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Consider the following two-variable linear regression model: yi = a + ßxi +  (1) where E(i) = 0 ? i E( 2 i ) = s 2 ? i E(ij ) = 0 ? i 6= j Consider its OLS estimator ˆa. We derived in one of the...

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Consider the following two-variable linear regression model: yi = a + ßxi +  (1) where E(i) = 0 ? i E( 2 i ) = s 2 ? i E(ij ) = 0 ? i 6= j Consider its OLS estimator ˆa. We derived in one of the classes that it could be expressed as a linear function of yi ’s: aˆ = Xn i=1 wiyi ; where wi = 1 n - (xi - x)x Pn 1 (xi - x XXXXXXXXXXDefine an arbitrary linear estimator of a: a˜ * = Xn i=1 aiyi (3) where ai ’s are non-stochastic weights. We also saw in the class that, if ˜a * is an unbiased estimator, the variance of ˜a * was: V (˜a * ) = E[(˜a * - a) 2 ] = s 2Xn i=1 a 2 i (4) Demonstrate that minimising (4) subject to conditions for unbiasedness gives the OLS weights of (2) for ai . 2. The data file “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 1 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 of 1,000 words. Print out any estimation outputs or test result you refer to in your report and submit them. 2
005_wq6o8jk-rzyetibh.pdf 005_ia6o8jk-sq4tcwae.gdt
Answered Same Day Dec 21, 2021

Solution

David answered on Dec 21 2021
127 Votes
1. Consider the a
itrary linear estimator of a
*
1
n
i i
i
a ya
where ai's are non-stochastic weights.
If *a is an unbiased estimator of a , then we have
*
1 1
( ) ( ) ( )
n n
i i i i
i i
E a E y a xa a b
which implies that we should have
1 1
1, 0
n n
i i i
i i
a a x
The variance of *a is given by
* 2 2
1
( )
n
i
i
V aa s
We have to find the value of ia so that...
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