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Article: Asymptotics for threshold regression under general conditions

TitleAsymptotics for threshold regression under general conditions
Authors
KeywordsExtreme value type III distribution
Local information
Non-homogeneous Poisson process
Rapidly varying
Regularly varying
Slowly varying
Stochastic equicontinuity failure
Strong identification
Threshold regression
Treatment effect
Weak identification
Discrete asymptotic distribution
Issue Date2013
Citation
Econometrics Journal, 2013, v. 16, n. 3, p. 430-462 How to Cite?
AbstractThe inference of the threshold point in threshold models critically depends on the assumption that the density of the threshold variable at the true threshold point is continuous and bounded away from zero and infinity. However, violation of this assumption may arise in several econometric contexts such as treatment effects evaluation. This paper presents a thorough characterisation of the asymptotic distributions in the least-squares estimation of such abnormal cases. First, the asymptotic results on the threshold point are different from the conventional case. For example, any convergence rate between zero and infinity is possible; the asymptotic distribution can be discrete, continuous or a mixture of discrete and continuous; the weak limits of the localised objective functions can be non-homogeneous instead of homogeneous compound Poisson processes. Second, this paper distinguishes threshold regression from structural change models by studying a problem unique in threshold regression. Third, the asymptotic distributions of regular parameters are not affected by estimation of the threshold point irrespective of the density of the threshold variable. Numerical calculations and simulation results confirm the theoretical analysis, and the density of the threshold variable in an application is checked to illustrate the relevance of the study in this paper. © 2013 The Author(s). The Econometrics Journal © 2013 Royal Economic Society.
Persistent Identifierhttp://hdl.handle.net/10722/202173
ISSN
2015 Impact Factor: 1.116
2015 SCImago Journal Rankings: 1.665
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorYu, Ping-
dc.contributor.authorZhao, Yongqiang-
dc.date.accessioned2014-08-22T02:57:45Z-
dc.date.available2014-08-22T02:57:45Z-
dc.date.issued2013-
dc.identifier.citationEconometrics Journal, 2013, v. 16, n. 3, p. 430-462-
dc.identifier.issn1368-4221-
dc.identifier.urihttp://hdl.handle.net/10722/202173-
dc.description.abstractThe inference of the threshold point in threshold models critically depends on the assumption that the density of the threshold variable at the true threshold point is continuous and bounded away from zero and infinity. However, violation of this assumption may arise in several econometric contexts such as treatment effects evaluation. This paper presents a thorough characterisation of the asymptotic distributions in the least-squares estimation of such abnormal cases. First, the asymptotic results on the threshold point are different from the conventional case. For example, any convergence rate between zero and infinity is possible; the asymptotic distribution can be discrete, continuous or a mixture of discrete and continuous; the weak limits of the localised objective functions can be non-homogeneous instead of homogeneous compound Poisson processes. Second, this paper distinguishes threshold regression from structural change models by studying a problem unique in threshold regression. Third, the asymptotic distributions of regular parameters are not affected by estimation of the threshold point irrespective of the density of the threshold variable. Numerical calculations and simulation results confirm the theoretical analysis, and the density of the threshold variable in an application is checked to illustrate the relevance of the study in this paper. © 2013 The Author(s). The Econometrics Journal © 2013 Royal Economic Society.-
dc.languageeng-
dc.relation.ispartofEconometrics Journal-
dc.subjectExtreme value type III distribution-
dc.subjectLocal information-
dc.subjectNon-homogeneous Poisson process-
dc.subjectRapidly varying-
dc.subjectRegularly varying-
dc.subjectSlowly varying-
dc.subjectStochastic equicontinuity failure-
dc.subjectStrong identification-
dc.subjectThreshold regression-
dc.subjectTreatment effect-
dc.subjectWeak identification-
dc.subjectDiscrete asymptotic distribution-
dc.titleAsymptotics for threshold regression under general conditions-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1111/ectj.12012-
dc.identifier.scopuseid_2-s2.0-84888125597-
dc.identifier.volume16-
dc.identifier.issue3-
dc.identifier.spage430-
dc.identifier.epage462-
dc.identifier.eissn1368-423X-
dc.identifier.isiWOS:000327305600007-

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