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If you’ve down­loaded and read the paper and pre­sen­ta­tion I post­ed in my pre­vi­ous entry, then there’s noth­ing new for you to read in the body of this post; the main addi­tion is the video below of my talk.

| Open Play­er in New Win­dow

That in part gives you rather too good a view of the back of the heads of Randy Wray and Dim­it­ry Papadim­itri­ou, both of whom sat down in front of the cam­era after my talk began, but the slides are still eas­i­ly vis­i­ble.

Soon I’ll pub­lish anoth­er post with the video of the talk I gave in New York to Debt­watch mem­bers, which has sub­stan­tial­ly more back­ground on the mod­el and the approach I take to mod­el­ling in gen­er­al, and an extreme­ly good and lengthy dis­cus­sion.

Abstract

My 1995 paper on mod­el­ing Min­sky’s Finan­cial Insta­bil­i­ty Hypoth­e­sis con­clud­ed with the state­ment that its “chaot­ic dynam­ics … should warn us against accept­ing a peri­od of rel­a­tive tran­quil­i­ty in a cap­i­tal­ist econ­o­my as any­thing oth­er than a lull before the storm” ((Keen 1995, p. 634)). That storm duly arrived, after the lull of the “Great Mod­er­a­tion”. Only a Fish­er-Keynes-Min­sky vision of the macro­econ­o­my can make sense of this cri­sis, and the need for a ful­ly fledged Min­skian mon­e­tary dynam­ic macro­eco­nom­ic mod­el is now clear­ly acute.

I also intro­duce a new free tool for dynam­ic mod­el­ing which is tai­lored to mod­el­ing finan­cial flows–QED. See pages 49–53 the Appen­dix for details.

Empirics

As Vic­ki Chick so suc­cinct­ly put it, Min­sky the Cas­san­dra was an opti­mist ((Chick 2001)). The sta­bi­liz­ing mech­a­nisms that Min­sky ini­tial­ly felt would help pre­vent “It” from hap­pen­ing again ((Min­sky 1982)) have been over­whelmed by a relent­less accu­mu­la­tion of pri­vate sec­tor debt, which have reached lev­els that dwarf those which caused “It” eighty years ago. Though “It” has not yet defin­i­tive­ly hap­pened again, nei­ther did our fore­bears in the 1930s real­ize that they were in “It” at the time—as a perusal of the Wall Street Jour­nal from those days will con­firm:

Mar­ket observers are watch­ing the cur­rent ral­ly close­ly since it has last­ed about 10 days, or about the same as the tech­ni­cal ral­ly start­ing in late April that gave way to a renewed bear move­ment. It’s believed “abil­i­ty of the ris­ing trend to car­ry on for sev­er­al days more would strength­en indi­ca­tions of a def­i­nite turn in the main trend of prices.” (Dim­itro­vsky 2008, Wall Street Jour­nal June 16 1931)

A com­par­i­son of 1930s data to today empha­sizes that the same debt-defla­tion­ary fac­tors that gave us the Great Depres­sion are active now; the only dif­fer­ences are that both the pri­vate sec­tor defla­tion­ary forces and the gov­ern­ment reac­tion are much greater today.

Pri­vate sec­tor debt is far high­er today than in the 1930s, both in the USA and else­where in the OECD. The data shown in Fig­ure 1 for the USA and Aus­tralia is repli­cat­ed to vary­ing degrees by most OECD nations ((See Table 1 in Bat­telli­no 2007, p. 14)).

Fig­ure 1: Debt to GDP ratios in the USA and Aus­tralia over the long term

So too is the impact of debt-financed eco­nom­ic activ­i­ty, both as an engine of appar­ent pros­per­i­ty dur­ing the “Great Mod­er­a­tion”, and as the force caus­ing the “Great Reces­sion” now. Fol­low­ing Min­sky, I regard aggre­gate demand in our dynam­ic cred­it-dri­ven econ­o­my as the sum of GDP plus the change in debt:

If income is to grow, the finan­cial mar­kets … must gen­er­ate an aggre­gate demand that, aside from brief inter­vals, is ever ris­ing. For real aggre­gate demand to be increas­ing, … it is nec­es­sary that cur­rent spend­ing plans, summed over all sec­tors, be greater than cur­rent received income and that some mar­ket tech­nique exist by which aggre­gate spend­ing in excess of aggre­gate antic­i­pat­ed income can be financed. It fol­lows that over a peri­od dur­ing which eco­nom­ic growth takes place, at least some sec­tors finance a part of their spend­ing by emit­ting debt or sell­ing assets. (Min­sky 1982, p. 6; empha­sis added)

That debt-financed com­po­nent of demand (where that demand is expend­ed upon both com­mod­i­ty and asset mar­kets) was far greater dur­ing the false boom after the 1990s reces­sion than it was dur­ing the 1920s, and the neg­a­tive con­tri­bu­tion today is also larg­er than for the com­pa­ra­ble time in the 1930s.

Fig­ure 2 shows the lev­els of debt and GDP in 1920–1940, while Fig­ure 3 shows how much debt added to demand dur­ing the 1920s, and sub­tract­ed from it dur­ing the 1930s.

Fig­ure 2: Debt and GDP before and dur­ing the Great Depres­sion

Fig­ure 3: Aggre­gate demand as the sum of GDP plus the change in debt

The change in debt was so great that it dom­i­nat­ed the impact of GDP itself in deter­min­ing changes in the lev­el of employ­ment. Fig­ure 4 cor­re­lates the change in debt with unem­ploy­ment; over the boom and bust years of 1920–1940, the cor­re­la­tion was ‑0.938—rising debt was strong­ly cor­re­lat­ed with falling unem­ploy­ment, and vice ver­sa.

Fig­ure 4: Change in debt and unem­ploy­ment before and dur­ing the Great Depres­sion

The same met­rics have played out between 1990 and today, but with far greater force. As Fig­ure 5 shows, the debt dom­i­nates GDP even more now than it did when “It” hap­pened.

Fig­ure 5: Pri­vate debt and GDP 1990–2010

The debt con­tri­bu­tion to demand dur­ing the boom years till 2008 is there­fore much greater (Fig­ure 6).

