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The Exact Distribution of LIML: I

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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Abstract

It is shown that the exact finite sample distribution of the limited information maximum likelihood (LIML) estimator in a general and leading single equation case is multivariate Cauchy. When the LIML estimator utilizes a known error covariance matrix (LIMLK) it is proved that the same Cauchy distribution still applies. The corresponding result for the instrumental variable (IV) estimator is a form of multivariate t density where the degrees of freedom depend on the number of instruments.

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File URL: http://cowles.econ.yale.edu/P/cd/d06b/d0658.pdf
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Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 658.

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Length: 22 pages
Date of creation: Dec 1982
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Publication status: Published in International Economic Review (February 1984), 25(1): 249-261
Handle: RePEc:cwl:cwldpp:658

Note: Extended version of CFDP 626. CFP 589.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Wegge, Leon L, 1971. "The Finite Sampling Distribution of Least Squares Estimators with Stochastic Regressors," Econometrica, Econometric Society, vol. 39(2), pages 241-51, March. [Downloadable!] (restricted)
  2. Phillips, P C B, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," Review of Economic Studies, Blackwell Publishing, vol. 47(1), pages 183-224, January. [Downloadable!] (restricted)
  3. Kelejian, Harry H, 1974. "Random Parameters in a Simultaneous Equation Framework: Identification and Estimation," Econometrica, Econometric Society, vol. 42(3), pages 517-27, May. [Downloadable!] (restricted)
  4. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May. [Downloadable!] (restricted)
  5. Mariano, Roberto S, 1977. "Finite Sample Properties of Instrumental Variable Estimators of Structural Coefficients," Econometrica, Econometric Society, vol. 45(2), pages 487-96, March. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. John C. Chao & Peter C.B. Phillips, 1996. "Bayesian Posterior Distributions in Limited Information Analysis of the Simultaneous Equations Model Using the Jeffreys Prior," Cowles Foundation Discussion Papers 1137, Cowles Foundation, Yale University. [Downloadable!]
  2. Giovanni Forchini, 2006. "The Asymptotic distribution of the LIML Estimator in a Partially Identified Structural Equation," Monash Econometrics and Business Statistics Working Papers 1/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  3. John Chao & Norman Swanson, 2003. "Alternative Approximations of the Bias and MSE of the IV Estimator Under Weak Identification With an Application to Bias Correction," Departmental Working Papers 200315, Rutgers University, Department of Economics. [Downloadable!]
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  4. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2009. "The Limited Information Maximum Likelihood Estimator as an Angle," CIRJE F-Series CIRJE-F-619, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  5. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 10-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
    Other versions:
  6. Peter C.B. Phillips, 1992. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Cowles Foundation Discussion Papers 1039, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  7. J. Dufour, . "Some Impossibility Theorems in Econometrics with Applications to Instrumental Variables, Dynamic Models and Cointegration," Sonderforschungsbereich 373 1995-27, Humboldt Universitaet Berlin.
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  8. Peter C.B. Phillips, 1987. "Conditional and Unconditional Statistical Independence," Cowles Foundation Discussion Papers 824R, Cowles Foundation, Yale University, revised Dec 1987. [Downloadable!]
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  9. Grant H. Hillier, 1987. "Joint Distribution Theory for Some Statistics Based on LIML and TSLS," Cowles Foundation Discussion Papers 840, Cowles Foundation, Yale University. [Downloadable!]
  10. Rodrigo Alfaro, 2008. "Higher Order Properties of the Symmetricallr Normalized Instrumental Variable Estimator," Working Papers Central Bank of Chile 500, Central Bank of Chile. [Downloadable!]
  11. Peter C. B. Phillips, 2005. "A Remark on Bimodality and Weak Instrumentation in Structural Equation Estimation," Cowles Foundation Discussion Papers 1540, Cowles Foundation, Yale University. [Downloadable!]
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  12. Jean-Marie Dufour, 2001. "Logiques et tests d'hypothèses : réflexions sur les problèmes mal posés en économétrie," CIRANO Working Papers 2001s-40, CIRANO. [Downloadable!]
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  13. Peter C.B. Phillips, 1983. "Finite Sample Econometrics Using ERA's," Cowles Foundation Discussion Papers 683, Cowles Foundation, Yale University. [Downloadable!]
  14. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  15. John C. Chao & Peter C.B. Phillips, 1998. "Jeffreys Prior Analysis of the Simultaneous Equations Model in the Case with n+1 Endogenous Variables," Cowles Foundation Discussion Papers 1198, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  16. Grant Hillier & Raymond Kan & Xiaolu Wang, 2008. "Computationally efficient recursions for top-order invariant polynomials with applications," CeMMAP working papers CWP07/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  17. Chirok Han & Peter C.B. Phillips, 2005. "GMM with Many Moment Conditions," Cowles Foundation Discussion Papers 1515, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
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