Dean,
You may want to read about correlated random effects models. This is a
more econometrically sounds approach that accomplishes what you are
trying to do. Below are a number of citations that reference these
types of models. Some of these can be estimated in stata using SUREG
and constraints. Others require a minimum distance approach or the
application of non-linear constraints, neither of which is
straightforward to do in stata to my knowledge.
Cheers,
Steve
Mundlak, Yair (1978), "On the Pooling of Time Series and Cross-section
Data", Econometrica, 46, 69-85.
Chamberlain, Gary (1984), "Panel Data", Handbook of Econometrics,
Chapter 22 in Vol. 2, 1247-1318, Elsevier Science B.V.
Ashenfelter, Orley and David J. Zimmerman (1997), "Estimates of the
Return to Schooling From Sibling Data: Fathers, Sons and Brothers", The
Review of Economics and Statistics, Vol. 79(1), February, .
Vella, Frank and M. Verbeek (1998), "Whose Wages Do Unions Raise? A
Dynamic Model of Unionism and Wage Rate Determination for Young Men",
Journal of Applied Econometrics, 13, 163-183.
******************************
Rodrigo,
Thank you for your reply to my post. Perhaps my subject line should have
been more appropriately titled "Constrained" random effect estimates.
I am looking for a reasonably practical and straightforward way of
correcting to some degree for the possible covariance between unobserved
and
observed explanatory variables in the random effects variant of my large
gravity trade model, without having to apply a Hausman-Taylor or other
instrumental variables approach. Thus, I am experimenting with
constraining
the random effects estimates to be equal to the fixed effects estimates
for
time-variant variables (through corresponding offsets to the dependent
variable), leaving the time-invariant explanatory variables to be the
sole
remaining source of possible covariance between unobserved and observed
explanatory variables in the model. Unfortunately, this approach does
not
allow further appeal to the Hausman specification test. However, I find
on
applying the approach to the empirical example in Table 7.4, p.129, of
Baltagi's 3rd edition textbook (Econometric analysis of panel data) that
the
resulting coefficient estimates for the time-invariant variables are
very
close to those reported by Baltagi using the Hausman-Taylor approach.
Hardly
a formal monte carlo test of my approach, but interesting results
nonetheless.
Dean DeRosa
Date: Thu, 25 May 2006 11:20:23 -0400
From: "Rodrigo A. Alfaro" <ralfaro76@hotmail.com>
Subject: st: Re: "Crude" Random Effects Estimates
Dear Dean
HT is computed in 3 steps: (1) FE for time-variant, (2) IV for
time-invariant and (3) IV for both (where the variables have the GLS
transformation to control for the random effect). As it is discussed in
the
paper (Econometrica, vol 49 n6 1981, 1377-1398) the last step is to
compute
efficient estimators. In (1) you have consistent estimators for
time-variant
variables, with these you compute a proxy of the unobservable and run a
regression of this proxy against time-invariant variables using
instruments
(2). These estimators (for time-invariant variables) are also
consistent. A
technical paper of Hahn and Meinecke (Econometric Theory 21, 2005.
455-469)
shows that we still have consistency for non-linear models (a
generalization
of HT). In conclusion, you can force the FE coefficient for the time
variant
variables... but you will need to compute a IV regression for the
time-invariant (in the second step as you suggest) dealing with the
decision
of instruments. Note that in the case of (manually) two-step regression
you
can include other instruments that are not in the model.
For practical purposes, I suggest you to run a FE model and compare the
coefficients of the time-variant variables with HT. If they are
different
you can gain something doing the 2-step procedure. In addition, find
other
exogenous variables (time-invariant) that can be used in the second
step.
Once, you estimate both set of parameters you have to compute the
standard
error for 2-steps. Maybe you could be interested in robust-estimation of
that. Wooldridge textbook offers the formulas to compute it.
Rodrigo.
-----Original Message-----
From: Dean DeRosa [mailto:dderosa@adr-i.com]
Sent: Thursday, May 25, 2006 10:45 AM
To: 'statalist@hsphsun2.harvard.edu'
Subject: "Crude" Random Effects Estimates
I am estimating the parameters of a gravity trade model, using a large
panel
data set of international trade flows and explanatory variables. A
number of
the explanatory variables are time-invariant, so I am mainly interested
in
obtaining random effects (within cum between) estimates. I am
experimenting
with Hausman-Taylor (HT) estimates using -xthtaylor- but so far find
these
estimates difficult to evaluate given that different combinations of
endogenous (versus instrumental) variables lead to a variety of
coefficient
estimates for the time-varying explanatory variables, with no decisive,
or
best, outcome in terms of the Hausman test of the difference between the
HT
and within estimates.
My query is whether it is tenable to run the random effects regression
command -xtreg, re- constraining the coefficient estimates for the
time-varying explanatory variables to be equal to "first-stage" fixed
effects (within) estimates. Per force, this would seem to eliminate
possible
correlation between the time-varying expanatory variables and the
unobservable specific effect variable, and to obviate the necessity of
evaluating the random effects estimates using the -hausman- test. But,
would
it still leave the "second stage" random effects estimates subject to
possible correlation between the time-invariant explanatory variables
and
the unobservable specific effect variable? Also, is there any precedent
in
the panel data literature for pursuing such a crude approach to
obtaining
random effects estimates?
Dean DeRosa
ADR INTERNATIONAL LTD | POTOMAC ASSOCIATES
Dean A. DeRosa
200 Park Avenue, Suite 306
Falls Church, Virginia 22046 USA
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