424 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAKICS SOCITY. CHINA
PROBABILISTIC GENERATION OF SCENARIOS FOR ARGENTINA,
USING A ELEMENTAL HARROD-DOMAR MODEL OF GROWTH.
Juan Rego Juan A. Vega
National Council of Scientific and
Technological Research of Argentina
ABSTRACT
The growing amount of the foreign debt of the developing countries shapes a
gloomy future for most of them. The chances for maintained growth fueled by
internal saving is nil if the service of the debt is satisfied, as it has to
be to avoid international isolation. This is particulary true in the case of
Argentina, with a debt equivalent to two thirds of its GDP, and its debt
service representing more than 5 per cent of GDP. After showing the
historical facts about ‘the Argentine economy, this paper presents a very
simple version of a growth model type Harrod-Domar, adapted to the parameters
of the local economy. Then the model is used for answering to "what-if" type
of questions, wich arise from different plausible scenarios, Finally, it is
analyzed the probabilistic generation of scenarios and related technical
problems using DYNAMO,.
1. INTRODUCTION
The crisis of the early Eighties surprised both, Latin-American debtor
countries, and creditor industrialized countries. Those showed sluggish
answers to ‘the impacts coming from the unstable world economic centers; these
were unable.to dominate the required financial adjustments to overcome the
emergency.
To. believe that the problems of the debtor countries are their own fault, and
therefore the solution has to be looked for internally is very unrealistic.
Unless the: world economic environment become more favorable for the developed
countries, the solution of the debt problem would be too far away (Dornbusch
1986). Therefore the eventual recovery of the Latin-American countries will
depend strongly on the improvement of the rate of growth of the industrialized
countries, net transfers of funds (inflow funds less debt and utilities
payments), trade opportunities, and row material prices (Feinberg, Ffrench--
Davies 1986, Dornbusch 1986), as well as internal restrictions on the debtor
countries. If this is true, then it should be far relevant the "what if”
simulation-experimenting approach, in a mainly outer generated future.
Then, which are the eventual futures open to Argentina? To examine this
question is the purpose of this paper, whose authors. recognize to be indebted
to the writers of a previous one (Broda, De Pablo 1985) with similar
objetives, but using econometric methods.
It is explored the ability of the SD methodology in analyzing the questions
posed in the mentioned article, freely used here, Beyond such initial
orientation it is also aimed to the incorporation of randomness in the
generation of the futures throught simulation, as suggested for Stover (1975,
1980) and Mosekilde (1982). To this purpose the usual routine of exploring
the consequences of discrete events, one at a time, is followed by scenarios
built upon the simultaneous occurence. of different events.
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 425
2. LAST TENDENCES OF ARGENTINE ECONOMIC HISTORY.
The clear positive tendence shown by the. Argentine economic growth, as
measured by its Gross Domestic Product, GDP, was broken to the énd of the
Seventies, when the foreign debt appeared as limitating factor of the
Argentine development and a voluminous transfer of resources for the servicing
of the debt began to compress the economy.
Figure 1 Historical Gross Domestic Product, External Debt, Saving
and Service of the Debt (1950-84).
(Source: Broda, De Pablo, 1985, millions of us $ 1985).
————— GPC, , 109.02)
109,23-— — - DEBTICA, 109, 28)
9208, -
[hae
59, 60, 7”, w, MN
During the last ten years it could be observed that, at the beginning, in
1976, the debt represented the 20% of the GDP, evaluated in 44,200 millions
of current American dollars. Ten years later the debt climbed up to 64% of
GDP, which amounts to 79,000 million of current dollars. Correspondingly, the
service of the debt arose, in the same period, from 1.1% of the GDP,
aproximately 5CO million dollars, to 6.7% of the GDP, over 5000 million
dollars, This means that the service of the debt grew 10 times, when in the
same period the Argentine economy ‘did not grow enough for duplicating its
initial GDP in terms of current dollars (Broda, De Pablo 1985).
‘To atribute the crisis to the national budget deficits of the debtor countries
426 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
is too easy an explanation. A more equilibrated judgement assigns equal
responsabilities to bad interna] management of Latin-American countries, world
economic conditions and unwisely granted credits (Dornbusch 1986).
