Stochastic specification and the estimation of share equations

The standard stochastic specification for a system of share equations is obtained by assuming that the shares have a joint normal distribution with means depending upon exogenous variables and a constant covariance matrix. This specification ignores the requirement that shares be between zero and unity by giving positive probability to shares outside this range. An alternative stochastic specification involving the Dirichlet distribution, which automatically limits shares to the unit simplex, is suggested. A comparison of results obtained from the two specifications is made using sampling experiments and data from three different empirical studies. The sampling experiments and empirical applications show that the results are generally quite close, thus providing some justification for the continued use of the normal distribution specification in the estimation of share equations.