Fig­ure 6: Aggre­gate demand 1990–2010

The cor­re­la­tion of changes in pri­vate debt with unem­ploy­ment, at ‑0.955 between 1990 and today, is even stronger than in the 1920–30s.

Fig­ure 7: Change in debt and unem­ploy­ment, 1990–2010

A use­ful met­ric in gaug­ing the impact of debt on demand is to com­pare the change in debt to the sum of GDP plus the change in debt (the dynam­ic mea­sure of aggre­gate demand as per (Min­sky 1982, p. 6)). Fig­ure 8 mea­sures this from the point at which the debt con­tri­bu­tion to demand was the great­est in the boom pri­or to the crises of 1930 and 2008—mid-1928 and Decem­ber 2007 respec­tive­ly. It also includes the con­tri­bu­tion to aggre­gate demand from gov­ern­ment debt. This, more than any oth­er mea­sure, tells us that the GFC is big­ger than the Great Depres­sion, and that we are still in its ear­ly days.

Fig­ure 8: The turn­around in debt-financed demand, Great Depres­sion and today

First­ly, the con­tri­bu­tion to demand from ris­ing pri­vate debt was far greater dur­ing the recent boom than dur­ing the Roar­ing Twenties—accounting for over 22% of aggre­gate demand ver­sus a mere 8.7% in 1928. Sec­ond­ly, the fall-off in debt-financed demand since the date of Peak Debt has been far sharp­er now than in the 1930s: in the 2 1/2 years since it began, we have gone from a pos­i­tive 22% con­tri­bu­tion to neg­a­tive 20%; the com­pa­ra­ble fig­ure in 1931 (the equiv­a­lent date back then) was minus 12%. Third­ly, the rate of decline in debt-financed demand shows no signs of abat­ing: delever­ag­ing appears unlike­ly to sta­bi­lize any time soon.

Final­ly, the addi­tion of gov­ern­ment debt to the pic­ture empha­sizes the cru­cial role that fis­cal pol­i­cy has played in atten­u­at­ing the decline in pri­vate sec­tor demand (reduc­ing the net impact of chang­ing debt to minus 8%), and the speed with which the Gov­ern­ment react­ed to this cri­sis, com­pared to the 1930s. But even with the Gov­ern­men­t’s con­tri­bu­tion, we are still on a sim­i­lar tra­jec­to­ry to the Great Depres­sion.

What we haven’t yet experienced—at least in a sus­tained manner—is defla­tion. That, com­bined with the enor­mous fis­cal stim­u­lus, may explain why unem­ploy­ment has sta­bi­lized to some degree now despite sus­tained pri­vate sec­tor delever­ag­ing, where­as it rose con­sis­tent­ly in the 1930s (Fig­ure 9).

Fig­ure 9: Com­par­ing unem­ploy­ment then and now

Here some cred­it may be due to “Heli­copter Ben”. Though Bernanke and Greenspan clear­ly played a role in encour­ag­ing pri­vate debt to reach the heights it did, it is cer­tain­ly con­ceiv­able that his enor­mous injec­tion of base mon­ey into the sys­tem in late 2008 avert­ed a nascent defla­tion (Fig­ure 10).

Fig­ure 10: Infla­tion, defla­tion and base mon­ey growth 2005-Now

Here Bernanke is replay­ing the tune from 1930s—though much more loud­ly. Though he accused his 1930 coun­ter­parts of caus­ing the Great Depres­sion via tight mon­e­tary pol­i­cy (Bernanke 2000, p. ix), a clos­er look at the data shows that he was mere­ly more deci­sive and suc­cess­ful than his pre­de­ces­sors: they too boost­ed M0 in an attempt to restrain defla­tion, but nowhere near as much, as quick­ly, or in such a sus­tained way.

Fig­ure 11: Infla­tion, defla­tion and base mon­ey growth in the 1930s

What he shares with them is par­tial respon­si­bil­i­ty for caus­ing the Great Reces­sion, since like them he ignored the impact of pri­vate debt on eco­nom­ic per­for­mance ((Bernanke 1995, p. 17) and (Bernanke 1983, p. 258 & note 5)), when that—and not “improved con­trol of infla­tion” ((Bernanke 2004))—was the real “pos­i­tive” cause of the “Great Mod­er­a­tion, as it is now the defin­ing neg­a­tive fac­tor of the Great Reces­sion.

Whether this suc­cess can con­tin­ue is now a moot point: the most recent infla­tion data sug­gests that the suc­cess of “the log­ic of the print­ing press” may be short-lived. The stub­born fail­ure of the “V‑shaped recov­ery” to dis­play itself ((Lazear and Mar­ron 2009, p. 54)) also reit­er­ates the mes­sage of Fig­ure 7: there has not been a sus­tained recov­ery in eco­nom­ic growth and unem­ploy­ment since 1970 with­out an increase in pri­vate debt rel­a­tive to GDP. For that unlike­ly revival to occur today, the econ­o­my would need to take a pro­duc­tive turn for the bet­ter at a time that its debt bur­den is the great­est it has ever been (Fig­ure 12).

Fig­ure 12: Debt to GDP and unem­ploy­ment 1970-Now

Debt-financed growth is also high­ly unlike­ly, since the trans­fer­ence of the bub­ble from one asset class to anoth­er that has been the by-prod­uct of the Fed’s too-suc­cess­ful res­cues in the past ((Min­sky 1982, pp. 152–153.)) means that all pri­vate sec­tors are now debt-sat­u­rat­ed: there is no-one in the pri­vate sec­tor left to lend to (Fig­ure 13).

Fig­ure 13: US debt by sec­tor, 1920-Now

Modeling Minsky

How do we make sense of this empir­i­cal real­i­ty? Cer­tain­ly main­stream eco­nom­ics, with its equi­lib­ri­um fetish and igno­rance of cred­it, is a waste of time—it func­tioned more as a means to divert atten­tion from what mat­tered in the econ­o­my than as a means to under­stand it. Min­sky pro­vides the foun­da­tion from which our predica­ment can be under­stood, but our ren­di­tion of his vision is still sparse com­pared to the worth­less but elab­o­rate Neo­clas­si­cal tapes­try. We need an inher­ent­ly mon­e­tary, his­tor­i­cal­ly real­is­tic and non-equi­lib­ri­um macro­eco­nom­ics.

