Complex Eigenvalues and Trend-Reverting Fluctuations

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