The Unnat­ural Rate Of Inter­est (Ultra-Wonk­ish)

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Paul Krugman’s lat­est col­umn—“Check Out Our Low, Low (Nat­ural) Rates” (which he didn’t flag as “Wonk­ish”, even though it is so in spades—noted that the “nat­ural real rate of inter­est” was falling, and that this jus­ti­fied the low inter­est rate set by the Fed­eral Reserve.

And this made me think about Karl Marx.

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About Steve Keen

I am Professor of Economics and Head of Economics, History and Politics at Kingston University London, and a long time critic of conventional economic thought. As well as attacking mainstream thought in Debunking Economics, I am also developing an alternative dynamic approach to economic modelling. The key issue I am tackling here is the prospect for a debt-deflation on the back of the enormous private debts accumulated globally, and our very low rate of inflation.
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  • Bhaskara II

    If you buy that GDP could be related to mone/credit spent. Then I have an answer for you.

    Real GDP is related the the num­ber of work­ers pro­duc­ing it. Unem­ploy­ment is related to the num­ber of work­ers employed. Nom­i­nal GDP is related to real GDP. Thus, if money/credit spent is related to GDP then it is also related to unem­ploy­ment.

    Throw­ing for­mu­las arround: 

    In the­ory the real GDP is directly related to the num­ber of peo­ple employed. Or, the labor pro­duces GDP. Also, paid labor has the money to spend on GDP. So, there is a feed back loop. 

    Y=real GDP
    L= num­ber of work­ers, employed
    Y(t)=a(t) L(t) , actu­ally func­tions over time.
    where the labor pro­duc­tiv­ity, a, a defined quan­tity by the fol­low­ing equiv­a­lent for­mula.

    To me it sounds a lit­tle like cir­cu­lar logic unless the def­i­n­i­tion of labor pro­duc­tiv­ity is stated first. But, if the labor pro­duc­tiv­ity changes more slowly than Y or L, I think Y and L roughly fol­low each other. 

    The labor pro­duc­tiv­ity has a small growth rate often pos­i­tive. Each laborer pro­duces more over time.

    And, data:

    GDP and Labor are so related…

    Real GDP and labor graphs shows excel­lent cor­re­la­tion:

    Labor pro­duc­tiv­ity, a=Y/L:

  • Bhaskara II

    One graph above should have been
    Log Log GDP and Labor:

  • Bhaskara II

    About the break down in sec­tors, I would guess that would take some about a half day to two days to do it the first time.

    You could prob­a­bly get the spend­ing from the Z.1 flow of funds report for sec­tors. You get the series name or code and try to find them in fred graph data. Or, use data down­load pro­gram link to down­load it directly from the flow of funds report and graph them. Or, you could search series in fred graph.

    Flow of funds would not have the employ­ment num­bers. But their series´ might be found in the fred graph site.

    For exam­ple I typed in, busi­ness sec­tor employ­ment. But, it was an index not num­ber of per­sons. Bet­ter to get series names from a report than guess­ing.

  • Tim Ward

    Hi, Bhaskara:

    Sup­pose we have an econ­omy with a large finan­cial sec­tor. And in that finance sec­tor, very large deals are made, high val­ued finan­cial instru­ments and con­tracts are exchanged. Ser­vice fees and com­mis­sions are col­lected for doing the deals. Exchang­ing finan­cial contracts/instruments does not enter into Y, because con­tracts are nei­ther con­sump­tion nor invest­ment, not goods, not ser­vices, nor tan­gi­ble invest­ment. But the ser­vice fees do enter into Y. 

    Also sup­pose large amounts of credit are cre­ated for doing these deals. Thus on trans­ac­tion, incomes and thus sav­ings accrue.

    Since we have a case where large amounts of credit exchange hands, become savings,(and some con­sump­tion) but no tan­gi­ble invest­ment and neg­li­gi­ble con­sump­tion occurs, is it still pos­si­ble that sav­ings = invest­ment? Or does the exis­tence of a large finan­cial sec­tor result in the S=I ‘account­ing iden­tity’ becom­ing no longer an iden­tity?

    In def­i­n­i­tions of invest­ment for GDP, finan­cial instru­ments do not fig­ure.

    Since large amounts of credit/debt are cre­ated, incomes and sav­ings occur in the finance sec­tor, with­out con­sump­tion nor tan­gi­ble invest­ment, it would would seem that sav­ings does not equal invest­ment. Income and sav­ings occur as a result of deals, but no con­sump­tion and no tan­gi­ble invest­ment.

    Is this way off?

