tag:blogger.com,1999:blog-6837159629100463303.post3440752642895467917..comments2023-06-18T01:25:08.748-07:00Comments on Information Transfer Economics: An RLC circuit with R = S and L = FJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger105125tag:blogger.com,1999:blog-6837159629100463303.post-20794605823314748552016-04-14T22:55:22.025-07:002016-04-14T22:55:22.025-07:00That is pretty cool!That is pretty cool!Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-35577240496413215032016-04-14T18:41:32.199-07:002016-04-14T18:41:32.199-07:00This one is better. I adjusted the time step and s...<a href="http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.002+6.450009306485578+24+25+43%0As+432+224+432+176+0+1+false%0Aw+432+384+432+448+0%0Al+640+272+640+384+2+1.151170249+0%0Aw+432+256+432+224+0%0Av+432+320+432+256+0+0+40+20+0+0+0.5%0Aw+432+176+640+176+0%0Ar+640+176+640+272+0+0.1%0Ar+704+448+704+176+0+0.4%0Aw+704+176+640+176+0%0Aw+640+448+704+448+0%0Ar+432+448+640+448+0+0.15%0Aw+640+384+640+448+0%0Ar+592+384+480+384+0+0.6%0Aw+592+384+640+384+0%0Aw+480+384+432+384+0%0Aw+432+384+432+320+0%0Ao+4+64+0+34+20+0.00009765625+0+-1%0Ao+15+64+0+33+0.0000762939453125+0.00009765625+1+-1%0Ao+12+64+0+33+0.0000762939453125+0.00009765625+2+-1%0Ao+2+64+0+33+0.0000762939453125+0.00009765625+3+-1%0A" rel="nofollow">This one is better.</a> I adjusted the time step and speed to make sense.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-88252734617403814182016-04-14T16:54:06.509-07:002016-04-14T16:54:06.509-07:00Jason, you might get a kick out of this: follow th...Jason, you might get a kick out of this: <a href="http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.0000049999999999999996+382.76258214399064+48+5+43%0As+176+112+176+64+0+1+false%0Aw+176+272+176+336+0%0Al+384+160+384+272+2+1.151170249+0%0Aw+176+144+176+112+0%0Av+176+272+176+144+0+0+40+20+0+0+0.5%0Aw+176+64+384+64+0%0Ar+384+64+384+160+0+0.1%0Ar+448+336+448+64+0+0.4%0Aw+448+64+384+64+0%0Aw+384+336+448+336+0%0Ar+176+336+384+336+0+0.15%0Aw+384+272+384+336+0%0Ar+336+272+224+272+0+0.6%0Aw+336+272+384+272+0%0Aw+224+272+176+272+0%0Ao+4+64+0+33+10+0.00009765625+0+-1%0Ao+12+64+0+33+0.0000762939453125+0.00009765625+1+-1%0Ao+2+64+0+33+0.0000762939453125+0.00009765625+2+-1%0A" rel="nofollow">follow this link to an online circuit model</a>, and then close the switch by clicking on it. The three plots across the bottom are (left to right), Y, T and H, modeled as currents in the system. G is modeled as the voltage. The explanation is <a href="http://banking-discussion.blogspot.com/p/first-order-lc-circuit-1.html" rel="nofollow">here</a>.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-27083402480595018702016-04-04T00:28:31.483-07:002016-04-04T00:28:31.483-07:00Jason,
I don't really want to get involved in...Jason,<br /><br />I don't really want to get involved in this discussion, but as my model has been mentioned here, I will make a few comments.<br /><br />The setting of ??? to 1 is not some choice I made. It is what happens in any DSGE model that contains more than one monetary asset. If you could show me a single DSGE model where they use a different value, I'd be genuinely interested to see it. This is also, of course, what happens in the national accounts of every country.<br /><br />The speed of adjustment in that model will depend on the parameters beta and epsilon, so it is not always the same if ??? = 1. But much more fundamentally, this is a very simple model. It strips out many things that we know are important in determining differences between countries and leaves us with the simplest behaviour possible. It will therefore tend to show similar patterns regardless of the parameters. That is after all the whole point of the exercise. <br />Nick Edmondshttps://www.blogger.com/profile/15342983814699700396noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-65601876188813260662016-04-03T13:40:28.576-07:002016-04-03T13:40:28.576-07:00Of course, that was a root locus in the Z-plane, n...Of course, that was a root locus in the <a href="https://en.wikipedia.org/wiki/Z-transform" rel="nofollow">Z-plane</a>, not the <a href="https://en.wikipedia.org/wiki/S-plane" rel="nofollow">S-plane</a>. (Jason, I know this is nothing new for you, but Roger has been interested in linear systems, so this is a great example of predicting a system's behavior based on frequency domain analysis).Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-76644327294399762222016-04-03T13:34:31.197-07:002016-04-03T13:34:31.197-07:00... and to complete my long winded "root locu...... and to complete my long winded <a href="https://en.wikipedia.org/wiki/Root_locus" rel="nofollow">"root locus"</a> explanation (that probably nobody cares about) as Γ goes to 0, the pole (A in this case) moves towards 1, and the time constant -> inf, and the system approaches a perfect integrator. At Γ = 0, it would be a perfect integrator, except B = 0, so you can only integrate any initial value H (i.e. H stays constant at its initial value). And finally for Γ < 0, then B < 0 and A > 1 (i.e. the pole moves outside the unit circle), and you get unstable exponential growth again, but without the oscillations. Whew! =)Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-18325793593148533282016-04-03T12:41:07.572-07:002016-04-03T12:41:07.572-07:00Jason I know why you get oscillations... Making ga...Jason I know why you get oscillations... Making gamma too big pushed the pole to the negative real axis... The same problem I had with Ramanan's method for adjusting the sample period if I tried to make it too large. In fact you should get oscillations with any gamma > 6.5 because if you look at my expression for A above when gamma is present you'll see A < 0 in that case (with the other params set to defaults). You can interpret gamma as a multiplier on alpha2 for this purpose, and 6.5x the old sample period was the limit for not producing oscillations with Ramanan's alpha2 scaling method. In fact if you scale alpha2 by 6.5 exactly (with gamma) the pole is at zero, and the system has a time constant of 0. Set gamma > 13 and your pole moves outside the unit circle and the oscillations grow without bound. Set gamma = 13 and the pole is at -1, and the system is marginally stable... Oscillating at constant amplitude forever in response to an impulse, and producing an oscillating ramp in response to a step: i.e. it becomes an oscillating integrator, oscillating at maximum real frequency pi radians per sample.Tom Brownhttp://www.google.comnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-53800842600837255762016-04-03T11:25:01.983-07:002016-04-03T11:25:01.983-07:00My last (I hope) statement on SIM. I think that th...My last (I hope) statement on SIM. I think that this discussion could use comments from someone like Lavoie, to clear up any ambiguities about the model and its toy economy.<br /><br />G&L: “We have therefore decided to start by constructing and studying a hypothetical economy in which there is **no private money at all**. . . . This detour will enable the student to master the main principles inherent in fully coherent stock-flow macroeconomics, including the principles of portfolio behaviour within a simple but yet complete stock-flow framework. ****Very strong simplifying assumptions will have to be made initially and the reader is asked to suspend disbelief until more realistic systems are introduced****.” (p. 57, emphasis mine)<br /><br />For pedagogical purposes, SIM is unrealistic, with no private money, only government money. Government money in the private economy is represented by H. <br /><br />G&L: “Let us start with the simplest meaningful model that can be built – Model SIM, for simplest. The economy is closed to the outside world: there are neither exports nor imports, nor foreign capital flows. We postulate a monetary economy in which economic agents, beyond the institution of government, can be divided conceptually into their business activities on the one hand, selling services and paying out wages and, on the other, receiving income, consuming and accumulating assets when they act as households. All production is undertaken by providers of services, who have no capital equipment and no intermediate costs of production. Production of services is assumed to be **instantaneous**, so that inventories do not exist. . . . **There are no private banks, no firms and no profits whatsoever.** We are in a **pure labour economy**, à la Adam Smith, where production is carried out by labour alone.” (p. 58, emphasis mine)<br /><br />With no profits, there are no profit sharing plans, and hence, no 401(k) accounts.<br /><br />G&L: “The government buys services and pays for them with ****money, which consists of pieces of paper which it prints****. Money is made acceptable as a means of payment because there is a law which makes it legal tender, which means that creditors are legally obliged to accept money in settlement of debts. The government also levies taxes and ordains that these be paid in ****money****, which people therefore have to obtain by selling their services for it. In other words, ****all transactions occur in government money****, that is, ****banknotes issued by government****. This ****government money**** is the vehicle via which people receive income, settle their debts, pay their taxes, and ****store their wealth****.” (p. 58, emphasis mine)<br /><br />Government spending, G, occurs with money that the government prints for that purpose. Government spending injects money into the private economy. Taxes, T, are paid with money that the government has already printed and spent into the private economy. Taxation extracts government money from the private economy. That is the operational meaning of the equation,<br /><br />∆H = G − T<br /><br />which holds for each interval of time.<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-81297269142349018892016-04-03T11:12:12.227-07:002016-04-03T11:12:12.227-07:00Another way to think about it is that Γ controls t...Another way to think about it is that Γ controls the rate of scrip production, or barter efficiency, bank openings, or something else.