{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:41:47Z","timestamp":1760240507376,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T00:00:00Z","timestamp":1561680000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>The aim of the paper is to provide a recent overview of Kalman filter employment in the non-accelerating inflation rate of unemployment (NAIRU) estimation. The NAIRU plays a key part in an economic system. A certain unemployment rate which is consistent with a stable rate of inflation is one of the conditions for economic system stability. Since the NAIRU cannot be directly observed and measured, it is one of the most fitting problems for the Kalman filter application. The search for original, NAIRU focused and Kalman filter employment studies was performed in three scientific databases: Web of Science, Scopus, and ScienceDirect. A sample of 152 papers was narrowed down to 25 studies, which were described in greater detail regarding the focus, methods, model features, limitations, and other characteristics. A group of studies using a purely statistical approach of decomposing unemployment into a trend and cyclical component was identified. The next group uses the reduced-form approach which is sometimes combined with statistical decomposition. In such cases, the models are usually based on the backward-looking Phillips curve. Nevertheless, the forward-looking, New Keynesian or rarely hybrid New Keynesian variant can also be encountered.<\/jats:p>","DOI":"10.3390\/systems7030033","type":"journal-article","created":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T11:20:26Z","timestamp":1561720826000},"page":"33","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Review of Kalman Filter Employment in the NAIRU Estimation"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5709-121X","authenticated-orcid":false,"given":"Katerina","family":"Fronckova","sequence":"first","affiliation":[{"name":"Department of Informatics and Quantitative Methods, University of Hradec Kralove, Rokitanskeho 62, 50003 Hradec Kralove, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9160-5758","authenticated-orcid":false,"given":"Pavel","family":"Prazak","sequence":"additional","affiliation":[{"name":"Department of Informatics and Quantitative Methods, University of Hradec Kralove, Rokitanskeho 62, 50003 Hradec Kralove, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3468-0270","authenticated-orcid":false,"given":"Ivan","family":"Soukal","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Hradec Kralove, Rokitanskeho 62, 50003 Hradec Kralove, Czech Republic"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A New Approach to Linear Filtering and Prediction Problems","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng."},{"key":"ref_2","first-page":"1","article-title":"The Role of Monetary Policy","volume":"58","author":"Friedman","year":"1968","journal-title":"Am. Econ. Rev."},{"key":"ref_3","unstructured":"Eurostat (2019, April 28). Total Unemployment Rate. Available online: https:\/\/ec.europa.eu\/eurostat\/tgm\/table.do?tab=table&init=1&language=en&pcode=tps00203&plugin=1."},{"key":"ref_4","unstructured":"World Bank (2019, April 28). Unemployment, Total (% of Total Labor Force) (Modeled ILO Estimate). Available online: https:\/\/data.worldbank.org\/indicator\/SL.UEM.TOTL.ZS."},{"key":"ref_5","unstructured":"Maybeck, P.S. (1979). Stochastic Models, Estimation and Control, Mathematics in Science and Engineering; Academic Press. [1st ed.]."},{"key":"ref_6","unstructured":"Grewal, M.S., and Andrews, A.P. (2015). Kalman Filtering: Theory and Practice Using MATLAB, John Wiley & Sons Inc.. [4th ed.]."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Simon, D. (2006). Optimal State Estimation: Kalman, H [Infinity] and Nonlinear Approaches, Wiley-Interscience. [1st ed.].","DOI":"10.1002\/0470045345"},{"key":"ref_8","first-page":"5","article-title":"Evaluation and Comparison of Discovery Tools: An Update","volume":"33","author":"Chickering","year":"2014","journal-title":"Inf. Technol. Libr."},{"key":"ref_9","unstructured":"Breeding, M. (2014). Library Resource Discovery Products: Context, Library Perspectives, and Vendor Positions, American Library Association."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1007\/s00181-005-0250-z","article-title":"Testing the significance and the non-linearity of the Phillips trade-off in the Euro Area","volume":"30","author":"Aguiar","year":"2005","journal-title":"Empir. Econ."},{"key":"ref_11","first-page":"6","article-title":"Using asymmetric Okun law and Phillips curve for potential output estimates: An empirical study for Romania","volume":"23","author":"Andrei","year":"2014","journal-title":"Adm. si Manag. Public"},{"key":"ref_12","first-page":"1","article-title":"Potential Output Estimate Using a Grey Production Function Approach","volume":"29","author":"Andrei","year":"2017","journal-title":"J. Grey Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1016\/j.jmoneco.2005.07.021","article-title":"New measures of the output gap based on the forward-looking new Keynesian Phillips curve","volume":"54","author":"Basistha","year":"2007","journal-title":"J. Monet. Econ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1093\/oep\/gpi037","article-title":"Measuring the UK short-run NAIRU","volume":"58","author":"Batini","year":"2006","journal-title":"Oxf. Econ. Pap."