john t. harvey - keynes´ chapter 22 - a system dynamics model

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Keynes' Chapter 22: A System Dynamics ModelAuthor(s): John T. HarveyReviewed work(s):Source: Journal of Economic Issues, Vol. 36, No. 2 (Jun., 2002), pp. 373-381Published by: Association for Evolutionary EconomicsStable URL: http://www.jstor.org/stable/4227787 .

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374 JohnT. Harvey

2. The tendencyof the rateof interest o riseovertheexpansionas the demand or

financingbegins to place pressureon supply.

3. The continuingupwardpressureon the rateof interestonce the collapsehasbegun (andagentsscrambleorliquidity).

4. The fallin the marginalpropensityo consume(MPC) hatwillaccompanyhe

decline n the valuesof portfolios assuminghe bustbringswith it a fall inasset

values).

5. The manner n which agentsform expectationsof the future.

Of these,3 and 4 make hemselves elt once theturningpointhas beenreachedand

the economy is in recession.1 and 2 cause the expansionto tend to lose strengthas it

matures.But, as we shall see, it is 5 that givesthe cycle ts characteristichape.Withoutit, the economy tends towarda situation in which investmentreachesa stable equilib-

rium (wheregrosscapital ormation ustoffsets depreciation).

Figure1. Keynes'Basic Model

Stockof - MarginalEfficiencyCapital - ofCapital

+ I 1 IInvestment

GDPRateof Interest

Consumption

To better illustrate this, Keynes'

modelwill be built in piecemealfashion,

beginningwith the ratherstraightforward

relationshipsshown in figure 1. Elimi-

nating the government and foreign sec-

tors for simplicity, GDP is a positivefunction of investmentandconsumption

(assuminga simple multiplier process).

Investment n turn is drivenby the MEC

andthe rate of interest.The determinants

of the MECare imited to the stock of cap-

ital to highlightthe latter's mpactin cre-

ating the trade cycle. As the stock of

capitalrises with net increases n invest-

ment, so the expectationof profit fromfutureadditions o the stock of capitalwill

decline.Hence, a rise in investment nevitablythoughnot immediately) reatesafallas

the economyworksthroughthe negative eedback oop show at the top of figure1:

flnvestment- IStock of Capital - IIMEC lInvestment.

The fallingMEC,rather hantherising nterestrateassuggestedn 2, creates he under-

lyingdynamicand is, according o Keynes, he more "typical, nd often the predomi-

nant"reason for collapse(1964, 315). Alone, however, t is no guaranteeof a business

cycle.This is illustrated n figure1.

Using the equations listed in the appendix, this simple systemwas modeled in

Powersim.Figure2 shows the schematic.Note that the negativefeedback oop men-



Keynes' hapter2: A SystemDynamicsModel 375

tioned above still appears.Also note

the addition of two new variables:

Depreciationand TargetStockof Cap-ital. The formeris simplythe rate at

which existingcapitaldecays,while the

latter is included on the assumption

that the MEC is a function of how

much the existing stockof capitaldif-

fers from some objectivelydetermined

target evel thatwouldpresumablyat-

isfy currentdemand.

Running this simulation showsthat it does not createa cycle.Though

it creates an underlying ogic for the

appearance f a turningpoint,by itself

the economy representedby figure 2

mayactually ield a stableequilibrium.

Figure2. Keynes'BasicModel in Powersim

StockofCapital

aTrget tockofCapital

etInvestment +Depreciation

Muc Efficiencyf Capital

Investmen -

InterestRate

+ Autonomous onsumption

The key s the specificationof the MEC. If wegiveMEC as a simple inearfunction, asin

equation (5) in the appendix, hen the economyseeks apointwherenet investmentwill

exactlyoffset depreciation.This occursin figure3, whereMEC fell as the gap between

the targetand actualstock of capitalwasfilled, but then settled off as net investment

came to restat zero (whichin this model occurswhen MEC exceeds interestby 5 per-

cent).Forsakeofbrevity,plotsof investmentandGDP arenot shown, butasthe former

is a functionof the differencebetween the MEC and the rate of interestand the latter

variesdirectlywith the former, heir patternscan be easily nferred.

A cyclecan be createdusing the simplemodel, but it requiresresorting o a conve-

nient and not necessarily ntuitiverespecification f the MEC. Equation 5), for exam-

Figure 3. LinearSpecificationsof MEC201'

15-

10- 1 1 1 -1- MEC

2- R

5- 22---2-------2- 22

0 , . , I

0 10 20 30 40 50 60

Time

ple, shows MECequal to

the squarerootof the dif-ference between the

actualand targetstock of

capital. This yields the

pattern shown in figure

4, which is much more

like that we would

expect.That we haveno a

priori reason to prefer

(5') to (5), however, is aweakness of this

approach.

