A Remark on Bimodality and Weak Instrumentation in Structural Equation Estimation

Peter C. B. Phillips ()

No 1540, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

Abstract: 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 and has a much faster rate of convergence under very weak instrumentation. The IV estimator is therefore more resistant to the attractive effect of the identity than OLS. Some of these limit results differ from conventional weak instrument asymptotics, including convergence to a constant in very weak instrument cases and limit distributions that are inverse normal.

Keywords: Attraction; Bimodality; Concentration parameter; Identity; Inverse normal; Point of compression; Structural Equation; Weak instrumentation (search for similar items in EconPapers)
JEL-codes: C30 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2005-12
Note: CFP 1171.
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Published in Econometric Theory (2006), 22(5): 947-960

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Related works:
Journal Article: A REMARK ON BIMODALITY AND WEAK INSTRUMENTATION IN STRUCTURAL EQUATION ESTIMATION (2006)
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