A dynamic mon­e­tary multi-sec­toral model of pro­duc­tion

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I will be speak­ing at the Inter­na­tional Sci­en­tific Sym­po­sium for Devel­op­ment devoted to the 110th anniver­sary of Simon Kuznets in Kyev, The Ukraine, next week. Simon Kuznets, one of the few recip­i­ents of the faux Nobel Prize in Eco­nom­ics whose work I respect, was one of the pio­neers of empir­i­cal research in eco­nom­ics, a stu­dent of busi­ness cycles, and a critic of sta­tic eco­nomic method­ol­ogy.

My paper for this con­fer­ence is repro­duced below. It def­i­nitely deserves the label “wonkish”–in fact it’s cer­tainly the most wonk­ish thing I’ve ever posted here.

A dynamic mon­e­tary multi-sec­toral model of pro­duc­tion

Steve Keen, Uni­ver­sity of West­ern Syd­ney
Click here for the paper in PDF

Though Keynes enti­tled his mag­num opus The gen­eral the­ory of employ­ment, inter­est and money (Keynes 1936), he acknowl­edged that money did not fea­ture heav­ily in his tech­ni­cal analy­sis, and that he saw a sub­stan­tial con­ti­nu­ity between mon­e­tary analy­sis and the Mar­shal­lian model of sup­ply and demand:

whilst it is found that money enters into the eco­nomic scheme in an essen­tial and pecu­liar man­ner, tech­ni­cal mon­e­tary detail falls into the back­ground. A mon­e­tary econ­omy, we shall find, is essen­tially one in which chang­ing views about the future are capa­ble of influ­enc­ing the quan­tity of employ­ment and not merely its direc­tion. But our method of ana­lyz­ing the eco­nomic behav­ior of the present under the influ­ence of chang­ing ideas about the future is one which depends on the inter­ac­tion of sup­ply and demand, and is in this way linked up with our fun­da­men­tal the­ory of value. We are thus led to a more gen­eral the­ory, which includes the clas­si­cal the­ory with which we are famil­iar, as a spe­cial case. (Keynes 1936, p. xxii)

After Keynes, macro­eco­nom­ics frag­mented around the impor­tance of both uncertainty—implicit in the state­ment above that “chang­ing views about the future are capa­ble of influ­enc­ing the quan­tity of employ­ment”, but strongly explicit else­where (Keynes 1936; Keynes 1937)—and money. Both con­cepts dis­ap­peared from main­stream macro­eco­nomic analy­sis, to be replaced ini­tially by IS-LM analysis—in which an exoge­nously deter­mined money played a minor role, but uncer­tainty dis­ap­peared (Hicks 1937; Min­sky 1975; Hicks 1981)—and ulti­mately by Real Busi­ness Cycle mod­el­ing (Kyd­land and Prescott 1982), in which “ratio­nal expec­ta­tions” neutered uncer­tainty com­pletely (Lucas 1972), and money was entirely absent.

On the periph­ery of the pro­fes­sion, a rump of self-described “Post Key­ne­sians” clung to the posi­tion that both money and uncer­tainty were essen­tial aspects of macro­eco­nom­ics. Going far fur­ther than Keynes him­self, this rump incor­po­rated Schumpeter’s argu­ments on the essen­tial role of endoge­nously cre­ated money in financ­ing growth (Schum­peter 1927; Schum­peter 1934; Moore 1979) and Fisher’s debt-defla­tion per­spec­tive (Fisher 1933) to develop the “Finan­cial Insta­bil­ity Hypoth­e­sis” (Min­sky 1975; Min­sky 1977; Min­sky 1982; Min­sky 1993), while it also rejected Mar­shal­lian analysis—following on this issue Sraffa (Sraffa 1926; Robert­son, Sraffa et al. 1930) rather than Keynes. Oth­ers added insights from the­o­ret­i­cal devel­op­ments like com­plex­ity the­ory, which post-dated Keynes, to argue that the macro-econ­omy was inher­ently cycli­cal (Good­win 1967; Good­win 1986; Good­win 1990).

This rump was ignored by the main­stream, which over time expunged not only uncer­tainty and money but even Keynes him­self from macro­eco­nom­ics (despite the fact that the dom­i­nant seg­ment of the main­stream described its work as “New Key­ne­sian”). Main­stream macro­eco­nom­ics became applied neo­clas­si­cal micro­eco­nom­ics, as Oliver Blan­chard, found­ing edi­tor of the jour­nal AER: Macro, out­lined in his sur­vey of macro­eco­nom­ics in 2009.

