Modeling Financial Instability

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This paper will be pub­lished in a forth­com­ing book on the cri­sis edit­ed by Malliaris, Shaw and She­frin. In what fol­lows, I derive a cor­rect­ed for­mu­la for the role of the change in debt in aggre­gate demand, which is that ex-post aggre­gate demand equals ex-ante income plus the cir­cu­la­tion of new debt, where the lat­ter term is the veloc­i­ty of mon­ey times the ex-post cre­ation of new debt.

The PDF is avail­able here: Keen2014ModelingFinancialInstability. The Min­sky mod­els used in this paper are here in a ZIP file. The lat­est ver­sion of Min­sky can be down­loaded from here.

  • Introduction

Lit­er­al­ly no-one dis­putes that the finan­cial sec­tor was the cause of the post-2007 eco­nom­ic cri­sis: dis­pu­ta­tion instead cen­ters on the causal mech­a­nisms. I fol­low Fish­er (Fish­er 1933) and Min­sky (Min­sky 1980) in assign­ing key roles to the growth and con­trac­tion of aggre­gate pri­vate debt (Keen 1995; Keen 2000), but this per­spec­tive is reject­ed by New Key­ne­sian econ­o­mists on the a pri­ori basis that pri­vate debts are “pure redis­tri­b­u­tions” that “should have no sig­nif­i­cant macro-eco­nom­ic effects” (Bernanke 2000p. 24), and as a corol­lary to the oft-repeat­ed tru­ism that “one per­son­’s debt is anoth­er per­son­’s asset” (Krug­man 2012c, p. 43).

My analy­sis also fol­lows the Post Key­ne­sian tra­di­tion of endoge­nous mon­ey (Moore 1979; Moore 1983) in see­ing the bank­ing sec­tor as an essen­tial com­po­nent of the macro­econ­o­my, yet this is also dis­missed by New Key­ne­sian econ­o­mists on the grounds that banks are mere­ly a spe­cial­ized form of finan­cial inter­me­di­ary (Krug­man 2012a; Krug­man 2012b; Krug­man 2013a; Sum­n­er 2013; Tobin 1963), all of which can be safe­ly ignored in macro­eco­nom­ic mod­els. When banks are intro­duced in New Key­ne­sian mod­els, they func­tion not as loan orig­i­na­tors but effec­tive­ly as bro­kers between savers and bor­row­ers (Eggerts­son and Krug­man 2012b, pp. 21–22).

In response, authors in the Post Key­ne­sian and Endoge­nous Mon­ey tra­di­tions express exas­per­a­tion that New Key­ne­sian authors ignore cred­it cre­ation and the account­ing mechan­ics of bank lend­ing (Full­wiler 2012; Roche 2013), as laid out in numer­ous Cen­tral Bank pub­li­ca­tions (Car­pen­ter and Demi­ralp 2010; ECB 2012; Holmes 1969; Keis­ter and McAn­drews 2009).

Giv­en the key pub­lic pol­i­cy role of eco­nom­ics, and the acknowl­edged fail­ure of Neo­clas­si­cal mod­els in gen­er­al to antic­i­pate the finan­cial cri­sis (Beze­mer 2009; Blan­chard 2009; Blan­chard, et al. 2010; OECD 2007), the exis­tence with­in aca­d­e­m­ic eco­nom­ics of two dia­met­ri­cal­ly opposed per­spec­tives which fail to com­mu­ni­cate is a dis­ser­vice to the pub­lic.

In this paper I attempt to con­clu­sive­ly deter­mine whether aggre­gate pri­vate debt and banks mat­ter in macro­eco­nom­ics by putting the two rival mod­els of lending—Loanable Funds and Endoge­nous Money—on a com­mon foot­ing. Using the dynam­ic Open Source mon­e­tary mod­el­ing pro­gram Min­sky, I first­ly put the New Key­ne­sian mod­el of bank­ing in Eggerts­son & Krug­man 2012b into a strict­ly mon­e­tary mod­el and I show that, if the struc­ture of lend­ing in this mod­el accu­rate­ly char­ac­ter­izes actu­al lend­ing, then the Neo­clas­si­cal per­spec­tive that aggre­gate debt is unim­por­tant, and that banks can safe­ly be ignored in macro­eco­nom­ics, is cor­rect. I then mod­i­fy this mod­el to match the Post Key­ne­sian per­spec­tive on the struc­ture of lend­ing, and show that in this struc­ture, changes in the aggre­gate lev­el of pri­vate debt have a direct impact upon aggre­gate demand, and banks there­fore play a cru­cial role in macro­eco­nom­ics.

  1. Loanable Funds vs Endogenous Money

The Neo­clas­si­cal mod­el of “Loan­able Funds” and the Post Key­ne­sian con­cept of “Endoge­nous Mon­ey” con­sti­tute the polar oppo­sites on the nature and sig­nif­i­cance of banks, debt and mon­ey in macro­eco­nom­ics. Both mod­els por­tray the mon­ey sup­ply as vari­able, and hence in one sense endoge­nous, though by very dif­fer­ent mech­a­nisms and to very dif­fer­ent degrees (Pal­ley 2013, p. 411). In the Loan­able Funds tra­di­tion, banks func­tion as “mere inter­me­di­aries” (Graziani 1989, p. 8) between savers and bor­row­ers, pri­vate debts are “pure redis­tri­b­u­tions” that “should have no sig­nif­i­cant macro-eco­nom­ic effects” (Bernanke 2000, p. 24), and banks, debt and mon­ey can be and are ignored in canon­i­cal macro­eco­nom­ic mod­els (Smets and Wouters 2007; Wood­ford 2009). In the Endoge­nous Mon­ey tra­di­tion, banks are cru­cial to macro­eco­nom­ics because they cre­ate mon­ey by cre­at­ing debt (Holmes 1969; Moore 1979), but no con­sen­sus has yet emerged on how to rep­re­sent this phe­nom­e­non in Post Key­ne­sian macro­eco­nom­ic mod­els (Pal­ley 1991; Pal­ley 2002).

