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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.

Suggested Citation

  • Robinson, P M, 1991. "Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models," Econometrica, Econometric Society, vol. 59(3), pages 755-786, May.
  • Handle: RePEc:ecm:emetrp:v:59:y:1991:i:3:p:755-86
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    Cited by:

    1. 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.
    2. 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.
    3. MEDDAHI, Nour & RENAULT, Éric, 1998. "Quadratic M-Estimators for ARCH-Type Processes," Cahiers de recherche 9814, Universite de Montreal, Departement de sciences economiques.
    4. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2005. "Bootstrap prediction intervals for power-transformed time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 219-235.
    5. Xiaohong Chen & David T. Jacho-Chávez & Oliver Linton, 2009. "An Alternative Way of ComputingEfficient Instrumental VariableEstimators," STICERD - Econometrics Paper Series 536, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    7. Hahn, Jinyong, 1997. "Efficient estimation of panel data models with sequential moment restrictions," Journal of Econometrics, Elsevier, vol. 79(1), pages 1-21, July.
    8. Calzolari, Giorgio & Fiorentini, Gabriele, 1994. "Conditional heteroskedasticity in nonlinear simultaneous equations," MPRA Paper 24428, University Library of Munich, Germany.
    9. 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.
    10. Christensen, Bent Jesper & Posch, Olaf & van der Wel, Michel, 2016. "Estimating dynamic equilibrium models using mixed frequency macro and financial data," Journal of Econometrics, Elsevier, vol. 194(1), pages 116-137.
    11. Hosoya, Yuzo & Terasaka, Takahiro, 2009. "Inference on transformed stationary time series," Journal of Econometrics, Elsevier, vol. 151(2), pages 129-139, August.
    12. Delgado, Miguel A. & Fiteni, Inmaculada, 2002. "External bootstrap tests for parameter stability," Journal of Econometrics, Elsevier, vol. 109(2), pages 275-303, August.
    13. Delgado, Miguel A. & Domínguez, Manuel A. & Lavergne, Pascal, 1998. "Asymptotic and bootstrap specification tests of nonlinear in variable econometric models," DES - Working Papers. Statistics and Econometrics. WS 4674, Universidad Carlos III de Madrid. Departamento de Estadística.

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