<br /><br />In SIM, the steady state should be the expected state of the economy, so agents should move it there immediately.<br /><br />[I also tried Γ > 1, and if Γ = 10, you induce oscillatory behavior at the start -- which is interesting.]Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-36419582165557881162016-04-03T11:05:33.404-07:002016-04-03T11:05:33.404-07:00Jason: "Go back and forth between these two p...Jason: "Go back and forth between these two pictures. The only difference is Γ = 0.5 and Γ = 1.0 in the equation:<br /><br />"ΔH = Γ (G - T)<br /><br />"Γ only changes the rate of approach to the steady state."<br /><br />Yes, I got that long ago. So far my reaction is a big so what?<br /><br />Jason: "There is no explanation of why we can do one and not the other -- other than saying Γ = 1 identically. Which is an assumption about the rate of approach. G&L assume Γ = 1 but never even mention the possibility that Γ < 1 or Γ > 1."<br /><br />G&L operationalize the equation, <br /><br />∆H = G − T<br /><br />such that it holds in every time period. There may be implications about the rate of approach to a steady state, but that has nothing to do with their definitions of H, G, and T.<br /><br />Previously you indicated that Γ is a money multiplier. However, there are no private banks in the SIM economy, so the standard meaning of that term does not apply. You also said that it is a kind of velocity multiplier, which you think is absent from SIM, so that V = 1. However, SIM does have a velocity multiplier, a Keynesian multiplier, and in their example V is always greater than 1. You have not spelled out an operational definition of Γ.<br /><br />Jason: "And this happens in all of the models."<br /><br />Their more advanced models do have private banks and loans and, hence, private money. Any money multiplier would show up in changes to loans, ΔL, and deposits, ΔM. All their models have a Keynesian multiplier, which shows up in *Y.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-68869324422374964142016-04-02T15:32:38.122-07:002016-04-02T15:32:38.122-07:00When I said:
Or you could say they actually spend...When I said:<br /><br /><i>Or you could say they actually spend their 401(k) on consumption they produce for each other -- re-labelling the account boxes -- leaving total 401(k) constant.</i><br /><br />... that is what G&L want you to think. And it only makes sense if Γ = 1.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-41780942076403633542016-04-02T15:28:50.730-07:002016-04-02T15:28:50.730-07:00However, the paper cash itself held by the public ...<i>However, the paper cash itself held by the public is still a debt of "the government" and an asset of the private sector. In that sense the paper cash itself is a kind of physical "government" bond paying a 0% nominal interest rate.</i><br /><br />That would be true if government issued the fiat currency in this model, but it does not appear that it does. It issues 401(k)s that people treat as wealth they don't (net) consume. That is all the model says.<br /><br />There's no real separation between "households" and "firms" -- there's just households and production. Imagine production is done by households (everyone farms and sells their particular food to each other). They issue scrip to pay for other's production (and allow others to buy their production). Imagine the scrip like tally marks on a tally stick ... like credit. You get some scrip when you sell your potatoes at the market and then use it buy some apples at the market. This is a liability (and an asset) of the households, not the government. It sums to zero.<br /><br />You could do the same thing above with the issuers of scrip being called banks. Scrip is an asset of households and a liability for the banks (and net zero for the private economy).<br /><br />Or you can say everyone barters for production. The value of what they barter is proportional to their 401(k).<br /><br />Or you could say they actually spend their 401(k) on consumption they produce for each other -- re-labelling the account boxes -- leaving total 401(k) constant.<br /><br />But all of those situations could be happening. Therefore H doesn't specify what money is -- H only specifies how much people consume beyond the fraction of their income they spend.<br /><br />And in each of those situations, Γ just controls how the rate at which 401(k)s increase decreases. This changes the rate of production of scrip (or the rate of increase in barter). In the steady state, there is a constant supply of scrip or a constant amount of barter.