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/s00181-010-0342-2","article-title":"Estimating Europe\u2019s natural rates","volume":"40","author":"Berger","year":"2011","journal-title":"Empir. Econ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1016\/j.jedc.2009.09.010","article-title":"Labour taxes and unemployment evidence from a panel unobserved component model","volume":"34","author":"Berger","year":"2010","journal-title":"J. Econ. Dyn. Control"},{"key":"ref_17","first-page":"163","article-title":"NAIRU estimates for Croatia","volume":"30","author":"Botric","year":"2012","journal-title":"Zbornik Radova Ekonomskog Fakulteta u Rijeci Proc. Rijeka Fac. Econ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2179","DOI":"10.1080\/00036840600701061","article-title":"Is the NAIRU more useful in forecasting inflation than the natural rate of unemployment?","volume":"38","author":"Claar","year":"2006","journal-title":"Appl. Econ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1016\/j.ecosys.2018.08.003","article-title":"Unemployment or credit: Which one holds the potential? Results for a small open economy with a low degree of financialization","volume":"42","author":"Constantinescu","year":"2018","journal-title":"Econ. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1198\/073500105000000315","article-title":"Estimating Potential Output, Core Inflation, and the NAIRU as Latent Variables","volume":"24","year":"2006","journal-title":"J. Bus. Econ. Stat."},{"key":"ref_21","first-page":"53","article-title":"Estimating the NAIRU for Israel, 1992\u20132013","volume":"14","author":"Elkayam","year":"2016","journal-title":"Isr. Econ. Rev."},{"key":"ref_22","first-page":"465","article-title":"The Phillips Curve and NAIRU Revisited: New Estimates for Germany","volume":"228","author":"Fitzenberger","year":"2008","journal-title":"J. Econ. Stat."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.econmod.2006.06.005","article-title":"Structural and reduced approaches of the equilibrium rate of unemployment, a comparison between France and the United States","volume":"24","author":"Heyer","year":"2007","journal-title":"Econ. Model."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1016\/j.econmod.2010.05.017","article-title":"A small New Keynesian state space model of the Australian economy","volume":"28","author":"Leu","year":"2011","journal-title":"Econ. Model."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1111\/j.1467-9485.2006.00387.x","article-title":"Hysteresis and the NAIRU in the euro area","volume":"53","author":"Logeay","year":"2006","journal-title":"Scott. J. Polit. Econ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"503","DOI":"10.18267\/j.pep.526","article-title":"Hysteresis and the NAIRU: The Case of Countries in Transition","volume":"24","author":"Marjanovic","year":"2015","journal-title":"Prague Econ. Pap."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1080\/1406099X.2009.10840460","article-title":"Assessment of the natural rate of unemployment and capacity utilisation in Latvia","volume":"9","author":"Zasova","year":"2009","journal-title":"Balt. J. Econ."},{"key":"ref_28","first-page":"1346","article-title":"The European unemployment gap and the role of monetary policy","volume":"30","author":"Napolitano","year":"2010","journal-title":"Econ. Bull."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1016\/j.jedc.2006.05.005","article-title":"How much has labour taxation contributed to European structural unemployment?","volume":"31","author":"Planas","year":"2007","journal-title":"J. Econ. Dyn. Control"},{"key":"ref_30","first-page":"149","article-title":"Estimating output gap, core inflation, and the NAIRU for Peru, 1979\u20132007","volume":"10","author":"Rodriguez","year":"2010","journal-title":"Appl. Econom. Int. Dev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.csda.2011.07.010","article-title":"Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters","volume":"56","author":"Ruiz","year":"2012","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_32","first-page":"109","article-title":"Rescuing the Phillips curve: Making use of long-term unemployment in the measurement of the NAIRU","volume":"1","author":"Rusticelli","year":"2014","journal-title":"OECD J. Econ. Stud."},{"key":"ref_33","first-page":"172","article-title":"Estimating Pakistan\u2019s time varying non-accelerating inflation rate of unemployment: An unobserved component approach","volume":"1","author":"Shaheen","year":"2011","journal-title":"Int. J. Econ. Financ. Iss."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1108\/JES-10-2011-0121","article-title":"Estimating the time varying NAIRU in Iran","volume":"40","author":"Valadkhani","year":"2013","journal-title":"J. Econ. Stud."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/S0165-1765(99)00111-1","article-title":"A theory-consistent system approach for estimating potential output and the NAIRU","volume":"64","author":"Apel","year":"1999","journal-title":"Econ. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s001810050061","article-title":"System estimates of potential output and the NAIRU","volume":"24","author":"Apel","year":"1999","journal-title":"Empir. Econ."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Harvey, A.C. (1989). Forecasting, Structural Time Series Models, and the Kalman Filter, Cambridge University Press. [1st ed.].","DOI":"10.1017\/CBO9781107049994"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Durbin, J., and Koopman, S.J. (2012). Time Series Analysis by State Space Methods, Oxford University Press. [2nd ed.].","DOI":"10.1093\/acprof:oso\/9780199641178.001.0001"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1214\/aos\/1176348139","article-title":"The Diffuse Kalman Filter","volume":"19","author":"Jong","year":"1991","journal-title":"Ann. Stat."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Hamilton, J.D. (1994). Time Series Analysis, Princeton University Press. [1st ed.].","DOI":"10.1515\/9780691218632"}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/7\/3\/33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:02:18Z","timestamp":1760187738000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/7\/3\/33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,28]]},"references-count":40,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["systems7030033"],"URL":"https:\/\/doi.org\/10.3390\/systems7030033","relation":{},"ISSN":["2079-8954"],"issn-type":[{"type":"electronic","value":"2079-8954"}],"subject":[],"published":{"date-parts":[[2019,6,28]]}}}