There is lit­tle com­mu­ni­ca­tion between the two approach­es, with authors in the Loan­able Funds tra­di­tion fre­quent­ly derid­ing those in the Endoge­nous Mon­ey camp (Krug­man 2012a; Krug­man 2012b; Krug­man 2012e; Krug­man 2012f), and dis­miss­ing the propo­si­tion that banks must be includ­ed in macro­eco­nom­ics (Krug­man 2012a; Krug­man 2012b; Krug­man 2012d; but see Rowe 2013; Sum­n­er 2013).

This dis­pute can be resolved by an appeal to the Occam’s Razor prin­ci­ple that unless a more com­plex mod­el makes dif­fer­ent and bet­ter pre­dic­tions than a less com­plex one, the sim­pler should be pre­ferred. There­fore, unless bank lend­ing nec­es­sar­i­ly affects vital macro­eco­nom­ic aggre­gates in a sig­nif­i­cant man­ner, then even though the “loans cre­ate deposits” account­ing per­spec­tive of Endoge­nous Mon­ey is tech­ni­cal­ly cor­rect (Car­ney 2012; ECB 2012; Holmes 1969)—as even Paul Krug­man has con­ced­ed (Krug­man 2013a)— the Loan­able Funds approach is jus­ti­fied, and banks should be exclud­ed from macro­eco­nom­ics. Con­verse­ly, if bank lend­ing nec­es­sar­i­ly affects macro­eco­nom­ic aggre­gates, then banks, debt and the endo­gene­ity of the mon­ey sup­ply are inte­gral to macro­eco­nom­ics, and mod­els that exclude them are not mod­els of a cap­i­tal­ist econ­o­my.

  1. A monetary model of Loanable Funds

Eggerts­son and Krug­man note that the vast major­i­ty of main­stream eco­nom­ic mod­els ignore debt:

If there is a sin­gle word that appears most fre­quent­ly in dis­cus­sions of the eco­nom­ic prob­lems now afflict­ing both the Unit­ed States and Europe, that word is sure­ly debt… one might have expect­ed debt to be at the heart of most main­stream macro­eco­nom­ic models—especially the analy­sis of mon­e­tary and fis­cal pol­i­cy. Per­haps some­what sur­pris­ing­ly, how­ev­er, it is quite com­mon to abstract alto­geth­er from this fea­ture of the econ­o­my. Even econ­o­mists try­ing to ana­lyze the prob­lems of mon­e­tary and fis­cal pol­i­cy at the zero low­er bound—and yes, that includes the present authors (see Krug­man 1998, Eggerts­son and Wood­ford 2003)—have often adopt­ed rep­re­sen­ta­tive agent mod­els in which every­one is alike and the shock that push­es the econ­o­my into a sit­u­a­tion in which even a zero inter­est rate is not low enough takes the form of a shift in every­one’s pref­er­ences. (Eggerts­son and Krug­man 2012a, pp. 1469–71)

In order to intro­duce debt into a New Key­ne­sian two-peri­od mod­el, Eggerts­son and Krug­man divid­ed agents into two groups who “dif­fer only in their rates of time pref­er­ence”: “patient agents” and “impa­tient agents” where the lat­ter have a high­er rate of time pref­er­ence than the for­mer, so that “In that case, ”impa­tient” indi­vid­u­als will bor­row from ”patient” indi­vid­u­als.” (Eggerts­son and Krug­man 2012ap. 1474). Debt was explic­it­ly mod­eled through­out this paper, and bank­ing was intro­duced in the Appen­dix (Eggerts­son and Krug­man 2012b) as an inter­me­di­at­ing func­tion between depos­i­tors and bor­row­ers, where bor­row­ing by impa­tient agents was strict­ly for invest­ment.

The authors describe their mod­el as a “just the stan­dard New Key­ne­sian mod­el”, with one twist, in that the nat­ur­al rate of inter­est, which is nor­mal­ly an exoge­nous para­me­ter in the IS equa­tion, is instead endoge­nous with bor­row­ers’ debt being one of its para­me­ters. There­fore the lev­el of pri­vate debt plays a macro­eco­nom­ic role:

we need to fig­ure out the evo­lu­tion of debt of the “bor­row­ers” to fig­ure out the nat­ur­al rate of inter­est. In par­tic­u­lar we see that if … the econ­o­my is “over­lever­aged” … it is easy to get endoge­nous­ly neg­a­tive nat­ur­al rate of inter­est. (Eggerts­son and Krug­man 2012b, p. 24)

The New Key­ne­sian and “Liq­uid­i­ty Trap” aspects of this mod­el (on which see Solow 2003; Solow 2008) are tan­gen­tial to the top­ic of this paper, which is a strict­ly struc­tur­al one: does bank lending—as opposed to lend­ing by non-bank agents to each other—significantly alter the macro­dy­nam­ics of the econ­o­my? To con­sid­er this ques­tion, I ren­der the Loan­able Funds aspects of Eggerts­son and Krug­man 2012b in a strict­ly mon­e­tary form in a Min­sky mod­el.

Min­sky is a sys­tem dynam­ics pro­gram which gen­er­ates dynam­ic mod­els of finan­cial flows from dou­ble-entry book­keep­ing tables (called “God­ley Tables” in the pro­gram), in which the columns rep­re­sent bank accounts and the rows are trans­ac­tions between accounts. The sam­ple mod­el shown in Fig­ure 1 gen­er­ates the dynam­ic equa­tions shown in Equa­tion (more details on Min­sky are giv­en in the Appen­dix).

