−1and tin the deviation
in occupation o's real wage rate. In other words, in periods in which a
policy elevates labour supply relative to labour demand, real wages
fall relative to their baseline values. However, short-term wage rates
are sticky, so the initial effect of the increase in labour supply is to
increase unemployment while only slowly decreasing the wage. The
positive parameter αgoverns the speed at which wages adjust in the
policy case to return the employment rate to its baseline value.
Fig. 1 describes all possible flows from categories to activities. We
describe below the possible flows in Fig. 1 in the context of each starting
category.
CAT
EMP
1,a,g,r,h
to CAT
EMP
z,a,g,r,h
This category describes people employed in
year t−1for a given age a, gender g,racerand HIV stage h.In
year t, people in this category can remain in the same occupation o
(flow a); move to a different occupation oo (flow b); move to
short-term unemployment (flow c); or move to the PDL activity
(flow d). Because wages are stickly, not all offers to employment
are necessarily accepted. Hence, to determine flows b, e, h and l,
we begin by defining vacancies in each employment activity oin
year tas the number of jobs less the incumbents (flow a).
7
Flow b
is modelled as being proportional to the vacancies in o, and the
share of category oo in the supply of labour to activity ofrom people
outside o. People who are employed in occupation oo and plan on
moving to occupation o, but are unable to move due to insufficient
vacancies in o, simply remain in oo. Flow c shows the number of
people moving to short-term unemployment as the sum of volun-
tary movesand involuntary moves. Involuntary moves are modelled
as a fixed fraction of the number of people in each employment
category. Flow d is only relevant to a proportion of people who
were employed and in HIV Stage 3 during year t−1. A proportion
of people in HIV Stage 3 will move to HIV Stage 4 at the beginning
of year t. They are grouped in an employment category with an
HIV stage of Stage 4. We do not allow anyone with a Stage 4 status
to be employed or unemployed. Instead, they move to the PDLactiv-
ity in year t.Wemodelflows g,jand nin a similar way.
CAT
S
a,g,r,h
This category describes people of a given age a, gender g,
race rand HIV stage h, who were not employed in year t−1, but
employed in year t−2.Inyeart, people in this category can move
to employment activity o(flow e); those who fail to secure employ-
ment move into the long-term unemployment activity (flow f); or
those with a Stage 4 status move to the PDL activity (flow g).
7
This is a non-technical description.For a technical description, see Eqs.(E.14) to (E.32)
and associated discussion in Roos (2013a).
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
2006
2008
2010
2012
2014
2016
2018
2020
2022
2024
2026
2028
2030
2032
2034
2036
2038
2040
2042
2044
Investment
Capital
Average rate of return
Fig. 4. Investment, capital stock and rates of return (percentage deviation from baseline).
128 E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
CAT
L
a,g,r,h
This category describes people of a given age a, gender g,
race rand HIV stage h, who were unemployed in years t−1
and t−2.Inyeart, people in this category can move to employment
activity o(flow h); those who do not secure employment simply re-
main in the long-term unemployment activity (flow i); or move to
the PDL activity (flow j).
CAT
PDL
a,g,r,h
This category describes people of a given age a, gender g,
race rand HIV stage h, who were PDL in year t−1. They are not con-
sidered part of the labour force and donot move to any employment
or unemployment activities. PDL also includes all persons with a
Stage 4 status. In year t, people in this category only move into the
PDL activity (flow k).
CAT
N
a,g,r,h
The final category describes people of a given age a, gender
g, race rand HIV stage h, who enter the labour force for the first time.
In year t, people in this category can move to employment activity o
(flow l); new entrants who fail to secure a job, move to the short-
term unemployment activity (flow m); or those with a Stage4 status
move to the PDL activity (flow n).
Finally, labour supply to activity ois defined as:
LS o
ðÞ ¼X
oo∈EUPN X
a∈AGE X
g∈GEN X
r∈RACE X
h∈STG
Loo;a;g;r;h;o
ðÞ ðE:6Þ
oo ∈EUPN,a∈AGE;g∈GEN;r∈RACE;h∈STG;o∈EUP.
where
LS
(o)
is the supply of labour to employment, unemployment and PDL ac-
tivities. The employment subset of LS defined in Eq. (E.6) appears in the
sticky wage adjustment mechanism, Eq. (E.5).
3. Description of the databases
Two large databases form the initial solution to the SAGE-H model.
The core CGE database is calibrated from the 2002 Supply-Use
Tables (Statistics South Africa, 2006, 2009).
8
In parameterising the
labour supply module we begin with working age population data on
labour market activities by gender and race (Statistics South Africa,
2005). We then create an age dimension using census data (Statistics
South Africa., 2003). The HIV detail is based on the ASSA2003 model's
age-, race- and gender-specific information of adults across different
HIV stages (Actuarial Society of South Africa, ASSA, 2005). This data
forms the basis of the activity matrix defined in Eq. (E.1a). Next we cre-
ate the transition matrix, which is the product of an age and an HIV sta-
tus/stage transition matrix.The transition matrix recordsthe proportion
of people in each labour market activity osurviving from age aa to aand
moving from HIV stage hh to h. These transition rates are unique over
gender and race. To infer the ageing transition rates, we used age, gen-
der and race-specific demographic and mortality data implicit in the
ASSA model (Actuarial Society of South Africa, ASSA, 2005). We adopt
age, gender and race-specific non-AIDS and AIDS death rates. Non-
AIDS death rates show a smooth increase from younger to older age
groups. The second set of age and gender-specific death rates describe
AIDS-related deaths. A distinct age and gender-specific pattern is ob-
served. For both genders, younger age groups have higher death rates
compared to the non-AIDS death rates. The high death rates are follow-
ed by a rapid decline in the AIDS death rates for older age groups. AIDS
deaths peak at 30–34 for females and 35–39 for males. To calculate
transition probabilities for the HIV dimension, we adopt data from the
ASSA model (Actuarial Society of South Africa, ASSA, 2005). The transi-
tion matrix ensures that people move sequentially through the 5 HIV
stages. For example, a person transitioning from HIV negative to HIV
positive moves from HIV negative to Stage 1. From Stage 1 they move
sequentially through the stages until they reach Stage 4. People cannot
move backward through the stages. The resulting set of transition rates
(T
(o,aa,g,r,hh,a,h)
—see E.1a) are non-uniform over age, gender, race and
labour market activity.
