st: test the equality of coefficients

[Kit Baum <baum@bc.edu>]

David said

I have a problem with how to test the equality of coefficients of three
regressions. I have a sample of 600,000 enrollees in one of our sick
funds in year 2004.
I have the cost of each individual including those who died during the
year. Some of the decedents died in January some in April and some in
December. I calculated the cost of the last year of life in two ways.
First, I just multiplied the cost by the inverse of the proportion of
year the individual lived, e.g. if some one died in February I
multiplied his cost by 12/2 (Since the last months of life are much
expensive than the first months of the year this method overestimates
the cost) and I called it c1.
I also multiplied the cost by a different weight that takes care of this
problem and called it c2.
The original cost is called c (the cost as is)
I regressed:
C=a + b1*age + b2*sex + b3*survive
C1=a1 + b11*age + b12*sex + b13*survive
C2=a2 + b21*age + b22*sex + b23*survive. (Survive is a dummy variable)
The only difference between the regressions is how I have calculated the
cost. The right side of the equation is the same.
I want to test the coefficient equalities: b3=b13=b23

How can I do it? Could I use suest? If so, do I have to adjust to the
fact I use the same sample?



Unless C, C1, C2 differ only by a linear transformation (which I'm  
sure they do not) how could you expect to have the same coefficients  
for each equation? Those coeffs. are estimates of \partial cost /  
\partial survive. As survive is a dummy, you have two condtional  
means for cost: one for non-survivors, one for survivors. The  
difference between those means could be constant iff the differences  
in cost between survivors and decedents were the same, no matter how  
you measured cost. The whole point of what you are saying, though, is  
that measuring cost differently will make a difference.

I don't think this is an econometric issue; I think it is a  
conceptual issue. Why would the difference between survivors' and  
decedents' costs be a _fixed dollar amount_, conditioned on age and  
sex, if you choose some other metric for measuring costs that is not  
a linear transformation of "original cost"?



Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


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