Advertisement

Computational Statistics

, Volume 33, Issue 3, pp 1429–1455 | Cite as

Semiparametric estimation of the link function in binary-choice single-index models

  • Alan P. Ker
  • Abdoul G. Sam
Original Paper
  • 146 Downloads

Abstract

We propose a new, easy to implement, semiparametric estimator for binary-choice single-index models which uses parametric information in the form of a known link (probability) function and nonparametrically corrects it. Asymptotic properties are derived and the finite sample performance of the proposed estimator is compared to those of the parametric probit and semiparametric single-index model estimators of Ichimura (J Econ 58:71–120, 1993) and Klein and Spady (Econometrica 61:387–421, 1993). Results indicate that if the parametric start is correct, the proposed estimator achieves significant bias reduction and efficiency gains compared to Ichimura (1993) and Klein and Spady (1993). Interestingly, the proposed estimator still achieves significant bias reduction and efficiency gains even if the parametric start is not correct.

Keywords

Bias reduction Link function Parametric start 

References

  1. Andrews DWK (1987) Consistency in nonlinear econometric models: a generic uniform law of large numbers. Econometrica 55:1465–1471MathSciNetCrossRefzbMATHGoogle Scholar
  2. Bierens HJ (1987a) Uniform consistency of Kernel estimators of a regression function under generalized conditions. J Am Stat Assoc 78:699–707MathSciNetCrossRefzbMATHGoogle Scholar
  3. Bierens HJ (1987b) Kernel estimators of regression functions. In: Bewley TF (ed) Advances in econometrics, vol 1. Cambridge University Press, CambridgeGoogle Scholar
  4. Chen S (2000) Efficient estimation of binary choice models under symmetry. J Econ 96:183–199MathSciNetCrossRefzbMATHGoogle Scholar
  5. Cosslett SR (1987) Efficiency bounds for distribution-free estimators of the binary choice and censored regression models. Econometrica 55:559–586MathSciNetCrossRefzbMATHGoogle Scholar
  6. Diiro G, Sam AG (2015) Agricultural technology adoption and nonfarm earnings in Uganda: a semiparametric analysis. J Dev Areas 49(2):145–62CrossRefGoogle Scholar
  7. Diiro G, Ker AP, Sam AG (2015) The Role of gender in fertiliser adoption in Uganda. Afr J Agric Resour Econ 10(2):117–30Google Scholar
  8. Fairlie RW (2005) An extension of the Blinder–Oaxaca decomposition technique to logit and probit models. J Econ Soc Meas 30(4):305–316Google Scholar
  9. Fristedt B, Gray L (1997) A modern approach to probability theory. Birkhäuser, BaselCrossRefzbMATHGoogle Scholar
  10. Frölich M, Huber M, Wiesenfarth M (2017) The finite sample performance of semi-and nonparametric estimators for treatment effects and policy evaluation. Comput Stat Data Anal 115:91–102CrossRefGoogle Scholar
  11. Glad IK (1998) Parametrically guided nonparametric regression. Scand J Stat 25:649–668CrossRefzbMATHGoogle Scholar
  12. Hjort NL, Glad IK (1995) Nonparametric density estimation with a parametric start. Ann Stat 23:882–904MathSciNetCrossRefzbMATHGoogle Scholar
  13. Horowitz JL (1992) A smoothed maximum score estimator for the binary response model. Econometrica 60:505–531MathSciNetCrossRefzbMATHGoogle Scholar
  14. Horowitz JL (1993) Semiparametric and nonparametric estimation of quantal response models. In: Maddala GS, Rao CR, Vinod HD (eds) Handbook of statistics, vol 11. North-Holland, AmsterdamGoogle Scholar
  15. Horowitz JL (1998) Semiparametric methods in econometrics. Springer, BerlinCrossRefzbMATHGoogle Scholar
  16. Horowitz JL, Härdle W (1996) Direct semiparametric estimation of single-index models with discrete covariates. J Am Stat Assoc 91(436):1632–1640MathSciNetCrossRefzbMATHGoogle Scholar
  17. Ichimura H (1993) Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. J Econ 58:71–120MathSciNetCrossRefzbMATHGoogle Scholar
  18. Ichimura H, Lee LF (1991) Semiparametric least squares estimation of multiple index models: single equation estimation. In: Barnett WA, Powell J, Tauchen G (eds) Nonparametric and semiparametric methods in econometrics and statistics. Cambridge University Press, CambridgeGoogle Scholar
  19. Jones MC, Signorini DF (1997) A comparison of higher-order bias kernel density estimators. J Am Stat Assoc 92:1063–1073MathSciNetCrossRefzbMATHGoogle Scholar
  20. Klein RW, Spady RH (1993) An efficient semiparametric estimator for binary response models. Econometrica 61:387–421MathSciNetCrossRefzbMATHGoogle Scholar
  21. Manski CF (1975) The maximum score estimation of the stochastic utility model of choice. J Econ 3:205–228MathSciNetCrossRefzbMATHGoogle Scholar
  22. Manski CF (1988) Identification of binary response models. J Am Stat Assoc 83:729–738MathSciNetCrossRefzbMATHGoogle Scholar
  23. Mishra K, Sam AG, Miranda MJ (2017) You are approved! Insured loans improve credit access and technology adoption of ghanaian farmers. Working paper, The Ohio State UniversityGoogle Scholar
  24. Pagan A, Ullah A (1999) Nonparametric econometrics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  25. Powell JL (1994) Estimation of semiparametric models. In: Engle RF, McFadden DL (eds) Handbook of econometrics, vol 4. North-Holland, AmsterdamGoogle Scholar
  26. Ruud PA (1983) Sufficient conditions for the consistency of maximum likelihood estimation despite misspecification of distribution in multinomial discrete choice models. Econometrica 51:225–228MathSciNetCrossRefzbMATHGoogle Scholar
  27. Sam AG, Jiang GJ (2009) Nonparametric estimation of the short rate diffusion process from a panel of yields. J Financ Quant Anal 44:1197–1230CrossRefGoogle Scholar
  28. Sam AG, Ker AP (2006) Nonparametric regression under alternative data environments. Stat Probab Lett 76(10):1037–1046MathSciNetCrossRefzbMATHGoogle Scholar
  29. Schuster E, Yakowitz S (1979) Contributions to the theory of nonparametric regression with application to system identification. Ann Stat 7:139–149MathSciNetCrossRefzbMATHGoogle Scholar
  30. Seah KY, Fesselmeyer E, Le K (2017) Estimating and decomposing changes in the whiteblack homeownership gap from 2005 to 2011. Urban Stud 54(1):119–36CrossRefGoogle Scholar
  31. Van Birke MS, Bellegem Van, Keilegom I (2017) Semi-parametric estimation in a single-index model with endogenous variables. Scand J Stat 44(1):168–91MathSciNetCrossRefzbMATHGoogle Scholar
  32. Yatchew A, Griliches Z (1985) Specification error in probit models. Rev Econ Stat 67:134–139CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institute for the Advanced Study of Food and Agricultural PolicyDepartment of Food, Agricultural and Resource Economics, University of GuelphGuelphCanada
  2. 2.Department of Agricultural, Environmental and Development EconomicsThe Ohio State UniversityColumbusUSA

Personalised recommendations