Burtless and Hausman(1978) consider the labour supply response of an individual facing a non-linear budget tax schedule. They specify the labour supply function and derive the indirect utility function. For the convex budget set case,
they search the optimal level of labour supply in the following procedure (two segment example):
1. In segment 1 , calculate the optimal amount of labour supply. If it can not be achieved in the first segment . Move to the 2nd segment.
2. Repeat step 1 for segment 2.
3. If optimal level of labour supply in segment 2 also can not be obtained, the optimal point is the kink point.
This procedure can be extended to multiple segments case and non-convex budget case.
To allow observationally equivalent individuals to choose different amount of hours, they allow additive stochastic error terms and random preference parameters. The estimation method is maximum likelihood. The computation burden should not be too much a problem because it only requires one dimensional numerical integration.
Model for health care demand :
The demand function is . The stochastic specifications are :
1. ), where x is a vector of individual characteristics, is an error term.
2. $latex\beta$ is randomly distributed in the population and has a mean of and variance of .
This model seems to be overly simplistic both conceptually and computationally. But it would be a first step towards structural approach. Plus, the data does not allow within year dynamics. So carry out this procedure first. And review the structural estimation of health care on April 25, 2014. Make a comparison between the literature and this simple model here.
Drawbacks :
1. Why do you specify the health demand function like that. Can you derive it from utility maximizing behaviour?
2. How does burtless and hausman rationalize their choice ? why wage and income enter the cobb-douglas function and other controls stays in the constant term .
3. How do you address the welfare question, optimal plan question from this model.