Share equations in econometrics: A story of repression,trustration and dead ends

Share equations play an important role in applied economic research, notably in marketing and demand analysis. Both market shares and budget shares have been used as dependent variables in econometric models which were partly motivated by microeconomic theory. However attempts of econometricians (and other statisticians) to treat share equations adequately led mostly to unsatisfactory approaches: Some researchers although admitting that shares satisfy a sum constraint simply repressed the fact that shares cannot be normally distributed. Some researchers looked in vain for a stochastic specification which at the same time is consistent and allows a flexible covariance structure. Last not least almost nobody has properly taken care of additional problems arising from dynamic share models. The paper discusses these three issues and proposes a possible way out of this dilemma which was first suggested by Aitchison (1982) and has been applied to econometric demand analysis by Considine and Mount (1984). Demandtheoretic implications as well as methods of estimation are discussed. An example using German import data illustrates some of the results. Research for this paper is financially supported by Deutsche Forschungsgemeinschaft, SFB 178 “Internationalisierung der Wirtschaft” at the University of Konstanz. Some results reported in this paper have been achieved jointly with Karl Ringwald whose permission for using unpublished joint work is gratefully acknowledged. Critical remarks by an anonymous referee helped to improve the exposition of the paper.