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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?

Suggested Citation

  • John Chao & Jerry Hausman & Whitney Newey & Norman Swanson & Tiemen Woutersen, 2013. "An Expository Note on the Existence of Moments of Fuller and HFUL Estimators," Departmental Working Papers 201311, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:201311

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    References listed on IDEAS

    1. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    2. Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, July.
    3. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, June.
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    More about this item


    endogeneity; instrumental variables; jacknife estimation; many moments; existence of moments;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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