9
There is little official statistical data to inform HIV-stage-specific
flows in L
(oo,a,g,r,h,o)
t
in Eq. (E.4). However there are some studies that
evaluate the impact of HIV and AIDS on absenteeism (Morris et al.,
2000; Orr and Patient, 2006). We draw upon these studies to inform
plausible flows based on HIV stage. For example, Orr and Patient
(2006) evaluate the impact of HIV and AIDS on absenteeism in the
8
At the time of developing the SAGE-H model, the2002 SUT was the most recent avail-
able data.
9
For a detailed description on the creation of the labour module database, see Roos
(2013b).
0
0.04
0.08
0.12
0.16
0.2
0.24
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
2031
2033
2035
2037
2039
2041
2043
2045
Employment (Wage-bill)
GDP
Capital
Employment (Persons)
Fig. 5. Real GDP, labour input and capital stock (percentage deviation from baseline).
129E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
South African hospitality industry. Their study shows a correlation be-
tween sick leave and the illnesses associated with the clinical stages of
infection. USAID (2001) states that during the early stages of HIV infec-
tions, managers may observe unexplained increases in the number of
sick days taken. As the illness progresses, managers may observe an in-
crease in disease such as TB or malaria which leads to increases in sick
days (USAID, 2001). As a consequence HIV positive workers may be
retained in their current position, moved toa less demanding job within
the company, or fired (USAID, 2001). We have drawn on these studies
to inform the values for Lin the following ways:
(i) HIV negative people offer more strongly to employment activi-
ties than do HIV positive persons.
(ii) An HIV positive employed person with a Stage 3 status is more
likely to offer to short-run unemployment than an HIV negative
person or a person who is HIV positive and in Stage 1 or 2.
(iii) People who are HIV positive and unemployed in year t−1offer
more weakly to employment activities in year tthan an HIV neg-
ative unemployed person.
(iv) A person with an HIV positive Stage 3 status who was part of the
labour forcein year t−1and moves to Stage 4 at the start of year
t, offers onlyto the “permanently departed from the labour force”
activity in year t. We assume that people who are “permanently
departed from the labour force”remain in this category.
After the creation of these databases, we move both databases for-
ward to 2011 via simulation, by imposing on the model as exogenous
shocks known outcomes for macroeconomic variables and HIV inci-
dence rates, using data from the South African Reserve Bank data and
Rehle et al. (2010).
4. A back-of-the-envelope representation of SAGE-H
In this section we outline a back-of-the-envelope model (BOTE)
describing a stylised representation of the key macroeconomic relation-
ships in SAGE-H relevant to the simulation results reported in Section VI.
BOTE will also prove useful when we explain how the results from the
ASSA model are introduced to SAGE-H. The BOTE equations are presented
in Table 1.Table 2 describes the variables in Table 1.
SAGE-H is a recursive dynamic model, linking a sequence of annual
equilibria through stock-flow accounting and transition probabilities.
In using BOTE to describe SAGE-H, we distinguish between equations
that describe:
(i) economic relationships within any given year of our year-on-
year simulations (Eqs. (B.1)–(B.14));
(ii) how the HIV status of adults changes between years
(Eqs. (B.15)–(B.18));
(iii) movements in other economic stock variables between years
(Eqs. (B.19)–(B.20)); and
(iv) the sticky wage adjustment mechanism (Eq. B.21).
Eq. (B.1) describes real gross domestic product (GDP) from the
expenditure side in constant price terms. Eq. (B.2) describes an
economy-wide constant returns to scale production function, relating
real GDP to inputs of capital and labour and primary-factor technical
efficiency. Eq. (B.3) relates the sum of private and public consumption
to real (consumption-price deflated) gross national income (GNP) via
a given average propensity to consume. Eq. (B.4) defines the ratio of
public to private consumption. Eq. (B.5) defines realGNP as real GDP ad-
justed by a positive function of the terms of trade, less interest payment
on real foreign debt. Eq. (B.6) relates aggregate import volumes to real
GDP and the terms of trade. Eq. (B.6) summarises our SAGE-H assump-
tion that agent-specific demand for an individual import is positively
related to the agent's activity level (proxied by real GDP in B.6) and
negatively related to the price of the import relative to the price of the
domestic substitute (proxied by the terms of trade in Eq. (B.6)).
Eq. (B.7) defines the terms of trade as the ratio of the export price
index to the import price index. In SAGE-H, the export volume for any
individual commodity is negatively related to its foreign-currency
price via a constant elasticity export demand function. At the economy-
wide level, we summarise this in BOTE in Eq. (B.8). Eq. (B.9) makes
investment a positive function of the rate of return on capital. Eq. (B.10)
defines the gross capital growth rate as the ratio of investment to capital.
Since the production function is constant returns to scale, marginal prod-
uct functions are homogenous of degree zero and can be expressed as
functions of the capital/labour ratio. This accounts for Eqs. (B.11) and
(B.12). Eq. (B.11) relates the profit-maximising capital/labour ratio to
the rate of return on capital, technical change, and the terms of trade.
Eq. (B.12) relates the real consumer wage to changes in the capital-
labour ratio, technical change and the terms of trade. Eq. (B.13) equates
labour demand with labour supply multiplied by the employment rate.