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-38533254322308346882016-04-02T15:06:36.224-07:002016-04-02T15:06:36.224-07:00Also, in case anyone is interested, this site prov...Also, in case anyone is interested, this site provides kind of an interesting interactive set of "macro balance sheets" you can experiment with:<br /><a href="http://econviz.org/macroeconomic-balance-sheet-visualizer/" rel="nofollow">http://econviz.org/macroeconomic-balance-sheet-visualizer/</a>Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-80139675204038470562016-04-02T15:02:48.354-07:002016-04-02T15:02:48.354-07:00Jason, thanks. That helps a lot! One question: in ...Jason, thanks. That helps a lot! One question: in the real world, paper cash which has been purchased from the Fed currently shows up as a liability (debt) on the Fed's balance sheet. If we draw a line around the Fed+Treasury and call the combination "the government" and we now suppose the Treasury issues a bond which the Fed purchases, and the Treasury spends the proceeds (in the form of paper cash) in the private sector: that bond is a debt (liability) of Treasury and an asset of the the Fed, thus in (given my definition) cancelling out as a net debt or asset for "the government" as a whole. However, the paper cash itself held by the public is still a debt of "the government" and an asset of the private sector. In that sense the paper cash itself is a kind of physical "government" bond paying a 0% nominal interest rate. Now back to SIM: how would the 20 dollars of cash and the government bonds issued into households' 401ks show up on the SIM government's balance sheet? It seems like they are both liabilities of the SIM government. So that 20 dollars spent by the government (and held by households) would be recorded as 40 dollars of net government debt (if the SIM government did accounting in a similar way to the US Fed+Treasury "government"). I don't see an offsetting asset for the SIM government that would bring the total government debt back down to just 20 dollars. Unless by "G spends 20 in the economy" you mean the SIM government does that spending exchanging 20 dollars worth of SIM government bonds into the private sector's 401ks, and there is no other form of government money (e.g. paper cash) spent at all.<br /><br />Also, I know almost nothing about SFC models, I've really only investigated SIM, but offhand it seems to me that an SFC model could be constructed with some of the elements you mention above made explicit: e.g. government issued 401ks, government bonds, and filling in the blanks on what counts as money (perhaps bank deposits as well as cash (M0 and M1)), and exactly which entities can create it (perhaps explicitly modeled banks, for example, in addition to the government). Perhaps in such a model, something taking on the role of Γ could be explicitly added from the start as well.<br /><br />Roger, re: honesty: yes, I was trying to address that by asking how the government ATM would know how much tax to collect. Of course instead of cash, it could be an all electronic system with all transactions processed on the government network, so it would know at all times exactly how much tax liability was generated from each household (and firms? do firms have tax liabilities in SIM?).Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-90458440900703535602016-04-02T14:43:44.912-07:002016-04-02T14:43:44.912-07:00"Where is money? No idea....................&..."Where is money? No idea...................."<br /><br />My idea is that G&L spending is done at beginning of the period in amount specified by G + α2*H−1 . Money circulates during the period. Then, finally, G&L tells us where the money sits at period end.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-6014688143561991162016-04-02T13:13:56.762-07:002016-04-02T13:13:56.762-07:00I should have said "rate of change of consump...I should have said "rate of change of consumption" rather than "level of consumption" in the last paragraph. Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-34564177002853541162016-04-02T13:06:17.603-07:002016-04-02T13:06:17.603-07:00Tom,
I think that is the picture G&L want you...Tom,<br /><br />I think that is the picture G&L want you to have in your head. I decided to have a think about this for awhile, and here's my "interpretation" of the model equations.<br /><br />G spends 20 in the economy. It 'borrows' the money for this from households by setting up a 401(k) for them, filling it with government bonds. This 401(k) is H.<br /><br />Note that G - T is effectively 'saving' (S) because<br /><br />G - T = Yd - C<br />G - T = Y - T - C = (C + T + S) - T - C = S<br /><br />Now note that those are identities and we have<br /><br />ΔH = G - T<br />ΔH = Yd - C<br /><br />These equations mean, in G&L's version, government debt (spending minus taxes) is the asset in everyone's 401(k) (disposable income minus consumption).<br /><br />This 401(k) produces a "wealth effect", and households consume an amount $\alpha_{2} H_{-1}$ (i.e. their 401(k) value from the previous period). <b>They do not spend their 401(k), though.</b> This is critically important. Equation (3.7) in G&L does not make the stock of government debt go down. <i>It makes the rate at which the stock of debt increases go down</i> because household consumption is output which is taxed at a rate $\theta$. Wealth effect spending produces output which increases tax revenue.