My con­tri­bu­tion to this has been to extend my orig­i­nal Min­sky mod­el ((Keen 1995))—built on the foun­da­tions of Good­win’s mod­el of a cycli­cal econ­o­my (Good­win 1967) —by devel­op­ing mod­els of endoge­nous mon­ey cre­ation derived from Cir­cuit The­o­ry ((Graziani 1989), (Graziani 2003)), and by–tentatively–combining the two.

My basic Min­sky mod­el extend­ed Good­win’s pio­neer­ing “preda­tor-prey” mod­el of a cycli­cal econ­o­my by replac­ing the unre­al­is­tic assump­tion that cap­i­tal­ist invest all their prof­its with the real­is­tic non­lin­ear propo­si­tion that they invest more dur­ing booms and less dur­ing slumps—with the vari­a­tion accom­mo­dat­ed by a finan­cial sec­tor that lends mon­ey at inter­est. That led to a chaot­ic mod­el which could, giv­en appro­pri­ate ini­tial con­di­tions, gen­er­ate a debt-induced crisis—but which had a sta­ble equi­lib­ri­um. This was part of the way towards Min­sky. How­ev­er, while the fact that the equi­lib­ri­um was sta­ble was con­sis­tent with (Fish­er 1933, p. 339, point 9), it was rather awk­ward when judged against Min­sky’s famous state­ment that “Stability—or tranquility—in a world with a cycli­cal past and cap­i­tal­ist finan­cial insti­tu­tions is desta­bi­liz­ing” ((Min­sky 1982, p. 101)).

What was miss­ing in my orig­i­nal Min­sky mod­el was Ponzi finance. Put sim­ply, this is debt-financed spec­u­la­tion on asset prices, which we can now see as the dri­ving force behind the accu­mu­la­tion of debt in the last two decades, and the con­se­quent infla­tion of asset prices. In my orig­i­nal mod­el, all debt was relat­ed to the con­struc­tion of new cap­i­tal equip­ment, which is inher­ent­ly a non-Ponzi behav­ior. I intro­duced a sim­u­lacrum of Ponzi finance ((Keen 2009)), with addi­tion­al debt being tak­en on when the rate of growth exceeds a thresh­old lev­el, with­out adding to the cap­i­tal stock (the 4^th equa­tion in ). This sim­u­lates spec­u­la­tion on asset prices, though with­out explic­it­ly mod­el­ing asset prices them­selves.

That gen­er­at­ed a mod­el in which sta­bil­i­ty was desta­bi­liz­ing, and in which the lev­el of debt that trig­gered a break­down was rather clos­er to the cur­rent empir­i­cal record (see Fig­ure 14).

Fig­ure 14: The mod­el in equa­tion as a sys­tems engi­neer­ing flow­chart

Circuit Theory

Though my Min­sky mod­el incor­po­rates debt, it is not an explic­it­ly mon­e­tary mod­el, and the active role that the finan­cial sec­tor has played in caus­ing this cri­sis makes it obvi­ous that its own dynam­ics must be incor­po­rat­ed in any real­is­tic mod­el of our cur­rent predica­ment. Cir­cuit the­o­ry gives the best foun­da­tion for under­stand­ing the dynam­ics of cred­it cre­ation, but ini­tial attempts to devise a mod­el from this the­o­ry reached para­dox­i­cal results—in par­tic­u­lar, the wide­spread con­clu­sion that cap­i­tal­ists could not make prof­its in the aggre­gate if they had to pay inter­est on bor­rowed mon­ey, or if work­ers saved any of their wages ((Graziani 1989, p. 5); (Bellofiore, Davan­za­ti et al. 2000, p. 410 note 9); (Rochon 2005, p. 125)).

It is rel­a­tive­ly easy to show that this con­ven­tion­al Cir­cuitist con­clu­sion is the prod­uct of con­fus­ing stock—specifically here an ini­tial injec­tion of mon­ey into an economy—with a flow—the amount of eco­nom­ic activ­i­ty that the stock of mon­ey can gen­er­ate in a giv­en time frame. I have done this by mod­el­ing a pure cred­it economy—one with­out fiat mon­ey in any sense—not because that is our actu­al finan­cial sys­tem, but because it is sim­pler to illus­trate that cap­i­tal­ists can bor­row mon­ey, pay inter­est, and make a net prof­it in a mod­el in which the only source of finance is pri­vate­ly issued debt.

To avoid being dis­tract­ed by sev­er­al con­tentious but, in this con­text, side-issues amongst mon­e­tary the­o­rists, I demon­strate that cap­i­tal­ists can indeed make mon­e­tary prof­its in a mod­el of the short-lived 19^th cen­tu­ry “Free Bank­ing” sys­tem ((Keen 2010)). The basic “con­stant mon­ey stock” mod­el sim­u­lates a pri­vate bank that has print­ed N of its own dol­lar notes like those shown in Fig­ure 15, and then lends them to firms, who hire work­ers that pro­duce out­put that is then sold to cap­i­tal­ists, work­ers and bankers.

Fig­ure 15: Bank of Flo­rence (Nebras­ka) dol­lar note ((Smith­son­ian Insti­tu­tion 2010))

The basic flow oper­a­tions that apply in this sys­tem are that:

1. The bank lends notes from its vault B_V to the firms’ deposit accounts F_D;
2. Firms pay inter­est on the loans from their deposit accounts to the bank’s trans­ac­tions account B_T;
3. The bank pays inter­est from its trans­ac­tions account to the firms’ deposit accounts;
4. Firms pay wages from their deposit accounts into work­ers’ deposit accounts W_D;
5. The bank pays inter­est from its trans­ac­tions account on work­ers’ account bal­ances;
6. Bank and work­ers pay for con­sump­tion of the out­put of firms; and
7. Firms repay their loans by trans­fer­ring dol­lars from their deposit accounts to the bank’s vault.

These oper­a­tions are shown in the rel­e­vant rows in Table 1, and since, as Wynne God­ley so prop­er­ly insist­ed, “every flow comes from some­where and goes some­where” (God­ley 1999, p. 394), these oper­a­tions sum to zero on each row.

