[Note: Homework 1 and homework 2 will both be due in lab in week 3.]

Economics 421/521

Winter 2012

Homework #1

**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 LOT_{i}– 2.0 AGE_{i}+ 10.0 BED_{i}– 4.0 FIRE_{i}+ 100 BEACH_{i}(29) (5.0) (1.1) (10.0) (3.0) (9.0)

where n = 30, R2 = .63, and PRICE_{i} = the price of the i^{th} house (in thousands of dollars), LOT_{i} = the size of the lot of the i^{th} house (in thousands of square feet), AGE_{i} = the age of the i^{th} house in years, BED_{i} = the number of bedrooms in the i^{th} house, FIRE_{i} = a dummy variable for a fireplace (1 = yes for the ith house), and BEACH_{i} = 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 each of these hypotheses 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.

2. Consider the following regression:

log(Qc_{i}) = 921.6 – 1.3 log(Pc_{i}) + 0.7 log(Pa_{i}) + 11.4 log(Inc_{i}) (121) (0.3) (0.05) (2.8)

where n = 30, R2 = 0.82, and where Qc_{i} = the total sales of CAMRY in the ith city in 2003, Pc_{i} = the price of a CAMRY in the i^{th} city in 2003 (in thousands), Pa_{i} = the price of an ACCORD in the i^{th} city in 2003 (in thousands), and Inc_{i} = the average income in the i^{th} 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(Pc_{i}). 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 R^{2}. Can we have a negative R^{2}?

**Part II. Short Answer**

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

**Part III. Estimation **

1. Given data on M2, real GDP, and the T-bill rate, estimate the following regression and test whether the coefficients differ from zero. Do the coefficients have the expected signs?:

M

_{t}= β_{0}+ β_{1}RGDP_{t}+ β_{2}Tbill_{t}+ e_{t}

Don't be surprised if the fit is very good. We'll explain why the good fit is misleading in this model later in the course.

Economics 421/521

Winter 2012

Homework #2

1. Using the EAEF data set, regress LGEARN on S, EXP, and ASVABC. Use F-tests to determine whether the coefficients on S and EXP are (a) jointly significant, and (b) equal. [Parts (a) and (b) are two separate tests.]

**Note**: Here are the variable definitions (see pages. 443-444 in Appendix B of the text):

- EARNINGS = current hourly earnings in $ reported in 2002 interview.
- S = Years of schooling (highest grade completed as of 2002).
- EXP = Total out-of-school work experience (years) as of the 2002 interview.
- ASVABC = Scaled standardized test score.

2. Problem 7.1 in the text.

3. Using this data set, repeat the example from class for the first of the three cases we discussed, i.e. first regress the log of salary on a constant and the two variables proxying for experience, years and years^{2}:

log(salary) = β_{0} + β_{1}*years + β_{2}*years^{2} + u_{t}

Then, form the estimated residual squared (resid^{2}) and perform the LM test for heteroskedasticity (note: resid is the estimated value of u_{t}).

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