Logical Pitfalls of Assuming Bounded Solutions to Expectational Difference Equations

The precedent for solving expectational difference equations has been to solve converging equations backwards and diverging equations forward by assuming the solution is bounded. This precedent often leads to incorrect solutions and has less than rigorous foundations. More rigorous procedures would be to determine the terminal condition in a finite model and take the limit of that terminal condition as the horizon goes to infinity. Also, whether one solves forward or backwards depends on the context of the difference equation, not on convergence or divergence. These new procedures reveal Woodford’s (2003) model of a cashless economy to be incomplete.