Using gret l for Principles of Econometrics, 4th Edition

IV Estimation

Gretl handles this estimation problem with ease using what is commonly referred to as two - stage least squares. In econometrics, the terms two-stage least squares (TSLS) and instrumental variables (IV) estimation are often used interchangeably. The ‘two-stage’ terminology is a legacy of the time when the easiest way to estimate the model was to actually use two separate least squares regressions. With better software, the computation is done in a single step to ensure the other model statistics are computed correctly. Since the software you use invariably expects you to specify ‘instruments,’ it is probably better to think about this estimator in those terms from the beginning. Keep in mind though that gretl uses the old-style term two-stage least squares (tsls) even as it asks you to specify instruments in it dialog boxes and scripts.

10.2.1 Least Squares Estimation of a Wage Equation

The example is model of wages estimated using mroz. gdt using the 428 women in the sample that are in the labor force. The model is

ln( wage) = ві + e2educ + ft^exper + e4exper2 + e (10.2)

In all likelihood a woman’s wages will depend on her ability as well as education and experience. Ability is omitted from the model, which poses no particular problem as long as it is not correlated with either education or experience. The problem in this example, however, is that ability is likely to be correlated with education. The opportunity cost of additional education for those of high ability is low and they tend to get more of it. Hence, there is an endogeneity problem in this model. The model is estimated using least squares to produce:

OLS, using observations 1-428
Dependent variable: Lwage

Coefficient

Std. Error

t-ratio

p-value

const

-0.522041

0.198632

-2.6282

0.0089

educ

0.107490

0.0141465

7.5983

0.0000

exper

0.0415665

0.0131752

3.1549

0.0017

sq_exper

-0.000811193

0.000393242

-2.0628

0.0397

Mean dependent var

1.190173

S. D. dependent var

0.723198

Sum squared resid

188.3051

S. E. of regression

0.666420

R2

0.156820

Adjusted R2

0.150854

F(3, 424)

26.28615

P-value(F)

1.30e-15

Log-likelihood

-431.5990

Akaike criterion

871.1979

Schwarz criterion

887.4344

Hannan-Quinn

877.6105

The estimated return to another year of schooling is 10.75%. That seems fairly high and if education and the omitted ability are correlated, then it is being estimated inconsistently by least squares.

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