3) Suppose you estimate the consumption function Y = a₁ + ax + u₁ And the savings function Z₁ =B₁ + B₂X+U₂ 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 a, and B,? 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?
3) Suppose you estimate the consumption function Y = a₁ + ax + u₁ And the savings function Z₁ =B₁ + B₂X+U₂ 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 a, and B,? 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?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Suppose you estimate the consumption function

Transcribed Image Text:3) Suppose you estimate the consumption function
Y₁ = a₁ + a₂x₁ + u₁
And the savings function
Z₁ =B₁ + B₂X + U₂
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 a, and B.? 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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