Consumption Smoothing - Flavin's Mispecification

Flavin's Mispecification

Flavin stated that

Flavin assumed that at period t+1, one still has the same number of incomes than at period t, i.e., sum of incomes from zero to infinity, instead of 1 to infinity. In fact, from one period to another, the number of income has to decline from n (where n tends to infinite) to n-1.

and found out that

and reached the Hall's conclusion that if the "expectations of future income are rational, the expectation of next period's revision in expectation,, is zero. Thus ."

To see Flavin's mispecification, lets assume the case that and that the is then

, where n tends to infinite and if one were to specify for that the sum varies from 1 to infinite, instead of 0 to infinite,

,

then the difference of consumption from one period to another is not zero but,