Table 7-5, found on the textbook's Web site, gives data on the real gross product, labor input, and real capital input in the Taiwanese manufacturing sector for the years 1958 to 1972. Suppose the theoretically correct production function is of the Cobb-Douglas type, as follows:
In Yt = B1 + B2 In X2t + B3 In X3t + ut
where In = the natural log.
a. Given the data shown in Table 7-5, estimate the Cobb-Douglas production function for Taiwan for the sample period and interpret the results.
b. Suppose capital data were not initially available and therefore someone estimated the following production function:
In Yt = C1 + C2 In X2t + vt
where v = an error term. What kind of specification error is incurred in this case? What are the consequences? Illustrate with the data in Table 7-5.
c. Now pretend that the data on labor input were not available initially and suppose you estimated the following model:
In Yt = C1 + C2 In X3t + wt
where w = an error term. What are the consequences of this type of specification error? Illustrate with the data given in Table 7-5. Consider the following models: