Introduction to Econometrics
Worksheet week # 10
1. Use data wage.gdt to estimate the returns to education equation.
(a) Estimate the baseline model of the impact of education and experience on wages:
ln(wagei) = β0 + β1educi + β2experi + εi .
Interpret the meaning of the coefficient β1.
(b) Reestimate the model using robust standard errors, comment on the differences.
(c) Test for heteroskedasticity in the model in part (a). Is it necessary to use robust
standard errors in this case?
(d) Estimate the model with quadratic specification of experience:
ln(wagei) = β0 + β1educi + β2experi + β3exper2
i + εi .
Comment on how and why the coefficient β2 changed with respect to part (a).
Did the coefficient β1 change as well? Why or why not?
(e) Do you believe that the coefficient β1 is correctly estimated? Is there anything
that could create a bias in this equation? If yes, how would you solve for this
problem?
(f) Include in the model the education of the mother and of the father of the
observed individuals:
ln(wagei) = β0+β1educi+β2experi+β3exper2
i +β4motheduci+β5fatheduci+εi .
i. Is there an impact on the coefficient β1? Does this signal there was a bias
in the model from part (d)? Comment on the sign of this bias.
ii. Are both motheduc and fatheduc individually significant? Are they jointly
significant?
iii. What happens if you exclude one these variables from the regression? Which
one would you keep?
(g) Instead of the education of parents, include the variable measuring ability in
the model:
ln(wagei) = β0 + β1educi + β2experi + β3exper2
+ β4abil + εi .
Is there an impact on the coefficient β1? Does this signal there was a bias in
the model from part (d)? Comment on the sign of this bias.
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2. Use data bwght1.csv to estimate the model describing the impact of smoking on birth
weight. The file contains data on births to women in the US.
bwght ... birth weight in ounces
cigs ... cigarettes smoked per day while pregnant
packs ... packs of cigarettes smoked per day while pregnant
(a) Import data into Gretl from csv file.
(b) Generate log of birth weight (using logbwght = log(bwght)).
(c) Define and estimate the model describing the impact of smoking on birth weight
(in logarithm).
i. Should we include both cigs and packs into the model?
ii. Which assumption might be violated if we do?
iii. How do we test for this assumption?
(d) Interpret the results of cigs and packs coefficients in the two separate models.
Are they significant? What is the interpretation of the coefficients magnitude?
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