An Optimal Modification of the LIML Estimation for Many Instruments and Persistent Heteroscedasticity

Naoto Kunitomo
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Naoto Kunitomo: Faculty of Economics, University of Tokyo

No CIRJE-F-576, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: We consider the estimation of coefficients of a structural equation with many instrumental variables in a simultaneous equation system. It is mathematically equivalent to an estimating equation estimation or a reduced rank regression in the statistical linear models when the number of restrictions or the dimension increases with the sample size. As a semi- parametric method, we propose a class of modifications of the limited information maximum likelihood (LIML) estimator to improve its asymptotic properties as well as the small sample properties for many instruments and persistent heteroscedasticity. We show that an asymptotically optimal modification of the LIML estimator, which is called AOM-LIML, improves the LIML estimator and other estimation methods. We give a set of sufficient conditions for an asymptotic optimality when the number of instruments or the dimension is large with persistent heteroscedasticity including a case of many weak instruments.

Pages: 30 pages
Date: 2008-07
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2008cf576

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