Fourth Order Pseudo Maximum Likelihood Methods

47 Pages Posted: 11 Jul 2009

See all articles by Alberto Holly

Alberto Holly

University of Lausanne

Alain Monfort

National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST); National Bureau of Economic Research (NBER); Maastricht University

Michael Rockinger

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne); Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Date Written: August 2008

Abstract

The objective of this paper is to extend the results on Pseudo Maximum Likelihood (PML) theory derived in Gourieroux, Monfort, and Trognon (GMT) (1984) to a situation where the first four conditional moments are specified. Such an extension is relevant in light of pervasive evidence that conditional distributions are non-Gaussian in many economic situations. The key statistical tool here is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in GMT(1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed which shows, in particular, that the QGPML2 method reaches the semi-parametric bound. The key numerical tool that we use is the Gauss-Freud integration scheme which solves a computational problem that has previously been raised in several econometric fields. Simulation exercises show the feasibility and robustness of the methods.

Keywords: Quartic Exponential Family, Pseudo Maximum Likelihood, Skewness, Kurtosis

JEL Classification: C01, C13, C16, C22

Suggested Citation

Holly, Alberto and Monfort, Alain and Rockinger, Georg Michael, Fourth Order Pseudo Maximum Likelihood Methods (August 2008). Swiss Finance Institute Research Paper No. 09-23, Available at SSRN: https://ssrn.com/abstract=1431841 or http://dx.doi.org/10.2139/ssrn.1431841

Alberto Holly

University of Lausanne ( email )

CH-1015 Lausanne
Switzerland

Alain Monfort

National Institute of Statistics and Economic Studies (INSEE) - Center for Research in Economics and Statistics (CREST) ( email )

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Malakoff Cedex, 1 92245
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National Bureau of Economic Research (NBER)

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Maastricht University

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Georg Michael Rockinger (Contact Author)

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne) ( email )

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Lausanne, 1015
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HOME PAGE: http://www.hec.unil.ch/mrockinger

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Swiss Finance Institute

c/o University of Geneva
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CH-1211 Geneva 4
Switzerland

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