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Aggregation of Simple Linear Dynamics: Exact Asymptotic Results

  • Marco Lippi
  • Paolo Zaffaroni

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.

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File URL: http://sticerd.lse.ac.uk/dps/em/em350.pdf
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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /1998/350.

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Date of creation: Apr 1998
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Handle: RePEc:cep:stiecm:/1998/350
Contact details of provider: Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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  1. Joseph G. Haubrich & Andrew W. Lo, . "The Sources and Nature of Long-Term Memory in the Business Cycle," Rodney L. White Center for Financial Research Working Papers 05-89, Wharton School Rodney L. White Center for Financial Research.
  2. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
  3. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September.
  4. Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
  5. Lars Peter Hansen & Thomas J. Sargent, 1979. "Formulating and estimating dynamic linear rational expectations models," Working Papers 127, Federal Reserve Bank of Minneapolis.
  6. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
  7. Al-Najjar, Nabil Ibraheem, 1995. "Decomposition and Characterization of Risk with a Continuum of Random Variables," Econometrica, Econometric Society, vol. 63(5), pages 1195-1224, September.
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