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Higher-order properties of approximate estimators

  • Dennis Kristensen

    (Institute for Fiscal Studies and University College London)

  • Bernard Salanie

    (Institute for Fiscal Studies and Columbia)

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.

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File URL: http://www.cemmap.ac.uk/wps/cwp451313.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP45/13.

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Date of creation: Sep 2013
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Handle: RePEc:ifs:cemmap:45/13
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  1. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of semiparametric models when the criterion function is not smooth," LSE Research Online Documents on Economics 2167, London School of Economics and Political Science, LSE Library.
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  7. Valentina Corradi & Norman R. Swanson, 2003. "Evaluation of Dynamic Stochastic General Equilibrium Models Based on Distributional Comparison of Simulated and Historical Data," Departmental Working Papers 200320, Rutgers University, Department of Economics.
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  13. Jinyong Hahn & Whitney Newey, 2003. "Jackknife and analytical bias reduction for nonlinear panel models," CeMMAP working papers CWP17/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  14. Geert Dhaene & Koen Jochmans, 2014. "Split-Panel Jackknife Estimation of Fixed-Effect Models," Sciences Po publications 2014-03, Sciences Po.
  15. Kristensen, Dennis & Rahbek, Anders, 2005. "ASYMPTOTICS OF THE QMLE FOR A CLASS OF ARCH(q) MODELS," Econometric Theory, Cambridge University Press, vol. 21(05), pages 946-961, October.
  16. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
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  19. Donald W.K. Andrews, 1999. "Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators," Cowles Foundation Discussion Papers 1230R, Cowles Foundation for Research in Economics, Yale University, revised Jan 2001.
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