Higher Order Properties of the Symmetricallr Normalized Instrumental Variable Estimator

This paper provides the second order bias for the Symmetrically Normalized Instrumental Variable Estimator (SNIV), using Edgeworth expansions for both the estimator and the minimum eigenvalue. SNIV was proposed by Alonso-Borrego and Arellano (1999) as an alternative for the Limited Information Maximum Likelihood Estimator (LIML), based solely on simulations. The paper shows that second order biases of SNIV and 2SLS are similar meanwhile LIML is second order unbiased. Previous results can be obtained in a specific design: small number of strong instruments, where biases of 2SLS, SNIV, and LIML are zero.