### Thursday, March 16, 2006

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

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. > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ >

* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

Tag: statalist