Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-19T16:28:41.564Z Has data issue: false hasContentIssue false
  • English
  • Français

THE ASYMPTOTIC DISTRIBUTION OF THE LIML ESTIMATOR IN A PARTIALLY IDENTIFIED STRUCTURAL EQUATION

Published online by Cambridge University Press:  07 October 2009

Giovanni Forchini
Get access Rights & Permissions [Opens in a new window]

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.

Type
Brief Report
Information
Econometric Theory , Volume 26 , Issue 3 , June 2010 , pp. 917 - 930
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I thank Richard Smith and two referees for useful comments. This research was partially supported by Australian Research Council grant DP0771445.

References

REFERENCES

Anderson, T.W., Kunitomo, N., & Sawa, T. (1982) Evaluation of the distribution function of the limited information maximum likelihood estimator. Econometrica 50, 1009–1028.Google Scholar
Bekker, P.A. (1994) Alternative approximations to the distributions of instrumental variable estimators. Econometrica 62, 657–681.Google Scholar
Chao, J.C. & Swanson, N.R. (2005) Consistent estimation with a large number of weak instruments. Econometrica 73(5), 1673–1692.Google Scholar
Choi, I. & Phillips, P.C.B. (1992) Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations. Journal of Econometrics 51, 113–150.Google Scholar
Forchini, G.. (2008) The Asymptotic Distribution of the LIML Estimator in a Partially Identified Structural Equation. Available at http://www.personal.buseco.monash.edu.au/~forchini/AsymLIML.pdf.Google Scholar
Fujikoshi, Y., Morimune, K., Kunitomo, N., & Taniguchi, M. (1982) Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system. Journal of Econometrics 18, 191–205.10.1016/0304-4076(82)90035-5Google Scholar
Han, C. & Phillips, P.C.B. (2006) GMM with many moment conditions. Econometrica 74, 147–192.Google Scholar
Hausman, J.A. (1983) Specification and estimation of simultaneous equation models. In Griliches, Z. and Intriligator, M.D. (eds.), Handbook of Econometrics, Vol. 1, pp. 391–448. North-Holland.Google Scholar
Hillier, G.H. (1985) On the joint and marginal densities of instrumental variable estimators in a general structural equation. Econometric Theory 1, 53–72.CrossRefGoogle Scholar
Hillier, G.H. & Skeels, C.L. (1993) Some further exact results for structural equation estimators. In Phillips, P.C.B. (ed.), Models, Methods and Applications of Econometrics. Essays in Honor of A.R. Bergstroms, pp. 117–139. Basil Blackwell.Google Scholar
Lebedev, N.N. (1972) Special Functions and Their Applications. Dover.Google Scholar
Muirhead, R.J. (1982) Aspects of Multivariate Statistical Theory. Wiley.Google Scholar
Phillips, P.C.B. (1983) Exact small sample theory in the simultaneous equation model. In Intriligator, M.D. and Griliches, Z. (eds.), Handbook of Econometrics, pp. 449–516. North Holland.Google Scholar
Phillips, P.C.B. (1984a) The exact distribution of exogenous variable coefficient estimators. Journal of Econometrics 26, 387–398.10.1016/0304-4076(84)90028-9CrossRefGoogle Scholar
Phillips, P.C.B. (1984b) The exact distribution of LIML: I. International Economic Review 25, 249–261.Google Scholar
Phillips, P.C.B. (1985) The exact distribution of the LIML: II. International Economic Review 26, 21–36.CrossRefGoogle Scholar
Phillips, P.C.B. (1989) Partially identified econometric models. Econometric Theory 5, 181–240.Google Scholar
Skeels, C.L. (1995) Some exact results for estimators of the coefficients on the exogenous variables in a single equation. Econometric Theory 11, 484–497.CrossRefGoogle Scholar
Slater, L.J. (1960) Confluent Hypergeometric Functions. Cambridge University Press.Google Scholar
Staiger, D. & Stock, J.H. (1997) Instrumental variables regression with weak instruments. Econometrica 65, 557–586.CrossRefGoogle Scholar
Stock, J.H. & Wright, J.H. (2000) GMM with weak identification. Econometrica 68, 1055–1096.10.1111/1468-0262.00151Google Scholar