lecture 6

Question 1

why do we use often use multiple regression models

Answer 1

omitted variables, show the true model

Question 2

what happens when the omitted variable is left out

Answer 2

it is absorbed into the error term, becomes an underspecified model

Question 3

why do we have u = SE

Answer 3

• vertical distance from the point to the line
• there are other factors influencing Y that aren’t in our regressive model

Question 4

what are the consequences of an omitted variable (underspecified model)

Answer 4

violate our 3 assumptions, starting with zero conditional mean because we cannot find 0 covariance and X and Y are not uncorrelated
- OLS estimators WILL NOT be unbiased
- OLS estimators WILL NOT be consistent

Question 5

if OLS is biased then

Answer 5

as X increases SE is not increasing or decreasing is not true

Question 6

how to sign the omitted variable bias

Answer 6

sign of the omitted variable bias = sign of B2 x sign between X and the omitted variable
how right side effects the left, positively or negatively

Question 7

bias is positive

Answer 7

sign of B2 x sign between X and the omitted variable = same sign
- larger than the true answer
upward bias

Question 8

bias is negative

Answer 8

sign of B2 x sign between X and the omitted variable - opposite signs
- estimate is smaller than the true answer
- downward bias

Question 9

if B2 or Cov(X,Z) = 0

Answer 9

then we can still get to zero, implying the omitted variable is irrelevant

Question 10

cases when omitting a variable does not result in omitted variable bias

Answer 10

1. B2 = 0, if the omitted variable does not influence y
2. cov(X,Y) or corr(X,Y) = 0

Question 11

example of omitted variable bias: foreign aid and growth

Answer 11

true model: growth = Bo + B1foreign aid + B2 poverty + v
underspecified= growth = Bo + B1foreign aid + u
sign of B2: negative, people who are poor are less effective
sign of correlation between X(foreign aid) and the omitted variable(poverty): positive, foreign aid is given more often to countries with poverty
bias is negative

Question 12

how to eliminate omitted variable bias

Answer 12

add the omitted variable as a regressor

Question 13

what does multiple regressors do to minimizing the sum of squared residuals

Answer 13

3 FOC,
1. u caret i = 0
2. u caret i Xi = 0
3. u caret i Zi = 0