Hello,

I´m a student and currently working on my masters thesis to conclude my accountancy study.

My question regards the use of OLS and GLS. I have a large panel data collection, consisting of about 1500 firms, with observations over max. 3 years. So OLS regression is bound to lead to biased errors, since the data have both time series and cross sectional dimensions. Therefore, I have estimated the model using the random effects GLS method, and the model seems to be valid. At the bottom of this mail I included the results.

There is however no Rsquare (or equivalent number) available in the output. Is it possible to obtain such a number for GLS?

On page 111 and 112 of the instruction manual, it states that GLS is equivalent to OLS using quasi demeaned variables. I don't completely understand the formula however. To obtain the fraction by which the variables should be demeaned, the between and within variances should be filled in to the formula. The Ti in the formula, does it refer to the total number of observations used to construct the model? (I have a total of 2689 firm year observations, so Ti = 2689??).

If the variable observations are demeaned by the calculated fraction of the mean of that variable, can I then use these new variables to construct an OLS model which is reliable, and thus obtain a Rsquare? Or is there a simpler way of obtaining a figure stating the the explanatory power of my model?

Thanks for the help! Dennis

Output of GLS regresion:

Model 8: Random-effects (GLS) estimates using 2689 observations

Included 1290 cross-sectional units

Time-series length: minimum 1, maximum 3

Dependent variable: LNFEE

Mean of dependent variable = 13,3439

Standard deviation of dep. var. = 1,20651

Sum of squared residuals = 906,323

Standard error of the regression = 0,584044

'Within' variance = 0,115462

'Between' variance = 0,30521

Akaike information criterion = 4772,68

Schwarz Bayesian criterion = 4967,28

Hannan-Quinn criterion = 4843,07

Breusch-Pagan test -

Null hypothesis: Variance of the unit-specific error = 0

Asymptotic test statistic: Chi-square(1) = 485,572

with p-value = 1,30992e-107

Hausman test -

Null hypothesis: GLS estimates are consistent

Asymptotic test statistic: Chi-square(15) = 113,98

with p-value = 2,76456e-017

Test for normality of residual -

Null hypothesis: error is normally distributed

Test statistic: Chi-square(2) = 339,203

with p-value = 2,20321e-074