# st: RE: RE : rho and wald test in heckman

 From "Julian Fennema" To Subject st: RE: RE : rho and wald test in heckman Date Fri, 26 Nov 2004 11:35:07 -0000

Dear Katarina,

The problem with the Wald test in ML estimation is that the negative Hessian
is used to compute the variance-covariance matrix. If the parameter
estimates are close to the population parameters this is fine, but the
smaller the sample size the less likely this is to be the case. Therefore,
if possible, it is best to try a LR test (see, for example, "ML estimation
with Stata", p. 5-6).

The LR test of no selection process in a Heckman can be obtained if you
estimate a Tobit on the structural equation, but this is not only one
restriction of rho=0 as is commonly asserted. It is actually more
complicated; the degrees of freedom is equal to the number of regressors in
the structural or threshold equations (the largest) plus one (rho). As a
statement this is confusing and I would suggest having a read of Johnston
and DiNardo, "Econometric Methods", 1997, p. 451 to decipher what I have
attempted to say.

Hope this helps,

Julian

_____

From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Naceur Khraief
Sent: 25 November 2004 20:24
To: statalist@hsphsun2.harvard.edu
Subject: st: RE : rho and wald test in heckman

There are a couple of things to notice. First, stata gave you estimates for
two equations( The results of the selection equation are in the bottom and
the results for the interest equation are on the top). Second, rho is the
correlation between the errors in the two equations. stata gives you an
estimate for rho, and tests that estimate. in your cas you can reject the
null that rho=0, indeed you should be using a simple selection model on your
data.

-------- Message d'origine--------
De: Katarina Lynch [mailto:ferkel999@hotmail.com]
Date: jeu. 2004-11-25 13:09
À: statalist@hsphsun2.harvard.edu
Cc:
Objet: st: rho and wald test in heckman

In  Heckman ML estimation how do I decide if there is a selection bias? On
the one hand, rho(the correlation between two equations) is non-zero, even
close to .95. On on the other hand, the Wald test at the bottom of the table
cannot reject the null hypothesis of independent equations. I have found a
power point presentation about heckman in STATA which sais that rho not
equal to zero is enough to infer that there is selection bias. If instead of
ML I do twostep, the IMR is insignificant, although there is nonzero
correlation between the outcome and selection equations. I am confused.
Would anyone spare a time to answer this simple question?

Thank you!

Katharina

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