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RE: st: dprobit/nocons/mfx question


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: dprobit/nocons/mfx question
Date   Sun, 22 Mar 2009 17:49:31 -0000

Thanks, Austin, that's very clear and really helpful.  I already
half-suspected that I was in the Land of Dubious Practice when I
realized that -mfx- would happily report marginal effects evaluated
where the two exhausive mutually exclusive dummies were both set to zero
(!).  Now I see why.  Time to head for civilization.

Cheers,
Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Austin Nichols
> Sent: 21 March 2009 22:00
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: dprobit/nocons/mfx question
> 
> Mark (Fellow of the Royal Society of Edinburgh! congrats!)--
> 
> I don't recommend using -dprobit- or -mfx- for this kind of problem.
> Their answers to any substantive question will often be very wrong in
> this kind of setting.  In fact, I think both -dprobit- and -mfx-
> should exit with an error immediately if specified with (or after) the
> -nocons- option, as that usually indicates someone is including a set
> of exhaustive mutually exclusive dummies, for which marginal effects
> cannot be sensibly calculated using the -mfx- approach (the -force-
> option could still force the command to continue even after an error
> message is issued).  Let's adopt the -mfx- language of "marginal
> effects" for dummies, as distasteful as it is to mix derivatives and
> discrete differences under the same moniker.
> 
> In general, the marginal effects of the two exhaustive mutually
> exclusive dummies in your example should be the negative of each
> other.  Note that the predicted probability of y given f==1 is .2273,
> the predicted probability of y given f==0 is .5769, regardless of
> which probit command you use, or using the column proportions from the
> -tabulate- call below.  In this case, we would call the marginal
> effect of f a reduction of 0.3497 in the predicted probability of y
> when f==1, relative to the case where f==0.  Likewise, we would call
> the marginal effect of d an increase of  0.3497 in the predicted
> probability of y, relative to the case where d==0 (f==1).   Note that
> -mfx- gets the right answer in this case after a probit with only one
> dummy, but fails to perform well with -nocons-.  -mfx- will usually be
> further from the right answer with more covariates included (because
> predictions will be made at the mean of the covariates rather than at
> each sample value; see also
> http://gelbach.eller.arizona.edu/~gelbach/ado/margfx.pdf), but that is
> a difference of method (not an outright mistake).
> 
> Another view of marginal effects might be to compare the case where f
> is known to be 1 to the case where its value is unknown, so we take
> the predicted probability over the whole sample, and compute the
> marginal effect of f as .22727-.47297 = -.2457 and the marginal effect
> of d as .57692-.47297 = .1040 (the difference of these two effects
> gives the same answer as above).  Even if this view is appealing, note
> that -mfx- after -probit y f d, nocons- does not return this
> answer--it adopts the view that the marginal effect is
> normal(_b[f]+.7*_b[d])-normal(.7*_b[d]) which does not make a lot of
> sense--the question for that answer is: "what would be the effect on
> the predicted probability of making a domestic car foreign,
> conditional on it being 70% domestic when it is domestic, and 70%
> domestic when it is foreign?" (a silly question IMHO).
> 
> I think -margeff- (see also
> http://www.stata-journal.com/sjpdf.html?articlenum=st0086) also
> reports the wrong answers with exhaustive mutually exclusive dummies
> and the -nocons- option, but at least you can extract the right answer
> with a modicum of algebra:
> 
> cap net inst margeff, from(http://web.uni-corvinus.hu/bartus/stata)
> sysuse auto, clear
> ren foreign f
> gen d=1-f
> gen y=(mpg<20)
> ta y f, col
> probit y f d, nocons nolog
> mfx
> mat mfx=e(Xmfx_dydx)
> loc mfx=mfx[1,1]-mfx[1,2]
> margeff, dummies(f d) replace
> mat b=e(b)
> loc mar=b[1,1]-b[1,2]
> probit y f, nolog
> mfx
> margeff, dummies(f d)
> di "Above -mfx- said " `mfx' ", -margeff- said " `mar'
> qui {
> replace f=1
> predict double p1
> replace f=0
> predict double p0
> su p0, meanonly
> loc p0=r(mean)
> su p1, meanonly
> loc p1=r(mean)
> }
> di "Marginal effect of f is " `p1'-`p0'
> 
> On Thu, Mar 19, 2009 at 3:21 PM, Schaffer, Mark E 
> <M.E.Schaffer@hw.ac.uk> wrote:
> > Hi folks.
> >
> > Does anyone know why -dprobit- doesn't allow -nocons-?
> >
> > What makes this a curious limitation is that -mfx- 
> following -probit-
> > has no problem with -nocons-.
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