Polynomial Chaos Expansion Efficient Evaluation and Estimation of Computational Models

Abstract

Polynomial chaos expansion (PCE) provides a method that enables the representation of a random variable, the quantity of interest (QoI), as a series expansion of other random variables, the inputs. Traditionally, uncertain parameters of the model are treated as random inputs, and the QoI is an element of the model’s solution, e.g., the policy function, the second moments of observables, or the posterior kernel. PCE then surrogates time-consuming repetition of model solutions and evaluations for different values of the inputs. Additionally, PCE allows to discretize the space of square-integrable distributions, including those containing mass points.The paper discusses the suitability of PCE for computational economics. We, therefore, introduce to the theory behind PCE, analyze the convergence behavior for different elements of the solution of the standard real business cycle model as illustrative example, and check the accuracy, if standard empirical methods are applied. The results are promising, both in terms of accuracy and efficiency.

Keywords: C11, C13, C32, C63