tag:blogger.com,1999:blog-6837159629100463303.post6431192573875791580..comments2023-06-18T01:25:08.748-07:00Comments on Information Transfer Economics: Scott Sumner's information equilibrium modelJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-6837159629100463303.post-43202021778651811672015-09-01T15:29:49.309-07:002015-09-01T15:29:49.309-07:00That's fine Tom. Actually, a lot of the earlie...That's fine Tom. Actually, a lot of the earlier posts never got any "peer review" from comments, so it could definitely help clear things up in some cases.<br /><br />The info eq model can't have a permanent one-time increase in the interest rate with a finite RGDP, but in general the effects are somewhat similar under certain conditions (i.e. kappa dependent):<br /><br /><a href="http://informationtransfereconomics.blogspot.com/2014/09/the-liquidity-effect-and.html" rel="nofollow">http://informationtransfereconomics.blogspot.com/2014/09/the-liquidity-effect-and.html</a>Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-11476746372148373042015-08-31T11:53:17.540-07:002015-08-31T11:53:17.540-07:00Jason, sorry for my abundance of stream of conscio...Jason, sorry for my abundance of stream of consciousness comments. Erase any that you like. (I left a few back on some of your April 2013 posts as well, especially the supply and demand post). BTW, you should check out <a href="http://johnhcochrane.blogspot.com/2015/08/whither-inflation.html#more" rel="nofollow">Cochrane's latest</a>: he get's all "mathy" Tom Brownhttp://www.google.comnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-78850382301235768592015-08-31T11:52:51.195-07:002015-08-31T11:52:51.195-07:00(That is you are right about the sign error.)(That is you are right about the sign error.)Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-62862543066508322312015-08-31T11:50:41.132-07:002015-08-31T11:50:41.132-07:00Hi Tom,
I think you are right; in the process of ...<br />Hi Tom,<br /><br />I think you are right; in the process of thinking Sumner's discussion was correct I confused myself between e. g. shifts of a demand curve and shifts along a demand curve. I will fix this and the discussion. Actually this is related to your questions about D0 and Dref.<br /><br />Also when F&B say floating and constant restriction, you should think general and partial equilibrium.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-54695139181638218892015-08-30T19:13:41.960-07:002015-08-30T19:13:41.960-07:00I've gone back to re-read your April 2013 post...I've gone back to re-read your April 2013 posts. You answered some questions then. I see you used Qref = Q0 = 1 in your example plots in<br /><br />"Supply and demand from information transfer"Tom Brownhttp://www.google.comnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-30718151461117809672015-08-30T15:44:14.372-07:002015-08-30T15:44:14.372-07:00I read about the fall process of a body in a gravi...I read about the fall process of a body in a gravitational field in here:<br />http://arxiv.org/pdf/0905.0610v4.pdf<br />Eq. 34 defines R_Planet. So the delta time and delta length reference variables (with the subscript "ref") are thus not arbitrary, but represent some solution up to that point: the object was observed to have fallen delta l meters in delta t amount of time. I think I asked you elsewhere if the "ref" variables were arbitrary. Clearly not then (if your problems here are analogous).<br /><br />I'm still having trouble with |delta y| const in eq. 20 and definition 4. Is there a way to relate the constant-restriction-part (giving rise to the solution with the exponential) to the simple gravitational example? The part I always find troubling is that |delta y| const = a constant, yet |delta y| seems to be written as if it's varying right there in the differential equation. Also your Taylor series expansion near a Yref, ... but what about Y0?... which are we closer to? I have a hard time thinking of what these mean in a concrete way, but the gravitational example is simple and I can see what's going on there.<br /><br />Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-58361805086120416972015-08-30T04:05:52.141-07:002015-08-30T04:05:52.141-07:00Following the development of eqs. 13 and 14 in you...Following the development of eqs. 13 and 14 in your paper:<br /><br />P = M/D0<br /><br />dD/D0 = dM/M<br /><br />(1/D0)*{integral from Dref to D of dD'} = integral from Mref to M of dM'/M'<br /><br />(1/D0)*(D - Dref) = log(M) - log(Mref) = log(M/Mref)<br /><br />exp((D - Dref)/D0) = M/Mref<br /><br />(Mref/D0)*exp((D - Dref)/D0) = M/D0 = P<br /><br />I'm missing a minus sign on the argument to exp(). Where did I go wrong? Likewise (I think) I end up with a sign reversal on your other equation:<br /><br />P = (M0/Dref)*exp(-(M-Mref)/M0)<br /><br /><br /><br /><br /><br /><br /><br /><br />Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-87438259304916990542015-08-29T14:17:47.017-07:002015-08-29T14:17:47.017-07:00Makes sense, thanks!Makes sense, thanks!Tom Brownhttp://www.google.comnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-45399343949516226322015-08-29T13:18:46.326-07:002015-08-29T13:18:46.326-07:00This is where I can just refer you to the paper. I...This is where I can just refer you to the paper. It's also the same partial equilibrium solution that's on the second or third post on this blog.<br /><br />Instead of integrating<br /><br />dD/D = dM/M<br /><br />Integrate<br /><br />dD/D0 = dM/M<br /><br />Or<br /><br />dD/D = dM/M0Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-84811108084750959142015-08-29T13:12:48.784-07:002015-08-29T13:12:48.784-07:00I'm good down to here:
"Next, let's ...I'm good down to here:<br /><br />"Next, let's check out partial equilibrium. We can solve the differential equation (constraining D or M alternately to be slowly varying around D0 and M0, respectively) to arrive at:"<br /><br />So the 1st equation under there, D is constrained to slowly vary around D0. What about M? Is M held constant? Why is "slowly vary" significant?<br /><br />There's only one differential equation I see there involving P: the one right after this:<br /><br />"In this format, we'd write (with k=1):"<br /><br />so that must be the one. You're also folding in P = Mref/Dref I guess. This is where I've been lost before I think.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-42102418145177792082015-08-29T12:32:01.336-07:002015-08-29T12:32:01.336-07:00P is price level
p is a generic priceP is price level<br />p is a generic priceJason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-24145209735274487222015-08-29T12:24:28.048-07:002015-08-29T12:24:28.048-07:00Jason, remind me: what's the difference betwee...Jason, remind me: what's the difference between p and P?Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.com