Introduction to Econometrics
Worksheet week # 7
1. Consider the following model describing the corporate investment behavior
It = β0 + β1Ft−1 + β2Kt−1 + εt , t = 1935, ..., 1953 ,
where It = current gross investment, Ft−1 = end-of-period value of outstanding
shares, and Kt−1 = end-of-period capital stock. The regression was estimated from
the data for General Motors Corporation (standard errors in parentheses):
ˆIt = − 109.8
97.436)
+ 0.1142
0.0235)
Ft−1 + 0.3261
0.0394)
Kt−1 , R2
= 0.8907 .
(a) Test that the amount of capital stock affects positively future investment be-
havior.
(b) Explain how you would test the hypothesis that no relevant explanatory variables
have been omitted using the RESET test.
2. Imagine that you want to estimate the race-specific crime rates. Given the data on
over 2000 criminals (crime2.gdt), estimate the relationship between the race and the
number of crimes committed. The dataset contains the following variables:
crime86 - number of crimes committed in 1986
race - race (=1 if black, =2 if Hispanic, =0 otherwise)
tottime - total number of months spent in prison since 18 years old
pcnv - proportion of prior convictions
qemp86 - number of quarters employed in 1986
inc86 - legal income in 1986, $100s
(a) Estimate the baseline model of the impact of race on number of crimes committed
in 1986:
crime86i = α0 + α1racei + εi .
(b) Interpret the results. Do you believe that the coefficient α1 is correctly estimated?
Under what assumptions would it be?
(c) Create two dummy variables for black and Hispanic individuals. Estimate the
equation again with these two variables. Interpret the results.
crime86i = β0 + β1blacki + β2hispanici + vi .
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(d) Is there anything that could still create a bias in this equation? If yes, how
would you solve for this problem? What direction of bias do you expect?
(e) Re-estimate the equation with variables controlling for crime history of a person:
crime86i = γ0 + γ1blacki + γ2hispanici + γ3tottimei + γ4pcnvi + ei .
(f) Control further for a current employment status and income of an individual:
crime86i = δ0+δ1blacki+δ2hispanici+δ3tottimei+δ4pcnvi+δ5qemp86i+δ6inc86i+ui .
(g) Interpret the results from part e and f (in comparison with c). How did the
coefficients of black and hispanic change? Did you expect this direction of
potential bias? Would you conclude that the additional variables indeed belong
to the model?
(h) Test the hypothesis that no relevant explanatory variables have been omitted
using the RESET test in Gretl (test for the model from part f).
3. 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.
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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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