A MODEL OF SELF GENERATING NEURON:
TfiE ARGENTWE CASE

THESIS FOR THE DEGREE OF Ph. D.

MICHEGAN STATE UNWERSH‘Y

DEAN S BUTTON

1968

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The Argentine Case

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Dean S Dutton

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ABSTRACT

A MODEL OF SELF GENERATING INFLATION:
THE ARGENTINE CASE

by Dean S Dutton

This model was constructed to explain the rather high rates
of inflation prevalent in most Latin American countries and other
underdeveloPed countries as well.

Some features common to these Latin American countries are:
(l) The central government runs a large fiscal deficit each year.
(2) The deficit is largely financed through the central bank. (3)
Because of the method of deficit financing, a large increase in the
money supply results. (4) The deficit is due partly to the govern-
ment's unwillingness to levy sufficient taxes to cover planned
expenditures and partly to the fact that the collection of taxes,
which have been assessed sometime in the past, do not increase with
the price level, but government expenditures do.

Because of these features the inflation tends to perpetuate
itself. The purpose of our hypothesis then is to show how this
process works, i.e., how the rate of change in the price level, the
money stock, and the deficit are all interrelated.

The model comprises a system of four simultaneous equations

wherein, (l) the rate of change of the price level is related to rates

0f change in the per capita money stock and to levels of real per

capita money balances, (2) the rate of change of the money stock is

Dean S Dutton

related to rates of change of the monetary base, (3) the rate of
change of the monetary base is related to rates of nominal deficit
expenditure, and (4) the rate of nominal deficit expenditure is related
to the rate of real deficit expenditure (assumed to be constant), a
previous period's price level, and the rate of change in the price
level during said period.

Price level, money supply, monetary base (currency held by
the public plus bank reserves), and increase in Central Bank claims
on the government (used as a proxy for the fiscal deficit) data for

Argentina for the period 1958-1966 were taken from International

 

Financial Statistics. Population data comes from the Statistical

 

 

Bulletin for Latin America.

The parameters in equations (1) and (4) were estimated by
direct least squares and those in equations (2) and (3) by two stage
least squares.

It was concluded that the system of four equations does
reasonably well in describing a self generating inflationary process
in Argentina for the period 1958-1966.

The dynamic analysis of the model indicates that the time
path of the rate of change in the price level free of any external
constraints or shocks, is one of damped oscillation which seeks an
equilibrium rate of -3.26% per quarter.

A government plan to halt the inflation by eliminating its
deficit thereby reducing the increase in the monetary base and the
rate of increase in the money stock will have the desired effect only
after some time.lag. Elimination of the deficit will have its full

impact on the monetary base within the current period. The adjustment

Dean S Dutton

process takes about a year, however for a 1% reduction in the monetary
base to cauSe a 3/4% reduction in the money stock. It takes another
year for a 1% reduction in the money stock to bring about a 1%
reduction in the price level. No less than two years would be
required to feel the effects of such a plan. However, it seems
possible to reduce the rate of price increase from about 3.5% per
quarter to 0.0% per quarter in about a year if the rate of increase
in the monetary base is reduced to zero.

The results of the study also show that the one equation
models of inflation, when applied to countries like Argentina, leave

much of the process yet to be explained.

A MODEL OF SELF GENERATING INFLATION:

THE ARGENTINE CASE

BY

Dean S Dutton

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1968

ACKNOWLEDGEMENTS

I express special thanks to Professors Thomas R. Saving and
Jan Kmenta, who gave freely of their time and ideas as I called upon
them to help me solve the problems which arose as the thesis progressed.
I am indebted to both for their teaching excellence, which stimulated
my enthusiasm for empirical research and for the study of economic
theory.

I also wish to thank Professor James Ramsey who served as
the third member of my committee.

I am particularly grateful to Professor Karl Brunner who
suggested the tOpic and the fundamental form of the hypothesis. His
classes in monetary theory stimulated my interest in the subject and
my desire for sCholarly achievement.

I am indebted to the Department of Economics at Michigan State
University for financial support during my three years of graduate
study. I also wish to thank the Bureau of Business and Economic
Research at the University of Iowa for their typing assistance.

Finally, I thank the Department of Economics at Brigham Young
University for providing typing facilities and Miss Linda Rytting for

her expert typing of the final manuscript.

ii

TABLE

ACKNOWLEDGMENTS . . . . . . .

LIST OF TABLES . . . . . . .

LIST OF ILLUSTRATIONS . . . .

LIST OF APPENDICES . . . . .

Chapter
I.
II.
III.
IV.
V.
VI.

BIBLIOGRAPHY

INTRODUCTION . .
THE MODEL . . .

EMPIRICAL RESULTS

DATA AND HISTORICAL SKETCH, 1958-1966

THE DYNAMIC PROPERTIES OF THE MODEL

CONCLUSIONS . .

OF CONTENTS

iii

Page
ii

iv

vi

14
37
51
55
62

77

LIST OF TABLES

Table Page

1. Percentage Change (Continuous Compounding) in the
Price Level and Money Stock . . . . . . . . . . . . 54

2. Time Path of Quarterly Rate of Change in the Price
Level 0 O O I O C O O O O O O O O I O O O O O O 0 0 60

iv

LIST OF ILLUSTRATIONS

Figure Page
1. Nominal Deficit Expenditure . . . . . . . . . . . 26
2. Actual and Estimated Deficit . . . . . . . . . . 48

LIST OF APPENDICES

Page
APPENDIX A O O O I O O O O O O O O I O O 0 O O O O O O O O O 67

APPENDIX B, MAL ‘ MODEL ‘ O O O O O O O O O O O O O O O I O O 70

vi

CHAPTER I
INTRODUCTION

The purpose of this study is to formulate a hypothesis of
inflation which is capable of explaining the rate of change in the
price level in a particular country when its institutional struc-
tures conform to the requirements set forth in the hypothesis.

