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Expansions of GMM statistics that indicate their properties under weak and/or many instruments and the bootstrap

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  • Frank Kleibergen

Abstract

We construct higher order expressions for Wald and Lagrange multiplier (LM) GMM statistics that are based on 2step and continuous updating estimators (CUE). We show that the sensitivity of the limit distribution to weak and many instruments results from superfluous elements in the higher order expansion. When the instruments are strong and their number is small, these elements are of higher order and result in higher order biases. When instruments are weak and/or their number is large, they are, however, of zero-th order and influence the limiting distributions. Edgeworth approximations do not remove the superfluous elements. The expansion of the LM-CUE statistic, which is Kleibergen's (2003) K-statistic, does not contain the superfluous higher order elements so it is robust to weak or many instruments. An Edgeworth approximation of its finite sample distribution shows that the bootstrap reduces the size distortion. We compute power curves for tests on the autocorrelation parameter in a panel autoregressive model to illustrate the consequences of the higher order.terms and the improvement that results from applying the bootstrap

Suggested Citation

  • Frank Kleibergen, 2004. "Expansions of GMM statistics that indicate their properties under weak and/or many instruments and the bootstrap," Econometric Society 2004 North American Summer Meetings 408, Econometric Society.
    • Handle: RePEc:ecm:nasm04:408
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    Cited by:

    1. Marcelo J. Moreira & Jack R. Porter & Gustavo A. Suarez, 2004. "Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak," NBER Technical Working Papers 0302, National Bureau of Economic Research, Inc.
    2. Mehmet Caner, 2005. "Higher Order Expansions in GMM with Nearly Weak and Many Nearly Weak Instruments," Working Paper 209, Department of Economics, University of Pittsburgh, revised Jan 2005.
    3. William James Adams & Ben R. Craig & James B. Thompson, 2006. "Does Small Business Administration guaranteed lending improve economic performance in lowincome areas?," Proceedings: Community Affairs Dept. Conferences, Federal Reserve Bank of Kansas City, issue Jul, pages 55-85.
    4. Ben R. Craig & William E. Jackson & James B. Thomson, 2006. "Small-firm credit markets, SBA-guaranteed lending, and economic performance in low-income areas," Working Papers (Old Series) 0601, Federal Reserve Bank of Cleveland.
    5. Ben R. Craig & William E. Jackson & James B. Thomson, 2006. "Small firm credit market discrimination, SBA-guaranteed lending, and local market economic performance," Working Papers (Old Series) 0613, Federal Reserve Bank of Cleveland.

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    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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