Skip to main content Accessibility help

Testing Identifiability and Specification in Instrumental Variable Models

  • John G. Cragg (a1) and Stephen G. Donald (a2)


The paper develops and explores tests, based on standard moment specifications, for the identifiability of parameters apparently estimable by instrumental variables. An asymptotic expansion under standard restrictive assumptions on the error distribution suggests a correction to the asymptotic distribution. A small sampling experiment indicates that the tests are of use.



Hide All
1.Anderson, T.W. The asymptotic distribution of certain characteristic roots and vectors. In Neyman, J. (ed.), Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 103130. Berkeley: University of California Press, 1951.
2.Anderson, T.W.Introduction to Multivariate Statistical Analysis. New York: Wiley, 1958.
3.Anderson, T.W. & Rubin, H.. Estimation of the parameters of a single equation in a complete system of equations. Annals of Mathematical Statistics 20 (1949): 4663.
4.Cragg, J.G.Identification in incomplete specifications. Discussion Paper 89–13, Department of Economics, University of British Columbia, 1989.
5.Cragg, J.G. & Donald, S.G.. Testing for identifiability of simultaneous-equation coefficients. Discussion Paper 89–23, Dept. of Economics, University of British Columbia, 1989.
6.Cragg, J.G. & Donald, S.G.. A result on testing dimensionality when the true dimension is less than the null. Mimeo, 1991.
7.Fujikoshi, Y.Asymptotic expansions of the distributions of the latent roots in MANOVA and the canonical correlations. Journal of Multivariate Analysis 7 (1977): 386396.
8.Fujikoshi, Y. Asymptotic expansions for the distributions of some multivariate tests. In Krishnaiah, P.R. (ed.), Multivariate Analysis-IV, pp. 5571. Amsterdam: North-Holland, 1977.
9.Goldberger, A.S.Econometric Theory. New York: Wiley, 1964.
10.Hansen, L.P.Large sample properties of generalized method of moments estimators. Econometrica 50 (1982): 10291055.
11.Hsu, P.L.On the limiting distribution of a determinantal equation. Journal of the London Mathematical Society 16 (1941): 183194.
12.Koopmans, T.C. & Hood, W.C.. The estimation of simultaneous linear economic relationships. In Hood, W.C. and Koopmans, T.C. (eds.), Studies in Econometric Method, pp. 112199. New York: Wiley, 1953.
13.Kunimoto, N., Morimune, K. & Tsukuda, Y.. Asymptotic expansions of the distribution of the test statistics for overidentifying restrictions in a system of simultaneous equations. International Economic Review 24 (1983): 199215.
14.Lawley, D.N.Tests of significance for the latent roots of covariance and correlation matrices. Biometrika 43 (1956): 171178.
15.Lawley, D.N.Tests of significance in canonical analysis. Biometrika 46 (1959): 5966.
16.Phillips, P.C.B.Partially identified econometric models. Econometric Theory 5 (1989): 151240.
17.Rao, C.R.Linear Statistical Inference. New York: Wiley, 1965.
18.Rothenberg, T.J. Approximating the distribution of econometric estimators and test statistics. In Griliches, Z. and Intrilligator, M.D. (eds.), Handbook of Econometrics, Vol. II, pp. 881935. Amsterdam: Elsevier, 1984.
19.Schmidt, P.Econometrics. New York: Marcel Dekker, 1976.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed