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Estimating the Link Function in Multinomial Response Models under Endogeneity and Quadratic Loss

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  • Judge, George G.
  • Mittelhammer, Ron C

Abstract

This paper considers estimation and inference for the multinomial response model in the case where endogenous variables are arguments of the unknown link function. Semiparametric estimators are proposed that avoid the parametric assumptions underlying the likelihood approach as well as the loss of precision when using nonparametric estimation. A data based shrinkage estimator that seeks an optimal combination of estimators and results in superior risk performance under quadratic loss is also developed.

Suggested Citation

  • Judge, George G. & Mittelhammer, Ron C, 2004. "Estimating the Link Function in Multinomial Response Models under Endogeneity and Quadratic Loss," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt4422n50w, Department of Agricultural & Resource Economics, UC Berkeley.
    • Handle: RePEc:cdl:agrebk:qt4422n50w
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    References listed on IDEAS

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    1. Mittelhammer, Ron C. & Judge, George G., 2005. "Combining estimators to improve structural model estimation and inference under quadratic loss," Journal of Econometrics, Elsevier, vol. 128(1), pages 1-29, September.
    2. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, January.
    3. Mittelhammer, Ronald C. & Judge, George G. & Schoenberg, Ron, 2003. "Empirical Evidence Concerning the Finite Sample Performance of EL-Type Structural Equation Estimation and Inference Methods," CUDARE Working Papers 25090, University of California, Berkeley, Department of Agricultural and Resource Economics.
    4. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    5. Judge G.G. & Mittelhammer R.C., 2004. "A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 479-487, January.
    6. Hong, Han & Tamer, Elie, 2003. "Endogenous binary choice model with median restrictions," Economics Letters, Elsevier, vol. 80(2), pages 219-225, August.
    7. Judge G.G. & Mittelhammer R.C., 2004. "A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 479-487, January.
    8. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
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    Citations

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    Cited by:

    1. Villas-Boas, Sofia B., 2006. "Vertical relationships between manufacturers and retailers: inference with limited data," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt0z26d2v9, Department of Agricultural & Resource Economics, UC Berkeley.
    2. Sofia Berto Villas-Boas, 2007. "Vertical Relationships between Manufacturers and Retailers: Inference with Limited Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 625-652.
    3. Mittelhammer, Ron C & Judge, George G. & Miller, Douglas J & Cardell, N. Scott, 2005. "Minimum Divergence Moment Based Binary Response Models: Estimation and Inference," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt1546s6rn, Department of Agricultural & Resource Economics, UC Berkeley.

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