let yi xi 1 le i le n be an iid sequence of

Question

Let {(y_i; x_i); 1 ≤ i ≤ n} be an i.i.d sequence of random variables where yi and xi satisfy the linear relationship y_i = β₀ + β₁x_i + ∈_i with Cov(x_i; ∈_i) = 0 and y_i ∈ {0, 1} (i.e. yi is a binary dependent variable).

(a) Describe the main limitations of estimating β₁ via OLS.

(b) Describe an alternative approach to estimation based on the Probit Model. Note that I expect you to be able to formulate the likelihood function.