The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd


  • Frank Kleibergen
Reference work entry


Hypothesis testing is the customary instrument for analysing the empirical validity of an economic theory. Hypothesis testing is thus an important tool for conducting statistical inference in economic models. In this article we show how an economic theory is tested in a statistical model. We begin with the discussion of the basic results on hypothesis testing and then focus on some recent developments that have improved testing in commonly used economic models such as the linear instrumental variables regression model. We use a real economic example to illustrate the main findings.


Anderson–Rubin statistic Bootstrap Generalized method of moments Hypothesis testing: see testing Lagrange multipliers Least squares Likelihood ratios Limited information maximum likelihood Linear models Maximum likelihood Neymann–Pearson Lemma Price elasticity Probability Statistical inference Testing Two-stage least squares Wald statistics 

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  1. Anderson, T., and H. Rubin. 1949. Estimators of the parameters of a single equation in a complete set of stochastic equations. Annals of Mathematical Statistics 21: 570–582.CrossRefGoogle Scholar
  2. Andrews, D., M. Moreira, and J. Stock. 2006. Optimal two-sided invariant similar tests for instrumental variables regression. Econometrica 74: 715–752.CrossRefGoogle Scholar
  3. Berndt, E. 1991. The practice of econometrics, classic and contemporary. Reading: Addison-Wesley.Google Scholar
  4. Bound, J., D. 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
  5. Dagenais, M., and J.-M. Dufour. 1991. Invariance, nonlinear models, and asymptotic tests. Econometrica 59: 1601–1615.CrossRefGoogle Scholar
  6. Dufour, J.-M. 1997. Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65: 1365–1388.CrossRefGoogle Scholar
  7. Durbin, J. 1954. Error in variables. Review of the International Statistical Institute 22: 23–32.CrossRefGoogle Scholar
  8. Engle, R. 1984. Wald likelihood ratio and Lagrange multiplier tests in econometrics. In Handbook of econometrics, ed. Z. Griliches and M. Intriligator, Vol. 2. Amsterdam: North-Holland.Google Scholar
  9. Hausman, J. 1978. Specification tests in econometrics. Econometrica 46: 1251–1272.CrossRefGoogle Scholar
  10. Hood, W., and T. Koopmans 1953. Studies in econometric method, vol. 14 of Cowles Foundation Monograph. New York: Wiley.Google Scholar
  11. Horowitz, J. 2001. The bootstrap. In Handbook of econometrics, ed. J. Heckman and E. Leamer, Vol. 5. Amsterdam: North-Holland.Google Scholar
  12. Kleibergen, F. 2002. Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70: 1781–1803.CrossRefGoogle Scholar
  13. Kleibergen, F. 2004. Expansions of GMM statistics that indicate their properties under weak and/or many instruments and the bootstrap. Working paper, Brown University.Google Scholar
  14. Kleibergen, F. 2005. Testing parameters in GMM without assuming that they are identified. Econometrica 73: 1103–1124.CrossRefGoogle Scholar
  15. Moreira, M. 2003. A conditional likelihood ratio test for structural models. Econometrica 71: 1027–1048.CrossRefGoogle Scholar
  16. Nelson, C., and R. Startz. 1990. Some further results on the exact small sample properties of the instrumental variables estimator. Econometrica 58: 967–976.CrossRefGoogle Scholar
  17. Nerlove, M., and F. Waugh. 1961. Advertising without supply control: Some implications of a study of the advertising of oranges. Journal of Farm Economics 43: 813–837.CrossRefGoogle Scholar
  18. Newey, W., and D. McFadden. 1994. Large sample estimation and hypothesis testing. In Handbook of econometrics, ed. R. Engle and D. McFadden, Vol. 4. Amsterdam: North-Holland.Google Scholar
  19. Staiger, D., and J. Stock. 1997. Instrumental variables regression with weak instruments. Econometrica 65: 557–586.CrossRefGoogle Scholar
  20. Theil, H. 1953. Estimation and simultaneous correlation in complete equation systems. Mimeo. The Hague: Central Planning Bureau.Google Scholar
  21. Wu, D.-M. 1973. Alternative tests of independence between stochastic regressors and disturbances. Econometrica 41: 733–750.CrossRefGoogle Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Frank Kleibergen
    • 1
  1. 1.