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st: RE: Instrumental variables and panel data


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Instrumental variables and panel data
Date   Thu, 8 Oct 2009 15:22:16 +0100

Jaime,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Jaime Gómez 
> Sent: 06 October 2009 23:13
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Instrumental variables and panel data
> 
> Dear Statalisters
> 
> We have a model in which firm performance depends on (1) the 
> order of entry and (2) a possibly endogenous variable and (3) 
> other variables, including time dummies. First, we were 
> suggested to use instrumental variable techniques and to 
> provide HAC standard errors, something we have already done 
> with the ivreg2 command in Stata and using an external 
> instrument. We tested for the exogeneity of the possibly 
> endogenous variable through the endog( ) option and the test 
> shows that the variable could be considered exogenous. 
> 
> In a second step, we have been suggested to use the panel 
> structure of our data and, simultaneously, to consider the 
> endogeneity problem. Ideally, we would like (1) to estimate a 
> panel data model with instrumental variables and HAC errors, 
> (2) to test for the exogeneity of our possible endogenous 
> variable and (3) to check whether the fixed or random effects 
> model is appropriate. So, it seems that the xtivreg or 
> xtivreg2 commands could be the solution. Nevertheless, we 
> have several problems:
> 
> 1) the order of entry is represented through time invariant 
> dummies (pioneer, second mover, third mover, ...) that drop 
> when we estimate a fixed effects model, but we are (very) 
> interested in the values of the coefficients. So it seems 
> that the only way of getting these coefficients is to 
> estimate a random effects model and check whether this is 
> appropriate with a Hausman test (If I reject the random 
> effects model, ¿could I get the order of entry coefficients 
> through another panel data technique?)
> 
> 2) Before doing so we have to find the way of getting HAC 
> standard errors. I think I would know how to do this with 
> xtivreg2 (I am assuming that the options are similar to the 
> ones in ivreg2), nevertheless it seems that there is no way 
> of estimating a random effects model with xtivreg2. The 
> problem with using xtivreg seems that the estimation and 
> postestimation options are much more restricted than with 
> xtivreg2 (for example, how do I get HAC errors? How do I test 
> for the endogeneity of the regressor? Should I use xtoverid 
> for testing for the appropriateness of the random effects model?). 
> 
> In summary, is there any way for treating all these issues 
> (possibly omitted variables that advise the use of panel data 
> techniques, time invariant variables of interest, HAC 
> standard errors and instrumental variables) at the same time? 
> Alternatively, could you suggest another strategy to tackle 
> all the problems with Stata (perhaps sequentially?)?

A couple of thoughts...

1.  You can use -xtoverid- with the undocumented -noisily- option to estimate a random effects model with various types of robust SEs.  There have been several threads on Statalist about it, so it should be pretty easy to find.  (I really have to get around to making -xtivreg2- do random effects....)

2.  Cluster-robust SEs are robust to arbitrary within-cluster correlation as well as heteroskedasticity, and you can think of them as a variety of HAC SEs.  The main difference between them and the usual kernel-based HAC SEs (as supported by -xtivreg2- et al.) is that the asymptotics for cluster-robust SEs have the number of clusters going off to infinity; the asymptotics for the usual kernel HAC SEs (Bartlett kernel aka Newey-West and all those guys) is that they require time to go off to infinity.  Most panels these days are small-T-large-N, so chances are you would be better off with cluster-robust.  Of course, it's up to you.

Cheers,
Mark

> Thanks a lot
> Sincerely
> Jaime Gómez
> Universidad de Zaragoza
> 
> 
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