Two Kinds of Pooling Information in Cross-Sectional Regression Model

Summary

This paper discusses two types of information pooling in cross-section and time series models: Pooling information by variance components and pooling information by a hierarchical regression model. The pooling problem with variance components was first discussed in Balestra and Nerlove (1966) for the special case of one variance component. The structure of the estimate was further investigated by Maddala (1971) and Learner (1978). In section 2 we show that the general case with two variance components can be expressed as matrix weighted averages and the resulting set of estimates are given by the so-called information contract curve (Learner (1978)). The reader is referred to Balestra and Nerlove (1966) and Wallace and Hussain (1969) for estimation problems of the variance components and asymptotic behavior of the estimates.

The second type of pooling is the so-called hierarchical model and discussed in section 3. Now we admit, that in the first stage the regression coefficients can be different for every block, but we assume in the second stage, that they belong to a common distribution. This model is equivalent to a random coefficient model (see Swamy (1971)) or a hierarchical model, developed by Lindley and Smith (1972) for a Bayesian analysis. Two types of models are discussed, based on the notion of exchangeability between regression vectors and within regression vectors.