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Iterative and Recursive Estimation in Structural Non-Adaptive Models

  • Sergio Pastorello
  • Valentin Patilea
  • Éric Renault

An inference method, called latent backfitting is proposed. It appears well suited for econometric models where the structural relationships of interest define the observed endogenous variables as a known function of unobserved state variables and unknown parameters. This nonlinear state space specification paves the way for iterative or recursive EM-like strategies. In the E-steps the state variables are forecasted given the observations and a value of the parameters. In the M-steps these forecasts are used to deduce estimators of the unknown parameters from the statistical model of latent variables. The proposed iterative/recursive estimation is particularly useful for latent regression models and for dynamic equilibrium models involving latent state variables. Practical implementation issues are discussed through the example of term structure models of interest rates. Nous proposons une méthode d'inférence appelée «latent backfitting». Cette méthode est spécialement conçue pour les modèles économétriques dans lesquels les relations structurelles d'intérêt définissent les variables endogènes observées comme une fonction connue des variables d'états non observées et des paramètres inconnus. Cette spécification espace-état non linéaire ouvre la voie à des stratégies itératives ou récursives de type EM. Dans l'étape E, les variables d'état sont prédites à partir des observations et des valeurs des paramètres. Dans l'étape M, ces prévisions sont utilisées pour déduire des estimateurs des paramètres inconnus à partir du modèle statistique des variables latentes. L'estimation itérative/récursive proposée est particulièrement utile pour les modèles avec équation de régression latente et les modèles dynamiques d'équilibre utilisant des variables d'état latentes. Les questions relatives à l'application de ces méthodes sont analysées à travers l'exemple des modèles de structure par termes des taux d'intérêt.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2003s-08.

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Length: 82 pages
Date of creation: 01 Apr 2003
Handle: RePEc:cir:cirwor:2003s-08
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