As space does not

permit a demonstration



376 JohnT. Harvey

Figure4. Nonlinear Specificationof MEC

60

40i-i-MEC

-2- R

20- 1

I I0 10 20 30 40 50 60

Time

of everyother permutationof

Keynes' five elements in a sys-

tem dynamics format, I willnowproceedby adding he oth-

ers individually to the basic

modelshown in figure2 so that

theircontributioncan be high-

lighted (with a complete model

presentedat the end).

Figure 5 shows Keynes'

simple model (with a linear

specificationof MEC), includ-ing the impact of a fluctuating

MPC and income multiplier 4

from the above list). The two

were modeled using equation

(6) from the appendix,wherethe multiplier(which had previouslybeen exogenously

determinedas "two")s expressedas an inversefunction the MEC(as a fallingMEC

would tend to depressassetvalues;note also thatmakingMPCendogenousrequireda

slightrespecification f equation(1),which now becomes (1')).As the only real differ-

ence between this economyand the one modeled in figure3 is in terms of size of the

multipliereffecton GDP, we see no difference n the plot of the MECand the rateof

interest.Justas in figure3, the economycomes to rest atthe pointwherenet investment

is zero.

Modelingthe interestrateendogenously i.e., usingboth 2 and 3 fromthe abovelist)wasslightlymorecomplicatedbut gavethe sameessentialresult.To begin,making

the interestrateafunction

of demand for cash both

for finance purposes andasahoardmeant inking t

to MEC (which impacts

negativelyon the rate of

interest, as falling MEC

implies sinking optimism

and a flight to cash) and

GDP (where rising GDP

raises interest rates). In

termsof modeling,the lat-ter link caused a problem

since the current rate of

interestcould not, in this

Figure5. LinearSpecificationof MEC,Endogenous

MPC

20-L

15-

10- - - - -1

-m-MEC

2 R

10 20 30 40 50 60

Time



Keynes' hapter2:A SystemDynamicsModel 377

sort of system, be

simultaneously a

function anda deter-minant of (through

investment) GDP.

This is an economy

in time where there

must exist a

sequence of events.

