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2004 exam and marking scheme solution(EC220).pdf

2004 exam and marking scheme solution(EC220).pdf - Summer...

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Summer 2004 examination EC220 Introduction to Econometrics Instructions to candidates Time allowed: 3 hours + 15 minutes reading time This paper contains nine questions. Answer four questions. All questions will be given equal weight (25%). You are supplied with: Graph paper Statistical tables Logarithm tables (available on request). You may also use: Electronic calculator (as prescribed in the examination regulations) © LSE 2004/EC220 Page 1 of 10

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1. (a) (i) [2 marks] Explain what is meant by a consistent estimator. (ii) [4 marks] Is it true that an unbiased estimator should always be preferred to a biased estimator? (b) A variable Y is determined by a variable X , the relationship being Y = β 1 + β 2 X + u where u is a disturbance term that satisfies the Gauss–Markov conditions. The values of X are drawn randomly from a population with variance . A researcher makes a mistake and regresses X on Y , fitting the equation 2 X σ Y d d X 2 1 ˆ + = where ) ( Var ) , ( Cov 2 Y Y X d = . When he realizes his mistake, he points out that the original relationship could be rewritten u Y X 2 2 2 1 1 1 β β β β + = and hence d 2 will be an estimator of 2 1 β . From this he could obtain an estimate of β 2 . (i) [2 marks] Explain why it is not possible to derive a closed form expression for the expected value of d 2 for a finite sample. (ii) [5 marks] Demonstrate that d 2 is an inconsistent estimator of 2 1 β and determine the direction of the large-sample bias, if this is possible. (iii) [5 marks] Suppose that there exists a third variable Z that is correlated with Y but independent of u . Demonstrate that if the researcher had regressed X on Y using Z as an instrument for Y , the slope coefficient would have been a consistent estimator of IV 2 d 2 1 β . (iv) [4 marks] Explain, with reference to the Gauss–Markov conditions, why d 2 yielded an inconsistent estimate of 2 1 β while yielded a consistent one. IV 2 d (v) [3 marks] At a seminar, someone suggests that X would be a valid instrument, and indeed the best possible instrument. Is this correct? © LSE 2004/EC220 Page 2 of 10