{"id":"https://openalex.org/W2148287167","doi":"https://doi.org/10.3386/t0308","title":"A, B, C's (and D)'s for Understanding VARs","display_name":"A, B, C's (and D)'s for Understanding VARs","publication_year":2005,"publication_date":"2005-06-01","ids":{"openalex":"https://openalex.org/W2148287167","doi":"https://doi.org/10.3386/t0308","mag":"2148287167"},"language":"en","primary_location":{"id":"doi:10.3386/t0308","doi":"https://doi.org/10.3386/t0308","is_oa":true,"landing_page_url":"https://doi.org/10.3386/t0308","pdf_url":"https://doi.org/10.3386/t0308","source":{"id":"https://openalex.org/S2809516038","display_name":"National Bureau of Economic Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4322614461"],"host_organization_lineage_names":["National Bureau of Economic Research"],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"National Bureau of Economic Research","raw_type":"report"},"volume":null,"type":"report","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.3386/t0308","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005262715","display_name":"Jes\u00fas Fern\u00e1ndez\u2010Villaverde","orcid":"https://orcid.org/0000-0001-8323-3261","observed_orcids":["https://orcid.org/0000-0001-8323-3261"]},"institutions":[{"id":"https://openalex.org/I119878761","display_name":"Federal Reserve Bank of Atlanta","ror":"https://ror.org/05qg1tz58","country_code":"US","type":"other","lineage":["https://openalex.org/I119878761","https://openalex.org/I1317239608"]},{"id":"https://openalex.org/I1286498122","display_name":"Hoover Institution","ror":"https://ror.org/04ce9mt19","country_code":"US","type":"facility","lineage":["https://openalex.org/I1286498122"]},{"id":"https://openalex.org/I1321305853","display_name":"National Bureau of Economic Research","ror":"https://ror.org/04grmx538","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1321305853"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jes\u00fas Fern\u00e1ndez-Villaverde","raw_affiliation_strings":["National Bureau of Economic Research (NBER), 1050 Massachusetts Avenue, Cambridge, MA 02138, United States","University of Pennsylvania - Department of Economics, 3718 Locust Walk, 160 McNeil Building, Philadelphia, PA 19104, United States","Department of Economics University of Pennsylvania 160 McNei 3718 Locust Walk Philadelphia, PA 19104","New York University and Hoover Institution 269 Mercer Street New York, NY 10003","Research Department Federal Reserve Bank of Atlanta 100 Peachtree Street NE Atlanta, GA 30309-4470"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Bureau of Economic Research (NBER), 1050 Massachusetts Avenue, Cambridge, MA 02138, United States","institution_ids":["https://openalex.org/I1321305853"]},{"raw_affiliation_string":"University of Pennsylvania - Department of Economics, 3718 Locust Walk, 160 McNeil Building, Philadelphia, PA 19104, United States","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"Department of Economics University of Pennsylvania 160 McNei 3718 Locust Walk Philadelphia, PA 19104","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"New York University and Hoover Institution 269 Mercer Street New York, NY 10003","institution_ids":["https://openalex.org/I1286498122","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Research Department Federal Reserve Bank of Atlanta 100 Peachtree Street NE Atlanta, GA 30309-4470","institution_ids":["https://openalex.org/I119878761"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045707834","display_name":"Juan Francisco Rubio-Ram\u0131\u0301rez","orcid":"https://orcid.org/0000-0003-0274-6546","observed_orcids":["https://orcid.org/0000-0003-0274-6546"]},"institutions":[{"id":"https://openalex.org/I119878761","display_name":"Federal Reserve Bank of Atlanta","ror":"https://ror.org/05qg1tz58","country_code":"US","type":"other","lineage":["https://openalex.org/I119878761","https://openalex.org/I1317239608"]},{"id":"https://openalex.org/I1286498122","display_name":"Hoover Institution","ror":"https://ror.org/04ce9mt19","country_code":"US","type":"facility","lineage":["https://openalex.org/I1286498122"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Juan Francisco Rubio-Ramirez","raw_affiliation_strings":["Federal Reserve Bank of Atlanta - Research Department, 1000 Peachtree Street, NE, Atlanta, GA 30309-4470, United States","Department of Economics University of Pennsylvania 160 McNei 3718 Locust Walk Philadelphia, PA 19104","New York University and Hoover Institution 269 Mercer Street New York, NY 10003","Research Department Federal Reserve Bank of Atlanta 100 Peachtree Street NE Atlanta, GA 30309-4470"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Federal Reserve Bank of Atlanta - Research Department, 1000 Peachtree Street, NE, Atlanta, GA 30309-4470, United States","institution_ids":["https://openalex.org/I119878761"]},{"raw_affiliation_string":"Department of Economics University of Pennsylvania 160 McNei 3718 Locust Walk Philadelphia, PA 