The most vis­i­ble out­comes of this new approach are the dynamic sto­chas­tic gen­eral equi­lib­rium (DSGE) mod­els. They are mod­els derived from micro foundations—that is, util­ity max­i­miza­tion by con­sumers-work­ers; value max­i­miza­tion by firms; ratio­nal expec­ta­tions; and a full spec­i­fi­ca­tion of imper­fec­tions, from nom­i­nal rigidi­ties to some of the imper­fec­tions dis­cussed above—and typ­i­cally esti­mated by Bayesian meth­ods. (Blan­chard 2009, p. 223)

As the end of the first decade of the 21st cen­tury approached, the main­stream was tri­umphal. At the pol­icy level, it took the credit for the decline in eco­nomic volatil­ity since the early 1980s:

As it turned out, the low-infla­tion era of the past two decades has seen not only sig­nif­i­cant improve­ments in eco­nomic growth and pro­duc­tiv­ity but also a marked reduc­tion in eco­nomic volatil­ity, both in the United States and abroad, a phe­nom­e­non that has been dubbed “the Great Mod­er­a­tion.” Reces­sions have become less fre­quent and milder, and quar­ter-to-quar­ter volatil­ity in out­put and employ­ment has declined sig­nif­i­cantly as well. The sources of the Great Mod­er­a­tion remain some­what con­tro­ver­sial, but as I have argued else­where, there is evi­dence for the view that improved con­trol of infla­tion has con­tributed in impor­tant mea­sure to this wel­come change in the econ­omy. (Bernanke 2004; empha­sis added)

At the level of pure the­ory, a sim­i­lar con­tent­ment pre­vailed. Though he acknowl­edged one notable dis­senter (Solow 2008), Blanchard’s sur­vey was unequiv­o­cal:

The state of macro is good. (Blan­chard 2009, p. 210)

Few more poorly timed state­ments have ever been made by promi­nent econ­o­mists. This paper was first pub­lished online as a work­ing paper in August 2008 (Blan­chard 2008)—one year after the event that is now regarded as the begin­ning of the finan­cial cri­sis (New York Times 2007) and 8 months after the NBER’s date for the com­mence­ment of the Great Reces­sion (NBER 2011). Its pub­li­ca­tion as a jour­nal paper in May 2009 pre­ceded the NBER’s date for the end of this reces­sion by one month (a deci­sion that I expect will prove pre­ma­ture).

Blan­chard was forced into recant­ing his opti­mism less than a year later (Blan­chard, Dell’Ariccia et al. 2010). But while he crit­i­cized macro­eco­nomic pol­icy prior to the cri­sis, he remained a believer in neo­clas­si­cal the­ory itself:

Iden­ti­fy­ing the flaws of exist­ing pol­icy is (rel­a­tively) easy. Defin­ing a new macro­eco­nomic pol­icy frame­work is much harder… It is impor­tant to start by stat­ing the obvi­ous, namely, that the baby should not be thrown out with the bath­wa­ter. Most of the ele­ments of the pre-cri­sis con­sen­sus, includ­ing the major con­clu­sions from macro­eco­nomic the­ory, still hold. Among them, the ulti­mate tar­gets remain out­put and infla­tion sta­bil­ity. The nat­ural rate hypoth­e­sis holds, at least to a good enough approx­i­ma­tion, and pol­i­cy­mak­ers should not design pol­icy on the assump­tion that there is a long-term trade-off between infla­tion and unem­ploy­ment. Sta­ble infla­tion must remain one of the major goals of mon­e­tary pol­icy. Fis­cal sus­tain­abil­ity is of the essence, not only for the long term but also in affect­ing expec­ta­tions in the short term. (Blan­chard, Dell’Ariccia et al. 2010, p. 207; empha­sis added)

Blanchard’s unwill­ing­ness to coun­te­nance the pos­si­bil­ity that the Great Reces­sion may be a Kuhn­ian crit­i­cal anom­aly for neo­clas­si­cal macro­eco­nom­ics (Beze­mer 2011) is rep­re­sen­ta­tive of this school of thought:

Indeed, the extreme sever­ity of this great reces­sion makes it tempt­ing to argue that new the­o­ries are required to fully explain it… But … it would be pre­ma­ture to aban­don more famil­iar mod­els just yet. (Ire­land 2011, p. 1; empha­sis added)