The inspiration for the study comes from the experiences of
most Latin American countries and other underdevelOped countries as
well, which have had substantial amounts of inflation.

Several features are common to all the Latin American
countries which have had large amounts of inflation: (l) The central
government runs a large fiscal deficit each year. (2) The deficit is
largely financed through the Central Bank. (3) Because of the method
of deficit financing, a large increase in the money supply results.
(4) The deficit is due partly to the government's unwillingness to
levy sufficient taxes to cover planned expenditures and partly to the
fact that the collection of taxes, which have been assessed sometbme
in the past, do not increase with the price level, but government
expenditures do. That is, government expenditures increase as the
price of goods and services increase even if real expenditures remain
fixed, but sales taxes, income taxes (not withheld), and prOperty
taxes are paid at their assessed level. The payment of these taxes is

sometimes deferred a considerable length of time after their assessment.

Because of these features the inflation tends to perpetuate
itself. The purpose of our hypothesis then is to show how this process
works, i.e.,how the rate of change in the price level, the money
stock, and the deficit are all interrelated. The model is then tried
on Argentine data.

Much of the research on inflation in underdevelOped countries
has been directed towards the effect of the inflation on the rate of
economic growth. The problem has been discussed from two diametrically
Opposed points of view: (1) the "structuralists" believe that infla-
tion is a necessary companion of economic growth, and (2) the
"monetarists" believe that inflation hinders economic growth.

The structuralists view inflation as a symptom of much deeper
structural problems. One such theory views the economy as being
divided into two principal sectors, i.e., agricultural and industrial.
The industrial sector manufactures mainly consumer goods which are
entirely absorbed within the country. The industrial sector must
import industrial materials and equipment for its use. The agricul-
tural sector provides the country's food supply and its export goods,
which in turn determine its import capacity. The agricultural supply
is very inelastic. The internal demand for food depends on real
income, but is large even when real income is not very high. The
expansion of the industrial sector under favorable terms of trade will
increase real income which will increase demand for food which will
increase its price since its supply is inelastic. The working class
experiencing an increase in the cost of goods will demand higher wages
through their unions, and manufacturers will pass the wage increase

on entirely in the form of higher prices. Thus, the general price

level increases. If the terms of trade are unfavorable and the country
is desirous of maintaining the same level of imports, then periodic
devaluation will probably occur which will increase the demand for

the exported food raising its price, and the above transmission process
is repeated so that the general price level rises. The inflation
occurs because of the structural rigidity of the food supply combined
with the policy of fostering a growing industrial sector.

Other such theories include a few more variables, but the
basis of all of them is the inability of the agricultural or some
other sector to expand output due to an increase in the demand for its
product. A steady increase in the price level is the necessary result.
Even if the large budget deficits and rapid expansion of the money
supply were eliminated, the price level would still continue to rise.

The monetarists, on the other hand, while recognizing
structural rigidities in the less developed countries like Argentina,
believe the major influences on inflation to lie in the manipulation
of the monetary and fiscal apparatus. The monetarists believe price
stability to be a necessary prerequisite for economic growth.

In their view, a continued inflation diminishes the volume

of resources available for domestic investment. Not only is
community saving reduced, but a significant part of this

saving is channeled to foreign rather than domestic invest-
ment, and simultaneously the flow of capital from abroad is
discouraged. Furthermore, a substantial part of the reduced
flow of resources for domestic investment is diverted to uses
which are not of the highest social priority. The accumulation
of large inventories is encouraged. There is a diversion of

saving away from capital markets, where investment decisions
would be subject to longer-term economic criteria, and toward

\

 

1Javier Villanueva, The Inflationary Process in Argentina,
1943-60, 2d Edition, Working Paper Inst. Torcuato Di Tella Centro
de Investigaciones Economicas, Buenos Aries: Editorial del Instituto
Torcuato Di Tella, 1966, pp. 112-125.

luxury housing and other kinds of investment which are socially
less useful, but may be highly profitable because of the infla-
tion. Balance of payments difficulties also result, and to
reduce the foreign deficits the authorities are forced to
resort to controls which in most cases protect uneconomic
production. . . . .

While the connection between inflation and economic growth is
certainly an important question, I shall not attempt in this study to
consider whether inflation assists or hinders economic growth. My
purpose is rather to formulate and test a theory which purports to
explain a significant part of the inflation which has occurred in
Argentina in the last several years.

Most of the work heretofore done in trying to explain infla-
tion in Argentina or in other Latin American countries under similar
conditions has been descriptive and non-analytical in nature.2 That
is, much has been said about the institutions and variables which
might be important, in varying degrees, in determining the course of
inflation, but little effort has been devoted to formulating tight
hypotheses and in testing their explanatory power empirically. The

work done for Chile by Arnold C. Harberger and for Argentina by

Adolfo C. Diz are notable exceptions.

 

1Werner Baer and Isaac Kerstenetzky (eds.), Inflation and
Growth in Latin America (Homewood, 111.: Richard D. Irwin, Inc.,
1964), pp. 3’40

2For an excellent historical account of the Argentine economy
and its inflation for 1943-60 see Villanueva. See also Aldo Ferer, The
Aggentina Economy (Berkeley: University of California Press, 1967).

3Arnold C. Harberger, "The Dynamics of Inflation in Chile" in
Measurement in Economics: Studies in Mathematical Economics and
Econometrics in Memory of Yehuda Grunfeld, ed. Carl F. Christ.
(Stanford, Ca1if.: Stanford University Press, 1963), and Adolfo C.
Diz, "Money and Prices in Argentina 1935-1962," unpublished Ph.D.
dissertation, Department of Economics, The University of Chicago,
1966.

