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The Asymptotic Distribution Of The Liml Estimator In A Partially Identified Structural Equation

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  • Forchini, Giovanni

Abstract

We derive a closed-form expression for the asymptotic distribution of the LIML estimator for the coefficients of both endogenous and exogenous variables in a partially identified linear structural equation. We extend previous results of Phillips (1989) and Choi and Phillips (1992), where the focus was on IV estimators. We show that partial failure of identification affects the LIML in that its moments do not exist even asymptotically.

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  • 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.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:03:p:917-930_99
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    References listed on IDEAS

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    1. Skeels, Christopher L., 1995. "Some Exact Results for Estimators of the Coefficients on the Exogenous Variables in a Single Equation," Econometric Theory, Cambridge University Press, vol. 11(3), pages 484-497, June.
    2. 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.
    3. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    4. Chirok Han & Peter C. B. Phillips, 2006. "GMM with Many Moment Conditions," Econometrica, Econometric Society, vol. 74(1), pages 147-192, January.
    5. Anderson, T W & Kunitomo, Naoto & Sawa, Takamitsu, 1982. "Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 50(4), pages 1009-1027, July.
    6. Fujikoshi, Yasunori & Morimune, Kimio & Kunitomo, Naoto & Taniguchi, Masanobu, 1982. "Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system," Journal of Econometrics, Elsevier, vol. 18(2), pages 191-205, February.
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    11. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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