Aggregation of Simple Linear Dynamics: Exact Asymptotic Results
Abstracthis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /1998/350.
Date of creation: Apr 1998
Date of revision:
Contact details of provider:
Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp
Aggregation; idiosymcratic-driven fluctuations; long memory; nonstationarity.;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Joseph G. Haubrich & Andrew W. Lo, 1989.
"The Sources and Nature of Long-term Memory in the Business Cycle,"
NBER Working Papers
2951, National Bureau of Economic Research, Inc.
- 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.
- Joseph G. Haubrich & Andrew W. Lo, 1991. "The sources and nature of long-term memory in the business cycle," Working Paper 9116, Federal Reserve Bank of Cleveland.
- 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 5-89, Wharton School Rodney L. White Center for Financial Research.
- 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.
- repec:fth:coluec:465 is not listed on IDEAS
- Francis X. Diebold & Glenn D. Rudebusch, 1988.
"Long memory and persistence in aggregate output,"
Finance and Economics Discussion Series
7, Board of Governors of the Federal Reserve System (U.S.).
- Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
- 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.
- Zaffaroni, Paolo, 2004. "Contemporaneous aggregation of linear dynamic models in large economies," Journal of Econometrics, Elsevier, vol. 120(1), pages 75-102, May.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.