Fixed Effects
The model (15.2) is reestimated using fixed effects. Race and education do not change for individuals in the sample, and their influences cannot be estimated using fixed effects.
1 open "c:Program Filesgretldatapoenels_panel. gdt"
2 list xvars = const educ exper exper2 tenure tenure2 south union black
3 panel lwage xvars —fixedeffects
4
4 xvars = educ black
5 panel lwage xvars —fixedeffects
Even though the parameters for black and educ are not identified in this model, we included them anyway in line 3 just to see how gretl handles this. The results are:
Fixedeffects, using 3580 observations
Included 716 crosssectional units
Timeseries length = 5
Dependent variable: lwage
Coefficient 
Std. Error 
tratio 
pvalue 

1.45003 
0.0401400 
36.1244 
0.0000 

exper 
0.0410832 
0.00662001 
6.2059 
0.0000 
exper2 
0.000409052 
0.000273333 
1.4965 
0.1346 
tenure 
0.0139089 
0.00327784 
4.2433 
0.0000 
tenure2 
0.000896227 
0.000205860 
4.3536 
0.0000 
south 
0.0163224 
0.0361490 
0.4515 
0.6516 
union 
0.0636972 
0.0142538 
4.4688 
0.0000 
Test for differing group intercepts – Null hypothesis: The groups have a common intercept Test statistic: F(715, 2858) = 15.145 with pvalue = P(F(715, 2858) > 15.145) = 0
Cleverly, gretl has dropped educ and black from the model. It also reports a test of the hypothesis that the individual differences are jointly equal to zero. Failure to reject this hypothesis would lead to the pooled least squares estimates. The pvalue is near zero and the equality of intercepts is rejected.
In line 5, we’ve used a special gretl trick that can be used to remove items from a list. The operator is = and in this line the variables educ and black are removed from the xvars list. You can add things to a list using +=.
As pointed out in POE4, when N is small you can create a set of dummy variables for the fixed effects and estimate the model using least squares. This is equivalent to using the fixed effects estimator. The nlspanel10.gdt contains a subset of 10 individuals from the larger set of 716 and we can use it to demonstrate some features of gretl and the equivalence of the two procedures.
The first step is to create a set of indicator variables for each individual.
1 open "@gretldirdatapoenls_panel10.gdt"
2 setobs id year —panelvars
3 genr unitdum
4 list x = exper exper2 tenure tenure2 union
5 ols lwage x du_*
6 panel lwage x —fixedeffects
Since the dataset has been declared to be a panel, gretl knows that the id variable identifies individuals. Hence, genr unitdum generates an indicator for each unique id. This is a special circumstance where the genr command must be used instead of series. The indicator variables are added to the dataset and are given names and variable ID numbers. The name of the first indicator is du_1 which takes a 1 if individual has id=1 and 0 otherwise. The remaining individuals also get an indicator variable, the last being du_10. The use of the wildcard * in line 5 reduces the amount of typing. The * will pick up every variable that begins dm. In this model dm* is equivalent to dml dm2 dm3 du_4 du_5 du_6 du_7 du_8 du_9 dm10.
The results from least squares dummy variable estimation and the equivalent fixed effects panel appear below in Table 15.1. The advantage of using the panel fixed effects version is that when there
Model 1: Pooled OLS, using 50 observations Included 10 crosssectional units Timeseries length = 5 Dependent variable: lwage
coefficient 
std. error 
tratio 
pvalue 

exper 
0.237999 
0.187757 
1.268 
0.2133 
exper2 
0.00818817 
0.00790482 
1.036 
0.3074 
tenure 
0.0123500 
0.0341433 
0.3617 
0.7197 
tenure2 
0.00229615 
0.00268846 
0.8541 
0.3989 
union 
0.113543 
0.150863 
0.7526 
0.4567 
du_1 
0.151905 
1.09675 
0.1385 
0.8906 
du_2 
0.186894 
1.07148 
0.1744 
0.8625 
du_3 
0.0630423 
1.35092 
0.04667 
0.9630 
du_4 
0.185626 
1.34350 
0.1382 
0.8909 
du_5 
0.938987 
1.09778 
0.8554 
0.3982 
du_6 
0.794485 
1.11177 
0.7146 
0.4796 
du_7 
0.581199 
1.23591 
0.4703 
0.6411 
du_8 
0.537925 
1.09750 
0.4901 
0.6271 
du_9 
0.418334 
1.08405 
0.3859 
0.7019 
du_10 
0.614558 
1.09018 
0.5637 
0.5765 
Model 2: 
Fixedeffects, using 50 observations 
Included 10 crosssectional units Timeseries length = 5 Dependent variable: lwage 
coefficient 
std. error 
tratio 
pvalue 

const 
0.434687 
1.14518 
0.3796 
0.7066 
exper 
0.237999 
0.187757 
1.268 
0.2133 
exper2 
0.00818817 
0.00790482 
1.036 
0.3074 
tenure 
0.0123500 
0.0341433 
0.3617 
0.7197 
tenure2 
0.00229615 
0.00268846 
0.8541 
0.3989 
union 
0.113543 
0.150863 
0.7526 
0.4567 
Table 15.1: Comparison of fixed effects and least squares dummy variable estimators. 
are many individuals, the output of the coefficients on the fixed effects themselves is suppressed. When N is large, you are seldom interested in the values of these parameters anyway.
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