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On The Bimodality Of The Exact Distribution Of The Tsls Estimator

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  • Forchini, G.

Abstract

We investigate the possible bimodality of the density of the two-stage least squares (TSLS) estimator in a just-identified/overidentified linear structural equation. By studying the interaction between weakness of instruments, degree of endogeneity, and degree of overidentification we are able to identify conditions for its existence.I thank Grant Hillier, Patrick Marsh, Don Poskitt, the editor Peter Phillips, and two anonymous referees for useful and encouraging comments.

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  • Forchini, G., 2006. "On The Bimodality Of The Exact Distribution Of The Tsls Estimator," Econometric Theory, Cambridge University Press, vol. 22(5), pages 932-946, October.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:05:p:932-946_06
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    1. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(5), pages 707-743, October.
    2. 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.
    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 181-183, January.
    4. 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.
    5. 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.
    6. Hillier, Grant, 2006. "Yet More On The Exact Properties Of Iv Estimators," Econometric Theory, Cambridge University Press, vol. 22(5), pages 913-931, October.
    7. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(05), pages 707-743, October.
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    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. 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 Group Publishing Limited.
    6. Phillips, Peter C.B., 2006. "A Remark On Bimodality And Weak Instrumentation In Structural Equation Estimation," Econometric Theory, Cambridge University Press, vol. 22(5), 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.

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    JEL classification:

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

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