 

The theory of inflation has been develOped from two points of
view--from the point of view of demand and from the point of view of
supply, FUrther, those who have looked at inflation primarily from
the demand side have espoused one of two positions.

. . . The quantity theory of money, with centuries of tradition
behind it, imputed price level changes to changes in the
quantity of money (a stock). An increase in this stock gen-
erated excess supply of money at existing prices and interest
rates, meaning excess demand for nonmonetary assets. The

other position, following Keynes's How to Pay for the War,
stressed the level of national expenditure (a flow) as the
main determinant of the price level, with increasing expen-
ditures opening an inflationary gap after full employment was
attained.

The model develOped in this study is an application of the
quantity theory of money, i.e., the rate of price change is related
to the rate of monetary expansion. This is only one equation of the
model, however. The money supply is not exogenous, but is related to
the fiscal deficit. And the deficit is dependent upon the rate of
change of the price level.2

Those who have used an adaptation of the quantity theory to
explain the path of inflation have used a one equation model. That
is, they have treated the money stock as an exogenous variable and
used the reduced form equation for the price level in a simple macro-
economic model as the single equation.

Assuming all exogenous variables except the nominal money

stock to be constant, the influence of changes in the nominal money

 

1Martin Bronfenbrenner and Franklin D. Holzman, "A Survey of
Inflation Theory," in Surveys of Economic Theory Vol. I (New York:
The Macmillan Co., 1966), p. 52.

2For an excellent survey of the work that has been done in
inflation theory in general--both demand and supply--see,
Bronfenbrenner and Holzman, ibid. '

stock on the price level follows essentially from the aggregate demand
for real cash balances. In a hypothetical society where the nominal
money supply consists entirely of a purely fiduciary currency issued
by a single monetary authority, the nominal money stock is whatever
the authority decides it should be. The real stock of money is
another matter, however. If peOple in the aggregate feel their real
cash balances are too high, they will attempt to reduce them by
increasing expenditures. As a result, nominal income and the price
level will rise thereby reducing real cash balances to the desired
level without altering the nominal money stock. Or if peOple in the
aggregate feel their real cash balances are too low, they will attempt
to increase them by reducing expenditures which leads to a reduction
in nominal income and the price level thereby increasing real cash
balances to the desired level. But again, the nominal stock of money
remains unaffected--it being at whatever level the monetary authority
has established. Given the level of real income and the nominal

stock of money, the ratio of nominal income to the nominal money stock,
or income velocity, is determined uniquely by the real stock of money.
Income velocity then is a reflection of the real quantity of money
that people desire to hold. "We can, therefore, speak more or less
interchangeably about decisions of holders of money to change their
real stock of money or to change the ratio of the flow of income to

the stock of money."1 And equilibrium between actual and desired real

 

1Milton Friedman, "The Demand for Money: Some Theoretical and
Empirical Results," The Journal of Political Economy, Vol. LXVII, No. 4,
August, 1959, pp. 330-331.

 

cash balances or equivalently between the actual and desired income
velocity is achieved through a movement in the price level.

Now if a stable functional relation between the real quantity

of money demanded and the variables that determine it can be found,
it is then possible to determine the effect of a change in the nominal
supply of money on the price level. Assuming equilibrium initially
between desired and actual real cash balances, an increase in the
stock of money will raise real balances above their desired level.
In their attempt to reduce them, the holders of money will increase
the flow of expenditures and hence money income and the price level
will rise, thereby reducing the real stock of money to its desired
level. Just the Opposite will occur in the case of a reduction in
the nominal stock of money.

An important develOpment illustrating the stability of the
velocity (or demand for real cash balances) function, while velocity
itself fluctuated tremendously,was Philip Cagan's study of seven
hyperinflations.1

Of all the determinants of the demand for real cash balances
specified in the theory of consumer behavior, Cagan makes a good case
for the centention that in an environment of rapid inflation it can
be explained largely by the cost of holding money. And the over-
shadowing portion of this cost is the rate of change in prices.2
He then expresses the demand for real cash balances as a function of

3
the expected rate of price change. After specifying the differential

 

1Philip Cagan, "The Monetary Dynamics of Hyperinflation" in
Studies in the Quantity Theory of Money, ed. Milton Friedman,
(Chicago: The University of Chicago Press, 1956).

21bid., pp. 27-33.

31bid., p. 35.

equation giving the time path of adjustments of the expected to the
actual rate of price change and making the assumption that actual and
desired real money balances are equal, he was then able to estimate
his demand for money function using observable monthly data.

In his study of the Argentine case, a much slower inflation
than the seven studied by Cagan, Diz uses approximately the same
functional form of the demand function, with the exceptions that he
tries to explain real per capita money balances and adds real income
(or permanent income) as an explanatOry variable.1 His assumption
of how expectations are formed is also equivalent to Cagan's. He
estimates his demand for money function using annual data and again
demonstrates its stability.

Specifying the demand for real cash balances as a function of
the rate of change in prices under the assumptions made by Cagan is
logically equivalent to specifying either the price level or the
rate of change in prices as a function of the level of and the rate
of change in the money stock. An appropriate transformation of the
demand for money function after substitution for the expected rate of
price change is all that is required. Cagan did this and expressed
the price level as a function of the current stock of money, the current
rate of change in the money stock,and all rates of change in the
stock of money from the initial to the current period.2

A similar transformation on Diz's demand for money function

yields the rate of change in the price level expressed as a function

 

1Diz, p. 40.

2Cagan, pp. 64-66.

of levels of the real per capita money stock, rates of change in per
capita money stock, and rates of change in per capita real income.

