The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Hypothesis Testing

  • Gregory C. Chow
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_810

Abstract

For those who believe that economic hypotheses have to be confirmed by empirical observations, hypothesis testing is an important subject in economics. As a classical example, when an economic relation is represented by a linear regression model:
$$ Y= X\beta +\upvarepsilon $$
where Y is a column vector of n observations on the dependent variable y, X is an n × k matrix with each column giving the corresponding n observations on each of k explanatory variables (which typically include a column of ones), β is a column of k regression coefficients and ε is a vector of n independent and identically distributed residuals with mean zero and variance σ2, it is of interest to test a hypothesis consisting of m linear restrictions on β:
$$ R\beta =r $$
where R is m × k and r is m × 1. A most common case occurs when there is only one restriction (m = 1) and (2) is reduced to βi = 0, the hypothesis being that the ith explanatory variable has no effect on y.
This is a preview of subscription content, log in to check access.

Bibliography

  1. Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle. In Proceedings of the 2nd international symposium for information theory, ed. B. Petrov and F. Cśaki. Budapest: Akademiai Kiadó.Google Scholar
  2. Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control AC-19: 716–723.CrossRefGoogle Scholar
  3. Belsley, D., and E. Kuh. 1986. Model reliability. Cambridge, MA: MIT Press.Google Scholar
  4. Belsley, D., E. Kuh, and R. Welsch. 1980. Regression diagnostics. New York: Wiley.CrossRefGoogle Scholar
  5. Box, G., and G.M. Jenkins. 1970. Time-series analysis: forecasting and control. San Francisco: Holden-Day.Google Scholar
  6. Chow, G. 1960. Tests of equality between sets of coefficients in two linear regressions. Econometrica 28: 591–605.CrossRefGoogle Scholar
  7. Chow, G. 1980. The selection of variates for use in prediction: a generalization of Hotelling’s solution. In Quantitative econometrics and development, ed. L. Klein, M. Nerlove, and S.C. Tsiang. New York: Academic Press.Google Scholar
  8. Chow, G. 1981a. A comparison of the information and posterior probability criteria for model selection. Journal of Econometrics 16: 21–33.CrossRefGoogle Scholar
  9. Chow, G. 1981b. Evaluation of econometric models by decomposition and aggregation. In Methodology of macro-economic models, ed. J. Kmenta and J. Ramsey. Amsterdam: North-Holland.Google Scholar
  10. Chow, G. 1983. Econometrics. New York: McGraw-Hill.Google Scholar
  11. Chow, G., and P. Corsi (eds.). 1982. Evaluating the reliability of macro-economic models. London: Wiley.Google Scholar
  12. Cox, D. 1961. Tests of separate families of hypotheses. In Proceedings of the 4th Berkeley symposium on mathematical statistics and probability. Berkeley: University of California Press.Google Scholar
  13. Cox, D. 1962. Further results on tests of separate families of hypotheses. Journal of the Royal Statistical Society Series B24: 406–424.Google Scholar
  14. Hausman, J. 1978. Specification tests in econometrics. Econometrica 46: 1251–1272.CrossRefGoogle Scholar
  15. Jeffreys, H. 1961. Theory of probability, 3rd ed. Oxford: Clarendon Press.Google Scholar
  16. Leamer, E. 1978. Specification searches. New York: Wiley.Google Scholar
  17. Mallows, C. 1973. Some comments on Cp. Technometrics 15: 661–675.Google Scholar
  18. Newey, W. 1985. Maximum likelihood specification testing and conditional moment tests. Econometrica 53: 1047–1070.CrossRefGoogle Scholar
  19. Neyman, J., and E. Pearson. 1928. On the use of interpretation of certain test criteria for the purpose of statistical inference. Biometrika 20A, Part I: 175–240; Part II: 263–294.Google Scholar
  20. Pratt, J. 1975. Comments. In Studies in Bayesian econometrics and statistics, ed. S. Fienberg and A. Zellner. Amsterdam: North-Holland.Google Scholar
  21. Quandt, R. 1974. A comparison of methods for testing nonnested hypotheses. Review of Economics and Statistics 56: 92–99.CrossRefGoogle Scholar
  22. Sawa, T. 1978. Information critiera for discriminating among alternative regression models. Econometrica 46: 1273–1292.CrossRefGoogle Scholar
  23. Schwarz, G. 1978. Estimating the dimension of a model. Annals of Statistics 6: 461–464.CrossRefGoogle Scholar
  24. Silvey, S. 1959. The Lagrangian multiplier test. Annals of Mathematical Statistics 30: 389–407.CrossRefGoogle Scholar
  25. Wald, A. 1943. Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society 54: 426–482.CrossRefGoogle Scholar
  26. White, H. 1982. Maximum likelihood estimation of misspecified models. Econometrica 50: 1–25.CrossRefGoogle Scholar
  27. Wu, D. 1973. Alternative tests of independence between stochastic regressors and disturbances. Econometrica 41: 733–750.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Gregory C. Chow
    • 1
  1. 1.