As a rep­re­sen­ta­tive of the Post Key­ne­sian and com­plex­ity the­ory rump, and one of the hand­ful of econ­o­mists to fore­see the Great Reces­sion (Keen 1995; Keen 2000; Keen 2006; Keen 2007; Keen 2007; Beze­mer 2009; Beze­mer 2011), I could not dis­agree more with Blan­chard and his col­leagues. Though neo­clas­si­cal econ­o­mists believe they are being method­olog­i­cally sound in apply­ing micro­eco­nomic con­cepts to model the macro-econ­omy, deep research long ago estab­lished that this is a fal­lacy. The Son­nen­schein-Man­tel-Debreu con­di­tions alone estab­lish that even the micro­eco­nom­ics of demand in a sin­gle mar­ket can­not be derived by extrap­o­la­tion from the behav­ior of a sin­gle util­ity-max­i­miz­ing agent, let alone the macro­eco­nom­ics of the whole econ­omy. As Solow him­self noted in the paper cited in Blan­chard (2009, p. 210):

Sup­pose you wanted to defend the use of the Ram­sey model as the basis for a descrip­tive macro­eco­nom­ics. What could you say? …

You could claim that … there is no other tractable way to meet the claims of eco­nomic the­ory. I think this claim is a delu­sion. We know from the Son­nen­schein-Man­tel-Debreu the­o­rems that the only uni­ver­sal empir­i­cal aggrega­tive impli­ca­tions of gen­eral equi­lib­rium the­ory are that excess demand func­tions should be con­tin­u­ous and homo­ge­neous of degree zero in prices, and should sat­isfy Wal­ras’ Law. Any­one is free to impose fur­ther restric­tions on a macro model, but they have to be jus­ti­fied for their own sweet sake, not as being required by the prin­ci­ples of eco­nomic the­ory. Many vari­eties of macro mod­els can be con­structed that sat­isfy those basic require­ments with­out impos­ing any­thing as extreme and prej­u­di­cial as a rep­re­sen­ta­tive agent in a favor­able envi­ron­ment. (Solow 2008, p. 244; empha­sis added; see also Solow 2001 and 2003)

I cover the myr­iad flaws in neo­clas­si­cal macro­eco­nom­ics in much more detail in Keen 2011b; suf­fice it to say here that, far from it being unwise to “throw the baby out with the bath­wa­ter”, neo­clas­si­cal macro­eco­nom­ics should never have been con­ceived in the first place. The Great Reces­sion will hope­fully prove to be the Bib­li­cal eco­nomic flood needed to finally sink this super­fi­cially appeal­ing but fun­da­men­tally flawed vision of how the macro-econ­omy func­tions.


How do I fault thee? Let me count the ways


The flaws of neo­clas­si­cal macro­eco­nom­ics are almost too numer­ous to enu­mer­ate, but the key weak­nesses are:

  1. Treat­ing a com­plex mon­e­tary mar­ket econ­omy as a barter sys­tem;
  2. Assum­ing that the macro-econ­omy is either in equi­lib­rium (par­tial or gen­eral, per­fect or imper­fect), or that it will return to equi­lib­rium rapidly if dis­turbed;
  3. Mod­el­ing the entire econ­omy using “applied micro­eco­nom­ics” and ignor­ing social class, when the Son­nen­schein-Man­tel-Debreu con­di­tions (Son­nen­schein 1972; Son­nen­schein 1973; Kir­man 1989; Shafer and Son­nen­schein 1993) estab­lish that, as Kir­man put it:

    we may well be forced to the­o­rise in terms of groups who have col­lec­tively coher­ent behav­iour. Thus demand and expen­di­ture func­tions if they are to be set against real­ity must be defined at some rea­son­ably high level of aggre­ga­tion. The idea that we should start at the level of the iso­lated indi­vid­ual is one which we may well have to aban­don” (Kir­man 1992, p. 138);

  4. Oblit­er­at­ing uncer­tainty from macro­eco­nomic the­ory with the absurd propo­si­tion that a ratio­nal indi­vid­ual is some­one who can accu­rately fore­see the future—which is what “ratio­nal expec­ta­tions” really means;
  5. Per­sist­ing with a sim­plis­tic “money mul­ti­plier” model of money cre­ation when the empir­i­cal evi­dence against this model is over­whelm­ing (Holmes 1969; Moore 1979; Moore 1988; Kyd­land and Prescott 1990); and
  6. Ignor­ing the piv­otal roles of credit and debt in the macro-econ­omy.

