Consider the simple Keynesian model of income determination:
Consumption function: Ct = p0 + p1Yt + ut 0 < p1 < 1 (18.2.3)
where C = consumption expenditure
Y = income
I = investment (assumed exogenous) S = savings t = time u = stochastic disturbance term p0 and p = parameters
The parameter is known as the marginal propensity to consume (MPC) (the amount of extra consumption expenditure resulting from an extra dollar of income). From economic theory, is expected to lie between 0 and 1. Equation (18.2.3) is the (stochastic) consumption function; and (18.2.4) is the national income identity, signifying that total income is equal to total consumption expenditure plus total investment expenditure, it being understood that total investment expenditure is equal to total savings. Diagrammatically, we have Figure 18.2.
From the postulated consumption function and Figure 18.2 it is clear that C and Yare interdependent and that Yt in (18.2.3) is not expected to be independent of the disturbance term because when ut shifts (because of a variety of factors subsumed in the error term), then the consumption function also shifts, which, in turn, affects Yt. Therefore, once again the classical least-squares method is inapplicable to (18.2.3). If applied, the estimators thus obtained will be inconsistent, as we shall show later.
CHAPTER EIGHTEEN: SIMULTANEOUS-EQUATION MODELS 721
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