Consider a regression model yt = x′t ???? + ut t = 1,…, T where ut is identically and independently distributed with mean 0 and variance ????2, and xt = (1 rt) where rt = t modulo 5. Thismeans that rt is the remainder after dividing t by 5, so it takes the values 1, 2, 3, 4, and 0 in sequence.

(a) Show, by citing the relevant results from asymptotic theory, that the regression of yt on xt, with estimator ????̂ , is consistent for ????.

(b) Show, similarly, that √
T(????̂ − ????) is asymptotically normally distributed.

(c) Find the asymptotic variance of ????̂ .