[This note develops a slightly different formulation of one of the basic results presented in a recent paper by Wallace and Hussain [5] on error components models for disturbances in relationships designed to explain cross-sectional observations over time. In their discussion, Wallace and Hussain derive the inverse of the variance-covariance matrix of the disturbances by trial and error. Unfortunately, their formulation does lead to a "natural" interpretation of the generalized least squares estimates, or of the relationships of these estimates to other estimates in the same way diagonalization of the variance-covariance matrix by means of an appropriate orthogonal transformation does. The characteristic roots of the variance-covariance matrix for the disturbances in a three component model which has been studied by Wallace and Hussain are derived here. It is shown how knowledge of these roots and the characteristic vectors associated with them leads to a form of the inverse matrix which may be more readily interpreted, as well as a number of other useful results, including an interpretation of the poor small sample properties of estimates which incorporate dummy variables for each individual.]

[Availability of data on a large number of individuals, but on each individual only over a very short period of time, has become increasingly common in a number of different fields in economics. Very often we would like to use such data to study behavioral relationships that are dynamic in character, i.e., that contain a distributed lag or other form of autogressive relationship. Since only a few observations are available over time, but a great many observations are available for different individuals at a point in time, it is exceptionally important to make the most efficient use of the data across individuals to estimate that part of the behavioral relationship containing variables that differ substantially from one individual to another, in order that the lesser amount of information over time can be used to best advantage in the estimation of the dynamic part of the relationship studied. As it turns out, the problem is far from simple: obvious devices such as the pooling of all observations and estimation by ordinary least squares, or the introduction of dummy variables for individuals, produce estimates having serious small sample bias. In earlier papers, the author and others have formulated a simple variance components model for the disturbance term in a relationship to be estimated from cross section data over time. This paper presents a series of Monte Carlo studies designed to explore the small sample properties of various types of estimates within this context. Not only is the bias of the obvious methods of estimation mentioned above confirmed, but certain serious deficiencies of the maximum likelihood approach which had been suspected earlier are also confirmed. A two-round estimation procedure is proposed which appears to work well for a wide variety of parameter values.]