Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-14T03:29:46.409Z Has data issue: false hasContentIssue false
  • English
  • Français

Which Moments to Match?

Published online by Cambridge University Press:  11 February 2009

A. Ronald Gallant and
George Tauchen
A. Ronald Gallant
Affiliation:
University of North Carolina
George Tauchen
Affiliation:
Duke University
Get accessRights & Permissions [Opens in a new window]

Abstract

We describe an intuitive, simple, and systematic approach to generating moment conditions for generalized method of moments (GMM) estimation of the parameters of a structural model. The idea is to use the score of a density that has an analytic expression to define the GMM criterion. The auxiliary model that generates the score should closely approximate the distribution' of the observed data but is not required to nest it. If the auxiliary model nests the structural model then the estimator is as efficient as maximum likelihood. The estimator is advantageous when expectations under a structural model can be computed by simulation, by quadrature, or by analytic expressions but the likelihood cannot be computed easily.

Information

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 4 , October 1996, pp. 657 - 681
Copyright
Copyright © Cambridge University Press 1996

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 307–346.CrossRefGoogle Scholar
Baldwin, L. (1992) Essays on Auctions and Procurement. Ph.D. Dissertation, Duke University.Google Scholar
Bansal, R., Gallant, A.R., Hussey, R., & Tauchen, G. (1995) Nonparametric estimation of structural models for high-frequency currency market data. Journal of Econometrics 66, 251–287.CrossRefGoogle Scholar
Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307–327.CrossRefGoogle Scholar
Botlerslev, T. (1987) A conditionally heteroskedastic time series model of speculative prices and rates of return. Review of Economics and Statistics 64, 542–547.CrossRefGoogle Scholar
Bollerslev, T. & Wooldridge, J.M. (1992) Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric Reviews 11, 143–172.CrossRefGoogle Scholar
Clark, P.K. (1973) A subordinated stochastic process model with finite variance for speculative prices. Econometrica 41, 135–56.CrossRefGoogle Scholar
Coleman, J. (1990) Solving the stochastic growth model by policy-function iteration. Journal of Business and Economic Statistics 8, 27–30.CrossRefGoogle Scholar
Duffle, D. & Singleton, K.I. (1993) Simulated moments estimation of Markov models of asset prices. Econometrica 61, 929–952.CrossRefGoogle Scholar
Ellner, S., Gallant, A.R., & Theiler, J. (1995) Detecting nonlinearity and chaos in epidemic data. In Mollison, D. (ed.), Epidemic Models: Their Structure and Relation to Data, pp. 54–78. Cambridge: Cambridge University Press.Google Scholar
Engle, R.F. (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.CrossRefGoogle Scholar
Engle, R.F. (1994) Indirect Inference on Volatility Diffusions and Stochastic Volatility Models. Manuscript, University of California at San Diego.Google Scholar
Engle, R.F. & Bollerslev, T. (1986) Modeling the persistence of conditional variance. Econometric Reviews 5, 1–50.CrossRefGoogle Scholar
Fenton, V. & Gallant, A.R. (1996) Convergence rates of SNP density estimators. Econometrica 64, 719–727.CrossRefGoogle Scholar
Gallant, A.R. (1977) Three stage least squares estimation for a system of simultaneous, nonlinear, implicit equations. Journal of Econometrics 5, 71–88.CrossRefGoogle Scholar
Gallant, A.R. (1987) Nonlinear Statistical Models. New York: Wiley.CrossRefGoogle Scholar
Gallant, A.R., Hsieh, D.A., & Tauchen, G. (1994) Estimation of stochastic volatility models with diagnostics. Manuscript, Duke University.Google Scholar