We distinguish in BOTE the labour supply of HIV positive and negative
individuals because our policy simulations involve interventions aimed
at reducing the number of persons entering the HIV positive category.
Eq. (B.14) defines start-of-year labour supply as the sum of HIV negative
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
2006
2008
2010
2012
2014
2016
2018
2020
2022
2024
2026
2028
2030
2032
2034
2036
2038
2040
2042
2044
GDP
Private consumption
Public consumption
Fig. 6. Private and public consumption and real GDP (percentage deviation from baseline).
130 E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
labour force participants and HIV-positive labour force participants
multiplied by their respective employment offer rates. Eq. (B.14) distin-
guishes the offer rates of HIV-negative and HIV-positive labour force par-
ticipants because, as discussed in Sections 2 and 3, SAGE-H recognises
that HIV-positive people make weaker offers to employment activities
relative to HIV-negative people.
Eqs. (B.15) to (B.18) determine year-on-year movements in the la-
bour force, distinguished by HIV status. In the BOTE framework, an
HIV negative adult in year t−1has three transition probabilities in
moving to year t:
(i) They might survive, and change their HIV status from HIV nega-
tive to HIV positive. We represent this probability by T
HIVn,HIVp
.
(ii) They might die, with probability DRT
HIVn
.
(iii) They might survive, and remain HIV negative, with probability
T
HIVn,HIVn
.
Since T
HIVn,HIVp
,DRT
HIVn
and T
HIVn,HIVn
exhaust the transition possi-
bilities for an HIV negative adult, Eq. (B.15) calculates T
HIVn,HIVn
as a re-
sidual of T
HIVn,HIVp
and DRT
HIVn
.
Eq. (B.16) relates the start-of-year number of HIV negative adults in
the labour force (LF
HIVn
) to the number of HIV negative adults in the la-
bour forcein year t−1 who surviveto year t(LF
t‐1
HIVn
×T
HIVn,HIVn
)andthe
number of HIV negative new entrants to the labour force (NEW
HIVn
).
Eq. (B.17) relates the start-of-year number of HIV positive people in
the labour force (LF
HIVp
) to the number of adults who were HIV positive
in year t−1 and survive to yeart (LF
t‐1
HIVp
(1 ‐DRT
HIVp
)),
10
the numberof
new HIV infections (HIV
new
) and the number of HIV positive new en-
trants to the labour force (NEW
HIVp
). Eq. (B.18) defines the start-of-
year number of new HIV infections (HIV
new
) among current labour
force participants as the product of the number of HIV negative adults
during year t−1(LF
t‐1
HIVn
) and the probability of changing HIV status
from HIV negative to HIV positive (T
HIVn,HIVp
).
11
Eq. (B.19) relates the start-of-year capital stock to investment in the
previous year and depreciation on the existing capital stock. Eq. (B.20)
relates start-of-year foreign debt to the previous year's foreign debt
and the excess of investment over savings.
12
Eq. (B.21) describes the path of the real wage in the policy. With
Eq. (B.21) activated in the policy simulation, the real wage deviation
will gradually decrease (increase) as long as the deviation in the labour
supply/demand balance lies above (below) its basecase level.
We now consider a closure for Eqs. (B.1) to (B.20) that reflects the
closure of SAGE-H. In doing so, we distinguish between equations that
describe economic relationships within any given year (Eqs. (B.1) to
(B.14)) and equations that describe start-of-the-year variables
(Eqs. (B.15) to (B.20)). We begin by noting that start-of-year values
for T
HIVn,HIVn
,LF
HIVn
,LF
HIVp
, HIV
new
, K and FDATT are uniquely deter-
mined by Eqs. (B.15) to (B.20). As such, T
HIVn,HIVn
,LF
HIVn
,LF
HIVp
,HIV
new
,
K and FDATT, while formally endogenous, are effectively exogenous
within any given year of a year-on-year simulation. Thus, recognising
that Eqs. (B.15) to (B.20) govern dynamics across years, our task of un-
derstanding the model closure narrows to choosing appropriate short-
run and long-run closures for Eqs. (B.1) to (B.14).
Eqs. (B.1) to (B.14) comprise 14 equations and 28 unknowns. Table 1
presents two closures: a short-run closure and an “effective”long-run
closure. By “effective”long-run closure, we mean that while ROR and
Ψare presented as exogenous in the long-run, no such exogeneity is ac-
tually imposed on these variables in SAGE-H simulations. Rather, in the
year-on-year dynamic simulations, Eqs. (B.9) and (B.19) lead the econ-
omy to a long-run state that can be described by the exogenous status of
ROR and Ψin BOTE.
A closure for Eqs.(B.1) to (B.14) that reflects the short-run closure
environment of SAGE-H would have X, Y, C, Γ, GNP, M, TOT, PX, I, Ψ,
ROR, LD, ER and LS determined endogenously, given exogenous values
for G, A, APC, FDATT, R, PM, F
d
,F
inv
,K,W,OR
HIVn
,OR
HIVp
,LF
HIVn
and
LF
HIVp
. This closure is described in column (1) of Table 1. Our description
of SAGE-H's long-run behaviour using BOTE differs in two respects from
this short-run closure. First, policy-case employment rates by occupa-
tion are returned to their baseline levels via real wage adjustment. In
BOTE, this is represented by long-run exogeneity of ER and endogeneity
of W. Second, the short-run operation of Eqs. (B.9) and (B.19) gradually
10
Note that thesurvival probability in Eq. (B.17) refers to the probability of an HIV pos-
itive person in year t −1 surviving to year t and still remain part of the labour force. In
BOTE we do not distinguish between the HIV positive stages.
