FIGHTING INFLATION IN ARGENTINA: THE CRISIS OF 1982:
A SD version of a small monetary model, Cagan’s fashion.
Juan C. Rego
Fellow
Nat. Council of Science & Tech. Research
Pedro Goyena 2561
= (1640) Martinez
Buenos Aires
Argentina
Abstract
Periodically, at different times of its history, the Argentine economy has been dominated
by a vicious circle, well known among developing countries. The Central Bank pays interest on
money and such interest is financed through emission of more. money thus, causing inflation.
In one of these periods: the corresponding to February: 1981-July.:1982, the accumulated
inflation increased to 250 per cent. In 1982, the government decided to reduce the interest rate
abruptly, in order to achieve a quick reduction of the inflation rate. However, the year 1982
witnessed the failure of the application of this financial reform. Although the growth rate of
liquid assets declined, the inflation rate for July 1982 duplicated the previous month rate. This
article reformulates a small economic model, in the Cagan tradition, due to Rodriguez (1986).
Tt was conceived to explain the historic dynamics of the financial indicators, after the reform.
Hopefully, the readability of the model should improve, when compared with the original
version. And, ‘instead of attributing the dynamics globally to the complex behavior of the
system, the paper identifies the causes of this dynamics throughout the causal structure that
produced it.
I. ‘Introduction
In the first place, the article presents the System Dynamics model. Secondly, the
simulation runs, proposed by. Rodriguez, are reproduced in order to. guarantee a right SD
translation of the original model. Finally, a causal tracing is carried out, taking advantage of.
what Vensim software offers for an effective causal assignment. Thus, the. action of successive
links, throughout the causal network, becomes more evident.
SYSTEM DYNAMICS '93 389
Il. The System Dynamics model
Regular practice in System Dynamics requires to start with the identification of the
control’s mechanism of the system. Therefore, it would be reasonable to assume the presence
of a negative or balancing loop. Its function would be to maintain the stock of real money at the
level demanded by people. Figure 1 shows this structure.
<money supply adjusting time>
real money
supply +
real money demand
rate of change of real money supply
unsatisfied ‘demand for real money
Figure'1: Real Money Supply’s Control Loop.
The loop appearing in figure 1 is: the starting point for the definition of the System
Dynamics model. Out of figure 1 immediately emerges the convenience of the definition of a
stock that accumulates the real monetary balances. Given a nominal money supply M, and the
price level P; the real money m refers to the ratio m=M/P. The equation 1 illustrates the state
equation that accumulates the mentioned stock. Its initial value represents an economy with a
monetization level about 15 percent.
T
n= H-o.15+fmae (a)
0
The-rate of change of real money stock is proportional to the difference between real
money demand and supply. The latter were previously defined, in equation 1. The adjustment
time of the stock, .7;,, reflects the speed of the: correction: This simple rule establishes the first
differential equation of the system, represented in equation 2. In Systems Dynamics terminology
such a decision rule represents the regulating valve for incoming flow to the stock.
390 SYSTEM DYNAMICS '93
dm {m@- Paro
m= 2M. = 2
a 2.5 (month) <3)
Before advancing onto the inflationary effects of monetary expansion, related with
equation 2, let us recall some elementary accounting of inflation. Taking logarithms to both sides
of the equality m=M/P, results In(m)=In(M)-In(P). Then, derivatives are taken to both sides of
the new equality and after the introduction:of nominal monetary expansion and rate of inflation
® concepts, the following accounting identity applies:
areas ee eye
or simply, real monetary expansion is what remains of nominal monetary expansion p, after
discounting inflation 7:
=p-n (4)
Nominal money emission has a dual objective. Traditionally, it is issued to finance the
normal deficit of the government, (d*M). This deficit is expressed as a percentage d of the
nominal money stock M. In Argentina 1982’s case, money was also issued to finance the interest
(i*M) that was paid on nominal money stock M. In equation 5, i stands for the nominal interest
rate, supported by the Central Bank. The emission should finance both items:
dM_
& =im+dm={i+dlor (5)
Solving the nominal monetary expansion p, in terms of deficit d and nominal rate of
interest i, equation 6 follows:
Hep={ird} (6)
SYSTEM DYNAMICS '93. 391
Factoring out current inflation x from equation 4 and taking into account equation 6, the
following equation 7 results:
se(Befra-()
The-current rate of inflation does not influence people directly. Its delayed version does.
