Generalized Semiparametric Binary Prediction |
Jeff Racine |
This paper proposes a semiparametric approach to the estimation of
‘generalized’ binary choice models. A ‘generalized’ binary choice model is one with
separate indices for each conditioning variable which constitutes a
generalization of the standard single-index approach typically employed in applied work.
The choice probability distribution is therefore a joint distribution across these
indices as opposed to the typical univariate distribution on a scalar index
commonly found in applied work. Interest lies in estimating choice probabilities
and the gradient of choice probabilities with respect to the conditioning
information, and these are estimated nonparametrically using the method of
kernels. A data-driven cross-validatory method for bandwidth selection and
index-parameter estimation is proposed for maximization of the nonparametric
likelihood function. The functional form of the indices enters this
nonparametric likelihood function thereby permitting data-driven determination of the
index functions in addition to the shape of the joint cumulative distribution |
Key Words: Semiparametric; Nonparametric methods. |
JEL Classification Numbers: C14 |