The art of the possible : tools and methods for solving models with substantial heterogeneity

• Main Author: Grasl, Tobias
• Published: Birkbeck (University of London) 2017
• Subjects: 339
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.715365

Macroeconomic models with rational, heterogeneous agents offer the opportunity to study both individual and aggregate economic outcomes, and the interaction between the two. Solving such models is diffcult: the non-trivial problem of solving a maximisation problem in the presence of uncertainty is complicated by the need to determine model-consistent expectations in an economy with a non-degenerate distribution of agents over states. This thesis provides both technical and mathematical tools which aid the economist in working with such models. Chapter 1 provides an introduction to the topic and discusses the literature. Chapter 2 presents software libraries which automate some of the steps, for example calculating expectations from policy functions. The economist can focus on the code which implements the model-specific solution to the optimisation problem. The libraries are shown to solve models far more efficiently than a comparable solution coded in Matlab. Chapter 3 introduces a new algorithm for calculating model-consistent expectations which relies on straightforward mathematics and a guess for the distribution of agents over states. The initial guess, the distribution obtained under constant aggregate conditions, yields good results. Multiple approaches for further improvement in the forecasting function are discussed. All solutions are computed using the libraries from chapter 2, and the algorithm is also implemented as part of those libraries for use in other models. Chapter 4 discusses a model of the labour market with matching and large, heterogeneous forms. The forms experience idiosyncratic demand shocks and adjust their size in response. Steady state solutions are computed for different values of the exogenous tax rate and the transition path demonstrates that, in contrast to the canonical matching model, employment does not adjust instantaneously to changes in market conditions. Chapter 5 discusses some avenues for potential future research.