In this paper an attempt is made to estimate a regression equation using a time series of cross sections. It is assumed that the coefficient vector is distributed across units with the same mean and the same variance-covariance matrix. The distribution of the coefficient vector is assumed to be invariant to translations along the time axis. A consistent and an asymptotically efficient estimator for the mean vector and an unbiased estimator for the variance-covariance matrix of the coefficient vector have been suggested. Some asymptotic procedures for testing linear hypotheses on the means and the variances of coefficients have been described. Finally, the estimation procedure is applied in the analysis of annual investment data, 1935-54, for eleven firms.