  • Bhaskara II

    Tim Ward,

    Right on. Much of text­book macro is quite wrong in my opin­ion.

    I would go one fur­ther and and point out that most large finan­cial cen­ters are doing large inter­na­tional busi­ness with global branches which does not really fit into the domes­tic part of GDP. Maybe that might fit in exports minus imports part, but I don´t know. 

    For­eign­ers for good eth­i­cal rea­sons (micro) do save and invest in other coun­tries. I think that is a pos­i­tive feed back sit­u­a­tion (macro).

    It as a sec­tion on debt related to GDP that pro­fes­sor Keen would like. 

    It, also men­tions other crit­i­cisms of GDP. “Aus­trian the­o­rist Henry Hazlitt argued that aggre­gate demand is a mean­ing­less con­cept in eco­nomic analysis.[8] Friedrich Hayek, another Aus­trian, argued that Keynes’ study of the aggre­gate rela­tions in an econ­omy is fal­la­cious, as reces­sions are caused by micro-eco­nomic factors.[9]”

  • Bhaskara II

    Pro­fes­sor Keen and John­Smith,

    The wiki page for Aggre­gate demand has a sec­tion on the rela­tion­ship with change in debt you might like.

  • Bhaskara II

    John­Smith and Tim Ward,

    Here are some orga­nized data related to some of our dis­cus­sions on GDP. The series can be plot­ted by click­ing on boxes and the add to graph but­ton or the link.*

    Has Invet­ment data:–07-01#heid_14898
    Types of prod­uct–07-01#heid_13323:
    Sec­tors of GDP:–07-01#heid_13417–07-01#heid_13479

    *Release tables were found by call­ing up the gdp graph in fred graph and click­ing on the i reversed cir­cle for infor­ma­tion. A pop up link for gdp is clicked and then look to the left for links to the Release Tables. These are orga­nized and are bet­ter than look­ing at indi­vid­ual series. **

    ** Release tables are on the left for the GDP graph but if you have more than one series on a graph click­ing i is the way to get there.

  • Bhaskara II


    You might be inter­ested in the abstract and con­clu­sion sec­tions of, “Credit and Eco­nomic Recov­ery: Demys­ti­fy­ing Phoenix Mir­a­cles”

  • Bhaskara II

    Tim Ward,


    Gross Sav­ings and Gross Pri­vate Domes­tic Invest­ment data series are very close!*

    *The ques­tions I would what are the defin­tions and is one derived by the other by def­i­n­i­tion? If one is derived by the other than it just says that. If they are indipen­dently near each other than it could be. 

    *I bet there is a deriva­tion some where.

    Large lines are data inter­sted in: Slope 1:1

  • Bhaskara II

    It looks like one is likely to be derived by the other.

    Def­i­n­i­tion of Gross Sav­ings:

    Invest­ment not sav­ings was in the GDP table I saw. So the sav­ings cal­cu­la­tion is likely to give what is under invest­ment in the GDP table.

  • Bhaskara II

    Tim Ward,

    It looks like one is likely to be derived by the other!

    Def­i­n­i­tion of Gross Sav­ings:

    Invest­ment not sav­ings was in the GDP table I saw. So the sav­ings cal­cu­la­tion is likely to give what is under invest­ment in the GDP table.

  • John­Smith

    Very inter­est­ing graphs!
    So the “mar­ginal pro­duc­tiv­ity” 😉 is about 100,000$ per employed per­son (in 2009 $).
    real GDP = 100,000$ * #employed — 2,000,000,000,000$.

    Do you know if this kind of very lin­ear rela­tion­ship also is true in other coun­tries?

  • Bhaskara II


    You are excel­lent at pick­ing out impor­tant num­bers! Now it is near $134K for the US for a 2000 hour year. We should all get a raise. :b

    I think here is your quan­ti­ta­tive answer. One might be able to fid­dle with the options. (I googled some thing like “BIS labor pro­duc­tiv­ity data” or added by coun­try.)
    Above linked from (

    ******** You can use the graph icon to make a line graph, in menu. Then pick the y axis vari­able by click­ing the tri­an­gle on the y axis.

    The­o­ret­i­cal equa­tions often imply, a, as expo­nen­tially grow­ing, beta=a´/a. (This is all in Keens min­sky and Good­win cycle papers.) It would only imply it if beta were con­stant but it is not. Beta is the growth rate of a. They say tech­nol­ogy increases a expo­nen­tially.

