Estimación de modelos de equilibrio general en economías dinámicas por métodos de Monte Carlo y Cadenas de Markov
Estimation of general equilibium model in dynamic economies using Markov Chain Monte Carlo methods
Gloria Estévez*+ Saba Infante†* Francisco Sáez‡* *Dirección para correspondencia
Resumen En este trabajo se describe un procedimiento general para hacer inferencia bayesiana basados en la evaluación de la verosimilitud de los modelos de equilibrio general estocásticos (MEGE) a través de los métodos de Monte Carlo por Cadenas de Markov (MCMC). La metodología propuesta requiere log linealizar los modelos, transformarlos en la forma espacio estado, luego utilizar el filtro de Kalman para evaluar la función de verosimilitud y finalmente aplicar el algoritmo Metropolis Hastings para estimar los parámetros de la distribución a posteriori. Se ilustra la técnica mediante el uso del modelo básico de crecimiento estocástico, considerando datos trimestrales de la economía venezolana comprendidos entre el primer trimestre de (1984) hasta el tercer trimestre de (2004). El análisis empírico realizado nos permite concluir que los algoritmos utilizados para estimar los parámetros del modelo trabajan de manera eficiente y a bajo costo computacional, las estimaciones obtenidas son consistentes, es decir, los estimados de las predicciones reflejan adecuadamente el comportamiento del producto, el empleo, el consumo y la inversión per capita del país. En las gráficas de los histogramas estimados se observa que tienen comportamientos bimodales y distribuciones asimétricas. Palabras clave: modelos de equilibrio general, inferencia bayesiana, algoritmos recursivos. Abstract This paper describes a general procedure to do Bayesian inference based on the likelihood evaluation of the stochastic general equilibrium models (MEGE) through Markov Chain Monte Carlo methods (MCMC). The proposed methodology involves log linearizing the model, transformed into state space form, then use the Kalman filter to evaluate the likelihood function and finally apply the Metropolis Hastings algorithm to estimate the posterior distribution parameters. Technique is illustrated using the stochastic growth of basic model, considering quarterly data on the Venezuelan economy between the first quarter of (1984) through the third quarter of (2004). The empirical analysis made allows us to conclude that the algorithms used to estimate the model parameters work efficiently and low computational cost, the estimates obtained are consistent, that is, estimates of the predictions adequately reflect the behavior of the product, employment, consumption and investment per capita in the country. The graphs of the estimated histograms show bimodal and skewed distributions. Keywords: General equilibrium models, Bayesian inference, recursive algorithms. Mathematics Subject Classification: 91B50.
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Agradecimientos Los autores agradecen las revisiones y comentarios de Juan Rubio quién facilitó los programas base para la realización de éste documento y motivo a escribir este artículo. Cualquier error u omisión es exclusiva responsabilidad de los autores.
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*Oficina de Investigaciones Económicas, Banco Central de Venezuela, Av. Urdaneta esq. Las Carmelitas, Caracas 1010 – Venezuela. E-Mail: gestevez@bcv.org.ve †Centro de Análisis, Modelado y Tratamiento de Datos, y Departamento de Matemática, Facultad de Ciencias y Tecnología, Universidad de Carabobo, Valencia 2008, Venezuela. E-Mail: sinfante@uc.edu.ve ‡Misma dirección que/Same address as G. Estévez. E-Mail: fransaez@bcv.org.ve
Received: 3-May-2010; Revised: 6-Nov-2011; Accepted: 7-Dec-2011
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