11
Note that the transition matrix in BOTE Eq. (B.18) refers to the probability of a person
moving from HIV negative to HIV positive (T
HIVn,HIVp
). In the description of the full
SAGE-H labour-market theo ry, this description specifically refers to the transition from
HIV negative to Stage 1 HIV status. In the SAGE-H model, additional dimensions distin-
guish transition probabilities by age, gender, race and occupation.
12
The start-of-the-year foreign debt can be written as FDATT = FDATT
t-1
+CADEF
t-1
.
This equation relates start-of-the-year foreign debt to the previous year’s foreign debt
and the current account deficit. The current account deficit is defined as X-M. We also
know that X-M = I-S. From BOTE, (B3) implies that national savings is given as (1-APC)
× GNP. Hence, CADEF = I-(1-APC) × GNP. Substituting CADEF into FDATT yields FDATT
=FDATT
t-1
+I
t-1
-(1-APC
t-1
) × GNP
t-1
.
-0.05
-0.01
0.03
0.07
0.11
0.15
0.19
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
2031
2033
2035
2037
2039
2041
2043
2045
GNE
Terms of trade
GDP
Imports
Exports
Fig. 7. Exports, imports, GDP and domestic absorption (percentage deviation from baseline).
131E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
drives therate of return back to its baseline value viacapital adjustment.
In BOTE, the end-point of this process is represented by ROR exogenous
and K endogenous.
5. Simulation design
We model two routes through which the increase in condom use has
a direct effect on the South African economy: (1) new HIV infection
numbers, and (2) the financing cost of expanded public distribution of
free condoms.
13
To implement the appropriate shocks in SAGE-H, we
must know the level, the composition and timeframe of these effects.
We obtain information on the impact of condom use on the number
of age, gender and race-specific new HIV infections by simulating the
Actuarial Society of South Africa epidemiological model (Actuarial
Society of South Africa, ASSA, 2005; Dorrington et al., 2005). We run
two simulations. The first simulation incorporates the default settings
in the ASSA modeland does not include our policy of an increase in con-
dom use. This simulation incorporates the baselinesettings for the ASSA
model's five sets of policy interventions (Dorrington et al., 2005). In the
second simulation we assume that the number of sex acts protected
from the HIV virus by condom use increases by 10% relative to base-
line.
14
We then calculate thepercentage deviations in new HIV casesbe-
tween the two ASSA simulations distinguished by age, gender and race.
Next we run a side-simulation with SAGE-H in which we impose the
ASSA model deviations in new HIV cases as exogenous shocks to
HIVNEW by age, gender and race (See Eq. (E.3)). HIVNEW is normally
endogenous. In our side simulation its exogenous status is supported
by the endogenous determination of the shift variable F2
(a,g,r,HivN,Stage1)
(normally exogenous) in Eq. (E.2).
15
Our policy simulation involves
returning SAGE-H to the standard closure in which new HIV cases
(HIVNEW) is endogenous and we shock F2 with the side-simulation
values. The ASSA model does not provide information on the number
of condoms required to achieve the ASSA model's outcome for averted
HIV infections. In the absence of independent information regarding
the quantity of additional condoms implicit in the ASSA model input as-
sumptions, we assume that an additional 113 million condoms must be
distributed.
16
An estimate of the unit cost of these condoms was obtain-
ed from the National Department of Health (Marumo, 2011).
17
13
There may be other important avenues of the impact of HIV that arenot addressed in
this paper.An obvious avenue is theimpact on the wider publichealth budget arisingfrom
a fall in new HIV cases.
14
For example, in the baseline ASSA simulation, for 14–19 year old Africans in the “at
risk”category, 42.33% of sex acts are protected via condom use. In the policy ASSA simu-
lation, this proportion becomes 46.56%.
15
With Eq. (E.2) endogenously determining the transition probability from negative to
Stage 1, we endogenously determine the transition probability of remaining HIV negative
as a residual under an assumption that age, gender and race-specific death rates for HIV-
negative individuals remain unchanged.
16
Given the current status of the epidemic in South Africa, it would be useful to know
how many condoms are required to avert one new HIV infection. This is a rather difficult
task as it depends on numerous factorssuch as the sexual behaviour of people in different
risk groups, HIV prevalence by risk group, STI rates and percentage of sex protected by a
condom. In the absence of independent information on the matter, we outline below a
set of simple equations (Eqs. (E.1) to (E.6)) to calculate the number of condoms required
to avoid the new HIV infections calculated in our ASSA simulations. Eq. (E.1) defines the
number of protecte d sex acts (P) as the product of the total numbe r of sex acts (Γ)
and the proportion of sex acts protected from the HIV virus due to condom use (Ψ).
(E.1) P=Γ×ΨEq. (E.2) states that the number of condoms used to protect sex acts (C)
is the product of the number of protected sex acts (P) and the number of condoms re-
quired to protect one sex act(E). (E.2) C = P × E SubstitutingEq. (E.1) into Eq. (E.2) yields
(E.3) C = Γ×Ψ× E Rewriting Eq. (E.3) into percentage changeform (E.4) c = γ+ψ+ε
Eq. (E.4)suggests that ifwe increase the proportion of protected sexacts (ψ) by 10%, while
holdingγand εconstant, the numberof condoms used rises by 10%.Eq. (E.5) defines total
condomssupplied in South Africaas the sum of condoms suppliedby the government (G)
and the private sector (B). (E.5) C = G + B Thepercentage changeform of Eq. (E.5) is (E.6)
C = Sg × g + Sb × b where Sg = G/Cand Sb = B / C The government is thelargest distrib-
utor of condomsin South Africa. On the basis of figures reported in Myer et al. (2001),we
assume that the public sector is responsible for 90% of condom supply in South Africa.
