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When are trend–cycle decompositions of GDP reliable?

Author

Listed:
  • Manuel González-Astudillo

    (Federal Reserve Board
    Escuela Superior Politécnica del Litoral, ESPOL)

  • John M. Roberts

    (Federal Reserve Board)

Abstract

In this paper, we examine the results of GDP trend–cycle decompositions from the estimation of bivariate unobserved components models that allow for correlated trend and cycle innovations. Three competing variables are considered in the bivariate setup along with GDP: the unemployment rate, the inflation rate, and gross domestic income. We find that the unemployment rate is the preferred variable to accompany GDP in the bivariate setup to obtain accurate estimates of its trend–cycle correlation coefficient and the cycle. We show that the key feature of the unemployment rate that allows for reliable estimates of the cycle of GDP is that its nonstationary component is small relative to its cyclical component. Using quarterly GDP and unemployment rate data from 1948:Q1 to 2019:Q1, we obtain a trend–cycle decomposition of GDP that resembles the conventional CBO estimates; we find positively correlated trend and cycle components.

Suggested Citation

  • Manuel González-Astudillo & John M. Roberts, 2022. "When are trend–cycle decompositions of GDP reliable?," Empirical Economics, Springer, vol. 62(5), pages 2417-2460, May.
    • Handle: RePEc:spr:empeco:v:62:y:2022:i:5:d:10.1007_s00181-021-02105-4
    DOI: 10.1007/s00181-021-02105-4
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    References listed on IDEAS

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    More about this item

    Keywords

    Unobserved components model; Trend–cycle decomposition; Trend–cycle correlation; Bayesian estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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