Re: Re: st: handling serial correlation in fixed effects estimations

[Philipp Ehmer <p_ehmer@hotmail.com>]

On Nov 29, 2013, at 2:33 AM, Philipp wrote:

> I am using panel data on countries (N = 18) and a time period of approx. 25 years (T = 25). It is an unbalanced panel and I have approx. 300 available data points. I would like to employ a fixed effects estimation and I always use the option ", robust" to avoid any kind of heteroskedasticity. A second potential problem I would like to mitigate is serial correlation in the errors.
> 
> I always look for serial correlation by using the commands "predict resid, e" and then "reg resid l.resid". This shows significant serial correlation in the residuals. My question is: what are my options to get rid of this serial correlation? I know that I can estimate the equation using first differences instead of levels but I would like to use levels. I know that another option is to use a lagged dependent variable as explanatory variable. And I heard of a third way which would be to include time-dummies, i.e. a dummy variable for each year - this sadly doesn't help.
> 
> First question: am I maybe doing something wrong with those time dummies? Stata omits one so that there is no perfect colinearity, so that seems to work fine so far. Only that when I test for serial correlation in the way that I described above, Stata tells me that there is still substantial serial correlation.
> 
> Second question: I know that Stata offers some other estimation tools: xtgls, xtpcse and xtregar. What about these tools, do they eliminate serial correlation in the residuals? For instance, when I use xtregar and then again "predict resid, e" and "reg resid l.resid" there is still significant serial correlation. Am I maybe testing it in a wrong way or does xtregar somehow not succeed in eliminating serial correlation? Is it possible that these methodes do not work with my rather small sample?
> 
> And my third question: my dependent variable seems to be a unit root process. Does this change anything regarding serial correlation? Does this mean, e.g. that I can't use a lagged dependent variable as explanatory variable to get rid of the serial correlation?

Regarding #3, yes, if the dependent variable is clearly a unit root process (although to determine that, I presume you have used some panel unit test, most of which do not work with unbalanced panels...) you should not be using a fixed effects estimator. However unit root tests do not have much power with 25 observations; panel unit root tests are devised to deal with this problem, but very few can handle unbalanced panels.

Regarding #1 and #2, in a panel context, it would be very plausible that any residual autocorrelation might differ across panels, so the idea of predicting residuals and estimating an AR(1) model doesn't make sense. I suspect that what you are seeing as autocorrelation is likely to reflect a misspecification of the model, with one or more important explanatory variables missing from the model (which might include lagged values of some of your explanatory variables). 

Kit Baum
Professor of Economics and Social Work, Boston College, Chestnut Hill MA, USA
DIW Research Professor, Department of Macroeconomics, DIW Berlin, Berlin, Germany
baum@bc.edu | http://ideas.repec.org/e/pba1.html

>>>>
Thanks for your help.
Regarding unit roots: my dependent variable is the current account balance as a ratio of GDP and according to the literature, there might (!) be a unit root but it seems not to be clear for the reasons you gave (difficult to proove 100%). IF there is indeed a unit root I shouldn't use fixed effects, you said. What about pooled OLS? If I subdivide my T = 25 in, say, 5 x T = 5 periods with averages of the yearly values and then use pooled OLS, this unit root problem doesn't bother me anymore, correct?

If I assume for now there is no unit root and I use fixed effects:
Regarding autocorrelation: the way I test autocorrelation (by predicting residuals and then estimating "reg resid l.resid") doesn't work properly since autocorrelation differs across panels, is that what you mean? What would be an appropriate way to test autocorrelation?
I already tested a lot of model varieties including models with lagged values of the explanatory variables, but the autocorrelation persists. So there is no way for me to get rid of it by specifying another model, I think. It only goes away when I use a lagged dependent variable or estimate the equation in first differences, but I'd like to avoid both options. Is there any other way to deal with autocorrelation? 		 	   		  
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