All these flaws are absent from the non-neo­clas­si­cal rump—especially in the work of Min­sky. But what the rump lacks, in com­par­i­son to the neo­clas­si­cal main­stream, is a coher­ent math­e­mat­i­cal expres­sion of its model that is widely accepted within that school. In this paper I con­tribute to the devel­op­ment of such a model (though I appre­ci­ate that my model is a long way from being accepted by my peers) using a mod­el­ing framework—which I call Mon­e­tary Cir­cuit The­ory (MCT)—that, in con­trast to the neo­clas­si­cal litany of sins above:

  1. Treats the econ­omy as inher­ently mon­e­tary;
  2. Makes no assump­tions about the nature of equi­lib­rium and mod­els the econ­omy dynam­i­cally;
  3. Mod­els behav­ior at the level of social classes rather than iso­lated agents;
  4. Pre­sumes ratio­nal but not prophetic behav­ior: peo­ple in social classes act in what they per­ceive as their best inter­ests given infor­ma­tion avail­able, but do not attempt to fore­cast the future state of the econ­omy (and they can­not do so in any case, because of the well-known fea­tures of com­plex sys­tems);
  5. Mod­els the endoge­nous cre­ation of money by the bank­ing sec­tor in a pure credit econ­omy (later exten­sions will incor­po­rate fiat money cre­ation by gov­ern­ments); and
  6. Gives credit and debt the piv­otal roles in eco­nomic the­ory that the Great Reces­sion has shown they have in the real world.


A framework for monetary macroeconomics


At one level, MCT is decep­tively sim­ple: all demand in the macro­econ­omy is treated as orig­i­nat­ing in bank accounts, where, in accor­dance with the empir­i­cal lit­er­a­ture (Holmes 1969; Moore 1979, 1988; Kyd­land and Prescott 1990), the bank­ing sys­tem has the capac­ity to endoge­nously cre­ate new credit-based money. The devel­op­ment of the frame­work is described else­where (see Keen 2006b, 2008, 2009); here I will sim­ply illus­trate MCT with the finan­cial flows used in the model of the 19th cen­tury “free bank­ing” sys­tem in Keen (2010). The core of MCT is a tab­u­lar lay­out of the finan­cial rela­tions between the eco­nomic enti­ties in the model, where each col­umn rep­re­sents an aggre­gate bank account, and each row rep­re­sents oper­a­tions on and between those accounts.

Table 1: Sam­ple Finan­cial Flows God­ley Table





Account Name

Bank Vault

Firm Loan

Firm Deposit

Worker Deposit

Bank Equity







Ini­tial con­di­tions






Lend Money



Record Loan


Com­pound Debt 


Ser­vice Debt 



Record Pay­ment


Deposit Inter­est






Deposit Inter­est







Repay Loan



Record Repay­ment




Using a sym­bolic alge­bra pro­gram, the place­hold­ers A to H are then replaced by suit­able func­tions:

The pro­gram then auto­mat­i­cally derives a set of dif­fer­en­tial equa­tions for this sys­tem, which can be ana­lyzed sym­bol­i­cally or sim­u­lated numer­i­cally:

This cov­ers the finan­cial side of the econ­omy. The real econ­omy is cou­pled to this via a price mech­a­nism (and links between the wages flow—which deter­mines employment—and invest­ment, which is not shown in the sim­ple model in Table 1, but which deter­mines the cap­i­tal stock in a larger model).

The price mech­a­nism is derived ana­lyt­i­cally in Keen 2010 (pp. 17–18), and cor­re­sponds to the exten­sive empir­i­cal lit­er­a­ture into how firms actu­ally set prices—which has noth­ing to do with mar­ginal cost and mar­ginal rev­enue (see Lee 1998, Blinder et al. 1998, and Keen & Stan­dish 2006 and 2010) but instead rep­re­sents a markup on the wage costs of pro­duc­tion


The real econ­omy itself is mod­eled using Goodwin’s growth cycle (Good­win 1967; see also Blatt 1983, pp. 204–216), but expressed in absolute val­ues (Employ­ment, Wages, etc.) rather than ratios (rate of employ­ment, wages share of out­put) as in Goodwin’s orig­i­nal model.


Applying the framework: a “corn economy” with a financial crisis


The sam­ple God­ley Table shown in Table 1 has to be extended to allow for invest­ment, which as Schum­peter argued is the sound basis on which the credit sys­tem endoge­nously cre­ates new debt-based money (Schum­peter 1934, pp. 95–101).

Table 2: God­ley Table for Corn Econ­omy Model





Account Name

Bank Vault

Firm Loan

Firm Deposit

Worker Deposit

Bank Equity







Lend from Vault 



Record Loan


Com­pound Debt 


Ser­vice Debt 



Record Pay­ment


Debt-financed Invest­ment


Record Invest­ment Loan





Deposit Inter­est








Repay Loan



Record Repay­ment



This God­ley Table results in the fol­low­ing generic sys­tem of finan­cial flows:

The sub­sti­tu­tions for this table are show in Equa­tion ; the rates of lend­ing, invest­ment and loan repay­ment (respec­tively A, D and J in Table 2) are now func­tions of the rate of profit, and wage pay­ments (E) are now wages times employ­ment.