Gallant, A.R. & Nychka, D.W. (1987) Semi-nonparametric maximum likelihood estimation. Econometrica 55, 363–390.CrossRefGoogle Scholar
Gallant, A.R., Rossi, P.E., & Tauchen, G. (1992) Stock prices and volume. Review of Financial Studies 5, 199–242.CrossRefGoogle Scholar
Gallant, A.R. & Tauchen, G. (1989) Seminonparametric estimation of conditionally constrained heterogeneous processes: Asset pricing applications. Econometrica 57, 1091–1120.CrossRefGoogle Scholar
Gallant, A.R. & Tauchen, G. (1992) A nonparametric approach to nonlinear time series analysis: Estimation and simulation. In Parzen, E., Brillinger, D., Rosenblatt, M., Taqqu, M., Geweke, J., & Caines, P. (eds.), New Dimensions in Time Series Analysis, pp. 71–92. New York: Springer-Verlag.Google Scholar
Gallant, A.R. & White, H. (1992) On learning the derivatives of an unknown mapping with multilayer feedforward networks. Neural Networks 5, 129–138.CrossRefGoogle Scholar
Gennotte, G. & Marsh, T.A. (1993) Variations in economic uncertainty and risk premiums on capital assets. European Economic Review 37, 1021–1041.CrossRefGoogle Scholar
Ghysels, E. & J, J.. Jasiak (1994) Stochastic volatility and time deformation: An application to trading volume and leverage effects. Manuscript, University of Montreal.Google Scholar
Gourie'roux, C, Monfort, A., & Renault, E. (1993) Indirect inference. Journal of Applied Econometrics 8, S85–S118.CrossRefGoogle Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.CrossRefGoogle Scholar
Hansen, L.P., Heaton, J., & Luttmer, E.J.G. (1995) Econometric evaluation of asset pricing models. The Review of Financial Studies 8, 237–274.CrossRefGoogle Scholar
Harvey, A.C. (1993) Long Memory in Stochastic Volatility. Manuscript, London School of Economics.Google Scholar
Harvey, A.C, Ruiz, E., & Shephard, N. (1993) Multivariate stochastic variance models. Review of Economic Studies 61, 247–264.CrossRefGoogle Scholar
Harvey, A.C. & Shephard, N. (1993) Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns. Manuscript, London School of Economics.Google Scholar
Jacquier, E., Poison, N.G., & Rossi, P.E. (1994) Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics 12, 371–388.CrossRefGoogle Scholar
Laffont, J.-J., Ossard, H., & Vuong, Q. (1991) The Econometrics of First-Price Auctions. Document de Travail 7, Institut d'Economie Industrielle, Toulouse.Google Scholar
McCaffrey, D.F. & Gallant, A.R. (1994) Convergence rates for single hidden layer feedforward networks. Neural Networks 7, 147–158.CrossRefGoogle Scholar
McFadden, D. (1989) A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica 57, 995–1026.CrossRefGoogle Scholar
Melino, A. & Turnbull, S.M. (1990) Pricing foreign currency options with stochastic volatility. Journal of Econometrics 45, 239–266.CrossRefGoogle Scholar
Milgrom, P. (1986) Auction theory. In Bewley, T. (ed.), Advances in Economic Theory, pp. 1–32. Cambridge: Cambridge University Press.Google Scholar
Nelson, D. (1991) Conditional heteroskedasticity in asset returns: A new approach. Economet-rica 59, 347–370.CrossRefGoogle Scholar
Paarsch, H.J. (1991) Empirical Models of Auctions and an Application to British Columbian Timber Sales. Discussion paper 91-19, University of British Columbia.Google Scholar
Pakes, A. & Pollard, D. (1989) Simulation and the asymptotics of optimization estimators. Econ-ometrica 57, 1027–1058.CrossRefGoogle Scholar
Smith, A.A. (1993) Estimating nonlinear time series models using vector autoregressions: Two approaches. Journal of Applied Econometrics 8, 63–84.CrossRefGoogle Scholar
Tauchen, G. (1990) Associate editor's introduction. Journal of Business and Economic Statistics 8, 1–1.Google Scholar
Tauchen, G. & Pitts, M. (1983) The price variability-volume relationship on speculative mar kets. Econometrica 51, 485–505.CrossRefGoogle Scholar