Beschreibung:
We propose a pseudospectral method to solve heterogeneous-agent models in continuous time. The solution is approximated using global basis functions, e.g. Chebyshev polynomials, represented by their values at collocation nodes. In a two-income model, this yields a simple algorithm to solve for the value function. The stationary distribution is obtained using finite differences or a more efficient mixed scheme. A benchmark against finite differences shows that spectral methods achieve far greater precision for a given number of nodes and for a given runtime. We showcase the power of the spectral approach for smooth, multi-dimensional problems by solving a model with diffusive income. Finally, we apply it to a power-law income model and a life-cycle model