econ

ECON 360 - Econometrics

Professor Victoria Prowse

Homework 2

Total points available: 18 (credit is equal to points scored divided by 3)

Question 1. Consider the population model y = β0 + β1x + u. Suppose that you have a

sample of size n. The OLS estimator of β1 is given by:

β̂1 =

∑n i=1(xi − x̄)yi∑n i=1(xi − x̄)2

.

a) Clearly stating any assumptions that you make, show that β̂1 is an unbiased esti-

mator of β1. [4 points]

b) Write down the formula for the variance of β̂1. [1 point]

c) List and discuss three factors that affect the variance of β̂1. [3 points]

Question 2. Consider the fitted multiple regression model ŵagei = β̂0 +β̂1educi +β̂2expi,

where wage is the hourly wage (in dollars), educ is years of schooling, and exp is year of

experience in employment. Suppose that educi and expi are negatively correlated.

a) Do you expect β̂1 and β̂2 to be positive or negative? Why? [2 points]

b) Interpret β̂2. [1 point]

c) Suggest a reason for the negative correlation between experience and education. [1

point]

d) What is the sign of δ̃1 in the following regression? Why? [2 point]

ẽxpi = δ̃0 + δ̃1educi.

e) Write down an equation that links β̂1 to β̃1, where β̃1 is defined by fitted simple

regression w̃agei = β̃0 + β̃1educi. [1 point]

f) Using your answer to the previous question, explain whether β̃1 will overestimate

or underestimate β̂1. [3 points].

1