tag:blogger.com,1999:blog-5908830827135060852.post7436035426272994198..comments2020-08-11T12:31:56.012-04:00Comments on Bond Economics: Finding The Solution In A Simple SFC ModelBrian Romanchukhttp://www.blogger.com/profile/02699198289421951151noreply@blogger.comBlogger43125tag:blogger.com,1999:blog-5908830827135060852.post-70079996803902216272016-04-11T10:07:39.745-04:002016-04-11T10:07:39.745-04:00I looked at the book again when I started this art...I looked at the book again when I started this article series, and I believe that they avoided the term "equilibrium." Within macroeconomics, the term is fairly meaningless at this point. The "steady state" term they use makes more sense, although it can be tricky to formally define in a growing economy (ratios go to a steady state, but individual variables are growing).<br /><br />The "in-period" equilibrium could represent practically any behaviour within the period. All that we know is that there is a solution to the equations. Although it's not completely supported by their discussion, one could argue that any number of micro behaviour schemes could be consistent with the equations, at least within an approximation error. (I am reading Anwar Shaikh's "Capitalism", and he discusses how different micro behaviours have emergent properties as a result of accounting constraints, and so they all end up with similar macro properties. However, Shaikh is somewhat critical of post-Keynesian models, so I am not saying that he endorses this model; rather I think one could draw a parallel to his analysis. I will be reviewing his book shortly.)Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-23013441986431385202016-04-11T09:54:37.298-04:002016-04-11T09:54:37.298-04:00Thanks, Brian. :)
G&L do refer to two equilib...Thanks, Brian. :)<br /><br />G&L do refer to two equilibria, one short term (within each time period) and one long term (steady state) (p. 70). They say that the periods could be years, quarters, or months. (Footnote 10, p. 72). I was sort of surprised that the short term equilibrium could be reached in one month. <br /><br />OC, the use of time periods is unrealistic, since both equilibrium processes should be occurring at the same time. But I understand the pedagogical value of separating them.<br /><br />BTW, Jason Smith ignores the short term equilibrium process, which makes him think that he has discovered a flaw in all the G&L models, namely that the velocity of money within each time period is 1. {shrug}Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-19511442196730707322016-04-11T06:40:01.655-04:002016-04-11T06:40:01.655-04:00For this model, the exact details would depend upo...For this model, the exact details would depend upon the time period. If the period were comparable to the payroll frequency, it would be very difficult to the system to adjust to government spending as a result of changing cash flows, rather it would have to rely on expectations.<br /><br />If the time period is one year, expectations would matter less. As workers spend more money, the firm would need to hire more people, and so the activity would be growing within the time period. The process then continues, and so the model activity grows during the second relative to the first.<br /><br />It needs to be kept in mind that this is the simplest possible model. The working of the multiplier would be more interesting in more advanced cases. The key is that business sector decisions with regards to investment and inventory will then show up.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-50915730816055331182016-04-10T22:19:42.817-04:002016-04-10T22:19:42.817-04:00Well, this post, excellent though it is, does not ...Well, this post, excellent though it is, does not answer my question of the working of the Keynesian multiplier within each time period. G&L do not spell it out, except that they indicate that it is what is in macroeconomic textbooks, and that the textbooks assume, unlike G&L, that it gives the only equilibrium value for Y. G&L assume that it produces only a short term equilibrium within each time period. Anyway, they don't spell the process out, and nobody seems to care. {shrug}Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-54132720255373742252016-04-08T00:24:59.003-04:002016-04-08T00:24:59.003-04:00ThanksThanksAnonymoushttps://www.blogger.com/profile/01023780064962157121noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-28087866046782466462016-03-23T15:22:05.164-04:002016-03-23T15:22:05.164-04:00OK, thanks. I looked at MathJax a couple of years ...OK, thanks. I looked at MathJax a couple of years ago, and the lack of support on some browsers made me avoid it. I'll try it out, and see whether people can follow it.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-83244863888849408132016-03-23T14:22:27.632-04:002016-03-23T14:22:27.632-04:00Also, AFAIK, you have to include that MathJax line...Also, AFAIK, you have to include that MathJax line in the HTML of every separate blog page you want it in. The good part is you won't mess up existing posts or comments which contain dollar signs. For example, I have a mix of pages: some with MathJax and some without. Also, there's probably a way to use a different escape character sequence... check the MathJax website.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-22220964222400884682016-03-23T11:43:07.731-04:002016-03-23T11:43:07.731-04:00Also, the Chrome browser on my android phone has t...Also, the Chrome browser on my android phone has trouble with some of the superscripts (they don't always appear in their entirety). Android Firefox works fine.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-88389358683642440802016-03-23T11:17:35.284-04:002016-03-23T11:17:35.284-04:00MathJax. Look at the source for my page, search fo...MathJax. Look at the <a href="http://banking-discussion.blogspot.com/2016/03/sim7-determining-both-time-constant-tc.html" rel="nofollow">source for my page</a>, search for MathJax, and then copy the lines you find (I think just one) at the top of your HTML editor page. I got mine from Jason. If somebody has that on their page, you can leave formatted comments on their page as well. One drawback: you loose your dollar sign. Anybody inadvertently putting a dollar sign in your comments will wonder what happened to their comment... it'll get screwed up.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-91454837707420334252016-03-23T06:31:37.463-04:002016-03-23T06:31:37.463-04:00OK.
