The use of restricted regressions in estimating demand systems

Abstract

The estimation of regression models subject to linear restrictions is a widely applied technique; however, aside from simple examples, the equivalence between the linear restricted case to the reparameterization and the substitution case is rarely employed. We believe this is due to the lack of a general transformation method for changing from the definition of restrictions in terms of the unrestricted parameters to the equivalent reparameterized model and conversely from the reparameterized model to the equivalent linear restrictions for the unrestricted model. In many cases, the reparameterization method is computationally more efficient especially when estimation involves an iterative met..