An Expository Note on the Existence of Moments of Fuller and HFUL Estimators

In: Essays in Honor of Jerry Hausman: Advances in Econometrics, Volume 29, Emerald, New York, 2012

20 Pages Posted: 16 Jul 2013

See all articles by John C. Chao

John C. Chao

University of Maryland

Jerry A. Hausman

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)

Whitney K. Newey

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)

Norman R. Swanson

Rutgers University - Department of Economics; Rutgers, The State University of New Jersey - Department of Economics

Tiemen Woutersen

University of Arizona

Date Written: July 2012

Abstract

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?

Keywords: endogeneity, instrumental variables, jackknife estimation, many moments, existence of moments

JEL Classification: C13, C31

Suggested Citation

Chao, John C. and Hausman, Jerry A. and Newey, Whitney K. and Swanson, Norman Rasmus and Swanson, Norman Rasmus and Woutersen, Tiemen, An Expository Note on the Existence of Moments of Fuller and HFUL Estimators (July 2012). In: Essays in Honor of Jerry Hausman: Advances in Econometrics, Volume 29, Emerald, New York, 2012, Available at SSRN: https://ssrn.com/abstract=2294120

John C. Chao

University of Maryland ( email )

Department of Economics
College Park, MD 20742
United States
301-405-1579 (Phone)
301-408-3542 (Fax)

Jerry A. Hausman

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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Whitney K. Newey (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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Cambridge, MA 02142
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617-253-6420 (Phone)

National Bureau of Economic Research (NBER) ( email )

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Norman Rasmus Swanson

Rutgers University - Department of Economics ( email )

NJ
United States

HOME PAGE: http://econweb.rutgers.edu/nswanson/

Rutgers, The State University of New Jersey - Department of Economics ( email )

75 Hamilton Street
New Brunswick, NJ 08901
United States
848-932-7432 (Phone)

HOME PAGE: http://econweb.rutgers.edu/nswanson/

Tiemen Woutersen

University of Arizona ( email )

Department of Economics
Tucson, AZ 85721
United States

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