Fig­ure 1: Sam­ple God­ley Table and bank­ing icon in Min­sky

The Loan­able Funds fea­tures of Eggerts­son and Krug­man (2012b) are:

  • that deposits by the “patient agents” enable loans to “impa­tient agents”; and
  • that banks inter­me­di­ate between saver and bor­row­er and prof­it by an inter­me­di­a­tion fee, but oth­er­wise play no role in lend­ing.

The Min­sky mod­el shown in Fig­ure 2 repli­cates these fea­tures using the bank accounts of four sep­a­rate enti­ties: the con­sump­tion goods sec­tor (with deposit account DepCons) which is the lender in (Eggerts­son and Krug­man 2012b); the invest­ment goods sec­tor (with account DepInv) which is the bor­row­er; Work­ers (with account Work­ers) who are employed by both the Con­sump­tion Sec­tor and the Invest­ment Sec­tor; and
the Bank­ing sec­tor (with the Asset account Reserves and equi­ty account BankersNW) which inter­me­di­ates the loans from
the Con­sump­tion Sec­tor to the Invest­ment Sec­tor, and charges a fee for doing so. Each sec­tor main­tains a finan­cial table show­ing the flows into and out of its accounts, and cal­cu­lates its net worth as a result as the dif­fer­ence between the val­ue of its assets and lia­bil­i­ties (account BankersNW for the bank­ing sec­tor).

Fig­ure 2: Loan­able Funds model—a 4 account view of Loan­able Funds gen­er­at­ed in Min­sky

Table 1 shows this finan­cial sys­tem from the bank­ing sec­tor’s per­spec­tive, and Table 2 shows it from the per­spec­tive of the lender, the Con­sump­tion Sec­tor. Fol­low­ing the con­ven­tions in Min­sky, assets are shown as pos­i­tive amounts, and lia­bil­i­ties and equi­ty are shown as neg­a­tives, while the source of any finan­cial trans­ac­tion is shown as a pos­i­tive and its des­ti­na­tion as a neg­a­tive. All entries in the table rep­re­sent flows, and Min­sky auto­mat­i­cal­ly gen­er­ates the result­ing sys­tem of dif­fer­en­tial equa­tions in LaTeX. The ten flows that define the mod­el are all shown in the bank­ing sec­tor’s table, and are respec­tive­ly:

  1. The Con­sump­tion Sec­tor lends to the Invest­ment Sec­tor via the flow “Lend” from the account DepCons to the account DepInv;
  2. The Invest­ment sec­tor makes Inter­est pay­ments “Int” to the con­sump­tion sec­tor;
  3. The Bank­ing Sec­tor charges the Con­sump­tion Sec­tor an inter­me­di­a­tion fee “IntFee”;
  4. The invest­ment Sec­tor makes debt repay­ments to the Con­sump­tion Sec­tor (“Repay”);
  5. The Con­sump­tion Sec­tor hires Work­ers via the flow “WagesC”;
  6. The invest­ment Sec­tor hires Work­ers via the flow “WagesI”;
  7. The Invest­ment Sec­tor pur­chas­es con­sump­tion goods (“ConsI”);
  8. The Con­sump­tion Sec­tor pur­chas­es invest­ment goods (“ConsC”);
  9. Work­ers pur­chase con­sumer goods (“ConsW”); and
  10. Bankers pur­chase con­sumer goods (“ConsB”);

Table 1: Loan­able Funds mod­el from the Bank­ing Sec­tor’s per­spec­tive

Bank­ing Sec­tor




Flows Accounts Reserves DepCons DepInv Work­ers BankersNW
1 Lend­ing Lend -Lend
2 Inter­est Pay­ments -Int Int
3 Bank Inter­me­di­a­tion Fee IntFee -IntFee
4 Debt Repay­ment -Repay Repay
5 Hire work­ers (Cons) WagesC -WagesC
6 Hire work­ers (Inv) WagesI -WagesI
7 Inter­sec­toral pur­chas­es by Inv -ConsI ConsI
8 Inter­sec­toral pur­chas­es by Cons ConsC -ConsC
9 Work­ers con­sump­tion -ConsW ConsW
10 Bankers con­sump­tion -ConsB ConsB


Lend­ing from the con­sump­tion to the invest­ment sec­tor is record­ed in the account Loans, which is an asset of the con­sump­tion sec­tor as shown in its finan­cial account (see Table 2; it also appears as a lia­bil­i­ty of the Invest­ment Sec­tor in its table of accounts; Table 2 also dis­plays the dynam­ics of the Con­sump­tion Sec­tor’s net worth in the col­umn “ConsNW”).

Table 2: Loan­able Funds mod­el from the Con­sump­tion Sec­tor’s per­spec­tive

Con­sump­tion Sec­tor Assets Equi­ty
Flows Accounts DepCons Loans ConsNW
1 Lend­ing -Lend Lend
2 Inter­est Pay­ments Int -Int
3 Bank Inter­me­di­a­tion Fee -IntFee IntFee
4 Debt Repay­ment Repay -Repay
5 Hire work­ers (Cons) -WagesC WagesC
6 Inter­sec­toral pur­chas­es by Inv ConsI -ConsI
7 Inter­sec­toral pur­chas­es by Cons -ConsC ConsC
8 Work­ers con­sump­tion ConsW -ConsW
9 Bankers con­sump­tion ConsB -ConsB


Since (for the sake of sim­plic­i­ty) hold­ings of cash are ignored in this mod­el, mon­ey is the sum of the amounts in the four deposit accounts DepCons, DepInv, Work­ers, and BankersNW shown in Table 1, while debt is the amount in the account Loans shown in Table 2. Equa­tion shows the equa­tions for the dynam­ics of mon­ey and debt in the mod­el, with the first 4 equa­tions derived from Table 1 show­ing the dynam­ics of mon­ey in the sys­tem while the final equa­tion, derived from Table 2, shows the dynam­ics of debt.

