tag:blogger.com,1999:blog-5908830827135060852.post8439465018833462464..comments2020-06-04T12:13:09.811-04:00Comments on Bond Economics: The Monetary Monopoly ModelBrian Romanchukhttp://www.blogger.com/profile/02699198289421951151noreply@blogger.comBlogger21125tag:blogger.com,1999:blog-5908830827135060852.post-46929159506322360872020-01-21T08:41:05.128-05:002020-01-21T08:41:05.128-05:00That is literally the same equation. Doing it that...That is literally the same equation. Doing it that way is bad, since it reverses the standard for notation. We are writing down an expression for M(1), and we write it down as the sum of terms that affect money holdings.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-76964275592480232872020-01-20T13:47:18.531-05:002020-01-20T13:47:18.531-05:00"At t=0, the accounting identity is:
M(1)=Pg(..."At t=0, the accounting identity is:<br />M(1)=Pg(0)Qg(0)−T(0)."<br /><br />The careful reader can figure out that you want the M(1) value to be the final sum of span-zero activity. It would make a lot more sense to me if you wrote<br /><br />At t=0, the accounting identity is:<br />Pg(0)Qg(0)−T(0) = M(1).<br /><br />Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-25209228373453414632020-01-18T09:19:07.794-05:002020-01-18T09:19:07.794-05:00The notation is consistent. It’s the beginning of ...The notation is consistent. It’s the beginning of period money balance. I might switch to end of period, but then that would force me to re-write everything to be consistent with that change. I would only do that when it goes into a book.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-57702790852393083712020-01-17T23:01:19.403-05:002020-01-17T23:01:19.403-05:00I think this is a great post, an important one for...I think this is a great post, an important one for MMT. The problem is that I remain unconvinced that the notation is consistent throughout.<br /><br />Could we try this:<br /><br />You write "Since the currency is created at time 0, we know that M(0)=0.."<br /><br />I would record a value of zero at position 0 on our time scale.<br /><br />Having recorded 0, money is introduced and variables Qg(x), Pg(x), M(x) and T(x) begin to play out. <i> How do we notate the variables that we record next on our time scale? </i><br /><br />My follow-up question would be if the same system is used consistently throughout the post?Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-13027528190094499362020-01-17T17:27:42.350-05:002020-01-17T17:27:42.350-05:00This comment has been removed by the author.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-23752246171208505472020-01-17T14:54:08.180-05:002020-01-17T14:54:08.180-05:00Look at a data release for monthly data. There are...Look at a data release for monthly data. There are values for months. There are no intermediate time points. A discrete time model determines relationships between such data.<br /><br />The government sets a price and tax for the month. The supplied goods (Q) will be offered during the month, but there is nothing in the model which tells us exactly when. All we know is the final total of the monthly flow.<br /><br />If the government changed the price during the month, the value of P would reflect the weighted average for the month, so that the accounting will work.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-90498298559298163442020-01-17T12:59:21.790-05:002020-01-17T12:59:21.790-05:00"...imagine that t=0 corresponds to January 2..."...imagine that t=0 corresponds to January 2010."<br /><br />The problems come at the transition points which are discrete points, not time-spans. So, using flow Q(0), the value increases systematically during the time span, revealing itself accurately only at the discrete transition point (to become fixed forever).<br /><br />"What is unusual about my notation is that the value used is the value at the beginning of the month, not the end."<br /><br />I would argue that the value for Q(0), M(0), and T(0) is not established until time-span(0) ends (which is the beginning of time-span(1)). <br /><br />Looking at P(0), I would agree that this value could be established by government at the beginning of time-span(0),<br /><br />What if government tries to establish Q(0), M(0) and T(0) by fiat at the beginning of time-span(0)? I think the assumed decision-making role of the private sector would determine the form of the mathematical expression.Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-80489644147181854172020-01-17T06:48:33.987-05:002020-01-17T06:48:33.987-05:00I covered this in http://www.bondeconomics.com/202...I covered this in http://www.bondeconomics.com/2020/01/mmt-primer-moslers-white-paper.html<br /><br />Although they sound similar, FTPL relies on infinite horizon expectations, while this model relies on transactions in the spot market. The FTPL is essentially non-falsifiable, and appears to predict that the price level ought to have big jumps (that do not happen).Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-34738529705067647342020-01-17T06:05:31.574-05:002020-01-17T06:05:31.574-05:00How does your approach in general compare with the...How does your approach in general compare with the Fiscal Theory of the Price Level?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-27678417641107525112020-01-16T19:23:04.183-05:002020-01-16T19:23:04.183-05:00The objective is to find a mathematical statement ...The objective is to find a mathematical statement about the quantity supplied. Leaving M(1) in the equation eliminates our ability to say much about Q. Since P, T are control variables set by the government, the statement Q(0) > T(0)/P(0) gives a relationship defined only by variables under the government’s control.<br /><br />The government gave a sum of money for goods its requisitioned, taxes were imposed, and M is what is left over. The government did not give M(1) or T(0).Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-77147695869066057962020-01-16T19:17:12.380-05:002020-01-16T19:17:12.380-05:00This is discrete time. From a mathematical standpo...This is discrete time. From a mathematical standpoint, there are no other notions of time. To interpret, imagine that t=0 corresponds to January 2010. The P(0) is assumed to be a fixed price for the month of January, and Q(0) is a flow that happened in that calendar month.<br /><br />What is unusual about my notation is that the value used is the value at the beginning of the month, not the end.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-28498083676541679492020-01-16T17:04:06.817-05:002020-01-16T17:04:06.817-05:00"Since M(1)≥0,
