A COMPANION TO Theoretical Econometrics

Seemingly Unrelated. Regression

Denzil G. Fiebig*

1 Introduction

Seemingly unrelated regression (SUR) is one of the econometric developments that has found considerable use in applied work. Not all theoretical develop­ments find their way immediately into the toolkit of the practitioner, but SUR is one of those which has. The popularity of the model is related to its applicability to a large class of modeling and testing problems and also the relative ease of estimation. Empirical studies that utilize SUR have been supported by a con­siderable amount of theoretical development; consequently much is known about the basic model and the extensions needed to accommodate more complex problems.

As noted by Griliches and Intriligator (1983, p. xiii) "The historical evolution of econometrics was driven both by the increased availability of data and by the desire of generations of scientists to analyze such data in a rigorous and coherent fashion." SUR falls neatly into this characterization. The increased availability of data representing a sample of cross-sectional units observed over several time periods provides researchers with a potentially rich source of information. At the same time, the nature of the data necessitates careful consideration of how regre­ssion parameters vary (if at all) over the cross-sectional and time series dimen­sions and the appropriate specification of the disturbance covariance matrix. SUR is able to provide estimates of how relationships can potentially vary over the data dimensions as well as providing a convenient vehicle for testing hypoth­eses about these relationships. The specification of the basic SUR model as first introduced by Zellner (1962) remains an important option in any modeling exer­cise using pooled data.

Given the voluminous growth in the SUR literature, this chapter is necessarily selective. Material found in the survey paper of Srivastava and Dwivedi (1979)

and the book by Srivastava and Giles (1987) serve to provide a good coverage of the literature until the mid to late 1980s. We concentrate on the more recent developments. While the SUR model has had a significant impact outside eco­nomics and business, these studies have largely been ignored to provide further focus for this current chapter.

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