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  • Giovanni Forchini (a1)

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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T.W. Anderson , N. Kunitomo , & T. Sawa (1982) Evaluation of the distribution function of the limited information maximum likelihood estimator. Econometrica 50, 10091028.

P.A. Bekker (1994) Alternative approximations to the distributions of instrumental variable estimators. Econometrica 62, 657681.

J.C. Chao & N.R. Swanson (2005) Consistent estimation with a large number of weak instruments. Econometrica 73(5), 16731692.

I. Choi & P.C.B. Phillips (1992) Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations. Journal of Econometrics 51, 113150.

Y. Fujikoshi , K. Morimune , N. Kunitomo , & M. Taniguchi (1982) Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system. Journal of Econometrics 18, 191205.

C. Han & P.C.B. Phillips (2006) GMM with many moment conditions. Econometrica 74, 147192.

J.A. Hausman (1983) Specification and estimation of simultaneous equation models. In Z. Griliches and M.D. Intriligator (eds.), Handbook of Econometrics, Vol. 1, pp. 391448. North-Holland.

R.J. Muirhead (1982) Aspects of Multivariate Statistical Theory. Wiley.

P.C.B. Phillips (1983) Exact small sample theory in the simultaneous equation model. In M.D. Intriligator and Z. Griliches (eds.), Handbook of Econometrics, pp. 449516. North Holland.

P.C.B. Phillips (1984a) The exact distribution of exogenous variable coefficient estimators. Journal of Econometrics 26, 387398.

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.

D. Staiger & J.H. Stock (1997) Instrumental variables regression with weak instruments. Econometrica 65, 557586.

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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