Mathematical Models and Economic Forecasting: Some Uses and Mis-Uses of Mathematics in Economics

We consider three 'cases studies' of the uses and mis-uses of mathematics in economics and econometrics.  The first concerns economic forecasting, where a mathematical analysis is essential, and is independent of the specific forecasting model and how the process being forecast behaves.  The second concerns model selection with more candidate variables than the number of observations.  Again, an understanding of the properties of extended general-to-specific procedures is impossible without advanced mathematical analysis.  The third concerns inter-temporal optimization and the formation of 'rational expectations', where misleading results follow from present mathematical approaches for realistic economies.  The appropriate mathematics remains to be developed, and may end 'problem specific' rather than generic.