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Indirect Estimation of Just-Identified Models with Control Variates

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  • Giorgio Calzolari

    ()
    (Università degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti")

  • F. Di Iorio

    ()
    (Istat, Istituto Nazionale di Statistica)

  • G. Fiorentini

    ()
    (Università di Firenze, Dipartimento di Statistica, Informatica, Applicazioni “G. Parenti”)

Abstract

Simulation estimators, such as indirect inference or simulated maximum likelihood, are successfully employed for estimating models where the likelihood function does not have a simple analytical expression. They adjust for the bias (inconsistency) produced by the estimation of an auxiliary model that can be manageable, but is essentially misspecified. The price to be paid is an increased variance of the estimated parameters. A component of the variance depends on the stochastic simulation involved in the estimation procedure. To reduce this undesirable effect, one should properly increase the number of simulations (or the length of each simulation) and thus the computational cost. Alternatively, this paper shows how variance reduction can be achieved, at virtually no additional computational cost, by use of control variates. This technique can be easily applied in the just-identified context, that is when the number of parameters is the same in the econometric model (the model of interest) and the auxiliary model. This is a case which often occurs in practical applications. Several models are explicitly considered and experimented with: moving average model, Arma model, stochastic differential equations, dynamic Tobit model, discrete time stochastic volatility models, logit models with random effects. Monte Carlo experiments show, in some cases, a global efficiency gain up to almost 50% over the simplest indirect estimator, obtained at about the same computational cost

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Bibliographic Info

Paper provided by Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" in its series Econometrics Working Papers Archive with number quaderno46.

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Length: 37
Date of creation: 1999
Date of revision:
Handle: RePEc:fir:econom:quaderno46

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Related research

Keywords: Efficient Monte Carlo; Variance reduction techniques; Control variates; Indirect inference; Arma models; Stochastic volatility; Stochastic differential equations; Logit model with random effects.;

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References

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  1. repec:fth:inseep:9821 is not listed on IDEAS
  2. Mealli, Fabrizia & Rampichini, Carla, 1999. "Estimating binary multilevel models through indirect inference," Computational Statistics & Data Analysis, Elsevier, vol. 29(3), pages 313-324, January.
  3. Gabriele Fiorentini & Francesca Di Iorio & Giorgio Calzolari, 1998. "- Control Variates For Variance Reduction In Indirect Inference: Interest Rate Models In Continuous Time," Working Papers. Serie AD 1998-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
  5. Calzolari, Giorgio & Sterbenz, Frederic P, 1986. "Control Variates to Estimate the Reduced Form Variances in Econometric Models," Econometrica, Econometric Society, vol. 54(6), pages 1483-90, November.
  6. Calzolari, Giorgio, 1979. "Antithetic variates to estimate the simulation bias in non-linear models," Economics Letters, Elsevier, vol. 4(4), pages 323-328.
  7. Hendry, David F. & Harrison, Robin W., 1974. "Monte Carlo methodology and the small sample behaviour of ordinary and two-stage least squares," Journal of Econometrics, Elsevier, vol. 2(2), pages 151-174, July.
  8. Chiara Monfardini, 1998. "Estimating stochastic volatility models through indirect inference," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C113-C128.
  9. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  10. Broze, Laurence & Scaillet, Olivier & Zako an, Jean-Michel, 1998. "Quasi-Indirect Inference For Diffusion Processes," Econometric Theory, Cambridge University Press, vol. 14(02), pages 161-186, April.
  11. Bianchi, C. & Cesari, R. & Panattoni, L., 1994. "Alternative Estimators of the Cox, ingersoll and Ross Model of the Term Structure of Interest Rates: A Monte Carlo Comparison," Papers 236, Banca Italia - Servizio di Studi.
  12. Bianchi, Carlo & Cleur, Eugene M, 1996. "Indirect Estimation of Stochastic Differential Equation Models: Some Computational Experiments," Computational Economics, Society for Computational Economics, vol. 9(3), pages 257-74, August.
  13. Monica Billio & Alain Monfort & Christian P, Robert, 1998. "The Simulated Likelihood Ratio (SLR) Method," Working Papers 98-21, Centre de Recherche en Economie et Statistique.
  14. Longford, N. T., 1994. "Logistic regression with random coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 17(1), pages 1-15, January.
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Cited by:
  1. Di Iorio, Francesca & Calzolari, Giorgio, 2006. "Discontinuities in indirect estimation: An application to EAR models," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2124-2136, April.
  2. Giorgio Calzolari & Francesca Di Iorio & Gabriele Fiorentini, 2001. "Indirect inference and variance reduction using control variates," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 39-53.
  3. Calzolari, Giorgio & Magazzini, Laura & Mealli, Fabrizia, 2001. "Simulation-based estimation of Tobit model with random effects," MPRA Paper 22985, University Library of Munich, Germany, revised 2001.
  4. Parrini, Alessandro, 2012. "Indirect estimation of GARCH models with alpha-stable innovations," MPRA Paper 38544, University Library of Munich, Germany.

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