Parameterized Expectations Algorithm and the Moving Bounds: a comment on convergence properties

In this paper we analyze the convergence properties of the moving bounds algorithm to initialize the Parameterized Expectations Algorithm suggested by Maliar and Maliar (2003) [Journal of Business and Economic Statistics 1, pp. 88-92]. We carry out a Monte Carlo experiment to check its performance against some initialization alternatives based on homotopy principles. We do so within the framework of two standard neoclassical growth models. We show that: (i) speed of convergence is poor as compared to alternatives; (ii) starting from a not very accurate initial guess might prevent convergence in relatively simple models. The results suggest the need to fine tune Maliar and Maliar's method to improve its convergence properties.