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7/28/2019 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-
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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
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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
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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).
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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
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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
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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)
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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.