Wednesday, August 8, 2012

Wallace 1981 AER Puzzle

I'm currently putting whatever spare time I can find into Neil Wallace's 1981 AER. I'm trying to understand every equation, term, and sentence, separately and in combination, completely, and with the important intuitions to the real world. Not an easy project, especially since this is not one of my areas, but I really wanted to see if there was anything to the amazing claims you hear justified with this paper [1]. So far it's gone surprisingly well. I've by and large decoded it – and this paper is amazingly terse, with little or no derivation or explanation.

What I'd like to look into, when I'm finished going through the paper, is expanding on it by adding an error term, Eh, to the true state return vector, and/or state probability vector, to model heterogeneity of investor beliefs. That's something that obviously exists in large measure in the real world. I think if I did this I could prove that the irrelevance proposition no longer holds, and may be able to get some interesting results as to how and why. Currently in the model all investors are identical clones; same exact beliefs, utility functions, age, and perfect information, perfect foresight, perfect optimization analysis.

But first, my puzzle, which I find really curious:

For the example in section IIe, the economy has no ability to produce, in expectation, other than its annual endowment of Y. The gross return vector has a geometric average of 1. So why is the expected lifetime consumption in his purported equilibrium greater than the endowment – and for all t? Each individual h, and this is true of every generation, only gets a lifetime endowment of y, yet his expected lifetime consumption in Wallace's claimed equilibrium is y/2 + .5(3y/8) + .5(3y/4) = 8.5/8y?! And there's no way for individual h, or his fellow identical clones, or the government, or anyone else, to invest or produce with a positive expected return? How can you have an equilibrium where every individual forever has an expected consumption of 8.5/8y, but expected production and endowment of only y?

[1] "No, in a liquidity trap, if the Fed purchases gold, it does not change the price of gold, just as it will not change the prices of Treasury bonds if it purchases them." – Stephen Williamson

"The Fed can buy all the government debt it wants right now, and that will be irrelevant, for inflation or anything else." – Stephen Williamson

"If it were up to me, I would have given Wallace the [Nobel] prize a long time ago, and I think Sargent would say the same. However, not everyone in the profession is aware of Wallace's contributions, and people who are aware don't necessarily get as excited about them as I do." – Stephen Williamson

"...the influence of Wallace [1981 AER] neutrality thinking on the Fed is clear from the emphasis the Fed has put on telling the world what it is going to do with interest rates in the future...I have a series of other posts also discussing Wallace neutrality. In fact, essentially all of my posts listed under Monetary Policy in the June+ 2012 Table of Contents are about Wallace neutrality." – Miles Kimball