CHAPTER 3 Conceptual Framework
3. Modeling stated preference
In this section, I first develop a probit model to examine the factors that affect decision-making and subsequently model the demand in two different ways, a
traditional count model approach and a random effects approach. This is followed by a mechanism to estimate the sharing weights that husband and wife welfare estimates should be given to compute joint household welfare estimates.
A. Patterns in decision-making: The All or Nothing Approach
One of the simple patterns in decision-making is the “all or nothing” approach in which the respondent either buys for all members or for no one. The choice can be modeled on the basis of Random Utility Theory (McFadden 1974, and Ben-Akiva and Lerman 1985). Each person derives a utility U by purchasing a certain number of vaccines based on his own income y, and individual attributes X, Price of the vaccine P, and member characteristics Z (which include his age, education, relationship, income, and other features). Thus, overall utility that a person in household i derives by purchasing a vaccine for all household members is
Ui = Vi +εi …(3.9)
The indirect utility can be modeled as
Vi = V(yi – P, Xi ; β) …(3.10)
The structural probit model can be written as: yi* = β Xi + εi
yi = 1 if yi* > 0, and 0 otherwise (Greene, 2000, pp.: 837)
B. A count model approach
In the conventional approach, adopted by Cropper et al (2004), to assess household demand, the optimal value for equation 3.4 is the sum of the vaccines purchased for each member within the household. Thus demand for entire household,
qk* =
∑
mmk
q …(3.12)
Where qmk = 1 if member m in household k receives a vaccine; 0 = Otherwise.
This model can be estimated using a variant of the Poisson Count Model, in which
= = = − where i ! ] [ n n e n q P i ni i i i iλ λ 0, 1, 2, 3,….. …(3.13) Where λi =eXiβ,= E[ni|xi] = expected number of events per period, β = vector
of parameters, Xi= vector of individual and household independent variables.
The household WTP for a vaccine is the area underlying the demand curve.
WTPi = e dp p p p Xi p
∫
2 − 1 ) ( β β =e p e dp p p Xi∫
− p 2 1 β β =[ ]
. 2 1 . ). 1 .( p pp p Xi e p e β β β − − …(3.14)Where β is the vector of coefficients except the price coefficient.
To determine the entire consumers’ surplus, integrate from price = 0 to infinity. Consumer’s surplus = − ).
[ ]
− ..∞0 1 .( p i p p X e e β β β = ).[ ]
1 0 1 .(− − p Xi e β β = p Xi e β β − …(3.15)Limitations of the count modeling approach
The count models are conceptually sound and are well established in literature. By the virtue of the exponent involved, they predict a positive WTP, and are able to predict a smooth demand curve. However, there are certain shortcomings associated with these models when they are used to analyze household demand for vaccines.
1. Household demand can be viewed through two different lenses, a continuous choice where the respondent chooses the number of vaccines that he may purchase, and a discrete choice, which indicates the person for whom the vaccine is being purchased. The count models do not capture all the information that is collected in a stated preference survey. Specifically it does not capture the heterogeneity reflected by the term εik in equations 3.5 and 3.6. For example, a person buying vaccines for
two daughters is the same as a person buying two vaccines for sons. As a result, we are unable to determine household willingness-to-pay for different household members, or the fact that preferences may be ordered (for example, eldest son more preferable than all other children). One way to resolve this problem is to run a series of count model with the count of a certain category of household members (say children) as the dependent variables. However, this approach does not account for correlation between demand for different age groups within each household. 2. The poisson models predict the expected number of events per period
(Greene, 2000). A referendum CV data analyzed by the traditional model using probit (or similar techniques) lets us estimate the probability that the specific person
aggregation where multiple households are interviewed using linear pooling techniques (discussed later).
C. A random effects approach
The basic assumption in a random effects probit approach is that the decision to buy vaccines for members of the household is a combination of correlated
decisions wherein the respondent considers each individual household member separately, and decides whether or not he will purchase a vaccine for that member. Thus the decision of a wife in a four-person household to purchase a certain number of vaccines is a result of four correlated yes-no decisions where she considers whether each individual within the household should receive a vaccine. The advantage of this design is that among other things, individual characteristics of specific household members could also be factored in the analyses.
The Random Utility Theory (McFadden 1974, and Ben-Akiva and Lerman 1985) can be used to model an individual’s choice of family members who receive a vaccine. Each person derives a utility U by purchasing a vaccine for member j based on his own income y, and individual attributes X, Price of the vaccine P, and member characteristics Z (which include his age, education, relationship, income, and other features).
Thus, overall utility that a person in household i derives by purchasing a vaccine for a member of household k is
Uik = Vik +εik …(3.15)
The indirect utility can be modeled as
Vik = V(yi – P, Xik ; β) …(3.16)
The structural probit model can be written as: yik* = β Xik +υj + εik
yik = 1 if yik* > 0, and 0 otherwise (Greene, 2000, pp.: 837)
…(3.17) (Here Xik includes all parameters including price and income)
yik = β. Xik + uj + eik …(3.18)
D. Aggregating preferences and sharing weights
If multiple household members are interviewed, differences in preferences could make preference aggregation a challenge. Some preference aggregation mechanism such as behavioral aggregation is necessary.
If we have aggregated household responses for household WTP for a vaccine, these along with separate responses of individual members can help us estimate the sharing weights among household members.
The algorithm to determine sharing weights for preferences of different household members can be developed on the basis of the model proposed by
Adamovicz et al (2005) (discussed in equation 2.3), in which the household utility is a weighted average sum of individual utilities.
Although the count model does not provide us with preference estimates, it does yield separate and aggregate welfare estimates in terms of WTP for a vaccine.
Assuming that the joint WTP is a function of separate husband and wife WTP as follows:
WTPJoint = ω.(WTPHusband,Separate)+ (1- ω ).(WTPWife,Separate) …(3.19)
This equation can be estimated by OLS regression (1) without a constant and (2) with a constraint that the sum of weights (i.e., sum of beta coefficients) to be equal to unity.