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Joint Distribution Theory for Some Statistics Based on LIML and TSLS

Listed author(s):
  • Grant H. Hillier

In the context of a single linear structural equation under classical assumptions, we derive the joint conditional density of the LIML endogenous coefficient estimator, and the usual characteristic root arising from the LIML procedure, given the OLS estimates of the reduced form coefficients for the excluded exogenous variables. This provides the joint distributions for various combinations of the statistics commonly used for inference in this model, and is hence an important stepping stone in the analysis of these procedures. The main result also leads to a new derivation of the density of the LIML estimator itself, and provides a result which is directly comparable to earlier results for IV estimators, including OLS and TSLS. We also consider briefly the density of the LIML structural variance estimator, and the joint density of the LIML and TSLS estimators for the endogenous coefficients.

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File URL: http://cowles.yale.edu/sites/default/files/files/pub/d08/d0840.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 840.

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Length: 31 pages
Date of creation: Jun 1987
Handle: RePEc:cwl:cwldpp:840
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Web page: http://cowles.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Phillips, Peter C B, 1985. "The Exact Distribution of LIML: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 21-36, February.
  2. Phillips, P. C. B., 1984. "The exact distribution of exogenous variable coefficient estimators," Journal of Econometrics, Elsevier, vol. 26(3), pages 387-398, December.
  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. Rhodes, George F, Jr, 1981. "Exact Density Functions and Approximate Critical Regions for Likelihood Ratio Identifiability Test Statistics," Econometrica, Econometric Society, vol. 49(4), pages 1035-1055, June.
  5. Hillier, Grant H., 1985. "On the Joint and Marginal Densities of Instrumental Variable Estimators in a General Structural Equation," Econometric Theory, Cambridge University Press, vol. 1(01), pages 53-72, April.
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