Algorithm accelerates heterogeneous-agent life-cycle models

The Sequence-Space Jacobian (SSJ) method, while powerful for heterogeneous-agent models, faces computational constraints with very large state spaces, particularly in heterogeneous-agent overlapping generations (HA-OLG) models.

This paper demonstrates how to exploit the unique properties of age—such as finite planning horizons and deterministic transitions—to compute Jacobians for a broad class of HA-OLG models orders of magnitude faster.

The authors provide rigorous proofs and age-specific Jacobians that decompose aggregate dynamics across cohorts.

An application to a life-cycle Krusell-Smith model with 75 distinct ages shows that solving for equilibrium paths, including the effects of secularly declining birth rates, takes only a few seconds on a modern laptop.

The method also facilitates isolating responses of different age groups, revealing that an aging working-age population can lead to hump-shaped paths of capital and labor per capita alongside a fall in the natural rate of interest.

This efficiency is crucial for analyzing complex demographic transitions and their macroeconomic impact.

The computational advantages of the new algorithm are substantial.

A benchmark comparison shows that a large-scale infinite-horizon Krusell-Smith model with 206,550 states requires 234 seconds and 26.65 GB of memory to compute a single Jacobian.

In contrast, a life-cycle version of the same model, with an identical state space, computes the Jacobian in just 2.19 seconds using only 0.24 GB of memory with the specialized algorithm.

This represents a reduction in computation time to less than a hundredth of the cost of solving an equivalent infinite-horizon model.

This efficiency stems from exploiting the sparsity of age-specific fake news matrices, where only 2.1% of entries are non-zero, and constructing these matrices progressively to lower peak memory requirements.