[Note: This **will be handed out in lab** this week.]

Economics 421/521

Winter 2006

Homework #1

[PDF FILE]

**Part I. Hypothesis Testing **

1. Suppose that you estimate a model of house prices to determine the impact
of having beach frontage on the value of a house. After researching the problem,
you decide to use the size of the lot instead of the size of the house as your
explanatory variable for a number of theoretical and data availability reasons.
The results (standard errors in parentheses) are:

PRICEi = 40 + 35.0 LOTi – 2.0 AGEi + 10.0 BEDi – 4.0 FIREi + 100 BEACHi

(29) (5.0) (1.1) (10.0) (3.0) (9.0)

where n = 30, R2 = .63, and PRICEi = the price of
the ith house (in thousands of dollars), LOTi = the size of the lot of the ith
house (in thousands of square feet), AGEi = the age of the ith house in years,
BEDi = the number of bedrooms in the ith house, FIREi = a dummy variable for a
fireplace (1 = yes for the ith house), and BEACHi = a dummy for having beach frontage
(1 = yes for the ith house).

a) You expect the variables LOT, BED, and BEACH to have positive
coefficients. Test this hypothesis at the 5 percent level.

b) You expect AGE to
have a negative coefficient. Test this hypothesis at the 10 percent level.

c) At
first you expect FIRE to have a positive coefficient, but one of your friends
says that fireplaces are messy and are a pain to keep clean, so you are not
sure. Run a two-sided t-test around zero to test the two-sided hypothesis at the
5 percent level.

d) What problems appear to exist in your equation? (Hint: Do
you have any unexpected signs? Do you have any coefficients that are not
significantly different from zero?)

e) Which of the problems that you outline in
part d above is the most worrisome? Explain.

2. Consider the following regression:

log(Qci) = 921.6 – 1.3 log(Pci) + 0.7 log(Pai) + 11.4 log(Inci)

(121) (0.3) (0.05) (2.8)

where n = 30, R2 = 0.82, and where Qci = the total sales of CAMRY
in the ith city in 2003, Pci = the price of a CAMRY in the ith city in
2003 (in thousands), Pai = the price of an ACCORD in the ith city in
2003 (in thousands), and Inci = the average income in the ith city, the
year of 2003 (in thousands). The numbers in the parentheses are
standard errors.

a) How is the constant term interpreted?

b) How would you interpret
the coefficient on log(Pci). Be explicit and explain, in terms of economic
theory, the importance of its magnitude.

c) Get t-values for the coefficients in
the regression. Are all of our coefficients statistically significant at the 5%
level of significance? How about at the 1% level of significance?

d) Interpret
R2. Can we have a negative R2?

**Part II. Short Answer**

1. State the Gauss-Markov Theorem and explain the term BLUE.

**Part III. Textbook Problems **

1. Chapter 5, Question 5.8., parts a and b only.

2. Chapter 5, Question 5.16.

3. Chapter 8, Question 8.14.

4. Chapter 8, Question 8.17.