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On the Bimodality of the Exact Distribution of the TSLS Estimator

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  • Giovanni Forchini

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Abstract

Nelson and Startz (Econometrica, 58, 1990), Maddala and Jong (Econometrica, 60, 1992) and Wolgrom (Econometrica, 69, 2001) have shown that the density of the two-stage least squares estimator may be bimodal in a just identified structural equation. This paper further investigates the conditions under which bimodality may arise in a just over-identified model.

Suggested Citation

  • Giovanni Forchini, 2005. "On the Bimodality of the Exact Distribution of the TSLS Estimator," Monash Econometrics and Business Statistics Working Papers 14/05, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2005-14
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2005/wp14-05.pdf
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    References listed on IDEAS

    as
    1. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(05), pages 707-743, October.
    2. 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.
    3. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-878, May.
    4. Hillier, Grant, 2006. "Yet More On The Exact Properties Of Iv Estimators," Econometric Theory, Cambridge University Press, vol. 22(05), pages 913-931, October.
    5. Woglom, Geoffrey, 2001. "More Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 69(5), pages 1381-1389, September.
    6. 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.
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    Citations

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    Cited by:

    1. Marcelo C. Medeiros & Eduardo Mendes & Les Oxley, 2014. "A Note on Nonlinear Cointegration, Misspecification, and Bimodality," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 713-731, October.
    2. Simon A. Broda & Raymond Kan, 2016. "On distributions of ratios," Biometrika, Biometrika Trust, vol. 103(1), pages 205-218.
    3. Jan F. Kiviet, 2013. "Identification and inference in a simultaneous equation under alternative information sets and sampling schemes," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 24-59, February.
    4. Poskitt, D.S. & Skeels, C.L., 2007. "Approximating the distribution of the two-stage least squares estimator when the concentration parameter is small," Journal of Econometrics, Elsevier, vol. 139(1), pages 217-236, July.
    5. repec:eme:aecozz:s0731-905320140000033013 is not listed on IDEAS
    6. Phillips, Peter C.B., 2006. "A Remark On Bimodality And Weak Instrumentation In Structural Equation Estimation," Econometric Theory, Cambridge University Press, vol. 22(05), pages 947-960, October.
    7. Forchini, Giovanni, 2007. "The exact distribution of the TSLS estimator for a non-Gaussian just-identified linear structural equation," Economics Letters, Elsevier, vol. 95(1), pages 117-123, April.
    8. Jan F. Kiviet & Jerzy Niemczyk, 2014. "On the Limiting and Empirical Distributions of IV Estimators When Some of the Instruments are Actually Endogenous," Advances in Econometrics,in: Essays in Honor of Peter C. B. Phillips, volume 33, pages 425-490 Emerald Publishing Ltd.

    More about this item

    Keywords

    Bimodality; Identification; Structural equation; Two Stage Least Squares.;

    JEL classification:

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

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