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Higher-order properties of approximate estimators

Author

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  • Dennis Kristensen

    (Institute for Fiscal Studies and University College London)

  • Bernard Salanie

    (Institute for Fiscal Studies and Columbia)

Abstract

Many modern estimation methods in econometrics approximate an objective function, for instance, through simulation or discretisation. These approximations typically affect both bias and variance of the resulting estimator. We provide a higher-order expansion of such 'approximate' estimators that takes into account the errors due to the use of approximations. This expansion allows us to establish general conditions under which the approximate estimator is first-order equivalent to the exact estimator. Moreover, we use the expansion to propose adjustments of the approximate estimator that remove its first-order bias and adjust its standard errors. These adjustments apply to a broad class of approximate estimators that includes all known simulation-based procedures. We also propose another approach to reduce the impact of approximations, based on a Newton-Raphson adjustment. A Monte Carlo simulation on the mixed logit model shows that our proposed adjustments can yield spectacular improvements at a low computational cost.

Suggested Citation

  • Dennis Kristensen & Bernard Salanie, 2013. "Higher-order properties of approximate estimators," CeMMAP working papers CWP45/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:45/13
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    File URL: http://www.cemmap.ac.uk/wps/cwp451313.pdf
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    8. Hong, Han & Li, Huiyu & Li, Jessie, 2021. "BLP estimation using Laplace transformation and overlapping simulation draws," Journal of Econometrics, Elsevier, vol. 222(1), pages 56-72.
    9. Jack Britton & Ben Waltmann, 2021. "Revisiting the solution of dynamic discrete choice models: time to bring back Keane and Wolpin (1994)?," IFS Working Papers W21/13, Institute for Fiscal Studies.
    10. Gupta, Abhimanyu, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.
    11. Laurent Delsol & Ingrid Van Keilegom, 2020. "Semiparametric M-estimation with non-smooth criterion functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 577-605, April.
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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