Numerical diagnostics and improvements for the solution of linear dynamic macroeconomic models

• Applicant: Professor Dr. Alexander Meyer-Gohde
• Subject Area: Statistics and Econometrics ; Economic Theory
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 465469938

Policy recommendations from macroeconomists demand quantitative answers. The limitations of our models and their approximations put our ability to provide such answers in question. While much of the literature has explored more complicated models and higher-order, nonlinear solutions, virtually no attention has been given to the numerical limitations of our most basic method: linear approximation. The importance of this is at least twofold: linear approximations are ubiquitous in macroeconomic analysis and many nonlinear methods build upon, and are hence subject to the limitations of, linear approximations.The project will first highlight the importance of taking the limitations of finite precision arithmetic into consideration when providing quantitative macroeconomic forecasts and policy assessments when solving linear dynamic stochastic general equilibrium (DSGE) models. Second, the project will provide researchers and practitioners with methods to assess and, if necessary, improve their analyses for such considerations. Finally, the project will revive methods, factorization and frequency domain, that have fallen into neglect by (1) providing state of the art methods for their implementation and (2) applying the methods to problems outside the reach of the current, time domain standard.In the course of the project, numerical algorithms will be programmed and freely disseminated that will allow researchers and practitioners to assess the numerical fulfillment, i.e. conditioning numbers, associated with the assumptions necessary for the unique stable solution of linear time domain models, that implement recent advances from the applied mathematics literature on quadratic matrix and eigenvalue problems, that implement alternative iterative methods, and that apply factorization and frequency domain techniques.

• DFG Programme: Research Grants