19104","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"New York University and Hoover Institution 269 Mercer Street New York, NY 10003","institution_ids":["https://openalex.org/I1286498122","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Research Department Federal Reserve Bank of Atlanta 100 Peachtree Street NE Atlanta, GA 30309-4470","institution_ids":["https://openalex.org/I119878761"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002088217","display_name":"Thomas J. Sargent","orcid":"https://orcid.org/0000-0002-5457-0944","observed_orcids":["https://orcid.org/0000-0002-5457-0944"]},"institutions":[{"id":"https://openalex.org/I119878761","display_name":"Federal Reserve Bank of Atlanta","ror":"https://ror.org/05qg1tz58","country_code":"US","type":"other","lineage":["https://openalex.org/I119878761","https://openalex.org/I1317239608"]},{"id":"https://openalex.org/I1286498122","display_name":"Hoover Institution","ror":"https://ror.org/04ce9mt19","country_code":"US","type":"facility","lineage":["https://openalex.org/I1286498122"]},{"id":"https://openalex.org/I1321305853","display_name":"National Bureau of Economic Research","ror":"https://ror.org/04grmx538","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1321305853"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas J. Sargent","raw_affiliation_strings":["National Bureau of Economic Research (NBER), 1050 Massachusetts Avenue, Cambridge, MA 02138, United States","New York University (NYU) - Department of Economics, Leonard N. Stern School of Business, 269 Mercer Street, New York, NY 10003, United States","Department of Economics University of Pennsylvania 160 McNei 3718 Locust Walk Philadelphia, PA 19104","New York University and Hoover Institution 269 Mercer Street New York, NY 10003","Research Department Federal Reserve Bank of Atlanta 100 Peachtree Street NE Atlanta, GA 30309-4470"],"raw_orcid":"https://orcid.org/0000-0002-5457-0944","affiliations":[{"raw_affiliation_string":"National Bureau of Economic Research (NBER), 1050 Massachusetts Avenue, Cambridge, MA 02138, United States","institution_ids":["https://openalex.org/I1321305853"]},{"raw_affiliation_string":"New York University (NYU) - Department of Economics, Leonard N. Stern School of Business, 269 Mercer Street, New York, NY 10003, United States","institution_ids":["https://openalex.org/I57206974"]},{"raw_affiliation_string":"Department of Economics University of Pennsylvania 160 McNei 3718 Locust Walk Philadelphia, PA 19104","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"New York University and Hoover Institution 269 Mercer Street New York, NY 10003","institution_ids":["https://openalex.org/I1286498122","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Research Department Federal Reserve Bank of Atlanta 100 Peachtree Street NE Atlanta, GA 30309-4470","institution_ids":["https://openalex.org/I119878761"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5005262715"],"corresponding_institution_ids":["https://openalex.org/I119878761","https://openalex.org/I1286498122","https://openalex.org/I1321305853","https://openalex.org/I57206974","https://openalex.org/I79576946"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":126,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10007","display_name":"Monetary Policy and Economic Impact","score":0.9437999725341797,"subfield":{"id":"https://openalex.org/subfields/2000","display_name":"General Economics, Econometrics and Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10007","display_name":"Monetary Policy and Economic Impact","score":0.9437999725341797,"subfield":{"id":"https://openalex.org/subfields/2000","display_name":"General Economics, Econometrics and Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.016200000420212746,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.010099999606609344,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/vector-autoregression","display_name":"vector autoregression","score":0.8740000128746033},{"id":"https://openalex.org/keywords/state-space-models","display_name":"state-space model","score":0.7229999899864197},{"id":"https://openalex.org/keywords/impulse-response","display_name":"impulse response","score":0.6499999761581421},{"id":"https://openalex.org/keywords/invertibility","display_name":"invertibility","score":0.6190000176429749},{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.5740000009536743},{"id":"https://openalex.org/keywords/linearization","display_name":"linearization","score":0.4259999990463257}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2799094319343567}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3386/t0308","doi":"https://doi.org/10.3386/t0308","is_oa":true,"landing_page_url":"https://doi.org/10.3386/t0308","pdf_url":"https://doi.org/10.3386/t0308","source":{"id":"https://openalex.org/S2809516038","display_name":"National Bureau of Economic Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4322614461"],"host_organization_lineage_names":["National