Between Estimator

Before discussing such tests, another estimator of the model’s parameters deserves mention. The between estimator is also used in some circumstances. The between model is

yi = ві + в2Х2 І + взХз І + Ui + ei (15.11)

where the yi is the average value of y for individual i, and xki is the average value of the kth regressor for individual i. Essentially, the observation in each group (or individual) are averaged over time. The parameters are then estimated by least squares. The variation between individuals is being used to estimate parameters. The errors are uncorrelated across individuals and homoskedastic and as long as individual differences are not correlated with regressors, the between estimator should be consistent for the parameters.

To obtain the between estimates, simply use the —between option of panel as shown below:

1 open "@gretldirdatapoenls_panel. gdt"

2 setobs id year –panel-vars

3 list x1 = educ exper exper2 tenure tenure2 union black south

4 panel lwage x1 –between

Dependent variable: lwage

(1)

(2)

(3)

(4)

Within

FGLS

Between

Pooled OLS

const

1.45**

0.534**

0.417**

0.477**

(36.1)

(6.68)

(3.07)

(5.65)

exper

0.0411**

0.0436**

0.0662**

0.0557**

(6.21)

(6.86)

(2.82)

(4.93)

exper2

-0.000409

-0.000561**

-0.00161

-0.00115**

(-1.50)

(-2.14)

(-1.61)

(-2.33)

tenure

0.0139**

0.0142**

0.0166

0.0150**

(4.24)

(4.47)

(1.36)

(2.10)

tenure2

-0.000896**

-0.000755**

-0.000495

-0.000486

(-4.35)

(-3.88)

(-0.704)

(-1.19)

south

-0.0163

-0.0818**

-0.105**

-0.106**

(-0.452)

(-3.65)

(-3.62)

(-3.92)

union

0.0637**

0.0802**

0.156**

0.132**

(4.47)

(6.07)

(4.39)

(4.89)

educ

0.0733**

0.0708**

0.0714**

(13.7)

(13.1)

(13.0)

black

-0.117**

-0.122**

-0.117**

(-3.86)

(-3.84)

(-4.16)

n

3580

3580

716

3580

R2

0.824

0.358

0.324

і

1.17e+003

-1.65e+003

-240

-1.63e+003

^statistics in parentheses * indicates significance at the 10 percent level ** indicates significance at the 5 percent level

The results for each of the estimators, in tabular form, are in Table 15.3. Wisely, gretl has omitted the R2 for the random effects model. Recall that R2 is only suitable for linear models estimated using OLS, which is the case for one-way fixed effects. There is not a lot of variation in these results, suggesting that perhaps the unobserved individual differences are not significantly correlated with the model’s regressors.

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