Combining Two Consistent Estimators

Abstract

This chapter shows how a weighted average of a forward and reverse Jackknife IV estimator (JIVE) yields estimators that are robust against heteroscedasticity and many instruments. These estimators, called HFUL (Heteroscedasticity robust Fuller) and HLIM (Heteroskedasticity robust limited information maximum likelihood (LIML)) were introduced by Hausman, Newey, Woutersen, Chao, and Swanson (2012), but without derivation. Combining consistent estimators is a theme that is associated with Jerry Hausman and, therefore, we present this derivation in this volume. Additionally, and in order to further understand and interpret HFUL and HLIM in the context of jackknife type variance ratio estimators, we show that a new variant of HLIM, under specific grouped data settings with dummy instruments, simplifies to the Bekker and van der Ploeg (2005) MM (method of moments) estimator.

Citation

Chao, J.C., Hausman, J.A., Newey, W.K., Swanson, N.R. and Woutersen, T. (2012), "Combining Two Consistent Estimators", Baltagi, B.H., Carter Hill, R., Newey, W.K. and White, H.L. (Ed.) Essays in Honor of Jerry Hausman (Advances in Econometrics, Vol. 29), Emerald Group Publishing Limited, Leeds, pp. 33-53. https://doi.org/10.1108/S0731-9053(2012)0000029007