The basic causal cycle in the Good­win model (to which the finan­cial flows above are attached) is quite sim­ple. Cau­sa­tion flows from left to right in equa­tions to :

  • The level of the phys­i­cal cap­i­tal stock deter­mines the level of phys­i­cal out­put per year:

  • Out­put per year deter­mines employ­ment :

  • The rate of employ­ment deter­mines the rate of change of the money wage—thus link­ing the phys­i­cal sec­tor to the mon­e­tary sec­tor; in keep­ing with Phillips’s orig­i­nal inten­tions (and in con­trast to most macro­eco­nomic mod­els), the wage change func­tion includes a reac­tion to the rate of change of employ­ment and the level of infla­tion, as well as a non­lin­ear reac­tion to the level of employ­ment:

  • The money wage deter­mines the rate of change of the price level :

  • The mon­e­tary value of out­put minus wages deter­mines profit:

  • The rate of profit deter­mines invest­ment (and hence the amount of new credit money needed should desired invest­ment exceed profit) and invest­ment minus depre­ci­a­tion deter­mines the rate of eco­nomic growth :

  • The inte­gral of invest­ment deter­mines the cap­i­tal stock:

  • The rate of change of the employ­ment rate is the rate of growth minus the rates of growth of labor pro­duc­tiv­ity and pop­u­la­tion:

  • Equa­tions for growth in labor pro­duc­tiv­ity and pop­u­la­tion com­plete the model:


The rates of lend­ing (A), debt-financed invest­ment (D) and loan repay­ment (J) are mod­eled as non­lin­ear func­tions of the rate of profit, while the Phillips Curve is also a non­lin­ear func­tion of the level of employ­ment. The basic func­tion used in all cases is a gen­er­al­ized expo­nen­tial func­tion where the argu­ments to the func­tion are an (xc,yc) coor­di­nate pair, the function’s slope at that point s, and its min­i­mum m:

The com­plete model is described by a set of ten dif­fer­en­tial equa­tions:

Given suit­able ini­tial con­di­tions and para­me­ter val­ues, this highly non­lin­ear mon­e­tary model can gen­er­ate the styl­ized facts of the last 20 years of macro­eco­nomic data: an appar­ent “Great Mod­er­a­tion” in employ­ment and inflation—which was actu­ally dri­ven by an expo­nen­tial growth in pri­vate debt—followed by a “Great Reces­sion” in which unem­ploy­ment explodes, infla­tion turns to defla­tion, and the debt level—absent of bank­ruptcy and gov­ern­ment intervention—goes purely expo­nen­tial as unpaid inter­est is com­pounded.

Fig­ure 1: US Data 1980–2008

As a com­plex sys­tems model, the behav­ior of this sys­tem depends upon its ini­tial con­di­tions as well as upon its inher­ent dynam­ics. In Keen 2011 I used a set of ini­tial con­di­tions that resulted in both a Great Mod­er­a­tion and a Great Recession—with no change to the under­ly­ing para­me­ters of the system—to indi­cate that this model fits Minsky’s cri­te­ria for a suc­cess­ful model of cap­i­tal­ism:

Can “It”—a Great Depression—happen again? And if “It” can hap­pen, why didn’t “It” occur in the years since World War II? These are ques­tions that nat­u­rally fol­low from both the his­tor­i­cal record and the com­par­a­tive suc­cess of the past thirty-five years. To answer these ques­tions it is nec­es­sary to have an eco­nomic the­ory which makes great depres­sions one of the pos­si­ble states in which our type of cap­i­tal­ist econ­omy can find itself.(Min­sky 1982 , p. 5; empha­sis added)

Fig­ure 2: Sim­u­la­tion Results with uncal­i­brated con­stant para­me­ter val­ues

This model cap­tures the macro­eco­nomic expe­ri­ence of the last 2 decades far more effec­tively than any neo­clas­si­cal model. How­ever, the Holy Grail of eco­nom­ics has always been to model the com­plex dynamic process by which com­modi­ties are pro­duced using other com­modi­ties and labor. In the next sec­tion I show that a struc­tured exten­sion of this corn econ­omy model—with finan­cial flows deter­min­ing demand, and pro­duc­tion mod­eled using Goodwin’s growth cycle—can gen­er­ate a coher­ent dynamic mon­e­tary mul­ti­sec­toral model of pro­duc­tion.


A dynamic monetary multisectoral model of production


First a strong caveat: this model is very ten­ta­tive, and many refine­ments need to be made. How­ever even in its ten­ta­tive state, it shows that a mon­e­tary, dynamic mul­ti­sec­toral model of pro­duc­tion can be con­structed.

