exam07-LSE - Summer 2007 examination EC220 Introduction to...

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Unformatted text preview: Summer 2007 examination EC220 Introduction to Econometrics Suitable for all candidates Instructions to candidates Time allowed: 3 hours + 15 minutes reading time This paper contains NINE questions. Answer any FOUR questions. All questions will be given equal weight (25%). You are supplied with: Graph paper Statistical tables Logarithm tables (available on request). Calculators are not allowed in this examination. © LSE 2007/EC220 Page 1 of 12 1. A researcher has data for 50 countries on N , the average number of newspapers purchased per adult in one year, and G , GDP per capita, measured in UK pounds, and fits the following regression (standard errors in parentheses; RSS = residual sum of squares; F is the F statistic for the equation) = 25.0 + 0.020 G R N ˆ 2 = 0.06, RSS = 4,000.0 (10.0) (0.010) F = 4.00 (a) Explain, with mathematical proofs, how the following components of the regression output would have differed if G had been measured in US dollars instead of UK pounds. You may assume, for convenience, that one UK pound = 2 US dollars. (i) [3 marks] the coefficient of G (ii) [3 marks] the intercept (iii) [3 marks] RSS (iv) [3 marks] the standard error of the coefficient of G (v) [2 marks] R 2 (vi) [2 marks] F (b) The researcher, still using UK pounds, realizes that she has underestimated G in every country by 100 pounds. She now regresses N on G *, where G * = G + 100. Explain, with mathematical proofs, how the following components of the output will change: (i) [2 marks] the coefficient of G (ii) [2 marks] the intercept (iii) [2 marks] RSS (iv) [1 mark] the standard error of the coefficient of G (v) [1 mark] R 2 (vi) [1 mark] F © LSE 2007/EC220 Page 2 of 12 2. (a) [8 marks] A researcher investigating the relationship between the age at death, AGE , and the sex of an individual, has sample data for 100 individuals who died in 2006. He decides to define a dummy variable D equal to 1 for females and 0 for males and to fit the line AGE = β 1 + β 2 D + u The scatter diagram is shown in the figure. The vertical height of the points A and B give the means of AGE for males and females respectively. Show from first principles that the ordinary least squares (OLS) regression line must pass through the points A and B. Hence obtain estimates of β 1 and β 2 and briefly provide an interpretation of them. Age A B 50 55 60 65 70 75 80 85 1 Female (b) A researcher has data on hourly earnings in dollars, EARNINGS , years of schooling (highest grade completed), S , and sector of employment, GOV , for 1,355 male respondents in the US National Longitudinal Survey of Youth for 2002. GOV is defined as a dummy variable equal to 0 if the respondent was working in the private sector and 1 if the respondent was working in the government sector. 91 percent of the private sector workers and 95 percent of the government workers had at least 12 years of schooling. The mean value of S was 13.5 for the private sector and 14.6 for the government sector. The researcher regresses the government sector....
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exam07-LSE - Summer 2007 examination EC220 Introduction to...

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