Arbeitspapier

The influence function of semiparametric estimators

There are many economic parameters that depend on nonparametric first steps. Examples include games, dynamic discrete choice, average consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function. The influence function is useful in formulating regularity conditions for asymptotic normality, for bias reduction, in efficiency comparisons, and for analyzing robustness. We show that the influence function of a semiparametric estimator is the limit of a Gateaux derivative with respect to a smooth deviation as the deviation approaches a point mass. This result generalizes the classic Von Mises (1947) and Hampel (1974) calculation to apply to estimators that depend on smooth nonparametic first steps. We characterize the influence function of M and GMM-estimators. We apply the Gateaux derivative to derive the influence function with a first step nonparametric two stage least squares estimator based on orthogonality conditions. We also use the influence function to analyze high level and primitive regularity conditions for asymptotic normality. We give primitive regularity conditions for linear functionals of series regression that are the weakest known, except for a log term, when the regression function is smooth enough.

Sprache
Englisch

Erschienen in
Series: cemmap working paper ; No. CWP06/17

Klassifikation
Wirtschaft
Estimation: General
Semiparametric and Nonparametric Methods: General
Single Equation Models; Single Variables: General
Single Equation Models: Single Variables: Instrumental Variables (IV) Estimation
Multiple or Simultaneous Equation Models: Instrumental Variables (IV) Estimation
Thema
Influence function
semiparametric estimation
NPIV

Ereignis
Geistige Schöpfung
(wer)
Ichimura, Hidehiko
Newey, Whitney K.
Ereignis
Veröffentlichung
(wer)
Centre for Microdata Methods and Practice (cemmap)
(wo)
London
(wann)
2017

DOI
doi:10.1920/wp.cem.2017.0617
Handle
Letzte Aktualisierung
20.09.2024, 08:23 MESZ

Datenpartner

Dieses Objekt wird bereitgestellt von:
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.

Objekttyp

  • Arbeitspapier

Beteiligte

  • Ichimura, Hidehiko
  • Newey, Whitney K.
  • Centre for Microdata Methods and Practice (cemmap)

Entstanden

  • 2017

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