All questions and materials are attached (the second question requires Gretl software) Document Preview: EC2020 Multiple Regression Analysis: Easter Project This is the project for this module that counts 20%. Each question carries 10%. The deadline for submission is 5:00pm, Monday 14th of May 2012. You can either hand it directly to me or submit it to the Economics reception in Astley Clarke. Do not email it to me, it will not be accepted. No extension will be given, and late submissions will not be accepted. It does not have to be typed as long as it is neatly written. 1. Consider the following two-variable linear regression model: yi = + xi + (1) where E(i) = 0 8 i E(2i) = 2 8 i E(ij) = 0 8 i 6= j Consider its OLS estimator ^. We derived in one of the classes that it could be expressed as a linear function of yis:^=Xn i=1 wiyi; where wi = 1n ?? P(xi ?? x)x n1 (xi ?? x)2 (2) Dene an arbitrary linear estimator of : ~= Xn i=1 aiyi (3) where ais are non-stochastic weights. We also saw in the class that, if ~is an unbiased estimator, the variance of ~was: V (~) = E[(~?? )2] = 2 Xn i=1 a2i(4) Demonstrate that minimising (4) subject to conditions for unbiasedness gives the OLS weights of (2) for ai. 2. The data le EC2020 Project.gdt (found on our EC2020 web site www.le.ac.uk/economics/teach/ec2020/ec2020.html) contains data on the following variables from 54 countries around the world, all collected in the year 2007. gdp pc Gross Domestic Product per capita, recorded in U.S. dollars age dep A measure of age dependency. The proportion of working-age population out of the total population ag The percentage share of real GDP occupied by the agricultural sector emp serv The proportion of the working population employed in the service sector 1exp te Expenditure on tertiary education, as a proportion of GDP per capita export Export of goods and services, in billions of U.S. dollars fdi The net inow of foreign direct investment into the country, as a proportion of GDP fuel exp Export of fuel (oil and gas) as a proportion of all exports inv Investment, as measured by gross Attachments: EC2020-Projec.pdf EC2020-Projec.gdt
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