Defin­ing mon­ey M as the sum of the first four accounts, it is obvi­ous that the change in the amount of mon­ey is zero:

There­fore the amount of money—which for con­ve­nience we can treat this as hav­ing been cre­at­ed by gov­ern­ment fiat, with­out need­ing to spec­i­fy a gov­ern­ment sec­tor in the model—remains con­stant:

With­out hav­ing to define a full eco­nom­ic mod­el, we can now spec­i­fy aggre­gate demand AD as being equiv­a­lent to the turnover of the mon­ey in the econ­o­my, using the veloc­i­ty of mon­ey v (see Fig­ure 3 and Equa­tion ).

Fig­ure 3: Veloc­i­ty of M2 mon­ey stock in the USA 1960–2013

As is well known, con­trary to Mil­ton Fried­man’s claims (Fried­man 1948; Fried­man 1959; Fried­man 1969; Fried­man and Schwartz 1963), the veloc­i­ty of mon­ey is not a constant—“it is also appar­ent that mon­ey veloc­i­ties are pro­cycli­cal and quite volatile” (Kyd­land and Prescott 1990, p. 14). How­ev­er the iden­ti­ty that can be used in this sim­ple mod­el to map from the mon­ey stock to the lev­el of aggre­gate demand.

Using the sub­script LM to indi­cate that this is aggre­gate demand in a Loan­able Funds mod­el, we have that aggre­gate demand at time t is the veloc­i­ty of mon­ey times the stock of mon­ey at that time:

Aggre­gate demand across any defined time peri­od t2-t1 will there­fore be this instan­ta­neous flow times the time peri­od itself:

Final­ly, using D for brevi­ty in place of Loans in Equa­tion , it is obvi­ous that there is no link between the dynam­ics of debt and either the stock or the turnover of mon­ey, and there­fore there is no direct rela­tion between pri­vate debt and aggre­gate demand. The amount of mon­ey in cir­cu­la­tion remains con­stant:

Giv­en the absence of a rela­tion­ship between lend­ing and the mon­ey sup­ply, the amount of debt in exis­tence can rise or fall sub­stan­tial­ly with only a minor impact on macro­eco­nom­ic activ­i­ty via relat­ed changes in the veloc­i­ty of mon­ey:

  1. A monetary model of Endogenous Money

This struc­tur­al mod­el of Loan­able Funds shown in Fig­ure 2 is con­vert­ed into a mod­el of Endoge­nous Mon­ey by three sim­ple changes:

  • Loans are shift­ed from the assets of the con­sump­tion sec­tor to the assets of the bank­ing sec­tor;
  • Inter­est pay­ments are trans­ferred to the equi­ty account of the bank­ing sec­tor, BankersNW; and
  • Since banks are loan orig­i­na­tors in this mod­el and receive inter­est pay­ments, the inter­me­di­a­tion fee is delet­ed.

This revised mod­el is shown in Fig­ure 4 and Table 3. The changes between the Loan­able Funds mod­el in Table 1 and the Endoge­nous Mon­ey mod­el of Table 3 all occur in the first four rows, with the row for an inter­me­di­a­tion fee delet­ed, and loca­tions of the flows Lend, Int and Repay altered as indi­cat­ed by the arrows. The two tables are oth­er­wise iden­ti­cal.

Fig­ure 4: Endoge­nous Mon­ey mod­el in Min­sky

Table 3: Endoge­nous Mon­ey mod­el from the bank­ing sec­tor’s per­spec­tive

Bank­ing Sec­tor




Flows Accounts Reserves Loans DepCons DepInv Work­ers BankersNW
1 Lend­ing Lend  <– -Lend
2 Inter­est Pay­ments –> Int -Int
3 Debt Repay­ment -Repay <– Repay
4 Hire work­ers (Cons) WagesC -WagesC
5 Hire work­ers (Inv) WagesI -WagesI
6 Inter­sec­toral pur­chas­es by Inv -ConsI ConsI
7 Inter­sec­toral pur­chas­es by Cons ConsC -ConsC
8 Work­ers con­sump­tion -ConsW ConsW
9 Bankers con­sump­tion -ConsB ConsB


The mon­ey and debt equa­tions of this mod­el are:

Despite the sim­plic­i­ty of the changes need­ed to move from Loan­able Funds to Endoge­nous Mon­ey, the dynam­ics of mon­ey are now pro­found­ly dif­fer­ent. The rate of change of mon­ey is pre­cise­ly equal to the rate of change of debt:

The stock of mon­ey in the econ­o­my is there­fore the sum of the ini­tial lev­el of mon­ey in exis­tence, plus the new mon­ey cre­at­ed by the exten­sion of new loans from the bank­ing sec­tor to the invest­ment sec­tor. Assum­ing for con­ve­nience that D(0)=0, this yields:

Using the sub­script EM to indi­cate that this is an Endoge­nous Mon­ey mod­el, aggre­gate demand is there­fore

Aggre­gate demand dur­ing some giv­en time peri­od t2-t1 is there­fore:

We can now com­pare the sym­bol­ic mea­sure of nom­i­nal aggre­gate demand in an Endoge­nous Mon­ey mod­el with its coun­ter­part in a Loan­able Funds mod­el (the numer­i­cal val­ues of veloc­i­ty, demand and debt will clear­ly dif­fer sub­stan­tial­ly, as the sim­u­la­tions in Sec­tion 6 illus­trate) to iden­ti­fy the sub­stan­tive dif­fer­ence between a Loan­able Funds view of the mon­e­tary sys­tem and that of Endoge­nous Mon­ey:

The Loan­able Funds mod­el thus omits the con­tri­bu­tion of the change in debt to the lev­el of aggre­gate demand.