Cagan does not attempt to estimate the parameters in his model
using the transformed price level function, but he does show that in
the German inflation his price level equation predicts pretty well
the actual movements in the price level upon substituting values of
the parameters into the equation which are close, but not exactly
equal to, the ones he obtained in estimating his demand function.

When Diz proceeds to explain fluctuations in the rate of
change in the price level, he follows the line of Harberger's study
of the Chilean inflation and Specifies a linear multiple regression
of the rate of change in prices on the current and lagged rates of
change in the money stock and some other variables.1 He does not
transform his demand for money function. In this part of his study,
he uses quarterly data. Assuming that the demand for money function
in a quarterly model would be similar to the one he uses in his annual
model, a function explaining the rate of change in the price level
would follow directly upon transformation.

Harberger does not confine himself to a specific demand for
money function, but rather suggests the variables that determine it.
He then indicates that a simple transformation of the demand function
will express the rate of change in prices as a function of the rate
of change in the quantity of money, the rate of change of real
income, and the rate of change in the expected cost of holding money.
After choosing the difference between the rate of inflation in the

past year and the rate of inflation in the year before that as the

 

lDiz, p. 69.

10

variable to represent the rate of change in the expected cost of
holding cash he runs his regressions. He uses quarterly and annual
data.1

One common feature of the three studies just mentioned is
that they attempt to explain the price level (Cagan) or the rate of
change in the price level (Harberger and Diz) as a function of the
current level or rate of change of the money stock and past rates
of change in the money stock plus perhaps some other variables--the
monetary variables being by far the most important.

For Argentina at least and probably for Chile and possibly
for the seven countries of Cagan's study, I believe a one equation
model which attempts to explain the rate of change in prices to be only
part of the story. The evidence for Argentina suggests that the
inflation is to a large degree self generating. It is necessary then
to specify the rest of the model. That is, it is necessary to specify
how the rate of change in prices, the rate of monetary expansion, and
the federal deficit are all interrelated. Let us review briefly the
heuristic arguments for such an interrelation beginning with the
deficit.

Part of the deficit results simply because the government .
plans it. To explain the rest of the deficit, assume that inflation
is in progress and that the central government makes a tax assess-
ment as some preportion of current expenditures. Because a signifi-
cant portion of the taxes are not collected until sometime after

their assessment (In 1960 sales taxes in Argentina were paid a year

 

1Harberger, p. 226.

11

after the sale, for example),1 and because they are based on the price
level prevailing at the time of assessment, the actual budget deficit
exceeds the planned deficit. This is so because of the increase in
the price level between the time of the assessment and the time of
the collection of taxes, i.e., expenditures increase with increasing
prices, but non-collected taxes do not.

Given the institutional structure of the tax system the
inflation generates a larger deficit than was planned by the government.

The major part of debt financing by the government originates
in the Central Bank.2 As a result, bank reserves and hence the
monetary base (bank reserves plus currency outside banks) are increased.
Fractional reserve banking3 allows a dollar increase in the monetary
base to cause an increase in the money supply of an amount greater
than a dollar. At any rate, the increase in the base leads to an
increase in the money supply.

The increase in the money supply causes the price level to
rise. As described above, the increase in the price level leads to
a deficit greater than the one planned by the government. The above
process is repeated over and over again and the inflation continues
until the entire deficit is eliminated or some other link in the chain
is broken.

While a model describing the effect of the rate of change in

the money stock on the rate of change in the price level is a

 

1Stanley S. Surry and Oliver Oldman, "Report of a Preliminary
Survey of the Tax System of Argentina," Public Finance, Vol. XVI,
No. 2, 3, 4, 1961, p. 317.

2International Monetary Fund, "Argentina-1966 Article XIV
‘Consultation,9 (Washington, D: C., 1967), p. 25.

3Diz, p. 16.

12

necessary part of an explanation of the inflationary process in
Argentina (and in other countries with similar institutions) it
becomes only one equation in a larger system. A.better under-
standing of the inflation can be had if a hypothesis can be formulated
which comprises the whole system.

In part one of Chapter II, the theoretical foundations of just
such a hypothesis are laid out. It consists of four equations:
First, from the theory of consumer choice, a demand for money function
is deduced expressing the demand for real per capita money balances
as a function of the expected rate of price change. After specifying
how expectations of price changes are formed, it is possible to elimi-
nate all non-observable variables by a simple transformation of the
demand for money function. This gives us our first equation expressing
the rate of change in the price level as a function of the current
period's rate of change in the price level and last period's real
per capita money stock.

Next, the second equation is develOped from a simple theory
of banking to explain how the money supply reacts to an increase in
the monetary base. That is, a function to explain the money supply
or in this case, the rate of change in the money supplygis incorporated
into the model. The rate of change in the money supply is expressed
as a geometric lag function of the current and all past values of the
rate of change in the monetary base.

The third equation explains the relationship between the
monetary base and the fiscal deficit. When any part of the deficit is
financed by the sale of securities to the Central Bank, currency

outside banks and bank reserves increase. This equation expresses

13

the rate of change in the monetary base as a function of the current
and the sum of past fiscal deficits.

In the fourth equation, the level of the fiscal deficit per
period is explained. The deficit is the result of two related
factors: (1) the inability or lack of desire on the part of the
government to finance its expenditures through taxation, and (2) the
increasing price level over the period causing the tax collections to
be less in real terms than planned. Therefore, the deficit is expressed
as a function of the planned real deficit, the price level at the
beginning of the period in which the deficit expenditure was con-
tracted, and the rate of change in the price level over said period.

In part two of Chapter II, the stochastic properties of each
of the equations are discussed and the method of estimation of the
parameters of the model is presented. The implications of various
assumptions made in constructing the model and of the estimating
technique are also discussed, i.e., the prOperties of the parameter
estimates and their reliability are discussed.