There are evidence that it was the abundance of international liquidity
originated by the deposits of revenue. coming from the oil export countries,
on the international banking system, that created the over-supply of fresh
funds ( Dadone, Pescarmona 1984). The less developed countries asked and
obtained a good proportion of this money for financing their development, but
without foreseeing the future. For them it made sense to accept a loan on a
basis of a nominal rate of interest of 5%, which was the historical rate on
long term loans for the period 1973-77, against a 10% inflation rate over the
same period. However, the effect of the oil revenues on the industrialized
countries, particulary in USA, was to accummulate deficits, financed by money
emission, which in turn triggered off an inflation process that pushed the
international interest rate of loans up. This inflation, added to low prices
of raw material and basic products in general, less liquidity and more
protectionism on the international scenario, caused an acceleration of the
growth of the debt, on the one hand, and lost of payment capacity of the
LDC's, on the other hand (Conesa 1985).
Whichever is the case, the pressure of the external debt on the economy in the
Figure 2 Balance, Saving, Consumption and Service of the Debt
relative to GDP (1950-84).
(Source: Broda, - Pablo 1986).
BBL 8 =~ = MNS
== — = SAVE A) — = RONG 75S
/
dl et . ae ze
aCe
aihy ar
1,863 ‘
a un oe
4 NM
4 |
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 427
Argentine instance, at least, produced a severe reduction of local saving,
rather than reducing consumption, as shown in Figure 1. None the less, the
pressure ‘upon the Argentine economy gave place to a interesting phenomena.
Effectively, the growth of the service of the debt produced, over the period
1980-85, a more favorable balance of payments, providing a badly needed
foreign currency. The bad news are the falling of the investments, compared
with a growing consumption (Broda, De Pablo 1985).
3. THE DYNAMO FORMULATION OF THE HARROD-DOMAR MODEL.
For the purpose of this paper, it is enough to use the simplest available
model, the one proposed by Harrod (1939) and Domar (1946), in order to analyze
the economic growth of Argentina. -Central to its theory is the dual role of
investment, which, on the one side, affects supply,’ because is capacity
generating; on the other side modifies demand, when it generates income and
the corresponding consumption.
The equation formulation requires the use of an adequate notation, coherent
with the DYNAMO language (Pugh 1°76). To this end, let j, k, and 1, be three
succesive points in time, wich define the jk and kl consecutive periods. Let
K.k be the capital in time point. k, that is available to the system during
starting period kl. In addition, let Y.k, C.k, KD.k and I.k, the income,
consumption, capital depreciation and gross investment flows, respectively,
measured in dollars-1985 per year, that happen during period kl, Also let kp,
a technological coristant, be the relationship between income and capital.
Finally, let alk be the average life of capital.
a) On the supply side, the use of the key parameter kp allows to convert
capital input available in time k, to new capacity, ready in period kl, for
supplying the market with new goods. Then
Y.k=K.k*kp q@)
The same identity holds for the previous period jk:
Y. jek. j*kp ’ Q)
And substracting
(Yok-¥.j)=(Kek-K. 5) *kpel. j#kp : @)
In other words,’ the growth of income is equal to kp times I.j, where I.j is
investment done during previus period jk, which become producing capital in
following period kl, able to generate extra income (Y.k-Y.j), also disposable
in period kl, It could be obtained an expression for the rate of growth of
income dividing both members of eq. 3 by Y.j, the income of the previous
period jk. Let v denote the ratio of investment incurred along the period jk,
to the income generated during the same intervale of time, or fraction of
income devoted to new. investment:
(Yek-¥.5)/Y. j=(1. §/Y. j)*kp=v*kp (4)
Equation 4 says that the rate of growth of income depends on the proportion
428 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
of income devoted to the creation of new capital and the productivity of the
new additions to capital. If both v.and kp remains constant, so will be the
rate of growth of income.
b) On the demand side, the consumption expenditures equation is obtained
multiplying the income by the average and marginal propensity to consume of
current income, noted apc:
C.k=Y.k¥ape (5)
Considering investment as a function of the change in income over the
inmediately preceding periods, it results the investment expenditures
equation, where ak is the acceleration coeficient of proportionality:
T.keak*(¥.k-Y¥.§) (6)
Adding eqs. 5 and 6, it results the total or aggregate demand of the society:
YokeC. k+l ke ¥ .k¥apcetak*(Y.k-Y.j) (7)
c) The keynesian static equilibrium condition S=I, considering both public and
private expenses as a whole, gives the required link. for stablishing the
differential equation that regulates the path of growth of the national
economy. This trajectory could “be found by solving that differential
equation. Knowing that saving is the ‘fraction of income not spent in
consumption, it follows that the condition means: .
