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
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TRADE POLICY ANALYSIS & ECONOMIC RESEARCH
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