How­ev­er there are oper­a­tions in bank­ing that are not flows, but account­ing entries made on the debt ledger:

1. The record­ing of the lend­ing of mon­ey by the bank to the firms on the debt ledger F_L;
2. The com­pound­ing of debt at the rate of inter­est;
3. The record­ing of pay­ments of inter­est in row 2 above by deduct­ing the amount paid from the lev­el of out­stand­ing debt; and
4. The record­ing of pay­ments of prin­ci­pal in row 7 above by deduct­ing the amount paid from the lev­el of out­stand­ing debt.

Table 1: Basic finan­cial trans­ac­tions in a Free Bank­ing econ­o­my

The columns in this table rep­re­sent the equa­tions of motion of this mod­el of free bank­ing, and the rate of change of each account is giv­en by the sym­bol­ic sum of each col­umn:

With the sub­sti­tu­tions shown in Table 2, the fol­low­ing mod­el results:

Table 2: Finan­cial oper­a­tions in the Free Bank­ing mod­el

As is eas­i­ly shown, with real­is­tic para­me­ter val­ues (see Table 3; the val­ues are explained lat­er) this describes a self-sus­tain­ing sys­tem in which all accounts set­tle down to equi­lib­ri­um val­ues, and in which cap­i­tal­ists earn a mon­e­tary prof­it.

Table 3: Para­me­ter val­ues

Fig­ure 16 shows the dynam­ics of this sys­tem; with an ini­tial stock of N=100 mil­lion dol­lar notes.

Fig­ure 16: Bank account bal­ances over time

The equi­lib­ri­um val­ues can be solved for sym­bol­i­cal­ly in this con­stant mon­ey stock mod­el:

From account balances to incomes

The year­ly wages of work­ers and gross inter­est earn­ings bankers can be cal­cu­lat­ed from the sim­u­la­tion, and they in part explain why, in con­trast to the con­ven­tion­al belief amongst Cir­cuitist writ­ers, cap­i­tal­ists can bor­row mon­ey, pay inter­est, and still make a prof­it. Though only $100 mil­lion worth of notes were cre­at­ed, the cir­cu­la­tion of those notes gen­er­ates work­ers’ wages of $151 mil­lion per annum (giv­en the para­me­ter val­ues used in this sim­u­la­tion), 1.5 times the size of the aggre­gate val­ue of notes in cir­cu­la­tion.

Fig­ure 17: Wages and Gross Inter­est

This indi­cates the source of the Cir­cuitist conun­drums: the stock of mon­ey has been con­fused with the amount of eco­nom­ic activ­i­ty that mon­ey can finance over time. A stock—the ini­tial amount of notes cre­at­ed in this model—has been con­fused with a flow.
In fact, for a wide range of val­ues for the para­me­ter f_D, the flows ini­ti­at­ed by the mon­ey bor­rowed by the firms over a year exceed the size of the loan itself.

This is pos­si­ble because the stock mon­ey can cir­cu­late sev­er­al times in one year—something that Marx accu­rate­ly enun­ci­at­ed over a cen­tu­ry ago in Vol­ume II of Cap­i­tal (though his numer­i­cal exam­ple is extreme­ly large):

“Let the peri­od of turnover be 5 weeks, the work­ing peri­od 4 weeks… In a year of 50 weeks … Cap­i­tal I of £2,000, con­stant­ly employed in the work­ing peri­od, is there­fore turned over 12½ times. 12½ times 2,000 makes £25,000.” (Marx and Engels 1885, Chap­ter 16: The Turnover of Vari­able Cap­i­tal)

Aggre­gate wages and aggre­gate prof­its there­fore depend in part upon the turnover peri­od between the out­lay of mon­ey to finance pro­duc­tion and the sale of that pro­duc­tion. This turnover peri­od can be sub­stan­tial­ly short­er than a year, in which case f_D will be sub­stan­tial­ly larg­er than 1, as I explain below.

The making of monetary profits

A sec­ond fun­da­men­tal insight from Marx lets us explain what f_D is, and simul­ta­ne­ous­ly derive an expres­sion for prof­its: the annu­al wages bill reflects both the turnover peri­od, and the way in which the sur­plus val­ue gen­er­at­ed in pro­duc­tion is appor­tioned between cap­i­tal­ists and work­ers. The val­ue of f_D there­fore reflects two fac­tors: the share of sur­plus (in Sraf­fa’s sense) that accrues to work­ers; and the turnover peri­od mea­sured in years—the time between M and M+. Labelling the share going to cap­i­tal­ists as s and the share to work­ers as (1‑s), and labelling the turnover peri­od as and express­ing it as a frac­tion of a year, I can per­form the sub­sti­tu­tion shown in Equa­tion :

Mon­ey wages are there­fore:

Since nation­al income resolves itself into wages and prof­its (inter­est income is a deduc­tion from oth­er income sources), we have also iden­ti­fied gross prof­it:

Using a val­ue of s=40%—which cor­re­sponds to his­tor­i­cal norm of 60% of pre-inter­est income going to work­ers (see Fig­ure 18)—this implies a val­ue for of 0.3.

Fig­ure 18: Wages per­cent­age of US GDP

This means that the turnover peri­od in Marx’s ter­mi­nol­o­gy is rough­ly 16 weeks. This is much longer than in Marx’s numer­i­cal illus­tra­tion above, but still suf­fi­cient to give cap­i­tal­ists prof­its that are sub­stan­tial­ly greater than the ser­vic­ing costs of debt. Fig­ure 19 shows the annu­al incomes for each class in soci­ety over time; all are pos­i­tive and the equi­lib­ri­um lev­els (once account lev­els sta­bi­lize) are $151 mil­lion, $98 mil­lion and $2.5 mil­lion for work­ers, cap­i­tal­ists and bankers respec­tive­ly out of a nation­al income of $192 mil­lion (see Equa­tion ).