The model repro­duces the struc­ture of the pre­ced­ing corn econ­omy model, extended to mul­ti­ple com­modi­ties in both pro­duc­tion (with each sec­tor need­ing to pur­chase inputs from other sec­tors pro­por­tional to its desired out­put level), and con­sump­tion. I also address one of the weak­nesses of input-out­put analysis—that pur­chases within a sec­tor are not explic­itly shown—by the sim­ple expe­di­ent of split­ting each sec­tor in two. There are 4 sec­tors in this sim­ple “proof of con­cept” model (notion­ally Cap­i­tal Goods, Con­sumer Goods, Agri­cul­ture and Energy).

The God­ley Table for this sys­tem has 19 sys­tem states— Bank Reserve, Bank Equity and Worker Deposit accounts as in the sin­gle sec­toral model, plus two Deposit and two Loan accounts per sector—and 16 finan­cial operations—debt com­pound­ing, debt repay­ing, money relend­ing and wages pay­ment as in the sin­gle sec­toral model, plus one inter­sec­toral pur­chase for pro­duc­tion and one for con­sump­tion per sec­tor. A styl­ized rep­re­sen­ta­tion of these flows is given in Table 3 (the inter­sec­toral flows are only par­tially indi­cated).

Table 3: Styl­ized rep­re­sen­ta­tion of mul­ti­ec­toral God­ley Table

Assets Lia­bil­i­ties Equity
Account Bank Reserve Sec­tor 1 Loan Sec­tor 2 Loan Sec­tor 1 Deposit Sec­tor 2 Deposit Worker Deposit Bank Equity
Sym­bol BR(t) FL1(t) FL1(t) FD1(t) FD2(t) WD(t) BE(t)
Com­pound Debt A1 A2
Deposit Inter­est B1 B2
Wages –C1 –C2 C1+C2
Worker Inter­est –D –D
Invest­ment K E –E
Inter­sec­toral C –F F
Inter­sec­toral A –G G
Inter­sec­toral E –H H
Con­sump­tion K I –I
Con­sump­tion C –J J
Con­sump­tion A –K K
Con­sump­tion E –L L
Pay Inter­est –M M
Repay Loans N –N
Recy­cle Reserves –O O O
New Money P P



An extract from the actual God­ley Table for this sys­tem (as imple­mented in Math­cad) is shown in Fig­ure 3.


Fig­ure 3: 7 of the 19 columns in the mul­ti­sec­toral God­ley Table

The rate of profit is now net of inter­sec­toral pur­chases for each sec­tor, and of course there is a dif­fer­ent rate of profit in each sec­tor. Inter­sec­toral pur­chases of inputs dif­fer for each sec­tor, and are pro­por­tional to the labor input needed to pro­duce the required out­put in each sector—signified by where the first sub­script rep­re­sents the sec­tor pur­chas­ing the inputs and the sec­ond the sec­tor from which the inputs are pur­chased. Equa­tion shows the rate of profit for­mu­lae for the cap­i­tal goods and con­sumer good sec­tors:


As with the sin­gle sec­toral model, behav­ior in five cru­cial areas is mod­eled as a non­lin­ear response to a rel­e­vant vari­able:

  • The rate of change of money wages as a func­tion of the rate of employ­ment;
  • The time con­stant in invest­ment deci­sions as a func­tion of the rate of profit;
  • The time con­stant in loan repay­ment as a func­tion of the rate of profit;
  • The time con­stant in money relend­ing as a func­tion of the rate of profit;
  • The time con­stant in new money cre­ation as a func­tion of the rate of profit;

Table 4: Para­me­ters for Behav­ioral Func­tions


With the pur­chases of inter­me­di­ate inputs taken care of in the mon­e­tary demand com­po­nent of the model, pro­duc­tion in each sec­tor is mod­eled as lagged response to installed cap­i­tal, and employ­ment is a lagged response to out­put. The func­tions for the con­sumer goods sec­tor, which are rep­re­sen­ta­tive of those for the other sec­tors, are shown in Equa­tion :

The full model is a sys­tem of dif­fer­en­tial equa­tions, where n is the num­ber of sec­tors, and the first set of terms spec­i­fies the equa­tions in the finan­cial sect­sor, the sec­ond the equa­tions in pro­duc­tion, and the final equa­tion is for pop­u­la­tion growth. In this sam­ple 4-sec­tor model, this results in a sys­tem of 40 non­lin­ear ODEs.




The rate of profit var­ied between sec­tors, and, once the sys­tem had set­tled into its limit cycle, ranged from 0.4% p.a. and 8.7%.

