INFERENCE WHEN A NUISANCE PARAMETER IS NOT IDENTIFIED UNDER THE NULL HYPOTHESIS

Authors
Citation
Be. Hansen, INFERENCE WHEN A NUISANCE PARAMETER IS NOT IDENTIFIED UNDER THE NULL HYPOTHESIS, Econometrica, 64(2), 1996, pp. 413-430
Citations number
23
Categorie Soggetti
Economics,"Social Sciences, Mathematical Methods","Mathematical, Methods, Social Sciences
Journal title
ISSN journal
00129682
Volume
64
Issue
2
Year of publication
1996
Pages
413 - 430
Database
ISI
SICI code
0012-9682(1996)64:2<413:IWANPI>2.0.ZU;2-8
Abstract
Many econometric testing problems involve nuisance parameters which ar e not identified under the null hypotheses. This paper studies the asy mptotic distribution theory for such tests. The asymptotic distributio ns of standard test statistics are described as functionals of chi-squ are processes. In general, the distributions depend upon a large numbe r of unknown parameters. We show that a transformation based upon a co nditional probability measure yields an asymptotic distribution free o f nuisance parameters, and we show that this transformation can be eas ily approximated via simulation. The theory is applied to threshold mo dels, with special attention given to the so-called self-exciting thre shold autoregressive model. Monte Carlo methods are used to assess the finite sample distributions. The tests are applied to U.S. GNP growth rates, and we find that Potter's (1995) threshold effect in this seri es can be possibly explained by sampling variation.