    But, a(t)=Y(t)/L(t) is a lin­ear rela­tion­ship. It is a lin­ear rela­tion­ship because, a is a quan­tity by com­put­ing it from Y and L data. This is your answer I think. And the above graph, is the data for other coun­tries.


    a:=Y/L, Def­i­n­i­tion of a
    so Y=aL
    dY/Y aprox = da/a + dL/L

    So da/a is the small space between the dY/Y and dL/L lines in Keen´s graph on page 6 of Keen´s, “Delever­ag­ing with a twist.” So, it is the lesser sig­nif­i­cant term in the equa­tion. But, it aver­ages out as pos­i­tive. That could mean vary­ing expo­nen­tial growth.

  • John­Smith

    Thank you again for all the excel­lent ref­er­ences!
    I was won­der­ing about how tech­no­log­i­cal advances enter the pic­ture. I was guess­ing that tech­nol­ogy should increase the “mar­ginal pro­duc­tiv­ity” of an employee. But in the graphs above one per­sons adds 100,000$ to GDP no mat­ter when he was living/working.
    Is there a neat, plau­si­ble (and not wrong ;)) explaina­tion for it?

  • Tim Ward

    Hi, Bhaskara; thanks, you’re putting a lot of labour into this. Cre­at­ing intel­lec­tual cap­i­tal I hope! 

    The mat­ter of deriva­tions you point out is seems likely to be cen­tral. Gov­ern­ment sta­tis­tics have no way of get­ting at shadow bank­ing. So they have no way of really get­ting at the level of sav­ings occur­ring in the shadow bank­ing sec­tor. So they just ignore it.

    The core activ­i­ties of invest­ment banks are sub­ject to reg­u­la­tion and mon­i­tor­ing by cen­tral banks and other gov­ern­ment insti­tu­tions — but it has been com­mon prac­tice for invest­ment banks to con­duct many of their trans­ac­tions in ways that do not show up on their con­ven­tional bal­ance sheet account­ing and so are not vis­i­ble to reg­u­la­tors or unso­phis­ti­cated investors.” from wikipedia, on shadow bank­ing sys­tem. So offi­cial sav­ings is not the true level of sav­ings.

  • Tim Ward

    And from that arti­cle, quote from Hayek: 

    There can be no doubt that besides the reg­u­lar types of the cir­cu­lat­ing medium, such as coin, notes and bank deposits, which are gen­er­ally recog­nised to be money or cur­rency, and the quan­tity of which is reg­u­lated by some cen­tral author­ity or can at least be imag­ined to be so reg­u­lated, there exist still other forms of media of exchange which occa­sion­ally or per­ma­nently do the ser­vice of money.…

    The char­ac­ter­is­tic pecu­liar­ity of these forms of credit is that they spring up with­out being sub­ject to any cen­tral con­trol, but once they have come into exis­tence their con­vert­ibil­ity into other forms of money must be pos­si­ble if a col­lapse of credit is to be avoided.”

    Min­sky says some­thing about this, in that the Fed winds up con­don­ing Wall St. tricks, ‘inno­va­tion’, when it has to sup­port the val­ues of such things, by buy­ing them, to pre­vent crashes.

  • Bhaskara II

    Minsky´s, “The Finan­cial Insta­bil­ity Hypoth­e­sis” is a good short read of 7 pages.

    “Expec­ta­tions of prof­its depend upon invest­ment in the future, and real­ized prof­its are deter­mined by invest­ment: thus, whether or not lia­bil­i­ties are val­i­dated depends upon invest­ment. Invest­ment
    takes place now because busi­ness­men and their bankers expect
    invest­ment to take place in the future.”

  • Bhaskara II

    The finan­cial insta­bil­ity hypoth­e­sis, there­fore, is a the­ory
    of the impact of debt on sys­tem behav­ior and also incor­po­rates
    the man­ner in which debt is val­i­dated.
    In con­trast to the
    ortho­dox Quan­tity The­ory of money,
    the finan­cial insta­bil­ity
    hypoth­e­sis takes bank­ing seri­ously as a profit-seek­ing activ­ity.”

  • Tim Ward

    Another issue with the Y = C + I +(…) and Y = C + S => S = I idea, besides the above, (that total sales does not include sub­stan­tial sales in the finance sec­tor, thus income and sav­ings are miss­ing) is that; 

    Sav­ings and invest­ment have inde­pen­dent exis­tences. Sav­ings can be wiped by bank­rupt­cies, with­out affect­ing invest­ment. Invest­ment can be wiped out by dis­as­ters, nat­ural or man made, with­out affect­ing sav­ings. Inven­to­ries can go bad, with­out affect­ing sav­ings. Market/nominal val­ues of invest­ments can also change. Write downs of bal­ance sheet quan­ti­ties may occur. So S=I doesn’t apply to all cases. (Of course I could be get­ting the ex post, ex ante ideas con­fused.)

