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

  • John Chao

    ()

    (University of Maryland)

  • Jerry Hausman

    ()

    (MIT)

  • Whitney Newey

    ()

    (MIT)

  • Norman Swanson

    ()

    (Rutgers University)

  • Tiemen Woutersen

    ()

    (University of Arizona)

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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Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 201311.

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Length: 20 pages
Date of creation: 16 Jul 2013
Date of revision:
Publication status: Published in: Essays in Honor of Jerry Hausman: Advances in Econometrics, volume 29, Emerald, New York, 2012, 87-106.
Handle: RePEc:rut:rutres:201311
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  1. Hausman & Newey & Woutersen & Chao & Swanson, 2009. "Instrumental Variable Estimation with Heteroskedasticity and Many Instruments," Economics Working Paper Archive 566, The Johns Hopkins University,Department of Economics.
  2. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
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