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RE: Macoreconometric dynamic panels (was: Re: st: panel autocorrelation)


From   "Salvati, Jean" <JSalvati@imf.org>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: Macoreconometric dynamic panels (was: Re: st: panel autocorrelation)
Date   Mon, 18 Oct 2004 13:07:49 -0400

Just correcting my previous post (Beware of Monday morning certainties :), and apologizing for involving Kit Baum in my errors:
 
> - As pointed by Kit Baum, the "within" or "fixed effect" 
> estimator implemented in -xtivreg, fe- is not consistent in the case 
> of a DPD model. If there is a lag of the dependent variable on the RHS 
> of your equation, you should never, ever use -xtivreg, fe- :)

Actually, there are DPD cases where the within estimator (-xtivreg,fe-) is consistent. Martin's original comment ("In the case of large T the FE-estimator is consistent (cf eg Bond [p. 5, fn 6])") was certainly correct. This result is also shown by Anderson and Hsiao (1981).

It's true that a basic OLS estimator will never be consistent with a DPD model, but the within estimator is not a basic OLS estimator. As noted by Arellano and Bover (1995) or Alvarez and Arellano (2003), the within estimator is equivalent to OLS on a model transformed by orthogonal deviations. To find out whether -xtivreg,fe- is consistent in your case, check out Anderson-Hsiao (1981) and Alvarez-Arellano (2003).  

Sorry about the confusion.

Just another point:

Martin Mathes wrote:

>However, I'd like to run a fixed effects-estimation and xtabond is, at least as far as I have understood, a random >effects-estimator.

The point that I wanted to make in my previous post is that the Arellano-Bond estimator deals with the individual effect in exactly the same way as the within "fixed effect" estimator: by getting rid of it. As noted by Wooldridge in "Econometric Analysis of Cross Section and Panel Data", the important distinction is not so much between "random" and "fixed". The important issue is the correlation between the individual effect and the regressors. Both the within estimator and the Arellano-Bond estimator can deal with an individual effect that is random a random variable correlated with the regressors.

References:

- Alvarez and Arellano (2003), "The time-series and cross-section asymptotics of dynamic panel data estimators", Econometrica.
- Anderson and Hsiao (1981), "Estimation of dynamic models with error components".
- Arellano and Bover (1995), "Another look at the instrumental variable estimation of error-components models", Journal of Econometrics.

