This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
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...
View Full Document
This note was uploaded on 09/04/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08