Sampling Distribution of OLS Under a Logit Model. This is based on Baltagi (2000). Consider a simple logit regression model yt = (xt) + ut

Sampling Distribution of OLS Under a Logit Model. This is based on Baltagi (2000).

Consider a simple logit regression model yt = Λ(βxt) + ut for t = 1, 2, where Λ(z) = ez/(1 + ez) for −∞ < z < ∞. Let β = 1, x1 = 1, x2 = 2 and assume that the ut’s are independent with mean zero.

(a) Derive the sampling distribution of the least squares estimator of β, i.e., assuming a linear probability model when the true model is a logit model.

(b) Derive the sampling distribution of the least squares residuals and verify the estimated variance of βOLS is biased.