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Higher Order Improvements for Approximate Estimators

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  • Dennis Kristensen

    (Columbia University)

  • Bernard Salanié

    (Columbia University)

Abstract

Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties of such approximate estimators at a low computational cost. The first two methods correct the objective function so as to remove the leading term of the bias due to the approximation. One variant provides an analytical bias adjustment, but it only works for estimators based on stochastic approximators, such as simulation-based estimators. Our second bias correction is based on ideas from the resampling literature; it eliminates the leading bias term for non-stochastic as well as stochastic approximators. Finally, we propose an iterative procedure where we use Newton-Raphson (NR) iterations based on a much finer degree of approximation. The NR step removes some or all of the additional bias and variance of the initial approximate estimator. A Monte Carlo simulation on the mixed logit model shows that noticeable improvements can be obtained rather cheaply.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics in its series CAM Working Papers with number 2010-04.

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Length: 43 pages
Date of creation: Apr 2010
Date of revision:
Handle: RePEc:kud:kuieca:2010_04

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Cited by:
  1. Michael Creel & Dennis Kristensen, 2011. "Indirect likelihood inference," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 874.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Dennis Kristensen & Yongseok Shin, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-58, School of Economics and Management, University of Aarhus.
  3. Dennis Kristensen & Bernard Salanie, 2013. "Higher-order properties of approximate estimators," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP45/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Joachim Freyberger, 2012. "Asymptotic theory for differentiated products demand models with many markets," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP19/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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