  1. Occam’s Razor pass­es Endoge­nous Mon­ey & fails Loan­able Funds

If banks make loans to non-banks—as is man­i­fest­ly the case—and cre­ate mon­ey in doing so by cred­it­ing the deposit accounts of their borrowers—as even the staunch advo­cate of Loan­able Funds Paul Krug­man has conceded—then the Loan­able Funds mod­el is too extreme a sim­pli­fi­ca­tion of the nature of cap­i­tal­ism. As Ein­stein put it in rela­tion to physics:

It can scarce­ly be denied that the supreme goal of all the­o­ry is to make the irre­ducible basic ele­ments as sim­ple and as few as pos­si­ble with­out hav­ing to sur­ren­der the ade­quate rep­re­sen­ta­tion of a sin­gle datum of expe­ri­ence. (Ein­stein 1934, p. 165, empha­sis added)

Omit­ting the capac­i­ty of banks to cre­ate mon­ey, and the impact this has on key macro­eco­nom­ic aggre­gates omits a vital “datum of expe­ri­ence” from macro­eco­nom­ic mod­els. The capac­i­ty of bank lend­ing to alter the lev­el of aggre­gate demand means that banks, debt and mon­ey must be includ­ed in any ade­quate mod­el of macro­eco­nom­ics.

In par­tic­u­lar, the acknowl­edge­ment of the macro­eco­nom­ic sig­nif­i­cance of Endoge­nous Mon­ey requires a dynam­ic rede­f­i­n­i­tion of aggre­gate demand to include the change in debt. Though this mod­el excludes sec­ond-order effects such as demand for idle cash bal­ances (Rowe 2013), the gener­ic for­mu­la relat­ing aggre­gate demand (AD) to income (Y) and the change of debt is:

This for­mu­la cor­rects a rule of thumb propo­si­tion that I have pre­vi­ous­ly assert­ed, that aggre­gate demand is the sum of income plus the change in debt (Keen 2014; see also Krug­man 2013b). The cor­rect propo­si­tion is that, in a world in which the bank­ing sec­tor endoge­nous­ly cre­ates new mon­ey by cre­at­ing new loans, aggre­gate demand in a giv­en peri­od is the sum of aggre­gate demand at the begin­ning of that peri­od, plus the change in debt over the peri­od mul­ti­plied by the veloc­i­ty of mon­ey.

If we con­sid­er a time peri­od of one year so that and , and spec­i­fy­ing the aver­age veloc­i­ty of mon­ey over that year as v(1) and the change in debt as DD(1), we have

Equa­tions and enable us to oper­a­tional­ize Key­nes’s dis­tinc­tion between ex-ante and ex-post, while prov­ing the con­sis­ten­cy of this dynam­ic for­mu­la with the stan­dard macro­eco­nom­ic account­ing iden­ti­ty that expen­di­ture equals income. In words, these equa­tions assert that ex-post expen­di­ture equals ex-ante expen­di­ture (and hence income), plus the veloc­i­ty of mon­ey mul­ti­plied by the ex-post change in debt.

Since the veloc­i­ty of mon­ey com­fort­ably exceeds uni­ty (though it is high­ly vari­able and pro-cycli­cal), the numer­i­cal impact of the change in debt on aggre­gate demand is there­fore larg­er than I have claimed in research pri­or to devel­op­ing this for­mal proof (Keen 2014; see also Rowe 2013).

  1. Sim­u­lat­ing Loan­able Funds and Endoge­nous Mon­ey

A sim­u­la­tion of the two mod­els con­firms the impor­tance of includ­ing the change in debt in aggre­gate demand. The sim­ple mod­els used here are iden­ti­cal except for the struc­ture of lend­ing, so that the dif­fer­ences in their behav­ior reflects sim­ply that issue. The mod­els use sim­ple vari­able time para­me­ters to relate the var­i­ous mon­e­tary flows to each oth­er and the mon­e­tary stocks, so that the results do not depend on any behav­ioral assump­tions (see the Appen­dix for the mod­el equa­tions and default para­me­ter val­ues). The val­ues of two of these parameters—the lend­ing and repay­ment rates—are var­ied over the sim­u­la­tions shown in Fig­ure 5 and Fig­ure 6.

Fig­ure 5: Loan­able Funds sim­u­la­tion in Min­sky

Fig­ure 6: Endoge­nous Mon­ey sim­u­la­tion in Min­sky

Vari­a­tions in the lend­ing and repay­ment rates have a minor effect on income in the Loan­able Funds mod­el (see Fig­ure 7) because they impact upon the veloc­i­ty of cir­cu­la­tion of mon­ey (see Fig­ure 8). How­ev­er the lev­el does not rise (or fall) sig­nif­i­cant­ly, and there is no trend, since vari­a­tions in the lev­el of debt have no impact upon the mon­ey sup­ply, which remains con­stant (see Fig­ure 9).

