Introduction to Econometrics
Home assigment # 4
(Deadline 10.12.2016, 23:59, no late submissions will be accepted, please scan your
solution and send it to 171922@mail.muni.cz)
1. For this exercise, use the data in fertil.gdt file. It contains information about a sample
of women in Botswana: their education (variable educ), their age (variable age), and
the number of children they have (variable children).
(a) Estimate the model
children = β0 + β1educ + ε ,
interpret the coefficient β1.
(b) Conduct the Breusch-Pagan test for heteroskedasticity. Does its result justify
the use of robust standard errors? If yes, reestimate the model using these
robust standard errors and comment on the difference with respect to the model
estimated by simple OLS.
(c) Redefine the model as
children = β0 + β1educ + β2age + β3age2
+ ε
and estimate it.
i. Does age have a significant impact on number of children of Botswana
women? State the hypothesis, and compute the test statistics by hand.
Interpret the results and compare it to the results of the test in Gretl.
ii. Do you find justification for the inclusion of age in quadratic form? [Hint:
State the four specification criteria and argue if they are satisfied for the
quadratic in age.]
iii. How does the coefficient β1 change when compared to part (a)? Does this
signal any bias in the model from part (a)? Where does it come from?
Explain the sign of this bias.
(d) Do you think the coefficient β1 from the model in part (c) may suffer from some
omitted variable bias? What variable(s) could be missing in the model and how
would the coefficient β1 change if they were included in the regression? (What
is the sign of the potential bias in coefficient β1?)
(e) Conduct the RESET test of the model from part (c) and interpret the results.
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2. Suppose following investment model was estimated with quarterly data from 1997-
2009 (standard errors in parenthesis):
It = 7.70
1.10)
+ 0.55
0.23)
Yt + 0.63
0.12)
Qt2 + 1.55
1.03)
Qt3 + 2.13
0.74)
Qt4 ,
n = 64 , R2
= 0.72 ,
where It is the investment in period t, Yt is the GDP in period t, and dummy variables
Qti are equal to 1 in the i-th quarter and zero otherwise (i = 2, 3, 4). Denote the
coefficients associated with the dummies δ2, δ3 and δ4.
(a) What restriction on these parameters would lead to the model:
It = β0 + βY Yt + δqt + εt ,
where qt = 0, 1, 2, 3 in the first, second, third and fourth quarters respectively?
Briefly discuss this restriction. [Hint: To find the restrictions, compare the
coefficients of the two models (restricted and unrestricted) for each quarter.]
(b) Test the restriction if the regression R2
of the restricted model was 0.68.
(c) Explain how would you test for presence of AR(4) autocorrelation of the error
term in this model. Describe all steps that you need to take to conduct the test,
the null and alternative hypothesis, and the test statistics.
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