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 —fixed-effects

4

4 xvars -= educ black

5 panel lwage xvars —fixed-effects

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:

Fixed-effects, using 3580 observations
Included 716 cross-sectional units

Time-series length = 5
Dependent variable: lwage

Coefficient

Std. Error

t-ratio

p-value

const

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 p-value = 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 p-value 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 nls-panel10.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 —panel-vars

3 genr unitdum

4 list x = exper exper2 tenure tenure2 union

5 ols lwage x du_*

6 panel lwage x —fixed-effects

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 cross-sectional units Time-series length = 5 Dependent variable: lwage

coefficient

std. error

t-ratio

p-value

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:

Fixed-effects, using 50 observations

Included 10 cross-sectional units Time-series length = 5 Dependent variable: lwage

coefficient

std. error

t-ratio

p-value

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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