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The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation
| Resumo: | This paper presents a new method to approximate the inverse of the spatial lag operator, used in the estimation of spatial lag models for binary dependent variables. The related matrix operations are approximated as well. Closed formulas for the elements of the approximated matrices are deduced. A GMM estimator is also presented. This estimator is a variant of Klier and McMillen’s iterative GMM estimator. The approximated matrices are used in the gradients of the new iterative GMM procedure. Monte Carlo experiments suggest that the proposed approximation is accurate and allows to significantly reduce the computational complexity, and consequently the computational time, associated with the estimation of spatial binary choice models, especially for the case where the spatial weighting matrix is large and dense. Also, the simulation experiments suggest that the proposed iterative GMM estimator performs well in terms of bias and root mean square error and exhibits a minimum trade-off between computational time and unbiasedness within a class of spatial GMM estimators. Finally, the new iterative GMM estimator is applied to the analysis of competitiveness in the U.S. Metropolitan Statistical Areas. A new definition for binary competitiveness is introduced. The estimation of spatial and environmental effects are addressed as central issues. |
|---|---|
| Autores principais: | Santos, Luís Silveira |
| Outros Autores: | Proença, Isabel |
| Assunto: | Matrix Approximation Matrix Factorization Spatial Binary Choice Model Spatial Lag Operator Inverse Competitiveness Environmental Effects |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| _version_ | 1866811150505607168 |
|---|---|
| author | Santos, Luís Silveira |
| author2 | Proença, Isabel |
| author2_role | author |
| author_facet | Santos, Luís Silveira Proença, Isabel |
| author_role | author |
| contributor_name_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Santos, Luís Silveira\"},{\"Person.name\":\"Proença, Isabel\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| datacite.creators.creator.creatorName.fl_str_mv | Santos, Luís Silveira Proença, Isabel |
| datacite.date.Accepted.fl_str_mv | 2019-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2023-08-03T18:16:53Z |
| datacite.date.embargoed.fl_str_mv | 2023-08-03T18:16:53Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Matrix Approximation Matrix Factorization Spatial Binary Choice Model Spatial Lag Operator Inverse Competitiveness Environmental Effects |
| datacite.titles.title.fl_str_mv | The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation |
| dc.contributor.none.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| dc.creator.none.fl_str_mv | Santos, Luís Silveira Proença, Isabel |
| dc.date.Accepted.fl_str_mv | 2019-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2023-08-03T18:16:53Z |
| dc.date.embargoed.fl_str_mv | 2023-08-03T18:16:53Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10400.5/28080 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Elsevier |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Matrix Approximation Matrix Factorization Spatial Binary Choice Model Spatial Lag Operator Inverse Competitiveness Environmental Effects |
| dc.title.fl_str_mv | The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | This paper presents a new method to approximate the inverse of the spatial lag operator, used in the estimation of spatial lag models for binary dependent variables. The related matrix operations are approximated as well. Closed formulas for the elements of the approximated matrices are deduced. A GMM estimator is also presented. This estimator is a variant of Klier and McMillen’s iterative GMM estimator. The approximated matrices are used in the gradients of the new iterative GMM procedure. Monte Carlo experiments suggest that the proposed approximation is accurate and allows to significantly reduce the computational complexity, and consequently the computational time, associated with the estimation of spatial binary choice models, especially for the case where the spatial weighting matrix is large and dense. Also, the simulation experiments suggest that the proposed iterative GMM estimator performs well in terms of bias and root mean square error and exhibits a minimum trade-off between computational time and unbiasedness within a class of spatial GMM estimators. Finally, the new iterative GMM estimator is applied to the analysis of competitiveness in the U.S. Metropolitan Statistical Areas. A new definition for binary competitiveness is introduced. The estimation of spatial and environmental effects are addressed as central issues. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://repositorio.ulisboa.pt/bitstreams/b54f9fcc-1b57-4e45-bef3-d3e4ce3d468e/download |
