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A method of moments estimator for semiparametric index models

  • Bas Donkers
  • Marcia M Schafgans

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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File URL: http://sticerd.lse.ac.uk/dps/em/em493.pdf
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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
Contact details of provider: Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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  1. Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January.
  2. Donkers, A.C.D. & Schafgans, M., 2003. "A Derivative Based Estimator for Semiparametric Index Models," Discussion Paper 2003-22, Tilburg University, Center for Economic Research.
  3. 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.
  4. Newey, Whitney K & Stoker, Thomas M, 1993. "Efficiency of Weighted Average Derivative Estimators and Index Models," Econometrica, Econometric Society, vol. 61(5), pages 1199-223, September.
  5. Serge Darolles & Christian Gourieroux & Joanna Jasiak, 2001. "Compound Autoregressive Models," Working Papers 2001-21, Centre de Recherche en Economie et Statistique.
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  7. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
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  10. Stoker, Thomas M, 1989. "Tests of Additive Derivative Constraints," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 535-52, October.
  11. repec:dgr:kubcen:200322 is not listed on IDEAS
  12. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(01), pages 32-51, February.
  13. Robinson, P M, 1989. "Hypothesis Testing in Semiparametric and Nonparametric Models for Econometric Time Series," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 511-34, October.
  14. Delecroix, Michel & Härdle, Wolfgang & Hristache, Marian, 2003. "Efficient estimation in conditional single-index regression," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 213-226, August.
  15. Whitney K. Newey, 2004. "Efficient Semiparametric Estimation via Moment Restrictions," Econometrica, Econometric Society, vol. 72(6), pages 1877-1897, November.
  16. Lee, Lung-fei, 1995. "Semiparametric maximum likelihood estimation of polychotomous and sequential choice models," Journal of Econometrics, Elsevier, vol. 65(2), pages 381-428, February.
  17. Yingcun Xia & Howell Tong & W. K. Li & Li-Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410.
  18. Hardle W. & Sperlich S. & Spokoiny V., 2001. "Structural Tests in Additive Regression," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1333-1347, December.
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