Eq. (E.6) implies that if we hold the number of condoms distributed by theprivate sector
constant, and require C to rise by 10%, then G must increase by 11.11%. The public sector
distributed 445 million condoms in 2010 (Marumo, 2011). An 11.11% increase in this
numberrepresents a 49.4 million increase in thenumber of condomssupplied by the gov-
ernment.However, we recognise thatnot all condoms distributedby the public sector are
used during sex. In their study, Myer et al. (2001) investigates what happens to condoms
which were distributed free of charge by the public sector. They found that 43.7% of the
condoms were used in sex. Hence, base d on their finding we assume that to secure a
49.4 million increase in condom use,113 million additional condoms must be distributed.
Our calculations make clear that in arrivingat our 113 millionunit estimate we havemade
three assumptions: no crowding out of privately supplied condoms (B is constant), no
change in wastage (E is constant), and no changein the number of sex acts (Γis constant).
We are aware of no studies that elucidate the elasticities of B, E and Γto G. Nevertheless,
we think it likely that the constancy of B, E and Γin the face of a rise in G is not assured.
As such, we view our estimate for the change in G of 113 millionunits as perhaps a good
order-of-magnitude estimate only.
17
The average unit cost of condoms is R0.23. On this basis, we assume that the annual
cost of providing an additional 113 million condoms will be R26 million. This is a once
off permanent increase in costs.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
2006
2008
2010
2012
2014
2016
2018
2020
2022
2024
2026
2028
2030
2032
2034
2036
2038
2040
2042
2044
African 15–44
African 45–65
Other 45–65
Other 15–44
Fig. 8. Labour supply from all labour force categories to employment activities by broad age group and race (percentage deviation from baseline).
132 E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
6. Results
In interpreting the results produced by SAGE-H we refer to the BOTE
equations listed in Table 1. The immediate effects of a decrease in the
probability of an adult moving from HIV negative to Stage 1 are: (1) a
fall in the number of new HIV infections, and (2) an increasein the sur-
vival probability of an HIV negative adult. This accounts for the positive
deviation in the number of HIV negative persons in Fig. 2. It also
accounts for the negative deviation in the number of HIV positive per-
sons by HIV Stage. Initially, the fall in new HIV cases is manifested as
negative deviation in Stage 1. Consistent with the HIV transition path-
way described by Eq. (E.1a), over time the fall in Stage 1 persons flows
through into negative deviations in persons in Stages 2–4. This accounts
for the pattern of staggered deviations in HIV positive stages in Fig. 2.
The pattern of initial trough and partial recovery in the number of
persons by HIV-positive category in Fig. 2 reflects the pattern of
subgroup-specific transition rates, in particular, the fact that for individ-
uals in certain high-risk groups, the condom programme delays, but
does not prevent, eventual infection. Nevertheless, over the entire
simulation period,the average probability of moving from HIV negative
to Stage 1 remains below its baseline values. In terms of BOTE, we
represent this as a fall in T
HIVn,HIVp
. Via BOTE Eq. (B.18), a decrease in
T
HIVn,HIVp
leads to fewer new HIV infections. A corollary of the decrease
in T
HIVn,HIVp
is that, with death rates (in BOTE, DRT
HIVn
) remaining at
their base levels, the diagonal transition rate of HIV negative adults
(T
HIVn,HIVn
) rises. In BOTE, this relationship is captured by Eq. (B.15).
In BOTE, the number of people of a given HIV status who are part of
the labour force at the start of the year is modelled by Eqs. (B.16) and
(B.17). Via Eq. (B.16) we see that the number of people who are HIV
negative depends on new entrants to the labour force and movements
in the survival probability of HIV negative adults. Eq. (B.17) summarises
the calculation of the number of HIV positive labour force participants,
noting that this depends upon the survival probability of existing HIV
positive persons, newly-infected existing members of the labour force,
and new entrants to the labour force who are already HIV positive.
Both Eqs. (B.16) and (B.17) summarise the more detailed modelling in
SAGE-H. In particular, Eqs. (B.16) and (B.17) are based upon SAGE-H
Eq. (E.1a),discussedinSection 2 above.
The prevention policy affects transition rates regulating the propen-
sity of HIV negative people in year t −1 to become HIV positive in year t.
In the policy simulation we assume that all other transition rates remain
set at their baseline values. The reader will recall that our underlying
theory specifies that a person who is HIV positive and in Stage 1
moves sequentially through stages 1 to 4. This accounts for the pattern
of lagged deviations in the number of persons categorised by HIVstatus
in Fig. 2, which shows thetiming of the negative deviations by HIV stage
moving sequentially through stages 1 to 4. In the long run the total
number of HIV positive persons is approximately 0.72% lower than
baseline and the number of HIV negative persons is approximately
0.45% higher than baseline.
Age- and gender-specific mortality rates rise with HIV status. Hence,
with fewer people moving into the HIV positive categories, the devia-
tion in South Africa's labour force is positive (Fig. 3). Note that the devi-
ation in labour supply exceeds the deviation in the labour force. As
discussed in Section 2, our labour market theory embodies lower labour
market attachment for HIV positive persons relative to those who are
HIV negative. Labour market attachment declines further as HIV posi-
tive persons move through successive HIV stages. As discussed in
Section 2, in the labour market theory of SAGE-H, declining labour
market attachment manifests as lower participation rates and higher
offers to voluntary unemployment. As is clear from Fig. 2, the policy
causes a positive deviation in HIV-negative individuals (with compara-
tively strong labour market attachment) and a negative deviation in
HIV-positive individuals (with comparatively weak labour market
attachment). In Fig. 3, this explains why the deviation in labour supply
exceeds the deviation in the labour force.
