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Exact Small Sample Properties of the Instrumental Variable Estimator. A View From a Different Angle

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Abstract

I derive the exact small sample properties of the instrumental variables estimator using a trigonometric approach. The distribution for the estimation error is decomposed into a product of three components - each with an intuitive interpretation. This approach helps the discussion on what underlies the exact shape of the estimator’s distribution and in particular the possibility of a bimodal distribution.

Suggested Citation

  • Mehlum, Halvor, 2004. "Exact Small Sample Properties of the Instrumental Variable Estimator. A View From a Different Angle," Memorandum 03/2004, Oslo University, Department of Economics.
  • Handle: RePEc:hhs:osloec:2004_003
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    File URL: http://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2004/Memo-03-2004.pdf
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    1. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
    2. Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 60(1), pages 181-183, January.
    3. Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516, Elsevier.
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    Keywords

    Instrument; variable; estimator;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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