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# EC2020 Econometrics I: Christmas Project This is the project for this module that counts 20%. Each question carries 10%. The deadline for submission...

Please do for me question 1b asap.
Thanks
EC2020 Econometrics I: Christmas Project This is the project for this module that counts 20%. Each question carries 10%. The deadline for submission is 4:00pm, Thursday 17th of January 2013. 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 model: y i = α + βx i + ± i ; i = 1 , 2 , ··· ,n (1) where x i is ﬁxed in repeated sampling, and the random disturbance term ± i satisﬁes the usual assumptions of E ( ± i ) = 0 V ( ± i ) = σ 2 i E ( ± i ± j ) = 0 i 6 = j (2) Denote by ˆ ± i , ˆ α and ˆ β the OLS estimates of the errors, and the parameters respectively. The regression model of (1) is ﬁtted to the data: ( x 1 ,y 1 ), ··· , ( x n ,y n ), giving least squares estimates ˆ α and ˆ β . Given a new value x n +1 for the explanatory variable, we wish to predict y n +1 . It can be assumed that y n +1 = α + βx n +1 + ± n +1 where ± n +1 satisﬁes the usual assumptions of a white noise so that: E ( ± n +1 ) = 0 V ( ± n +1 ) = σ 2 E ( ± i ± n +1 ) = 0 i = 1 , 2 , ··· ,n (3) The natural predictor for y n +1 is: ˆ y n +1 = ˆ α + ˆ βx n +1 Let the prediction error be denoted by e n +1 . In class exercise 3, we saw that this prediction error could be expressed as: e n +1 = ( α - ˆ α ) + ( β - ˆ β ) x n +1 + ± n +1 (4) and that the mean of the distribution of e n +1 was 0. Answer the following questions. a ) Show that this prediction error can also be expressed as: e n +1 = n X i =1 d i ± i + ± n +1 where d i = - " 1 n + ( x n +1 - x )( x i - x ) n j =1 ( x j - x ) 2 # , with x = 1 n n X i =1 x i (5) b ) Using the result in a ), show that the variance of the prediction error is: V ( e n +1 ) = σ 2 ± 1 + 1 n + ( x n +1 - x ) 2 n i =1 ( x i - x ) 2 ² (6) 1
2. The data ﬁle “EC2020 Project.gdt” 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 exp 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 inﬂow 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 capital formation, in billions of U.S. dollars health Expenditure on health care, as a proportion of GDP female lf Female labour participation rate, measured by the proportion of working women out of all working-age women aged above 15 Conduct an investigation into the determinants of per capita GDP using this data set. Write an intelligent report, maximum 1,000 words. Print out any estimation outputs or test result you refer to in your report and submit them. 2

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