TokeS.lee(Yek-C.k) e®
It is clear that net investment NI.k is the rate of change of the capital
stock K, and it is equal to investment after discounting the capital
depreciation KD.k. The capital stock decays with time representing ‘the
obsolescence and usage rate of the equipament affected to the production of
goods to be consumed in the current period kl.
KD.k=K.k/alk ‘ ()
Now the net investment flow incurred in period kl can be expressed as:
aK/dt=NI.kl=(Y.k-C.k)=-KD. k= (10)
=(K.k*kp)=(K.k*kp*apc)=(K.k/alk)=
=k.k*((kp)-(ape*kp)-(1/alk) )=
=K.k* Constant 1
Equation 10 is a very simple differential equation, homogenous of first order,
solved by a function that shows exponential growth. DYNANO simulation program
obtains this solution for the state-variable K as the integral of the net
investment NI flowing into it, using the Ruler integration method with a fixed
step size of time, dt. The accumulative equation is:
Kikek. j+(dt)*NI. jk (il)
The following Figure 3 shows the feedback structure behind the Harrod—Domar
‘THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 429
model, which represents the key notion of capital accumulation, cause of
economic growth. The labor, combined with the capital stock inherited at the
beginning of period jk, praduces a flow of output, wich priced becomes income
of this period jk.. A fraction of income is saved and invested in period jk,
thus further enlarging the capital stock, available at period kl (Branson
1979). Therefore a positive feedback loop is closed, pushing the growth
process up.
Figure 3 Causal Structure of the Harrod-Domar Model
4. EXPLAINING ARGENTINE GROWTH WITH THE HARROD-DOMAR MODEL.°
For the most part of the period 1950-85, the historical growth of Argentine
income is conveniently simulated by the Harrod-Domar model, when local
parameters are used in the simulation. For that period, the doubling time is ©
about years, Then the solution for eq. 10 requires to know the average
life capital, estimated in 15 years (Ffrench-Davies 1986), and the propensity
to consumption. Next Figure 4 displays the historical consumption relative
to GDP, plotted against its OLS adjusted regression (Broda, De Pablo 1985).
For the sake of simplicity, apc is assumed in this paper, unless otherwise
adverted, as being constantly equal to 0.80, so that the eq. 10 is solved for
kp=0.485, Therefore K inicial=GDP inicial/kp=4631/0.485=9262.
The model works well when simulates GDP and consumption, as shown in Figure
430 THE 1987 INTERNATIONAL CONFERENCE.OF THE SYSTEM DYNAMICS SOCITY. CHINA
5, but tends to underestimate the flow of the net investments and does not
foresee the crisis to the end of the period. The problem clearly appears in
the last 5 years, when the service of the debt becomes unbearable and
additional causal links should be incorporated to the structure shown in
Figure 3, for a more realistic representation.
Figure 4 Historical Consumption Relatiye to GDP and Simulated by an
OLS Adjusted Regression Against GDP.
(Source: Broda, De Pablo 1986).
Frese 2..Aunias — — = RUC somren
Fea
' : (7
i -_
58, 68. 78, a8. 84,
TINE
Even when available statistics only allows to estimate marginal productivities
of gross and net investments, it is interesting to compare the historical
values of these marginal concepts with the ones produced by simulation. To
this purpose it is necessary, firstly, to obtain one year lagged time series
for both historical and computer generated time series, for GDP, gross and net
investments. This is done by using the pipeline type of delay, feature of
DYNAMG (Pugh 1976), available as well in DYSNAP (Cavana, Coyle 1982). For
example, the one~jear lagged variables for actual GDP (pbi) and net investment
(ntinv) are oldvpbi, oldvginv and oldvnti, respectively:
oldvpbi.k=delayp(pbi.k,1,pbippl) (12)
oldvginy -kedelayp(grinv.k,1,gippl) (13)
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 431
oldvnti.k=delayp(ntinv.k,1,ntppl) (14)
Figure 5 Historical and Simulated Argentine CDP, Consumption and
Net' Investment (1950-84), millions of us $ 1985.
get forte
34, 64. 9. 8, A,
Then the marginal productivities of historical gross (mgpginv.k) and net
(mgpninv.k) investments are, by definition:
ngpginv.k=(pbi.k-oldvpbi.k)/oldvginv.k as)
mgpninv .k=(pbi.k-oldvpbi.k)/oldvnti.k, (16)
Similarly, for simulated gross (i.k) and net (ni.k) investments, the equations
for marginal productivities of net (mgpni) and gross (mgpgi) investments are:
ngpni.k=(y .k~oldvy .k)/oldvni.k (47)
ingpgi..k=(y.k-oldvy.k)/oldvi.k (18)
The equation formulation has been solved satisfactorily. Figure 6 presents
historical and simulated marginal productivities of gross and net investments.
