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Reconciling Output Gaps: Unobserved Components Model and Hodrick-Prescott Filter

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  • Joshua C.C. Chan
  • Angelia L. Grant

Abstract

This paper reconciles two widely used trend-cycle decompositions of GDP that give markedly different estimates: the correlated unobserved components model yields output gaps that are small in amplitude, whereas the Hodrick-Prescott (HP) filter generates large and persistent cycles. By embedding the HP filter in an unobserved components model, we show that this difference arises due to differences in the way the stochastic trend is modeled. Moreover, the HP filter implies that the cyclical components are serially independent - an assumption that is decidedly rejected by the data. By relaxing this restrictive assumption, the new model provides comparable model fit relative to the standard correlated unobserved components model.

Suggested Citation

  • Joshua C.C. Chan & Angelia L. Grant, 2016. "Reconciling Output Gaps: Unobserved Components Model and Hodrick-Prescott Filter," CAMA Working Papers 2016-44, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2016-44
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    File URL: https://crawford.anu.edu.au/sites/default/files/2025-08/44_2016_Chan_Grant.pdf
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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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