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Midterm

# Test 3

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McMaster University

Economics

ECON 3U03

Shintaro Yamaguchi

Fall

Description

ECON 3U03: Test 3
Instructor: Shintaro Yamaguchi
November 22, 2011
▯ Do not start or read problems starting from the next page until you are told to do so
(or get 10% penalty on this test).
▯ Only university calculator (Casio FX991) is allowed.
▯ There are 4 questions. The marks for each question are indicated.
▯ Your answer must be supported by a clear explanation unless otherwise noted.
▯ Answer concisely. Writing something that is not directly related to the right answer may
result in deduction.
▯ No mark may be awarded if your answer makes little sense or if it is not comprehensible to
the marker, even if it includes some words which should appear in the correct answer.
▯ When ﬁnished, submit only the answer sheet to the place assigned by the invigilator. Invigi-
lators do not pick it up from you. Keep this sheet for your study.
▯ A student who does not respect the time limits during the test will get a 10% penalty on this
test.
1 1. (21 marks) Answer the following questions.
(a) (7 marks) I would like to estimate the following equation w = b +b s +b m +e i 1 2 i 3 i i
where w is hourly wage, s is years of schooling, m is motivation, and e is an error
i i i i
term. However, my data set does not include a measure of motivation m . So, I estimate i
w = b +b s +e instead. What is the problem with this? Choose the most relevant
i 1 2 i i
one from the following.
i. Biased estimates.
2
ii. Lower explanatory power of the model (lower R ).
iii. Not statistically independent estimates.
iv. Less precise estimates (larger standard errors.)
v. Not economically signiﬁcant estimates.
(b) (7 marks) To avoid the problem from omitted variables, an analyst includes all available
variables. What is the problem with this? Choose the most relevant one from the
following.
i. Biased estimates.
2
ii. Lower explanatory power of the model (lower R ).
iii. Not statistically independent estimates.
iv. Less precise estimates (larger standard errors.)
v. Not economically signiﬁcant estimates.
(c) (7 marks) An analyst estimates the following equation Y = b +b AN +b AC +ei 1 2 i 3 i i
where Y isisales of a restaurant, AN is the ad ixpenditure on news paper, AC is the i
coupon ad expenditure, and e is an erior term. She notices that AN and AC are highly i i
correlated with each other. What is the problem with this? Choose the most relevant
one from the following.
i. Biased estimates.
2 2
ii. Lower explanatory power of the model (lower R ).
iii. Not statistically independent estimates.
iv. Less precise estimates (larger standard errors.)
v. Not economically signiﬁcant estimates.
2. (14 marks) I would like to estimate a price function for a laptop computer
pi = b +b0CPU +1 HDD ib MEM2+b APPiE +b 3ELL +b iTHER4 +e ; i 5 i 6 i i
where CPU is the speed of the CPU, HDD is the hard drive capacity, MEM is the memory
size, APPLE is the dummy variable that takes one if the laptop is made by Apple and takes
zero otherwise, DELL is the dummy variable that takes one if the laptop is made by Dell
and takes zero otherwise, and OTHERS is the dummy variable that takes one if the laptop is
made by other manufacturer than Apple or Dell and takes zero otherwise.
(a) (7 marks) The equation above cannot be estimated. Why? Explain. The answer must
not exceed 2 lines or no marks will be given.
(b) (7 marks) To make the model estimable, I dropped the variable APPLE. What is the
interpretation of b ?5The answer must not exceed 2 lines or no marks will be given.
3. (25 marks) This question studies the beer consumption per household per month,
q = b +b ln p +b ln p +b ln p +b lnm +e
i 1 2 B;i 3 L;i 4 R;i 5 i i
where q ii the quantity of beer consumed, p B;i is the price of beer, p L;iis the price of other
liquor, p R;iis the price of all other goods, m is income, and e is an eiror term. According
to the economic theory, if prices of everything and income double, demand for beer remains
the same (no money illusion exists). I would like to test this hypothesis.
(a) (15 marks) Prove that this null hypothesis can be formulated as b +b +b +b = 0.
2 3 4 5
3 (b) (2 marks) State the alternative hypothesis by an equation
(c) (8 marks) Suppose the hypotesis is tested by the F-test. What is a restricted model?
4. (40 marks) Consider the following wage equation
wage t = b +b 1du +b2exp te 3 t t
where wage is log hourly wage, edu is years of education, exp is years of labour market ex-
perience, and e is an error term that satisﬁed the ﬁve standard assumptions for the multiple
t
linear regression model (MR1-5). I estimate this wage equation for a sample of 66 individ-
uals. The estimation results are intuitive. Namely, the coefﬁcients for b and b are positive
2 3
and signiﬁcant at 5% level. The sum of squared residuals SSE is 113.32. Now I extend this
equation such that
wage t = b +b1edu +2 exp tb wh3te +btmale4+b (white ▯m5le )+et 6 t t t
where white is a dummy variable that takes 1 if an individual is white and takes 0 otherwise
and male is a dummy variable that takes 1 if an individual is male and takes 0 otherwise. The
estimated coefﬁcients b , b4, a5d b are p6sitive, but none of them is statistically signiﬁcant
at 1% level. The sum of squared residuals SSE of this mode

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