Estimating Macroeconomic Models: A Likelihood Approach

This paper shows how particle filtering allows us to undertake likelihood-based inference in dynamic macroeconomic models. The models can be nonlinear and/or non-normal. 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.

Estimating Nonlinear Dynamic Equilibrium economies: A Likelihood Approach

This paper presents a framework to undertake likelihood-based inference in nonlinear dynamic equilibrium economies. We develop a Sequential Monte Carlo algorithm that delivers an estimate of the likelihood function of the model using simulation methods. This likelihood can be used for parameter estimation and for model comparison. The algorithm can deal both with nonlinearities of the economy and with the presence of non-normal shocks. We show consistency of the estimate and its good performance in finite simulations. This new algorithm is important because the existing empirical literature that wanted to follow a likelihood approach was limited to the estimation of linear models with Gaussian innovations. We apply our procedure to estimate the structural parameters of the neoclassical growth model.Likelihood-Based Inference, Dynamic Equilibrium Economies, Nonlinear Filtering, Sequential Monte Carlo)

Estimating Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood

This paper compares two methods for undertaking likelihood-based inference in dynamic equilibrium economies: a Sequential Monte Carlo filter proposed by Fernández-Villaverde and Rubio-Ramírez (2004) 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, even if 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.Likelihood-Based Inference, Dynamic Equilibrium Economies, Nonlinear Filtering, Kalman Filter, Sequential Monte Carlo

A multi-layered Bayesian network model for structured document retrieval

New standards in document representation, like for example SGML, XML, and MPEG-7, compel Information Retrieval to design and implement models and tools to index, retrieve and present documents according to the given document structure. The paper presents the design of an Information Retrieval system for multimedia structured documents, like for example journal articles, e-books, and MPEG-7 videos. The system is based on Bayesian Networks, since this class of mathematical models enable to represent and quantify the relations between the structural components of the document. Some preliminary results on the system implementation are also presented

MEDEA: A DSGE Model for the Spanish Economy

In this paper, we provide a brief introduction to a new macroeconometric model of the Spanish economy named MEDEA (Modelo de Equilibrio Dinámico de la Economía EspañolA). MEDEA is a dynamic stochastic general equilibrium (DSGE) model that aims to describe the main features of the Spanish economy for policy analysis, counterfactual exercises, and forecasting. MEDEA is built in the tradition of New Keynesian models with real and nominal rigidities, but it also incorporates aspects such as a small open economy framework, an outside monetary authority such as the ECB, and population growth, factors that are important in accounting for aggregate fluctuations in Spain. The model is estimated with Bayesian techniques and data from the last two decades. Beyond describing the properties of the model, we perform different exercises to illustrate the potential of MEDEA, including historical decompositions, long-run and short-run simulations, and counterfactual experiments.DSGE Models, Likelihood Estimation, Bayesian Methods

Convergence Properties of the Likelihood of Computed Dynamic Models

This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, economists approximate the policy functions of the agents in the model with numerical methods. But this implies that, instead of the exact likelihood function, the researcher can evaluate only an approximated likelihood associated with the approximated policy function. What are the consequences for inference of the use of approximated likelihoods? First, we show that as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we prove that the approximated likelihood converges at the same rate as the approximated policy function. Third, we find that the error in the approximated likelihood gets compounded with the size of the sample. Fourth, we discuss convergence of Bayesian and classical estimates. We complete the paper with three applications to document the quantitative importance of our results.computed dynamic models, likelihood inference, asymptotic properties

A, B, C’s (And D’s) For Understanding VARS

The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A,B,C,D) that define a state space system. An associated state space system (A,K,C, Sigma) determines a vector autoregression for observables available to an econometrician. We review circumstances under which the impulse response of the VAR resembles the impulse response associated with the economic model. We give four examples that illustrate a simple condition for checking whether the mapping from VAR shocks to economic shocks is invertible. The condition applies when there are equal numbers of VAR and economic shocks.VARs , Invertibility, Estimation of Dynamic Equilibrium Models, economic shocks, innovations

Comparing Solution Methods for Dynamic Equilibrium Economies

This paper compares solution methods for dynamic equilibrium economies. We compute and simulate the stochastic neoclassical growth model with leisure choice using Undetermined Coefficients in levels and in logs, Finite Elements, Chebyshev Polynomials, Second and Fifth Order Perturbations and Value Function Iteration for several calibrations. We document the performance of the methods in terms of computing time, implementation complexity and accuracy and we present some conclusions about our preferred approaches based on the reported evidence.Dynamic Equilibrium Economies, Computational Methods, Linear and Nonlinear Solution Methods