By Patrick Kent Watson, Sonja Sabita Teelucksingh
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Additional info for A Practical Introduction to Econometric Methods Classical and Modern
But the true situation may be, not that an explanatory variable has no effect, but rather that the sample data set has not allowed us to pick up the actual effect. Multicollinearity therefore is indicative of a problem in the data being used in the regression, and does not necessarily negate the underlying economic theory. All that is occurring is that the data are rendering us ill equipped to either validate or invalidate the theory. Finally, coefficient estimates tend to become, in the presence of multicollinearity, very sensitive to particular sample data sets.
Consider, for instance, the import function. We may have an idea about the value of the marginal propensity to import that may be in stark contrast to the value obtained from application of the regression. If this happens, we simply cannot abandon our own feelings on the matter on the pretext that “the computer says so”. Clearly, we cannot ignore what the results are telling us but neither must we accept them unquestioningly. As we advance in our study of econometrics, we will see that there are many occasions and situations (due to data inadequacies, for instance) that will further justify the need for our personal interventions.
As a result, the addition of a few or 2 Vectors xi and xj are said to be orthogonal if x′i xj = 0, i ≠ j. 42 A Practical Introduction to Econometric Methods: Classical and Modern more observations may produce dramatic shifts in some of the coefficient values, sometimes to the extent that the signs of the estimates may actually change. Let us consider for illustrative purposes, the following simple case: y = β1x1 + β 2 x 2 + u where the x vectors contain variables measured from the mean – for example, the first element of x1 is (x11 − x1 ) , and a typical element x1 is (x1t − x1 ), where x1 = Σx1t n .
A Practical Introduction to Econometric Methods Classical and Modern by Patrick Kent Watson, Sonja Sabita Teelucksingh
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