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Consistent Estimation with a Large Number of Weak Instruments

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  • John Chao

    (University of Maryland)

  • Norman Swanson

    (Rutgers University)

Abstract

This paper analyzes the conditions under which consistent estimation can be achieved in instrumental Variables (IV) regression when the available instruments are weak, in the local-to-zero sense of Staiger and Stock (1997) and using the many-instrument framework of Morimune (1983) and Bekker (1994). Our analysis of an extended k-class of estimators that includes Jackknife IV (JIVE) establishes that consistent estimation depends importantly on the relative magnitudes of rn, the growth rate of the concentration parameter, and Kn, the number of instruments: In particular, LIML and JIVE are consistent when (Kn)^.5 /rn goes to zero, while two-stage least squares is consistent only if (Kn)^.5 /rn goes to zero, as n goes to infinity. We argue that the use of many instruments may be bene¯cial for estimation, as the resulting concentration parameter growth may allow consistent estimation, in certain cases.

Suggested Citation

  • John Chao & Norman Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Departmental Working Papers 200421, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:200421
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    More about this item

    Keywords

    instrumental variables; k-class estimators; local to zero framework; pathwise asymptotics; weak instruments;
    All these keywords.

    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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