What is the added value of using a 2-part model over an OLS model on a subsample when estimating health care expenditures? I want to estimate the impact of having health insurance on health care expenditures and have a hunch that it is best to use a two-part model to first estimate the probability of using any health care and then estimating the amount spent by those who used health care. However, I am not clear on the advantage of using a two-part model over just running ordinary least squares regression on the subsample of people who used any health care. Any insight into the advantages of the 2-part model over OLS on the subsample of users, and the differences in these two approaches would be much appreciated!
 A: Sarah, 
I was a little puzzled to think about whether there is a selection bias here. It seems that health insurance is bundled with other job benefits, and there is no self selection. However, those people who do not have health insurance are very different from those who do.
If there is a selection bias, OLS is biased and inconsistent. Selection bias is interpreted as a problem of omitted variables which can be corrected with the inverse mills ratio in your OLS. 
The Heckman's procedure gets unbiased OLS parameter estimates. Testing their significance requires additional work, since the estimates of the covariance matrix of the parameter estimates are inconsistent - use bootstrapping to derive the appropriate asymptotic standard errors and test statistics.
See http://en.wikipedia.org/wiki/Heckman_correction.
M
A: I think you are assuming something like this. People use health care if they are sick. If they use health care, than they spend more money on it. But, sick people will see more value on insurance and will be more likey to be insured. So, you will find out that insured people spends more money on health care, but this may be so due to selection bias.
And you seem to think that, if you use only the subsample of people who used health care, than you don't have this problem. However, think of this example. Assume you have a woman who wants to be pregnant and a man who doesn't want to have a child, both on their 30's. The woman than gets insured, but the man not. Both get sick and use health care, so they both are in your subsample. However, they have different probabilities of being insured and they will spend different amount of money if she is pregnant. Thus selection bias will occur anyway.
So, what I'm saying is that restricting your subsample will not solve the selection bias problem. You still have to account for the different probabilities of people getting insurance.
A: Sara, to understand the difference in the two models is to ask you what question you are trying to find an answer to:


*

*What is the health care expenditure of those who have it? 

*What is the impact on having health insurance on health care expenditure? 


To answer the first question, you have a subsample (as you refer to it) of those who have health insurance and there is observed health care expenditures as well as other explanatory variables (age, occupation, etc.). In this case, you are trying to explain variation in health care expenditures of people who choose to have health insurance. There is no way two answer your fist question.
The second question is more general. You need to have two groups of people with and without insurance. Also, if you just use OLS here on the subsample of insured people, you will get biased and inconsistent OLS parameter estimates due to self-selection bias, and you would not be able to correctly estimate the impact of having the insurance on the expenditure. So, Heckman's!
I hope that helps.
M 
