Discrete-time, infinite-horizon, general equilibrium models are routinely used in macroeconomics and in public finance for exploring the quantitative features of model economies and for counterfactual policy analysis. With the development of powerful desktop computers, economists have started to use modern numerical methods for integration, interpolation, and for solving nonlinear systems of equations. Depending on the exact specification of the model – for example, whether there is one representative agent or several agents, whether agents are finitely lived or infinitely lived, or whether there is uncertainty in the model or not – there are various computational methods for approximating equilibria numerically. This paper focuses on computational methods for stochastic equilibrium models with heterogeneous agents and aggregate uncertainty where the welfare theorems fail and the equilibrium allocation cannot be decentralized by a simple (convex) social planner problem. These could be models with overlapping generations (as in, e.g., Krueger and Kubler, 2006; Favilukis et al., 2010; or Harenberg and Ludwig, 2014), models with heterogeneous producers (as in, e.g., Khan and Thomas, 2013 or Bloom et al., 2012), or models with infinitely lived heterogeneous consumers (as in, e.g, Bhandari et al., 2013; Brumm et al., 2015; Chien et al., 2011; Krueger et al., 2015; or McKay and Reis, 2013).
There are many excellent surveys on the computation of equilibria in these models and we will discuss the most popular methods briefly below. Instead of comparing those methods in detail, the main part of this paper focuses on a particular high-performance computing (HPC) approach for solving models with large heterogeneity. This approach was first introduced in Brumm and Scheidegger (2017) and we will expand it in this paper to tackle models with overlapping generations and with idiosyncratic risk.
Our approach makes use of two recent developments in scientific computing. First, advances in numerical analysis enable researchers to approximate very-high-dimensional functions. Employing standard discretization methods for the domain of such functions is computationally infeasible, as these approaches yield too many gridpoints at which the functions have to be evaluated.