tag:blogger.com,1999:blog-6837159629100463303.post6375588846577229768..comments2021-09-21T07:38:36.762-07:00Comments on Information Transfer Economics: Expectations (rational or otherwise) and information lossJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-6837159629100463303.post-38523272802002679452014-11-04T14:21:29.940-08:002014-11-04T14:21:29.940-08:00In a sense that is correct; the information transf...In a sense that is correct; the information transfer index measures the relative information in a unit of AD versus a unit of aggregate supply when they are matched up. The index is fundamentally a ratio of the logarithms of probabilities from Shannon's definition of information:<br /><br /><a href="http://en.wikipedia.org/wiki/Quantities_of_information#Entropy" rel="nofollow">http://en.wikipedia.org/wiki/Quantities_of_information#Entropy</a><br /><br />The index is first defined on this blog here:<br /><br /><a href="http://informationtransfereconomics.blogspot.com/2013/04/the-information-transfer-model.html" rel="nofollow">http://informationtransfereconomics.blogspot.com/2013/04/the-information-transfer-model.html</a><br /><br />It (and the rest of the information transfer model) comes from a paper by Fielitz and Borchardt cited at the link.<br /><br />I've been working on trying to write more clearly as other commenters have also pointed out that many of my posts are not very easy to read. With each post I write I hope I'm getting a little better at it.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-76610377718194039942014-11-03T19:32:59.668-08:002014-11-03T19:32:59.668-08:00Hmmm, your work presents an interesting puzzle -- ...Hmmm, your work presents an interesting puzzle -- and an interesting approach to macroeconomics.<br /><br />I have spent some time on the March 15, 2014 post "How Money Transfers Information". Maybe I misconstrued some of the associations.<br /><br />I interpreted the Information Transfer Index as representing the number of transactions that each added to AD. I thought you reached the ITI by carrying information about transactions by enumerating in logarithmic notation, and then, when appropriate, turned the log notation back to a numerical form to get ITI = 1/k.<br /><br />To me, this approach made a lot of sense because it was a reasonable attempt to carry the relatively constant number of transactions in an economy (annual basis) into the AD measurement (which is ultimately GDP).<br /><br />Your posts have a lot of content--they are not easy reads. I will continue studying them. Thanks for making them available.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-91553532753965116882014-11-03T17:43:52.485-08:002014-11-03T17:43:52.485-08:00Hi Roger,
The information we're talking about...Hi Roger,<br /><br />The information we're talking about here is in the information theory sense of information, not 'facts'. <a href="http://en.wikipedia.org/wiki/Entropy_%28information_theory%29" rel="nofollow">See here, for example.</a><br /><br />In this sense sending a random binary sequence through a communication channel transfers the maximum amount of information, whereas sending a constant string of 1's transfers almost zero information.<br /><br />The KL divergence above is zero when the distribution B = A, and is positive for all other B's ... so our guess B of the real distribution A always represents information loss, unless B = A. There can't be a "surplus of information" -- you either have knowledge of A or you have incomplete knowledge of A.<br /><br />I say a little bit more about this in a different way here:<br /><br /><a href="http://informationtransfereconomics.blogspot.com/2014/07/rationality-is-beside-point.html" rel="nofollow">http://informationtransfereconomics.blogspot.com/2014/07/rationality-is-beside-point.html</a>Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-57942691636940976622014-11-03T16:56:58.673-08:002014-11-03T16:56:58.673-08:00Because we assumed that there is ALWAYS informatio...Because we assumed that there is ALWAYS information loss, I would expect that the equation would work for information loss like theft or fire.<br /><br /> What if there was, instead of an information loss, a surplus of information (for example, additional information from an unexpected source)? <br /><br />It seems to me that term M would change so we would need to leave term dM in the final formula.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-67186190546216763752014-11-03T11:23:37.387-08:002014-11-03T11:23:37.387-08:00Oops
Formula should read:
$$
\frac{\Delta I}{M \...Oops<br /><br />Formula should read:<br /><br />$$<br />\frac{\Delta I}{M \log M} = P - \frac{1}{\kappa} \frac{N}{M}<br />$$Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-39990982104976789592014-11-03T11:22:54.439-08:002014-11-03T11:22:54.439-08:00This comment has been removed by the author.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-50646423753593444702014-11-03T11:21:56.669-08:002014-11-03T11:21:56.669-08:00Some additional notes:
1.
I actually think keepi...Some additional notes:<br /><br />1.<br /><br />I actually think keeping $N/M$ in the formula would be a better simplification (there should be a small error term introduced when replacing $N/M \rightarrow dN/dM + \epsilon$. In that case, equation (1) should read:<br /><br />$$<br />\frac{\Delta I}{M \log M} = P - \frac{N}{M}<br />$$<br /><br />2.<br /><br />Due to the arbitrariness of the normalization of the price level, the relative normalization of $N^{*}$ and $N$ is not fixed (it's a free parameter).<br /><br />One way to think of this is that at the point you start the model (initial conditions), you can take $N^{*} = N$ (no information loss) and project it forward (e.g. numerically solving the differential equation). Information loss accumulates from that point forward. <br /><br />This represents the freedom of choosing the year to normalize the price level.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.com