To model this effect, an expected rate of inflation x” is defined, as a first order delay, related
to what econometricians know as transformation of Koyck. The rate of change of expected
inflation (equation 8) is proportional to the difference between the current rate of inflation x and
the expected rate of inflation x”. Correction’s speed depends on the time 7, that the economic
agents require to learn from perception mistakes. Equation 8 is the second differential equation
of the system.
pee GIR"). (m-m*) 2 (n-2*)
dt q;
7 S (month) (8)
Next state variable (equation 9) accumulates the expected inflation. Its initial value is
about 17 percent, monthly:
r
n=0.17+/a*dt gy
i
The desired degree of real monetary balances depends on the inflation level of economy.
A variation of a Cagan function is used for the determination of real money demand m‘. As the
holding of monetary balances is remunerated by the Central Bank, the money demand can be
formulated as a positive function of the opportunity cost of money. This cost is appraised by the
difference between the nominal interest rate i that is paid-on money and the expected inflation
rate, a *.
me=qe'*=gerli-s") =9 2 ef (i-n) (10)
The causal structure of the complete model is exhibited in figure 2. There the negative loop
already shown in figure 1 appears. This takes charge of keeping the real money stock, at the
levels demanded by the public. But figure 2 also displays the consequences of the money stock’s
alterations. They are extended, though delayed, through two other loops. One of them is
392 SYSTEM DYNAMICS '93:
positive and the other is negative. Although different, they share most.of the causal chain which
follows the outline of figure.2. Furthermore, there are two accumulations or stocks of the
system, corresponding to the integrations:shown in equations 1 and 9. However, they have very
different functions within. thesystem. While the delayed inflation passively follows the current
inflation, the real money stock is.a-controlled variable, regarding a goal-of the system. Such
controlling effect.is evident in figure.4 below. Towards the end of the simulation run, money
supply comes back to. 15 percent, its initial value.
forecast error adjusting time
lexpected rate}
of inflation
nominal
rate of
interest
deficit
A
real money demand ~ rate of change of expected inflation
*
nominal monetary expansi
<Time>
ef
current rate of inflation
real money
supply
real.monetary expansion
unsatisfied demand for real money *
rate of change of real money supply
Be :
money supply adjusting time
Figure 2:-Causal structure of the complete model.
III. Simulation of the Model.
The simulation experiment disturbed the initial equilibrium, around 17 percent of
inflation rate, by reducing the exogenous rate of nominal interest rate to zero. Such a level of
inflation rate was consistent with a monetization level of about 15 percent. Figure 3 shows the
response of the system to the fall of the nominal interest rate. The dynamics exhibit a counter-
intuitive behavior. Inflation rate jumps up, reaching at once 20 percent. It takes a complete
SYSTEM DYNAMICS '93 393
month to fall back to the initial 17 percent level. After suffering strong oscillations, inflation
-becomes ‘stationary, almost 20 months later, at a lower 7 percent level. But this time was too
long and the government-had not the required political strength to achieve the goals of the
financial reform. This fact caused a crisis which abruptly ended the reform. Although there are
numerical differences; ‘the simulation shown in figure’3 observes a similar dynamics to ‘the one
observed in the original experiments carried out by Rodriguez (1986, figure 1): However,
neither the overshooting is so high, nor the fall so low. It should be noted that in Rodriguez’s
paper the inflation was estimated by the increase in the logarithm of the index price. Such a
formulation was only an approximation to the real inflation rate.
Basic Simulation Run
| —
° a |—]
0 3 6 9 12 15 18 21 24 27
Months since June 1, 1982
current rate of inflation - 1/Month
Sat Mar 20, 1993 8:56PM
Figure 3: Inflation’s overshooting.
394 SYSTEM DYNAMICS '93
IV. Causal Tracing.
Then, the consequences of the
exogenous shock throughout the causal
network are tracked, using the facilities that
the Vensim program offers (Eberlain 1990).
The exogenous nominal interest rate acts
directly on the rate of nominal monetary
expansion (See figure 2). It isan obvious
leverage point of the system. But the nominal
interest rate also acts on the opportunity cost
of money. Of the two possible set points for
the tracking of the causality, we chose the one
more detached from the variable that presents
the undesirable symptoms: the opportunity cost
of money. Then, we follow the consequences
of the shock trough to inflation rate.
Figure 4 represents a set of graphics,
produced by Vensim, one on top of another.
They represent the dynamics of the vcriable to
explain and its immediate causes. Thesé
graphics share the horizontal time axis.
Initially in equilibrium, the opportunity cost of
money is minus 7 per cent; since money
holding earns 10 percent, in an inflationary
context around 17 percent. This causes
minimal levels of real money demand, about
15 percent. :
. Of the two causes that affect the
opportunity cost of money, the effect of the
shock dominates initially. Expected inflation
grows slowly, from 17 per cent to 17.7
percent, monthly. The opportunity cost of
money collapses below minus 17 percent,
reproducing the fall of the nominal interest
rate.
unsatisfied demand for real money
.06
.03
0
-.03
-.06
real money supply
+15, iN
a |
teal money demand
1
expected rate of inflation
2 .
