We consider the estimation of coefficients of a dynamic panel structural equation
in the simultaneous equation models. As a semi-parametric method, we introduce
a class of modifications of the limited information maximum likelihood (LIML) estimator
to improve its asymptotic properties as well as the small sample properties
when we have individual heteroscedasticities. We shall show that an asymptotically
optimal modification of the LIML estimator, which is called AOM-LIML,
removes the asymptotic bias caused by the forward-filtering and improves the
LIML and other estimation methods with individual heteroscedasticities.