Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T17:56:55.441Z Has data issue: false hasContentIssue false
  • English
  • Français

Instrumental Variables Estimation in Misspecified Single Equations

Published online by Cambridge University Press:  11 February 2009

Christopher L. Skeels
Christopher L. Skeels
Affiliation:
Australian National University
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper examines the exact sampling behavior of a family of instrumental variables estimators of the coefficients in a single structural equation when the model has been misspecified by the incorrect inclusion or exclusion of variables. It is found that such specification errors can have implications for the structure of the exact results obtained. A brief numerical examination of the analytical results is also provided.

Type
Articles
Information
Econometric Theory , Volume 11 , Issue 3 , June 1995 , pp. 498 - 529
Copyright
Copyright © Cambridge University Press 1995

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.)

References

REFERENCES

Anderson, T.W., Kunitomo, N., & Morimune, K. (1986) Comparing single equation estimators in a simultaneous equation system. Econometric Theory 2, 1–32.CrossRefGoogle Scholar
Anderson, T.W., Kunitomo, N., & Sawa, T. (1982) Evaluation of the distribution function of the limited information maximum likelihood estimator1. Econometrica 50, 1009–1027.CrossRefGoogle Scholar
Anderson, T.W. & Sawa, T. (1979) Evaluation of the distribution function of the two-stage least squares estimate. Econometrica 47, 163–182.CrossRefGoogle Scholar
Chikuse, Y. & Davis, A.W. (1986) A survey on the invariant polynomials with matrix arguments in relation to econometric distribution theory. Econometric Theory 2, 232–248.CrossRefGoogle Scholar
Constantine, A.G. (1963) Some noncentral distribution problems in multivariate analysis. Annals of Mathematical Statistics 34, 1270–1285.CrossRefGoogle Scholar
Constantine, A.G. & Muirhead, R.J. (1976) Asymptotic expansions for distributions of latent roots in multivariate analysis. Journal of Multivariate Analysis 6, 369–391.CrossRefGoogle Scholar
Davis, A.W. (1979) Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory. Annals of the Institute of Statistical Mathematics 31 (part A), 465–485.CrossRefGoogle Scholar
Hale, C, Mariano, R.S., & Ramage, J.G. (1980) Finite sample analysis of misspecification in simultaneous equation models. Journal of the American Statistical Association 75, 418–427.CrossRefGoogle Scholar
Hillier, G.H. (1985a) Marginal Densities of Instrumental Variables Estimators: Further Exact Results. Mimeo, Monash University.Google Scholar
Hillier, G.H. (1985b) 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. (1990) On the normalization of structural equations: Properties of direction estimators. Econometrica 58, 1181–1194.CrossRefGoogle Scholar
Hillier, G.H., Kinal, T.W., & Srivastava, V.K. (1984) On the moments of ordinary least squares and instrumental variable estimators in a general structural equation. Econometrica 52,185–202.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 Honour of A. R. Bergstrom, ch. 9, pp. 117–139. Cambridge, Massachusetts: Basil Blackwell.Google Scholar
James, A.T. (1955) The non-central Wishart distribution. Proceedings of the Royal Society (London) A 229, 364–366.Google Scholar
James, A.T. (1964) Distributions of matrix variates and latent roots derived from normal samples. Annals of Mathematical Statistics 35, 475–501.CrossRefGoogle Scholar
Kinal, T.W. (1980) The existence of moments of k-class estimators. Econometrica 48, 241–249.CrossRefGoogle Scholar
Kinal, T.W. (1986) The Exact Distribution of OLS and Instrumental Variable Estimates of the Coefficients of the Exogenous Variables in a Structural Equation. Mimeo, State University of New York at Albany.Google Scholar
Knight, J.L. (1982) A note on finite sample analysis of misspecification in simultaneous equation models. Economics Letters 9, 275–279.CrossRefGoogle Scholar
Knight, J.L. (1986) Non-normal errors and the distribution of OLS and 2SLS structural estimators. Econometric Theory 2, 75–106.CrossRefGoogle Scholar
Nagar, A.L. (1959) The bias and moment matrix of the general k-class estimators of the parameters in simultaneous equations. Econometrica 27, 575–595.CrossRefGoogle Scholar
Owen, A.D. (1976) A proof that both the bias and mean square error of the two–stage least squares estimator are monotonically non-increasing functions of sample size. Econometrica 44, 409–411.CrossRefGoogle Scholar
Phillips, P.C.B. (1980) The exact finite sample density of instrumental variable estimators in an equation with n + 1 endogenous variables. Econometrica 48, 861–868.CrossRefGoogle Scholar
Phillips, P.C.B. (1982) Small Sample Distribution Theory in Econometric Models of Simultaneous Equations. Cowles Foundation discussion paper 617, Yale University.Google Scholar
Phillips, P.C.B. (1983a) Exact small sample theory in the simultaneous equations model. In Griliches, Z. & Intriligator, M.D. (eds.), Handbook of Econometrics, vol. 1, ch. 8, pp. 449–516. Amsterdam: North–Holland.CrossRefGoogle Scholar
Phillips, P.C.B. (1983b) Marginal densities of instrumental variable estimators in the general single equation case. Advances in Econometrics, 2 1–24.Google Scholar
Phillips, P.C.B. (1984a) The exact distribution of exogenous variable coefficient estimators. Journal of Econometrics 26, 387–398.CrossRefGoogle Scholar
Phillips, P.C.B. (1984b) The exact distribution of LIML: I. International Economic Review 25, 249–261.CrossRefGoogle Scholar
Phillips, P.C.B. (1985) The exact distribution of LIML: II. International Economic Review 26, 21–36.CrossRefGoogle Scholar
Rhodes, G.F. & Westbrook, M.D. (1981) A study of estimator densities and performance under misspecification. Journal of Econometrics 16, 311–337.CrossRefGoogle Scholar
Skeels, C.L. (1989) Estimation in Misspecified Systems of Equations: Some Exact Results. Unpublished Ph.D. Thesis, Department of Econometrics, Monash University.Google Scholar
Skeels, C.L. (1990) A conditional canonical approach to simulation studies of IV estimators in simultaneous equations models. Journal of Quantitative Economics 6, 311–329.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