Computing Economic Equilibria Using Projection Methods

Abstract

The analysis of dynamic economic models routinely leads to the mathematical problem of determining an unknown function for which no closed-form solution exists. Economists must then resort to methods of numerical approximation when analyzing such models. Among the computational methods that have been successfully applied in economics and finance, one set of techniques stands out due to its flexibility and robustness: projection methods. In this article, we describe the basic steps of these methods for several different applications, surveying many successful applications of projection methods to dynamic economic models. Importantly, we emphasize that the ever-increasing complexity and dimensionality of dynamic models have made the previously used simpler methods obsolete and the applications of projection methods all but mandatory. We closely examine the most recent endeavors in the literature on solving economic models with projection methods. Expected final online publication date for the Annual Review of Economics, Volume 12 is August 3, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Macro-Finance Models with Nonlinear Dynamics

“…Methodological and empirical challenges have arisen along the way. First, advanced nonlinear solution methods and estimation approaches are necessary, if one wishes to guarantee that key nonlinear dynamics in financial markets and the macroeconomy are eventually captured in quantitative analysis (e.g., Brunnermeier & Sannikov 2016;Miftakhova, Schmedders & Schumacher 2020). Second, data availability and tail risk measurement constitute a central challenge to the evaluation and validation of macro-finance models with nonlinear dynamics.…”