Errors in Variables

  • Vincent J. Geraci
Part of the The New Palgrave book series

Abstract

This essay surveys the history and recent developments on economic models with errors in variables. These errors may arise from the use of substantive unobservables, such as permanent income, or from ordinary measurement problems in data collection and processing. The point of departure is the classical regression equation with random errors in variables:
$$y = {X^*}\beta + u,$$
where y is a n × 1 vector of observations on the dependent variable, X* is a n × k matrix of unobserved (latent) values on the k independent variables, ß is a k × 1 vector of unknown coefficients, and u is a n × 1 vector of random disturbances. The matrix of observed values on X* is
$$X = {X^*} + V,$$
where V is the n × k matrix of measurement errors. If some variables are measured without error, the appropriate columns of V are zero vectors. In the conventional case the errors are uncorrelated in the limit with the latent values X* and the disturbances u; and the errors have zero means, constant variances, and zero autocorrelation. In observed variables the model becomes
$$y = X\beta + (u - V\beta ).$$

Keywords

Covariance Income Autocorrelation Defend 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Aigner, D.J. 1974. An appropriate econometric framework for estimating a labor-supply function from the SEO file. International Economic Review 15(1) February, 59–68.Google Scholar
  2. Aigner, D.J., Hsiao, C., Kapteyn, A. and Wansbeek, T. 1984. Latent variable models in econometrics. In Handbook of Econometrics, ed. Z. Griliches and M.D. Intriligator. Amsterdam: Elsevier Science, ch. 23.Google Scholar
  3. Attfield, C.L.G. 1980. Testing the assumptions of the permanent-income model. Journal of the American Statistical Association 75, March, 32–8.Google Scholar
  4. Bentham, J. 1789. An Introduction to the Principles of Morals and Legislation. London: Clarendon Press, 1907; New York: Hafner Publishing Company, 1948.Google Scholar
  5. Chamberlain, G. and Griliches, Z. 1975. Unobservables with a variance-components structure: ability, schooling, and the economic success of brothers. International Economic Review 16(2), June, 422–49.Google Scholar
  6. Friedman, M. 1957. A Theory of the Consumption Function. Princeton: Princeton University Press.Google Scholar
  7. Frisch, R. 1934. Statistical Confluence Analysis by Means of Complete Regression Systems. Oslo: University Institute of Economics.Google Scholar
  8. Garber, S. and Klepper, S. 1980. Administered pricing, or competition coupled with errors of measurement. International Economic Review 21(2), June, 413–35.Google Scholar
  9. Geary, R.C. 1942. Inherent relationships between random variables. Proceedings of the Royal Irish Academy 47, 63–76.Google Scholar
  10. Geraci, V.J. 1974. Simultaneous Equation Models with Measurement Error. PhD dissertation. New York: Garland, 1982.Google Scholar
  11. Geraci, V.J. and Prewo, W. 1977. Bilateral trade and transport costs. Review of Economics and Statistics 59(1), February, 67–74.Google Scholar
  12. Geweke, J.F. 1977. The dynamic factor analysis of economic time-series models. In Latent Variables in Socioeconomic Models, ed. D.J. Aigner and A.S. Goldberger, Amsterdam: North-Holland, ch. 19.Google Scholar
  13. Geweke, J.F. and Singleton, K.J. 1981. Latent variable models for time series: a frequency domain approach with an application to the permanent income hypothesis. Journal of Econometrics 17(3), December, 287–304.Google Scholar
  14. Goldberger, A.S. 1971. Econometrics and psychometrics. Psychometrika 36, June, 83–107.Google Scholar
  15. Goldberger, A.S. 1972a. Maximum-likelihood estimation of regressions containing unobservable independent variables. International Economic Review 13(1), February, 1–15.Google Scholar
  16. Goldberger, A.S. 1972b. Structural equation methods in the social sciences. Econometrica 40(6), November, 979–1001.CrossRefGoogle Scholar
  17. Griliches, Z. 1974. Errors in variables and other unobservables. Econometrica 42(6), November, 971–98.CrossRefGoogle Scholar
  18. Griliches, Z. and Mason, W.M. 1972. Education, income and ability. Journal of Political Economy 80(3), Pt II, May-June, 74–103.Google Scholar