In Chapter III, the empirical results of the estimation are
presented. The implications of the parameters are discussed and some
comparisons are made between the results obtained in this study and
results obtained in other studies.

In Chapter IV, the data sources and a brief history of
Argentina's inflation during the period of this study are given.

In Chapter V, the dynamic properties of the model are dis-
cussed, i.e., the time path of the rate of change in the price level,
free of any external constraints or shocks, is computed and discussed.

The conclusions of the study and the policy implications are

discussed in Chapter VI..

CHAPTER II
THE MODEL

Theoretical DevelOpment of the Model

The model to be deve10ped consists of four simultaneous equa-
tions wherein, (l) the rate of change of the price level is related
to rates of change in the per capita money stock and to levels of real
per capita money balances, (2) the rate of change of the money stock
is related to rates of change of the monetary base, (3) the rate of
change of the monetary base is related to rates of nominal deficit
expenditure, and (4) the rate of nominal deficit expenditure is related
to the rate of real deficit expenditure (assumed to be constant), a
previous period's price level, and the rate of change in the price
level during said period.1

Each equation will be deve10ped separately and then the entire
model will be presented at the end of this section.

The rate of change in the price leve1.--Since the equation
explaining the rate of change in the price level is derived from a
demand for money function we shall first show the theoretical justi-

fication for the demand for money function which we use.

 

1The money stock is defined to be currency outside banks plus
demand deposits held by the public; the monetary base includes
currency held by the public plus bank reserves; the deficit is
expenditures minus tax receipts of the central government; and the
price level is measured by an index of consumer prices. All stocks
and the price index are end of quarter values.

14

15

Let us assume that the total time available to a consumer during
any period is allocated to working, undertaking transactions, and
leisure. Under these conditions the time allocated to undertaking
transactions, Tt, leisure, Lt, and work, Wt, during any time period, t,

will all sum~ to one, i.e.,
(i) Tt + Lt + Wt = 1
Therefore, we can write

Let us further assume that real income earned per period, yt,

is a function of the time spent working during the period.
yt = C(wt) = C(1'1Tt + Lt] )

upon substitution for Wt. This can be rewritten as

(iii) yt = G*(Tt, Lt)
where 3G* < 0 SE: < O and 326* - -§3§3 - 0
5Tt ’ aLt 3T 2 - 3L 2 - °
t t

Now assume the time spent in undertaking transactions during
the period to be a function of the rate of real consumption expendi-

tures, ct, and the average level of real cash balances, m

t

(iv) Tt = T(ct, mt)

2
where 31' >.o, LT— <0, and 3— > o, 9.2. > 0.
act amt act ami

 

16

Income can now be expressed as

L)

a **
(v) yt G (ct. mt. t

upon substitution of equation (iv) into equation (iii) where

 

 

G** ** 2 2 2
g <0,_§G_.>o,gG_**.<o.ndac**<o,a_ezt<o,m..o,
ct mt Lt ac: 3mg 8L%

Assuming certainly the consumer's total wealth, 4? , over his
horizon is equal to the capitalized value of his earned income stream
plus the capitalized value of his initial assets minus the capitalized

value of the opportunity cost of holding money, i.e.,

H H-t n+1
(vi) ¢ = tEO (1+r) G** (ct, mt, Lt) + (1+r) ao
H H-t
' 2 (1+?) (Pint)!!!t
t=O

where H is his horizon, r is the real rate of interest assumed to be
greater than minus one and constant, a0 is his initial asset holdings

including money, and "t is the rate of change in prices, i.e., n

t
log P

 

equals d (where Pt is an index of prices) and is approximated
by the difference in the logarithms of the successive values of the
index of prices.1 The rate of interest, r, measuresthe amount of real
income foregonein period t by holding one dollar of real money balances,

and the rate of price change, n , measures the depreciation in value

t
in period t of one dollar of real money balances.

Given the rate of consumption expenditure, ct, the rate of

leisure, Lt’ the horizon, H, the level of initial asset holdings, a0,

 

1This logarithmic difference is the relative rate of change,
compounded continuously, for the price level, provided e‘is the base
of these logarithms. Throughout this study, e is taken to be the base
of the logarithms used.

17

the rate of interest, r, and the rate of change in prices, "t, the
consumer will adjust his money holdings so as to maximize his total

wealth, ¢.

Assuming that G** is continuous and at least twice different-

able, the maximization of 6 requires that

H
_ a **

(vii) dd> - ; (1+r) H ttfi— - (r+nt)]dmt ._. o

t=0
and

H 2
2 H-t 3 G** 2

(Vi-ii) d 9 = 2 (1+r) —2—dm < O

t=O amt t

 

BG** equals the marginal revenue of a unit of money and (r+flt)
m.
t

is the marginal cost of a unit of money. Since dmt is some arbitrary

increment in mt, for (vii) to hold it is necessary and sufficient that

 

(1x) BG_*§ = r+1rt, for all t 5 [0,11]
amt
2
O I O a G** O 0
Now since (1+r) is always pOS1tive and a 2 is always negative,
m
t

equation (viii), the sufficient condition for maximization, is always
satisfied. Therefore, the solution of equation (ix) gives the level

of mt, which maximizes wealth.

