Complex Eigenvalues and Trend-Reverting Fluctuations

Posted: 19 Aug 2008

See all articles by Costas Azariadis

Costas Azariadis

Federal Reserve Banks - Federal Reserve Bank of St. Louis

James Bullard

Federal Reserve Banks - Federal Reserve Bank of St. Louis

Lee E. Ohanian

University of California, Los Angeles (UCLA) - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: October 1998

Abstract

Autoregressions of quarterly or annual aggregate time series provide evidence of trend-reverting output growth and of short-term dynamic adjustment that appears to be governed by complex eigenvalues. This finding is at odds with the predictions of reasonably parameterized, convex one-sector growth models, most of which have positive real characteristic roots. We study a class of one-sector economies, overlapping generations with finite life spans of L greater than or equal to 3, in which aggregate saving depends nontrivially on the distribution of wealth among cohorts. If consumption goods are weak gross substitutes near the steady state price vector, we prove that the unique equilibrium of a life cycle exchange economy converges to the unique steady state via damped oscillations. We also conjecture that this form of trend reversion extends to production economies with a relatively flat factor-price frontier, and we test this conjecture in several plausible parameterizations of 55-period life cycle economies.

Keywords: Eigenvalues, Life Cycle, Economies, Cyclical Fluctuations

JEL Classification: E3

Suggested Citation

Azariadis, Costas and Bullard, James and Ohanian, Lee E., Complex Eigenvalues and Trend-Reverting Fluctuations (October 1998). Available at SSRN: https://ssrn.com/abstract=1229202

Costas Azariadis (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of St. Louis ( email )

411 Locust St
Saint Louis, MO 63011
United States

James Bullard

Federal Reserve Banks - Federal Reserve Bank of St. Louis ( email )

P.O. Box 442
411 Locust Street
St. Louis, MO 63166
United States
314-444-8576 (Phone)

Lee E. Ohanian

University of California, Los Angeles (UCLA) - Department of Economics ( email )

Box 951477
8283 Bunch Hall
Los Angeles, CA 90095-1477
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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