Suppose you estimate the consumption function
Yi = α1 + α2 Xi + u1i
and the savings function
Zi = β1 + β2 Xi + u2i
where Y = consumption, Z = savings, X = income, and X = Y + Z, that is, income is equal to consumption plus savings.
a. What is the relationship, if any, between α2 and β2 ? Show your calculations.
b. Will the residual sum of squares, RSS, be the same for the two models? Explain.
c. Can you compare the R2 terms of the two models? Why or why not?