10.26. Klein and Goldberger attempted to fit the following regression model to the U.S. economy:
Yi = β1 + β2 X2i + β3 X3i + β4 X4i + ui
where Y = consumption, X2 = wage income, X3 = nonwage, nonfarm income, and X4 = farm income. But since X2, X3, and X4 are expected to be highly collinear, they obtained estimates of β3 and β4 from cross- sectional analysis as follows: β3 = 0.75β2 and β4 = 0.625β2 . Using these estimates, they reformulated their consumption function as follows:
Yi = β1 + β2 ( X2i + 0.75 X3i + 0.625 X4i ) + ui = β1 + β2 Zi + ui
where Zi = X2i + 0.75 X3i + 0.625 X4i .
a. Fit the modified model to the data in Table 10.11 and obtain esti- mates of β1 to β4 .
b. How would you interpret the variable Z?
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