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YET MORE ON THE EXACT PROPERTIES OF IV ESTIMATORS

Published online by Cambridge University Press:  30 August 2006

Grant Hillier
Grant Hillier
Affiliation:
University of Southampton
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Abstract

We revisit the exact properties of two-stage least squares and limited information maximum likelihood estimators in a structural equation/instrumental variables regression under Gaussian assumptions. Simple derivations based on conditioning serve both to demystify the apparently complicated formulas, and to isolate the key quantities that determine the properties of the estimators. Some recent results obtained under weak-instrument asymptotics are sharpened and clarified by the exact analysis.Thanks to Peter Phillips and several anonymous referees for helpful comments that improved the paper considerably.

Information

Type
MISCELLANEA: BIMODALITY AND WEAK INSTRUMENTATION
Information
Econometric Theory , Volume 22 , Issue 5 , October 2006 , pp. 913 - 931
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Anderson, T.W. & H. Rubin (1949) Estimation of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics 20, 46–63.Google Scholar
Chamberlain, G. (2005) Decision Theory Applied to an Instrumental Variables Model. Mimeo, Harvard University.
Chao, J.C. & P.C.B. Phillips (1998) Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior. Journal of Econometrics 87, 49–86.Google Scholar
Chao, J.C. & P.C.B. Phillips (2002) Jeffreys prior analysis of the simultaneous equations model in the case with n + 1 endogenous variables. Journal of Econometrics 111, 251–283.Google Scholar
Chao, J.C. & N.R. Swanson (2005) Consistent estimation with a large number of weak instruments. Econometrica 73, 1673–1692.Google Scholar
Chao, J.C. & N.R. Swanson (2006) Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction. Journal of Econometrics, forthcoming.Google Scholar
Forchini, G. (2006) On the bimodality of the exact distribution of the TSLS estimator. Econometric Theory 22, 932–946 (this issue).Google Scholar
Forchini, G. & G.H. Hillier (2003) Conditional inference for possibly unidentified structural equations. Econometric Theory 19, 707–743.Google Scholar
Forchini, G. & G.H. Hillier (2005) Ill-Conditioned Problems, Fisher Information, and Weak Instruments. Cemmap Working paper CWP04/05.
Hillier, G.H. (1985) On the joint and marginal densities of instrumental variable estimators in a general structural equation. Econometric Theory 1, 53–72.Google Scholar
Hillier, G.H. (1987) Joint Distribution Theory for Some Statistics Based on LIML and TSLS. Cowles Foundation Discussion paper 840.
Hillier, G.H. (1990) On the normalization of structural equations: Properties of direction estimators. Econometrica 58, 1181–1194.Google Scholar
Hillier, G.H. & M. Armstrong (1999) The density of the maximum likelihood estimator. Econometrica 67, 1459–1470.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, 181–184.Google Scholar
Marsaglia, G. (1965) Ratios of normal variables and the roots of sums of uniform variables. Journal of the American Statistical Association 60, 193–204.Google Scholar
Morimune, K. (1983) Approximate distributions of k-class estimators when the degree of overidentifiability is large compared to the sample size. Econometrica 51, 821–841.Google Scholar
Muirhead, R.J. (1982) Aspects of Multivariate Statistical Theory. Wiley.
Nelson, C. & R. Startz (1990) Some further results on the exact small sample properties of the instrumental variable estimator. Econometrica 58, 967–976.Google Scholar
Newey, Whitney K. (2004) Many Instrument Asymptotics. Mimeo, MIT.
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 equation model. In M.D. Intriligator & Z. Griliches (eds.), Handbook of Econometrics, pp. 449–516. North-Holland.
Phillips, P.C.B. (1984) The exact distribution of LIML, part I. International Economic Review 25, 249–261.Google Scholar
Phillips, P.C.B. (1985) The exact distribution of LIML, part II. International Economic Review 26, 21–36.Google Scholar
Phillips, P.C.B. (1989) Partially identified econometric models. Econometric Theory 5, 181–240.Google Scholar
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
Sargan, J.D. (1976) Econometric estimators and the Edgeworth approximation. Econometrica 44, 421–448.Google Scholar
Staiger, D. & J.H. Stock (1997) Instrumental variables regression with weak instruments. Econometrica 65, 557–586.Google Scholar
Stock, J.H., J.H. Wright, & M. Yogo (2002) A survey of weak instruments and weak identification in generalized method of moments. Journal of Business & Economic Statistics 20, 518–529.Google Scholar
Woglom, G. (2001) More results on the exact small sample properties of the instrumental variable estimator. Econometrica 69, 1381–1389.Google Scholar