CAPITULO IV. DIAGNÓSTICO DEL ÁREA DE INGENIERÍA
4.11 Resultados de la tercera etapa Seis Sigma
De Walque (2002) provides a two-period mathematical model of rational behaviour related to sexual activity and HIV/AIDS that will be of assistance in testing for the presence and implications of the HIV/AIDS-poverty cycle. An individuals’ utility is determined by their consumption of goods (ct) and the number of sexual partners they have (nt),66 and is separable in consumption and the number of sexual partners:
( ) ( ) ( )
c n u c v nU , = + (3.1)
where u(.) and v(.) are increasing and concave in c and n respectively. Individuals maximise utility across two time periods, period 1 and period 2. The probability of survival from period 1 to period 2 is denoted Q, where 0 ≤ Q ≤ 1. The probability of survival to period 2 is determined in period 1 multiplicatively by the number of sexual partners n1, the proportion of the sexually active population that is infected with HIV γ1, and the proportion of sexual encounters that were not protected (for example by using a condom) (1-π1):
(
(
γ1 1 1−π1))
=Q n
Q (3.2)
66 The model assumes that each individual has the same number of sexual contacts with each of their nt sexual partners.
where Q(.) is a decreasing function. In this model, it is assumed that it is not possible for the individual to know whether he/she is infected or not. Only the overall proportion of the population that is infected is known to the individual,67 i.e. γt is taken as given. Exposure to the HIV virus is zero if the individual abstains from sexual activity (n1 = 0), if nobody in the sexually active population is infected with HIV (γ1 = 0), or if the individual only has protected sexual encounters (π1 = 1). The price of consumption goods is the same across both periods. The price of protection of sexual intercourse68 is denoted as pπ. The price of a sexual partner69 is denoted as pn.
The model has two types of individuals: those with low human capital KL, and those with high human capital KH. The wage w(Ki) is an increasing function of the level of human capital Ki with i∈L,H , and:
(3.3)
( )
KH w(
KLw >
)
This means that the two types of individuals correspond to those with a high income (and high human capital), and those with a low income (and low human capital). Provided consumption goods are normal goods then:
(3.4)
L
H c
c1 > 1
That is, individuals with higher wages (and higher human capital) consume more goods. Since u(.) is concave, then:
( ) ( )
cH u cLu′ 1 < ′ 1 (3.5)
67 This assumption may be reasonable given the long incubation period between when an individual becomes infected with HIV, and when they begin to exhibit symptoms of AIDS.
68 Including the price of condoms, the cost of HIV testing, and the costs of monitoring the partner’s fidelity.
69 In the case of commercial sex, this would be the market price. In the case of non-commercial sex, this may be the shadow price, or determined by the cost of gifts, dowry, etc.
Assuming a perfect annuity market, the wealth of the individual, W, which is carried forward to the second period is:
( )
discount factor. Agents will choose their level of consumption, the number of sexual partners they have, and the proportion of protection of sexual encounters, in order to maximise their utility. The maximisation problem can be described as:( ) ( )
1 1(
1 1(
1) ) ( ) ( ) [
2 2]
subject to the budget constraint:
[ ] ( ) ( ( ) ) [ ( ) ]
and subject to the following additional conditions:
[ ]
θ n1 ≥0;[ ]
ϕ π1 ≥0;[ ]
φ 0≤π1 ≤1 (3.7c)De Walque (2004) also shows that where there is no information about the HIV/AIDS epidemic then Q=Q and:
( )
n u( )
c pnv′ 1 = ′ 1 (3.8)
However, using the more realistic function for the probability of survival, the first order conditions for solving equation (3.7a) include:
[ ]
c1 : u′( )
c1 =λ (3.9)De Walque (2004) shows that, where all sexual encounters are protected (i.e. π1 = 1), then: larger for those with higher incomes, then the left-hand side of equation (3.12) is higher for higher income earners. For the inequality in equation (3.12) to hold there must be a cut-off level of HIV infection,γ1, where the agents would decide to protect all sexual encounters, and:
L
That is, higher income earners would protect all of their sexual encounters at lower levels of HIV infection among the sexually active population. In this simple model, higher income earners have higher wealth and a higher level of utility in the second period, thereby providing greater incentives to avoid decreasing the probability of survival. This can be seen in equation (3.12) where the terms
( ) ( )
[ ]
( )
1 22
c u
n v c u
′
+ and W are larger for higher income earners, meaning that they
would face a higher shadow cost of unprotected sex with many partners. De Walque (2004) also shows an alternative result where higher income earners have fewer sexual partners than lower income earners in period 1. If this model holds, then it agrees with the existence of a poverty-HIV/AIDS cycle in that the poor (lower income earners) are at greater risk of HIV infection.
3.4 Hypothesis
The overall hypothesis that will be tested in this thesis is:
Rural Northeast Thailand exhibits characteristics that support the existence of a poverty-HIV/AIDS cycle.
The testing of this hypothesis will rely on testing specific hypotheses relating to each section of the poverty-HIV/AIDS cycle. Specifically, the following will be tested:
(a) That there is a significant relationship between previous HIV infection and current wealth or poverty, i.e. that HIV infection significantly adversely affects the wealth of individuals (including Type I, Type II, Type III, and Type IV impacts) and places the individuals at a higher risk of poverty;
(b) That there is a significant relationship between wealth or poverty, and HIV/AIDS knowledge, i.e. that the poor are significantly less likely to have accurate information about HIV/AIDS on which to base behavioural decisions;
(c) That there is a significant relationship between previous wealth or poverty, and current HIV infection, i.e. that the poor are significantly more likely to be infected with HIV; and
(d) That there is a significant relationship between previous migration (of the individual or another adult member of their household) and current HIV infection, i.e. that members of migrant households are more likely to be infected with HIV.
Hypothesis (a) demonstrates the relationship from HIV/AIDS to poverty, and will be tested in Chapter 5. Hypotheses (b), (c), and (d) demonstrate the relationship from poverty to HIV infection (through high-risk behaviour), and will be tested in Chapter 6.
Chapter 4
Methods
This chapter contains the conceptual framework and research methods employed in the thesis, including survey data collection, data transformation and descriptive statistics for each of the surveys conducted. Specific methods that were used for data analysis are described in the relevant chapters.