tag:blogger.com,1999:blog-6837159629100463303.post4779780964506380282..comments2021-07-22T00:29:53.205-07:00Comments on Information Transfer Economics: The Economy at the End of the Universe, part IIJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6837159629100463303.post-63019677652670499002016-08-10T19:13:31.731-07:002016-08-10T19:13:31.731-07:001. I agree that the neo-Fisher model critically de...1. I agree that the neo-Fisher model critically depends on what happens "at infinity". As you correctly state, the big difference between the neo-Fisher view and the more mainstream view comes from future times T where T ≫ τ > t (where t is now and τ is the discounting time).<br /><br />In a sense, the neo-Fisher view is that M(T) for τ < T < ∞ matters and the more traditional view is that it doesn't. However, I'd argue that the neo-Fisher view is a kind of "hyperrational expectations" or "<b><i>hypo</i></b>bolic discounting" and that the traditional view essentially says that people could expect any value for M(T) for τ < T < ∞. Monetary policy could be anything beyond the horizon.<br /><br />But if you have rational expectations up to some horizon and then ignore what's beyond it, as you move that horizon out the traditional view deforms into the neo-Fisher view (depending on the rate of discounting).<br /><br />In any case, the question is what effect the boundary condition at infinity has on the present. Neo-Fisher says it is important, the contra argument (which I am more inclined to believe) says it isn't. But it's hard to argue the contra argument is as devoted to rational expectations as the neo-Fisher argument -- in fact, I think the neo-Fisher argument is the <b>correct</b> application of rational expectations for all times T, even those where τ < T < ∞.<br /> <br />2. It's funny you should mention that because that was what was taking me so long to get right (in my head at least). The unanticipated version can be effectively modeled by a perfect foresight with near-zero horizon up until the monetary policy change (monetary policy e.g. one second ahead is anticipated) at which point the anticipated solution kicks in.<br /><br />This turns out to have limited effect on the solution shown above, just making the initial transition a bit sharper and deeper -- but not changing the main conclusion that the path gets farther away. So I left it out. You can think of it as a weighted average of the rational expectations solution and an adaptive expectations solution. Agents would jump immediately to the perfect foresight solution in the way Robinson Crusoe immediately jumps to the optimal saddle path. This jump might take some time, which leads to a bit of dynamics at the leading edge, but the trailing edge looks the same.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-231836996334861272016-08-10T04:08:21.551-07:002016-08-10T04:08:21.551-07:00Thanks Jason.
I'm (as usual) not following al...Thanks Jason.<br /><br />I'm (as usual) not following all of this. Two points:<br /><br />1. "Note that times T≫τ>t don't contribute much to the integral."<br /><br />Yes (if I understand it correctly). That was the point I was making in my post. What people expect to happen in the very distant future doesn't matter much for what happens today, in the Cagan model. And in the limit, as "very distant" goes to infinity, it doesn't matter at all. That is very different to the Neo-Fisherian model.<br /><br />2. What you are graphing is an *anticipated* change to money growth at time 0. What I was talking about in the post was an *unanticipated* change in money growth at time 0. (people think that money growth will always be 0%, then at time 0 the central bank makes a surprise announcement, and says that from now on it will grow at 1% instead).Nick Rowehttps://www.blogger.com/profile/04982579343160429422noreply@blogger.com