Fig­ure 19: Class incomes after inter­est pay­ments

The val­ue of also deter­mines the ratio of nom­i­nal GDP to the pro­por­tion of the mon­ey stock in cir­cu­la­tion (the equiv­a­lent of M1-M0 in mon­e­tary sta­tis­tics, since in this pure cred­it mod­el there is no fiat mon­ey), which is 3 giv­en the para­me­ters used in this sim­u­la­tion. This is with­in the high­ly volatile range sug­gest­ed by his­tor­i­cal data (see Fig­ure 20).

Fig­ure 20: US GDP to Mon­ey Sup­ply ratios

Table 4 sum­maris­es the equi­lib­ri­um val­ues for account bal­ances, gross and net incomes in this hypo­thet­i­cal pure cred­it econ­o­my:

Table 4

Other parameters and time lags

The para­me­ters r_L and r_D are nom­i­nal inter­est rates and their val­ues are rough­ly in line with his­tor­i­cal norms at times of low-infla­tion; that leaves the para­me­ters b_V, f_L,w_D and b_T to account for.

The val­ues for b_V and f_L were cho­sen so that the equi­lib­ri­um val­ue of B_V would be rough­ly the val­ue not­ed by (Boden­horn and Hau­pert 1996, p. 688) of 15 per­cent of avail­able notes:

The para­me­ters w_D and b_T sig­ni­fy how rapid­ly work­ers and bankers respec­tive­ly spend their bank bal­ances on the out­put pro­duced by firms: work­ers turnover their accounts 26 times a year, while bankers turnover their account just once.

In the remain­der of the paper, these para­me­ters are expressed using the sys­tems engi­neer­ing con­cept of a time con­stant,
which gives the fun­da­men­tal fre­quen­cy of a process. In every case, the time con­stant is the inverse of the para­me­ter used thus far; for instance, the val­ue of 26 for w_D cor­re­sponds to work­ers’ con­sump­tion hav­ing a fun­da­men­tal fre­quen­cy of 1/26^th of a year, or two weeks.

Table 5: Time con­stants in the mod­el

Para­me­ter and val­ue	Time con­stant and val­ue	Mean­ing
bV = ¾		Banks lend their reserve hold­ings of notes every 15 months
fL= 1/7		Firms repay their loans every 7 years
wD = 26		Work­ers spend their sav­ings every 2 weeks
bT = 1		Bankers spend their sav­ings every 1 year
		Time con­stant in price set­ting (intro­duced in Equa­tion )
		Banks dou­ble the mon­ey sup­ply every 15 years (intro­duced in Table 7 on page 31)

Production, prices and monetary profits

Con­sid­er a sim­ple pro­duc­tion sys­tem in which out­put is pro­por­tion­al to the labor input L with con­stant labor pro­duc­tiv­i­ty a:

Labor employed in turn equals the mon­e­tary flow of wages divid­ed by the nom­i­nal wage rate W:

Prices then link this phys­i­cal out­put sub­sys­tem to the finan­cial mod­el above. In equi­lib­ri­um, it must be the case that the phys­i­cal flow of goods pro­duced equals the mon­e­tary demand for them divid­ed by the price lev­el. We can there­fore derive that in equi­lib­ri­um, the price lev­el will be a markup on the mon­e­tary wage, where the markup reflects the rate of sur­plus as defined in this paper.

To answer Rochon’s vital ques­tion, M becomes M+ via a price-sys­tem markup on the phys­i­cal sur­plus pro­duced in the fac­to­ry sys­tem. This markup can be derived sim­ply by con­sid­er­ing demand and sup­ply fac­tors in equi­lib­ri­um. The flow of demand is the sum of wages and prof­its (since inter­est pay­ments are a trans­fer and do not con­tribute to the val­ue of output—despite Wall Street’s bleat­ings to the con­trary). The mon­e­tary val­ue of demand is thus:

The phys­i­cal units demand­ed equals this mon­e­tary demand divid­ed by the price lev­el:

In equi­lib­ri­um this phys­i­cal demand will equal the phys­i­cal out­put of the econ­o­my:

Solv­ing for the equi­lib­ri­um price P_e yields:

The markup is thus the inverse of work­ers’ share of the sur­plus gen­er­at­ed in pro­duc­tion. Cir­cuit the­o­ry there­fore pro­vides a mon­e­tary expres­sion of Marx’s the­o­ry of sur­plus val­ue, as it was always intend­ed to do.

With these phys­i­cal and price vari­ables added to the sys­tem, we are now able to con­firm that prof­it as derived from the finan­cial flows table cor­re­sponds to prof­it as the dif­fer­ence between the mon­e­tary val­ue of out­put and the wage bill (in this sim­ple sin­gle-sec­toral mod­el).

Table 6: Para­me­ters and vari­ables for phys­i­cal pro­duc­tion sub­sys­tem

Vari­able, Para­me­ter or Ini­tial Con­di­tion	Def­i­n­i­tion	Val­ue
a	Labour pro­duc­tiv­i­ty a = Q/L	2
W	Nom­i­nal wage	1
Pe	Equi­lib­ri­um price	0.833
P0	Ini­tial Price	1
Le	Equi­lib­ri­um employ­ment	151.216
Qe	Equi­lib­ri­um out­put	302.432

Using the val­ues giv­en in Table 6, it is eas­i­ly con­firmed that the equi­lib­ri­um lev­el of prof­its derived from the finan­cial flows cor­re­sponds to the lev­el derived from the phys­i­cal pro­duc­tion sys­tem:

The price rela­tion giv­en above applies also only in equi­lib­ri­um. Out of equi­lib­ri­um, it is rea­son­able to pos­tu­late a first-order con­ver­gence to this lev­el, where the time con­stant reflects the time it takes firms to revise prices. This implies the fol­low­ing dynam­ic pric­ing equa­tion:

A sim­u­la­tion also con­firms that the mon­e­tary flows (demand) and the mon­e­tary val­ue of phys­i­cal flows (sup­ply) con­verge over time (Fig­ure 21).

Fig­ure 21: Sup­ply, Demand and Price con­ver­gence

This solves the para­dox of mon­e­tary prof­its: it was not a para­dox at all, but a con­fu­sion of stocks with flows in pre­vi­ous attempts to under­stand the mon­e­tary cir­cuit of pro­duc­tion.

