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

 From "Rodrigo A. Alfaro" To Subject st: Re: RE: RE: "Crude" Random Effects Estimates Date Thu, 1 Jun 2006 10:55:12 -0400

```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. 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. 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.

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.

----- 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

tudium/ws0506/
>
> 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,
> 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
> 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-----
> 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
> 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-----
> 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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