Linear Probability Model

Question 1

What makes the Linear Probability Model different to a normal model

Answer 1

• The dependent variable becomes a dummy variable
• This means that it becomes a probability

Question 2

What is the random variable that takes values 0 and 1

Answer 2

• The bernoulli random variable
• Where y = 1 with probability p and y = 0 with probability (1-p)

Question 3

What is the expected value and variance of the Bernoulli

Answer 3

• E(y) = p
• Var(y) = p(1-p)

Question 4

How are b0 and bx interpreted in the Linear probability model

Answer 4

• b0 is the average probability of y
• b1 is the increase/decrease in probability for each unitary increase/decrease in x

Question 5

What is the main criticism of the LPM

Answer 5

• The fitted values from an OLS regression are never guaranteed to be between zero and one
• This means that probabilities may end up being greater than 1 or less than 0

Question 6

What is another criticism of the LPM

Answer 6

• The bernoulli random variable has heteroskedastic variance
• Linear regression requires homoscedastic variance