Share equations in econometrics: A story of repression, frustation 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 unsatis-factory approaches: Some researchers although admitting that shares satisfy a sum constraint simply repressed the fact that shares cannot be norgially dls-tributed. 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 pro-poses 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). Demand-theoretic implications as well as methods of estimation are discussed. An example using German import data illustrates some of the results.