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Hi Everyone,

I need some help in panel data. I have a sample of 69 countries. I have 20 years data converted to 5 year averages. So i have 4 observations per country. The Hausman test rejects random effect model and hence fixed effect model is preferred. Now i am choosing both time fixed effect as well as cross section fixed effect model and selecting the option (White cross-section) from the lower menu to correct for heteroskedasticity. when i do this, i am getting the regression output and there is written( The coefficient covariance matrix is of reduced rank? Now please any body tell me the about the method i am following is correct or not? What should i do? Help will be highly appreciated.

When you choose White-cross-section for the covariance, you are saying that your data are contemporaneously correlated, or put differently that they are clustered by period. You can create an estimate of the covariance matrix that accounts for this, but you should be aware that this reduces the number of "effective" observations in the covariance matrix to the number of periods.

What the error message is telling you is that your estimated covariance matrix does not have full rank (the asymptotic results require that the number of clusters approaches infinity; you only have 4 clusters). Given the way you are computing the covariance there is nothing you can do about this. Some hypothesis tests using the covariance may be estimable, but some will not. We are just warning you that you should use the covariance matrix with caution.

Thank you very much for such a nice explanation. I got it. Just clarify this to me as well. My regression results are reliable in this case or not?

The coefficients are unchanged with the choice covariance method. The reliability of the covariance estimates depends on asymptotics in the number of periods, which I think it is fair to say you don't have. I would be very nervous about any Wald test statistics using those estimates.

Thank You very much,
Following your explanation, if i use white period, which is robust to serial correlation within cross sections and changing variances overtime, i can avoid the problem of reduced rank of the coefficient covariance matrix. Is it the right way of doing this estimation? So well this strategy control both serial correlation and heteroskedasticity effectively?

That is one approach to handling the covariance estimation. I won't comment on it except to say that it does assume that there is no contemporaneous correlation. But it does allow for serial correlation and heteroskedasticity.

Hello,
What does it exactly mean by ( to use the covariance matrix with caution)? Do i have to worry about that this warning message? Or i can go with these regression results? Well there is any other way to avoid the warning message? Thanks

What it means is that the assumptions required for this approach to offer a good estimator of the coefficient covariance are likely violated. The asymptotic results require that the number of periods goes to infinity, which, with 4 observations obviously doesn't hold. You can do some tests with this covariance matrix (there will be some where the singularity will generate an error), but I wouldn't be too confident in any results.

The easiest way to get around this, given the assumption of contemporaneous correlation, is to get a longer time series dimension in your data. You could try the Cross-section SUR estimator, which will mask the issue, but the underlying requirement that you have more time periods is still there.

Wooldridge has some approaches for finite size sample clustering...

http://econ.ucsb.edu/~doug/245a/Papers/ ... etrics.pdf

If I recall correctly, in this paper the clustering is the opposite direction (clustering by cross-section instead of by period), so you'll have to mentally reverse the indices.

Thank you so much for such a nice explanation...

Hi everybody,
I have a question about when we use random or fixed effects in estimation. I have to examine the goverment bond yieldspreads in European Union with daily data from 2000 until 2011, but I am not sure which specification to use. I tend to Fixed effects specifiaction. Also, if I choose fixed effects, is better to make the estimation with EGLS in case of the existence of heteroskedasticity or autocorrelation? Generally, can somebody explain me the possitives and the negatives of each specification? Thank you all in advance. :)

Dear Sir, As i have mentioned earlier that i have 4 observations per country because the data is converted to five year averages. My sample is 69 countries and i have 6 independent variables. I read something on sample size today in which the authors are saying about sample size is ' from the pure statistical point of view, it is always necessary to have more observations than number of parameters'. So i want to know that can i estimate a model with 6 independent variables? total observations are 69*4=276. Thanks in advance