Estimation of Two-States Proportional Hazard Rates Models with Unobserved Heterogeneity

This article examines two-state proportional hazard rate models with unobserved heterogeneity specific to each state, a framework that is especially relevant for labor market transitions. To make estimation feasible in large longitudinal datasets, we implement hshaz2s, a Stata routine that uses anal...

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Detalles Bibliográficos
Autores: Congregado Ramírez de Aguilera, Emilio, Troncoso Ponce, David, Rubino, Nicola, Morales Kirioukhina, Alejandro
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universidad de Huelva (UHU)
Repositorio:Arias Montano. Repositorio Institucional de la Universidad de Huelva
Idioma:inglés
OAI Identifier:oai:dnet:ariasmontano::c6d3ed4cfa2748090cb99411128b0380
Acceso en línea:https://hdl.handle.net/10272/28264
Access Level:acceso abierto
Palabra clave:Duration models
Unobserved heterogeneity
D2 ml method
Hshaz2s
Gradient vector
Hessian matrix
Multistate duration models
Proportional hazard rates models
5302 Econometría
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spelling Estimation of Two-States Proportional Hazard Rates Models with Unobserved HeterogeneityCongregado Ramírez de Aguilera, EmilioTroncoso Ponce, DavidRubino, NicolaMorales Kirioukhina, AlejandroDuration modelsUnobserved heterogeneityD2 ml methodHshaz2sGradient vectorHessian matrixMultistate duration modelsProportional hazard rates models5302 EconometríaThis article examines two-state proportional hazard rate models with unobserved heterogeneity specific to each state, a framework that is especially relevant for labor market transitions. To make estimation feasible in large longitudinal datasets, we implement hshaz2s, a Stata routine that uses analytical expressions for the gradient vector and Hessian matrix of the log-likelihood function through the dual second-order moment (d2 ml) method. The empirical application estimates a discrete-time duration model for transitions between employment and unemployment using Spanish labor market microdata for young low-skilled workers over 2000–2019. The results show that apprenticeship contracts are associated with lower exit rates from employment than other temporary contracts, but not with faster transitions from unemployment back into employment. The estimates also reveal substantial state-specific unobserved heterogeneity, with a large latent group characterized by persistent spells in both states. Analytical second-order information also markedly reduces convergence time under richer heterogeneity structures. Overall, the article makes this class of two-state hazard models operational for applied research and provides new evidence on apprenticeship and temporary contracts in Spain.MDPI20262026-01-0120262026-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10272/28264reponame:Arias Montano. Repositorio Institucional de la Universidad de Huelvainstname:Universidad de Huelva (UHU)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:dnet:ariasmontano::c6d3ed4cfa2748090cb99411128b03802026-06-02T14:58:11Z
dc.title.none.fl_str_mv Estimation of Two-States Proportional Hazard Rates Models with Unobserved Heterogeneity
title Estimation of Two-States Proportional Hazard Rates Models with Unobserved Heterogeneity
spellingShingle Estimation of Two-States Proportional Hazard Rates Models with Unobserved Heterogeneity
Congregado Ramírez de Aguilera, Emilio
Duration models
Unobserved heterogeneity
D2 ml method
Hshaz2s
Gradient vector
Hessian matrix
Multistate duration models
Proportional hazard rates models
5302 Econometría
title_short Estimation of Two-States Proportional Hazard Rates Models with Unobserved Heterogeneity
title_full Estimation of Two-States Proportional Hazard Rates Models with Unobserved Heterogeneity
title_fullStr Estimation of Two-States Proportional Hazard Rates Models with Unobserved Heterogeneity
title_full_unstemmed Estimation of Two-States Proportional Hazard Rates Models with Unobserved Heterogeneity
title_sort Estimation of Two-States Proportional Hazard Rates Models with Unobserved Heterogeneity
dc.creator.none.fl_str_mv Congregado Ramírez de Aguilera, Emilio
Troncoso Ponce, David
Rubino, Nicola
Morales Kirioukhina, Alejandro
author Congregado Ramírez de Aguilera, Emilio
author_facet Congregado Ramírez de Aguilera, Emilio
Troncoso Ponce, David
Rubino, Nicola
Morales Kirioukhina, Alejandro
author_role author
author2 Troncoso Ponce, David
Rubino, Nicola
Morales Kirioukhina, Alejandro
author2_role author
author
author
dc.contributor.none.fl_str_mv
dc.subject.none.fl_str_mv Duration models
Unobserved heterogeneity
D2 ml method
Hshaz2s
Gradient vector
Hessian matrix
Multistate duration models
Proportional hazard rates models
5302 Econometría
topic Duration models
Unobserved heterogeneity
D2 ml method
Hshaz2s
Gradient vector
Hessian matrix
Multistate duration models
Proportional hazard rates models
5302 Econometría
description This article examines two-state proportional hazard rate models with unobserved heterogeneity specific to each state, a framework that is especially relevant for labor market transitions. To make estimation feasible in large longitudinal datasets, we implement hshaz2s, a Stata routine that uses analytical expressions for the gradient vector and Hessian matrix of the log-likelihood function through the dual second-order moment (d2 ml) method. The empirical application estimates a discrete-time duration model for transitions between employment and unemployment using Spanish labor market microdata for young low-skilled workers over 2000–2019. The results show that apprenticeship contracts are associated with lower exit rates from employment than other temporary contracts, but not with faster transitions from unemployment back into employment. The estimates also reveal substantial state-specific unobserved heterogeneity, with a large latent group characterized by persistent spells in both states. Analytical second-order information also markedly reduces convergence time under richer heterogeneity structures. Overall, the article makes this class of two-state hazard models operational for applied research and provides new evidence on apprenticeship and temporary contracts in Spain.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-01-01
2026
2026-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10272/28264
url https://hdl.handle.net/10272/28264
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Arias Montano. Repositorio Institucional de la Universidad de Huelva
instname:Universidad de Huelva (UHU)
instname_str Universidad de Huelva (UHU)
reponame_str Arias Montano. Repositorio Institucional de la Universidad de Huelva
collection Arias Montano. Repositorio Institucional de la Universidad de Huelva
repository.name.fl_str_mv
repository.mail.fl_str_mv
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