Analysing the GFC

We can now use this frame­work to con­sid­er one aspect of the cur­rent finan­cial cri­sis: if a “cred­it crunch” occurs, what is the best way for gov­ern­ment to address it?—by giv­ing fiat mon­ey to the banks to lend, or by giv­ing it to the debtors to spend?

Our cur­rent cri­sis is, of course, more than mere­ly a “cred­it crunch”—a tem­po­rary break­down in the process of cir­cu­la­tion of cred­it. It is also arguably a sec­u­lar turn­ing point in debt akin to that of the Great Depres­sion ((Keen 2009)), as Fig­ure 22 illus­trates. How­ev­er the mod­el devel­oped here can assess the dif­fer­en­tial impact of a sud­den injec­tion of fiat mon­ey to res­cue an econ­o­my that has expe­ri­enced a sud­den drop in the rate of cir­cu­la­tion and cre­ation of pri­vate cred­it. This is an impor­tant point, since although the scale of gov­ern­ment response to the cri­sis was enor­mous across all affect­ed nations, the nature of that response did vary: notably, the USA focused its atten­tion on boost­ing bank reserves in the belief, as expressed by Pres­i­dent Oba­ma, that the mon­ey mul­ti­pli­er made refi­nanc­ing the banks far more effec­tive than res­cu­ing the bor­row­ers:

And although there are a lot of Amer­i­cans who under­stand­ably think that gov­ern­ment mon­ey would be bet­ter spent going direct­ly to fam­i­lies and busi­ness­es instead of banks – “where’s our bailout?,” they ask – the truth is that a dol­lar of cap­i­tal in a bank can actu­al­ly result in eight or ten dol­lars of loans to fam­i­lies and busi­ness­es, a mul­ti­pli­er effect that can ulti­mate­ly lead to a faster pace of eco­nom­ic growth. (Oba­ma 2009, p. 3. Empha­sis added)

Fig­ure 22: Pri­vate debt to GDP ratios, USA & Aus­tralia

The Aus­tralian pol­i­cy response to the GFC, on the oth­er hand, was pith­ily summed up in the advice giv­en by its Trea­sury: “go ear­ly, go hard, go house­holds” ((Gru­en 2008)). Though many oth­er fac­tors dif­fer­en­ti­ate these two countries—notably Aus­trali­a’s posi­tion as a com­mod­i­ty pro­duc­ing sup­pli­er to China—the out­comes on unem­ploy­ment imply that the Aus­tralian mea­sures more suc­cess­ful than the Amer­i­can “mon­ey mul­ti­pli­er” approach (See Fig­ure 23).

Fig­ure 23: Unem­ploy­ment rates USA and Aus­tralia

The mod­el is extend­ed in the next sec­tion to con­sid­er a grow­ing econ­o­my, and then a dif­fer­en­tial response to a cred­it crunch is con­sid­ered: an iden­ti­cal injec­tion of funds at the same time into either the banks’ equi­ty accounts—simulating the USA’s pol­i­cy response—or into the Work­ers’ Deposit accounts—simulating the Aus­tralian response.

Endogenous money creation and economic growth

To mod­el a cred­it crunch in a grow­ing econ­o­my, while oth­er­wise main­tain­ing the struc­ture of the Free Banking/pure cred­it mon­ey mod­el above, I move beyond the lim­i­ta­tions of a pure paper mon­ey sys­tem to allow for endoge­nous mon­ey cre­ation as described in (Moore 1979):

“In the real world banks extend cred­it, cre­at­ing deposits in the process, and look for the reserves lat­er” ((Moore 1979, p. 539) cit­ing (Holmes 1969, p. 73); see also more recent­ly (Disy­atat 2010, “loans dri­ve deposits rather than the oth­er way around”, p. 7)).

In the mod­el, new cred­it to sus­tain a grow­ing econ­o­my is cre­at­ed by a simul­ta­ne­ous increase in the loan and deposit accounts for the bor­row­er.

The finan­cial flows in this sys­tem are giv­en in Table 7. The two changes to Free Bank­ing mod­el are the addi­tion of row 12 (and its ledger record­ing in row 13), with the qual­i­ta­tive­ly new oper­a­tion of Mon­ey Cre­ation being added to the pre­vi­ous oper­a­tion of Mon­ey Trans­fer; and a “Deus Ex Machi­na” injec­tion of fiat mon­ey into either Bank Equi­ty or Work­er Deposit accounts at a after a cred­it crunch.

Table 7: Endoge­nous mon­ey cre­ation

Again, sim­ply to illus­trate that the sys­tem is viable, a con­stant growth para­me­ter has the banks dou­bling the stock of loans every 15 years (see Table 3 on page 18):

A cred­it crunch is sim­u­lat­ed by vary­ing the three cru­cial finan­cial flow para­me­ters , , and at an arbi­trary time in the fol­low­ing sim­u­la­tion (at t=25 years):
and are dou­bled and is halved, rep­re­sent­ing banks halv­ing their rates of cir­cu­la­tion and cre­ation of new mon­ey and firms try­ing to repay their loans twice as quick­ly. The gov­ern­ment fiat-mon­ey res­cue is mod­elled as a one-year long injec­tion of a total of $100 mil­lion one year after the cred­it crunch.

Pre-cred­it crunch	Post-cred­it crunch	Impact of Cred­it Crunch
?V = 4/3 years		Banks lend their reserve hold­ings of notes every 15 months
?L= 7 years		Firms repay their loans every 3.5 years
? M= 15 years		Banks dou­ble the mon­ey sup­ply every 30 years
K=$100 mil­lion		Inject­ed either into Bank Equi­ty BE or Work­er Deposit WD at year 26, one year after the cred­it crunch

Sev­er­al exten­sions to the phys­i­cal side of the mod­el are required to mod­el eco­nom­ic growth. In the absence of Ponzi spec­u­la­tion, growth in the mon­ey sup­ply is only war­rant­ed if eco­nom­ic growth is occur­ring, which in turn requires a grow­ing pop­u­la­tion and/ or labour pro­duc­tiv­i­ty. These vari­ables intro­duce the issue of the employ­ment rate, and this in turn rais­es the pos­si­bil­i­ty of vari­able mon­ey wages in response to the rate of unemployment—a Phillips curve. These addi­tion­al vari­ables are spec­i­fied in Equa­tion :

The para­me­ter val­ues and func­tion­al form for this phys­i­cal growth exten­sion are shown in Table 8.

