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Re: st: Hausman test implementation - what's on Base Ref. Manual V4,

From   [email protected] (Vince Wiggins, StataCorp)
To   [email protected]
Subject   Re: st: Hausman test implementation - what's on Base Ref. Manual V4,
Date   Wed, 18 Feb 2004 14:45:59 -0600

Michael Creel <[email protected]> asks how the covariance matrix is formed
in the -hausman- command,

> I'm not a Stata user, but a reviewer of a research paper of mine has
> referred me to the Stata Base Reference Manual, Vol. 4, pages
> 126-147. Not being a user, I don't have a copy of that around, and
> our library doesn't either. I'm interested to know how the Hausman
> test is implemented in Stata, Version 8.  Specifically, how is the
> variance of the difference of parameters calculated?  Is it simply
> the difference of the two separate estimated covariances, or
> something more complicated?

The -hausman- command implements the test as proposed by Hausman (1978,
Econometrica), meaning that the variance-covariance matrix (VCE) for the test
is just the difference of the VCEs of the consistent estimator and the fully
efficient estimator.

For a test of two specific estimators, there are generally a number of
augmented regression tests that are asymptotically equivalent to the Hausman
test; see for example Davidson and MacKinnon, Econometric Theory and Methods,
2004 for examples using instrumental variables regression; or Baltagi, 2001,
Econometric Analysis of Panel Data, for examples using panel data.  These
augmented regression tests often have better behavior in finite samples, in
that they never produce tests that cannot be computed due to
non-positive-definite matrices, but not necessarily better properties.

If both of the estimators produce observation-level scores, the -suest-
command can be used to perform a test similar to the the Hausman test, but one
that does not require either estimator to be fully efficient.  In particular,
-suest- (seemingly unrelated estimation) uses the scores to form a full VCE of
both sets of estimates.  Because this VCE is formed using the sandwich
estimator (linearization/Huber/white estimator), it is robust to many
distributional assumptions and is amenable to clustering.  To find out more,
see [R] suest or Weesie, 1999, Stata Technical Bulletin, STB-52.

-- Vince
   [email protected]

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