Besides the initial year, when the variables exhibit transient behaviour due
to the use of emptied pipeline delays, the results obtained are not so bad,
except for the tendence of the model, already met in Figure 5, to
i
432 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
underestimate the real values over the end of the run and the fact that the
model can not forecast the recession accompanying the acceleration of the rate
of growth of the.external debt of Argentina. The historical marginal
productivity of gross investment fluctuates widely around the 0.485 constant
value of tie corresponding simulated productivity, being 0.485 also the value
of the productivity of the capital found as solution of previous eq. 11.
Likewise, the marginal productivity of the net investment floats around 0.15,
the simulated value of such productivity, and coincidently, the arithmetic
mean of the serie 1953-1984 (Broda, De Pablo 1985).
Figura 6 Historical and Simulated Marginal Productivities of Gross
and Net Investments, and Capital Productivity of the Model.
ASPGINY — urstorrcat seseseees HORN] Smetarep
sae SIMULATED a
= === BENT) ost
ey
50, 68, 1. 8, 94,
TIME
For representing the present circumstances of Argentina it is convenient ‘to
modify the. simple Harrod~Domar structure shown in previous Figure 3. The
investment capacity, after capital depreciation, should also take into account
the drainage of funds due to the service of the debt and, eventually, fresh
money coming from the international banking system. The following Figure 7
represents the modified structure of the-model, where the service of the debt,
sdbt.k, is expressed as a fraction, fgdp, of the GDP devoted to the debt, and
the inflow of money, exf, as an exogenous input. The amount of the external
debt is recorded by an auxiliar state variable, or level variable, D.k, wich
is ‘fed or depleted by the débt growth rate, dgr, depending on the due payment
of the debt service, dpdbt, compared with the actual flow of Argentine
N & 1
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 433
payments, sdbt.k
Figure 7 Causa] Structure of the Harrod-Domar Modified Model.
ape Baie
Capital Marginal « Average, Fraction of gdp
‘Productivity Propensity to devoted “to
y nsum pFion Sarviee of Debt
>
Troms +
Consemprion
Sat
kk + kd i Actval Service
Capital = + Capital Capital Gross of the debt
if Depreciation pene
\ ni A
Net
ext Investment -
Inflow ae S dpdbt
; +
seen mie Due Payment ear
Funds Wer la . Debt Growth
Hatt of the Debt Service Rie
‘Intereet
‘Rate
Debt a
+
This again could be represented by another first order diferential equation,
where the constant C2 is smaller than Cl.
aK/dt=NI.k1=1.k-KD.k= (19)
=(Y.K-C.k~SDB
=(K.k*kp)=(Kle *kp*fgdp)-(K.k/alk)=
=K.k*(kp-(ape*kp)-(kp*fgdp)-(1/alk))=
=K.k* Constant 2.
Nevertheless, the lineality of the system should be abandoned, because of the
necessity of appealling to the use of a STEP fiction when the equation for
capital productivity is formulated. Until 1980, the required value of capital
productivity for overcoming the historical service of the debt, traditionally
about 1% of GDP, introduced as an exogenous time serie, and simultaneously
able to explain the growth of GDP is 9.50. This value was not found as a
solution of a differential equation, but for extensive experimentation with
the DYNAMC simulator. On reaching year 1980, the actual GDP levelled off,
requiring a smaller capital productivity, kp=0.45, for a better adjustment.
This again found trough DYNANO simulation.
434 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
Next Figure 8 shows historical and simulated behaviour of Argentine GDP,
consumption and net investment, using a modified Harrod-Domar model ‘whose
service of the debt is the historical one for the period 1950-84. It could
be seen the effects of the debt on GDP growth over the last 10 years.
Figure 8 Historical and Simulated GDP, Consumption and Net Investment
(1950-1984).
50,03
78, a. 04.
i —
The behaviour of the marginal simulated productivities of gross and net
investments follow the drop of kp, falling suddenly in 1980,: for recovering -
slowly, later on, at a lower level in the case of net investment, and gross
investment productivity nearly reaching the capital productivity value level.
