Chapter 12 Approximation, perturbation, and projection methods in economic analysis

This chapter examines local and global approximation methods that have been used or have potential future value in economic and econometric analysis. The chapter presents the related projection method for solving operator equations and illustrates its application to dynamic economic analysis, dynamic games, and asset market equilibrium with asymmetric information. In the chapter, it is shown that a general class of techniques from the numerical partial differential equations literature can be usefully applied and adapted to solve nonlinear economic problems. Despite the specificity of the applications discussed in the chapter the general description makes clear the general usefulness of perturbation and projection methods for economic problems, both theoretical modeling and empirical analysis. The application of perturbation and projection methods and the underlying approximation ideas have substantially improved the efficiency of economic computations. In addition, exploitation of these ideas will surely lead to progress.