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Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models

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  • Robinson, P M

Abstract

A method is presented for estimating nonlinear simultaneous equations and transformation models in the presence of disturbance distribution of unknown form. It asymptotically achieves the lower variance bound for instrumental variables estimates. The author avoids smoothed nonparametric estimation, his instruments averaging over the unsmoothed empirical distribution of preliminary residuals. He allows for stationary serial dependence. In various settings, estimates are proposed and large-sample inference rules justified, these being unaffected if the optimal instruments use only an arbitrarily small vanishing fraction of the residuals. The author investigates theoretically the effect of such computational savings on the goodness of the normal approximation. Copyright 1991 by The Econometric Society.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 59 (1991)
Issue (Month): 3 (May)
Pages: 755-86

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Handle: RePEc:ecm:emetrp:v:59:y:1991:i:3:p:755-86

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Cited by:
  1. Hosoya, Yuzo & Terasaka, Takahiro, 2009. "Inference on transformed stationary time series," Journal of Econometrics, Elsevier, vol. 151(2), pages 129-139, August.
  2. MEDDAHI, Nour & RENAULT, Éric, 1998. "Quadratic M-Estimators for ARCH-Type Processes," Cahiers de recherche 9814, Universite de Montreal, Departement de sciences economiques.
  3. Y Nishiyama & Peter M Robinson, 1999. "Studentization in Edgworth Expansions for Estimates of Semiparametric Index Models - (Now published in C Hsiao, K Morimune and J Powell (eds): Nonlinear Statistical Modeling (Festschrift for Takeshi A," STICERD - Econometrics Paper Series /1999/374, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  4. Oliver Linton, 2000. "Edgeworth Approximations for Semiparametric Instrumental Variable Estimators and Test Statistics," STICERD - Econometrics Paper Series /2000/399, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. Calzolari, Giorgio, 1992. "Stima delle equazioni simultanee non-lineari: una rassegna
    [Estimation of nonlinear simultaneous equations: a survey]
    ," MPRA Paper 24123, University Library of Munich, Germany, revised 1992.
  6. Tianxi Cai & Lu Tian & L. J. Wei, 2004. "Semi-parametric Box-Cox Power Transformation Models for Censored Survival Observations," Harvard University Biostatistics Working Paper Series 1006, Berkeley Electronic Press.
  7. Oliver Linton, 1993. "Second Order Approximation in the Partially Linear Regression Model," Cowles Foundation Discussion Papers 1065, Cowles Foundation for Research in Economics, Yale University.
  8. Calzolari, Giorgio & Fiorentini, Gabriele, 1994. "Conditional heteroskedasticity in nonlinear simultaneous equations," MPRA Paper 24428, University Library of Munich, Germany.
  9. Delgado, Miguel A. & Fiteni, Inmaculada, 2002. "External bootstrap tests for parameter stability," Journal of Econometrics, Elsevier, vol. 109(2), pages 275-303, August.
  10. Oliver Linton, 1997. "Second Order Approximation in a Linear Regression with Heteroskedasticity for Unknown Form," Cowles Foundation Discussion Papers 1151, Cowles Foundation for Research in Economics, Yale University.
  11. Hahn, Jinyong, 1997. "Efficient estimation of panel data models with sequential moment restrictions," Journal of Econometrics, Elsevier, vol. 79(1), pages 1-21, July.

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