Some Flexible Parametric Models for Partially Adaptive Estimators of Econometric Models

Christian B Hansen,James B Mcdonald,Panayiotis Theodossiou

doi:10.5018/economics-ejournal.ja.2007-7

Christian B Hansen, James B Mcdonald + Show 1 more

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https://doi.org/10.5018/economics-ejournal.ja.2007-7

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Abstract

Abstract This paper provides a survey of three families of flexible parametric probability density functions (the skewed generalized t, the exponential generalized beta of the second kind, and the inverse hyperbolic sine distributions) which can be used in modeling a wide variety of econometric problems. A figure, which can facilitate model selection, summarizing the admissible combinations of skewness and kurtosis spanned by the three distributional families is included. Applications of these families to estimating regression models demonstrate that they may exhibit significant efficiency gains relative to conventional regression procedures, such as ordinary least squares estimation, when modeling non-normal errors with skewness and/or leptokurtosis, without suffering large efficiency losses when errors are normally distributed. A second example illustrates the application of flexible parametric density functions as conditional distributions in a GARCH formulation of the distribution of returns on the S&P500. The skewed generalized t can be an important model for econometric analysis.

Highlights

Assumptions about the distributions of economic variables are useful for much of economic modeling; it is important that the assumed models are consistent with the stylized facts
An Application to Regression Models: A Simulation Example We provide a simple example that illustrates the potential usefulness of the flexible distributions discussed above in regression modeling
This paper has reviewed three families of flexible parametric probability density functions: the skewed generalized t distribution, the exponential generalized beta of the second kind, and the inverse hyperbolic sine distribution

Summary

Introduction

Assumptions about the distributions of economic variables are useful for much of economic modeling; it is important that the assumed models are consistent with the stylized facts. In specific applications, the use of semiparametric procedures requires the specification of user specified objects, such as a kernel and window width in kernel regression, and since little structure is assumed, the resulting models may not be parsimonious. We explore an intermediate ground between the specification of a simple parametric form for the probability density function and semi-parametric estimation. This approach is based on “flexible” parametric density functions that involve few parameters but can accommodate a wider range of data characteristics than are available with such commonly used distributions as the normal, lognormal, or the student t distribution.

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Summary and conclusions