| id | ul_7fd4cede53bc162bf38f2effd51c52c1 |
| identifier.url.fl_str_mv | http://hdl.handle.net/10400.5/28080 |
| instacron_str | ul |
| institution | Universidade de Lisboa |
| instname_str | Universidade de Lisboa |
| language | eng |
| network_acronym_str | ul |
| network_name_str | Repositório da Universidade de Lisboa |
| oai_identifier_str | oai:repositorio.ulisboa.pt:10400.5/28080 |
| organization_str_mv | urn:organizationAcronym:ul |
| person_str_mv | Santos, Luís Silveira Proença, Isabel |
| publishDate | 2019 |
| publisher.none.fl_str_mv | Elsevier |
| reponame_str | Repositório da Universidade de Lisboa |
| repository_id_str | urn:repositoryAcronym:ul |
| service_str_mv | urn:repositoryAcronym:ul |
| spelling | engElsevierpt_PTThis paper presents a new method to approximate the inverse of the spatial lag operator, used in the estimation of spatial lag models for binary dependent variables. The related matrix operations are approximated as well. Closed formulas for the elements of the approximated matrices are deduced. A GMM estimator is also presented. This estimator is a variant of Klier and McMillen’s iterative GMM estimator. The approximated matrices are used in the gradients of the new iterative GMM procedure. Monte Carlo experiments suggest that the proposed approximation is accurate and allows to significantly reduce the computational complexity, and consequently the computational time, associated with the estimation of spatial binary choice models, especially for the case where the spatial weighting matrix is large and dense. Also, the simulation experiments suggest that the proposed iterative GMM estimator performs well in terms of bias and root mean square error and exhibits a minimum trade-off between computational time and unbiasedness within a class of spatial GMM estimators. Finally, the new iterative GMM estimator is applied to the analysis of competitiveness in the U.S. Metropolitan Statistical Areas. A new definition for binary competitiveness is introduced. The estimation of spatial and environmental effects are addressed as central issues.application/pdfpt_PTThe inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximationSantos, Luís SilveiraProença, IsabelHostingInstitutionOrganizationalRepositório Científico de Acesso Aberto da ULisboae-mailmailto:repositorio@reitoria.ulisboa.ptrepositorio@reitoria.ulisboa.ptISSNIsPartOf0166-0462DOIIsPartOf10.1016/j.regsciurbeco.2019.01.0032023-08-03T18:16:53Z20192019-01-01T00:00:00ZHandlehttp://hdl.handle.net/10400.5/28080http://purl.org/coar/access_right/c_abf2open accessMatrix ApproximationMatrix FactorizationSpatial Binary Choice ModelSpatial Lag Operator InverseCompetitivenessEnvironmental Effects1268150 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorio.ulisboa.pt/bitstreams/b54f9fcc-1b57-4e45-bef3-d3e4ce3d468e/download |
| spellingShingle | The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation Santos, Luís Silveira Matrix Approximation Matrix Factorization Spatial Binary Choice Model Spatial Lag Operator Inverse Competitiveness Environmental Effects |
| status | SINGLETON |
| subject.fl_str_mv | Matrix Approximation Matrix Factorization Spatial Binary Choice Model Spatial Lag Operator Inverse Competitiveness Environmental Effects |
| title | The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation |
| title_full | The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation |
| title_fullStr | The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation |
| title_full_unstemmed | The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation |
| title_short | The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation |
| title_sort | The inversion of the spatial lag operator in binary choice models: Fast computation and a closed formula approximation |
| topic | Matrix Approximation Matrix Factorization Spatial Binary Choice Model Spatial Lag Operator Inverse Competitiveness Environmental Effects |
| topic_facet | Matrix Approximation Matrix Factorization Spatial Binary Choice Model Spatial Lag Operator Inverse Competitiveness Environmental Effects |
| url | http://hdl.handle.net/10400.5/28080 |
| visible | 1 |