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The Reparametrization of Linear Models Subject to Exact Linear Restrictions

Author

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  • Hirschberg, J.G.
  • Slottje, D.J.

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.

Suggested Citation

  • Hirschberg, J.G. & Slottje, D.J., 1999. "The Reparametrization of Linear Models Subject to Exact Linear Restrictions," Department of Economics - Working Papers Series 702, The University of Melbourne.
  • Handle: RePEc:mlb:wpaper:702
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    Cited by:

    1. Mishra, Ashok K. & Harris, James Michael & Erickson, Kenneth W. & Hallahan, Charles B., 2008. "What Drives Agricultural Profitability in the U.S.: Application of the DuPont Expansion Model," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6413, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

    More about this item

    Keywords

    ECONOMIC MODELS ; CONSUMPTION ; MATHEMATICAL ANALYSIS;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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