1. Explain intuitively why this should be so.
EXERCISE 1.9
1.9 A researcher has international cross-section data on aggregate wages, W, aggregate profits, P, and aggregate income, Y, for a sample of n countries. By definition,
Y = W + P
The regressions
are fitted using OLS regression analysis. Show that the regression coefficients will automatically satisfy the follow-ing equations:
a2 + b2 = 1
a1 + b1 = 0
Explain intuitively why this should be so. 1

2. EXERCISE 1.9
The slope coefficients are given by the standard expressions. 2

3. EXERCISE 1.9
The expressions have the same denominator and a common factor in the numerator. This allows one to combine the numerators as shown. 3

4. EXERCISE 1.9
The sum of Wi and Pi is Yi, by definition. The same is true of their sample means. 4

5. EXERCISE 1.9
Since the numerator is just an expansion of the denominator, the ratio is equal to 1. 5

6. EXERCISE 1.9
The intercepts are given by the standard expressions. 6

7. EXERCISE 1.9
The order of the terms has been changed. 7

8. EXERCISE 1.9
The first two terms are equal to the mean value of Y. The last two are equal to minus the mean value of Y. Hence a1 + b1 is equal to 0. 8

9. Copyright Christopher Dougherty 1999–2006
Copyright Christopher Dougherty 1999– This slideshow may be freely copied for personal use.