Re: [Gretl-users] Question regarding the HIP function
On Wed, 19 Oct 2016, Juehui Shi wrote:
Thanks, Prof. Cottrell.
Professors, I have one additional question.
Although the coefficient estimates of HIP match those of Stata IV Probit
exactly, I have found that the endogeneity test (Wald) result is a little
bit different. For example, the HIP give me Wald (t = 4.06864, p = 0.0437),
but the Stata gives me Wald (t = 3.68, p = 0.0551). My sample size N =
2204. Cragg-Donald shows 107.096 and both AR and Wald tests reject the null
of weak instruments.
As shown, this is a delicate situation. My question is that should I reject
or not to reject the null of exogeneity in this case? and What might
attribute to the difference in the test? Thanks.
Stata and HIP compute the endogeneity test in a slightly different way,
that is equivalent asymptotically but will give different results in
finite samples.
What I would do if I were you is keep in mind what a test statistic
ultimately is: it's a number that should be "small" in "most"
cases if
your hypothesis was true. The p-value is just a rough indicator of how
"small" your number is. In your case, your number is right on the
threshold that we conventionally use to make a decision and even small
modifications in irrelevant details can push your test either side of the
boundary. This means that any decision you make should be considered as
tentative and provisional.
However, the hypothesis is in this case that your regressor is exogenous.
Fortunately, the consequence of making the wrong decision are rather
benign, because your IV estimates would be consistent anyway (assuming no
other problems, of course). Using an IV estimator when the null is true
only implies that your procedure could be a little inefficient compared to
ordinary, non-IV probit; but OTOH, why care? In the end, you're just
trading some (possible) inefficiency for the sake of robustness.
HTH,
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------