Chapter 14 The Use of Restricted Regressions in Estimating Demand Systems
Quantifying Consumer Preferences
ISBN: 978-1-84855-312-5, eISBN: 978-1-84855-313-2
Publication date: 29 May 2009
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 method. But the linear restriction case allows a simple method for adding and removal of restrictions.
In this chapter, we derive a general relationship that allows the conversion between the two forms of the restricted models. Examples emphasizing systems of demand equations, polynomial lagged equations, and splines are given in which the transformation from one form to the other are demonstrated as well as the combination of both forms of restrictions. In addition, we demonstrate how an alternative Wald test of the restrictions can be constructed using an augmented version of the reparameterized model.
Keywords
Citation
Hirschberg, J.G., Lye, J.N. and Slottje, D.J. (2009), "Chapter 14 The Use of Restricted Regressions in Estimating Demand Systems", Slottje, D.J. (Ed.) Quantifying Consumer Preferences (Contributions to Economic Analysis, Vol. 288), Emerald Group Publishing Limited, Leeds, pp. 363-381. https://doi.org/10.1108/S0573-8555(2009)0000288017
Publisher
:Emerald Group Publishing Limited
Copyright © 2009, Emerald Group Publishing Limited