Evaluating Approximate Equilibria of Dynamic Economic Models

This paper evaluates the performances of Perturbation Methods, the Parameterized Expectations Algorithm and Projection Methods in finding approximate decision rules of the basic neoclassical stochastic growth model. In contrast to the existing literature, we focus on comparing numerical methods for a given functional form of the approximate decision rules, and we repeat the evaluation for many different parameter sets. We find that significant gains in accuracy can be achieved by moving from linear to higher-order approximations. Our results show further that among linear and quadratic approximations, Perturbation Methods yield particularly good results, whereas Projection Methods are well suited to derive higher-order approximations. Finally we show that although the structural parameters of the model economy have a large effect on the accuracy of numerical approximations, the ranking of competing methods is largely independent from the calibration.