INFORMATION-THEORETIC APPROACHES TO INFERENCE IN MOMENT CONDITION MODELS

One-step efficient GMM estimation has been developed in the recent pap ers of Back and Brown (1990), Imbens (1993), and Qin and Lawless (1994 ). These papers emphasized methods that correspond to using Owen's (19 88) method of empirical likelihood to reweight the data so that the re weighted sample obeys all the moment restrictions at the parameter est imates. In this paper we consider an alternative KLIC motivated weight ing and show how it and similar discrete reweightings define a class o f unconstrained optimization problems which includes GMM as a special case. Such KLIC-motivated reweightings introduce M auxiliary ''tilting '' parameters, where M is the number of moments; parameter and overide ntification hypotheses can be recast in terms of these tilting paramet ers. Such tests are often startlingly more effective than their conven tional counterparts. These differences are not completely explained by differences in the leading terms of the asymptotic expansions of the test statistics.