<br /><br />Where is money? No idea. But enough of it must be created for households to be able to spend their additional 'wealth effect' consumption. That is to say some amount of money must be created (somewhere) that is (in the simplest version) proportional to H.<br /><br />Eventually, this wealth effect produces enough output that taxes collect enough of national income that no more debt is issued. After that point the wealth effect is constant and taxes are constant, so consumption is constant.<br /><br />So what is Γ in this? It's the fraction of the value of the government bonds issued that go into everyone's 401(k). If Γ < 1, then only a fraction of the bonds go into household 401(k)s. If Γ > 1, then the value of the 401(k)'s is greater than the value of government bonds. If Γ = 1 (as in G&L), everyone's 401(k) is made up of government bonds.<br /><br />In this explanation, maybe it is best to think of Γ as a Keynesian multiplier -- the value of everyone's 401(k) can go up by more than the amount of government deficit spending, or less.<br /><br />But in a monetary economy, Γ changes the level of consumption supported by government issued money (= G - T), which is basically a multiplier. H is kind of like electronic reserves. It sits in banks and props up the lending that creates our deposits (M1). But it's never spent on anything itself. Only 'M1' = $\alpha_{2} H_{-1}$ is ever spent (but note: M1 is just proportional to H, it's not actually H).Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-56229505288898954792016-04-02T06:23:31.142-07:002016-04-02T06:23:31.142-07:00Tom, I think I would add one more observation.
Al...Tom, I think I would add one more observation.<br /><br />All of the firms and employees are very honest and follow the rules. The rule they must follow is "when you receive the money you earned, send x% to the ATM." This is the tax rule that they follow.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-19138164231153458102016-04-01T15:41:03.468-07:002016-04-01T15:41:03.468-07:00... I think I already covered this, but just for e...... I think I already covered this, but just for emphasis: at any one point in time, steady state, or not steady state, if you went to each household in this SIM world and took an inventory of all the ATM cash each had stored in their house (firms are non-profit, so they don't store any), that total would exactly match the ATM's running total of (total cash printed - total cash shredded). Since there are no banks, bank deposits, Bitcoin, foreign currencies or any other cash substitutes in the SIM world we can stop there with our inventory.<br /><br />With the default SIM parameters (and with or without Γ), that total reaches a steady state of 80 dollars and never changes after that, which means that although (total cash printed) and (total cash shredded) continue to each climb by 20 dollars each period, their difference stays fixed in steady state at 80 dollars.<br /><br />I can imagine a more complex world "created" by a fancier SFC model in which banks create deposits (for example) by using them to purchase things (e.g. loans, office furniture, etc), and in that world the instantaneous inventory of net government ATM cash printed <= the instantaneous inventory of everything that counts as money (say for tax purposes) owned by households. And these banks perhaps need to consider how much government ATM cash exists, since they must exchange deposits for this cash (in a 1:1 ratio) on demand. The government ATM is under no such constraint (a point Nick Rowe always brings up). But that wouldn't be the SIM world.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-68037347871519287282016-04-01T15:12:32.914-07:002016-04-01T15:12:32.914-07:00This comment has been removed by the author.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-1357133518248134052016-04-01T14:11:10.773-07:002016-04-01T14:11:10.773-07:00Jason, what is your mental picture of what H is? T...Jason, what is your mental picture of what H is? This is mine:<br /><br />The government is like a fancy ATM machine that contains both a printer and a shredder. The firms produce 20 dollars worth of batteries, paper and ink for it to keep running every period and the firms put those items in the "inbox", and every period the ATM responds to this by printing up 20 dollars in paper cash and shoots it out into its "outbox" in exchange. The firms do not leave money in the outbox, they use all of it to pay their employees (households). There's one other "inbox" and that's for paying taxes: you put the cash (that this same ATM previously printed) in and it just shreds it. There are no banks or deposits in this world (so no M1 or M2 or MZM)... there's just this cash from this government ATM playing the role of money, and inside it keeps a running total of the net amount it's printed so far, i.e. (total printed - total shredded) and that total is H. In steady state it prints 20 dollars each period and shreds exactly 20 dollars as well. So at any one point in time the ATM knows exactly how much cash is out circulating in the economy. It has no idea how many times it changes hands (its velocity) between households and firms over any one period, but it knows the total amount.