In the simple macroeconomic model
C = β1 + β2Y + u
Y = C + I,
described in Exercise 10.1, demonstrate that OLS would yield inconsistent results if used to fit the consumption function, and investigate the direction of the bias in the slope coefficient.
Exercise 10.1
A simple macroeconomic model consists of a consumption function and an income identity:
C = β1 + β2Y + u
Y = C + I,
where C is aggregate consumption, I is aggregate investment, Y is aggregate income, and u is a disturbance term. On the assumption that I is exogenous, derive the reduced form equations for C and Y.