Week 12: Binary Outcome Models and Maximum Likelihood Estimation

Question 1

How else can we evaluate estimators?

Answer 1

Evaluating their asymptotic properties.

Question 2

What are asymptotic properties?

Answer 2

What happens when the sample size grows to infinity.

Question 3

List 2 facts that are true if the sample was to grow to infinity.

Answer 3

• If n → ∞, our estimator should get closer and closer to the estimand (consistency)
• If n → ∞, the sampling distribution of our estimator should get closer and closer to the normal distribution (asymptotic normality)

Question 4

List the 3 features of the OLS estimator.

Answer 4

• Unbiased: in expectation it produces the true parameters (βs and σ^2), under certain conditions
• Consistent: as n → ∞, we get increasingly close to the true parameters
• Normally Distributed in large samples

Question 5

What is the Gauss-Markov Theorem?

Answer 5

The OLS estimator is BLUE – the Best Linear Unbiased
Estimator.

Question 6

List 5 assumptions of the Gauss-Markov Theorem.

Answer 6

• The true model is a linear function of the parameters
• The observations are randomly sampled
• No explanatory variable (X) is constant, and there is no ‘perfect multicollinearity’ (no X is a linear combination of other Xs)
• The expected value of εi conditional on xi is 0 (zero conditional mean assumption). Rules out bias from omitted variables
• The variance of the errors is constant (homoscedasticity)