This paper shows how particle filtering facilitates likelihood-based inference in dynamic macroeconomic models. The economies can be nonlinear and/or nonnormal. We describe how to use the output from the particle filter to estimate the structural parameters of the model, those characterizing preferences and technology, and to compare different economies. Both tasks can be implemented from either a classical or a Bayesian perspective. We illustrate the technique by estimating a business cycle model with investment-specific technological change, preference shocks, and stochastic volatility.

This paper reviews Bayesian methods that have been developed in recent years to estimate and evaluate dynamic stochastic general equilibrium (DSGE) models. We consider the estimation of linearized DSGE models, the evaluation of models based on Bayesian model checking, posterior odds comparisons, and comparisons to vector autoregressions, as well as the nonlinear estimation based on a second-order accurate model solution. These methods are applied to data generated from correctly specified and misspecified linearized DSGE models, and a DSGE model that was solved with a second-order perturbation method. (JEL C11, C32, C51, C52)

This paper compares two methods for undertaking likelihood-based inference in dynamic equilibrium economies: a sequential Monte Carlo filter and the Kalman filter. The sequential Monte Carlo filter exploits the nonlinear structure of the economy and evaluates the likelihood function of the model by simulation methods. The Kalman filter estimates a linearization of the economy around the steady state. We report two main results. First, both for simulated and for real data, the sequential Monte Carlo filter delivers a substantially better fit of the model to the data as measured by the marginal likelihood. This is true even for a nearly linear case. Second, the differences in terms of point estimates, although relatively small in absolute values, have important effects on the moments of the model. We conclude that the nonlinear filter is a superior procedure for taking models to the data. Copyright © 2005 John Wiley & Sons, Ltd. 1.

We present an algorithm and software routines for computing nthorder Taylor series approximate solutions to dynamic, discrete-time rational expectations models around a nonstochastic steady state. The primary advantage of higher-order (as opposed to first- or secondorder) approximations is that they are valid not just locally, but often globally (i.e., over nonlocal, possibly very large compact sets) in a rigorous sense that we specify. We apply our routines to compute first- through seventh-order approximate solutions to two standard macroeconomic models, a stochastic growth model and a life-cycle consumption model, and discuss the quality and global properties of these solutions.

Bank of Canada discussion papers are completed research studies on a wide variety of technical subjects relevant to central bank policy. The views expressed in this paper are those of the author. No responsibility for them should be attributed to the Bank of Canada.

This paper shows how changes in the volatility of the real interest rate at which small open emerging economies borrow have a quantitatively important effect on real variables like output, consumption, investment, and hours worked. To motivate our investigation, we document the strong evidence of time-varying volatility in the real interest rates faced by a sample of four emerging small open

This paper explores the application of the changes of variables technique to solve the stochastic neoclassical growth model. We use the method of Judd (2003) to change variables in the computed policy functions that characterize the behavior of the economy. We report how the optimal change of variables reduces the average absolute Euler equation errors of the solution of the model by a factor of three. We also demonstrate how changes of variables correct for variations in the volatility of the economy even if we work with first order policy functions and how we can keep a linear representation of the laws of motion of the model if we use a nearly optimal transformation. We discuss how to apply our results to estimate dynamic equilibrium economies.

participants at several seminars for useful comments, and Béla Személy for invaluable research assistance. Beyond the usual disclaimer, we must note that any views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta, the Federal Reserve Bank of Philadelphia, or the Federal Reserve System. Finally, we also thank the NSF for financial support.

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with recursive preferences such as those in Epstein and Zin (1989 and 1991). Models with these preferences have recently become popular, but we know little about the best ways to implement them numerically. To fill this gap, we solve the stochastic neoclassical growth model with recursive preferences using four different approaches: second and third-order perturbation, Chebyshev polynomials, and value function iteration. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy. Our main finding is that a third-order perturbation is competitive in terms of accuracy with Chebyshev polynomials and value function iteration, while being an order of magnitude faster to run. Therefore, we conclude that perturbation methods are an attractive approach for computing this class of problems.

In this paper, I review the literature on the formulation and estimation of dynamic stochastic general equilibrium (DSGE) models with a special emphasis on Bayesian methods. First, I discuss the evolution of DSGE models over the last couple of decades. Second, I explain why the profession has decided to estimate these models using Bayesian methods. Third, I brie‡y introduce some of the techniques required to compute and estimate these models. Fourth, I illustrate the techniques under consideration by estimating a benchmark DSGE model with real and nominal rigidities. I conclude by o¤ering some pointers for future research.