Assignment-
Consider the following Cobb Douglas production function where Y is maize output, X1 is labour input, and X2 is the capital. Data for estimating this equation is given in the Table below.
Y = β0Xβ11iXβ22ieui
|
Year
|
Output, Y
|
Labor days (millions of days), X2
|
Real capital input (million of NT $), X3
|
|
1958
|
16,607.7
|
275.5
|
17,803.7
|
|
1959
|
17,511.3
|
274.4
|
18,096.8
|
|
1960
|
20,717.2
|
269.7
|
18,271.8
|
|
1961
|
20,932.9
|
267.0
|
19,167.3
|
|
1962
|
20,406.0
|
267.8
|
19,647.6
|
|
1963
|
20,831.6
|
275.0
|
20,803.5
|
|
1964
|
24,806.3
|
283.0
|
22,076.6
|
|
1965
|
26,465.8
|
300.7
|
23,445.2
|
|
1966
|
27,403.0
|
307.5
|
24,939.0
|
|
1967
|
28,628.7
|
303.7
|
26,713.7
|
|
1968
|
29,904.5
|
304.7
|
29,957.8
|
|
1969
|
27,508.2
|
298.6
|
31,585.9
|
|
1970
|
29,035.5
|
295.5
|
33,474.5
|
|
1971
|
29,281.5
|
299.0
|
34,821.8
|
|
1972
|
31,535.8
|
288.1
|
41,794.3
|
1. This model specification cannot be estimated by using OLS in its current form, explain.
2. Derive the model specification that can be estimated by using the ordinary least squares (OLS) technique.
3. From the specification in "2" derive the expressions for obtaining OLS estimators.
4. Use the data above to derive OLS estimators. Note: Use of statistical or econometric software is not allowed. You are encouraged to use excel and submit your excel file together with your assignment.
5. Find the variances of the OLS estimators.
6. Compute and interpret the R-squared, the t-ratios, and the F-statistic.
7. Test for the existence of constant returns to scale.
8. Test the model for multicollinerity by using the variance inflation factor.