In Fig. 3 we see that the deviation in employment tracks close to, but
initially lags, the deviation in laboursupply. This reflectsour assumption
of transient stickiness in the real wage. In BOTE, we represent this in the
short-run by setting W exogenous in column (1) of Table 1.WithW
exogenous, LD is largely determined by Eq. (B.12).
18
Hence, in the
short-run, the positive deviation in LS causes a negative deviation in
the employment rate.
19
This accounts for the initial growing negative
18
Eq. (B.12) has 2 endogenous variables in the short run, TOT and LD. Scope for large
movements in TOT is limited by South Africa's high demand elasticities (−5) in SAGE-H.
With movements in TOT limited, and with K, A and W exogenous in the short run,
Eq. (B.12) can be viewed as largely determining LD.
19
While we treat W as short-run exogenous in BOTE,in SAGE-H we assume thatthe de-
viation in W is a positive function of the deviation in the employment rates (ER in BOTE).
This renders W sticky in short-run applications of SAGE-H. In BOTE, we represent this
short-runstickiness in the wage by exogenous determination of W. Interms of BOTE, this
implies, via Eqs. (B.13) and (B.21), that a rise in labour supply will be matchedby a fall in
employment rate. However in SAGE-H, a short-run negative deviation in ER produces a
negative deviation in W, allowing a short-run positive deviation in LD via Eq. (B.12).
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
2009
2011
2013
2015
2017
2019
2021
2023
2025
2027
2029
2031
2033
2035
2037
2039
2041
2043
2045
Agriculture
Mining
Construction
Service
Manufacturing
Utilities
Dwellings
Fig. 9. Output by broad sector (percentage deviation from baseline).
133E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
deviation in the average employment rate, manifested in Fig. 3 by the
gap between the deviations in labour supply and employment. Because
our HIV prevention programme generates a growing positive deviation
in labour supply (Fig. 3), the negative deviation in the employment rate
persists. However, via the sticky wage mechanism (Eq. (B.21)) it nar-
rows over time, ensuring that accretions to labour supply from earlier
periods eventually manifest as a rise in employment. In the long-run,
as the growth rate of the deviation in labour supply declines, (Fig. 3),
wage flexibility allows the employment deviation to catch-up with the
labour supply deviation, allowing the employment rate to return
towards its baseline level. In BOTE, we represent SAGE-H's property
of medium- to long-run wage flexibility by the endogenous status of
W and the exogenous status of ER in column (2) of Table 1.Via
Eqs. (B.13) and (B.21), we expect that the deviation in long-run labour
demand will match the long-run deviation in labour-supply. We see
this confirmed by the long-run convergence of the employment and
labour supply deviations in Fig. 3.
Although the policy change leads to an increase in the total number
of people employed, the improvement in health status leads to a lower
increase in labour input measured by wage-bill weights relative to per-
son weights. In terms of contribution to GDP, labour input is calculated
as the number of employment activities weighted by their respective
wage rates, reflecting differences in productivity across occupational
groups. In Fig. 5 we see that long-run wage bill-weighted labour input
increases by 0.2% relative to baseline, slightly less than the long-run
deviation in employed persons of 0.23%. This reflects the fact that the
employment-promoting effects of the policy are weighted towards
relatively low wage occupations such as craft and plant and machine
operators.
With employment higher, but capital stocks slow to adjust in the
short-run, the capital/labour ratio declines relative to baseline (Fig. 5).
Via Eq. (B.11) the short-run negative deviation in the capital/labour
ratio generates a positive deviation in the rate of return on capital.
This accounts for the growing positive deviation in the rate of return
on capital in the first half of the simulation period (Fig. 4). The positive
rate of return deviation causes positive deviations in the capital growth
rate (Ψ) and with it, real investment through BOTE Eqs. (B.9) and (B.10)
(column 1 of Table 1). This accounts for the positive deviation in real in-
vestment in Fig. 4. As discussed in Section 3, in BOTE, we represent the
long-run outcome of the process described by Eqs. (B.9) and (B.10)
(namely, a positive deviation in the capital growth rate so long as the
rate of return on capital exceeds a given normal rate of return) via the
exogenous status of the capital growth rate (Ψ)andtherateofreturn
on capital (ROR). In Fig. 4, we see these two long-run properties of the
SAGE-H model expressed, respectively, in the convergence of the in-
vestment and capital deviations, and the gradual elimination of the
rate of return deviation.
Via long-run BOTE Eq. (B.11), we expect that, for a given terms of
trade the long-run growth in employment generated by the policy
should produce a corresponding positive deviation in the long-run cap-
ital stock. Broadly, we see this expectation confirmed in Fig. 5. Note
however that in Fig. 5 we find the deviation in the capital stock lies
below the deviation in (wagebill-weighted) employment. This implies
that in the long-run there is a small decline in the capital-labour ratio
relative to baseline. As we explain below, the policy generates a long-
run decline in South Africa's terms of trade. Via Eq. (B.11) this causes a
negative deviation in the long-run capital/labour ratio. Via Eq. (B.2),
the positive deviations in employment and the capital stock generate
Table 2
BOTE variable descriptions.
