The Reparametrization of Linear Models Subject to Exact Linear Restrictions

Joseph Hirschberg and Daniel Slottje

No 702, Department of Economics - Working Papers Series from The University of Melbourne

Abstract: 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 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.

Keywords: ECONOMIC MODELS; CONSUMPTION; MATHEMATICAL ANALYSIS (search for similar items in EconPapers)
JEL-codes: C51 C63 D12 (search for similar items in EconPapers)
Pages: 32 pages
Date: 1999
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Citations: View citations in EconPapers (1)

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