A NOTE ON THE CONSISTENCY OF LS ESTIMATES IN LINEAR MODELS

It is well known that when the random errors are iid. with finite variance, the week andthe strong consistency of LS estimate of multiple regression coefficients are equivalent. Thisnote, by constructing a counter-example, shows that this equivalence no longer holds true incase that the random errors possess only the r-th moment with 1 ≤ r ＜ 2.