Which order is too much? An application to a model with staggered price and wage contratcs

A recent literature have proposed different methods to produce second-order accurate approximation to the solutions to DGSE's from a straightforward second-order approximation of the model. Among others, Judd (2002), Jin and Judd (2002) show how to compute approximation of arbitrary order on discrete-time models. Collard and Juillard (2001b), Anderson and Levin (2002), Schmitt-Grohe and Uribe (2004) apply pertubation methods of higher than first order. Sims (2002) generalised the approaches of Judd (1998), Judd and Gaspar (1997) and Judd and Guu (1993) in order to find a second-order accurate solution of discrete-time dynamic equilibrium models. Kim et al. (2003) propose an algorithm in order to compute a second-order approximation in which the error in the approximation is claimed to converge in probability to zero and does not depend on strict boundedness of the support of the distribution of the shocks. In this paper, we investigate the accuracy of k-order perturbation method in approximating the solution of a DSGE model. As a benchmark model, we use a version of Erceg, Henderson and Levin (2000) model with staggered price and wage contracts. Using different criteria, we assess to what extent the order of the approximation matters and which order is reliable. Our results show that standard first-order and second-order approximation may lead to misleading interpretations. At the same time, over-approximating the model may also conduct to substantial distortions.