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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
    DOI: 10.1787/112875725526
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    More about this item

    Keywords

    Kalman filter; NAIRU; standard errors; unobserved component models;
    All these keywords.

    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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