The descripted dynamic is exposed in Figure 9.
4, CONCEIVABLE FUTURES FOR ARGENTINA.
After building some sort of confidence in the Harrod~Domar model - for
representing the elemental facts of Argentine economic history, is quite a
“straightforward procedure to generate conceivable futures for Argentina. It
can be done, simply, by using different set values for the exogenous variables
and parameters, wich would shape the future of Argentina. Also, it could be
examined the likelihood of each one of the scenarios generated because of the
utilization of the input sets. However, it is useful to obtain firstly, a
4
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 435
quick profile of these scenarios by means of the DYNAMO simulator’ program.
The variables and parameters used are, let it be repeated, the flow of fresh
external funds, exf, destined to net investments; the capital productivity,
kp, the fraction of GDP devoted to the service of the debt, sdbt and the
average propensity to consumption. Another parameter to be applied is the
world markets interest rate, wmir, wich defines the payment annual amount.
Figure 9 Historical and Simulated Argentine Marginal Productivities
of Gross and Net Investment, and Capital Productivity.
,) spmaren
= HRGIN-2,, 2, sone = HPAL (-2,
en sous ee RO A, HR)
aed JatsTorIcaL
\_Al
lee | — =
ApA EL 8 Z man SAN ua
OO, 8, 0, 84,
50 él a=”
Firstly, it can be tought of the lost future because of the recession. This
scenario is obtained by simple extrapolation of the historical growth of
Argentina during the 1950-1980 period to the future, ignoring the ..erely: at
the beginning of the Zighties, as if the debt did not exist. .
Secondly, if the previous one constitutes a lost opportunity, it could be
imagined another where the stagnation of the present decade could not be
defeated. There is not external help and the «capital productivity does not
recover its 0.50 historical value. The disposable income ,after consumption
is not enough for the payment of the debt services. Therefore, what actually
happens in the scenario is that the economic system is desinvesting, arriving
to year 2000 to a level of GDP 3.4% below the starting 1985 value.
436 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
Thirdly, like families bearing hardship, the citizens can fasten their belts,
diminishing the fraction of income ‘consumend. In this case it has been
assumed 2 gradual drop to 0,72 from the historical 0.80, in five years time
and from then on that. lower remains constant level, until the end of the
simulation run, in year 2000. It is easy to understand the internal political
difficulties of this scenario, which makes. so difficult its implementation
despite of the significant recovery made possible because of it.
Fourthly, the reference proyection of Argentine development represents the
most likely evolution of its economy if not major changes in policy are made
and external conditions do no alter significantly, like the drop of the
international interest rate or’the rise of prices of Argentina traditional
export goods. In this case, and assuming the historical value of 0.50 for
capital productivity, 15 years of average life capital, the historical 0.80
everage propensity to consumption, a service of the debt of 5: 7% of GDP and
no external inflow of fresh money coming in the ‘next 15 years..- This
foreseeable future of Argentine, the one which is felt like the bussines-as--
usual scenario, does not stop paying the service of the debt. Argentina just
manages to invest the necessary amount which enables the GDP to grow 7.5% over
the next 15 years, which means an annual rate of -growth of about.0.4%, This
is about 10% of the historical rate for. the period 1950-1980. As population
continues growing at its usual 1.65% annual rate, the available GDP per capita
decreases nearly 16%, compasred with the 1985's standars.
Fifthly, it could be tried to maintain at least the life standards enjoyed
about the middle of the Seventies, before the external debt crisis. This
objetive can be accomplished by borrowing. A steady annual inflow of fresh
money of about 2300 million $. 1985, allows to support a constant GDP per
capita and an increment of 27.9% in GDP over the 15 years. Sixthly,
aproximately the same than in the previous scenario could be achieved by
virtue of a gradual improving of the productivity of the capital, thanks to
a better management, so that from the, starting 0.45 value the economic
national system reaches the 0.56 mark, at.’an 0.8% “annual rate of improvement.
Seventhly, duplicating the borrowing mentigned in the fifth scenario permits
an annual rate of growth of nearly 2.3%, and 48.3% of GDP increment over the
15 years. Eighthly, duplicating thé rate at which the productivity improves
achieves an overall increment of 57.4% over the 15 years period, at an 3.0%
annual rate of growth. And finally, a grand scenario could be built imagining
the duplication of both borrowing and improvement of the productivity
simultaneously, which means,to grow.114% until the end.of,the XX Century, at
an 5.2% annual rate. .The. following, Table 1 summarizes: the, zeeults obtained
when running the different | scenarios: in, the computers BG syed rays
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 437
Table 1. Performance of Argentine Economic Indicators under
Alternative Scenarios Conditions.
