Paul Krugman, Nick Rowe and an Endogenous Money Model

By Steve Keen

Paul Krugman posted on a familiar topic yesterday—the failure of most inflation hawks to admit that they were wrong—and included praise for one such hawk who has indeed changed his mind and said so:

There’s an interesting contrast with one of the real intellectual heroes here, Narayana Kocherlakota of the Minneapolis Fed, who has actually reconsidered his views in the light of overwhelming evidence. In our political culture, this kind of switch is all too often made into an occasion for gotchas: you used to say that, now you say this. But learning from experience is a good thing, not a sign of weakness. (“A Tale of Two Fed Presidents”)

If this was all there was to the arti­cle, I would have fin­ished the (as usual) enjoy­able read, and moved on to the next link from Twit­ter. But then there was this statement:

Look, some of us came into the cri­sis with a more or less fully formed intel­lec­tual frame­work — extended IS-LM (with endoge­nous money) — and sub­stan­tial empir­i­cal evi­dence from Japan…

Huh? “extended IS-LM (with endoge­nous money)”??? Paul has of course exposited on and pro­moted IS-LM many times in the past. But “with endoge­nous money”? Nor­mally this is some­thing he has derided. In the past, his per­spec­tive has been “IS-LM with Loan­able Funds”, not “with Endoge­nous Money”.

Paul Krugman ISLM endogenous money

Now I could be read­ing too much into this phrase. As Nick Rowe said in the very intel­li­gent and civil dis­cus­sion on his excel­lent post “What Steve Keen is maybe try­ing to say”, the phrase can mean dif­fer­ent things to dif­fer­ent people:

I don’t find the “exoge­nous vs endoge­nous money” dis­tinc­tion help­ful in this con­text, sim­ply because dif­fer­ent peo­ple seem to mean many dif­fer­ent things by that. (Nick Rowe)

Paul could mean some­thing quite dif­fer­ent to what I mean by “endoge­nous money” too, and I could be read­ing far too much into this sin­gle phrase (heck, it could even be a typo!). But if he is shift­ing his posi­tion in the “money and banks don’t mat­ter” and “money and banks are cru­cial” debate, even a lit­tle, that’s some­thing to be applauded in pre­cisely the same man­ner in which he praised Kocher­lakota for mov­ing on infla­tion. And if not—if he meant some­thing entirely dif­fer­ent to the inter­pre­ta­tion I put on that statement—well then doubt­less we’ll find out. We’ll surely get a clar­i­fi­ca­tion in due course.

What­ever that clar­i­fi­ca­tion turns out to be, this unex­pected phrase has moti­vated me to pub­lish, ahead of sched­ule, a model com­par­ing Loan­able Funds to Endoge­nous Money that I promised to pro­vide in the dis­cus­sion on Nick’s blog:

If the lender is a non-bank, then the repay­ment of a debt lets the lender spend because both debt and loan are on the lia­bil­ity side of the bank­ing system’s ledger; but if the lender is a bank, then the repay­ment of the loan takes money out of cir­cu­la­tion (I pre­fer that expres­sion to “destroys money”) because the debt is on the asset side of the ledger. That’s the essen­tial dif­fer­ence between Loan­able Funds & Endoge­nous Money, which I’m try­ing to illus­trate in a pair of very sim­ple mod­els that I’ll post on my blog shortly—and link to Nick’s dis­cus­sion here. (A com­ment by me on Nick Rowe’s post)

I have since devel­oped that pair of mod­els; there’s much more analy­sis needed before I’m will­ing to pub­lish an aca­d­e­mic paper on the topic, but here’s what I think is the sim­plest pos­si­ble model con­trast­ing Loan­able Funds—in which banks, money and (except dur­ing a liq­uid­ity trap) pri­vate debt don’t mat­ter to macroeconomics—and Endoge­nous Money—in which banks, debt and money are cru­cial to macro­eco­nom­ics at all times.

A mon­e­tary model of Loan­able Funds

My start­ing point is Krugman’s descrip­tion of the essence of lend­ing as being a trans­fer between Patient and Impa­tient agents:

Think of it this way: when debt is ris­ing, it’s not the econ­omy as a whole bor­row­ing more money. It is, rather, a case of less patient people—people who for what­ever rea­son want to spend sooner rather than later—borrowing from more patient peo­ple. (Paul Krug­man, 2012, pp. 146–47. Empha­sis added)

In the New Key­ne­sian model of a liq­uid­ity trap that he and Eggerts­son devel­oped (Gauti B. Eggerts­son and Paul Krug­man, 2012), lend­ing was for the pur­poses of con­sump­tion, and while there was debt, there were nei­ther banks nor money:

We assume ini­tially that bor­row­ing and lend­ing take the form of risk-free bonds denom­i­nated in the con­sump­tion good. (Gauti B. Eggerts­son and Paul Krug­man, 2012, p. 1474)

My model of Loan­able Funds embeds this vision of lend­ing as being a trans­fer from Patient to Impa­tient agents in a mon­e­tary model of the economy—one in which all trans­ac­tions involve the trans­fer of money in bank accounts—and one in which “Patient agents” and “Impa­tient agents” are both cap­i­tal­ists, who need money to hire work­ers and also buy inputs from each other. Though the bank­ing sec­tor exists in this model it is entirely pas­sive: it is just where “Patient agents” deposit their cash, and lend­ing is seen as a trans­fer from the deposit accounts of the Patient agents to the deposit accounts of the Impa­tient agents.

I also treat lend­ing as being pri­mar­ily for pro­duc­tion rather than con­sump­tion. Both Patient and Impa­tient agents are cap­i­tal­ists who need money to hire work­ers and buy inputs for pro­duc­tion (as well as for con­sump­tion) from each other. The basic finan­cial oper­a­tions are:

  • An ini­tial deposit of 90 by the Patient agents and loan to the Impa­tient agents of 10, both of which are stored in bank accounts;
  • Lend­ing by the Patient Agents to the Impa­tient Agents;
  • Pay­ment of interest;
  • Repay­ment of the debt;
  • Hir­ing of work­ers by both groups of agents;
  • Con­sump­tion by all agents from both Patient and Impatient.

The oper­a­tions are shown below in Table 1, fol­low­ing the con­ven­tions in the Min­sky pro­gram that assets are shown as pos­i­tives, lia­bil­i­ties and equity are shown as neg­a­tives, the source of any flow is a pos­i­tive and its des­ti­na­tion is a neg­a­tive: these con­ven­tions ensure that all rows have to sum to zero to be cor­rect in account­ing terms (the pro­gram also sup­ports the account­ing approach of using DR and CR).

Financial transaction in Loanable Funds


Loans them­selves don’t turn up on the bank­ing sector’s ledger because they are trans­fers between the Patient and Impa­tient agents. Instead loans are assets of the Patient agents and a lia­bil­i­ties of the Impa­tient agents. Table 2 shows Loans from the Patient agents’ per­spec­tive, while Table 3 shows the same oper­a­tions from the Impa­tient agents’ perspective.

Lending, reayment and interest from patient agent's perspective

Lending, reayment and interest from impatient agent's perspective

The Min­sky pro­gram (click here for the lat­est beta build) is pri­mar­ily designed for numer­i­cal simulation—and I’ll get to that shortly—but it also gen­er­ates the dynamic equa­tions in the model, and they are instruc­tive enough for those who don’t suf­fer the MEGO effect (“My Eyes Glaze Over”) when look­ing at equa­tions (if you do, skip most of this and just check the sim­u­la­tions below). The equa­tions of motion of the key accounts in this model (click here to down­load the model) are shown in Equa­tion . The first four equa­tions describe the dynam­ics of money in this model; the last equa­tion describes the dynam­ics of debt.

ISLM with endoenous money 2

The key points from these equa­tions are:

  • The total amount of money in the sys­tem is the sum of the four accounts Impa­tient, Patient, Work­ers and NWBank (for “Net Worth of the Bank­ing sec­tor”, which is zero in this model), and this doesn’t change: the sum of the first 4 equa­tions is zero:

ISLM with endoenous money 3

  • The total amount of money in the firm sec­tor is the sum of the first two accounts—Patient and Impatient—and the annual turnover of this amount is the annual GDP of this model. It is unaf­fected by lend­ing, repay­ment and debt ser­vice, so GDP is also unaf­fected by lend­ing, repay­ment and debt service:

ISLM with endoenous money 4

  • Finally, the dynam­ics of debt in this model are

ISLM with endoenous money 5

This struc­ture means that, no mat­ter what behav­ioral rela­tions are used to model lend­ing, repay­ment, con­sump­tion, etc., changes in the level of debt have no impact on the macro­econ­omy. This is con­firmed by the rela­tions I used to sim­u­late this model, which used sim­ple time con­stants to spec­ify all flows. In Fig­ure 1 I ran the model with a time con­stant of 7 years for lend­ing and 9 years for repay­ment until the debt to GDP ratio sta­bi­lized at 0.24 (which took about 60 years), and then altered time constants—firstly sim­u­lat­ing a slump in lend­ing, then a boom, and finally a return to the ini­tial rates. The level of debt and the debt to GDP ratio var­ied dra­mat­i­cally, but GDP sailed on undisturbed. So if Loan­able Funds accu­rately char­ac­ter­ized actual lend­ing, banks, money and (except dur­ing a liq­uid­ity trap) debt would indeed by irrel­e­vant to macre­oe­co­nom­ics.

