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:
“It is the will of God that we must have critics, and missionaries, and Congressmen, and humorists, and we must bear the burden. Meantime, I seem to have been drifting into criticism myself. But that is nothing. At the worst, criticism is nothing more than a crime, and I am not unused to that.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“Cubism had been an analysis of the object and an attempt to put it before us in its totality; both as analysis and as synthesis, it was a criticism of appearance. Surrealism transmuted the object, and suddenly a canvas became an apparition: a new figuration, a real transfiguration.”
—Octavio Paz (b. 1914)
“The greater the decrease in the social significance of an art form, the sharper the distinction between criticism and enjoyment by the public. The conventional is uncritically enjoyed, and the truly new is criticized with aversion.”
—Walter Benjamin (1892–1940)