SUMMER TERM 2019 ECON0019: QUANTITATIVE ECONOMICS AND ECONOMETRICS TIME ALLOWANCE: 3 hours Answer ALL TWO questions from Part A and answer ONE question from Part B. Questions in Part A carry 60 per cent of the total mark and questions in Part B carry 40 per cent of the total. Tables for the normal and F-distribution are at the end of the examination paper. In cases where a student answers more questions than requested by the examination rubric, the policy of the Economics Department is that the student’s first set of answers up to the required number will be the ones that count (not the best answers). All remaining answers will be ignored. PART A Answer all questions from this section. A.1 You wish to quantify the e↵ect of cannabis consumption on student performance. You carry out a survey asking a random sample of your fellow students about their average mark after two years of studies and number of times they have consumed cannabis in the last 30 days. Let AMi and SMi be student i’s self-reported average mark and number of times used, i = 1, ..., n, where n is the number of students in the sample. (a) Suppose that AM is observed with measurement error while SM is observed without. That is, AMi = AM⇤i +vi, where AM⇤i is the actual average mark and vi is the measurement error. The measurement error is assumed to be fully independent of (SMi, ui) with E [vi] = 0, i = 1, ..., n. Suppose that the actual average mark satisfies AM⇤i = 0 + 1SMi + ui, (1) and that SLR.1-SLR.5 are satisfied in the above model. Derive the (conditional on SM1, ..., SMn) mean and variance of the OLS estimator of 1 obtained by regressing AM on SM . ANSWER: With u˜ = u v, AMi = 0 + 1SMi + u˜i. (2) SLR.1-SLR.5 combined with E [vi] = 0 and (SMi, ui) ? vi yield E [u˜i|SMi] = 0 and Var (u˜i|SMi) = 2u + 2v . Thus, (2) also satisfies SLR.1-SLR.5 and we obtain E h