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Unformatted text preview: University of California D. Steigerwald Department of Economics Economics 140A Exercise 3 1. Consider the model Y t = X t + U t , t = 1,2,...,n , where X t is the period- t value of an exogenous variable with mean zero, is an unknown parameter, the period- t error U t ~ IN(0, 2 ) with known variance, and . n n X Y Let B be the ordinary least square estimator of . a) Derive the mean, variance, and distribution of B . Determine the smallest interval such that there is a 95 percent probability that B lies in the interval. b) Construct a 95 percent confidence interval for . Why do we use the word confidence? Give an intuitive description of the relation between probability and confidence. c) Consider the following axioms of probability: (i) P(A) for any event A in the sample space, S ; ( i i ) P(S) = 1 . If we interpret S as the parameter space, does the concept of confidence satisfy probability axioms (i) and (ii)? (For example, if is the parameter space, does...
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- Fall '08