A ‘random coefficient’ model of the relationship between a random series y1,…, yT and a1,…, aT , a collection of observed constants, is yt = at(???? + ut), where ut ∼ i.i.d.(0, ????2). Compare and contrast the following proposed estimators of ????.

(a) The sample mean of the series y1∕a1, · · · , yT∕aT .

(b) Least squares regression of yt onto at.

(c) The ratio

̄y

̄a, where ̄y and ̄a are the sample means of the two series.