Re: st: 3sls, selection

["joe jacob" <otharain@hotmail.com>]

Hi Chris,

Your comments have been quite useful.  Many thanks for that.

I think dropping IRD(learning from embodied R&D, which is an endogenous 
variable) from export intensity (EXPINT) and export decision equations can 
solve one big problem. (I agree that cost related factors are crucial to 
export (and so are technological). I am using these variables in the export 
intensity equation.)

I still wonder if I could combine the selection and simultaneous estimation 
procedures (The idea is to derive IMR from heckman selection estimation and 
then insert that in the export intensity equation in the simultaneous 
estimation procedure). I describe these as Stata commands below.

(1)Deriving IMR for use in step 2.

.heckman EXPINT drd droy wagerate  skill size size2 forg
twostep select(drd droy wagerate skill  outshare gov forg)
mills(IMR)

(2)Estimating simultaneously equations with dependent variables IRD and 
EXPINT using 3sls

.reg3 (IRD  EXPINT drd droy skill outshare gov forg ) (EXPINT IMR drd droy 
wagerate  skill size size2 forg ) 3sls  inst(drd droy  wagerate   skill  
outshare   size size2 gov forg)

Note that IMR estimated from step 1 is used in step 2 (in the second part 
where EXPINT is the dependent variable). My concern now is, is inserting IMR 
from step 1 in step 2 the right way of addressing selection bias?

An alternative is to discard the question of bias as you hinted and do only 
the simultaneous estimation of step 2 above (without IMR variable).

Thanks in advance,

Joe



> From: Chris Rohlfs <car@uchicago.edu>
> Reply-To: statalist@hsphsun2.harvard.edu
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: 3sls, selection
> Date: Tue, 9 Sep 2003 10:06:23 -0500 (CDT)
>
> joe,
>
> this is a difficult problem.
>
> so heckman wrote the two-step method with the particular example of
> education in mind, where agents have perfect foresight & face a decision
> between a wage offer in the high school labor market versus a wage offer
> in the college labor market.  the primary feature of the model is that
> agents maximize a known function based on variables unobservable to the
> econometrician.  and that the variable they're maximizing (in this case
> wages) is the dependent variable of interest.  in this education example,
> you can use the model to estimate how much an agent's schooling decision
> affects his/her wages.
>
> ok -- so let's say you had a simple model in which firms decide whether or
> not to enter the international sector or remain in the domestic sector
> based entirely on long-term profits.  in that case, i think the heckman
> two-step would apply -- and you could use such a model to determine how
> much the decision to export affects a company's profits.
>
> i think it makes a big difference that you're using REVENUE (as far as i
> can tell, that's what EXPINT is) rather than PROFITS.  i'd think that most
> of the factors that firms consider are cost-related, not revenue-related
> -- most of the variation in REVENUE is going to be driven by scale.  even
> if you had the profits data, though -- my feeling is that the model is
> getting extremely complicated at this point & a simpler model would
> probably do a much better job of explaining the data in a credible way.
>
> i would strongly recommend considering another approach toward modeling
> selection.  you do have a lot of cost-related variables.  you might want
> to consider just assuming that the selection is entirely based on observed
> cost variables (in which case unweighted least squares would still be
> unbiased).
>
> chris
>
> On Tue, 9 Sep 2003, joe jacob wrote:
>
> > Chris and others,
> >
> > I should apologise for not describing the variables in the first mail. 
> Let
> > me explain.
> >
> > I have an establishment level data set for about 8 years (100,000 plus
> > observations)
> >
> > The key equation of interest is
> > IRD=  EXPINT+ drd+ droy+ skill+ outshare+gov+ forg  /*Eqn 1.*/
> >
> > where, IRD captures learning efforts from embodied R&D (derived from
> > sectoral R&D stock of OECD countries and distributed across 
> establishments
> > of a developing country) EXPINT is the export intensity variable.(Other
> > variables are basically control variables.)  Since this variable 
> (EXPINT) is
> > an endogenous variable we have a second equation,
> >
> > EXPINT = IRD+ drd+ droy+ wagerate+  skill+ size+ size2+ forg  /*Eqn 2.*/
> >
> > This calls for using a simultaneous estimation procedure like 3sls.
> >
> > The problem is, since all firms don't export, there is a selection bias,
> > which has to be accounted for using the Heckman procedure.
> >
> > The selection variables for EXPINT are the following.
> >
> > IRD, drd, droy,wagerate, skill,  outshare, gov, forg.
> >
> >
> > What I originally thought (albeit not probably correctly) was to 
> estimate
> > Eqn2 using heckman procedure, calculate the inverse mills ratio (IMR), 
> and
> > then plug this variable in equation 2 and apply 3sls to equation 1 and 
> 2.
> > But when I do heckman I can't account for the endogeneity of the 
> variable
> > IRD.
> >
> > Hope the problem is clear now.
> >
> > Thanks in advance for any help.
> >
> > Joe
> >
> > >From: Chris Rohlfs <car@uchicago.edu>
> > >Reply-To: statalist@hsphsun2.harvard.edu
> > >To: statalist@hsphsun2.harvard.edu
> > >Subject: Re: st: 3sls, selection
> > >Date: Mon, 8 Sep 2003 15:36:58 -0500 (CDT)
> > >
> > >jacob,
> > >
> > >could you please describe the variables you're looking at ?
> > >
> > >chris
> > >
> > >On Mon, 8 Sep 2003, joe jacob wrote:
> > >
> > > > Dear all,
> > > >
> > > > This is my first mail to statalist and this mail is made after days 
> of
> > > > learning from the discussions in the listserver.
> > > >
> > > > I have a two-equation system to estimate.
> > > >
> > > > Eq. (1)  y1 = y2 + x1 + x2 +x3+x4+  u
> > > > Eq. (2)  y2 = y1 + x1 + x2+v,
> > > >
> > > > with the endogenous variables y1 and y2 (both continuous) appearing 
> in
> > >the
> > > > RHS of both equations. Thus a simultaneous equation is of course the
> > >right
> > > > way to proceed.
> > > >
> > > > But variable y1 needs to be corrected for the Selection hazard using 
> the
> > > > Heckman procedure. This is because some observations are zero due to
> > >'self
> > > > selection'. Thus we have a selection equation involving the 
> variables
> > >(y2,
> > > > x1, x2 ,x3,x4,x5).
> > > >
> > > > One approach I could think of is to calculate the IMR from heckman
> > > > estimation of equation 1, plugging it back in the same equation and
> > >running
> > > > a 3sls estimation involving equations 1 and 2. BUT I think that does 
> not
> > > > make much sense because IMR is calculated from two equations (Eqn 1 
> and
> > >the
> > > > selection equation) that has an endogenous explanatory variable 
> (y2).
> > > >
> > > > My question is how could I take care of these two problems. 1. The
> > > > endogeneity (simultaneity) of y1 and y2 , 2.the selection bias
> > >pertaining to
> > > > variable y1.
> > > >
> > > > Thanks in advance for your kind suggestions.
> > > >
> > > > Sincerely,
> > > >
> > > > Itty Jacob
> > > >
> > > > PS: My apologies for any wrong terminology.
> > > >
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