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RE: st: 3 Problems in Panel Data Analysis


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: 3 Problems in Panel Data Analysis
Date   Tue, 14 Oct 2008 17:08:30 +0100

Fardad et al.,

A small addendum to what Nils and Martin have said, specifically
regarding the Hausman test of fixed vs. random effects: the standard
form of this test is not valid in the presence of heteroskedasticity or
serial correlation.  A test that is valid in the presence of these
problems is implemented by -xtoverid-, downloadable from ssc archives in
the usual way.

Why is it implemented in an overid program?  Because the Hausman test in
this case is a form of overid test.  The fixed effects estimator assumes
only that the regressors are orthogonal to the idiosyncratic error term
e_it.  The random effects estimator uses more orthogonality conditions,
namely that the regressors are also orthogonal to the group-specific
error term u_i.  These extra orthogonality conditions are
overidentifying restrictions, and as such they can be tested.  See -help
xtoverid- and the references therein.

HTH,
Mark

Prof. Mark Schaffer
Department of Economics
School of Management & Languages
Heriot-Watt University
Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
http://ideas.repec.org/e/psc51.html
 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Nils Braakmann
> Sent: 14 October 2008 14:38
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: 3 Problems in Panel Data Analysis
> 
> Hi Fardad,
> 
> no problem. Replys below
> 
> 
> > 1- concerning point 1: do you know an other test in place of Hausman
> > test? Is there any formal way to test for the conditions of RE (i.e.
> > correlation between unobserved heterogeneity and the variables of
> > interest)? How can tell something justifiable about this 
> correlation?
> > Only based on theoretical arguments or is there any test whatsoever
> > for this purpose?
> 
> Well, as far as I know the standard approach for choosing between FE
> and RE is the Hausman test. Looking at the correlation between the
> individual fixed effects and the explanatory variables might work but
> I would be sceptical: As long as the time dimension of your data is
> not large (that is you have both a large number of firms and a large
> number of observations for each firm where "large" refers to the
> ususal "to infinity" asymptotics) your firm effects will be poorly
> estimated and their correlation with any other variable would not be
> particularly meaningful. As a more general point: I would generally
> assume that there is unoberserved heterogeneity as long as I don't
> have an unusually rich data set or have compelling evidence (e.g.
> experimental data) that suggests the opposite.
> 
> > As an alternative you suggest using IV. But you suggest that the IV
> > should not be correltated with the outcome. I think you meant the
> > other way around. Right? Nevertheless, in my case there is no
> > meaningful, relevant IV available; so, this approach is out of
> > question.
> 
> Nope, the usual setup for an IV-estimate is that the instrument is
> correlated with the outcome only through its correlation with the
> (instrumented) variable of interest (see e.g. Cameron, A. Colin and
> Prvain K. Trivedi, 2005 "Microeconometrics - Methods and
> Applications", Cambridge University Press, pp. 96-98). However, this
> does not seem to be a solution in your case.
> 
> > 2- to be honest, I didn't exactly get your point. Sorry for 
> my limited
> > econometric knowledge. What I know is that if my error terms are
> > heteroskedasticit, then the estimates will be biased. As a remedy,
> > robust coefficients should be estimated. Is there any other way to
> > deal with the problem? Could you explain what you meant in your
> > answer?
> 
> First, as Martin already pointed out: Heteroscedasticity does bias the
> estimates of the stadard errors but not the coefficients. Second, as
> you have panel data you have an additional (and usually worse)
> problem: Your error terms will be correlated within firms across time.
> Using clustered standard errors corrects for arbitrary forms of
> heteroscedasticity and autocorrelation within clusters (=firms in your
> example).
> 
> > My specific problem is that -xttobit- in contrast to -xtreg- doesn't
> > have any robust options in Stata. How would you recommend 
> me to reduce
> > the unwanted effects of heteroskedasticity?
> 
> Puh, never used -xttobit-. You might want to try bootstrapped standard
> errors but resample clusters of obervations (=firms with all
> obervations for that firm) instead of obervations
> (firm-year-obervations that is). I am not sure if this works with
> -xttobit- though.
> 
> > 3- You refer to RHS variables in your answer. Do you mean 
> variables of
> > interest in the set of explanatory variables? With respect to your
> > suggestion, do you think SYS-GMM will resolve the problems of both
> > simultaneity and unobserved heterogeneity in my sample?
> 
> By RHS(=right hand side) variables I referred to all explanatory
> variables. System GMM should in principle help but you should refer to
> the two papers by Roodman first as it is easy to do something stupid
> with this estimator. You could also use -xtivreg- or its extension
> -xtivreg2- by Mark Schaffer Baum, Schaffer with first differences and
> additonal lags as instruments.
> 
> > what are the commands to use first-difference and lagged independent
> > variables at the same time in Stata, if any?
> 
> -xtivreg- and -xtivreg2- by Mark Schaffer for example.
> 
> > To be specific, how would compare xtabond, xtabond2 and 
> xtdpdsys with
> > each others? Which one would you compare? What are the required
> > conditions to be able to safely use these methods?
> 
> Well, the last time I used a dynamic panel estimator, I was using
> Version 9.2 which only had -xtabond- and -xtabond2- as an ado-file. I
> am neither sure about the capabilities of the -xtabond-command in
> Version 10.1 nor did I ever look at -xtdpdsys- in detail. A rather
> detailed and accessible exposition of the necessary assumption for
> Arelano-Bond/System GMM can be found in the papers by Roodman.
> 
> > 4- As to my still remaining question, in a panel data setting, what
> > pre- and post-tests do you recommend in  general to check for the
> > underling conditions and assumptions? What can one do to 
> increase the
> > reliability and validly of the results?
> 
> Well, for the standard RE estimator the crucial assumption is that the
> explanatory variables are both uncorrelated with the unobserved
> heterogeneity and the contemporaneous error. The standard FE estimator
> allows for correlation between the unobserved heterogeneity and the
> explanatory variables but still requires the latter to be uncorrelated
> with the contemporaneous error. As all assumptions refer to
> unobservables they are obviously hard to test... In fact, I am simply
> not aware of any formal test though there might be one.
> 
> Best regards,
> Nils
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