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Hypothesis Testing in Demand Systems: Some Examples of Size Corrections Using Edgeworth Approximations

Published online by Cambridge University Press:  18 October 2010

Ray Byron  and
Mercedes C. Rosalsky
Ray Byron*
Affiliation:
Australian National University
Mercedes C. Rosalsky
Affiliation:
University of Florida, Gainesville
*
*To whom correspondence should be addressed: Dr. R. P. Byron, Department of Statistics, Australian National University, P.O. Box 4, Canberra, A.C.T. 2601, Australia.
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Abstract

A size correction to adjust the critical values of asymptotic χ2 tests in a SUR context has been developed by Rothenberg and verified by Phillips. The adjustment centers the distribution of the observed test statistic so that it coincides more closely with its hypothetical distribution. The correction itself is an approximation to O(T−1), and while the adjustment should be superior to the asymptotic test (no adjustment) in small-sample situations, its performance can be expected to deteriorate as the sample size decreases. The Edgeworth corrections, using formulas provided by Phillips, are calculated for the Wald, likelihood ratio, and Lagrange multiplier tests in the context of symmetry testing in demand analysis using the Laitinen–Meisner simulated data set. The sample consists of 31 observations and the corrections were “adequate to useful” in the context of 5, 8, and 11 equations. However, in the extreme case of 14 equations the corrections typically only took up 60% of the adjustment required. The computational cost of calculating the Edgeworth correction for large SUR systems with a large number of restrictions also turns out to be quite heavy. The conclusion reached is that while Edgeworth corrections are not totally satisfactory, they are easy to include in a program and provide a useful critical value correction.

Type
Brief Report
Information
Econometric Theory , Volume 1 , Issue 3 , December 1985 , pp. 403 - 408
Copyright
Copyright © Cambridge University Press 1985 

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References

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