By Peter Kennedy
6th version and the final version there'll ever be, because the writer handed away.
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Extra info for A Guide to Econometrics (6th Edition)
Since the R2 measure is used as an index of how well an data. See Mosteller et al. ( 1 9 8 1 ). - Chapter 2 • • • estimator"fits" the sample data, the OLS estimator is often called the "best-fitting" estimator. " Because the R2 and OLS criteria are formally identical, objections to the latter apply to the former. " Further, a high R2 is not necessary for "good" estimates; R2 could be low because of a high variance of the disturbance terms, and our estimate of f3 could be "good" on other criteria, such as those discussed in later sections of this chapter.
Mean Square Error Preference for the MSE criterion over the unbi asedness criterion often hinges on the use to which the estimate is put. As an example of this, consider a man betting on horse races. If he is buying "win" tickets, he will want an unbiased estimate of the winning horse, but if he is buy ing "show" tickets it is not important that his horse wins the race (only that his horse finishes among the first three), so he will be willing to use a slightly biased estimator of the winning horse if it has a smaller variance.
Monte Carlo studies (see section 2. 1 0) have shown that in general this supposition is warranted. The message of the discussion above is that when estimators with attractive small sample properties cannot be found, one may wish to choose an estimator on the basis of its large-sample properties. There is an additional reason for interest in asymptotic properties, however, of equal importance. Often the derivation of small-sample prop erties of an estimator is algebraically intractable, whereas derivation of large-sample properties is not.