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st: RE: Re: RE: RE: "Crude" Random Effects Estimates


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Re: RE: RE: "Crude" Random Effects Estimates
Date   Thu, 1 Jun 2006 16:39:30 +0100

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Rodrigo A. Alfaro
> Sent: Thursday, June 01, 2006 3:55 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Re: RE: RE: "Crude" Random Effects Estimates
> 
> Dear Mark,
> 
> I found this paper long time ago when I was working with the 
> Hausman-Taylor estimator (HT) -a topic that we discussed 
> early in the list. The new thing in the paper is that they 
> propose an non-IV estimator, called Fixed-Effects Vector 
> Decomposition (VD) -nice name right? Moreover, they compare 
> their results with HT finding evidence against HT.

This is one of the bits I didn't understand.  In their Table 1, they say
that the coefficient beta6 on the time-invariant endogenous variable z6
is badly biased in the HT estimations as well as in their xtfevd
estimation.  But if you look at the kernel density graphs on the last
page, the HT estimator isn't very precise, but it does look consistent -
the peak is near the true value, isn't it?  And only HT should generate
consistent estimates of beta6.  But maybe I am misreading this.

> I did some 
> Monte-Carlo experiments -cheap and fast- and VD looks to be 
> stronger under different
> settings: high and low correlation between instruments and 
> instrumented, different n or T, etc.
> 
> The estimator proposed is LS (not a BE), where they used and 
> 'orthogonal' 
> proxy of the unobservable. Then steps 1 and 2 are computed to 
> get this orthogonal proxy of the unobservable. (1) is the 
> classical -and fair- FE step that allows us to get the 
> coefficients for time-variant variables, probably (2) is the 
> weird step, where you compute the coefficients without 
> instruments.

Stage 2 is the BE-like step (equation 8 in their paper).  This is the
regression of the estimated fixed effects on the time invariant
variables.  There are only N observations (not NT), so it's very much
like a BE estimation, which is also a regression on N observations
(means).

> But the procedure uses the residual, which but 
> construction will be orthogonal. With this proxy the put it 
> into LS regression controlling for the lost of degree of freedom.

But it's all linear regressions, residuals, etc., and my intuition (for
what that's worth) is that we should be able to describe the estimator
in terms of orthogonality conditions.  The FE estimator uses the within
transformation and orthogonality with the idiosyncratic e_it.  The BE
estimator uses the between transformation and orthogonality with the
time-invariant unobservable u_i.  The random effects estimator uses
both, which is why it's efficient, but also why it's inconsistent if
either set of orthogonality conditions fails.  But what are the
orthogonality conditions that xtfevd uses, and for what?  I couldn't
work it out from the paper.

> I used the ado-file created by the authors of the papers in 
> an empirical application, comparing FE, RE, HT, 
> Amemiya-Macurdy (AM) and VD. I found no big differences in 
> the estimated coefficients, but a very small standard errors 
> using VD, even smaller than FE!! Std errors for FE, RE, HT 
> and AM are in some sense very close to each other. In other 
> word, I didn't have any change in significance for FE, RE, HT 
> and AM. Maybe you can help here.
> 
> Rodrigo.
> PS: I didn't understand the joke 0.02.

This is an Americanism.  When someone says, "This is just my two cents",
they mean they are making only a small contribution.  Two cents = $0.02.
Believe me, it's not my joke.  I didn't make this up!

Cheers,
Mark

Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University
Edinburgh EH14 4AS  UK
44-131-451-3494 direct
44-131-451-3296 fax
http://www.sml.hw.ac.uk/cert
 

> 
> ----- Original Message -----
> From: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
> To: <statalist@hsphsun2.harvard.edu>
> Sent: Thursday, June 01, 2006 8:27 AM
> Subject: st: RE: RE: "Crude" Random Effects Estimates
> 
> 
> Dean, Rodrigo,
> 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Dean DeRosa
> > Sent: 01 June 2006 13:14
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: RE: "Crude" Random Effects Estimates
> >
> > Rodrigo and Steve,
> >
> > Thank you for your replies to my posts regarding tenable
> > approaches to deriving "constrained" RE estimates. I find the
> > Thomas Plumper-Vera Troeger
> > (2004) paper on estimating time-invariant variables in FE
> > models particularly appealing because it follows a similar
> > vein as I had in mind, but adds statistical rigor and an
> > available Stata .ado routine to boot. I highly commend the
> > paper and routine to others working with FE vs. RE models and
> > panel data sets, for consideration and further evaluation.
> 
> I saw Rodrigo's post, was intrigued, and read the paper, and to be
> honest I had trouble understanding what they were proposing.  
> I couldn't
> work out what orthogonality conditions their estimator used 
> that aren't
> used by the within, between or random effects estimator.  Can you help
> here?
> 
> Also, I thought it would be helpful to compare their proposed 
> estimator
> to the between estimator; they look closely related.  The 
> former is the
> standard estimator for getting at effects caused by 
> characteristics that
> are constant within groups.
> 
> Just my 0.02!
> 
> Cheers,
> Mark
> 
> > http://scholar.google.com/url?sa=U&q=http://www.soz.unibe.ch/s
> tudium/ws0506/
> > downloads/Plumper%2520paper-fixed%2520effects%2520PAFE_59_l.pdf
> >
> > Regards,
> >
> > Dean DeRosa
> >
> >
> >
> > -----------------------------------
> >
> > Date: Tue, 30 May 2006 10:11:13 -0400
> > From: "Rodrigo A. Alfaro" <ralfaro76@hotmail.com>
> > Subject: st: Re: RE: "Crude" Random Effects Estimates
> >
> > Dean,
> >
> > I understood that you approach does not use IV variables. So
> > far, I don't know an algorithm to deal with random-effects
> > and time-invariant variables.
> > A different approach (to IV) was developed by Pluemper-Vega
> > (2004) "The Estimation of Time-Invariant Variables in Panel
> > Analyses with Unit Fixed Effects".
> >
> > I hope this helps you
> > Rodrigo.
> >
> > ----------------------------------
> >
> > Date: Wed, 31 May 2006 03:00:57 +1200
> > From: "Steve Stillman" <stillman@motu.org.nz>
> > Subject: st: "Crude" Random Effects Estimates
> >
> > 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.
> >
> >
> >
> > -----Original Message-----
> > From: Dean DeRosa [mailto:dderosa@adr-i.com]
> > Sent: Monday, May 29, 2006 12:16 PM
> > To: 'statalist@hsphsun2.harvard.edu'
> > Subject: RE: "Crude" Random Effects Estimates
> >
> >
> >
> > 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
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