# Assignment 2

1. The data set gives data on per capita output in Chinese yuan, number (SI) of workers in the factory, land area (SP) of the factory in square meters per worker, and investment (I) in yuans perworker for 17 factories in Shanghai.
1. Using least squares, fit a model expressing output in terms of the other variables.
2. In addition to the variables in part i, add SI2 and SP×I and obtain another model.
3. Using the model of part ii, find the values of SP, SI, and I that maximize per capita output.

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2. The data set, obtained from KRIHS (1985), gives data on the number car per person (AO), per capita GNP (GNP), average car price (CP), and gasoline price after taxes (OP) in South Korea from 1974 to 1983. GNP and car prices are in 1000 Korean wons, while gasoline prices are in wons per liter. Let D before a variable name denote first differences, e.g., DAOt=AOt+1-AOt where AOt is the value of AO in the tth year. Use DAO as the dependent variable and estimate parameters of models which have:
1. GNP, CP and OP as the independent variables,
2. DGNP, DCP and DOP as the independent variables,
3. DGNP DCP and OP as independent variables, and
4. DGNP, CP and OP as independent variables.

Examine the models you get along with their R2. 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 R2 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.]

1. 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:

1. Consider the model V=αKtβ1Ltβ2εt , where the subscript t indicates year, Vis value added, Kt  is capital, Lt  is labor, and εt  is an error term with E(log(εt))=0 and var(log(εt)) a constant. Assuming that the errors are independent, and taking logs of both sides of the above model, estimate β1  and β2 .

2. The model given in part i above is said to be of the Cobb-Douglas form. It is easier to interpret if β1 + β2 =1. Estimate β1 and β2  under this constraint.

3. Sometimes the model  V=αγtKtβ1Ltβ2εt  is considered, where γt  is assumed to account for technological development. Estimate β1 and β2  for this model.

4. Estimate  β1 and β2  in the model in part iii, under the constraint  β1 + β2 =1.

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