Bureau of Economic Research"],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"National Bureau of Economic Research","raw_type":"report"},{"id":"doi:10.2139/ssrn.717963","doi":"https://doi.org/10.2139/ssrn.717963","is_oa":true,"landing_page_url":"https://doi.org/10.2139/ssrn.717963","pdf_url":null,"source":{"id":"https://openalex.org/S4210172589","display_name":"SSRN Electronic Journal","issn_l":"1556-5068","issn":["1556-5068"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1318003438","host_organization_name":"RELX Group (Netherlands)","host_organization_lineage":["https://openalex.org/I1318003438"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},{"id":"pmh:oai:RePEc:fip:fedawp:2005-09","doi":null,"is_oa":false,"landing_page_url":"http://www.frbatlanta.org/filelegacydocs/wp0509.pdf","pdf_url":"http://www.frbatlanta.org/filelegacydocs/wp0509.pdf","source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"preprint"},{"id":"pmh:oai:RePEc:nbr:nberte:0308","doi":null,"is_oa":true,"landing_page_url":"http://www.nber.org/papers/t0308.pdf","pdf_url":"http://www.nber.org/papers/t0308.pdf","source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"preprint"},{"id":"pmh:oai:econstor.eu:10419/100923","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/10419/100923","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:workingPaper"}],"best_oa_location":{"id":"doi:10.3386/t0308","doi":"https://doi.org/10.3386/t0308","is_oa":true,"landing_page_url":"https://doi.org/10.3386/t0308","pdf_url":"https://doi.org/10.3386/t0308","source":{"id":"https://openalex.org/S2809516038","display_name":"National Bureau of Economic Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4322614461"],"host_organization_lineage_names":["National Bureau of Economic Research"],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"National Bureau of Economic Research","raw_type":"report"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.5699999928474426,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2148287167.pdf","grobid_xml":"https://content.openalex.org/works/W2148287167.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1480041752","https://openalex.org/W1492034291","https://openalex.org/W1503128159","https://openalex.org/W1505915647","https://openalex.org/W1539154292","https://openalex.org/W1540369740","https://openalex.org/W1550405231","https://openalex.org/W1598805064","https://openalex.org/W1598928703","https://openalex.org/W1602041800","https://openalex.org/W1870480295","https://openalex.org/W1964347824","https://openalex.org/W1976140283","https://openalex.org/W1994581954","https://openalex.org/W2026103080","https://openalex.org/W2031594662","https://openalex.org/W2033872062","https://openalex.org/W2041175506","https://openalex.org/W2048585019","https://openalex.org/W2081845494","https://openalex.org/W2085528624","https://openalex.org/W2089853409","https://openalex.org/W2142182841","https://openalex.org/W2163427003","https://openalex.org/W2271352622","https://openalex.org/W2293807537","https://openalex.org/W2797289203","https://openalex.org/W3022712314","https://openalex.org/W3122253332","https://openalex.org/W3122955745","https://openalex.org/W3125979221","https://openalex.org/W4232457426","https://openalex.org/W4237506774","https://openalex.org/W4298131784","https://openalex.org/W4301672661","https://openalex.org/W6630188278","https://openalex.org/W6814022521"],"related_works":["https://openalex.org/W3123168430","https://openalex.org/W7098209182","https://openalex.org/W1966731843","https://openalex.org/W7097769406","https://openalex.org/W2742570610","https://openalex.org/W7095660140","https://openalex.org/W2135994081","https://openalex.org/W238019691","https://openalex.org/W7099353628","https://openalex.org/W1994581954"],"abstract_inverted_index":{"The":[0,84],"dynamics":[1],"of":[2,16,50,92],"a":[3,21,33,68],"linear":[4],"(or":[5],"linearized)":[6],"dynamic":[7],"stochastic":[8],"economic":[9,60,80,95],"model":[10],"can":[11],"be":[12],"expressed":[13],"in":[14],"terms":[15],"matrices":[17],"(A,B,C,D)":[18],"that":[19,66],"define":[20],"state":[22,27],"space":[23,28],"system.":[24],"An":[25],"associated":[26,57],"system":[29],"(A,K,C,":[30],"Sigma)":[31],"determines":[32],"vector":[34],"autoregression":[35],"for":[36,71],"observables":[37],"available":[38],"to":[39,79],"an":[40],"econometrician.":[41],"We":[42,62],"review":[43],"circumstances":[44],"under":[45],"which":[46],"the":[47,51,54,59,74],"impulse":[48,55],"response":[49,56],"VAR":[52,77,93],"resembles":[53],"with":[58],"model.":[61],"give":[63],"four":[64],"examples":[65],"illustrate":[67],"simple":[69],"condition":[70,85],"checking":[72],"whether":[73],"mapping":[75],"from":[76],"shocks":[78,81],"is":[82],"invertible.":[83],"applies":[86],"when":[87],"there":[88],"are":[89],"equal":[90],"numbers":[91],"and":[94],"shocks.":[96]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":12}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}