Table 8: Para­me­ters and func­tion for growth mod­el

Vari­able or para­me­ter	Descrip­tion	Val­ue
	Rate of growth of labor pro­duc­tiv­i­ty	1% p.a.
	Rate of growth of pop­u­la­tion	2% p.a.
Pop	Pop­u­la­tion	Ini­tial val­ue = 160
	Employ­ment rate	Ini­tial val­ue = 94.5%
	Phillips curve:

Fig­ure 24 shows the impact of the cred­it crunch upon bank accounts: loans and deposits fall while the pro­por­tion of the mon­ey sup­ply that is lying idle in bank reserves ris­es dra­mat­i­cal­ly.

Fig­ure 24: Bank accounts before and after a Cred­it Crunch

The US empir­i­cal data to date has dis­played a sim­i­lar pat­tern, though with a much sharp­er increase in bank reserves as shown in Fig­ure 25.

Fig­ure 25: St Louis FRED AJDRES and BUSLOANS

A very sim­i­lar pat­tern to the empir­i­cal data is evi­dent in the mod­el when the US pol­i­cy of increas­ing bank reserves is sim­u­lat­ed (Fig­ure 26).

Fig­ure 26: Sim­u­lat­ing US bank-ori­ent­ed pol­i­cy towards a cred­it crunch

The sim­u­la­tion of the Aus­tralian house­hold-ori­ent­ed poli­cies gen­er­ates a very dif­fer­ent dynam­ic .

Fig­ure 27: Sim­u­lat­ing Aus­tralian house­hold-ori­ent­ed pol­i­cy towards a cred­it crunch

Cru­cial­ly from the pol­i­cy per­spec­tive, the house­hold-ori­ent­ed approach has a far more imme­di­ate and sub­stan­tial impact upon employ­ment (Fig­ure 28). Con­trary to the expec­ta­tions of Pres­i­dent Oba­ma and his main­stream eco­nom­ic advis­ers, there is far more “bang for your buck” out of a house­hold res­cue than out of a bank res­cue.

Fig­ure 28: Com­par­ing bank-ori­ent­ed and house­hold-ori­ent­ed poli­cies

The para­dox of mon­e­tary prof­its is there­fore solved sim­ply by avoid­ing the prob­lem so wit­ti­ly expressed by Kalec­ki, that eco­nom­ics is “the sci­ence of con­fus­ing stocks with flows” ((cit­ed in God­ley and Lavoie 2007)). With that con­fu­sion removed by work­ing in a frame­work that explic­it­ly records the flows between bank accounts and the pro­duc­tion and con­sump­tion they dri­ve, it is obvi­ous that Cir­cuit The­o­ry achieves what it set out to do: to pro­vide a strict­ly mon­e­tary foun­da­tion for the Marx-Schum­peter-Keynes-Min­sky tra­di­tion in eco­nom­ics. As an explic­it­ly mon­e­tary mod­el, it also pro­vides an excel­lent foun­da­tion for explain­ing the process­es that led to the “Great Reces­sion”, and for test­ing pos­si­ble pol­i­cy respons­es to it.

Monetary Minsky

To devel­op an explic­it­ly mon­e­tary Min­sky mod­el, I use the same tab­u­lar approach to mod­el­ling the finan­cial sys­tem, but include non­lin­ear func­tions that mod­el the real-world phe­nom­e­non that firms bor­row mon­ey to finance invest­ment under­tak­en with “euphor­ic” expec­ta­tions dur­ing booms, and repay banks by invest­ing less than prof­its dur­ing slumps.

Table 9: Finan­cial oper­a­tions in a basic mon­e­tary Min­sky mod­el

Where­as the pre­vi­ous mod­el replaced these flow mark­ers with con­stant para­me­ters, in this mod­el non­lin­ear func­tions that mim­ic gen­er­al ten­den­cies in actu­al behaviour–workers secur­ing high­er nom­i­nal wage ris­es when unem­ploy­ment is low, cap­i­tal­ists invest­ing more than prof­its when the rate of prof­it is high.

Table 10: Sub­sti­tu­tions

Oper­a­tion	Descrip­tion
A	Loan Inter­est
B	Pay­ment of inter­est on loan
C	Invest­ment as a non­lin­ear func­tion of the rate of prof­it
D	Wages (W) as a non­lin­ear func­tion of the rate of employ­ment and the rate of infla­tion
E	Inter­est on Firm deposits
F	Inter­est on work­ers deposits
G	Bank con­sump­tion
H	Work­er con­sump­tion
I	Loan repay­ment as a non­lin­ear func­tion of the rate of prof­it
J	Relend­ing by banks as a func­tion of the rate of prof­it

The fol­low­ing mod­el of finan­cial flows results:

Fig­ure 29: Finan­cial sec­tor dynam­ic mod­el, gen­er­at­ed in Math­cad

This now has to be com­bined with a mod­el of the labour and phys­i­cal flows, in which phys­i­cal out­put is now a func­tion of cap­i­tal as in the orig­i­nal Good­win mod­el:

The rate of change of phys­i­cal cap­i­tal is a func­tion of invest­ment minus depre­ci­a­tion, where invest­ment is a non­lin­ear func­tion of the rate of prof­it:

The rate of prof­it is the mon­e­tary val­ue of out­put minus wages and inter­est pay­ments, divid­ed by the mon­e­tary val­u­a­tion of the cap­i­tal stock:

Prices, labor pro­duc­tiv­i­ty and pop­u­la­tion growth are as defined ear­li­er. Wage set­ting how­ev­er has one mod­i­fi­ca­tion: nom­i­nal wages are shown as respond­ing to both the employ­ment lev­el and the rate of infla­tion:

The full sys­tem is now as shown in Fig­ure 30.

Fig­ure 30: Full mon­e­tary Min­sky mod­el

The dynam­ics of this sys­tem com­bine the short-term trade-cycle behav­ior of the ear­li­er non-mon­e­tary mod­el, and add the phe­nom­e­non of a debt-defla­tion, in which falling prices ampli­fy the debt to GDP ratio once the cri­sis com­mences.