  • Bhaskara II

    Tim Ward, John Smith

    Eeeeww GDP is not even GROSS

    I used to think one of GDP´s prob­lems was it was gross, not net. Of course, there are the aggre­ga­tion prob­lems, but stuff is left out. So, its not not even a bunch of rock (aggre­gate).

    So, this is a prob­lem with using eco­nomic data. If you use it as data the mud is still left on your shoes,

    So, if we look at cor­re­la­tions with GDP or do math­e­mat­i­cal analy­sis might we/I be wast­ing time. Per­haps an other mea­sure is bet­ter?

    I have a ques­tion maybe you or any one might be able to answer. If not don´t spend much time on it because its gross. 

    Where is the per­sonal income tax take in the GDP? GDP seems to have a gross income part and a gross out­put part. I have not been able to find the per­sonal income tax take. I found it in the flow of funds, but I have not seen it acknowl­eged in GDP.

    By the way if the gross income = gross out­put of GDP than I think some how to the com­posers of the data have not acknowl­edged the exis­tance of debt and money print­ing!

  • Tim Ward

    Tax receipts:
    in pdf or excel.

    Not quite sure what you mean, Bhaskara since you know more about this than me.
    If I’ve got this right, it’s the ‘G’ that’s acknowl­edged in the GDP, Y=C+I+G+… as you point out above. So the taxes sim­ply come back into the GDP as gov con­sump­tion.
    Var­i­ous tax receipts are of course sim­ply spent so Y=C+I+G+… So G=tax+deficit {or -(sur­plus)} . And from the data, taxes are sev­eral times the deficit. Cur­rent deficit ~tril­lion­ish.

    For me, the macro for­mu­la­tion is like a zeroth order, ped­a­gog­i­cal device. Use­ful for exam­ple to see that gov sur­pluses means shrink­ing the econ­omy. But not use­ful to tell about such things as what chan­nels are gov spend­ing going into? Pol­icy (spend­ing chan­nels) deter­mine a lot about the char­ac­ter of the econ­omy, and future prospects. And the poli­cies are macro act­ing. So they should be exam­ined. Along with the debt and money cre­ation chan­nels, as you men­tion, for the real econ­omy and the shadow sec­tor and finance. Huge amounts of claims on wealth are cre­ated in the shadow/finance sec­tor that even­tu­ally have to act on the real econ­omy =>debt defla­tion.

  • Tim Ward

    In that post, Prof. Keen points out about the extra debt (and incomes) not in the GDP. The nat­ural or deduc­tive result is that some sav­ings from that are also beyond the sav­ings from the GDP data, Y=C+S.

    So to reform eco­nom­ics, all the data, includ­ing the finance and shadow sec­tors, needs to be put on the table. With­out the bank­ing and the finance sec­tor, eco­nom­ics will always be incom­plete. All that extra debt has to be paid for, it will really only be paid for from the real econ­omy.

  • Postkey

    Bhaskara II Novem­ber 10, 2015 at 3:45 pm

    If you buy that GDP could be related to mone/credit spent. Then I have an answer for you.”

    The answer is that you are con­fus­ing the short run with the long run,

  • nils­de­graaf

    Dear Steve,

    Let me explain why you can’t con­vince lead­ing econ­o­mists, I notice it is a return­ing theme in your arti­cles.

    Hope you know the old the­o­log­i­cal dis­cus­sion of a god who is both almighty and omni­scient. These two don’t go together. Either god knows that I will drink a cup of thea same day next year, or he can kill me next week. As soon as he knows that I am still alive next year he looses the power to kill me in the time in between. So he is either omni­scient or almighty but not both.

    Now we go back to your friends at the Fed and all those other places with pow­er­ful econ­o­mists at the helm. Do they pre­fer to be omni­escient or almighty? You hope the first but I am afraid it is the lat­ter. As a result they can­not face a truth which will vastly restrict their room for manou­vre.

  • Griz­zle

    The high neg­a­tive cor­re­la­tion between pri­vate debt and unem­ploy­ment appears to me to be an arte­fact of what­ever are the dri­vers of a pri­vate debt bub­ble. A pri­vate debt bub­ble is depen­dent on the demand for pri­vate debt (which banks will seek to meet if unre­strained) and as asset val­ues rise at some point exces­sive growth enters as those who can raise pri­vate debt per­ceive an oppor­tu­nity to make super prof­its. A mania devel­ops — a heuris­tic feed­back. does your min­sky model accom­mo­date this?