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Creator: Duprey, James N. and Litterman, Robert B. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 128 Palabra clave: Vector autoregression, Money market model, and Monetary policy Tema: C53 - Forecasting Models; Simulation Methods and C11 - Bayesian Analysis: General
Creator: Roberds, William Series: Business analysis committee meeting Abstract:
One of the more significant developments in econometric modeling over the past decade has been the invention of the forecasting technique known as Bayesian vector autoregression (BVAR). This paper provides a detailed description of the process of specifying a BVAR model of quarterly time series on the U.S. macroeconomy. The postsample forecasting performance of the model is evaluated at an informal level by comparing the model's performance to certain naive forecasting methods, and is evaluated at a formal level by means of efficiency tests. Although the null hypothesis of efficiency is rejected for the model's forecasts, the accuracy of the model exceeds that of naive forecasting methods, and seems comparable to that of commercial forecasting firms for early quarter forecasts.
Palabra clave: BVAR, Vector autoregression, and Bayesian analysis Tema: C11 - Bayesian Analysis: General and C53 - Forecasting Models; Simulation Methods
Creator: Geweke, John Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 532 Abstract:
This paper integrates and extends some recent computational advances in Bayesian inference with the objective of more fully realizing the Bayesian promise of coherent inference and model comparison in economics. It combines Markov chain Monte Carlo and independence Monte Carlo with importance sampling to provide an efficient and generic method for updating posterior distributions. It exploits the multiplicative decomposition of marginalized likelihood into predictive factors, to compute posterior odds ratios efficiently and with minimal further investment in software. It argues for the use of predictive odds ratios in model comparison in economics. Finally, it suggests procedures for public reporting that will enable remote clients to conveniently modify priors, form posterior expectations of their own functions of interest, and update the posterior distribution with new observations. A series of examples explores the practicality and efficiency of these methods.
This paper was prepared for the inaugural Colin Clark Lecture, Australasian Meetings of the Econometric Society, July 1994.
Palabra clave: Computation, Model comparison, Bayesian inference, and Econometric modeling Tema: C53 - Forecasting Models; Simulation Methods and C11 - Bayesian Analysis: General
Creator: Doan, Thomas, Litterman, Robert B., and Sims, Christopher A. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 243 Abstract:
This paper develops a forecasting procedure based on a Bayesian method for estimating vector autoregressions. The procedure is applied to ten macroeconomic variables and is shown to improve out-of-sample forecasts relative to univariate equations. Although cross-variables responses are damped by the prior, considerable interaction among the variables is shown to be captured by the estimates. We provide unconditional forecasts as of 1982:12 and 1963:3* We also describe how a model such as this can be used to make conditional projections and to analyse policy alternatives. As an example, we analyze a Congressional Budget Office forecast made in 1982:12. While no automatic causal interpretations arise from models like ours, they provide a detailed characterization of the dynamic statistical interdependence of a set of economic variables, which may help in evaluating causal hypotheses, without containing any such hypotheses themselves.
Palabra clave: Forecasting, Macroeconomics, and Bayesian methods Tema: E27 - Macroeconomics: Consumption, Saving, Production, Employment, and Investment: Forecasting and Simulation: Models and Applications and C11 - Bayesian Analysis: General
Creator: Schorfheide, Frank and Song, Dongho Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 701 Abstract:
This paper develops a vector autoregression (VAR) for macroeconomic time series which are observed at mixed frequencies – quarterly and monthly. The mixed-frequency VAR is cast in state-space form and estimated with Bayesian methods under a Minnesota-style prior. Using a real-time data set, we generate and evaluate forecasts from the mixed-frequency VAR and compare them to forecasts from a VAR that is estimated based on data time-aggregated to quarterly frequency. We document how information that becomes available within the quarter improves the forecasts in real time.
Palabra clave: Macroeconomic forecasting, Bayesian methods, Real-time data, and Vector autoregressions Tema: C32 - Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models, C11 - Bayesian Analysis: General, and C53 - Forecasting Models; Simulation Methods
Creator: Geweke, John and Petrella, Lea Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 553 Abstract:
This paper provides a general and efficient method for computing density ratio class bounds on posterior moments, given the output of a posterior simulator. It shows how density ratio class bounds for posterior odds ratios may be formed in many situations, also on the basis of posterior simulator output. The computational method is used to provide density ratio class bounds in two econometric models. It is found that the exact bounds are approximated poorly by their asymptotic approximation, when the posterior distribution of the function of interest is skewed. It is also found that posterior odds ratios display substantial variation within the density ratio class, in ways that cannot be anticipated by the asymptotic approximation.
Palabra clave: Bayesian inference, Markov-chain Monte Carlo, Normal mixture, and Probit model Tema: C11 - Bayesian Analysis: General and C63 - Computational Techniques; Simulation Modeling
Creator: Geweke, John Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 540 Abstract:
The reduced rank regression model arises repeatedly in theoretical and applied econometrics. To date the only general treatment of this model have been frequentist. This paper develops general methods for Bayesian inference with noninformative reference priors in this model, based on a Markov chain sampling algorithm, and procedures for obtaining predictive odds ratios for regression models with different ranks. These methods are used to obtain evidence on the number of factors in a capital asset pricing model.
Palabra clave: Factor model, Capital asset pricing model, and Predictive odds Tema: C11 - Bayesian Analysis: General and C15 - Statistical Simulation Methods: General
Creator: Fernandez-Villaverde, Jesus and Rubio-Ramírez, Juan Francisco Series: Joint committee on business and financial analysis Abstract:
This paper presents a method to perform likelihood-based inference in nonlinear dynamic equilibrium economies. This type of models has become a standard tool in quantitative economics. However, existing literature has been forced so far to use moment procedures or linearization techniques to estimate these models. This situation is unsatisfactory: moment procedures suffer from strong small samples biases and linearization depends crucially on the shape of the true policy functions, possibly leading to erroneous answers. We propose the use of Sequential Monte Carlo methods to evaluate the likelihood function implied by the model. Then we can perform likelihood-based inference, either searching for a maximum (Quasi-Maximum Likelihood Estimation) or simulating the posterior using a Markov Chain Monte Carlo algorithm (Bayesian Estimation). We can also compare different models even if they are nonnested and misspecified. To perform classical model selection, we follow Vuong (1989) and use the Kullback-Leibler distance to build Likelihood Ratio Tests. To perform Bayesian model comparison, we build Bayes factors. As an application, we estimate the stochastic neoclassical growth model.
Palabra clave: Sequential Monte Carlo methods, Nonlinear filtering, Dynamic equilibrium economies, and Likelihood-based inference Tema: C11 - Bayesian Analysis: General, C10 - Econometric and Statistical Methods and Methodology: General, C13 - Estimation: General, and C15 - Statistical Simulation Methods: General