How are you generating the HTML for equations...OK.<br /><br />How are you generating the HTML for equations in a comment? When I looked into equation formatting, it involved addins that might not work everywhere.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-71360412321087263762016-03-23T01:38:27.947-04:002016-03-23T01:38:27.947-04:00Brian, you might be interested in this brief comme...Brian, you might be interested in <a href="http://informationtransfereconomics.blogspot.com/2016/03/an-rlc-circuit-with-r-s-and-l-f.html?showComment=1458710509317#c2767176829220687661" rel="nofollow">this brief comment</a> (I worked out exactly how determine SIM's parameters given both a desired steady state and a system time constant Tc)Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-8962638283087584952016-03-22T17:03:35.373-04:002016-03-22T17:03:35.373-04:00The Cambridge Engineering department got a version...The Cambridge Engineering department got a version of Phillip's hydraulic analog models working awhile ago, and had a video. Looked at it quickly (trying to see if I recognized anyone...).Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-43957548008173916992016-03-22T16:45:17.414-04:002016-03-22T16:45:17.414-04:00A water model... or perhaps a mass, spring and das...A water model... or perhaps a mass, spring and dashpot? (All you need for SIM are the spring and the dashpot... or the mass and the dashpot). Gotta have that dashpot thought! Lol<br /><br />Maybe the "water" model is better... especially if it's not water.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-39812285558884771582016-03-22T14:20:17.373-04:002016-03-22T14:20:17.373-04:00I no longer have access to an oscilloscope, so ana...I no longer have access to an oscilloscope, so analog computing is definitely out for me. (Unless I do a Phillips(?) water model...) <br /><br />Simulating a continuous time analog computer on a digital computer, so that I can use it to simulate a discrete time model sounds like something I would have done as a grad student after too many pints.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-23405783790970290872016-03-22T14:17:01.538-04:002016-03-22T14:17:01.538-04:00Exactly.
Without either, the model could produce...Exactly.<br /><br /> Without either, the model could produce infinite output; money recirculates at an infinite speed between households and business, and there are no real constraints in this model. In order to pin down a solution, money needs to be drained from income. This is done by taxes and savings.<br /><br />In this case, a representative household assumption may be more "reasonable". What limits output in that framework is the fact that households can only work 24 hours a day...Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-17715163962406379422016-03-22T13:41:12.072-04:002016-03-22T13:41:12.072-04:00I took a good look at the model last night.
Pleas...I took a good look at the model last night.<br /><br />Please comment on my interpretation.<br /><br />The excel sim takes two decay rates, one for taxes and one for savings. Decay removes money from the system with each transaction.<br /><br />The tax rate is applied to the first transaction which reduces the remainder available for building consumption IN THE FIRST PERIOD.<br /><br />The entire remainder (12.3) is assigned to savings. <br /><br />The amount of tax collected provides the measure of consumption, with a limit of C = T/theta. THIS SETS THE RESULTS FOR THE FIRST PERIOD.<br /><br />Beginning in the second period, a portion of household savings is added to (unchanged) government spending. The tax rate is applied to this sum and the identical sequence followed again. THIS SETS THE RESULTS FOR THE SECOND PERIOD.<br /><br />This sequence is repeated until taxes equal the initial jump in government spending. At that point, the system has returned to stability at a higher level of consumption and wealth.<br /><br /><b> I believe we could think of this as a system with two stabilizing forces, taxes and savings. </b>Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-14606122188103765152016-03-22T12:56:44.498-04:002016-03-22T12:56:44.498-04:00Yes, I know they're dated. I actually used one...Yes, I know they're dated. I actually used one in my undergrad EE course. Lol... Probably the last year that was required.Tom Brownhttp://www.google.comnoreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-39098246659583143172016-03-22T08:33:16.315-04:002016-03-22T08:33:16.315-04:00Oops. I mixed up your work and Jason's; I see ...Oops. I mixed up your work and Jason's; I see that you had only one state variable. Deleted the misleading comment.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-22500252576762237612016-03-22T07:37:50.289-04:002016-03-22T07:37:50.289-04:00This comment has been removed by the author.