Testing overidentifying restrictions with a restricted parameter space. (English) Zbl 1431.62027
Summary: We show that the standard test for testing overidentifying restrictions, which compares the J-statistic [L. P. Hansen, Econometrica 50, 1029–1054 (1982; Zbl 0502.62098)] to \(\chi^2\) critical values, does not control asymptotic size when the true parameter vector is allowed to lie on the boundary of the (optimization) parameter space. We also propose a modified J-statistic that, under the null hypothesis, is asymptotically \(\chi^2\) distributed, such that the resulting test does control asymptotic size.
Citations:
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