An Expository Note on the Existence of Moments of Fuller and HFUL Estimators
John Chao, Jerry A. Hausman, Whitney K. Newey, Norman R. Swanson and Tiemen Woutersen , ( 29 )
Essays in Honor of Jerry Hausman: Advances in Econometrics

In a recent paper, Hausman et al. (2012) propose a new estimator, HFUL (Heteroscedasticity robust Fuller), for the linear model with endogeneity. This estimator is consistent and asymptotically normally distributed in the many instruments and many weak instruments asymptotics. Moreover, this estimator has moments, just like the estimator by Fuller (1977). The purpose of this note is to discuss at greater length the existence of moments result given in Hausman et al. (2012). In particular, we intend to answer the following questions: Why does LIML not have moments?

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