High Dimensional Binary Choice Model with Unknown Heteroskedasticity or Instrumental Variables
arXiv (Cornell University)(2023)
摘要
This paper proposes a new method for estimating high-dimensional binary
choice models. The model we consider is semiparametric, placing no
distributional assumptions on the error term, allowing for heteroskedastic
errors, and permitting endogenous regressors. Our proposed approaches extend
the special regressor estimator originally proposed by Lewbel (2000). This
estimator becomes impractical in high-dimensional settings due to the curse of
dimensionality associated with high-dimensional conditional density estimation.
To overcome this challenge, we introduce an innovative data-driven dimension
reduction method for nonparametric kernel estimators, which constitutes the
main innovation of this work. The method combines distance covariance-based
screening with cross-validation (CV) procedures, rendering the special
regressor estimation feasible in high dimensions. Using the new feasible
conditional density estimator, we address the variable and moment (instrumental
variable) selection problems for these models. We apply penalized least squares
(LS) and Generalized Method of Moments (GMM) estimators with a smoothly clipped
absolute deviation (SCAD) penalty. A comprehensive analysis of the oracle and
asymptotic properties of these estimators is provided. Monte Carlo simulations
are employed to demonstrate the effectiveness of our proposed procedures in
finite sample scenarios.
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