## Abstract

When using the linear statistical model, economists and other social scientists face a variety of problems that are caused by the nonexperimental nature of their disciplines. Several problems of this sort are discussed in this book and include uncertainty about model specification, both the form of the relationship between the variables and which variables should be included in the model (Chapter 18), the nature of the error process (Chapters 9 and 10), structural changes in the process generating the data (Chapters 14 and 15), and the problem discussed in the current chapter, multicollinearity. Multicollinearity is a problem associated with the fact that nonexperimental scientists *observe* the values that both the independent and dependent variables take. This is in marked contrast to an experimental setting in which the values of the independent variables are *set* by the experimenter and the resulting values of only the dependent variable are observed. A regression analysis is, of course, an attempt to explain the variation in the dependent variable by the variation in the explanatory variables. In the experimental setting the researcher can set the values of the explanatory variables so that the values of each variable vary independently of the values of each of the other variables. In such a case the separate effects of each variable can be estimated precisely if sufficient care is taken in designing and executing the experiment. Frequently in nonexperimental situations, some explanatory variables exhibit little variation, or the variation they do exhibit is systematically related to variation in other explanatory variables. While it is usually the second of these cases that is labeled as multicollinearity, we will not distinguish between them as there is really no essential difference.

## Keywords

Characteristic Vector Ridge Regression Characteristic Root Principal Component Regression Multicollinearity Problem## Preview

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## References

- Belsley, D. and Klema, V. (1974). Detecting and assessing the problems caused by multicollinearity: a use of the singular value decomposition. Working Paper No. 66, National Bureau of Economic Research, Cambridge, MA.Google Scholar
- Belsley, D., Kuh, E., and Welsh, R. (1980).
*Regression Diagnostics.*New York: Wiley.CrossRefGoogle Scholar - Casella, G. (1977).
*Minimax Ridge Estimation.*Unpublished Ph.D. Dissertation, Purdue University, Lafayette, IN.Google Scholar - Farrar, D. and Glauber, R. (1967). Multicollinearity in regression analysis: the problem revisited.
*Review of Economics and Statistics*,**49**, 92–107.CrossRefGoogle Scholar - Fomby, T. and Hill, R. (1978). Multicollinearity and the value
*of a priori*information.*Communications in Statistics*, A,**8**, 477–486.Google Scholar - Fomby, T., Hill, R., and Johnson, S. (1978). An optimality property of principal components regression.
*Journal of the American Statistical Association*,**73**, 191–193.CrossRefGoogle Scholar - Gorman, J. W. and Toman, R. J. (1966). Selection of variables for fitting equations to data.
*Technometrics*,**8**, 27–51.CrossRefGoogle Scholar - Greenberg, E. (1975). Minimum variance properties of principal components regression.
*Journal of the American Statistical Association*,**70**, 194–197.CrossRefGoogle Scholar - Haitovsky, T. (1969). Multicollinearity in regression analysis: comment.
*Review of Economics and Statistics*,**51**, 486–489.CrossRefGoogle Scholar - Hill, R., Fomby, T., and Johnson, S. (1977). Component selection norms for principal components regression.
*Communications in Statistics*, A,**6**, 309–333.Google Scholar - Hill, R. C. and Ziemer, R. F. (1982). Small sample performance of the Stein-rule in non-orthogonal designs.
*Economics Letters*,**10**, 285–292.CrossRefGoogle Scholar - Hill, R. C. and Ziemer, R. F. (1984). The risk of general Stein-like estimators in the presence of nulticollinearity,
*Journal of Econometrics*, forthcoming.Google Scholar - Hoerl, A. and Kennard, R. (1970a). Ridge regression: biased estimation of nonorthogonal problems.
*Technometrics*,**12**, 55–67.CrossRefGoogle Scholar - Hoerl, A. and Kennard, R. (1970b). Ridge regression: applications to nonorthogonal problems.
*Technometrics*,**12**, 69–82.CrossRefGoogle Scholar - Johnson, S., Reimer, S., and Rothrock, T. (1973). Principal components and the problem of multicollinearity.
*Metroeconomica*,**25**, 306–317.CrossRefGoogle Scholar - Jeffers, J. M. R. (1967). Two case studies in the application of principal component analysis.
*Applied Statistics*,**16**, 225–236.CrossRefGoogle Scholar - Judge, G., Griffiths, W., Hill, R., and Lee, T. (1980).
*The Theory and Practice of Econometrics.*New York: Wiley.Google Scholar - Kumar, T. (1975). Multicollinearity in regression analysis.
*Review of Economics and Statistics*,**57**, 365–366.CrossRefGoogle Scholar - Longley, J. W. (1967). An appraisal of least squares programs for the electronic computer from the point of view of the user.
*Journal of the American Statistical Association*,**62**, 819–841.CrossRefGoogle Scholar - Mason, R., Gunst, R., and Webster, J. (1975). Regression analysis and problems of multicollinearity.
*Communications in Statistics*, A,**4**, 277–292.Google Scholar - Massey, W. (1965). Principal components regression in exploratory statistical research.
*Journal of the American Statistical Association*,**60**, 234–256.CrossRefGoogle Scholar - O’Hagen, J. and McCabe, B. (1975). Tests for the severity of multicollinearity in regression analysis: a comment.
*Review of Economics and Statistics*,**57**, 368–370.CrossRefGoogle Scholar - Silvey, S. (1969). Multicollinearity and imprecise estimation.
*Journal of the Royal Statistical Society*, B,**31**, 539–552.Google Scholar - Strawderman, W. (1978). Minimax adaptive generalized ridge regression estimators.
*Journal of the American Statistical Association*,**73**, 623–627.CrossRefGoogle Scholar - Theil, H. (1971).
*Principles of Econometrics.*New York: Wiley.Google Scholar - Thisted, R. (1977).
*Ridge Regression, Minimax Estimation and Empirical Bayes Methods.*Unpublished Ph.D. Dissertation, Stanford University, Stanford, CA.Google Scholar - Vinod, H. (1978). A survey of ridge regression and related techniques for improvements over ordinary least squares.
*Review of Economics and Statistics*,**60**, 121–131.CrossRefGoogle Scholar - Vinod, H. and Ullah, A. (1981).
*Recent Advances in Regression Methods.*New York: Marcel Dekker.Google Scholar - Willan, A. and Watts, D. (1978). Meaningful multicollinearity measures.
*Technometrics*,**20**, 407–412.CrossRefGoogle Scholar