Qg(0)≥T(0)/Pg(0)"
Sorry..."Since M(1)≥0,<br /><br />Qg(0)≥T(0)/Pg(0)"<br /><br />Sorry to keep bugging you, but:<br /><br />Because the time series "Pg(t)Qg(t)−T(t)" is backward looking, at the end of period t=0 it should have the value M(1). You correctly write "M(1)=Pg(0)Qg(0)−T(0)".<br /><br />While M(1) could be zero, I don't think we should leave it out of the equation to come to any conclusion about Qg(0). Therefore, I would rearrange to find<br /><br />(Pg(0))(Qg(0)) = M(1) + T(0).<br /><br />All I gain from this equation is recognition that government has given the private sector a sum of money plus taxes marked paid in exchange for a priced bundle of goods.<br /><br />Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-10468655847676585912020-01-16T15:50:13.416-05:002020-01-16T15:50:13.416-05:00I can accept what you are saying. However:
I wond...I can accept what you are saying. However:<br /><br />I wonder if this is the source of considerable economic math confusion. "Pg(t)Qg(t)−T(t)" is the sum of time series playing out over the interval between points x(t) and x(t+1) <i> OR </i> x(t) and x(t-1). Your notation uses the first choice, which seems to me to be a valid option.<br /><br /><br /><br />Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-30427133992790405762020-01-16T14:34:48.652-05:002020-01-16T14:34:48.652-05:00My notation is standard for discrete-time systems....My notation is standard for discrete-time systems. All time series are defined on the time axis 0,1,2,... <br /><br />Using your notation (which is common), only one series is defined for t=-1, other series are defined on 0,1,2,... One wants to avoid creating special cases in notation. <br /><br />If someone wants to use your notation (it is entirely possible I used that notation in my sfc_models code), all variables need to have a value inserted for t=-1. This can create other problems.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-34480620964050970762020-01-16T14:18:01.766-05:002020-01-16T14:18:01.766-05:00I can't get my mind around your notation. Usin...I can't get my mind around your notation. Using your notation, the time series "Pg(t)Qg(t)−T(t)" becomes known at the same point in time as M(t+1) but carries a different locating time label. We seem to have two time locating systems in one equation.<br /><br />Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-40279383847438772982020-01-16T14:06:54.667-05:002020-01-16T14:06:54.667-05:00Money in this model - M - is only government issue...Money in this model - M - is only government issued money. As discussed in the text, whether other monetary instruments exist is outside the model.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-64415046509552214352020-01-16T13:16:41.643-05:002020-01-16T13:16:41.643-05:00I take your point on the notation. Does the model ...I take your point on the notation. Does the model as defined abstract away from systems with market based or government based credit and money creation? If so what happens when credit is added to the model?Joe Leotehttps://www.blogger.com/profile/01292763300917387201noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-3481717517680695272020-01-16T13:04:34.642-05:002020-01-16T13:04:34.642-05:00If you look at the definitions used, adding privat...If you look at the definitions used, adding private sector monetary instruments has no effect on the equations. (You decided to redefine M to be an end-of-period balance, which causes severe difficulties for notation.)<br /><br />I wrote multiple times that if we add more complicated behaviour to the private sector, more behavioural equations are needed.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-56930613987646912102020-01-16T12:59:14.281-05:002020-01-16T12:59:14.281-05:00I wrote that M refers to beginning of period balan...I wrote that M refers to beginning of period balances. It is done exactly this way to avoid having time series exist at t=-1, which mathematically is not part of the system of equations. Your M refers to the end of period balance, and doing so breaks the notation.Brian Romanchukhttps://www.blogger.com/profile/02699198289421951151noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-60607874607076416982020-01-16T11:24:02.758-05:002020-01-16T11:24:02.758-05:00Define series of discrete time steps with interval...Define series of discrete time steps with interval 1:<br /><br />t = 0,1,2,...,N<br /><br />Specify initial condition:<br /><br />M(0) = 0<br /><br />Change in money supply:<br /><br />M(t) - M(t-1) = Pg(t)Qg(t)-T(t)<br /><br />If the government or private firms issue credit against assets then there is a second market psychology driven mechanism for setting prices in the society. The government would have to choose what price to set as a price floor when the credit system tries to shrink its balance sheet or destroy money. The government would have to regulate the credit system to prevent rampant inflation when certain positive price feedbacks are driven by balance sheet expansion in the private credit markets.Joe Leotehttps://www.blogger.com/profile/01292763300917387201noreply@blogger.comtag:blogger.com,1999:blog-5908830827135060852.post-28907506947325363982020-01-15T21:41:33.517-05:002020-01-15T21:41:33.517-05:00"The accounting identity for the money supply..."The accounting identity for the money supply is:<br />M(t+1)=M(t)+Pg(t)Qg(t)−T(t)."<br /><br />My math is very rusty so my comment may be off-base--but I think this is not quite correct.<br /><br />The money supply held, if any, is incremented by the sum of the two time series recorded in the current time span. Hence, at the end of the current time span, the money supply should be the carry-over from previous period plus current period change.<br /><br />To me, that would result in notation like this:<br /><br />M(t)=M(t-1)+Pg(t)Qg(t)−T(t).<br /><br />If I am correct, the change messes up your later argument because M(t) would exist even in the beginning year.<br /><br />?????Roger Sparkshttps://www.blogger.com/profile/01734503500078064208noreply@blogger.com