Fig­ure 7: GDP as a func­tion of Lend­ing & Repay­ment rates in Loan­able Funds

Fig­ure 8: Mon­ey veloc­i­ty as a func­tion of Lend­ing & Repay­ment rates in Loan­able Funds

Fig­ure 9: Mon­ey and Debt as func­tions of Lend­ing & Repay­ment rates in Loan­able Funds

In con­trast, vari­a­tions in the lend­ing and repay­ment rates have a dra­mat­ic impact upon GDP in the Endoge­nous Mon­ey mod­el (see Fig­ure 10), because as well as hav­ing an impact upon the veloc­i­ty of mon­ey (see Fig­ure 11) they alter the rate of cre­ation and destruc­tion of mon­ey (see Fig­ure 12).

Fig­ure 10: GDP as a func­tion of Lend­ing & Repay­ment rates in Endoge­nous Mon­ey

Fig­ure 11: Mon­ey veloc­i­ty as a func­tion of Lend­ing & Repay­ment rates in Endoge­nous Mon­ey

Fig­ure 12: Mon­ey and Debt as func­tions of Lend­ing & Repay­ment rates in Endoge­nous Mon­ey

  1. Modeling financial instability

The pre­ced­ing proof pro­vides a the­o­ret­i­cal jus­ti­fi­ca­tion for the key role giv­en to the lev­el and change in aggre­gate pri­vate debt in Min­sky’s Finan­cial Insta­bil­i­ty Hypoth­e­sis. Empir­i­cal research by Fama and French pro­vid­ed fur­ther sup­port, by con­clud­ing that the cor­re­la­tions they found (includ­ing a 0.79 cor­re­la­tion between aggre­gate cor­po­rate invest­ment and change in long term cor­po­rate debt) “con­firm the impres­sion that debt plays a key role in accom­mo­dat­ing year-by-year vari­a­tion in invest­ment” (Fama and French 1999, p. 1954).

Min­sky pro­vid­ed a suc­cinct sum­ma­ry of his Finan­cial Insta­bil­i­ty Hypoth­e­sis, which empha­sized the cen­tral of pri­vate debt to his analy­sis (Min­sky 1978; reprint­ed in Min­sky 1982):

The nat­ur­al start­ing place for ana­lyz­ing the rela­tion between debt and income is to take an econ­o­my with a cycli­cal past that is now doing well. The inher­it­ed debt reflects the his­to­ry of the econ­o­my, which includes a peri­od in the not too dis­tant past in which the econ­o­my did not do well. Accept­able lia­bil­i­ty struc­tures are based upon some mar­gin of safe­ty so that expect­ed cash flows, even in peri­ods when the econ­o­my is not doing well, will cov­er con­trac­tu­al debt pay­ments. As the peri­od over which the econ­o­my does well length­ens, two things become evi­dent in board rooms. Exist­ing debts are eas­i­ly val­i­dat­ed and units that were heav­i­ly in debt pros­pered; it paid to lever. After the event it becomes appar­ent that the mar­gins of safe­ty built into debt struc­tures were too great. As a result, over a peri­od in which the econ­o­my does well, views about accept­able debt struc­ture change. In the deal­mak­ing that goes on between banks, invest­ment bankers, and busi­ness­men, the accept­able amount of debt to use in financ­ing var­i­ous types of activ­i­ty and posi­tions increas­es. This increase in the weight of debt financ­ing rais­es the mar­ket price of cap­i­tal assets and increas­es invest­ment. As this con­tin­ues the econ­o­my is trans­formed into a boom econ­o­my.

Sta­ble growth is incon­sis­tent with the man­ner in which invest­ment is deter­mined in an econ­o­my in which debt-financed own­er­ship of cap­i­tal assets exists, and the extent to which such debt financ­ing can be car­ried is mar­ket deter­mined. It fol­lows that the fun­da­men­tal insta­bil­i­ty of a cap­i­tal­ist econ­o­my is upward. The ten­den­cy to trans­form doing well into a spec­u­la­tive invest­ment boom is the basic insta­bil­i­ty in a cap­i­tal­ist econ­o­my. (Min­sky 1982, pp. 66–67)

I mod­eled this process by extend­ing Good­win’s cycli­cal growth model—in which prof­it-rate-moti­vat­ed invest­ment and employ­ment-rate-moti­vat­ed wage demands gen­er­at­ed a closed lim­it cycle in employ­ment and income dis­tri­b­u­tion (Good­win 1967)—to include debt-financed invest­ment. Good­win’s mod­el reduced to two cou­pled dif­fer­en­tial equa­tions in the employ­ment rate (?) and wages share of out­put (?), where is a Phillips-curve rela­tion and is an invest­ment func­tion depend­ing on the rate of prof­it :

I replaced Good­win’s “stark­ly schema­tized” (Good­win 1967, p. 54) assump­tion that invest­ment equalled prof­it at all times with an invest­ment func­tion in which invest­ment exceed­ed prof­it at high rates of prof­it, and was below prof­it at low rates. An equa­tion to rep­re­sent debt-financed invest­ment was added—Equation —and prof­it was rede­fined as earn­ings net of inter­est pay­ments :

This trans­formed Good­win’s mod­el into a three-state mod­el of Min­sky’s hypoth­e­sis, with the extra equa­tion being the dynam­ics of the pri­vate debt to out­put ratio (see Keen 2013, pp. 236–38 for the deriva­tion):

In (Keen 1995; Keen 2000) I used non­lin­ear func­tions for both invest­ment deter­mi­na­tion and wage set­ting; here I use lin­ear func­tions to empha­size that both the cycli­cal behav­ior of Good­win’s mod­el and the debt-induced break­down in the Min­sky mod­el are endem­ic, rather than being prod­ucts of the assumed func­tion­al forms. In the sim­u­la­tions shown in Fig­ure 13 and Fig­ure 14, the invest­ment and wage change func­tions are:

Fig­ure 13 shows the fixed cycle in Good­win’s basic mod­el.

