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Re: st: Asymptotic covariance matrix for a structural probit equation in a selection model


From   "Robert Duval" <rduval@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Asymptotic covariance matrix for a structural probit equation in a selection model
Date   Thu, 16 Mar 2006 13:23:33 -0500

So far as I know you need to make the matrix multiplications
"manually". But this is actually simple to do once you define the
appropriate gradients.

Also look at the user-written packange movestay which should solve
half of your problem (part I), most likely with the correct s.e.'s

robert

On 3/16/06, Goran Skosples <skosples@uiuc.edu> wrote:
> dear all,
>
> i am running a selection model with endogenous switching and limited
> dependent variables described in the maddala book (1983) explained on pages
> 236-238. this is also the type of a model that is equivalent to lee's union
> wages model (1978).
>
> to summarize, i have two regime functions
> (1) y1 = B1'X + u1
> (2) y2 = B2'X + u2
>
> and a criterion function
> (3)  C = A'B + d(y1-y2) + u
>
> so, the procedure is to estimate the reduced form of (3) and to get the
> selectivity terms (inverse mills ratios).
>
> (I) then, use the estimated selectivity ratios to predict y1^ and y2^.
> (II) finally, i have to plug the estimated y1^ and y2^ (second-stage) into
> the stuctural probit equation (3) to get the coefficient d.
>
> firstly, to my understanding, procedure (I) does not provide the correct
> standard errors because of the fact that selectivity terms (inverse mills
> ratios) are estimated. in this case, standard errors are underestimated.
> as far as i understand the problem, LIMDEP takes care of this problem and
> provides consistent standard errors. my first question is whether there is a
> procedure already developed in stata that takes care of this? or, does one
> have to manually adjust the standard errors by constructing the correct
> covariance matrix?
>
> secondly, since y1 and y2 are estimated in the first stage, when i use them
> in the second stage (II) to estimate the structural probit equation, i also
> run into a problem of incorrect standard errors. maddala mentions that
> standard errors are also underestimated in the second stage because y1^ and
> y2^ are estimated in the first step. he mentions lee's (1978) example how
> his standard errors are underestimated (p. 238 of maddala) and points to the
> appendix (p. 255) where the derivation of the correct covariance matrix is
> shown. so, my question is again, whether there is a command in stata that i
> am overlooking or does one have to construct the correct covariance matrix
> by hand?  to my understanding, LIMDEP also does not take care of this
> automatically.
>
>
> it might be that case that i just cannot find already existing solution to
> this problem and i'd appreciate if someone could point me in the right
> direction.
>
> sincerely,
>
> goran.
>
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