Jean Salvati
 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Salvati, Jean
> Sent: Monday, October 18, 2004 11:31 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: RE: Macoreconometric dynamic panels (was: Re: st: 
> panel autocorrelation)
> 
> Hi Martin,
> 
> A few remarks:
> 
> - As pointed by Kit Baum, the "within" or "fixed effect" 
> estimator implemented in -xtivreg, fe- is not consistent in 
> the case of a DPD model. If there is a lag of the dependent 
> variable on the RHS of your equation, you should never, ever 
> use -xtivreg, fe- :)
> 
> - The Anderson-Hsiao estimator is consistent for T->infty, 
> N->infty, or both. Unfortunately, the -xtivreg, fd- 
> implementation of this estimator cannot be used for inference 
> and hypothesis testing. The problem is that the 
> Anderson-Hsiao (or Arellano-Bond, for that matter) 
> orthogonality conditions involving lags of the dependent 
> variable are only valid when the error term in the levels 
> equation is not serially correlated. However, when the error 
> term in the levels equation is not serially correlated, the 
> error term in the first-difference equation exhibits negative 
> first-order autocorrelation. Unfortunately, the 
> Anderson-Hsiao estimator relies on the first-difference 
> equation, and -xtivreg, fd- does not report robust standard 
> deviations for the coefficients.
> 
> - The Arellano-Bond GMM estimator is a random-effect 
> estimator in the sense that the individual effect is treated 
> as a random variable. However, like the "within fixed effect" 
> estimator implemented in -xtivreg, fe-, the Arellano-Bond 
> estimator is perfectly valid when the individual effect is 
> correlated with some of the regressors (or even all the 
> regressors). Any estimator that relies on first-differencing 
> or orthogonal deviations can cope with the correlation 
> between the individual effect and the regressors. In 
> contrast, the estimators implemented in -xtivreg, re- are not 
> valid when the individual effect is correlated with some of 
> the regressors.
> 
> - As I said in my response to Edlira, additional consistency 
> results for the GMM DPD estimators are provided in the recent 
> paper by Alvarez and Arellano (2003), "The time-series and 
> cross-section asymptotics of dynamic panel data estimators", 
> Econometrica, July. Check it out. You might be happily surprised :)
> 
> Jean Salvati
> Econometric Support
> (202) 623-7804
> IS 12-1328
>  
> 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Martin 
> > Mathes
> > Sent: Sunday, October 17, 2004 12:57 PM
> > To: statalist@hsphsun2.harvard.edu
> > Subject: Macoreconometric dynamic panels (was: Re: st: panel
> > autocorrelation)
> > 
> > Dear Christopher, dear Listers,
> > 
> > the topic of our discussion is moving slightly towards a very 
> > interesting (and fundamental) question:
> > 
> > What estimator to apply in case of a macroeconometric (!) dynamic 
> > panel?
> > 
> > I haven't mentioned that my panel is a macroeconometric one 
> so (1) it 
> > tends to T>N and (2) fixed effects can be assumed to be 
> more adequate 
> > than random effects (in the case of absence of LDVs).
> > The following considerations led me to employ xtreg, fe or/and 
> > xtivreg:
> > In the case of large T the FE-estimator is consistent (cf 
> eg Bond [p. 
> > 5, fn 6]). Employing RE instead of FE can afaik be assumed 
> to lead to 
> > a bias in a case in which FE should obviously be the prefered 
> > estimator.
> > Furthermore, the paper "Estimating Dynamic Panel Data Models: 
> > A Practical Guide for Macroeconomists" by Judson/Owen 
> > (http://papers.ssrn.com/sol3/Delivery.cfm/Delivery.cfm/9705013.pdf?a
> > bstractid=1904&mirid=1) concludes after running a Monte 
> Carlo analysis 
> > comparing variants of Arellano-Bond-GMMs and
> > Anderson- Hsiao-ivregs that with small Ns the latter outperform the 
> > first. (Their tab 4 indicates that with *very* small N even OLS-FE 
> > outperforms AB- GMM, at least as far as I have understood.)
> > 
> > It seems to me that - in general - there might be a 
> conflict between a 
> > panel's quality of beeing a macroeconometric one (-> xtreg fe or 
> > something xtivreg-like preferable) and a dynamic one (-> xtabond 
> > preferable). Could including group-dummies in a  xtabond-estimation 
> > provide a solution? I haven't seen this to be done or discussed yet.
> > 
> > As I am really no expert on this (at least so far...), I would 
> > appreciate your (and the listers') comments on this issue very much.
> > 
> > And last but not least: If I kept my initial choice of estimators, 
> > would there be any possibility to test for autocorr?
> > 
> > Martin
> >  
> > 
> > > Drop the notion of the fixed effects estimator. It does not
> > make sense
> > > in a dynamic context (for good reason, as any paper 
> underlying the 
> > > Arellano-Bond approach indicates) as an OLS technique is 
> unable to 
> > > cope with the correlation between the demeaned LDV and 
> the demeaned 
> > > error process. (You would run into the same trouble if 
> you did the 
> > > XTREG,FE 'by hand' with firm dummies, or with 'areg'). An 
> excellent 
> > > guide to the DPD estimators is provided in Steve Bond's ``Dynamic 
> > > panel data models: a guide to microdata methods and practice", 
> > > available from EconPapers (CeMMAP working paper 09/02 at
> > Institute for
> > > Fiscal Studies): http://econpapers.repec.org I don't see
> > that in the
> > > presence of a LDV that you can successfully employ FE.
> > > 
> > > Kit Baum, Boston College Economics      baum@bc.edu
> > > http://ideas.repec.org/e/pba1.html
> > > 
> > > *
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> > 
> > Martin Mathes
> > Universität Trier
> > FB IV - VWL
> > Europäische Wirtschaftspolitik
> > D-54286 Trier
> > Tel.: ++49-651-201-2747, -2739
> > Fax: ++49-651-201-3934
> > e-mail: mathes@uni-trier.de
> > 
> > 
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> > 
> > 
> 
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> 

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