Coefficient varys over the distribution of the dependent variable

[Soeren Dallmeyer]

Hi,

I am estimating a two-part model were my dependent variable is healthcare expenditure and my independent variable of interest is sport participation. My model also includes a bunch of control variables.

My results indicate that sport participation increases the probability of healthcare expenditure occurring at all (first part) and has a negative effect on the size of healthcare expenditure (second part).

Since theory suggests that sport participation is mainly responsible for smaller healthcare expenditure, I want to find out if the effect on the size of healthcare expenditure differs across the different quartiles of healthcare expenditure.
Do you have any suggestions how to test that? Quantile regression could be problematic as 35% of my observations have zero healthcare expenditure.

[Carlo Lazzaro]

Soeren:
welcome to the list.
Chapter 16 of http://www.stata.com/bookstore/microeconometrics-stata/ covers two-step models (I was not able to see any reference for quantile regression, though).

[Phil Bromiley]

With 35% of your observations having zero expenditures, you'll probably need to look at tobit or a similar estimator. There are also zero inflated versions of some standard estimators. The Microeconometrics text Carlo suggested does a good job here.

While it can be modeled, when you say the influence of x on y varies with values of y, you can't do many of the standard interaction models we would normally use (since y appears on both sides of the equation). There are Stata routines that will handle a tobit dv along with endogeneity, but they're not that simple. Do you have some exogenous variable that might be used as the moderator of the effect of x on y? Would a non-linear influence of participation work?