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Economics 140A Spring 2011 Professor Startz Sketched Out Sample Midterm Answers Note that not all the details are shown here. The sketches here are just to point you in the right direction. 1. a. Both are unbiased estimators of the true , so there’s no reason to expect one to be higher than the other. b. The variance formula is ± ² ³´µ ² . In the second case the error variance has gone up by a factor of ² , so the variance of the second estimator is higher by a factor of 4. c. The probability of rejecting a true null is always the size of the test, say 5 percent. That’s how the test is set up. So the probability is the same for both regressions. 2. a. The 5% critical value is smaller than the 1% critical value. So if the test statistic lands in between the two you reject the former but not the latter. If the test statistic is greater than the 1% critical value you reject both. b.

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