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
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“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)
“Like speaks to like only; labor to labor, philosophy to philosophy, criticism to criticism, poetry to poetry. Literature speaks how much still to the past, how little to the future, how much to the East, how little to the West.”
—Henry David Thoreau (1817–1862)
“To be just, that is to say, to justify its existence, criticism should be partial, passionate and political, that is to say, written from an exclusive point of view, but a point of view that opens up the widest horizons.”
—Charles Baudelaire (1821–1867)