2

**

3G to be continuous, 3 G**
amt an

all the arguments of G** except mt to be held coastant, equation (ix)

to be negative, and

 

 

Since I assume

can be solved explicitly for mt giving the demand for real balances as

(x) mt = F(ct, L

18

Of all the variables in equation (x), m and?!t are the only

t
ones on which we have adequate data over the period of study. However,
the level and variability of the rate of inflation have been so high
that it probably dominates the other variables in explaining the demand
for real balances. With the goal in mind of a demand for money function
which can be used in the empirical part of the study, let us assume

that ct, Lt’ and r are constant. The demand for real money balances

can then be expressed as a function of the rate of change in prices

alone with ct, Lt’ and r entering as shifting parameters.
(xi) mt = 1‘*("t; ct. Lt. r)

DrOpping the assumption of certainty, the consumer seeks to
maximize his expected wealth--which is now a function of expected
levels of consumption, leisure, the interest rate, the rate of change
in prices, and real cash balances. We are assuming here that the con-
sumer is interested only in expected values and not in variances around
these expected values. We can proceed here as we did before in the
case of certainty allowing us now to solve for the demand for real
cash balances as a function of the expected levels of consumption,
leisure, the rate of interest, and the rate of change in the price
level. Assuming that the expected values of all variables except the
rate of change in the price level are equal to their actual values at

any point in time, and again assuming that c , Lt’ and r are constant,

t

the desired level of real balances can then be expressed as a function

of the expected rate of price change.1

 

1For a detailed deve10pment of the demand for money, see
Boris P. Pesek and Thomas R. Saving, Money,4Wealth, and Economic
Theogy. New York: The Macmillan Co., 1967.

19

In Argentina over the period of this study, income distribu-
tion remained quite constant. And it is quite reasonable to assume
that roughly the same price changes and level of the interest rate
were experienced by the entire population. Let us further assume that
the distribution of leisure time consumption did not change over the
period. It is then possible to aggregate the individuals' demands for
real balances and divide by papulation to get the aggregate demand for

real per capita cash balances. We can now write
(x11) (PL) . r*<.,;c9_>,<L_), r)
NPt NPt NPt

where ($3) is the aggregate demand for real per capita money balances,
"t is the texpected rate of price change, (Ii—P)t is the real per capita
level of consumption (assumed constant), CE.) is the real per capita
level of leisure consumption (assumed constant), and r is the rate of
interest (assumed constant).

The specific functional form of equation (xii) assumed here is
approximately like the one used by Phillip Cagan in his study of
hyperinflation.

O O M
X111) 10 -——) = Y - GE
( 8(NP t t

where Et is the expected rate of price change at the end of quarter t,
N is p0pu1ation at the same point in time, and Y and o are positive
constants.1

If we further assume that desired and actual real per capita

money balances are always equal, then (fl—) is an observable quantity.
NP
t

 

1Cagan, p. 35.

20

Since Et’ the expected rate of price change, is a non-
observable variable, it is necessary to specify it as a function of
observable variables. It is reasonable that individuals would base
expectations of price change on past actual rates of change on the
price level. Let us assume that the expected rate of price change is

th

revised during the t quarter according to the following rule:

(xiv) AEt = B(AIOgPt_1 ' Et-l)

where AEt = E - Et-l (the expected rate of price change at the end of

t
quarter t minus the expected rate of price change at the end of

quarter t-l), AlogP = logP - logPt_2 (the actual rate of price

t-l t-l

change during the (t-l)St

quarter), and B is a positive constant less
than one. The solution of difference equation (xiv) expresses the
expected rate of price level change as a gemoetric lag function of
all previous actual rates of price level change.
Upon taking first differences of equation (xiii) we get

M _
(XV) A log(—) - -aAE

NP t t

and upon lagging equation (xiii) one quarter and solving for Et-l we

get

(xiiia) Et_1 = in - 103(5) ]
a NP t-l

Now substitute equation (xiiia) into equation (xiv) and the result

from this substitution into equation (xv) yielding

(xvi) Alog(-'1—) = -aB[AlogP — .1. (Y — log(M_) )]
NP t t-1 a NP t 1

21

which eliminates all expected rates of price change and reduces
equations (xiii) and (xiv) to a single relation between observable
variables. After rearranging variables in equation (xvi), the current
rate of price change in quarter t is expressed explicitly as a
function of the current rate of change in the per capita money stock,
the previous quarter's rate of change in the price level, and the

level of the previous quarter's prices and the per capita money stock.

(1) AlogPt = -BY + Alog(-'1) + oBAlogP
N t t‘].

'M
+ 8 lo —- - 10 P
( 8(N)t-1 g t_1)

It can readily be seen that the current rate of price change

can be expressed as a geometric lag function of the nominal and real

per capita money stocks, i.e.,

 

(la) AlogPt = - 8' + Z (agimogcbé) , + Z 0181+110g(!-) .

1-08 i=0 t‘l i=0 NP 12-1-1
where GB is assumed to be less than one. Equation (1) can be derived
from equation (la) by a Koyck transformation. Simply lag equation
(la) one quarter, multiply by 08, and then subtract the resulting

equation from equation (la).

Several comments are in order regarding equation (1a). The

 

sum of the weights on the AlogCfl) term is equal to 1 > 1,

N t-i l-aB
which implies that an upward and sustained shift in the rate of per
capita monetary expansion will produce a somewhat greater percentage
increase in the price level after all lagged adjustments have taken

place. This is partially borne out in this study by the fact that

the average rate of price increase over the period considered was about

22

7.5% per quarter while the average rate of per capita monetary expansion
was about 5.9% per quarter. This is consistent with the theory of the
demand for money specified in equation (xiii), which implies that a
lower level of desired real cash balances is consistent with a higher

expected rate of price change. The sum of the weights on the

B

>
1-a8 <

 

log(-M—) term is equal to
NP t-i-l ‘

as B'iIi; <1 but the combined sums of the weights are equal to
a

1+8 , 1
1-u8 °

 

The rate of change in the money stock.--An increase in the
monetary base means an increase in the total of currency outside banks
plus bank reserves. Let us assume that the increase in the monetary
base is accomplished through an increase in currency outstanding which
is the result of the government printing money to finance a deficit.
The individuals whose currency holdings have increased find their port-
folio balance between currency and demand deposits disturbed. They
will proceed to reduce their currency holdings and thereby increase
their holdings of demand deposits. These individuals would make this
adjustment over a certain length of time, and the resulting increase
in demand deposits would increase bank reserves.

