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Modeling financial instability

from Steve Keen

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 Assets Lia­bil­i­ties Equity
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 Assets Lia­bil­i­ties Equity
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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– See more at: http://www.debtdeflation.com/blogs/2014/02/02/modeling-financial-instability/#sthash.u8gAvjCL.dpuf

  1. February 7, 2014 at 4:48 pm

    Endogenous money was explained in detail in my animated feature movies, Money as Debt (2006) and Money as Debt II – Promises Unleashed (2009) Both have been viewed by many millions worldwide. Money as Debt is online in at least 24 languages.

    My model takes into account that endogenous money subsequently becomes loanable funds, which professor Keen’s model overlooks. Professor Keen was challenged to refute this model more than 2 years ago and chose instead to ignore it. The only economist to attempt to refute it conceded he could not.

    The full explanation of “twice-lent” money is the animation at the bottom of the page:

    My full analysis:

    As always, every economist on this list is invited to refute my logic and facts.

    • Marko
      February 7, 2014 at 8:41 pm

      It seems to me that the obvious metric to follow in order to assure that we haven’t violated the “once-lent” rule is overall leverage. If combined public + private debt/gdp is stable or falling over time , it means incomes are growing with debt loads , and payoffs are sufficiently offsetting new loans such that debt/gdp doesn’t rise.

      The sad thing is that we achieved this happy state of affairs during the vast majority of the past century. The two big increases in leverage , outside of the depression , were in the early ’80s and the 2000s. If we had maintained the historical post-WWII leverage ratio thru those periods , we wouldn’t be in this mess.

      • February 8, 2014 at 6:41 pm

        Marko, your happy times scenario was dependent on perpetual growth of debt to banks and there is no such thing as a ONCE-lent bank loan. Here is why.

        Bank credit created as a loan is twice-lent by the design of the system and cannot be otherwise. It is created as a debt of a borrower to a bank, spent by the borrower and deposited by a depositor. Now you have the borrower’s scheduled debt to the bank of origin (LOAN 1) and the second bank’s unrelated, unscheduled and indefinite debt of the same amount to its depositor (LOAN 2).

        That is the real state of “endogenous money”. It always takes the form of TWO entirely DISCONNECTED DEBTS of the SAME PRINCIPAL, one usually on a finite time schedule for repayment and the other on no schedule at all, and in fact permanent in the aggregate. How this can be totally overlooked and ignored is mind-boggling, to say the least.

        If the depositor keeps 75% of that original money-as-debt deposited in bank savings or lends it out as existing money indefinitely, what will the original borrower use to pay off his loan?

        Rather obviously, 75% of the original loan will have to be paid off with the Principal of some other loan. Now that loan is short its Principal. And now we have a Perpetual Debt of 75% of the original Principal. As long as 75% of the original money-as-debt stays deposited as savings or lent out as existing money by a non-bank, the supply of new bank credit can never decrease or slow down without causing mathematically inevitable defaults.

        If all money were in this position in the REAL WORLD, M2 minus M1 (mostly term deposit savings) would never decrease and would account for 75% of the total money supply. Recessions would happen when the supply of new money (M1) decreases while the amount of M2-M1 continues to increase.

        Oh look! That is exactly the case just screaming at us from this ever so familiar graph.


        On this graph, we had prosperity when M2-M1 fell as low as 66% and we had the big Crash when M2-M1 hit 80%.

        Here’s my WEA published paper on the subject:
        Proposed new metric: the Perpetual Debt Level

        I provide empirical evidence and very simple logic to explain causation. I challenge you to refute my argument on its own terms, instead of reverting to the delusional concepts of failure-ridden conventional economics which do not apply because they ignore the true nature of money as “twice-lent” Principal.

  2. Marko
    February 8, 2014 at 12:40 am

    I really want Keen to be successful , because we need to get the political discussion focused on the private debt burdens , and not just in the U.S. — it’s a problem almost everywhere you look.

    I think he’s making an error here , however. Using M2 velocity is going to yield outsize numbers for the debt contribution to aggregate demand. One of the problems he has with getting heard by most economists is that they don’t recognize “aggregate demand” that looks like this :

    Velocity is gdp divided by the “money” stock in question. Thus , in this case , when we’re considering the private stock of debt as our “money” , the appropriate velocity to use is gdp divided by the private debt stock measure. Here’s what that looks like :


    ( note : The calculation of private debt as Keen uses it is shown as Domestic nonfinancial debt minus ( federal plus state&local debt) )

    As you can see , my alternative velocity multiplier is currently ~ 0.7 , while the M2 velocity shown above in Steve’s paper is almost 1.6 .Here’s what both multipliers will yield when applied to the change in private debt ( M2 in red , my alternative measure in blue ):


    Those are quarterly figures , so on an annual basis the M2 multiplier will show over $4 trillion at the peak of the housing bubble. Clearly , there was nowhere near that contribution to what most people define as aggregate demand.

    I know Keen figures that some of the debt contribution ends up in asset values , and I think it’s fine to pursue that line of thinking. But for the ‘aggregate demand’ component , I think he’d be better served by sticking to the conventional definition , and take up the asset component separately.

    • February 8, 2014 at 6:42 pm

      Velocity makes $1000 (or any number) of interest payments possible with only $1 in existence because interest is spent back into circulation. The single dollar can be paid and earned 1000 times.

      Velocity cannot do the same for Principal. Principal is lent by definition. $1 of Principal can only pay off $1 of Principal Debt.

      P of money < 2 P of debt of that money is the DESIGN of the bank credit system.

      Perpetual Debt, the growth imperative, out-of-control income disparity, chronic instability totalitarianism, war and/or anarchy are the inevitable outcomes repeated throughout history.

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