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The Asymptotic distribution of the LIML Estimator in a Partially Identified Structural Equation

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  • Giovanni Forchini

Abstract

We derive general formulae 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.

Suggested Citation

  • 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.
    • Handle: RePEc:msh:ebswps:2006-1
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2006/wp1-06.pdf
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    References listed on IDEAS

    as
    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. Chirok Han & Peter C. B. Phillips, 2006. "GMM with Many Moment Conditions," Econometrica, Econometric Society, vol. 74(1), pages 147-192, January.
    4. 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.
    5. Phillips, P. C. B., 1984. "The exact distribution of exogenous variable coefficient estimators," Journal of Econometrics, Elsevier, vol. 26(3), pages 387-398, December.
    6. Byron, R P, 1974. "Testing Structural Specification Using the Unrestricted Reduced Form," Econometrica, Econometric Society, vol. 42(5), pages 869-883, September.
    7. 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.
    8. Hausman, Jerry A., 1983. "Specification and estimation of simultaneous equation models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 7, pages 391-448, Elsevier.
    9. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    10. 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.
    11. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    12. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    13. 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(1), pages 53-72, April.
    14. BYRON, Ray P., 1974. "Testing structural specification using the unrestricted reduced form," LIDAM Reprints CORE 192, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. repec:cup:etheor:v:11:y:1995:i:3:p:484-97 is not listed on IDEAS
    16. Choi, In & Phillips, Peter C. B., 1992. "Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 113-150.
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    More about this item

    Keywords

    LIML estimator; Partial Identification; Linear structural equation; Asymptotic distribution;
    All these keywords.

    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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