The equal increase in both demand deposits and reserves will
cause the actual reserves to deposits ratio to rise above the desired
reserves to deposits ratio of banks Operating in a fractional reserve
system. Banks will respond by creating new demand deposits to equate
the actual to the desired reserves to deposits ratio. This causes the

money supply to increase.

23

Again, this expansion of the money supply through new demand
deposit creation is not instantaneous, however, but can be accomplished
only over some length of time. We would expect, though, that after
some specific number of time periods most of the effect of an increase
in the monetary base on the money supply would have been felt. Let
us assume that the rate of change in the nominal money stock is a
geometric lag function of the current and past rates of change in the
monetary base, i.e.,

(2a) AlogM =A°£ (l-A)iAlogB
t i=0

t-i
where 0<A<l and £§6(l-l)i = 1.
This Specific formulation conforms with our expectations that in
period t a 1% increase in the monetary base results in only A% increase
in the money stock, and the effect of this 1% increase in the monetary
base on the money stock diminishes as time passes.

Again with the use of a Koyck transformation equation (2a)
can be simplified. Lag equation (2a) one quarter and multiply by

(l-A). Subtract this from equation (2a) and rearrange the resulting

equation to get

A = -
(2) loth AAlogBt + (1 A)Aloth-1

Here we have the current rate of change in the nominal money stock
being determined by the current rate of change in the monetary base
and last quarter's rate of change in the nominal money stock.

The rate of change in the monetary base.--Where the government
finances any of its deficit by the sale of securities to the Central
Bank an increase in currency outside banks and bank reserves will be

the result. That is, a fiscal deficit financed in this manner results

24

in an increase in the monetary base. In Argentina quite a large portion
of the deficit is financed by the sale of government securities to the
Central Bank. Therefore, the portion of the deficit financed in this
manner would cause the monetary base to increase by that amount. This

relationship can be expressed in the following equation form.

(3a) ABt = a + th

where ABt is the change in the monetary base during quarter t, Dt is
the rate of deficit expenditure during the same quarter, and a and b
are constants. b is the prOportion of the deficit that is financed by
the sale of securities to the Central Bank. a accounts for the other
factors (assumed here to be constant) which cause changes in the mone-
tary base. Solving equation (3a) for the total base in terms of an
initial value B(_1).(B(_1) is the level of the monetary base at the
beginning of quarter zero) and the increments in the base from the

beginning of the initial quarter up to the end of quarter t gives

'1 t
3b B = B + 2 AB. = B +— 2 + bD. = B
( ’ t (-1> i=0 1 <-1) i=0<a 1) <-1>
t
+ at-+‘bz D.
, 1
1=0

Dividing equation (33) by equation (3b) gives the relative rate of
change in Bt which is approximated by AlogBt. Therefore, we write

a + th

 

(3) AlogBt =

t

i=0 i

which specifies the rate of change in the monetary base being determined

25

by the current and all rates of nominal deficit expenditure since the
initial period.

The rate of deficit expenditure.--The nominal deficit, which in
total is caused by insufficient taxes to cover government expenditures,
results from two sources: (1) the government plans a given positive
deficit, and (2) a positive rate of price increase over the period in
which the expenditure was contracted causes the nominal expenditure to
rise but leaves the fixed tax assessment unaffected.

We have no data on planned real deficit expenditures per
quarter, so to simplify the analysis, let us assume that the planned
real deficit per quarter is constant (=g1). The nominal deficit in
quarter t, Dt resulting from this real deficit expenditure gl, will
depend on first, the price level at the beginning of the quarter in
which the expenditures were initiated, second, the rate of change in
the price level during the quarter, and third, the time path of the
real deficit expenditure, g(x), during the quarter. Assuming a positive
rate of price change, the nominal deficit would be greater if the
entire real deficit, g1, were spent on the last day of the quarter
than if it were spent on the first day.

Government expenditures are almost always contracted at some
date previous to the date of actual disbursement. That is, the govern-
ment will arrange to buy something on a given date at the price
prevailing on that date. The payment for the itemiwill take place
usually at some later date. The amount paid for the item then reflects
the price level at the earlier date when the purchase was contracted.
Therefore, a nominal deficit in the current period will reflect pur-

chases of earlier periods. Let us assume that this lag is two

26

quarters long. That is, the central government contracts to buy some-
thing on a given day at that day's prices but pays for it six months
later.

Therefore, the nominal deficit expenditure during quarter t,
Dt’ will be given by evaluating the line integral of the price level
function, F(x,g) B Pt_3eXA1°gPt'2, along the time path of deficit
expenditures, g(x), i.e.,
(4a) Dt = fPt_3eXA1°gPt'2dg(x)

g(x) -

where Pt-3 is the price level at the beginning of the quarter six
months before the current quarter t, and AlogPt_2 is the rate of price

change over the quarter. O<x<l (i.e., the length of the period over

F(x,g) xAlo
gPt-2
P e
/ t-3

t-3

 

“\ru

/

 

 

g,\‘ g(x

1/

Fig. l.--Nominal Deficit Expenditure

 

 

8

27

which the expenditure is made is one quarter), and O§g(x):g1. The

evaluated integral gives the area between the time path of real govern-

xAlogP
t-3e

projected onto the F(x,g), g plane between g=O and g=g1 as shown in

ment expenditure line, g(x), and the F(x,g)=P t-2 surface
Figure 1 above. The continuity of g(x) and F(x,g) is sufficient for
the existence of the line integral. Let us assume that real deficit
expenditures are undertaken evenly over the quarter, i.e., g(x)=g1x.
Both g(x) and F(x,g) are therefore continuous.

