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

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Giovanni Forchini ()

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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.

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File URL: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/2006/wp1-06.pdf
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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 1/06.

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Length: 18 pages
Date of creation: Jan 2006
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Handle: RePEc:msh:ebswps:2006-1

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Related research
Keywords: LIML estimator; Partial Identification; Linear structural equation; Asymptotic distribution;

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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  1. repec:cup:etheor:v:11:y:1995:i:3:p:484-97 is not listed on IDEAS
  2. 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(03), pages 484-497, June. [Downloadable!]
  3. Phillips, Peter C B, 1984. "The Exact Distribution of LIML: I," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 249-61, February. [Downloadable!] (restricted)
    Other versions:
  4. Byron, R P, 1974. "Testing Structural Specification Using the Unrestricted Reduced Form," Econometrica, Econometric Society, vol. 42(5), pages 869-83, September. [Downloadable!] (restricted)
  5. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    Other versions:
  6. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation, Yale University, revised Aug 1988. [Downloadable!]
  7. 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. [Downloadable!] (restricted)
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  8. 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, 09. [Downloadable!] (restricted)
    Other versions:
  9. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. 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 1009-27, July. [Downloadable!] (restricted)
  12. Phillips, P. C. B., 1984. "The exact distribution of exogenous variable coefficient estimators," Journal of Econometrics, Elsevier, vol. 26(3), pages 387-398, December. [Downloadable!] (restricted)
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  13. Chirok Han & Peter C.B. Phillips, 2005. "GMM with Many Moment Conditions," Cowles Foundation Discussion Papers 1515, Cowles Foundation, Yale University. [Downloadable!]
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  14. 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. [Downloadable!] (restricted)
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