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A Remark On Bimodality And Weak Instrumentation In Structural Equation Estimation, Peter C.B. Phillips
A Remark On Bimodality And Weak Instrumentation In Structural Equation Estimation, Peter C.B. Phillips
Cowles Foundation Discussion Papers
In a simple model composed of a structural equation and identity, the finite sample distribution of the IV/LIML estimator is always bimodal and this is most apparent when the concentration parameter is small. Weak instrumentation is the energy that feeds the secondary mode and the coefficient in the structural identity provides a point of compression in the density that gives rise to it. The IV limit distribution can be normal, bimodal, or inverse normal depending on the behavior of the concentration parameter and the weakness of the instruments. The limit distribution of the OLS estimator is normal in all cases …
Gmm With Many Moment Conditions, Chirok Han, Peter C.B. Phillips
Gmm With Many Moment Conditions, Chirok Han, Peter C.B. Phillips
Cowles Foundation Discussion Papers
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 covering moderate time spans and with 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 …