Now dg(x)=g1dx, and along g(x)=g1x when g=0, x=0 and when
g=g1, x=l. Substituting these values for the differential of g(x)
and the upper and lower limits of x corresponding to the upper and

lower limits of g(x) we get

1 xAlogPt”2
(4b) Dt =f Pt_3e gldx
0
1 xAlogPt_2
= Pt_3g13 6 dx

The integration yields

P g AlogP
t-3 l t-2
(4) Dt = ———(e -1)
AlogPt_2
which shows the explicit relationship between the current nominal
deficit, the real deficit, the level of prices six months previous to
the beginning of the current quarter, and the rate of change in

prices over said quarter.

For simplicity in discussing equation (4), let us write

u = AlogPt“2 so that

u
e -1

(4) Dt = Pt-381T

28

Note that aim Dt = Pt-3 gl. In other words, as the rate of price
change approaches zero, the nominal deficit becomes equal to the price
level at the beginning of the period when the deficit was contracted
times the level of real deficit expenditures. Or in other words, the
actual equals the planned deficit.

Note also that equation (4) is a strictly increasing function
of u, which means that as the rate of price change increases, so does

the nominal deficit. This is shown by taking the derivative

d Dt = ueu - eu + l
2

 

 

du u

which we must show to be positive. Using L'Hospital's rule, we

 

establish that lig dth = 0. Now for u>o the denominator is positive.
u
For u=o the numerator is equal to zero. So if the numerator increases

Dt
du

as u increases, then we have shown that

 

> o for all positive u.

This is so if

3% (ueu - eu+ l)= ueu>o

which is true for all u>0.

Summagy.--In summary we can now write the system of four
simultaneous equations which explain, (1) the rate of change in the
price level, (2) the rate of change in the money stock, (3) the rate
of change in the monetary base, and (4) the rate of deficit expendi-
ture. From the model follows the self generating nature of the

inflation.

M
1 A1P=- +1 — + 1
( ) 0g t BY A 08(N)t aBA ogPt_1

29

 

(2) A10 M - AAlo B + (l-l)Alo
s t s t th_1
a + bD
(3) AlogBt - t t
B + ati-bz Di
(‘1) 1.0
P g AlogP _
(4) Dt . __£:§_le.(e t 2-1)
AlogP
t-2
AlogPt, Aloth, AlogBt, and Dt are endogenous, AlogPt_1,

Aloth_1, Dt_1’(i-l, ..., n, where n is the number of quarters since

).

that quarter in which the amount of base money was equal to B( 1)

AlogPt_2 and Pt-3 are lagged endogenous, and only t and N are

exogenous variables.

Estimation

The procedure in this section is to add a stochastic element
at a spot in the deve10pment of each equation which seems to be reason-
able and then to estimate the parameters. The prOperties of the
parameters are then discussed.

The rate of change in the price level.--Let us assume that the
demand for real per capita money balances is a random variable of the

following form

M
' —- a -
(xiii ) log( )t y aEt + alt

2
where eltWNID(O,o ). We continue to assume that
l

(xiv) AEt - B(AlogPt-_1 - Et-l)

With these assumptions, equation (1) becomes

30

M
A1 P - Al I - + Al P
og t ogtfidt BY 08 og t-

1
+ 8(1og(§) - logP )
t-l t-l
' 81: + (1-8)€lt-l
or
. NP ,
' Al ——- - - + A1 P
(1 ) 08(M )t BY «8 Os t_1
+ Buoy!) - 103p ) + e*
N 12-1 12-]. 1t

where aft - (l-B)elt_l - Elt.

For purposes of estimation, the dependent variable is now
AlogCfiE'. It is clear that sit is not an independently diatributed
random variable, but is serially correlated.1 The least square
estimates of the parameters in equation (1') are therefore inefficient.
We are also unable to express sit as a simple firstcnder autoregressive

scheme and therefore the alternative procedures for obtaining

efficient estimates of the parameters are not open to us.

 

 

1The correlation coefficient of Elt and 6* l is given by
It-
E6* 8*
p* a It lt-l
1
E6* 2
1t

___ “(l-melt-l-Elt] [(1-3)81t-2 ’ e1::-1'

, 2
E[(1.8)611:-1"€1t;]

31

It is clear that both AlogPt,1 and 108(NP)t 1 are correlated
with the disturbance term, 8ft, since AlogPt_1 is a function of

* .E_ -
alt-1’ and log(NP)t_ is a function of €1t_1, both of which are cor

1
related with aft. As a result, the least square estimates of a and B
are also biased and inconsistent.

Another result of the autocorrelated disturbance terms is that
.the standard errors of the estimates are likely to be biased downward
so that the inefficiency of the estimates is concealed.

The rate of change in the money stock.--Let us assume that

the rate of change in the money stock is a stochastic variable of the

following form

°° 1
I _
(2a ) Aloth - Ai;o(l-A) AlogBt_1 + €2t

q 2
where as before 0<A<l, 1150(l-A)i = l and eZt'M NID(ON32).

 

2
(1-8) E8“: 6: _2 - (l-B)Ee

-1 1t lt-l E1t:-1

 

2 2 2
(1-3) Eelt-l - 2(1-B)Eeltelt_1 + Ee1t

(1' B)E51t_2€ 1t 'E 611: e1t-1

 

_ 2 2 _ _ 2 ..
(l B) Belt-1 2(1 mEEltELt-l + Eelt
2
(1‘301 (1—8)

 

(1-8)20:'+of l + (1-8)2

32

Applying the Koyck transformation to equation (2a') we get

lfloth - (l-A)Alog‘Mt_1 = AAlogBt - (l-A)62t_1 + €2t

or

' - -
(2 ) Aloth - Aloth_1 - MAlogBt Aloth_1) + