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A Unified Theory of Consistent Estimation for Parametric Models

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  • Charles Bates
  • Halbert White

Abstract

We present a general theory of consistent estimation for possibly misspecified parametric models based on recent results of Domowitz and White. This theory extends the unification of Burguete, Gallant, and Souza by allowing for heterogeneous, time-dependent data and dynamic models. The theory is applied to yield consistency results for quasi-maximum-likelihood and method of moments estimators. Of particular interest is a new generalized rank condition for identifiability.
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Suggested Citation

  • Charles Bates & Halbert White, 1984. "A Unified Theory of Consistent Estimation for Parametric Models," Working papers 359, Massachusetts Institute of Technology (MIT), Department of Economics.
    • Handle: RePEc:mit:worpap:359
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    Cited by:

    1. Benedikt M. Potscher & Ingmar R. Prucha, 1994. "On the Formulation of Uniform Laws of Large Numbers: A Truncation Approach," NBER Technical Working Papers 0085, National Bureau of Economic Research, Inc.
    2. Marmer, Vadim & Otsu, Taisuke, 2012. "Optimal comparison of misspecified moment restriction models under a chosen measure of fit," Journal of Econometrics, Elsevier, vol. 170(2), pages 538-550.
    3. Demian Pouzo & Zacharias Psaradakis & Martin Sola, 2023. "A Note on Quasi-Maximum-Likelihood Estimation in Hidden Markov Models with Covariate-Dependent Transition Probabilities," Working Papers 234, Red Nacional de Investigadores en Economía (RedNIE).
    4. Andrews, Donald W. K. & Fair, Ray C., 1987. "Inference in Econometric Models with Structural Change," Working Papers 636, California Institute of Technology, Division of the Humanities and Social Sciences.
    5. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    6. Phillips, Robert F., 1996. "Forecasting in the presence of large shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1581-1608.
    7. Ian Domowitz, 1985. "New Directions in Non-linear Estimation with Dependent Observations," Canadian Journal of Economics, Canadian Economics Association, vol. 18(1), pages 1-27, February.
    8. Demian Pouzo & Zacharias Psaradakis & Martín Sola, 2024. "On the Robustness of Mixture Models in the Presence of Hidden Markov Regimes with Covariate-Dependent Transition Probabilities," Department of Economics Working Papers 2024_04, Universidad Torcuato Di Tella.
    9. Donald W.K. Andrews, 1986. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers," Cowles Foundation Discussion Papers 790, Cowles Foundation for Research in Economics, Yale University.
    10. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.
    11. Chunliang Deng & Xingfa Zhang & Yuan Li & Qiang Xiong, 2020. "Garch Model Test Using High-Frequency Data," Mathematics, MDPI, vol. 8(11), pages 1-17, November.
    12. Krupskii, Pavel & Joe, Harry, 2020. "Flexible copula models with dynamic dependence and application to financial data," Econometrics and Statistics, Elsevier, vol. 16(C), pages 148-167.

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