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-14028710363665040772016-03-22T07:07:18.241-04:002016-03-22T07:07:18.241-04:00My dad did a project using an analog computer when...My dad did a project using an analog computer when he was in university -- in the 1950s. (Economists actually used hydraulic analog computers.) We may or may not have had exercises doing simulations in one of our labs in the 1980s, but analog computing is somewhat dated...<br /><br />The discrete time system for SIM has a single state variable, with a certain rise time. You would have to tune your RLC circuit to match that rise time, based on your arbitrary sample frequency. You cannot fix all 3 of R,L,C, which Jason suggests, since you could then only simulate a single discrete time system (if we fix the sampling frequency).<br /><br />Even though I trained as an electrical engineer -- why would we care? There is an infinite number of models whose behaviour can be captured by the same state space model. However, there is no reason for those systems to have anything else in common.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-30987746695153504052016-03-22T01:47:05.553-04:002016-03-22T01:47:05.553-04:00Probably no one cares, but my 1st link is wrong. I...Probably no one cares, but my 1st link is wrong. It should have been <a href="http://informationtransfereconomics.blogspot.com/2016/03/an-rlc-circuit-with-r-s-and-l-f.html" rel="nofollow">this</a>.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-52333261590911712232016-03-22T01:03:01.540-04:002016-03-22T01:03:01.540-04:00Brian, Jason has drawn an analogy between SFC mode...Brian, <a href="" rel="nofollow">Jason has drawn an analogy</a> between SFC models and RLC (resistance, inductance, capacitance) circuits. He selected Fig 1 of <a href="https://en.wikipedia.org/wiki/RLC_circuit" rel="nofollow">this Wikipedia article</a>, with a voltage source v(t) in series with resistor R, inductor L and capacitor C, and then solves for current i(t).<br /><br />Lining that up with SIM (G&L's SIM), I say you can make an analog computer out of that circuit if (for example) you get rid of the capacitor and replace it with a short (a wire) and just leave R and L. Here's one way to program the analog computer (forgetting about all the outputs and just concentrating on h (the continuous time equivalent of H, where h(n*T) = H[n], and g'(n*T) = G(n)):<br /><br />di/dt = -(R/L)*i + (1/L)*v<br /><br />is the analog computer for<br /><br />dh/dt = a*h + b*g'<br /><br />With the following equivalences:<br /><br />h(t) in dollars = i(t) in amps<br />g'(t) in dollars/period = v(t) in volts<br />Ts = 1 "period" = 1 second<br /><br />R = 0.25 ohms<br />L = 1.496521 henrys<br /><br />Of course to make it correspond exactly to G&L's example at each sample time (0 sec, 1 sec, 2 sec, etc), v(t) should be a 20 volt step:<br /><br />v(t) = 20 volts for t >=0, and v(t) = 0 for t < 0<br /><br />But it can match G&L for any v(t) that stays constant between sample times.<br /><br />... Ah, it looks like you've already found the post. Do you agree with my analog computer programing? Of course you can easily scale that to different electrical circuit times (other than 1 sec = 1 G&L period), so it's not unique in that sense, but given a particular electrical period, the solution is unique (for R and L). And of course you could switch v for i, or use difference correspondences (scalings) there too or make an RC circuit instead of an RL, etc.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-25296913545573680312016-03-21T17:42:16.183-04:002016-03-21T17:42:16.183-04:00... I'm sure EViews is much easier!... I'm sure EViews is much easier!Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-67468881428602592242016-03-21T17:41:13.680-04:002016-03-21T17:41:13.680-04:00"after some matrix algebra"
Actually yo..."after some matrix algebra"<br /><br />Actually you don't need any matrices for SIM: A and B are scalars here.<br /><br />"...any number of changes will make the system nonlinear, and you have to use some numerical techniques to solve the system."<br /><br />I've actually used the free online version of Excel to solve vector Newton iterations in making <a href="http://banking-discussion.blogspot.com/2014/04/blog-post.html" rel="nofollow">an interactive version of one of Nick Edmond's models</a>. I fixed the number of iterations ahead of time (I used six per time sample). It was a bit of a pain, but it worked and I tried to set it up so it could be reused for a different model.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-86294525942824578732016-03-21T17:32:57.033-04:002016-03-21T17:32:57.033-04:00This comment has been removed by the author.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.com