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Iterative and Recursive Estimation in Structural Non-Adaptive Models

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  • Sergio Pastorello
  • Valentin Patilea
  • Éric Renault

Abstract

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.

Suggested Citation

  • Sergio Pastorello & Valentin Patilea & Éric Renault, 2003. "Iterative and Recursive Estimation in Structural Non-Adaptive Models," CIRANO Working Papers 2003s-08, CIRANO.
  • Handle: RePEc:cir:cirwor:2003s-08
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    References listed on IDEAS

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    Cited by:

    1. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2015. "Parametric Inference and Dynamic State Recovery From Option Panels," Econometrica, Econometric Society, vol. 83(3), pages 1081-1145, May.
    2. Fan, Yanqin & Gentry, Matthew & Li, Tong, 2011. "A new class of asymptotically efficient estimators for moment condition models," Journal of Econometrics, Elsevier, vol. 162(2), pages 268-277, June.
    3. David T. Frazierz & Éric Renault, 2016. "Efficient Two-Step Estimation via Targeting," CIRANO Working Papers 2016s-16, CIRANO.
    4. Garcia, René & Lewis, Marc-André & Pastorello, Sergio & Renault, Éric, 2011. "Estimation of objective and risk-neutral distributions based on moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 22-32, January.
    5. Altissimo, Filippo & Mele, Antonio, 2005. "Simulated nonparametric estimation of dynamic models with applications to finance," LSE Research Online Documents on Economics 24658, London School of Economics and Political Science, LSE Library.
    6. Li, Junye & Favero, Carlo & Ortu, Fulvio, 2012. "A spectral estimation of tempered stable stochastic volatility models and option pricing," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3645-3658.
    7. Dumitru, Ana-Maria & Holden, Tom, 2017. "A Hawkes model of the transmission of European sovereign default risk," EconStor Conference Papers 168431, ZBW - German National Library of Economics.
    8. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    9. Li, Tong, 2010. "Indirect inference in structural econometric models," Journal of Econometrics, Elsevier, vol. 157(1), pages 120-128, July.
    10. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76 Elsevier.
    11. Adam Canopius, 2006. "Practitioners' Corner," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 346-351.
    12. repec:eee:econom:v:201:y:2017:i:2:p:212-227 is not listed on IDEAS
    13. Liu, Sheen & Shi, Jian & Wang, Junbo & Wu, Chunchi, 2007. "How much of the corporate bond spread is due to personal taxes?," Journal of Financial Economics, Elsevier, vol. 85(3), pages 599-636, September.
    14. Andreasen, Martin M. & Christensen, Bent Jesper, 2015. "The SR approach: A new estimation procedure for non-linear and non-Gaussian dynamic term structure models," Journal of Econometrics, Elsevier, vol. 184(2), pages 420-451.
    15. Torben G. Andersen & Nicola Fusari & Viktor Todorov & Rasmus T. Varneskov, 1001. "Unified Inference for Nonlinear Factor Models from Panels with Fixed and Large Time Span," CREATES Research Papers 2018-03, Department of Economics and Business Economics, Aarhus University.
    16. Damiaan Persyn & Wouter Torfs, 2013. "A gravity equation for commuting - with an application to estimating regional and language border effects in Belgium," ERSA conference papers ersa13p599, European Regional Science Association.
    17. repec:eee:econom:v:202:y:2018:i:1:p:75-91 is not listed on IDEAS

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