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The Exact Distribution of Exogenous Variable Coefficient Estimators

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Abstract

This paper derives the exact probability density function of the instrumental variable (IV) estimator of the exogenous variable coefficient vector in a structural equation containing n+1 endogenous variables and N degrees of overidentification. A leading case of the general distribution that is more amenable to analysis and computation is also presented. Conventional classical assumptions or normally distributed errors and nonrandom exogenous variables are employed.

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  • Peter C.B. Phillips, 1983. "The Exact Distribution of Exogenous Variable Coefficient Estimators," Cowles Foundation Discussion Papers 681, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:681
    Note: CFP 602.
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    1. Phillips, P C B, 1986. "The Distribution of FIML in the Leading Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 239-243, February.
    2. Forchini, Giovanni, 2010. "The Asymptotic Distribution Of The Liml Estimator In A Partially Identified Structural Equation," Econometric Theory, Cambridge University Press, vol. 26(3), pages 917-930, June.
    3. Cheung Ip, Wai & Phillips, Garry D. A., 1998. "The non-monotonicity of the bias and mean squared error of the two stage least squares estimators of exogenous variable coefficients," Economics Letters, Elsevier, vol. 60(3), pages 303-310, September.
    4. Grant H. Hillier, 1987. "Joint Distribution Theory for Some Statistics Based on LIML and TSLS," Cowles Foundation Discussion Papers 840, Cowles Foundation for Research in Economics, Yale University.
    5. Zhentao Shi, 2016. "Estimation of Sparse Structural Parameters with Many Endogenous Variables," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1582-1608, December.
    6. Hillier, Grant & Kan, Raymond & Wang, Xiaolu, 2009. "Computationally Efficient Recursions For Top-Order Invariant Polynomials With Applications," Econometric Theory, Cambridge University Press, vol. 25(1), pages 211-242, February.

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