  19. Hausman, J. 1977. Errors in variables in simultaneous equation models. Journal of Econometrics 5(3), May, 389–401.CrossRefGoogle Scholar
  20. Hsiao, C. 1976. Identification and estimation of simultaneous equation models with measurement error. International Economic Review 17(2), June, 319–39.CrossRefGoogle Scholar
  21. Hsiao, C. 1977. Identification of a linear dynamic simultaneous error-shock model. International Economic Review 18(1), February, 181–94.CrossRefGoogle Scholar
  22. Hsiao, C. and Robinson, P.M. 1978. Efficient estimation of a dynamic error-shock model. International Economic Review 19(2), June, 467–79.Google Scholar
  23. Hurwicz, L. and Anderson, T.W. 1946. Statistical models with disturbances in equations and/or disturbances in variables. Unpublished memoranda. Chicago: Cowles Commission.Google Scholar
  24. Jöreskog, K.G. 1970. A general method for the analysis of covariance structures. Biometrika 57(2), August, 239–51.CrossRefGoogle Scholar
  25. Jöreskog, K.G. and Goldberger, A.S. 1975. Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of the American Statistical Association 70, Pt I, September, 631–9.Google Scholar
  26. Kadane, J.B., McGuire, T.W., Sanday, P.R. and Stuelin, P. 1977. Estimation of environmental effects on the pattern of I.Q. scores over time. In Latent Variables in Socioeconomic Models, ed. D.J. Aigner and A.S. Goldberger, Amsterdam: North-Holland, ch. 17.Google Scholar
  27. Koopmans, T.C. 1937. Linear Regression Analysis of Economic Time Series. Haarlem: De Erven F. Bohn N. V.Google Scholar
  28. Koopmans, T.C. 1979. Economics among the sciences. American Economic Review 69(1), March, 1–13.Google Scholar
  29. Lahiri, K. 1977. A joint study of expectations formation and the shifting Phillips curve. Journal of Monetary Economics 3(3), July, 347–57.CrossRefGoogle Scholar
  30. Leontief, W. 1971. Theoretical assumptions and nonobserved facts. American Economic Review 61(1), March, 1–7.Google Scholar
  31. Liviatan, N. 1961. Errors in variables and Engel curve analysis. Econometrica 29, July, 336–62.CrossRefGoogle Scholar
  32. Madansky, A. 1959. The fitting of straight lines when both variables are subject to error. Journal of the American Statistical Association 54, March, 173–205.CrossRefGoogle Scholar
  33. Maravall, A. and Aigner, D.J. 1977. Identification of the dynamic shock-error model. In Latent Variable Models in Socioeconomic Models, ed. D.J. Aigner and A.S. Goldberger, Amsterdam: North-Holland, ch. 18.Google Scholar
  34. Morgenstern, 0. 1950. On the Accuracy of Economic Observations. 2nd edn, Princeton: Princeton University Press, 1963.Google Scholar
  35. Pareto, V. 1927. Manual of Political Economy. New York: Augustus M. Kelley, 1971.Google Scholar
  36. Reiersl, O. 1950. Identifiability of a linear relation between variables which are subject to error. Econometrica 18, October, 375–89.CrossRefGoogle Scholar
  37. Robins, P.K. and West, R.W. 1977. Measurement errors in the estimation of home value. Journal of the American Statistical Association 73, June, 290–94.CrossRefGoogle Scholar
  38. Robinson, P.M. and Ferrara, M.C. 1977. The estimation of a model for an unobservable variable with endogenous causes. In Latent Variable Models in Socioeconomic Models, ed. D.J. Aigner and A.S. Goldberger, Amsterdam: North-Holland, ch. 9.Google Scholar
  39. Sargan, J.D. 1958. The estimation of economic relationships using instrumental variables. Econometrica 26, July, 393–415.CrossRefGoogle Scholar
  40. Singleton, K.J. 1977. The cyclical behavior of the term structure of interest rates. Unpublished PhD dissertation, Madison: University of Wisconsin.Google Scholar
  41. Stapleton, D. 1984. Errors-in-variables in demand systems. Journal of Econometrics 26(3), December, 255–70.CrossRefGoogle Scholar
  42. Zellner, A. 1970. Estimation of regression relationships containing unobservable independent variables. International Economic Review 11, October, 441–54.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Limited 1990

Authors and Affiliations

  • Vincent J. Geraci

There are no affiliations available

Personalised recommendations