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
Coefficient
Std. Error
t-ratio
p-value
const
3,9247
0,185476
21,1601
<0,00001
***
DMERG
-0,0297729
0,023798
-1,2511
0,21102
DYEND
0,148343
0,0355846
4,1687
0,00003
***
CUR
-0,0502722
0,00775962
-6,4787
<0,00001
***
LNASS
0,54088
0,0107991
50,0856
<0,00001
***
LEV
0,116304
0,0726841
1,6001
0,10969
RECINV
0,77681
0,108092
7,1865
<0,00001
***
DLOSS
0,0905454
0,0266356
3,3994
0,00069
***
DFORSAL
0,178978
0,0298617
5,9936
<0,00001
***
GROWTH
-0,0380927
0,0295275
-1,2901
0,19714
Dagicult
-0,284019
0,219346
-1,2948
0,19549
Dmining
-0,286592
0,104809
-2,7344
0,00629
***
Dfood
-0,120614
0,0970142
-1,2433
0,21388
Dtextiles
-0,107272
0,079442
-1,3503
0,17703
Ddrugs
0,132128
0,0813666
1,6239
0,10452
Dchem
-0,0255039
0,0904682
-0,2819
0,77803
Drefin
-0,344315
0,103874
-3,3147
0,00093
***
Drubbr
-0,124968
0,0778424
-1,6054
0,10853
Delectr
0,181519
0,0949686
1,9114
0,05607
*
Dmisceq
0,0947427
0,0754278
1,2561
0,20920
Dcompu
-0,0075002
0,0749831
-0,1000
0,92033
Dtransp
-0,329837
0,089881
-3,6697
0,00025
***
Dutil
-0,445682
0,0908753
-4,9043
<0,00001
***
Dretail
-0,328033
0,0738928
-4,4393
<0,00001
***
Dbank
0,296416
0,288526
1,0273
0,30435
Dservic
-0,0239899
0,0872035
-0,2751
0,78326
Dmiscel
-0,313397
0,328379
-0,9544
0,33998
DBIG4_5
0,067776
0,0556034
1,2189
0,22298
DAND
-0,468338
0,0386425
-12,1198
<0,00001
***
AUDCHG
-0,206686
0,0289029
-7,1511
<0,00001
***
REPLAG
4,23836e-05
0,000167129
0,2536
0,79983
LSEG
0,279646
0,0338728
8,2558
<0,00001
***
ROA
-0,0512651
0,0842163
-0,6087
0,54275
_________________________________________________________________
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