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

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.

[1]  J. Horowitz.  Semiparametric Methods in Econometrics , 2011 .

[2]  R. Fairlie.  An Extension of the Blinder-Oaxaca Decomposition Technique to Logit and Probit Models , 2006, SSRN Electronic Journal.

[3]  James L. Powell,et al.  Estimation of semiparametric models , 1994 .

[4]  W. Härdle,et al.  Direct Semiparametric Estimation of Single-Index Models with Discrete Covariates dpsfb950075.ps.tar = Enno MAMMEN J.S. MARRON: Mass Recentered Kernel Smoothers , 1996 .

[5]  N. Hjort,et al.  Nonparametric Density Estimation with a Parametric Start , 1995 .

[6]  Songnian Chen.  Efficient estimation of binary choice models under symmetry , 2000 .

[7]  Thomas M. Stoker.  Consistent estimation of scaled coefficients , 2011 .

[8]  J. Horowitz.  SEMIPARAMETRIC ESTIMATION OF A WORK-TRIP MODE-CHOICE MODEL / , 1993 .

[9]  K. Le,et al.  Estimating and decomposing changes in the White–Black homeownership gap from 2005 to 2011 , 2017 .

[10]  Abdoul G. Sam,et al.  Nonparametric Estimation of the Short Rate Diffusion from a Panel of Yields , 2008 .

[11]  J. Horowitz.  A Smoothed Maximum Score Estimator for the Binary Response Model , 1992 .

[12]  I. Glad.  Parametrically guided nonparametric . regression , 2015 .

[13]  M. C. Jones,et al.  A Comparison of Higher-Order Bias Kernel Density Estimators , 1997 .

[14]  S. Cosslett.  Efficiency Bounds for Distribution-free Estimators of the Binary , 1987 .

[15]  H. Ichimura,et al.  SEMIPARAMETRIC LEAST SQUARES (SLS) AND WEIGHTED SLS ESTIMATION OF SINGLE-INDEX MODELS , 1993 .

[16]  T. Iwami.  Japan’s experiences under the Bretton Woods System: capital controls and fixed exchange rate , 2013 .

[17]  C. Manski.  MAXIMUM SCORE ESTIMATION OF THE STOCHASTIC UTILITY MODEL OF CHOICE , 1975 .

[18]  Thomas M. Stoker,et al.  Semiparametric Estimation of Index Coefficients , 1989 .

[19]  Aman Ullah,et al.  Nonparametric Econometrics: Introduction , 1999 .

[20]  Manuel Wiesenfarth,et al.  The Finite Sample Performance of Semi- and Nonparametric Estimators for Treatment Effects and Policy Evaluation , 2017, Comput. Stat. Data Anal..

[21]  H. Bierens.  Advances in Econometrics: Kernel estimators of regression functions , 1987 .

[22]  W. Härdle,et al.  Optimal Smoothing in Single-index Models , 1993 .

[23]  Ingrid K. Glad,et al.  Parametrically Guided Non‐parametric Regression , 1998 .

[24]  P. Ruud.  Sufficient Conditions for the Consistency of Maximum Likelihood Estimation Despite Misspecifications of Distribution in Multinomial Discrete Choice Models , 1983 .

[25]  Herman J. Bierens,et al.  Uniform Consistency of Kernel Estimators of a Regression Function under Generalized Conditions , 1983 .

[26]  S. Yakowitz,et al.  Contributions to the Theory of Nonparametric Regression, with Application to System Identification , 1979 .

[27]  Bert Fristedt,et al.  A modern approach to probability theory , 1996 .

[28]  I. Van Keilegom,et al.  Semi‐parametric Estimation in a Single‐index Model with Endogenous Variables , 2017 .

[29]  Abdoul G. Sam,et al.  Agricultural Technology Adoption and Nonfarm Earnings in Uganda: A Semiparametric Analysis , 2014 .

[30]  D. Andrews.  CONSISTENCY IN NONLINEAR ECONOMETRIC MODELS: A GENERIC UNIFORM LAW OF LARGE NUMBERS , 1987 .

[31]  Zvi Griliches,et al.  Specification Error in Probit Models , 1985 .

[32]  Joel L. Horowitz,et al.  2 Semiparametric and nonparametric estimation of quantal response models , 1993 .

[33]  Alan P. Ker,et al.  Nonparametric Regression Under Alternative Data Environments , 2004 .

[34]  C. Manski.  Identification of Binary Response Models , 1988 .

[35]  A. Ullah,et al.  Nonparametric Econometrics: Semiparametric and Nonparametric Estimation of Simultaneous Equation Models , 1999 .

[36]  Matthew P. Wand,et al.  Kernel Smoothing , 1995 .

[37]  A. Ker,et al.  The role of gender in fertiliser adoption in Uganda , 2015 .

[38]  R. Spady,et al.  AN EFFICIENT SEMIPARAMETRIC ESTIMATOR FOR BINARY RESPONSE MODELS , 1993 .