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Higher-order properties of approximate estimators

Kristensen, D; Salanié, B; (2017) Higher-order properties of approximate estimators. Journal of Econometrics , 198 (2) pp. 189-208. 10.1016/j.jeconom.2016.10.008. Green open access

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Abstract

Many modern estimation methods in econometrics approximate an objective function, for instance, through simulation or discretization. These approximations typically affect both bias and variance of the resulting estimator. We first provide a higher-order expansion of such “approximate” estimators that takes into account the errors due to the use of approximations. We show how a Newton–Raphson adjustment can reduce the impact of approximations. Then we use our expansions to develop inferential tools that take into account approximation errors: we propose adjustments of the approximate estimator that remove its first-order bias and adjust its standard errors. These corrections apply to a class of approximate estimators that includes all known simulation-based procedures. A Monte Carlo simulation on the mixed logit model shows that our proposed adjustments can yield significant improvements at a low computational cost.

Type: Article
Title: Higher-order properties of approximate estimators
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jeconom.2016.10.008
Publisher version: https://doi.org/10.1016/j.jeconom.2016.10.008
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Extremum estimators; Numerical approximation; Simulation-based estimation; Higher-order expansion; Bias adjustment
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/1559334
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