Fig­ure 4

The aggre­gate real rate of eco­nomic growth var­ied between minus 1 and plus 5 per­cent p.a., and growth fol­lowed a saw­tooth pat­tern:

Fig­ure 5

This shape cor­re­sponds with the styl­ized nature of the busi­ness cycle, as Blatt observed:

In the real world, upswings are slow; down­swings go with an almighty rush. In the words of Gal­braith:

The usual image of the busi­ness cycle was of a wave­like move­ment, and the waves of the sea were the accepted metaphor… The real­ity in the nine­teenth and early twen­ti­eth cen­turies was, in fact, much closer to the teeth of a rip­saw which go up on a grad­ual plane on one side and drop pre­cip­i­tately on the other…” (Blatt 1983, pp. 203–204, cit­ing Gal­braith 1975, p. 104)

The growth rate and the debt to out­put level moved together, and the debt ratio cycled between 50 and 110 per­cent of GDP.

Fig­ure 6

The dis­tri­b­u­tion of income was real­is­tic, though the dynam­ics were rather more volatile than in actual data:

Fig­ure 7

The rate of infla­tion was unre­al­is­tic, with a min­i­mum of 8 per­cent p.a. and a max­i­mum of 45 per­cent.

Fig­ure 8

These last two empir­i­cal weak­nesses prob­a­bly reflect the spec­i­fi­ca­tion for the Phillips curve, and the ten­dency of the model to oper­ate in over-full employ­ment (defined as a ratio of 1 in this sim­ple model) given the para­me­ters used for cap­i­tal­ist and banker behav­ior.

Fig­ure 9

Finally, finan­cial dynam­ics were an essen­tial part of this model: money is far from neu­tral in this model (and in the real world). Peri­ods of falling eco­nomic growth coin­cided with an increase in bank reserves, and a decline in the level of loans.

Fig­ure 10




Though this pre­lim­i­nary model has many short­com­ings, the fact that it works at all shows that it is pos­si­ble to model the dynamic process by which prices and out­puts are set in a mul­ti­sec­toral econ­omy. The fail­ure of the neo­clas­si­cal school to achieve this objective—which it has had since the time of Walras—may relate to the abstrac­tions it made with the inten­tion of mak­ing this process eas­ier to model. These devices—everything from Walras’s taton­nement, to ignor­ing the role of money—may in fact be why they failed. The real world is com­plex and the real econ­omy is mon­e­tary, and com­plex mon­e­tary mod­els are needed to do it jus­tice.

Given the com­plex­ity of this model and the sen­si­tiv­ity of com­plex sys­tems to ini­tial con­di­tions, it is rather remark­able that an obvi­ous limit cycle devel­oped out of an arbi­trary set of para­me­ter val­ues and ini­tial conditions—with most (but by no means all) vari­ables in the sys­tem keep­ing within real­is­tic bounds. A con­jec­ture is that this limit cycle is a man­i­fes­ta­tion of the well-known insta­bil­ity of an input-out­put matrix (Jor­gen­son 1960; Jor­gen­son 1960; Jor­gen­son 1961; Jor­gen­son 1961; Hahn 1963; Blatt 1983; Fleiss­ner 1990; Heester­man 1990; John­son 1993), com­bined with non­lin­ear rela­tions that reverse the insta­bil­ity prop­er­ties of the sys­tem as it diverges from its equi­lib­rium. This con­jec­ture was first made by Blatt in a dis­cus­sion of both the his­tor­i­cal evi­dence of the busi­ness cycle and the dual insta­bil­ity of the equi­lib­rium growth path:

At this stage of the argu­ment, we feel free to offer a con­jec­ture: The repeated devel­op­ment of an unsta­ble state of the econ­omy is asso­ci­ated with, and indeed is an unavoid­able con­se­quence of, the local insta­bil­ity of the state of bal­anced growth. (Blatt 1983, p. 161)

The pres­ence of mon­e­tary buffers—in the guise of deposit accounts—surely also plays a role in the system’s capac­ity, despite its insta­bil­ity, to stay within real­is­tic bounds, in con­trast to most (if not all) other dynamic mul­ti­sec­toral mod­els.

I doubt that Kuznets would have been sur­prised by the fail­ure of equi­lib­rium-ori­ented attempts to build dynamic mul­ti­sec­toral mod­els of eco­nomic growth, since he argued long ago that dynam­ics had to be dif­fer­ent to sta­t­ics, and in par­tic­u­lar that the fetish with equi­lib­rium had to be aban­doned:

Accord­ing to the econ­o­mists of the past and to most of their mod­ern fol­low­ers, sta­tic eco­nom­ics is a direct step­ping stone to the dynamic sys­tem, and may be con­verted into the lat­ter by the intro­duc­tion of the gen­eral ele­ment of change… Accord­ing to other econ­o­mists, the body of eco­nomic the­ory must be car­di­nally rebuilt, if dynamic prob­lems are to be dis­cussed effi­ciently…

