Intro to Econometric Theory Heinz School, Carnegie Mellon University 90-906, Spring 2003-4

Homework #2

1. You have collected a dataset on consumers’ purchases of wine and cars. In particular, for each of 100 consumers, you know the price of their most recent bottle of wine and the price of their most recent car.

\overline{P_{wine}} = 6in$
σ̂_{wine}^{2} = 10
\overline{P_{car}} = 18in$
σ̂_{car}^{2} = 10
Ĉov(P_{w}, P_{c}) = 5

Now, suppose we wish to model the relationship between these two prices as:

P_{c} = β_{0} + β_{1}P_{w} + ϵ  (1)

What are the OLS estimates for β_{0} and β_{1}?

2. Should the clever people at General Motors start distributing expensive wine?

3. Suppose instead we model:

P_{w} = β_{2} + β_{3}P_{c} + ϵ  (2)

What are the OLS estimates for β_{0} and β_{1}?

4. One might expect that β_{1,OLS} = \frac{1}{β_{3,OLS}}. True? Why or why not?

5. Exercise 6 on page 63 of Greene.