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43
Bayesian analysis of DSGE models
 ECONOMETRICS REVIEW
, 2007
"... 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 ..."
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Cited by 130 (5 self)
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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 secondorder 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 secondorder perturbation method. (JEL C11, C32, C51, C52)
Estimating macroeconomic models: a likelihood approach
, 2006
"... This paper shows how particle filtering facilitates likelihoodbased 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 prefer ..."
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Cited by 102 (27 self)
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This paper shows how particle filtering facilitates likelihoodbased 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 investmentspecific technological change, preference shocks, and stochastic volatility.
Supplement to “Time series analysis via mechanistic models”.
 Ann. Appl. Statist., Supporting
, 2008
"... The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the cons ..."
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Cited by 36 (10 self)
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The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plugandplay property. Our work builds on recently developed plugandplay inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae. 1. Introduction. A dynamical system is a process whose state varies with time. A mechanistic approach to understanding such a system is to write down equations, based on scientific understanding of the system, which describe how it evolves with time. Further equations describe the relationship of the state of the system to available observations on it. Mechanistic time series analysis concerns drawing inferences from the available data about the hypothesized equations
The Econometrics of DSGE Models
, 2009
"... 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 decide ..."
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Cited by 31 (1 self)
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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.
Fortune or Virtue: TimeVariant Volatilities Versus Parameter Drifting in U.S. Data ∗
, 2010
"... 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 ..."
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Cited by 29 (7 self)
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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.
2006) Convergence Properties of the Likelihood of Computed Dynamic Models
 Econometrica
"... This paper studies the econometrics of computed dynamic models. Since these models generally lack a closedform solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function ..."
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Cited by 26 (3 self)
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This paper studies the econometrics of computed dynamic models. Since these models generally lack a closedform solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function rather than the exact likelihood implied by the exact policy function. What are the consequences for inference of the use of approximated likelihoods? First, we find conditions under which, as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we show that second order approximation errors in the policy function, which almost always are ignored by researchers, have first order effects on the likelihood function. Third, we discuss convergence of Bayesian and classical estimates. Finally, we propose to use a likelihood ratio test as a diagnostic device for problems derived from the use of approximated likelihoods.
How structural are structural parameters
 NBER Macroeconomics Annual 122
, 2007
"... conference for comments. 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 or the Federal Reserve System. Finally, we also thank the NSF for financial support. This paper studies how sta ..."
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Cited by 22 (0 self)
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conference for comments. 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 or the Federal Reserve System. Finally, we also thank the NSF for financial support. This paper studies how stable over time are the socalled “structural parameters” of dynamic stochastic general equilibrium (DSGE) models. To answer this question, we estimate a mediumscale DSGE model with real and nominal rigidities using U.S. data. In our model, we allow for parameter drifting and rational expectations of the agents with respect to this drift. We document that there is strong evidence that parameters change within our sample. We illustrate variations in the parameters describing the monetary policy reaction function and in the parameters characterizing the pricing behavior of firms and households. Moreover, we show how the movements in the pricing parameters are correlated with inflation. Thus, our results cast doubts on the empirical relevance of Calvo models.
A Parallel CuttingPlane Algorithm for the Vehicle Routing Problem With Time Windows
, 1999
"... In the vehicle routing problem with time windows a number of identical vehicles must be routed to and from a depot to cover a given set of customers, each of whom has a specified time interval indicating when they are available for service. Each customer also has a known demand, and a vehicle may on ..."
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Cited by 19 (1 self)
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In the vehicle routing problem with time windows a number of identical vehicles must be routed to and from a depot to cover a given set of customers, each of whom has a specified time interval indicating when they are available for service. Each customer also has a known demand, and a vehicle may only serve the customers on a route if the total demand does not exceed the capacity of the vehicle. The most effective solution method proposed to date for this problem is due to Kohl, Desrosiers, Madsen, Solomon, and Soumis. Their algorithm uses a cuttingplane approach followed by a branchand bound search with column generation, where the columns of the LP relaxation represent routes of individual vehicles. We describe a new implementation of their method, using Karger's randomized minimumcut algorithm to generate cutting planes. The standard benchmark in this area is a set of 87 problem instances generated in 1984 by M. Solomon; making using of parallel processing in both the cuttingpla...
Likelihood estimation of DSGE models with EpsteinZin preferences
, 2008
"... This paper illustrates how to perform likelihoodbased inference in dynamic stochastic general equilibrium (DSGE) models with EpsteinZin preferences. This class of preferences has recently become a popular device to account for asset pricing observations and other phenomena that are challenging to ..."
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Cited by 17 (5 self)
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This paper illustrates how to perform likelihoodbased inference in dynamic stochastic general equilibrium (DSGE) models with EpsteinZin preferences. This class of preferences has recently become a popular device to account for asset pricing observations and other phenomena that are challenging to address within the traditional stateseparable utility framework. However, there has been little econometric work in the area, particularly from a likelihood perspective, because of the difficulty in computing an equilibrium solution to the model and in deriving the likelihood function. To fill this gap, we build a real business cycle model with EpsteinZin preferences and longrun growth, solve it with perturbation techniques, and evaluate its likelihood with the particle filter. We estimate the model using U.S. macro and yield curve data. We discuss the ability of the model to explain the business cycle, asset prices, the comovements between these two, and the implications of our point estimates for the welfare cost of the business cycle.
Efficient Likelihood Evaluation of StateSpace Representations
, 2009
"... We develop a numerical procedure that facilitates efficient likelihood evaluation in applications involving nonlinear and nonGaussian statespace models. The procedure approximates necessary integrals using continuous approximations of target densities. Construction is achieved via efficient impor ..."
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Cited by 12 (1 self)
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We develop a numerical procedure that facilitates efficient likelihood evaluation in applications involving nonlinear and nonGaussian statespace models. The procedure approximates necessary integrals using continuous approximations of target densities. Construction is achieved via efficient importance sampling, and approximating densities are adapted to fully incorporate current information. We illustrate our procedure in applications to dynamic stochastic general equilibrium models.