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Exercise 4 - Economics 241B Exercise 4 1 Asymptotic...

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Economics 241B Exercise 4 1. Asymptotic Normality to Consistency You undertake a research project on carbon sequestration with a colleague from the geology department. He defers to you as the expert on statistics. a. In one discussion, you note that the estimator you are using is consistent and asymptotically normal. He then asks the natural question, "What are the advantages of using an estimator that is consistent and asymptotically normal?" Please respond. b. Several weeks later, the geologist proposes an estimator that is common in his °eld, but with which you are not familiar. He proudly notes that the estimator, ^ ° n , is asymptotically normal (a concept he learned from you) and displays an equation he copied down p n ° ^ ° n ° ° 0 ± d ! N ² 0 ; ± 2 ³ : He is puzzled, however, by the fact that he could not °nd out if the estimator is consistent for the population value ° 0 . Please show why the asymptotic normality result does, or does not, establish consistency.
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