This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak or uninformed) instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter, and conditions for consistent GMM estimation are given. A general framework for the GMM limit distribution theory is developed based on epiconvergence methods. Some illustrations are provided, including consistent GMM estimation of a panel model with time varying individual effects, consistent limited information maximum likelihood estimation as a continuously updated GMM estimator, and consistent IV structural estimation using large numbers of weak or irrelevant instruments. Some simulations are reported. Copyright The Econometric Society 2006.

We examine legislative policy making in institutions with two empirically relevant features: agenda setting occurs in real time and the default policy evolves. We demonstrate that these institutions select Condorcet winners when they exist, provided a sufficient number of individuals have opportunities to make proposals. In policy spaces with either pork barrel or pure redistributional politics (where a Condorcet winner does not exist), the last proposer is effectively a dictator or near-dictator under relatively weak conditions. Copyright The Econometric Society 2006.