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Re: st: dynamic panel with selection and more endogeneous


From   "Rodrigo A. Alfaro" <raalfaroa@gmail.com>
To   <statalist@hsphsun2.harvard.edu>, <nicola.baldini2@unibo.it>
Subject   Re: st: dynamic panel with selection and more endogeneous
Date   Fri, 23 Mar 2007 01:24:21 -0400

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?

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