Age properties accelerate heterogeneous-agent models
A new Federal Reserve paper introduces a method to compute Sequence-Space Jacobians for heterogeneous-agent overlapping generations (HA-OLG) models orders of magnitude faster. The approach exploits the special properties of age, such as finite planning horizons and deterministic transitions.
Unlocking complex life-cycle models
Heterogeneous-agent overlapping generations (HA-OLG) models, crucial for understanding macro dynamics, have historically been computationally prohibitive due to their vast state spaces, often involving hundreds of age periods.
Existing perturbation methods, while advanced, struggle with these capacity constraints.
This paper introduces a novel approach that exploits the unique properties of age—specifically, finite planning horizons and deterministic transitions between ages—to dramatically accelerate computations.
The method allows for the calculation of Jacobians for a general class of HA-OLG models orders of magnitude faster.
For instance, a life-cycle model with 75 ages and 206,550 states, previously requiring minutes and significant memory with traditional infinite-horizon methods, can now be solved in seconds on a modern laptop, using less than a hundredth of the computational cost.
Demographic shifts and the natural rate
The paper formalizes age's special properties within the sequence-space Jacobian (SSJ) framework, providing a practical guide.
It derives age-specific Jacobians and fake news matrices, whose inherent sparsity dramatically reduces computational requirements for HA-OLG models.
An adapted algorithm further optimizes memory and operations.
This method is applied to study the dynamic general-equilibrium effects of secularly declining birth rates, using a U.S.-calibrated Krusell-Smith model.
The simulation reveals a 75-year demographic transition that reshapes the age distribution, leading to hump-shaped paths for capital and labor per capita and a substantial fall in the natural rate of interest.