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  • Giovanni Forchini (a1)
  • DOI:
  • Published online: 01 October 2009

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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*Address correspondence to Giovanni Forchini, Department of Econometrics and Business Statistics, Monash University, Clayton, Victoria 3800, Australia; e-mail:
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P.C.B. Phillips (1984b) The exact distribution of LIML: I. International Economic Review 25, 249261.

P.C.B. Phillips (1985) The exact distribution of the LIML: II. International Economic Review 26, 2136.

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J.H. Stock & J.H. Wright (2000) GMM with weak identification. Econometrica 68, 10551096.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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