However, this was

solved as shown in

figure 6. Here,today's nvestment s

a resultofyesterday's

MEC and rate of

interest, which

implies that firms

made profit projec-

tions and secured

funding one period

ahead of actual

spending.Hence the

delayed ink between

Figure6. Keynes'BasicModelplus LiquidityPreference n

Powersim

Stock ofCapital

+eTget Stock ofCapital

Ne nvestmentDepreciation

Mar=gnalfficienc of Capital

+ Delayed\ \

+ ~~~Linqklannedt\Li~~~nv<nestment

\ \

Investment InterestRate

GDP C

Autonomious Consumption

plannedinvestmentand investment.

All this made little difference n the end, as interestratesandthe MEC once again

cameto restat apointwhere the latterwas5 percentagepointsabovethe former thisis

shownin figure7). The only difference s that now the rate of interest s not set exoge-

nouslyat 5 percentbut is determinedbyGDP andMEC(andin thiscase reachesequi-

librium at 3.69 percent).Still, no cycle is generatedwhen the specificationof MEC islinear.

It isonlywhenthe particularwayexpectationsareformed staken nto account hat

we see a real tradecycle.Agentsin Keynes'GeneralTheoryformtheir forecasts n an

environmentof uncertainty.This leads those forecasts o be (a)held with little confi-

dence and(b) based argely n the agent's mpressionsofwhat othersbelievethe market

will do (relianceon conventional wisdom in the face of individualignorance).But

agentsarealsoinherentlyoptimistic.It is thisoptimism,combinedwith investorsbeing

too busyforecastingmarket entiment(whichwouldof late havebeenbullish),and not

industryconditions, that leads to them to continue to expect positive returns wellbeyond the point that the increasing ize of the stock of capitalandrising costs of pro-

duction would suggest.Once reality ets in (asrealizedprofitsarecomparedwithprior

projections), he flimsyfoundation of the expectationsmeans that the re-evaluations

"suddenand even catastrophic"Keynes1964, 316).



378 JohnT. Harvey

Figure7. LinearSpecificationof MEC, Liquidity

Preference

20-

15-

10

-,-MEC

52 2 2 R

C- I i

10 20 30 40 50 60Time

To model this,the useful

dichotomy employed by

Keller andCarlson

(1982)was adopted. They distin-

guished betweenan objective

MEC, which "reflectsa yield

based on a fundamentalrate

of return,"and a speculative

MEC, or one derivative of

"individual businessmens

calculation of yields which

reflectpredictionsof majorityopinion in the marketplace"

(406). In the systemdynamics

model, the old linear specificationof MEC was usedfor the objectiveMEC,while the

speculativeone requireda seriesof new equations.Modelingexpectationsnecessitated

the following adjustments:

1. Investment s affectedby the speculativeMEC and not MEC.

2. A bandwagoneffect occurs such thatconsecutivepositivevalues for objective

MEC contributea "bonus" o speculativeMEC-these accumulateup to the

point of crisis.

3. A similar, though less powerful,bandwagonworks in reverse (such that

depressed xpectationsbeget depressed xpectations).

4. A crisis in expectationsoccurs wheneverthere are three consecutiveperiods

during which the speculativeMEC exceedsthe objectiveone-at that point

there is a collapse n the speculativeMEC.

Figure 8. LinearSpecificationof MEC,ExpectationsModeled

10a

tob t I j W ,i-Objective

I I I~~~MEC

5 1-I

- 27;-- Speculative

a ) v MEC

10 m : Ao m O

Time

Finally, a trade cycle is

created,as shown in figure8(note that this model leaves

the multiplierandinterestas

exogenous and adds only

expectations to the basic

model). Just as one would

expect, the fall is much

steeper than the climb and

the speculativeMEC shows

much more volatility thanthe objective. Furthermore,

Keynes argument that

over-investment in a strict

sense is not the causeof the



Keynes' hapter 2: A SystemDynamicsModel 379

cycle is supported since the

objectiveMECnever fallsbelow

the artificial loor createdbytherateof interest,andcertainlynot

below zero.

The picture is even clearer

in figure 9, which, at last, gives

the complete model,with expec-

tations modeled and interest

and the MPC/multiplier reated

as endogenous (interest, inci-

dentally, is now linked to thespeculativeMEC and not the

objectiveone). The storyis basi-

cally the same as that shown in

figure8, but with interest luctu-

Figure9. LinearSpecificationof MEC,

ExpectationsModeled,Liquidity

Preference,and EndogenousMEC

-i- Objective

--7- Speculative

10 m 20D '0 10

Timle

F'igure10. CompleteModel 'inPowers'im

StockofCapitalrgettockofCapital

Epctations

a nescnte anoiir wgonl Changen<

D epre cizaton + f o C /ExpectsatonsA

/ peelci + Neaive B_ndwagJ

+ + Paaic /

X ~~P'lanned<\\ InirestmenteSyd \v

+ , A )- \

, Investment(

GDw ~~~~~Interest

ate

\/ ~~~~MultiplierAutonomu Consumption



380 JohnT. Harvey

atingin a manner that makeseconomicrecovery ven more difficult.Figure10 shows

the completemodel.

Conclusions

With Keynes'chapter22 in a systemdynamics rameworkt can be demonstrated

that he offereda viableexplanationof crisisoverhalf acenturyago.Italso becomesclear

that key to panic and collapseis the meansby which agentsform expectations,with

other factorsaddingvital elements(includingespeciallyhe fluctuatingobjectiveMEC).

His chapter22 offers an excellentbaseformorecomplextheories of cycleand crisis.

Appendix

Specification f theSimpleKeynes-StyleTradeCycle

Thismodel consistedof fiveequations, ourconstants,and aninitialization alue.

Equations:

(1) GDP = 2*(Investment AutonomousConsumption)(2) Investment= 100*(Marginal fficiency f Capital InterestRate)

(3) Net Investment Investment Depreciation

(4) Stock of Capital= PreviousStock of Capital+ Net Investment

(5) MarginalEfficiencyof Capital= ((TargetStockof Capital Stock of Capital)/

Stock of Capital)* 00

(5') MarginalEfficiencyof Capital= (TargetStockof Capital Stock of Capital)0

Constants:

AutonomousConsumption= 2250.

Depreciation= 500.

InterestRate= 5.

TargetStock of Capital= 30000.

Stock of CapitalInitialValue= 25000.

In addition,Investmentwaslimited so that it could varyonly from 100 to 1600.

AddingMarginalPropensityo Consume/Multiplier

(6) Multiplier= 1.8 + MEC/35

(1) GDP = Multiplier*(InvestmentAutonomousConsumption)



Keynes' hapter2:A SystemDynamicsModel 381

AddingLiquidity reference

(7) Rate of Interest= 2 + GDP/1200-

MEC/3

Note that making he rate of interestendogenous requires agging nvestment.

AddingExpectations

Spacedoes not permitan explanationof this aspectof the model beyondwhat is

offered n the text.However, he author s happy o forward copyof the model andits

component equationsto interestedreaders.

References

Keller,RobertR.,andJ.LonCarlson."ANeglectedChapter n Keynes'GeneralTheory." ournalfPostKeynes-

ian Economics, no. 3 (spring1982): 404-412.

Keynes,John Maynard.The GeneralTheory f Employment,nterest,ndMoney.New York: HarcourtBrace

Jovanovich,Publishers,1964.

Minsky,Hyman.Stabilizingn Unstable conomy. ew Haven:Yale UniversityPress, 1986.

-. Can"It"HappenAgain?EssaysnInstabilitynd Finance.Armonk,N.Y.: M. E.Sharpe,1982.

john t. harvey - keynes´ chapter 22 - a system dynamics model

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