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A method of moments estimator for semiparametric index models

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Author Info
Bas Donkers
Marcia M Schafgans

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Abstract

We propose an easy to use derivative based two-step estimation procedure for semi-parametric index models. In the first step various functionals involving the derivatives of the unknown function are estimated using nonparametric kernel estimators. The functionals used provide moment conditions for the parameters of interest, which are used in the second step within a method-of-moments framework to estimate the parameters of interest. The estimator is shown to be root N consistent and asymptotically normal. We extend the procedure to multiple equation models. Our identification conditions and estimation framework provide natural tests for the number of indices in the model. In addition we discuss tests of separability, additivity, and linearity of the influence of the indices.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2005/493.

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Date of creation: Jul 2005
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Handle: RePEc:cep:stiecm:/2005/493

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Related research
Keywords: Semiparametric estimation; multiple index models; average derivative functionals; generalized methods of moments estimator; rank testing;

Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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  1. B. Donkers & M. Schafgans, 2003. "A derivative based estimator for semiparametric index," Econometric Institute Report 313, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
  2. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November. [Downloadable!] (restricted)
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