In this paper we study the properties of the ordinary least squares estimator ofthe coefficients of linear macor models when the coefficients of linear micro relations are random with identical mean and variance. It is shown that the ordinary least squares estimator is equal to a minimum variance linear unbiased estimator of the coefficients of a linear macro equation obtained by aggregating over all micro relations. Futher, some problems associated with estimating the covariance matrix of the ordinary least squares estimator, using only aggregate data, are indicated.