… as long as sta­tic eco­nom­ics will remain a strictly uni­fied sys­tem based upon the con­cept of equi­lib­rium, and con­tinue to reduce the social phe­nom­e­non to units of rigidly defined indi­vid­ual behav­ior, its ana­lytic part will remain of lit­tle use to any sys­tem of dynamic eco­nom­ics… the sta­tic scheme in its entirety, in the essence of its approach, is nei­ther a basis, nor a step­ping stone towards a proper dis­cus­sion of dynamic prob­lems. Kuznets, S. (1930, pp. 422–428, 435–436; empha­sis added)

Yet the sta­tic approach—masquerading as dynam­ics via word games such as using the moniker “Dynamic Sto­chas­tic Gen­eral Equi­lib­rium” to describe bas­tardized Ram­say-Solow equi­lib­rium growth models—still dom­i­nate eco­nom­ics, even after the con­tin­u­ing dis­as­ter of the cri­sis of 2007. Part of the rea­son for this per­sis­tence, I believe, is the seduc­tive sim­plic­ity of the “Mar­shal­lian Cross” that forms the basis of edu­ca­tion in eco­nom­ics: it con­forms to Henry Menchen’s apho­rism that “Expla­na­tions exist; they have existed for all time; there is always a well-known solu­tion to every human problem—neat, plau­si­ble, and wrong”. For eco­nom­ics to escape the trap of sta­tic equi­lib­rium think­ing, we need an alter­na­tive foun­da­tion method­ol­ogy that is neat, plau­si­ble, and—at least to a first approximation—right.

I offer this model and the tools used to con­struct it as a first step towards such a neat, plau­si­ble and gen­er­ally cor­rect approach to macro­eco­nom­ics. A col­league has imple­mented the God­ley Table method for build­ing a dynamic model of finan­cial flows in a pro­to­type dynamic mod­el­ing pro­gram QED, which is freely down­load­able from my blog. A Math­e­mat­ica imple­men­ta­tion is being devel­oped as part of a project with the CSIRO, and it will also be freely avail­able from my blog when it is com­pleted. The ulti­mate objec­tive is to develop a stand­alone dynamic mon­e­tary macro­eco­nomic mod­el­ing tool that is more suited to finan­cial flows than exist­ing sys­tems dynam­ics pro­grams like Simulink (http://www.mathworks.com/products/simulink/), Ven­sim (http://www.vensim.com/) and Vis­sim (http://www.vissim.com/).

The global econ­omy was blindly led into our cur­rent finan­cial cri­sis by an eco­nom­ics pro­fes­sion that had deluded itself into the belief that such phe­nom­ena can­not occur. Hope­fully, dur­ing this cri­sis, mon­e­tary macro­eco­nomic dynam­ics will finally sup­plant the sta­tic method against which Kuznets inveighed so elo­quently at the start of capitalism’s pre­vi­ous great finan­cial cri­sis.




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This work results from a col­lab­o­ra­tive research effort between the United Nations Envi­ron­ment Pro­gram (UNEP) and CSIRO Sus­tain­able Ecosys­tems to estab­lish a regional report on Resource Effi­ciency: Eco­nom­ics and Out­look for Asia?Pacific. I thank Peter Humphreys of the UWS School of Account­ing (and pre­vi­ously Man­ager in the Group Account­ing Research and Pol­icy Sec­tion of the Com­mon­wealth Bank of Aus­tralia) for advice on bank­ing prac­tice.

About Steve Keen

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

    Dear keen, I ‘ve read all your mod­els on web­site, and find they are inter­est­ing . They do show some qual­i­ta­tive char­ac­ter­is­tics of eco­nomic process. My ques­tion is , can your method–simulation, be used to solve real eco­nomic prob­lems quan­ta­tively and accu­rately? I mean , that most para­me­ters now you use in the mod­els are the­o­ret­i­cal, not from real world. If we use , for exam­ple ‚real US eco­nomic datas of last three years, can we model out accu­rately what will hap­pen next year ? or because of sen­si­tiv­ity to ini­tial con­di­tion, accu­rate fore­cast is impos­si­ble? then what peo­ple can do to the eco­nomic real­ity? How can they make eco­nomic deci­sion more eff­ciently?

  • Alen Wang

    In a extreme con­di­tion like this Sub­preme Cri­sis, we know some­thing bad will hap­pen using your model,although we do not know when and how. But in a much more nor­mal con­di­tion, what eco­nomic prin­ci­ple can be used to guide our action if we do not its con­se­quence in a com­plex and chaos sit­u­a­tion? Is it another kind of casino cap­i­tal­ism?

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  • John Hawkins

    Shouldn’t cap­i­tal goods be the most volatile rather than the least volatile indus­try?