[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 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 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(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. 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?:
Mt = β0 + β1RGDPt + β2Tbillt + et
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.