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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.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2005/wp14-05.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 14/05.

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Length: 19 pages
Date of creation: May 2005
Date of revision:
Handle: RePEc:msh:ebswps:2005-14

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

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References

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  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, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Working Papers 88-06, University of Washington, Department of Economics.
  3. Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 60(1), pages 181-83, January.
  4. 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 861-78, May.
  5. Woglom, Geoffrey, 2001. "More Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 69(5), pages 1381-89, September.
  6. Hillier, Grant, 2006. "Yet More On The Exact Properties Of Iv Estimators," Econometric Theory, Cambridge University Press, vol. 22(05), pages 913-931, October.
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Cited by:
  1. Jan F. Kiviet, 2012. "Identification and Inference in a Simultaneous Equation under Alternative Information Sets and Sampling Schemes," Tinbergen Institute Discussion Papers 12-128/III, Tinbergen Institute.
  2. Peter C. B. Phillips, 2005. "A Remark on Bimodality and Weak Instrumentation in Structural Equation Estimation," Cowles Foundation Discussion Papers 1540, Cowles Foundation for Research in Economics, Yale University.
  3. Simon A. Broda & Raymond Kan, 2013. "On Distributions of Ratios," UvA-Econometrics Working Papers 13-10, Universiteit van Amsterdam, Dept. of Econometrics.
  4. 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.
  5. Jan F. Kiviet, 2012. "Identification and Inference in a Simultaneous Equation under Alternative Information Sets and Sampling Schemes," Tinbergen Institute Discussion Papers 12-128/III, Tinbergen Institute.
  6. Jan F. KIVIET & Jerzy NIEMCZYK, 2013. "On the limiting and empirical distributions of IV estimators when some of the instruments are actually endogenous," Economic Growth centre Working Paper Series 1311, Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre.
  7. M.C. Medeiros & E. Mendes & Les Oxley, 2010. "A Note on Nonlinear Cointegration, Misspecification and Bimodality," Working Papers in Economics 10/01, University of Canterbury, Department of Economics and Finance.
  8. 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.
  9. Simon A. Broda, 2014. "On Distributions of Ratios," Tinbergen Institute Discussion Papers 13-211/VI, Tinbergen Institute.

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