Fig­ure 13: Good­win’s mod­el with lin­ear behav­ioral func­tions sim­u­lat­ed in Min­sky

Fig­ure 14 shows a typ­i­cal run of the Min­sky mod­el, which has three key char­ac­ter­is­tics:

  • The ini­tial behav­ior of the mod­el involves a reduc­tion in the volatil­i­ty of employ­ment and output—effectively a “Great Mod­er­a­tion”;
  • Work­ers’ share of out­put has a sec­u­lar ten­den­cy to fall; and
  • The ini­tial reduc­tion in employ­ment and out­put volatil­i­ty gives way to increas­ing volatil­i­ty as the debt to out­put lev­el ris­es (with the ulti­mate out­come of a debt-induced col­lapse in out­put and employ­ment).

Fig­ure 14: Min­sky’s FIH with lin­ear behav­ioral func­tions sim­u­lat­ed in Min­sky

The fact that this sim­ple mod­el gen­er­at­ed out­comes that, in a very styl­ized way, mir­ror the empir­i­cal record of the recent eco­nom­ic past, empha­sizes the impor­tance of devel­op­ing an approach to macro­eco­nom­ics in which banks and pri­vate debt play inte­gral roles. The empir­i­cal data, inter­pret­ed in the light of the the­o­ret­i­cal argu­ments giv­en here, fur­ther empha­sizes the impor­tance of pay­ing close pol­i­cy atten­tion to the hith­er­to ignored phe­nom­e­non of the growth of pri­vate debt.

  1. Empirical Data

For­tu­nate­ly, though main­stream eco­nom­ic the­o­ry has ignored the role of pri­vate debt, sta­tis­ti­cal agen­cies have col­lect­ed the data. Fig­ure 15 is an imput­ed series com­bin­ing actu­al Fed­er­al Reserve quar­ter­ly data on house­hold plus non-finan­cial cor­po­rate debt since 1952 (and year­ly data from 1945 till 1952) with US Cen­sus data from 1916–1970, and par­tial Cen­sus data on bank loans from 1834 to 1970 (Cen­sus 1949; Cen­sus 1975).

Fig­ure 15: US pri­vate debt since 1834

The causal role of the change in debt in aggre­gate demand iden­ti­fied in this paper implies that there should be a strong empir­i­cal rela­tion­ship between change in debt and macro­eco­nom­ic data such as the unem­ploy­ment rate—in con­trast to the Loan­able-Funds-based pre­sump­tion that “Absent implau­si­bly large dif­fer­ences in mar­gin­al spend­ing propen­si­ties among the groups … pure redis­tri­b­u­tions should have no sig­nif­i­cant macro-eco­nom­ic effects…” (Bernanke 2000, p. 24). This Loan­able Funds pre­sump­tion is strong­ly reject­ed by the data. As Fig­ure 16 shows, the cor­re­la­tion of the change in debt times veloc­i­ty (divid­ed by GDP) with the lev­el of unem­ploy­ment since 1990 is ‑0.92.

Fig­ure 16: Change in debt times veloc­i­ty and US Unem­ploy­ment (Cor­re­la­tion ‑0.92)

The first dif­fer­ence of also implies a strong rela­tion­ship between the change in the change in debt over two time peri­ods and change in unem­ploy­ment over that peri­od. Set­ting , the change in aggre­gate demand between peri­ods t2-t1 and t1-t0 (nor­mal­ized by divid­ing by ) is:

Set­ting , the cor­re­la­tion between equa­tion , which we term the Cred­it Accel­er­a­tor (see also Big­gs and May­er 2010; Big­gs, et al. 2010), and the annu­al per­cent­age change in the unem­ploy­ment rate over the peri­od from 1975 till today is ‑0.78 (see Fig­ure 17).

Fig­ure 17: Cred­it accel­er­a­tion and change in unem­ploy­ment (Cor­re­la­tion ‑0.78)

  1. Conclusion

Giv­en that bank lend­ing cre­ates mon­ey and repay­ment of debt destroys it, the change in debt plays an inte­gral role in macro­eco­nom­ics by dynam­i­cal­ly vary­ing the lev­el of aggre­gate demand. The omis­sion of this fac­tor from main­stream eco­nom­ic mod­els is the rea­son that these mod­els failed to warn of the dan­gers of the dra­mat­ic buildup in pri­vate debt since WWII—and espe­cial­ly since 1993, when the debt-financed recov­ery from the 1990s reces­sion took the aggre­gate pri­vate debt lev­el past the peak caused by defla­tion in the 1930s (see Fig­ure 15). It is also the rea­son why they failed to antic­i­pate the cri­sis that began in 2007, and instead pre­dict­ed that, as the OECD put it in June 2007, “the cur­rent eco­nom­ic sit­u­a­tion is in many ways bet­ter than what we have expe­ri­enced in years… Our cen­tral fore­cast remains indeed quite benign” (OECD 2007). Pol­i­cy mak­ers rely­ing upon main­stream econ­o­mists as experts on the func­tion­ing of the econ­o­my thus not only received no warn­ing about the worst eco­nom­ic cri­sis since the Great Depres­sion, but were false­ly led to expect benign rather than malig­nant eco­nom­ic con­di­tions.

The erro­neous neglect of the dynam­ics of pri­vate debt by the eco­nom­ics pro­fes­sion has there­fore result­ed in enor­mous social and eco­nom­ic harm to soci­ety. This is the oppo­site of the intend­ed goal of eco­nom­ic the­o­ry and pol­i­cy. If eco­nom­ic the­o­ry and pol­i­cy are to ful­fil their intend­ed role, it is imper­a­tive that a reformed macro­eco­nom­ics be devel­oped in which banks, mon­ey and the dynam­ics of debt play inte­gral roles.

