Question: Suppose you estimate the consumption function Y i = 1 + 2 X i + u 1i and the savings function Z i

Suppose you estimate the consumption function

Yi = α1 + α2Xi + u1i

and the savings function

Zi = β1 + β2Xi + 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?

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