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Heteroscedasticity

  • Thomas B. Fomby
  • Stanley R. Johnson
  • R. Carter Hill

Abstract

There are certain circumstances in which the assumption of constant error variance, homoscedasticity, in the linear model is not tenable. For example, in cross-sectional analysis in economics, the units under investigation are usually firms, households, or individuals, and the degree to which the linear equation explains their behavior may depend upon their specific characteristics. We illustrate this point by the use of three examples.

Keywords

Error Variance Maximum Likelihood Estimator Likelihood Ratio Statistic Advertising Expenditure Chow Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aitchison, J. and Silvey, S. D. (1960). Maximum-likelihood estimation procedures and associated tests of significance. Journal of The Royal Statistical Society, B, 22, 154–171.Google Scholar
  2. Amemiya, T. (1977). A note on a heteroscedastic model. Journal of Econometrics, 6, 365–370.CrossRefGoogle Scholar
  3. Breusch, T. S. and Pagan, A. R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica, 47, 1287–1294.CrossRefGoogle Scholar
  4. Chow, G. C. (1960). Tests of equality between sets of coefficients in two linear regressions. Econometrica, 28, 591–605.CrossRefGoogle Scholar
  5. Crain, W. M. and Zardkoohi, A. (1978). A test of the property-rights theory of the firm: water utilities in the United States. Journal of Law and Economics, 21, 395–408.CrossRefGoogle Scholar
  6. Duesenberry, J. S. (1949). Income, Saving and the Theory of Consumer Behavior. Cambridge, MA: Harvard University Press.Google Scholar
  7. Gleisjer, H. (1969). A new test for heteroscedasticity. Journal of The American Statistical Association, 64, 316–323.CrossRefGoogle Scholar
  8. Goldfeld, S. M. and Quandt, R. E. (1965). Some tests for homoscedasticity. Journal of the American Statistical Association, 60, 539–547.CrossRefGoogle Scholar
  9. Goldfeld, S. M. and Quandt, R. E. (1972). Nonlinear Methods in Econometrics. Amsterdam: North Holland.Google Scholar
  10. Greenberg, E. (1980). Finite sample moments of a preliminary test estimator in the case of possible heteroscedasticity. Econometrica, 48, 1805–1813.CrossRefGoogle Scholar
  11. Harvey, A. C. (1974). Estimation of parameters in a heteroscedastic regression model. Paper presented at the European Meeting of The Econometric Society, Grenoble, September.Google Scholar
  12. Harvey, A. C. (1976). Estimating regression models with multiplicative heteroscedasticity. Econometrica, 44, 461–465.CrossRefGoogle Scholar
  13. Imhof, J. P. (1961). Computing the distribution of quadratic forms in normal variables. Biometrika, 48, 419–426.Google Scholar
  14. Jayatissa, W. A. (1977). Tests of equality between sets of coefficients in two linear regressions when disturbance variances are unequal. Econometrica, 45, 1291–1292.CrossRefGoogle Scholar
  15. Mincer, J., (1974). Schooling, Experience, and Earnings. New York: National Bureau of Economic Research.Google Scholar
  16. Prais, S. J. and Houthakker, H. S. (1955). The Analysis of Family Budgets. New York: Cambridge University Press.Google Scholar
  17. Schmidt, P. and Sickles, R. (1977). Some further evidence on the use of the Chow test under heteroscedasticity. Econometrica, 45, 1293–1298.CrossRefGoogle Scholar
  18. Taylor, W. E. (1978). The heteroscedastic linear model: exact finite sample results. Econometrica, 46, 663–675.CrossRefGoogle Scholar
  19. Toyoda, T. (1974). Use of the Chow test under heteroscedasticity. Econometrica, 42, 601–608.CrossRefGoogle Scholar
  20. White, H. (1980). A heteroscedasticity-consistent covariance matrix estimator and a direct test for heteroscedasticity. Econometrica, 48, 817–838.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • Thomas B. Fomby
    • 1
  • Stanley R. Johnson
    • 2
  • R. Carter Hill
    • 3
  1. 1.Department of EconomicsSouthern Methodist UniversityDallasUSA
  2. 2.The Center for Agricultural and Rural DevelopmentIowa State UniversityAmesUSA
  3. 3.Department of EconomicsLouisiana State UniversityBaton RougeUSA

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