Fig­ure 31: Bank accounts

This is a mod­el only of the process by which a cri­sis devel­ops; it does not con­tem­plate what might hap­pen in its after­math to end it–such as bank­rupt­cy and debt mora­to­ria reduc­ing the out­stand­ing debt and allow­ing eco­nom­ic activ­i­ty to com­mence again. The ter­mi­nal col­lapse that fol­lows from the run­away growth of debt in this mod­el empha­sis­es the point that Michael Hud­son has made so often: “Debts that can’t be repaid, won’t be repaid”.

Fig­ure 32: Cycli­cal­ly ris­ing debt to GDP

The employ­ment-wages share dynam­ics of the orig­i­nal Good­win mod­el give way to a finan­cial vor­tex that dri­ves wages share cycli­cal­ly down pri­or to the com­plete debt-defla­tion­ary col­lapse.

Fig­ure 33: Wage share falls cycli­cal­ly as debt defla­tion approach­es

The final debt-dri­ven col­lapse, in which both wages and prof­itabil­i­ty plunge, gives the lie to the neo­clas­si­cal per­cep­tion that crises are caused by wages being too high, and the solu­tion to the cri­sis is to reduce wages.

What their blink­ered igno­rance of the role of the finance sec­tor obscures is that the essen­tial class con­flict in finan­cial cap­i­tal­ism is not between work­ers and cap­i­tal­ists, but between finan­cial and indus­tri­al cap­i­tal. The ris­ing lev­el of debt direct­ly leads to a falling work­er share of GDP, while leav­ing indus­tri­al cap­i­tal’s share unaf­fect­ed until the final col­lapse dri­ves it too into obliv­ion.

Fig­ure 34: Income dis­tri­b­u­tion cycles and the sec­u­lar trend to falling wages and a ris­ing finance share

The macro­eco­nom­ic per­for­mance before the cri­sis would also fool any econ­o­mist who ignored the role of the finance sec­tor and the dan­ger of a ris­ing debt to GDP ratio–as indeed neo­clas­si­cal econ­o­mists did in the runup to this cri­sis, when they waxed lyri­cal about “The Great Mod­er­a­tion”:

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)

Fig­ure 35: Mod­er­a­tion is not good for your eco­nom­ic health

Instead of a sign of eco­nom­ic suc­cess, the “Great Mod­er­a­tion” was a sign of fail­ure. It was the lull before the storm of the Great Reces­sion, where the lull was dri­ven by the same force that caused the storm: ris­ing debt rel­a­tive to GDP in an econ­o­my that had become behold­en to Ponzi finance.

Appendix

Table 11: Details of the Min­sky mod­el with Ponzi Finance exten­sion in Equa­tion

QED

QED stand for “Ques­nay Eco­nom­ic Dynam­ics”. It is a new soft­ware pro­gram that has been devel­oped by a cor­re­spon­dent and col­lab­o­ra­tor (who for the moment wish­es to remain anony­mous) which imple­ments my tab­u­lar method of devel­op­ing dif­fer­en­tial equa­tions.

It can be down­loaded for free from www.debtdeflation.com/blogs/qed. Updates will be post­ed fre­quent­ly as is devel­oped fur­ther over time.

To test run the pro­gram, choose File/Open and select the mod­el “FreeBankingModel.sgr”. This is the first mod­el devel­oped in this paper. To see the mod­el itself, click on the “Actions” menu item and select “God­ley Table”. This table will then appear:

Godley Table

Fig­ure 36: The core of QED, the God­ley Table

Variables and Equations

The equa­tions in the mod­el are stored in two oth­er tables acces­si­ble from the “Actions” menu item on the main win­dow: “Var/Equations” and “C.O.D. Equa­tions” respec­tive­ly. The for­mer gives val­ues to para­me­ters and the like; the lat­ter gives the equa­tions for the flows between the accounts:

Fig­ure 37: The ele­ments of the dynam­ic sys­tem are defined here

To run the mod­el, click on the “Phillips Dia­gram” menu item on the main QED pro­gram win­dow, which will show the fol­low­ing dynam­ic flow­chart that was gen­er­at­ed by this table. Now click on the “Show Play­er” check­box at the top of the win­dow, and a play­er will appear down the bot­tom. Click on “Play” and the amounts in the reser­voirs (bank accounts) and flow valves (labelled A to I and with the same descrip­tors as in the left hand col­umn of the Ques­nay Table) will change. If you run it for five years (watch the “MODELTIME” counter in the top right hand side of the dia­gram and click on Stop), you should see the fol­low­ing:

Phillips Diagram

Fig­ure 38: The sim­u­la­tion is dis­played live in a “hydraulic” mod­el, in hon­our of Bill Phillips

There is also a “For­rester Dia­gram”, which is more like a con­ven­tion­al sys­tems engi­neer­ing pro­gram. You can also add vari­ables and rela­tions between them here, as with pro­grams like Vis­sim and Simulink–click on the type of enti­ty to be cre­at­ed (Stock, flow, text, vari­able) and insert a new one by hold­ing down the con­trol key when you click any­where on the dia­gram. Dou­ble-click on any enti­ty to see and/or alter its def­i­n­i­tion.

Forrester Diagram

Fig­ure 39: Sim­i­lar to pro­grams like Simulink, this dia­gram is pro­duced auto­mat­i­cal­ly from the God­ley Table

There’s a lot more to the pro­gram, as you will find if you play with it, using the two mod­els here and also devel­op­ing your own mod­els. To my knowl­edge it’s the only pro­gram around that uses a tab­u­lar inter­face to devel­op dynam­ic mod­els, and also pro­vides seam­less each-way devel­op­ment of a sys­tems engi­neer­ing dia­gram from a table of equa­tions. It is ide­al­ly suit­ed to mod­el­ling finan­cial flows, and it’s my (and my col­lab­o­ra­tor’s) con­tri­bu­tion to help­ing the world under­stand how mon­ey works–which is the first step in under­stand­ing why our finan­cial sys­tem has per­formed so bad­ly.

Fig­ure 40: Up to four graph sur­faces can be defined

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