[Note: The assignment will be due next week in lab.]

Economics 421/521

Winter 2011

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.