Fig­ure 1: Sim­u­la­tion of Loan­able Funds

ISLM with endoenous money

Endoge­nous Money pro­po­nents, on the other hand, insist that most lend­ing is not between non-banks, but from banks to non-banks, and that this makes all the dif­fer­ence in the world. That is eas­ily illus­trated by mak­ing just 3 sim­ple changes to this model:

  • Lend­ing is shown as being a flow from Banks to Impa­tient Agents;
  • Inter­est pay­ments go not from Impa­tient to Patient but from Patient to the NWBank; and
  • When the model is sim­u­lated, lend­ing is related to the cur­rent level of lend­ing rather than to the amount of money in the Patient Agents’ accounts.

So what dif­fer­ence did these sim­ple struc­tural changes make? A lot.

A mon­e­tary model of Endoge­nous Money

The mon­e­tary sys­tem from the bank­ing sector’s point of view is shown in Table 4: Loans are now an asset of the bank­ing sec­tor, while lend­ing, repay­ment and debt ser­vice are all rela­tions between the Impa­tient agents and the bank­ing sec­tor. The dif­fer­ences of this model with Loan­able Funds are high­lighted in bold in the Table (click here to down­load the model).

Financial transaction in Endogenous Money

The equa­tions of motion of this sys­tem are:

ISLM with endoenous money 7

There are three sig­nif­i­cant ways in which this model dif­fers from Loan­able Funds:

  • The total amount of money in the sys­tem is, as before, the sum of the four accounts Impa­tient, Patient, Work­ers and NWBank (for “Net Worth of the Bank­ing sec­tor”, which is not zero in this model), and this now is altered by the change in debt:

ISLM with endoenous money 8

  • The total amount of money in the firm sec­tor is the sum of the first two accounts—Patient and Impatient—and the annual turnover of this amount is the annual GDP of this model. It is also altered by lend­ing, repay­ment and debt ser­vice, and there­fore so is GDP:

ISLM with endoenous money 9

  • Finally, the dynam­ics of debt in this model are the same as in Loan­able Funds, but now this is also iden­ti­cal to the dynam­ics of the money supply:

ISLM with endoenous money 10

I sim­u­lated the model for 250 years with con­stant para­me­ters (it took that long for the debt to GDP ratio to sta­bi­lize at 0.32), and then repeated the exper­i­ment of a slump in lend­ing fol­lowed by a boom and then a return to nor­mal­ity. The results in Fig­ure 2 shows how dif­fer­ent an Endoge­nous Money view of the world is to Loan­able Funds.

Firstly, in Endoge­nous money, the growth of debt is not macro­eco­nom­i­cally neuteal but causes GDP to grow: rather than the change in debt being irrel­e­vant to the macro­econ­omy as in Loan­able Funds, in Endoge­nous Money it alters the level of demand. Sec­ondly, alter­ations in the rate of change of debt had dras­tic effects on the econ­omy: a decline in lend­ing caused a slump and an increase in lend­ing caused a boom.

Fig­ure 2: Sim­u­la­tion of Endoge­nous Money

ISLM with endoenous money 11

IS-LM and Endoge­nous Money?

If—and it’s a big if—this phrase sig­ni­fies a shift in how Krug­man mod­els IS-LM, then it will surely mean some­thing very dif­fer­ent to what I’ve shown above. For starters, it’s likely to be an equi­lib­rium model, when as Nick Rowe rightly con­cluded, my story is a dis­e­qui­lib­rium one (some­thing that Hicks argued long ago can’t be done with IS-LM—see (John Hicks, 1981)):

We are talk­ing about a Hayekian process in which indi­vid­u­als’ plans and expec­ta­tions are mutu­ally incon­sis­tent in aggre­gate. We are talk­ing about a dis­e­qui­lib­rium process in which people’s plans and expec­ta­tions get revised in the light of the sur­prises that occur because of that mutual incon­sis­tency. (Nick Rowe)

Of course, it could sig­nify no more than a rebadg­ing of Krugman’s estab­lished approach—or even a typo. We’ll have to await an elab­o­ra­tion. But I do hope that it does sig­nify a fur­ther thaw­ing in the rela­tions between ortho­dox econ­o­mists and those from the non-orthodox end of the spec­trum after Nick Lowe’s recent contribution.