APrimary-factor augmenting technical change
APC,APC
t−1
Average propensity to consume, years t and t −1
CReal private consumption
Depr Depreciation rate
DRT
HIVn
Death rate of HIV negative adults
DRT
HIVp
Death rate of HIV positive adults
FDATT Real net foreign liabilities in the current year
FDATT
t−1
Real net foreign liabilities in year t −1
F
d
Export demand shift variable
F
inv
Normal rate of return on capital
GReal government consumption
GNP,GNP
t−1
Real (consumption price deflated) gross national product, years t and t −1
HIV
new
New HIV infections at the start of year t
I,I
t−1
Real investment expenditure, years t and t −1 respectively
K,K
t−1
Capital stock, years t and t −1 respectively
LD,LD
base
Labour demand in the policy and base simulation in year t
OR
HIVn
,OR
HIVp
Offer rates to employment, HIV negative and positive (OR
HIVn
NOR
HIVp
)
LS,LS
base
Labour supply in the policy and base simulation in year t
LF
t−1
HIVn
Number of HIV negative people in the labour force in year t −1
LF
t−1
HIVp
Number of HIV positive people in the labour force in year t −1
LF
HIVn
Number of HIV negative people in the labour force at the start of year t
LF
HIVp
Number of HIV positive people in the labour force at the start of year t
MImport volumes
NEW
HIVn
HIV negative new entrants to the labour force
NEW
HIVp
HIV positive new entrants to the labour force
PX,PM Foreign-currency export price, foreign-currency import price
RInterest rate on foreign liabilities
ROR Rate of return on capital
T
HIVn,HIVn
Survival probability of an HIV negative adult
T
HIVn,HIVp
Probability of a person surviving to the next year and changing their HIV status from HIV negative to HIV positive
TOT Terms of trade
W,W
base
Real (CPI-deflated) wage in the policy and base simulation in year t
W
t−1
,Wbase
t−1Real (CPI-deflated) wage in the policy and base simulation in year t −1
XExport volumes
YReal gross domestic product (GDP)
ΓRatio of public to private consumption
ΨGross capital growth rate
134 E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
a positive deviation in real GDP. This accounts for the long-run positive
deviation in real GDP of approximately 0.17% reported in Fig. 5.
20
We assume that public and private consumptions are a fixed propor-
tion of gross national product (GNP). GNP in turn is a function of real
GDP, the terms of trade, and foreign interest payments. In BOTE, we
represent these relationships via Eqs. (B.3), (B.4) and (B.5). In
Eq. (B.5) we see that, for a given level of the terms of trade and foreign
debt, movements in real GNP depend on movements in real GDP. This
explains why, in Fig. 7, the real consumption deviations (which are
indexed to real GNP via Eqs. B.3 and B.4) closely track the real GDP
deviation. Ultimately, the real GNP deviation and with it, the real
consumption deviation, lie below the real GDP deviation. This is so for
two reasons. First, the policy causes a negative deviation in the terms
of trade (Fig. 7). Second, the positive deviation in real investment
exceeds the deviation in real national savings. Via Eq. (B.20) this gener-
ates a positive deviation in net foreign debt,and with it, foreign interest
payments on that debt. Together, thenegative deviation in the terms of
trade and the positive deviation in net foreign debt damp the real GNP
deviation relative to the real GDP deviation.
As discussed above, the long-run deviation in real GDP is approxi-
mately 0.17% (Fig. 5). With the long-run negative deviation in the
terms of trade, and the long-run positive deviation in net foreign liabil-
ities, the real GNP deviation is slightly below this, at0.15%. As discussed
in Section 4,inSAGE-Hwemodelthecondomdistributionprogramme
via an increase in public spending on the relevant commodities. This is
financed via a direct tax on households. In Fig. 6, this explains why the
private consumption deviation lies below the public consumption
deviation.
The policy generates a negative deviation in the terms of trade
(Fig. 7). This reflects the modelling of commodity-specific export vol-
umes in SAGE-H, which are assumed to be inversely related to foreign
currency export prices. In BOTE, we represent this by Eq. (B.8). The
policy generates a growing positive deviation in South Africa's export
volumes (Fig. 7). It is this positive deviation in exports, which, via
Eqs. (B.8) and (B.7), accounts for the negative deviation in the terms
of trade. We trace the long-run positive deviation in export volumes
to the operation of Eqs. (B.1) and (B.6). In Eq. (B.6) we see that aggre-
gate imports are determined by two broad forces: an activity effect
(represented by movements in Y) and a real exchange rate effect (rep-
resented by TOT). The importance of the activity effect is clear from
Fig. 7, where we see that the import volume deviation broadly tracks
the real GDP deviation. To explain the long-run export volume devia-
tion, we turn our attention to Eq. (B.1). In Fig. 6 and the attendant
discussions above, we saw that the real consumption deviations broadly
track the real GDP deviation. In Figs. 4 and 5 and the attendant discus-
sions above, we saw that the real capital deviation broadly tracked the
real GDP deviation, and the real investment deviation broadly tracked
the capital deviation. By extension the real investment deviation
broadly tracks the real GDP deviation. With the deviations in C, I and
G broadly tracking the deviation in real GDP, in Fig. 7 we find that the
real GNE deviation broadly tracks the real GDP deviation. With the
import volume deviation broadly tracking the real GDP deviation, and
with the GNE deviation broadly tracking the real GDP deviation, via
Eq. (B.1) the export volume deviation must also track the real GDP
deviation (Fig. 7).
The foregoing discussion explains why the export and import
volume deviations in Fig. 7 broadly track the real GDP deviation. What
remains is to explain why the export volume deviation initially lies
below the real GDP deviation, before ending the simulation period
above the real GDP deviation, while the import volume deviation ex-
hibits the reverse pattern. First, we note that in the short-run, the real
investment deviation greatly exceeds the real GDP deviation. In the ini-
tial years ofthe simulation, this causes the real GNE deviation to exceed
the real GDP deviation, pushing the deviation in the real balanceof trade
towards deficit via Eq. (B.1). This explains why the import volume devi-
ation lies above the export volume deviation during the first two
decades of the simulation period (Fig. 7). Towards the end of the simu-
lation period, the real investment deviation moves below the real GDP
deviation. At the same time, the negative deviation in the terms of
trade and the positive deviation in net foreign liabilities cause the real
consumption deviation to lie below the real GDP deviation (Fig. 6). In
the long-run, with the deviations in C, I and G lying below the deviation
in real GDP, the real balance of trade must move towards surplus. It is
this long-run movement towards trade surplus that explains why,
during the last decade of the simulation period, the export volume devi-
ation comes to lie above the import volume deviation (Fig. 7).
