Trend-reverting fluctuations in the life-cycle model

Aggregate time series provide evidence of short-term dynamic adjustment that appears to be governed by complex or negative real eigenvalues. This finding is at odds with the predictions of reasonably parameterized, convex one-sector growth models with complete markets. We study life-cycle economies in which aggregate saving depends non-trivially 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 non-monetary steady state via damped oscillations. We also discuss examples and extensions.