Fh tala og kl SE Na oe a
Scenarios Parameters and Exogenous Perfomance
Variables in Scenarios. Indicators
Inflow Gapital Debt Consump- . Rat
External Produc~ Ser- tion prow +
tivity vice pensity” : GDP GDP/cap.
% isy % Isy toxse
ea) % year % year (385)
arc eo
Historical
9.50 1.0 0.80 * CKS4y)
(19sesi9e0) ;
Tl) The lost = 0.30 1.0 0.80 7218.7 - 134500
Paradise. aie Pit seeess
2. Unbeaten -- 0.45 5.7 0.80 -13.4 -92.4 76880
Stagnation. =619 “=81§ sees
3. Fastening 9 -> 0.65 5.7 0.72 32.1 3.9 117700
the belts. a7 0.2 = cuuel
4. Business =~ 9.50 5.7 0.80 19.5 -13.5
es-usual. 0.6 0.9
5. Keepin
po Rien
el
Seventies,
Bue borrow- 2325 9.50 3.7 0.80 27.8 9.0 113100
ing: ie 00
&. The same,
but grad-
ually im 9.50
proving (1985)
reduc = - H 5:70.80 38.8 s22800
ivity. (2908) Be aSsse=
7. Duplicat=
ing the 4650 0.50 3.7 0.30 48.2 16.1 4131200
borrowing. <7 OF saess=
8. Duplicat-
ing. th 9.50
i (1985) z
: 5.7 0.8 72.2 38.1 1s2G00
ec) 317 “Blo =eeeee
9.50
(1985)
4650 0.43 3.7 0.8 112.6 188100
¢2000) S.2 masse
488 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
The next Figure 10 displays the simulated’ GDP and debt for different
conceivables scenarios which were generated according the parameter value sets
described in Table 1, The mechanism of the debt formation, outlined in Figure
7, is a very simple one. The debt growth rate depends on the difference
between its due service and the money actually paid by Argentina. If this
difference is positive the debt grows; if it is negative the debt falls, It
is understood that if payments equal exactly the due service, Argentina is
paying only the: interest, without any variation of the amount of the debt.
The interest rate used for simulating the dynamic of the economy is the
corresponding to historical economic data series of the industrialized
countries, deflacted by the price of their exporting goods, about 6% (Ffrench—
Davies 1986).
Obviously,» both income and debt should be’ considered at the same time, when
preferences are ‘expressed. So, even when scenario 9 displays the biggest
income at the end of the simulation run, this has.to be balanced with the fact
that its debt is not. so far from the, debt of scenario 7, the worst from the
viewpoint of the debt formation. However, heavily borrowing accompanied by
the vigorous improving of the production, as happens in scenario 9, leaves at
‘the end a falling debt, because of the payment capacity generated by a
powerful economy. Undoubtedly, the best from the debt angle is the scenario
8, where an acceptable expansion of the economy is only internally supported,
without any foreign help. Fastening the belts,-as in scenario 3 does not help
too much; it is nearly equivalent to scenario 6, which instead of deppressing
consumption, push productivity mildly up, wich 43 more accéptable politically.
If the stagnation of the last decade does not change for the better, that is,.
capital productivity does not return to the historical levels, external help’
is not required and the service’ of the debt is satisfied, as in scenario 2,
Argentina should prepare herself for a black future.
6. PROBABILISTIC GENERATION OF SCENARIOS.
The model which produced previous simulation runs has not information about
the future, except that included in some of the tests when the step or ramp
functions are used. But even so, such information about’ declining average
consumption, step changes in productivity or supply of fresh funds is used
considered every phenomena in isolation form all others. The model can be
modified to include mutual interactions between external parameters and both
ways causal relationships between these parameters and the model variables,
as suggested by Stover (1975, 1980). “The problem with the Stover. solution is
that the DYNAMO compiler failed in its attempt to compile the model because
of simultaneous equations do not avoided by Stover. The following Figure 11
shows the closed loop proposed by Stover (1980) which is lacking of the
corresponding level variables,
The purpose of this section of the paper is to modify the Stover calculating
scheme for overcoming: the compiling dificulties. So what follows is a
modified sequence of calculation which is able to generate scenarios at
random. Even when this technique pays off when several events are included
in the analysis, say 10 o more, only 4 events are considered here, because of
the deliberate simplicity of thé model presented in this paper. More
complicated versions will require greater number of events and obviously,
bétter Antormation, for a full application of the methodology here discussed.
