Department of Economics and Business Economics

Higher-order properties of approximate estimators

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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.

Original languageEnglish
JournalJournal of Econometrics
Pages (from-to)189-208
Number of pages20
Publication statusPublished - 1 Jun 2017

    Research areas

  • Bias adjustment, Extremum estimators, Higher-order expansion, Numerical approximation, Simulation-based estimation

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