The LIML estimator has finite moments!

The Limited Information Maximum Likelihood estimator of the vector of coefficients of a structural equation in a simultaneous equation model is the vector that defines the linear combination maximizing the effect variance relative to the error variance. If this “eigenvector” solution is normalized by setting a designated coefficient equal to 1, the second-order moment of the estimator may be unbounded. However, the second-order moment is finite if the normalization sets the sample error variance of the linear combination equal to 1.