Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-22T02:20:23.680Z Has data issue: false hasContentIssue false
  • English
  • Français

A NONPARAMETRIC SIMULATED MAXIMUM LIKELIHOOD ESTIMATION METHOD

Published online by Cambridge University Press:  01 August 2004

Jean-David Fermanian  and
Bernard Salanié
Jean-David Fermanian
Affiliation:
CDC Ixis Capital Markets and CREST
Bernard Salanié
Affiliation:
CREST, GRECSTA-CNRS, and CEPR
Get access Rights & Permissions [Opens in a new window]

Abstract

Existing simulation-based estimation methods are either general purpose but asymptotically inefficient or asymptotically efficient but only suitable for restricted classes of models. This paper studies a simulated maximum likelihood method that rests on estimating the likelihood nonparametrically on a simulated sample. We prove that this method, which can be used on very general models, is consistent and asymptotically efficient for static models. We then propose an extension to dynamic models and give some Monte-Carlo simulation results on a dynamic Tobit model.We thank Jean-Pierre Florens, Arnoldo Frigessi, Christian Gouriéroux, Jim Heckman, Guy Laroque, Oliver Linton, Nour Meddahi, Alain Monfort, Eric Renault, Christian Robert, Neil Shephard, and two referees for their comments. Remaining errors and imperfections are ours. Parts of this paper were written while Bernard Salanié was visiting the University of Chicago, which he thanks for its hospitality.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 4 , August 2004 , pp. 701 - 734
Copyright
© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ai, C. (1997) A semiparametric maximum likelihood estimator. Econometrica 65, 933–963.Google Scholar
Azzalini, A. (1983) Maximum likelihood estimation of order m for stationary stochastic processes. Biometrika 70, 381–387.Google Scholar
Bickel, P. (1982) On adaptive estimation. Annals of Statistics 70, 647–671.Google Scholar
Börsch-Supan, A. & V. Hajivassiliou (1993) Smooth unbiased probability simulators for maximum likelihood estimation of limited dependent variable models. Journal of Econometrics 58, 347–368.Google Scholar
Bosq, D. & J.-P. Lecoutre (1987) Théorie de l'estimation fonctionnelle. Economica.
Carrasco, M. & J.-P. Florens (2002a) Efficient GMM Estimation Using the Empirical Characteristic Function. Mimeo, IDEI Toulouse.
Carrasco, M. & J.-P. Florens (2002b) Simulation-based method of moments and efficiency. Journal of Business and Economic Statistics 20, 482–492.Google Scholar
Diggle, P. & R. Gratton (1984) Monte Carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society, Series B 46, 193–227.Google Scholar
Feuerverger, A. & P. McDunnough (1981a) On some Fourier methods for inference. Journal of the Royal Statistical Society, Series B 43, 20–27.Google Scholar
Feuerverger, A. & P. McDunnough (1981b) On the efficiency of empirical characteristic function procedures. Journal of the American Statistical Association 78, 379–387.Google Scholar
Gallant, R. & D. Nychka (1987) Semi-nonparametric maximum likelihood estimation. Econometrica 55, 363–390.Google Scholar
Gallant, R. & G. Tauchen (1996) Which moments to match? Econometric Theory 12, 657–681.Google Scholar
Gouriéroux, C. & A. Monfort (1996) Simulation-Based Econometric Methods. Oxford University Press.
Gouriéroux, C., A. Monfort, & E. Renault (1993) Indirect inference. Journal of Applied Econometrics 8, S85–S118.Google Scholar
Hajivassiliou, V. & D. McFadden (1998) The method of simulated scores for the estimation of limited-dependent variable models. Econometrica 66, 863–896.Google Scholar
Hajivassiliou, V. & P. Ruud (1994) Classical estimation methods for LDV models using simulation. In R. Engle & D. McFadden (eds.), Handbook of Econometrics, vol. 4, pp. 2384–2441. Elsevier.
Jacquier, E., N. Polson, & P. Rossi (1994) Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics 12, 371–417.Google Scholar
Laroque, G. & B. Salanié (1989) Estimation of multimarket fix-price models: An application of pseudo-maximum likelihood methods. Econometrica 57, 831–860.Google Scholar
Laroque, G. & B. Salanié (1993) Simulation-based estimation of models with lagged latent variables. Journal of Applied Econometrics 8, S119–S133.Google Scholar
Laroque, G. & B. Salanié (1994) Estimating the canonical disequilibrium model: Asymptotic theory and finite sample properties. Journal of Econometrics 62, 165–210.Google Scholar
Lee, L.F. (1995) Asymptotic bias in simulated maximum likelihood estimation of discrete choice models. Econometric Theory 11, 437–483.Google Scholar
Lerman, S. & C. Manski (1981) On the use of simulated frequencies to approximate choice probabilities. In C. Manski & D. McFadden (eds.), Structural Analysis of Discrete Data with Econometric Applications, pp. 305–319. MIT Press.
McFadden, D. (1989) A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica 57, 995–1026.Google Scholar
Pakes, A. (1986) Patents as options: Some estimates of the value of holding European patent stocks. Econometrica 54, 755–784.Google Scholar
Pakes, A. & D. Pollard (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1057.Google Scholar
Sandmann, G. & S. Koopman (1998) Estimation of stochastic volatility models via Monte Carlo maximum likelihood. Journal of Econometrics 87, 271–301.Google Scholar
Smith, A. (1993) Estimating nonlinear time series models using simulated vector autoregressions. Journal of Applied Econometrics 8, S63–S84.Google Scholar
Stern, S. (1997) Simulation-based estimation. Journal of Economic Literature 35, 2006–2039.Google Scholar
Stone, C. (1975) Adaptive maximum likelihood estimation of a location parameter. Annals of Statistics 3, 267–284.Google Scholar