st: Test for significance of the difference between knee locations?

[Jordan Silberman <silberman.stata@gmail.com>]

Hi Stata folks,

I'm searching for a method I can run in Stata that will allow me to
test whether the location of the knee for one quadratic model
significantly differs from that of another quadratic model.

I have 2 quadratic models, each modeling a different category of
healthcare costs as a function of age. Let's say, for illustrative
purposes, that the knee of the first quadratic model occurs at age 45,
and the knee for the second model occurs at age 55.

Can anybody suggest a method for testing whether the former "knee age"
differs significantly from the latter "knee age?" The idea is to test
the hypothesis that there is a difference across the 2 models in the
age at which the costs growth rate begins to increase.

Any suggestions would be greatly appreciated.

Thanks,
Jordan
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