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Fourth Order Pseudo Maximum Likelihood Methods

  • Alberto HOLLY

    (Institute of Health Economics and Management (IEMS) and University of Lausanne)

  • Alain MONFORT

    (CNAM and CREST)

  • Michael ROCKINGER

    (Swiss Finance Institute, University of Lausanne and CEPR)

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.

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Paper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 09-23.

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Length: 47 pages
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Handle: RePEc:chf:rpseri:rp0923
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