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Re: st: 3 Problems in Panel Data Analysis


From   "Nils Braakmann" <nilsbraakmann@googlemail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: 3 Problems in Panel Data Analysis
Date   Tue, 14 Oct 2008 15:38:07 +0200

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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