Applications Of Penalized Binary Choice
Estimators With Improved Predictive Fit
Author(s)
D. J. Miller &W.-H. Liu
Abstract
This paper presents applications of penalized ML estimators for binary choice
problems. The penalty is based on an information theoretic measure of predictive
fit for binary choice outcomes, and the resulting penalized ML estimators are
asymptotically equivalent to the associated ML estimators but may have a better
in-sample and out-of-sample predictive fit in finite samples. The proposed methods
are demonstrated with a set of Monte Carlo experiments and two examples
from the applied finance literature.
Keywords: binary choice, information theory, penalized ML, prediction.
1 Introduction
The sampling properties of the maximum likelihood (ML) estimators for binary
choice problems are well established. Much of the existing research has focused
on the properties of estimators for the response coefficients, which is important for
model selection and estimating the marginal effects of the explanatory variables.
However, the use of fitted models to predict choices made by agents outside the
current sample is very important in practice but has attracted less attention from
researchers. In some cases, the ML estimators may exhibit poor in-sample and
out-of-sample predictive performance, especially when the sample size is small.
Although several useful predictive goodness-of-fit measures have been proposed,
there are no standard remedies for poor in-sample or out-of-sample predictive fit.
As noted by Train [1], there is a conceptual problem with measuring the insample
predictive fit – the predicted choice probabilities are defined with respect to
the relative frequency of choices in repeated samples and do not indicate the actual
Keywords
binary choice, information theory, penalized ML, prediction.
Related Book
Other papers in this volume
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