st: Instrument Variable Hausman test with p-weights

[Mo Patel <madhatter101@gmail.com>]

Hi there,

my name is Muhammed Patel and i'm currently working with STATA for my
masters dissertation. I'm testing the relationship between income and
health, which is expected to be endogenous, from the literature. I'm
running a series of regressions on various health outcomes, using the
cmp command, and comparing 'ordinary' regressions to instrument
variable regressions, the latter of which account for the endogeneity
of income. The data that i am using has associated p-weights, for
population-level inferences. Post-estimation, i need to test whether
the IV specification is superior to OLS, in terms of consistency,
which is usually achieved by running the Hausman test.

However, when i run the Hausman test, i get an error message stating
that the Hausman test cannot be run with p-weights. I've been advised
to run the Hausman tests purely on the sample data, without applying
the p-weights, and infer the credibility of OLS vs instrument-variable
model at the population-level from this. Is there anyway of testing
which model is superior at the population level, using the p-weights
and the Hausman test? I feel that inferring the superiority of a model
from just the sample data is a long shot.

Thanks & regards,
Muhammed Patel
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