YADA Manual — Computational Details

YADA (Yet Another Dsge Application) is a Matlab program for Bayesian estimation and evaluation of Dynamic Stochastic General Equilibrium and vector autoregressive models. This paper provides the mathematical details for the various functions used by the software. First, some rather famous examples of DSGE models are presented and all these models are included as examples in the YADA distribution. YADA supports a number of different algorithms for solving log-linearized DSGE models. The fastest algorithm is the so called Anderson-Moore algorithm (AiM), but the approaches of Klein and Sims are also covered and have the benefit of being numerically more robust in certain situations. The AiM parser is used to translate the DSGE model equations into a structural form that the solution algorithms can make use of. The solution of the DSGE model is expressed as a VAR(1) system that represents the state equations of the state-space representation. Thereafter, the different prior distributions that are supported, the state-space representation and the Kalman filter used to evaluate the log-likelihood are presented. Furthermore, it discusses how the posterior mode is computed, including how the original model parameters can be transformed internally to facilitate the posterior mode estimation. Next, the paper provides some details on the algorithms used for sampling from the posterior distribution: the random walk Metropolis and slice sampling algorithms. In order to conduct inference based on the draws from the posterior sampler, tools for evaluating convergence are considered next. We are here concerned both with simple graphical tools, as well as formal tools for single and parallel chains. Different methods for estimating the marginal likelihood are considered thereafter. Such estimates may be used to evaluate posterior probabilities for different DSGE models. Various tools for evaluating an estimated DSGE model are provided, including impulse response functions, forecast error variance decompositions, historical forecast error and observed variable decompositions. Forecasting issues, such as the unconditional and conditional predictive distributions, are examined in the following section. The paper thereafter considers frequency domain analysis, such as a decomposition of the population spectrum into shares explained by the underlying structural shocks. Estimation of a VAR model with a prior on the steady state parameters is also discussed. The main concerns are: prior hyperparameters, posterior mode estimation, posterior sampling via the Gibbs sampler, and marginal likelihood calculation (when the full prior is proper), before the topic of forecasting with Bayesian VARs is considered. Next, the paper turns to the important topic of misspecification and goodness-of-fit analysis, where the DSGE-VAR framework is considered in some detail. Finally, the paper provides information about the various types of input that YADA requires and how these inputs should be prepared. Remarks: Copyright c © 2006–2015 Anders Warne, Monetary Policy Research Division, Directorate General Research, European Central Bank. I have received valuable comments and suggestions by past and present members of the NAWM team: Kai Christoffel, Günter Coenen, José Emilio Gumiel, Roland Straub, Michal Andrle (Česká Národní Banka, IMF), Juha Kilponen (Suomen Pankki), Igor Vetlov (Lietuvos Bankas), and Pascal Jacquinot, as well as our consultant from Sveriges Riksbank, Malin Adolfson. A special thanks goes to Mattias Villani for his patience when trying to answer all my questions on Bayesian analysis. I have also benefitted greatly from a course given by Frank Schorfheide at the ECB in November 2005. Moreover, I am grateful to Juan Carlos Martínez-Ovando (Banco de México) for suggesting the slice sampler, and to Paul McNelis (Fordham University) for sharing his dynare code and helping me out with the Fagan-Lothian-McNelis DSGE example. And last but not least, I am grateful to Magnus Jonsson, Stefan Laséen, Ingvar Strid and David Vestin at Sveriges Riksbank, to Antti Ripatti at Soumen Pankki, and to Tobias Blattner, Boris Glass, Wildo González, Tai-kuang Ho, Markus Kirchner, Mathias Trabandt, and Peter Welz for helping me track down a number of unpleasant bugs and to improve the generality of the YADA code. Finally, thanks to Dave Christian for the Kelvin quote.