An expository note on the existence of moments of Fuller and HFUL estimators

John Chao; Jerry Hausman; Whitney Newey; Norman Swanson; Tiemen Woutersen

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? Why does the Fuller modification lead to estimators with moments? Is normality required for the Fuller estimator to have moments? Why do we need a condition such as Hausman et al. (2012), Assumption 9? Why do we have the adjustment formula?

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Year of publication:	2013
Authors:	Chao, John C. ; Hausman, Jerry A. ; Newey, Whitney K. ; Swanson, Norman R. ; Woutersen, Tiemen
Publisher:	New Brunswick, NJ : Dep. of Economics, Rutgers, the State Univ. of New Jersey
Subject:	endogeneity \| instrumental variables \| jackknife estimation \| many moments \| existence of moments \| Schätztheorie \| Estimation theory \| Momentenmethode \| Method of moments \| IV-Schätzung \| Instrumental variables