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Comparing Semi-Structural Methods to Estimate Unobserved Variables: The HPMV and Kalman Filters Approaches

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  • Laurence Boone

Abstract

Economists often seek to estimate unobserved variables, representing “equilibrium” or “expected” values of economic variables, as benchmarks against which observed, realised values of these variables may be evaluated. Such comparisons are often used as economic policy indicators, for example the output gap, as measured by the ratio of actual to potential GDP, is commonly used as a measure of excess demand in assessing inflation pressures. To estimate these unobserved variables, a popular approach is the so-called semi-structural approach which includes: the Hodrick Prescott multivariate filter (developed by Laxton and Tetlow, 1992) and the Kalman filter (see, among others Harvey, 1992 and Cuthberson et al., 1992). This paper shows that the two approaches are closely linked, and specifically, it explains how to reproduce theHodrick Prescott multivariate filter using the Kalman filter. Being able to do so has at least two possible advantages. First, while the traditional HPMV filter ... Les économistes cherchent fréquemment à estimer des variables non observables, utilisées comme valeur d’équilibre ou de référence. La différence entre cette valeur estimée et la valeur observée est ensuite un indicateur des tensions économiques : par exemple, l’écart de PIB, mesuré par la différence entre le PIB potentiel et le PIB courant, est souvent utilisé pour évaluer les pressions inflationnistes. Une approche fréquemment utilisée pour estimer des variables inobservées est l’approche dite semi-structurelle, qui englobe notamment le filtre de Hodrick Prescott multivarié (développé par Laxton et Tetlwo 1992) et le filtre de Kalman (voir, entre autres, Harvey 1992 et Cuthberson et al. 1992). Ce document présente le lien entre ces deux filtres et explique comment reproduire le filtre HP multivarié avec un filtre de Kalman. L’intérêt de cette démarche est double. Tout d’abord, alors qu’il n’est pas possible de produire une mesure de confiance d’un estimateur HP multivarié, le ...

Suggested Citation

  • Laurence Boone, 2000. "Comparing Semi-Structural Methods to Estimate Unobserved Variables: The HPMV and Kalman Filters Approaches," OECD Economics Department Working Papers 240, OECD Publishing.
  • Handle: RePEc:oec:ecoaaa:240-en
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    File URL: http://dx.doi.org/10.1787/112875725526
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    Cited by:

    1. Éric Heyer & Frédéric Reynès & Henri Sterdyniak, 2005. "Variables observables et inobservables dans la théorie du taux de chômage d'équilibre. Une comparaison France/États-Unis," Revue économique, Presses de Sciences-Po, vol. 56(3), pages 593-603.
    2. Alessandro Cianci, 2016. "Disoccupazione strutturale in Italia e regole europee di bilancio," a/ Working Papers Series 1601, Italian Association for the Study of Economic Asymmetries, Rome (Italy).
    3. Edoardo Otranto, 2005. "Extraction of Common Signal from Series with Different Frequency," Econometrics 0502011, EconWPA.
    4. Bozena Kaderabkova, 2016. "Development of the economic cycle on labour market in the national economy and industry of the Czech Republi," Proceedings of Business and Management Conferences 4407037, International Institute of Social and Economic Sciences.
    5. Carlos Cortinhas, 2006. "Asymmetry of Shocks and Convergence in Selected Asean Countries: A Dynamic Analysis," NIPE Working Papers 3/2006, NIPE - Universidade do Minho.
    6. Nicoletta Batini & Jennifer V. Greenslade, 2006. "Measuring the UK short-run NAIRU," Oxford Economic Papers, Oxford University Press, vol. 58(1), pages 28-49, January.
    7. Eliana González & Luis F. Melo & Luis E. Rojas & Brayan Rojas, 2011. "Estimations of the Natural Rate of Interest in Colombia," Money Affairs, Centro de Estudios Monetarios Latinoamericanos, vol. 0(1), pages 33-75, January-J.
    8. Jennifer V Greenslade & Richard G Pierse & Jumana Saleheen, 2003. "A Kalman filter approach to estimating the UK NAIRU," Bank of England working papers 179, Bank of England.
    9. repec:spo:wpecon:info:hdl:2441/2129 is not listed on IDEAS
    10. repec:spo:wpecon:info:hdl:2441/2005 is not listed on IDEAS
    11. Borio, Claudio, 2014. "The financial cycle and macroeconomics: What have we learnt?," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 182-198.
    12. L Christopher Plantier & Ozer Karagedikli, 2005. "Do so-called multivariate filters have better revision properties? An empirical analysis," Computing in Economics and Finance 2005 250, Society for Computational Economics.
    13. Silvia Fabiani & Ricardo Mestre, 2004. "A system approach for measuring the euro area NAIRU," Empirical Economics, Springer, vol. 29(2), pages 311-341, May.
    14. ODIA NDONGO, Yves Francis, 2007. "Les sources des fluctuations marcoéconomiques au Cameroun," MPRA Paper 1308, University Library of Munich, Germany.
    15. Emilie Jašová & Božena Kaderábková, 2012. "Comparing NAIRU and Economic Cycle from the Perspective of Labour Market in the Countries of the Visegrad Group," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 4, pages 3-23.
    16. repec:iab:iabmit:v:36:i:4:p:411-427 is not listed on IDEAS
    17. Matthieu Lemoine & Florian Pelgrin, 2003. "Introduction aux modèles espace-état et au filtre de Kalman," Revue de l'OFCE, Presses de Sciences-Po, vol. 86(3), pages 203-229.
    18. Emilie Jasova, 2014. "A Model for Estimation of NAIRU Extended by Demand Shocks and its Application to Business Cycle Analysis in the Labour Market in Hungary and Poland," Proceedings of Economics and Finance Conferences 0401788, International Institute of Social and Economic Sciences.
    19. Beissinger, Thomas, 2003. "Strukturelle Arbeitslosigkeit in Europa: Eine Bestandsaufnahme," University of Regensburg Working Papers in Business, Economics and Management Information Systems 389, University of Regensburg, Department of Economics.
    20. Beissinger, Thomas, 2003. "Strukturelle Arbeitslosigkeit in Europa : eine Bestandsaufnahme (Structural unemployment in Europe * an inventory)," Mitteilungen aus der Arbeitsmarkt- und Berufsforschung, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany], vol. 36(4), pages 411-427.
    21. Emilie Jašová & Božena Kadeřábková & Klára Čermáková & Pavel Procházka, 2016. "Působení institucionálních faktorů na strukturální a cyklickou nezaměstnanost v zemích Visegrádské skupiny
      [Influence of Institutional Factors on Structural and Cyclical Unemployment in the Countri
      ," Politická ekonomie, University of Economics, Prague, vol. 2016(1), pages 34-50.
    22. Alvaro Aguiar & Manuel M. F. Martins, 2003. "Trend, cycle, and non-linear trade-off in the Euro Area 1970-2001," FEP Working Papers 122, Universidade do Porto, Faculdade de Economia do Porto.

    More about this item

    Keywords

    Kalman filter; NAIRU; standard errors; unobserved component models;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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