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Examine the models you get along with their R^{2}. Which of the models makes the best intuitive sense? and why?
[Hint: It seems intuitively reasonable that rapid increases in auto ownership rates would depend on increases in income, rather than income itself. The high R^{2} for model in part i is possible due to the fact that DAO is, more or less, increasing over t, and GNP is monotonically increasing.]
The data set gives information on capital, labor and value added for each of three economic sectors: Food and kindred products (20), electrical and electronic machinery, equipment and supplies (36) and transportation equipment (37). For each sector:
Consider the model V_{t }=αK_{t}^{β1}L_{t}^{β2}ε_{t }, where the subscript t indicates year, V_{t }is value added, K_{t} is capital, L_{t} is labor, and ε_{t} is an error term with E(log(ε_{t}))=0 and var(log(ε_{t})) a constant. Assuming that the errors are independent, and taking logs of both sides of the above model, estimate β_{1} and β_{2}_{ }.
The model given in part i above is said to be of the Cobb-Douglas form. It is easier to interpret if β_{1 }+ β_{2} =1. Estimate β_{1} and β_{2}_{ } under this constraint.
Sometimes the model V_{t }=αγ^{t}K_{t}^{β1}L_{t}^{β2}ε_{t} is considered, where γ^{t} is assumed to account for technological development. Estimate β_{1} and β_{2}_{ } for this model.
Estimate β_{1} and β_{2}_{ } in the model in part iii, under the constraint β_{1 }+ β_{2} =1.
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