IV Estimation
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 1428
Dependent variable: Lwage
Coefficient 
Std. Error 
tratio 
pvalue 

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 
Pvalue(F) 
1.30e15 
Loglikelihood 
431.5990 
Akaike criterion 
871.1979 
Schwarz criterion 
887.4344 
HannanQuinn 
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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