The Reparameterization of Linear Models Subject to Exact Linear Restrictions

The estimation of regression models subject to exact linear restrictions, is a widely applied technique, however, aside from simple examples, the reparameterization method is rarely employed except in the case of polynomial lags. 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. In many cases the reparameterization method is computationally more efficient especially when estimation involves an iterative method. The general relationship that converts the two forms of the restricted model is derived. Examples involving systems of demand equations, polynomial lagged equations, and Splines are given in which the transformation from one form to the other are demonstrated. In addition, we demonstrate how a Wald test of the restrictions can be constructed using an augmented version of the reparameterized model. A computer program example is presented to demonstrate the equivalence.