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.
KeywordsCharacteristic Vector Ridge Regression Characteristic Root Principal Component Regression Multicollinearity Problem
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