Learning Ordinary Differential Equations for Macroeconomic Modelling

This article describes an empirical approach to the macroeconomic modelling of the Euro zone. Data for the period 1971 -- 2007 has been used to learn systems of ordinary differential equations (ODE) linking inflation, real interest and output growth. The equation discovery algorithm LAGRAMGE was used in conjunction with a grammar defining a potentially large range of possible parametric equations. The coefficients of each equation are automatically fitted on the training data and the ones with the lowest error rates returned as a result. We have added a tool for out-of-sample error evaluation to the in-sample evaluation built in LAGRAMGE. The paper compares the performance of ODE models to previous work on the learning of ordinary equations for the same purpose.