faa
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 439
Figure 10. Historical and Simulated GDP and Debt for Argentine
Conceivable Futures (1950-2000), millions of -us $ 1985.
ip
a oO - pete son i
We
He
i
J
ND os
= Hy
y
&
1 \k
: \A 5 a, 2
: < “ =
| 4
eee
Tag
x]
ae
m 2 >
neenesl .
pra i" a
yi 4
tot =
oa i Ac
Pha — 315
ee = a “a rt
Lad Foard ’ a 5
ay te = BS
440 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
igure 11 Probabilistic Scenario Generating Loop.
pommene Probabilities, Expechs In ay
Events 4 toe £ Pe Poreation
Olde of events @— Graca~Lmpack Matrix
th
Initial Odd
of events Ato“
Initial Foka bilities,
of events to
randorn | Indicators of | Model
Romnbers | Scorrence of | Simolation
flowehions Levents tied! Rons
Incremental
Probabilities
of Events
Nerney Probabilities of events 1404
during the lack ealotion interval
First thing to do i8 to define the events to be included, which are the ones
that conformed the scenarios descripted in Tabla 1: el, improvement of capital
productivity from 0.50 to 0.56; 2, improvement of capital productivity from
0.50 to 0.63; e3, annual. provision of fresh money from industrialized
countries, equivalent to 2,325 millions of 1985 american dollars; | e4,
doubling the supply of money to 4,650 miilions.dollar. The -next Table 2 shows
an initial estimate of the probability of each event by some future year, Say.
1990, and the conditional probability matrix. Expert opinion should be sought
for determining these probabilities and their alterations with the occurrence
of the other events, or conditional probabilities. Meanwhile an educated
guess has been made for the authors to ilustrate the technique.
The conditional probability matrix shown in Table 2 expresses the probability
of an event given the occurrence of another event. Each probability can be
converted to. its corresponding odds, according to the transformation rule
“odds e=probability e/ (1-probability e)". -Then, the odds ratio of the impact
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 441
Table 2. Cross-impact Matrix Showing Conditional Probabilities.
SESLHIAEHAASNNSRUHOR READ RNHSS IAD SY AOAURESENES DNNARADSUHTNEDUAEONAEDY
If this event occurs. The probability of
probability Enis avane pucomes,
by 1990 2
© 1. Improving, capital
productivity. 9.30 at 0.20
e 2. Greater improvement of
Capital productivity. 0.15 0.0L «- HHBH 0.25 LIS
© 3. Eresh money su of 5
£7585 miritons Bas,
annually. 0.20 0.25 0.12 #88 (0.20
© 4. Doubling the su
honey bo 4,650 pely of
e87 aneualty. 0.10 0.15 0.10 0.01 a
of event i on event j is defined as the odds of the event j given the
occurrence of event i divided by the initial odds of event j, in isolation.
The matrix shown in Table 2 contains the odds ratio for every possible pair
of events,
Table 3. Occurrence Odds Matrix Ratios.
AMNAANGAAAAANTARATHTAN STARA ARH ATA T HAH ERA RAHA ATR EE OR
If this event occurs The odds of this event are miltipliew by
e 1, Improving kp 1.00 1.22
@ 2. Improving twice kp 1.33 1.58
e 3. Borrowing $2,325 4 ane 2.25
e@ 4. Doubling borrowing 0.41 0.62 0.04 aaae
"Having done the matrix which evaluate mutual interactions between events, the
DYNAMO programme goes as follows; the probability of the event 1 to 4 are
calculated from its odds:
probi.k=oddst.k/(1+todds1.k)
Fodds4 7K 7¢
proba.
The odds of events 1 to 4 are ¢aléWlated as the initial odds times the impact.
odds ratios times the impact of model variables on events: ~~
442 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
odds
k=ioddsl.k*iolol io2ol
k¥io301.k*ioGgol.keivart be.
«ahd
(@2)
The event initial probabilities given as arguments of table functions of tine,
are provided for the determination of their initial odds. Stover suagests
that these values should be requested to experts, who had to estimate such
probabilities for years 1990, 1995 and 2000. After calculating the median
estimates of the series supplied by the experts a S-shaped curve should be fit
to these points to yield a cumulative probability curve (Stove 1975).
