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A parametric test of the negativity of the substitution matrix
Author(s) -
Kodde David A.,
Palm Franz C.
Publication year - 1987
Publication title -
journal of applied econometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.878
H-Index - 99
eISSN - 1099-1255
pISSN - 0883-7252
DOI - 10.1002/jae.3950020306
Subject(s) - wald test , mathematics , statistics , parametric statistics , matrix (chemical analysis) , test statistic , statistic , substitution (logic) , upper and lower bounds , statistical hypothesis testing , econometrics , computer science , mathematical analysis , materials science , composite material , programming language
The negativity of the substitution matrix implies that its latent roots are non‐positive. When inequality restrictions are tested, standard test statistics such as a likelihood ratio or a Wald test are not X 2 ‐distributed in large samples. We propose a Wald test for testing the negativity of the substitution matrix. The asymptotic distribution of the statistic is a mixture of X 2 ‐distributions. The Wald test provides an exact critical value for a given significance level. The problems involved in computing the exact critical value can be avoided by using the upper and lower bound critical values derived by Kodde and Palm (1986). Finally the methods are applied to the empirical results obtained by Barten and Geyskens (1975).