The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Instrumental Variables

  • Charles E. Bates
Reference work entry


Instrumental variables methods are an essential tool in modern econometric practice. The method itself is of ancient lineage and historically is closely connected with the econometrics of simultaneous equations. This article describes the statistical foundations of instrumental variables methods with a focus on their classical development.


Central limit theorems Errors in variables Euler equations Generalized method of moments estimation Instrumental variables Law of large numbers Natural experiments Returns to schooling Serial correlation Simultaneous equations models Treatment effect Two-stage least squares estimator 

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  1. Aitken, A.C. 1935. On least squares and linear combinations of observations. Proceedings of the Royal Society of Edinburgh 55: 42–48.CrossRefGoogle Scholar
  2. Amemiya, T. 1974. The nonlinear two-stage least-squares estimator. Journal of Econometrics 2: 105–110.CrossRefGoogle Scholar
  3. Andrews, D., and J. Stock. 2006. Inference with weak instruments. In Advances in econometrics: Proceedings of the Ninth World Congress of the Econometric Society, ed. R. Blundell, W. Newey, and T. Persson. Cambridge: Cambridge University Press.Google Scholar
  4. Angrist, J., and A. Krueger. 1991. Does compulsory school attendance affect schooling and earnings? Quarterly Journal of Economics 106: 979–1014.CrossRefGoogle Scholar
  5. Angrist, J.D., G.W. Imbens, and D.B. Rubin. 1996. Identification of causal effects using instrumental variables (with discussion). Journal of the American Statistical Association 91: 444–472.CrossRefGoogle Scholar
  6. Basmann, R.L. 1957. A generalized classical method of linear estimation of coefficients in a structural equation. Econometrica 25: 77–83.CrossRefGoogle Scholar
  7. Bates, C.E., and H. White. 1986a. Efficient estimation of parametric models. Working Paper No. 166, Department of Political Economy, Johns Hopkins University.Google Scholar
  8. Bates, C.E., and H. White. 1986b. An asymptotic theory of estimation and inference for dynamic models. Working paper, Department of Political Economy, Johns Hopkins University.Google Scholar
  9. Bound, J.D., D.A. Jaeger, and R. Baker. 1995. Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. Journal of the American Statistical Association 90: 443–450.Google Scholar
  10. Donald, S., and W. Newey. 2001. Choosing the number of instruments. Econometrica 69: 1365–1387.CrossRefGoogle Scholar
  11. Dufour, J.-M. 2003. Identification, weak instruments, and statistical inference in econometrics. Canadian Journal of Economics 36: 767–808.CrossRefGoogle Scholar
  12. Dufour, J.-M., and M. Taamouti. 2005. Projection-based statistical inference in linear structural models with possibly weak instruments. Econometrica 73: 1351–1365.CrossRefGoogle Scholar
  13. Geary, R.C. 1949. Determination of linear relations between systematic parts of variables with errors in observation, the variances of which are unknown. Econometrica 17: 30–58.CrossRefGoogle Scholar
  14. Goldberger, A.S. 1972. Structural equation methods in the social sciences. Econometrica 40: 979–1001.CrossRefGoogle Scholar
  15. Hahn, J. 2002. Optimal inference with many instruments. Econometric Theory 18: 140–168.CrossRefGoogle Scholar
  16. Hausman, J.A. 1983. Specification and estimation of simultaneous equation models. In Handbook of econometrics, ed. Z. Griliches and M.D. Intriligator, vol. 1. Amsterdam: North-Holland.Google Scholar
  17. Hansen, L. 1982. Large sample properties of generalized method of moments estimators. Econometrica 50: 1029–1054.CrossRefGoogle Scholar
  18. Heckman, J. 1996. Randomization as an instrumental variable. Review of Economics and Statistics 78: 336–341.CrossRefGoogle Scholar
  19. Heckman, J. 1997. Instrumental variables: A study of implicit behavioral assumptions used in making program evaluations. Journal of Human Resources 32: 441–462.CrossRefGoogle Scholar
  20. Jorgenson, D.W., and J. Laffont. 1974. Efficient estimation of nonlinear simultaneous equations with additive disturbances. Annals of Economic and Social Measurement 3: 615–640.Google Scholar
  21. Reiersøl, O. 1941. Confluence analysis by means of lag moments and other methods of confluence analysis. Econometrica 9: 1–24.CrossRefGoogle Scholar
  22. Reiersøl, O. 1945. Confluence analysis by means of instrumental sets of variables. Arkiv for Mathematik, Astronomi och Fysik 32A: 1–119.Google Scholar
  23. Sargan, J.D. 1958. The estimation of economic relationships using instrumental variables. Econometrica 26: 393–415.CrossRefGoogle Scholar
  24. Staiger, D., and J. Stock. 1997. Instrumental variables regression with weak instruments. Econometrica 65: 557–586.CrossRefGoogle Scholar
  25. Stock, J., and J. Wright. 2000. GMM with weak instruments. Econometrica 68: 1055–1096.CrossRefGoogle Scholar
  26. Theil, H. 1953. Estimation and simultaneous correlation in complete equation systems. The Hague: CentraalPlanbureau.Google Scholar
  27. White, H. 1982. Instrumental variables regression with independent observations. Econometrica 50: 483–500.CrossRefGoogle Scholar
  28. White, H. 1984. Asymptotic theory for econometricians. Orlando: Academic.Google Scholar
  29. White, H. 1985. Instrumental variables analogs of generalized least squares estimators. Journal of Advances in Statistical Computing and Statistical Analysis 1: 173–227.Google Scholar
  30. Wright, S. 1925. Corn and Hog correlations. Washington, DC: US Department of Agriculture, Bulletin 1300.Google Scholar
  31. Zellner, A. 1962. An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American Statistical Association 57: 348–368.CrossRefGoogle Scholar
  32. Zellner, A., and H. Theil. 1962. Three-stage least squares: Simultaneous estimation of simultaneous equations. Econometrica 30: 54–78.CrossRefGoogle Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Charles E. Bates
    • 1
  1. 1.