  1. Appendix

    1. Loanable Funds model

Differential equations for money and debt

Other differential equations

  1. Endogenous Money model

Differential equations for money and debt

Other differential equations

Common Definitions

Common Parameters to Loanable Funds and Endogenous Money models

  1. Goodwin model

  1. Minsky model (new and modified equations only)

  1. Common parameters to Goodwin & Minsky models

  1. Minsky

Min­sky is an addi­tion to the fam­i­ly of sys­tem dynam­ics pro­grams that began with Jay For­rester’s pio­neer­ing work on devel­op­ing a visu­al metaphor for con­struct­ing and sim­u­lat­ing dynam­ic mod­els of com­plex social and eco­nom­ic process­es (For­rester 1968). For­rester’s metaphor was the flow­chart (see Fig­ure 18): a draw­ing of the rela­tion­ships in a sys­tem became the frame­work for devel­op­ing a math­e­mat­i­cal mod­el of that sys­tem:

The pro­posed mod­el struc­ture and method of solu­tion retain a one-to-one cor­re­spon­dence between the pre­sumed form of the real eco­nom­ic world and the quan­ti­ties, coef­fi­cients, vari­ables, and deci­sion cri­te­ria of the mod­el. For­mu­la­tion in terms of a “flow dia­gram” is pos­si­ble so that a pic­to­r­i­al rep­re­sen­ta­tion of the rela­tion­ships with­in the sys­tem is avail­able at all times. (For­rester 2003p. 344 )

Fig­ure 18: The first sys­tem dynam­ics dia­gram from For­rester 2003 (1956)

There are now at least a dozen pro­grams imple­ment­ing this mod­el­ing phi­los­o­phy, rang­ing from the free Open Source pro­gram Xcos to the $20,000-a-copy com­mer­cial pro­gram Simulink. This par­a­digm is now per­va­sive in engi­neer­ing, but it failed to take root in eco­nom­ics, despite the fact that For­rester’s con­cept was twice antic­i­pat­ed in economics—firstly by Irv­ing Fish­er in 1891 with a hydraulic mod­el for cal­cu­lat­ing equi­lib­ri­um val­ues in a Wal­rasian mod­el (Brainard and Scarf), and then by the engi­neer-turned econ­o­mist Bill Phillips with gen­uine­ly dynam­ic ana­log com­put­er sys­tems (Hayes 2011; Lee­son 1994a; Lee­son 1994b; Lee­son 1995; Lee­son 2000; Phillips 1950; Phillips 1954; Phillips 1957) some years before For­rester. How­ev­er, there was no devel­op­ment in eco­nom­ics com­pa­ra­ble to For­rester’s inno­va­tion (in con­junc­tion with the com­put­er pro­gram­mers Phyl­lis Fox and Alexan­der Pugh–see Lane 2007) of a dig­i­tal com­put­er program—DYNAMO—to pro­vide a gen­er­al pur­pose foun­da­tion for build­ing dynam­ic mod­els of com­plex sys­tems.

Fig­ure 19: Fish­er’s 1891 hydraulic machine for cal­cu­lat­ing Wal­rasian equi­lib­ri­um prices, from Brainard and Scarf, p. 69

Fig­ure 20: Phillip­s’s schemat­ic dia­gram of a dynam­ic mul­ti­pli­er-accel­er­a­tor mod­el, from Phillips 1954, p. 306

The core par­a­digm in sys­tem dynam­ics pro­grams is the con­struc­tion of math­e­mat­i­cal equa­tions via flow­charts iden­ti­cal in spir­it to that devel­oped by Phillips (see Fig­ure 20). For exam­ple, Fig­ure 21 is the sys­tem dynam­ics equiv­a­lent of the dif­fer­en­tial equa­tion for expo­nen­tial pop­u­la­tion growth .

Fig­ure 21: A sim­ple alge­bra­ic equa­tion in a sys­tem dynam­ics pro­gram (Min­sky)

Sim­ple expres­sions like this are just as eas­i­ly ren­dered in equa­tions or stan­dard text-ori­ent­ed com­put­er pro­grams, but the sys­tem dynam­ics approach makes it eas­i­er to com­pre­hend much more com­plex models—hence its dom­i­nance in the engi­neer­ing field today.

Min­sky pro­vides this clas­sic sys­tem dynam­ics approach, and also adds a new method of con­struct­ing dif­fer­en­tial equa­tions to the sys­tem dynam­ics toolk­it that is supe­ri­or for mod­el­ling finan­cial flows: the God­ley Table. Based on the account­ing con­cept of dou­ble-entry book­keep­ing, each col­umn rep­re­sents the dynam­ic equa­tion of a giv­en finan­cial account, while each row rep­re­sents trans­ac­tions between accounts. This is a more nat­ur­al way to por­tray finan­cial trans­ac­tions which also helps enforce the fun­da­men­tal rules of accounting—that Assets equal Lia­bil­i­ties plus Equi­ty.

Min­sky ensures this in three ways. First­ly, all row oper­a­tions in a God­ley Table must sum to zero—otherwise an error is flagged. Sec­ond­ly, the source of any trans­ac­tion is shown as a pos­i­tive while the des­ti­na­tion (or “sink” in sys­tem dynam­ics par­lance) is shown as a neg­a­tive. Third­ly, Assets are shown as pos­i­tive while Lia­bil­i­ties and Equi­ty are shown as neg­a­tive. Fig­ure 22 illus­trates these three conventions—including show­ing what hap­pens when they are breached.

Fig­ure 22: A sam­ple God­ley Table


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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.