+15
a
.05
0
nominal rate of interest
2
+15
oa
.05
i)
10) 15.00
Time
Sat Mar 20, 1993 9:09PM
30
Figure 4: Variables affecting real money
demand.
Due to the drop of the opportunity cost of money, the demand for money also falls, from
15 percent to 10 percent. It recovers itself slowly, by means of the parsimonious increase of the
expected inflation. The latter is a delayed variable. The demand of money, that is, a flow
variable, reacts quicker to the exogenous shock than the stock of real money, due to its inertia.
Thanks to these differences in speed, unsatisfied demand also follows’ the dynamics of the
previously established demand.
SYSTEM DYNAMICS '93
995
Shrinking supply of real money
follows naturally to a contracting money
demand, but more gently, as can be expected
from an inertial state variable. Therefore the
top graphic of figure 4 exhibits a negative
gap between money demand and supply as a
consequence of the financial reform.
The analysis of figure 5 allows
uncovering the causes of inflation’s
overshooting. Starting again at the bottom
, graphic of figure 5, we find again the above
described fall and successive recovering of
unsatisfied demand for real money. Such
negative gap determines that the rate of
cxange of real money stock, which initially
is zero, should take negative values, about
minus 2 percent monthly. Th? reason for this
negative rate of change being the need of
eliminating the excess of money supply. And
the real money supply begins to decrease
after the shock.
In equilibrium conditions, with stock
of real money being constant, the real
monetary expansion is zero. Rut it does not
mean that nominal monetary expansion is
also zero. Inflation finances ordinary
expenses and the remuneration of the money
stock. In equilibrium, the nominal monetary
expansion 4 amounts roughly 17 percent,
monthly.
As mentioned, the anti-inflationary
shock produces a contraction of real money
supply. The level of government expenses is
reduced to cover just the defivit, about 7
percent. This reduction in the expenses is not
big enough to compensate the contraction of
the real money expansion. The savings
because of the reform, which amount. to
approximately 10 percent, are neutralized by
the extra 12-13 percent generated: by the
current rate of inflation
4
3
2
1 ——
0 “1
nominal monetary expansion
2
15
1
-05
i] .
real monetary expansion
2
A a
0
-1
-.2
real money supply
2
175
15 \
-125
1
rate of change of real money supply
02
.01
AN
an
-01
02 975.00 30
Time
Figure 5: Variables affecting current rate
of inflation.
squeezing of the real monetary expansion. Then, the level of inflation required to support such
expenses grows suddenly to the region of 20-21% monthly. é
SYSTEM DYNAMICS '93
Vv. Summary.
The purpose of this exercise was to translate a small economic model in homelike terms
to SD practitioners, while trying to preserve the original mathematical structure. There were
positive and negative loops operating. Negative or balancing loops were responsible of the
control of real monetary supply. Time allowed, this could have been achieved, but there was
impatience for results. Why the failure of this reform? These negative loops, combined with a”
positive or reinforcing loop, produced an unexpected amplification of the inflation (counter-
intuitive overshooting). The fall of the nominal interest rate and the consequent collapse of the
speed of nominal monetary expansion did not compensate the contraction of demand by real
monetary balances. And the inflation rate over-reacted. The present reformulation replicates the
results of simulations done with the original model and the causal structure of the system has the
flavor of an authentic Systems Dynamics model. The "invisible hand" operating on the monetary
market found its cybernetic equivalent, in valves and flow terms. A cybernetic model is ruled
by its objectives. It is equivalent to what economists call endogenously determined models. In
this case, the Cagan’s function, in its character of behavioral equation, implicitly contains the
target pursued by the system. As it was seen, in figure 4, the system, after the shock, comes
back to the initial levels of monetization: The system targets are inserted in the form of Cagan’s
function. Another form would turn the system to another level of monetization.
Bibliography
Eberlain, R., D. Peterson & W.. Wood (1990) "Causal Tracing: One Technical Solution to
the Modeling Dilemma" Proceedings of the 1990 International System Dynamics Conference,
Boston, Massachusetts, 341-354.
Rodriguez, C, (1986) "Un andlisis éstilizado de la Reforma Financiera de Julio de 1982" Centro
de Estudios Macroeconémicos de Argentina. Documento de Trabajo # 52. Buenos Aires, July
1986. .
SYSTEM DYNAMICS '93 397
