IDEAS home Printed from https://ideas.repec.org/p/cep/stiecm/350.html
   My bibliography  Save this paper

Aggregation of Simple Linear Dynamics: Exact Asymptotic Results

Author

Listed:
  • Marco Lippi
  • Paolo Zaffaroni

Abstract

his paper deal with aggregation of AR(1) micro variables driven by a common and idiosyncratic shock with random coefficients. We provide a rigorous analysis, based on results on sums of r.v.'s with a possibly finite first moment, of the aggregate variance and spectral density, as the number of micro units tends to infinity. If the AR coefficients lie below a critical away from unity, the aggregate process may exhibit infinite variance and long memory. Surprisingly, if the key parameter of the density function of the AR coefficients lies below a critical value (high density near unity), common and idiosyncratic components have the same importance in explaining aggregate variance, whereas the usual result, i.e. a vanishing importance of the idiosyncratic component, is obtained when the parameter lies above the critical value (low density near unity). Empirical analysis relative to major U.S. macroeconomic series, both in previous literature and in this paper, provides estimates of the parameter below the critical value.

Suggested Citation

  • Marco Lippi & Paolo Zaffaroni, 1998. "Aggregation of Simple Linear Dynamics: Exact Asymptotic Results," STICERD - Econometrics Paper Series 350, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  • Handle: RePEc:cep:stiecm:350
    as

    Download full text from publisher

    File URL: https://sticerd.lse.ac.uk/dps/em/em350.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jan Beran & Haiyan Liu & Sucharita Ghosh, 2020. "On aggregation of strongly dependent time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 690-710, September.
    2. Zaffaroni, Paolo, 2004. "Contemporaneous aggregation of linear dynamic models in large economies," Journal of Econometrics, Elsevier, vol. 120(1), pages 75-102, May.
    3. Manmohan S. Kumar & Tatsuyoshi Okimoto, 2007. "Dynamics of Persistence in International Inflation Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(6), pages 1457-1479, September.
    4. Proietti, Tommaso & Maddanu, Federico, 2024. "Modelling cycles in climate series: The fractional sinusoidal waveform process," Journal of Econometrics, Elsevier, vol. 239(1).
    5. Beran, Jan & Schützner, Martin & Ghosh, Sucharita, 2010. "From short to long memory: Aggregation and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2432-2442, November.
    6. Thornton, Michael A., 2014. "The aggregation of dynamic relationships caused by incomplete information," Journal of Econometrics, Elsevier, vol. 178(P2), pages 342-351.

    More about this item

    Keywords

    Aggregation; idiosymcratic-driven fluctuations; long memory; nonstationarity.;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cep:stiecm:350. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://sticerd.lse.ac.uk/_new/publications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.