ECON 705 Midterm: 2015-705-Fall Econometrics Prelim Exam-v2
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Friday august 7, 2015 time limit: 150 minutes. Instructions: (i) the exam consists of two parts. Two random variables, y , and x, have a joint distribution characterized by the following probability density function (pdf): p(y, x) = cx(x + y), Explain. (iii) (8 points) suppose that (yi, xi) are iid with density given by p(y, x) in (1). An econometrician observes a sample of n observations and runs a regression of the form. Derive the probability limit (as n ) of the ols estimator of . Question 2: statistical inference (16 points) (i) (4 points) suppose you have a test (y ; 0) of a null hypothesis h0 : = 0 with type-i error . Explain how this test can be inverted to obtain a 1 con dence set. (ii) (6 points) consider the location model y n ( , 1). Propose a test for the hypothesis h0 : 0 with size and derive its power against the alternative.
