2. Asymptotic variance of OLS and heteroskedasticity robust standard errors. Consider

the following regression model:

Y₁ = x;ß+Ui, i = 1, ..., ,

(1)

where x₁ = (1, ₁)': ; a dummy variable taking on the value -1 with probability p/2 > 0, the

value +1 with probability p/2, and the value 0 with probability 1- p. Assume E (u₂|x;) = 0,

and E (u²|x₁) = 2+2₁. Suppose that a random sample (yi, ;), i = 1, ..., n., is available. Let 3 be

the OLS estimator of 3. Recall that the asymptotic variance-covariance matrix of 3 is defined

as the variance-covariance matrix of the distributional limit of √(-3) as n → ∞o. Find an

explicit expression of the asymptotic variance-covariance matrix of 3 in terms of p. How are

the heteroskedasticity robust standard errors of the coefficients of 3 related to the matrix you

have found?