Provisional estimations have been made by the authors:
babut(tiprdbt, time-ks855100,5)
1639/4327 23!
ipreb4, time. 85,100; :
es .14 (23)
What comes next is the cross-impact matrix formulation, The impact of event
ion event j, ioioj, is set equal to 1, that is without any effect, if event
i-has not occurred, or the odds ratio expressing the effect of event i on j,
which appears in Table 3, if event i has occurred. Obviously the impact of
event i onto itself is 1.
First pow
iolol.k=t
fofoaiksfifgelilagsisei
Second row
fifgeto. 02) 1,02. k1,0.10)
eee eee eee 1a)
Third row
ioBol.k=Fifge(O.77.1,e3.k1s0.10)
joBe4 kaFifge(2.25.1.e3 L110.
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 443
urth row
iphol. Kent geto'. 41> yeh k1sO. 10)
Can)
Equation simultaneousness was ‘broken up by a new formulation of the events.
occurrence. To this purpose el to e4 levels, shown in Figure 11 as a box
drawn in dashed lines, are being fed by the random occurrence of elr to e4r
flows and depleted in such a way that once any event happens, its level will
remain equal to 1 for the rest of the run. Mutual impacts between events are
triggered off by the occurrence of events 1 to 4:
elsksel. jrdte( (air. jk/dt)-Cel. jeter. jk/dt))
sep genininis CBiaveteitts
DjeeGs jes dbs . eaSy
For the events to happen, their corresponding random numbers have to. exceed
the complement to 1 of the current probability of each one of those events:
ifge(O,1,(1-prob1l.k)srni.k)
¢aey
Finally, the random number are generated by using the noise function, which
provides a. pseudo-random sequence of numbers uniformely distributed. between
~1/2 and +1/2 (Plugh 1976), used as argument of the equations 26.
rnl.k=noise()+0.5
Fad ckenoise(S46/5 ’ (a7)
Once the formulation of equations required, for the generation. of random
generated ‘scenarios is finished, this sector of the programme is easily
connected to the Harrod-Domar model. The following equations record the
impacts of the events on the model: Es : 4
kp kes tokptranp(sipt. +k 985) tramp (s1p2.ks85)
stgkp=0
zlpisk=0. OQ45¥et
$1p2.k=0.009*e2. 0. 428)
ext. k=0re8. k¥2325+e4 #4650 (a9)
So, the occurrence and timing of events él, e2, e3, and e4, are regulated by
eqs. 20 to 27. They are ‘able to generate scenarios which will differ widely
one another. Therefore, for every solution interval, the model modifies’ the
probability of the events el to e4, each time. the model run. This. resulting
in the happening or not of these events, whose impacts are transferred to the
Harrod-Domar model through eqs 28 ‘and.29, which: provide the required link.
444 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
The following Figure 12 summarizes the results of a large number of separate
runs performed with Dynamo III/F. The simulated time series were transversely
analyzed, yielding.an average value and the. standard deviation for every
solution interval, This Figure 12 displays the historical behaviour of the
Argentine GDP and external debt until 1985, in millions of 1985 american
dollars, since 1950, After 1985, it can be observed the resulting simulated
income and debt, noted y and d, respectively, for a particular random
generated scenario. On top of this, has been put the average trayectories of
the simulated income and debt and their confidence bands resulting from the
experiments. The relevance assigned to the results shown in. Figure 12
should be moderate, according’ to the provisional assumptions made in Table 2.
Figure 12. Average Trayectories of Simulated GDP and Debt and their Confidence
Bands, Superimposed on a Particular Simulation Run.
O° , wessee oy
Ty ne
----- 2
CONCLUSIONS
A very simple Harrod-Domar model is able to yield relevant results when it is
used for analysing different scenarios at a macroeconomic level, in the
Argentine case, once. the model's dynamics shows an acceptable nearness to
historical economic data for Argentina. Then the model is used to verify the
Stover (1980) solution to the probabilistic generation of futures, using
System Dynamics type of programming. Slight modifications are required to
avoid equation simultaneousness in such solution.
THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA 445
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Branson, W.H..(1979), Macroeconomic Theory end Policy, @nd. ed..
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be
Harrod, R.F. (1939); "An Essay in Dynamic Theory", Econom
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