Re: st: dynamic panel with selection and more endogeneous

["Rodrigo A. Alfaro" <raalfaroa@gmail.com>]

Nicola,

(1) Hausman-Taylor model, Arellano-Bond and other estimators in the same 
line are constructed by the assumption of y(i,t) = a(i) + x(i,t)'b + e(i,t), 
where x(i,t) can include time variant and time invariant variables and a(i) 
is the unobservable. The definition of unobservable is more general than FE 
or RE and this point is based on Wooldridge (2002) textbook.

(2) Linear Panel Data autoregressive with unobservable can be estimated by 
FE with slightly bias on the coefficient if T is large. I just found a paper 
from Bum and Carree (2005) in the Journal of Business & Economic Statistic 
that proposes another bias correction!! They said that is more accurate than 
Hahn and Kuersteiner bias correction, even for small T. The Monte Carlo 
experiment includes T=3!!

(3) My suggestion on simulation is the following: given that there is not 
such a model in the literature close to your problem, it would be a good 
idea to simulate data under some specification of the parameters, then you 
try different estimators and see the performance of these estimators. 
Suppose that extra endogenous are z3 and z4. Then

set obs 100
gen a = invnorm(uniform())
gen id = _n
expand 5
bysort id: gen t = _n
drawnorm exog1 exog2 exog3 exog4 v1 v2 v3 v4
forv i=1/4 {
gen z`i' = (exog1 + exog2  +  exog3 + exog4)/4 + v`i'
}
tsset id t
gen y = a/0.2
gen y1 = y
gen y2 = y
replace y1 = a + 0.8*L.y1 + z3 + z4 if t>1
replace y2 = a + 0.8*L.y + z1 + z2 z3 + z4 if t>1
replace y = y1
replace y = y2 if z1>0
drop y1 y2

Fixing the code for your case, with z1 and z2 proportions and less time 
variability for z3 and z4, you have a simulated dataset. Introducing this 
into a loop you can create datasets that after you can use to evaluate the 
performance of different estimators.

R.


----- Original Message ----- 
From: <nicola.baldini2@unibo.it>
To: <statalist@hsphsun2.harvard.edu>
Cc: <raalfaroa@gmail.com>
Sent: Wednesday, March 21, 2007 7:16 AM
Subject: Re: st: dynamic panel with selection and more endogeneous



> My knowledge of statistics has big gaps. What does "simulate the model (as 
> a reduced model) and see which estimator is better" mean?
> Anyway, thanks Rodrigo for your suggestion: I never thought 
> about -xthtaylor-
> It sounds like enjoying the benefits of the FE without actually imposing 
> them.
> I knew from the manual of -xtabond2- that if T is large, dynamic panel 
> bias can be worked around with FE. First, my T=15 and I was not sure that 
> it is large enough, given that according to the manual T=9 seems not (and, 
> playing on web dataset abdata, I have found that FE actually exhacerbate 
> the problem), but I will have a look at your suggested papers. More 
> important, I thought the problem to be more complicated, given that past y 
> influences not only present y, but also the likelihood that the event 
> "change from regime 1 (z1=0) to 2 (z1>0)" happens. Can FE work this 
> additional complication?
>
> P.S. My exogenous variables are only four. I am not taking care of the 
> possible unobservable in the model; rather, I needed something to use as 
> instruments.
>
> At 02.33 21/03/2007 -0400, "Rodrigo A. Alfaro" wrote:
>
> > Nicola,
> >
> > It is crucial to put y(t-1) or t (something like that) in your RHS. For a
> > large T, you can use -xtreg, fe-, it is known that the bias in the lagged
> > dependent variable decreases with T. Two papers in Econometrica analyze
> > this: Hahn and Kuersteiner (2002) and Alvarez and Arellano (2003). If you
> > are interested in the z's coefficients maybe you can take a look of
> > Hausman-Taylor estimator -help xthtaylor-, again you could modify to allow
> > more instruments in the last step. For several exogenous variables, maybe
> > you are taking care of the possible unobservable in the model then pooled
> > least-square is an option. Anyway, if there is a few number of endogenous
> > variables, I suggest you to simulate the model (as a reduced model) and 
> > see
> > which estimator is better.
> >
> > R.
> >
> > - ----- Original Message ----- 
> > > I have the following PANEL model:
> > > Regime 1 (observed if z1 = 0): y = y(t-1) + exog
> > > Regime 2 (observed if z1 > 0): y = y(t-1) + exog + z1 + z2 + endog
> > > At t=0, all observations are in regime 1; changing from 1 to 2 depends 
> > > on
> > > y(t-1) and exog; changing from 2 to 1 not possible.
> > > y is a count variable, y(t-1) is past y (I am uncertain about using 
> > > lagged
> > > y or a depreciated stock up to t-1; in regime 2, alternatively, I can 
> > > use
> > > a "years-since regime 2" time counter), z1 and z2 are proportions
> > > (endogenous; my key independent variables), endog are additional
> > > endogenous variables, exog are exogenous. To put it differently, in 
> > > regime
> > > 1 all endogenous are 0, while in regime 2 z1 is not 0 (and remaining
> > > endogenous may be 0 or not).
> > > All endogenous variables are almost time-invariant (e.g.
> > > 0/0/0/0/0/0/0/0/50/50/50/50/50/50/50; 0/0/0/0/0/0/0/0/0/0/0/0/0/0/0;
> > > 0/0/0/0/0/0/0/0/0/0/0/0/25/25/50; etc...).
> > > I have thought about xtivreg y (z1 z2 endog y(t-1) = exog).
> > > Do you have any suggestion or better idea?
*
*   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/