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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”.

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).

Table 1: Finan­cial trans­ac­tion in Loan­able Funds on bank­ing sys­tem’s ledger

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.

Table 2: Lend­ing, repay­ment and inter­est from the Patient agents’ per­spec­tive

Table 3: Lend­ing, repay­ment and inter­est from the Impa­tient agents’ 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.

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 NW_Bank (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:

• 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:

• Final­ly, the dynam­ics of debt in this mod­el are

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

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 NW_Bank; 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).

Table 4: Finan­cial trans­ac­tion in Endoge­nous Mon­ey on bank­ing sys­tem’s ledger

The equa­tions of motion of this sys­tem are:

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 NW_Bank (for “Net Worth of the Bank­ing sec­tor”, which is not zero in this mod­el), and this now is altered by the change in debt:

• 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:

• 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:

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

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.