Consistent with the age and race categories most at risk from HIV in-
fection being young African adults, the condom distribution policy has
its largest initial impact on the labour supply of these individuals
(Fig. 8). Hence, while the policy generates positive deviations for all
employment activities, it produces relatively large increases in those
occupations to which young African adults most intensively supply
their labour, in particular those classified as unskilled and semi-skilled
employment activities.
For reporting purposes, we aggregate the output results for the
model's 28 industries into seven broad sectors (Fig. 9). The policy gen-
erates positive deviations in output for all sectors. The output deviations
of four sectors, Services, Manufacturing, Dwellings and Utilities, track
broadly in line with real GDP. The positive deviation in output is the
lowest for the Agricultural and Mining sectors, despite these sectors
being relatively intensive users of unskilled and semi-skilled labour.
This reflects our assumption that inputs of agricultural land and sub-
soil mining assets in the policy simulation cannot deviate from their
baseline forecast values. The strong positive deviation in the output of
the Construction sector is mainly due to the positive deviation in invest-
ment, to which Construction sells just under two-thirds of its output.
In Table 3 we summarise the main SAGE-H outcomes as they relate
to assessing the policy's potential net benefits. Rows 1 and 2 summarise
the outputs of the ASSA model. Over the simulation period, just over
200,000 new HIV cases are averted (row 1). This implies an average
annual decrease of 5888 new HIV cases (row 2). When input to SAGE-
H,thefallinnewHIVcasesgeneratesapositivedeviationinemployment
20
By 2045, long-run wage-bill weighted employme nt is 0.20% above b ase and the
rental-weighted capital stock is 0.15% above base. Land is assumed to be unchanged from
base. The shares of returns to employment, capital and land in GDP in 2045 are 40%, 56%
and 4% respectively. Changes in factor supply therefore explain0.164% of the 2045 devia-
tion in real GDP (=0.4 ∗0.204 + 0.56 ∗0.15 + 0.04 ∗0).
Table 3
Summary of result2012–2046.
Source: Author's calculations.
1 Total number of new HIV cases averted by 2046 206,067
2 Average annual number of new HIV cases averted 5888
Rand million USD$ million
3 Total real gross consumption gains 653,923 87,540
4 Total cost of the prevention programme 1051 141
5 Present value of real gross consumption gains 219,124 29,334
6 Present value of the cost of the prevention programme 544 73
7 Present value of the net benefit of the programme 218,580 29,261
8 Present value of the net benefit of the programme per household 15,613 2090
135E.L. Roos, J.A. Giesecke / Economic Modelling 39 (2014) 123–137
viaanincreaseinlong-runlaboursupply. As discussed in the main body
of Section 6, the positive employment deviation generates a positive devi-
ation in South African real consumption. Row 3 reports the total of the
positive deviations in real consumption over the period. Row 4 reports
the programme's total real cost. In rows 5 and 6 we apply a 4% discount
rate to the undiscounted streams of real benefits and costs summarised
in rows 3 and 4. The present value of the programme's potential gross
gains is approximately USD 29.3 billion (row 5). The present value of
the programme's cost is less than USD $0.1 billion.
21
The programme's
net benefit is thus in the vicinity of USD $29.2 billion (row 7). Expressed
on a per-household basis, this represents a net benefit, in present value
terms, of USD $2090 (row 8).
22
7. Concluding remarks
In this paper, we use a detailed economy-wide model (SAGE-H) to
investigate the economy-wide effects of a 10% increase in the propor-
tion of sex acts protected from the HIV virus by condom use. We
began by using an epidemiological model (ASSA) to calculate the
change in HIV infections resulting from such a policy. We shocked tran-
sition rates between HIV-negative and Stage 1 within SAGE-H to track
the ASSA model outputs. SAGE-H embodies two salient features of HIV
and the South African labour market that are relevant to calculating
the policy's economy-wide effects: (1) HIV incidence and transmission
rates follow distinct patterns by age, gender, race and occupation; and
(2) the disease progresses through a number of stages.
Over the simulation period the prevention policy leads to a fall in
new HIV infections of approximately 200 thousand. With fewer people
moving into HIV positive categories, the long-run deviation in employ-
ment is 0.23%. This generates long-run positive deviations in real GDP
and real consumption of 0.17% and 0.14% respectively. Expressed in
terms of present value per household, the net benefit of the programme
is in the vicinity of $USD 2000. This benefit calculation captures only the
gains from expansion in employment, net of the costs of the pro-
gramme. It excludes other important sources of potential gain, such as
reduced rates of infection from other STDs, and lower spending on phar-
maceuticals and health care. Another benefit not discussed in this paper
is the decrease in future treatment and care costs. With fewer new HIV
infections, future expenditure on home care and treatment as well as
future government spending on treatment may fall.
The South African government has greatly expanded its condom
distribution programme in recent years (Marumo, 2011), and rates of
new HIV infection have fallen (Shisana et al., 2009; Simbayi, 2009).
This fall in infection rates has been linked to the expansion in condom
distribution (Shisana et al., 2009). Nevertheless, there remains signifi-
cant scope for further expansion in condom distribution (Motsoaledi,
2010). Our economic modelling results can be interpreted in two
ways. By measuring the effects of an incremental (10%) change in
the number of sex acts protected from the HIV virus, our results can
either be used to support current government efforts to reduce HIV
infection rates via condom distribution, should cuts to the programme
be considered; or, to the extent that epidemiological and public health
evidence points to a continuing deficiency in condom distribution, our
results can be used to support expansion in public financing of such
programmes.
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21
Valued in South African Rand, the present value of the cost is approximately Rand
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22
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