<br /><br />So how does it know how much tax to collect each period? Well that's the rub. If ALL transactions had to take place at just one time per period, each household being allowed exactly one purchase from the firms, and this was somehow monitored by the ATM, then I could see how it would know.<br /><br />Also, all the firms are non-profits and they don't trade with each other. They simply accept payment for their products (from the government ATM and the households) and they pay wages to households.<br /><br />Now if there were banks in the model, then this ATM would not know (necessarily) about the deposits they created. It wouldn't necessarily know what the "money multiplier" was in that case.<br /><br />Anyway, that's my mental image of the world modeled by SIM, and I suspect that maybe some other readers have a similar kind of mental image. It's difficult to see what exactly Γ is in that world in concrete terms, or perhaps what your mental image of H is.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-56516743407749729132016-04-01T13:46:12.763-07:002016-04-01T13:46:12.763-07:00This comment has been removed by the author.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-15834873342359725442016-04-01T09:50:20.141-07:002016-04-01T09:50:20.141-07:00after you put Γ in your spreadsheet, go back to th...<i>after you put Γ in your spreadsheet, go back to this balance sheet and see if each of the rows and columns still sum to zero at every sample period</i><br /><br />Tom, they won't unless you take ΔH → (1/Γ)ΔH because that balance sheet defines the equation ΔH = G - T in the third column.<br /><br />That's why I said G&L sneak in the assumption Γ = 1 by calling it "accounting" when in fact it is no such thing. When you couple a stock to a flow, you get a velocity per Nick Rowe (as I link to above). Sure, velocity can be 1 -- but it doesn't have to be.<br /><br />The reason Γ doesn't affect the steady state is that we must have ΔH = 0 in the steady state (otherwise H would change, contradicting the steady state assumption). Therefore G - T must be zero (because Γ $\neq$ 0), therefore Γ doesn't matter in the steady state because Γ (G - T) = 0.<br /><br />That should give a hint about the meaning of the equation ΔH = G - T. It doesn't matter in the steady state at all. So it can't be doing anything important in the model that would still be necessary in the steady state. E.g. it can't define "money" because you need money for the steady state economy to work too. It has to define something dynamic.<br /><br />But it's also the only equation that defines anything about money. H-1 is an input to consumption, but that's only because ΔH = YD - C -- and that is just a couple identities away from ΔH = G - T, namely Y ≡ YD + T ≡ C + G.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-51749302479575941532016-04-01T09:02:30.401-07:002016-04-01T09:02:30.401-07:00"Thanks Tom, I think I understand better now...."Thanks Tom, I think I understand better now."<br /><br />You do? Great! Now you can explain it to me. :D<br /><br />Here's what I understand: Why Γ does not affect the steady state and why it changes the time constant.<br /><br />Here's a fun exercise for you: introduce Γ into your spreadsheet, like I have in my comment above (which I think matches Jason, but you might want to double check). Instead of stimulating his system with a step (as I do in my spreadsheets), Jason has stimulated his with an impulse (G = 20 for just one period), and then he accumulates (calculates a running summation) the results for each variable (G,H,Y,T,YD,C). These are equivalent in terms of final outputs, and the underlying model is the same (except for Γ and the accumulation operation at the end of course). So if you replicate Jason's expressions and stimulate it with G = a step, don't do the final accumulation, or you'll get the wrong answer!<br /><br />Here's a fun exercise: after you put Γ in your spreadsheet, go back to <a href="https://3.bp.blogspot.com/-qJN42YeHCJo/VtjW6VCuPnI/AAAAAAAAJEA/Or9X83aCzeU/s1600/stock%2Bflow%2Bgodley.png" rel="nofollow">this balance sheet</a> and see if each of the rows and columns still sum to zero at every sample period (not just in the steady state). That's probably equivalent to checking to see if <a href="https://4.bp.blogspot.com/-KKkQf2zscr4/VtjXISV_4wI/AAAAAAAAJEE/iI9TIv_8oBQ/s1600/godley%2B2.png" rel="nofollow">all these expressions</a> are satisfied in every sample period.<br /><br />I have not done this. If you do it, please let me know what your results are.Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-65682495267401626632016-04-01T05:24:09.779-07:002016-04-01T05:24:09.779-07:00Thanks Tom, I think I understand better now.
If I...Thanks Tom, I think I understand better now.<br /><br />If I am correct, Γ controls the step increments (and number of steps) without changing the final steady state convergence value.<br /><br />Γ is a scaling factor. Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.com