Nick’s post—a reminder

As I acknowl­edged in “An out­break of com­mu­ni­ca­tion”, Nick’s post accu­rately stated my argu­ments on the cre­ation of aggre­gate (or effec­tive) demand via the cre­ation of money by loans from the bank­ing sys­tem to the public:

So with that very big caveat under­stood, here’s what I think Steve Keen is maybe try­ing to say:

Aggre­gate planned nom­i­nal expen­di­ture equals aggre­gate expected nom­i­nal income plus amount of new money cre­ated by the bank­ing sys­tem minus increase in the stock of money demanded. (All four terms in that equa­tion have the units dol­lars per month, and all are refer­ring to the same month, or what­ever.)

And let’s assume that peo­ple actu­ally realise their planned expen­di­tures, which is a rea­son­able assump­tion for an econ­omy where goods and pro­duc­tive resources are in excess sup­ply, so that aggre­gate planned nom­i­nal expen­di­ture equals aggre­gate actual nom­i­nal expen­di­ture. And let’s recog­nise that aggre­gate actual nom­i­nal expen­di­ture is the same as actual nom­i­nal income, by account­ing iden­tity. So the orig­i­nal equa­tion now becomes:

Aggre­gate actual nom­i­nal income equals aggre­gate expected nom­i­nal income plus amount of new money cre­ated by the bank­ing sys­tem minus increase in the stock of money demanded.

Noth­ing in the above vio­lates any national income account­ing iden­tity. (Nick Rowe)

This is, from my per­spec­tive, the essence of the sig­nif­i­cance of Endoge­nous Money. If this wasn’t true—if the cre­ation of new money by the bank­ing sys­tem didn’t some­how impact on actual income and demand—then by Occam’s Razor, there would be no macro­eco­nomic sig­nif­i­cance to Endoge­nous Money, and we’d be bet­ter off ignor­ing the bank­ing sec­tor in macro­eco­nom­ics, as the model of Loan­able Funds does. Nick pro­vided an excel­lent ver­bal state­ment of this—and a log­i­cal argu­ment behind it which I think any econ­o­mist should be able to fol­low, regard­less of his/her school of thought:

Start with aggre­gate planned and actual and expected income and expen­di­ture all equal. Now sup­pose that some­thing changes, and every indi­vid­ual plans to bor­row an extra $100 from the bank­ing sys­tem and spend that extra $100 dur­ing the com­ing month. He does not plan to hold that extra $100 in his chequing account at the end of the month (the quan­tity of money demanded is unchanged, in other words). And sup­pose that the bank­ing sys­tem lends an extra $100 to every indi­vid­ual and does this by cre­at­ing $100 more money. The indi­vid­u­als are bor­row­ing $100 because they plan to spend $100 more than they expect to earn dur­ing the com­ing month.

Now if the aver­age indi­vid­ual knew that every other indi­vid­ual was also plan­ning to bor­row and spend an extra $100, and could put two and two together and fig­ure out that this would mean his own income would rise by $100, he would imme­di­ately revise his plans on how much to bor­row and spend. Under full infor­ma­tion and fully ratio­nal expec­ta­tions we couldn’t have aggre­gate planned expen­di­ture dif­fer­ent from aggre­gate expected income for the same com­ing month.

But maybe the aver­age indi­vid­ual does not know that every other indi­vid­ual is doing the same thing. Or maybe he does know this, but thinks their extra expen­di­ture will increase some­one else’s income and not his. Aggre­gate expected income, which is what we are talk­ing about here, is not the same as expected aggre­gate income. The first aggre­gates across indi­vid­u­als’ expec­ta­tions of their own incomes; the sec­ond is (someone’s) expec­ta­tion of aggre­gate income. It would be per­fectly pos­si­ble to build a model in which indi­vid­u­als face a Lucasian signal-processing prob­lem and can­not dis­tin­guish aggregate/nominal from individual-specific/real shocks.

So at the end of the month the aver­age indi­vid­ual is sur­prised to dis­cover that his income was $100 more than he expected it to be, and that he has $100 more in his chequing account than he expected to have and planned to have. This means the actual quan­tity of money is $100 greater than the quan­tity of money demanded. And next month he will revise his plans and expec­ta­tions because of this sur­prise. How he revises his plans and expec­ta­tions will depend on whether he thinks this is a tem­po­rary or a per­ma­nent shock, which has its own signal-processing prob­lem. And these revised plans may cre­ate more sur­prises the fol­low­ing month. (Nick Rowe)


Eggerts­son, Gauti B. and Paul Krug­man. 2012. “Debt, Delever­ag­ing, and the Liq­uid­ity Trap: A Fisher-Minsky-Koo Approach.” Quar­terly Jour­nal of Eco­nom­ics, 127, 1469–513.

Hicks, John. 1981. “Is-Lm: An Expla­na­tion.” Jour­nal of Post Key­ne­sian Eco­nom­ics, 3(2), 139–54.

Krug­man, Paul. 2012. End This Depres­sion Now! New York: W.W. Norton.

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