Fourth Order Pseudo Maximum Likelihood Methods

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 rst four conditional moments are specied.Such an extension is relevant in light of pervasive evidence that conditional distributionsare non-Gaussian in many economic situations. The key statisticaltool here is the quartic exponential family, which allows us to generalize thePML2 and QGPML1 methods proposed in GMT(1984) to PML4 and QGPML2methods, respectively.[...]