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Aggregate Output Measurements: A Common Trend Approach


  • Sentana, Enrique
  • Almuzara, Martin
  • Fiorentini, Gabriele


We analyze a model for N different measurements of a persistent latent time series when measurement errors are mean-reverting, which implies a common trend among measurements. We study the consequences of overdifferencing, finding potentially large biases in maximum likelihood estimators of the dynamics parameters and reductions in the precision of smoothed estimates of the latent variable, especially for multiperiod objects such as quinquennial growth rates. We also develop an R2 measure of common trend observability that determines the severity of misspecification. Finally, we apply our framework to US quarterly data on GDP and GDI, obtaining an improved aggregate output measure.

Suggested Citation

  • Sentana, Enrique & Almuzara, Martin & Fiorentini, Gabriele, 2021. "Aggregate Output Measurements: A Common Trend Approach," CEPR Discussion Papers 15758, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:15758

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    References listed on IDEAS

    1. Ryan Greenaway-McGrevy, 2011. "Is GDP or GDI a better measure of output? A statistical approach," BEA Working Papers 0076, Bureau of Economic Analysis.
    2. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781316510520, November.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    4. Sentana, Enrique & Almuzara, Martin & Amengual, Dante & Fiorentini, Gabriele, 2022. "GDP Solera: The Ideal Vintage Mix," CEPR Discussion Papers 17196, C.E.P.R. Discussion Papers.
    5. Fiorentini, Gabriele & Galesi, Alessandro & Sentana, Enrique, 2018. "A spectral EM algorithm for dynamic factor models," Journal of Econometrics, Elsevier, vol. 205(1), pages 249-279.
    6. Weale, Martin, 1992. "Estimation of Data Measured with Error and Subject to Linear Restrictions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(2), pages 167-174, April-Jun.
    7. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781108400022, November.
    8. Richard J. Smith & Martin R. Weale & Steven E. Satchell, 1998. "Measurement Error with Accounting Constraints: Point and Interval Estimation for Latent Data with an Application to U.K. Gross Domestic Product," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 109-134.
    9. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781108400008, November.
    10. Martín Almuzara & Dante Amengual & Enrique Sentana, 2019. "Normality tests for latent variables," Quantitative Economics, Econometric Society, vol. 10(3), pages 981-1017, July.
    11. Honoré,Bo & Pakes,Ariel & Piazzesi,Monika & Samuelson,Larry (ed.), 2017. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781108414982, November.
    12. Watson, Mark W. & Engle, Robert F., 1983. "Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models," Journal of Econometrics, Elsevier, vol. 23(3), pages 385-400, December.
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    Cited by:

    1. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "Tests for Random Coefficient Variation in Vector Autoregressive Models," Advances in Econometrics, in: Essays in Honour of Fabio Canova, volume 44, pages 1-35, Emerald Group Publishing Limited.
    2. Jan P. A. M. Jacobs & Samad Sarferaz & Jan-Egbert Sturm & Simon van Norden, 2022. "Can GDP Measurement Be Further Improved? Data Revision and Reconciliation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 423-431, January.
    3. Eiji Goto & Jan P.A.M. Jacobs & Tara M. Sinclair & Simon van Norden, 2023. "Employment reconciliation and nowcasting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(7), pages 1007-1017, November.

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    More about this item


    Cointegration; Gdp; Gdi; Overdifferencing; Signal extraction;
    All these keywords.

    JEL classification:

    • 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
    • E01 - Macroeconomics and Monetary Economics - - General - - - Measurement and Data on National Income and Product Accounts and Wealth; Environmental Accounts

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