In an earlier article (Swamy and Mehta 1975), we formulated a particular decomposition for the coefficient vector in a relationship to be estimated from a time series of cross sections. Specifically, we expressed the coefficient vector as the sum of a common mean vector and two random vectors. One of these random vectors differs among individuals both at a point in time and through time, while the other differs among individuals only. In this article, we state some conditions under which the estimators of the first two moments of the coefficient vector developed in Swamy and Mehta (1975) are weakly consistent and asymptotically normal.