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Minimum divergence moment based binary response models : estimation and inference

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Author Info

  • Mittelhammer, Ronald C.
  • Judge, George G.

    ()
    (University of California, Berkeley. Dept of agricultural and resource economics and policy)

  • Miller, Douglas
  • Cardell, Nicholas Scott

Abstract

This paper introduces a new class of estimators based on minimization of the Cressie-Read (CR)power divergence measure for binary choice models, where neither a parameterized distribution nor a parameterization of the mean is specified explicitly in the statistical model. By incorporating sample information in the form of conditional moment conditions and estimating choice probabilities by optimizing a member of the set of divergence measures in the CR family, a new class of nonparametric estimators evolves that requires less a priori model structure than conventional parametric estimators such as probit or logit. Asymptotic properties are derived under general regularity conditions and finite sampling properties are illustrated by Monte Carlo sampling experiments. Except for some special cases in which the general regularity conditions do not hold, the estimators have asymptotic normal distributions, similar to conventional parametric estimators of the binary choice model. The sampling experiments focus on the mean square errors in the choice probability predictions and the probability derivatives with respect to the response variable values. The simulation results suggest that estimators within the CR class are more robust than conventional methods of estimation across varying probability distributions underlying the Bernoulli process. The size and power of test statistics based on the asymptotics of the CR-based estimators exhibit behavior similar to those based on conventional parametric methods. Overall, the new class of nonparametric estimators for the binary response model is a promising and potentially more robust alternative to the arametric methods often used in empirical practice.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Paper provided by University of California at Berkeley, Department of Agricultural and Resource Economics and Policy in its series CUDARE Working Paper Series with number 0998.

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Length: 42 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:are:cudare:0998

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Related research

Keywords: econometric models; econometrics; estimation theory; information theory; monte carlo analysis;

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References

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  1. Judge, George G. & Mittelhammer, Ronald C, 2004. "Estimating the link function in multinomial response models under endogeneity and quadratic loss," CUDARE Working Paper Series 0970, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  2. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, Econometric Society, vol. 61(2), pages 387-421, March.
  3. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, Econometric Society, vol. 60(3), pages 505-31, May.
  4. Kenneth Train, 2003. "Discrete Choice Methods with Simulation," Online economics textbooks, SUNY-Oswego, Department of Economics, SUNY-Oswego, Department of Economics, number emetr2, Spring.
  5. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, Elsevier, vol. 3(3), pages 205-228, August.
  6. 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, American Statistical Association, vol. 99, pages 479-487, January.
  7. McFadden, Daniel L., 1984. "Econometric analysis of qualitative response models," Handbook of Econometrics, Elsevier, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 24, pages 1395-1457 Elsevier.
  8. Mittelhammer,Ron C. & Judge,George G. & Miller,Douglas J., 2000. "Econometric Foundations Pack with CD-ROM," Cambridge Books, Cambridge University Press, number 9780521623940, 9.
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