Criticism
Although Hall's proof, is extremely short, just nine lines, Hall's corollary 4, can be found in Flavin. Wu has shown that changes in consumption being zero is the result of an error. Wu's proof is shown below applying the same definitions and techniques found in Sargent.
A consumer maximizes
- subject to
- , where, under a stochastic process, is
- where is consumption, is non-human assets, is labor income, is gross rate of return (all at the beginning of period). is expectation, is time.
Under the "Euler equation approach," optimal consumption for period t is given by
- , where, is the lag operator
Repeating Euler optimization, one should find that consumption, should be given by
- . . .
Assuming ,
Since can be expanded as
and by definition of lag operator
implies
thus for any n
then
and for n = 1
Read more about this topic: Consumption Smoothing
Famous quotes containing the word criticism:
“I, with other Americans, have perhaps unduly resented the stream of criticism of American life ... more particularly have I resented the sneers at Main Street. For I have known that in the cottages that lay behind the street rested the strength of our national character.”
—Herbert Hoover (1874–1964)
“I hold with the old-fashioned criticism that Browning is not really a poet, that he has all the gifts but the one needful and the pearls without the string; rather one should say raw nuggets and rough diamonds.”
—Gerard Manley Hopkins (1844–1889)
“A friend of mine spoke of books that are dedicated like this: “To my wife, by whose helpful criticism ...” and so on. He said the dedication should really read: “To my wife. If it had not been for her continual criticism and persistent nagging doubt as to my ability, this book would have appeared in Harper’s instead of The Hardware Age.””
—Brenda Ueland (1891–1985)