Frontier Sequence-Space Methods for Heterogeneous-Agent Models

Households differ in terms of their consumption, income, wealth, location, or information sets; firms differ in terms of their prices, productivity, or balance sheet positions. A large body of research has shown that this type of heterogeneity matters for macroeconomic dynamics, yet models that take heterogeneity into account remain difficult to solve, limiting the speed of progress in the field. This research extends earlier work by the principal investigators in the theory and computation of heterogeneous-agent macroeconomic models, to deal with different types of heterogeneity, such as household location choice or heterogeneity among firms, and to enable new applications, such as portfolio choice and the calculation of optimal rules. The research team will continue the development of a codebase available for use by all researchers and decision makers, expanding its functionality and documentation. It will also continue teaching sequence-space methods at an annual workshop for graduate students, as well as developing related teaching material.

This research provides innovations that significantly expand the set of models that can be solved in the sequence space and the economic questions that can be tackled with this approach. First, it provides a method for solving for the first-order solution of models which have many endogenous variables to solve for?such as models with a large number of locations with heterogeneous agents in each location?by leveraging the structure of sequence-space Jacobians to provide a rapid iterative method to obtain the solution. Second, it provides a method for solving for the portfolios of agents, who can choose to invest in multiple assets based on risk-return considerations, jointly with equilibrium macroeconomic dynamics. Third, it provides a method for solving for the steady state of Ramsey optimal plans when the underlying economy features heterogeneous agents that face idiosyncratic risk. Finally, it provides a method for solving for the general second-order solution in the sequence space, unlocking applications such as the calculation of generalized impulse responses featuring state and sign dependence as well as the effect of aggregate risk on average outcomes. For each of these new methods, the researchers will release accessible and documented code as well as teaching material, facilitating adoption and progress in the field.