HANDOUT 8

Question 1

Equation showing mis-recorded X variable

Answer 1

Xi* = Xi + Ui
recorded = actual + an error term

Question 2

What do we assume about the misrecordings?

Answer 2

That they are purely random
Ui - N(0, sigma^2 u)
Average mistake is zero
Constant variance in mistakes across all i.

Question 3

What is the issue with measurement error in the explanatory variable?

Answer 3

New error term = €i - B1Ui
COV(Xi*, (€i - B1Ui)) = COV(€i, Xi*) 
-B1 COV(Xi*, Ui)
First covariance is 0, second we have -B1(+VE) ≠ 0 --> biased coefficients
E(b1) < B1

Question 4

What is COV(Xi*, Ui)?

Answer 4

COV(Xi, Ui) = E(Xi x Ui) = E(Xi x Ui) + E(Ui^2) = sigma^2 u ≠ 0

Question 5

Solution to measurement error in the explanatory variable

Answer 5

IV ESTIMATION

- use whenever we have a non-zero covariance between explanatory variables and the error term

Question 6

Is measurement error in the dependent variable an issue? Why/why not?

Answer 6

NOT AN ISSUE as long as Ui is PURELY RANDOM. Because Xi is still unrelated to the error term (€i + Ui) so E(b1) = B1 –> UNBIASED