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ON THE BIMODALITY OF THE EXACT DISTRIBUTION OF THE TSLS ESTIMATOR

Published online by Cambridge University Press:  30 August 2006

G. Forchini
G. Forchini
Affiliation:
Monash University
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Abstract

We investigate the possible bimodality of the density of the two-stage least squares (TSLS) estimator in a just-identified/overidentified linear structural equation. By studying the interaction between weakness of instruments, degree of endogeneity, and degree of overidentification we are able to identify conditions for its existence.I thank Grant Hillier, Patrick Marsh, Don Poskitt, the editor Peter Phillips, and two anonymous referees for useful and encouraging comments.

Type
MISCELLANEA: BIMODALITY AND WEAK INSTRUMENTATION
Information
Econometric Theory , Volume 22 , Issue 5 , October 2006 , pp. 932 - 946
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Bekker, P.A. (1994) Alternative approximations to the distributions of instrumental variable estimators. Econometrica 62, 657–681.Google Scholar
Chao, J.C. & N.R. Swanson (2005) Consistent estimation with a large number of weak instruments. Econometrica 73, 1673–1692.Google Scholar
Han, C. & P.C.B. Phillips (2006) GMM with many moment conditions. Econometrica 74, 147–192.Google Scholar
Hillier, G.H. (1990) On the normalization of structural equations: Properties of direction estimators. Econometrica 58, 1181–1194.Google Scholar
Hillier, G.H. (2006) Yet more on the exact properties of IV estimators. Econometric Theory 22, 913–931 (this issue).Google Scholar
Kiviet, J.F. & J. Niemczyk (2005) The Asymptotic and Finite Sample Distributions of OLS and IV in Simultaneous Equations. UVA Econometrics, Discussion paper 2005/01.
Maddala, G.S. & J. Jeong (1992) On the exact small sample distribution of the instrumental variable estimator. Econometrica 60, 181–183.Google Scholar
Nelson, C.R. & R. Startz (1990) Some further results on the small sample properties of the instrumental variable estimator. Econometrica 58, 967–976.Google Scholar
Phillips, P.C.B. (1980) The exact distribution of instrumental variable estimators in an equation containing n + 1 endogenous variables. Econometrica 48, 861–878.Google Scholar
Phillips, P.C.B. (1983) Exact small sample theory in the simultaneous equations model. In Z. Griliches & M.D. Intriligator (eds.), Handbook of Econometrics, vol. 1, pp. 449–516. North-Holland.
Phillips, P.C.B. (2006) A remark on bimodality and weak instrumentation in structural equation estimation. Econometric Theory 22, 947–960 (this issue).Google Scholar
Phillips, P.C.B. & M.R. Wickens (1978) Exercises in Econometrics, vol. 2. Ballinger and Philip Allan.
Slater, L.J. (1960) Confluent Hypergeometric Functions. Cambridge University Press.
Woglom, G. (2001) More results on the exact small sample properties of the instrumental variable estimator. Econometrica 69, 1381–1389.Google Scholar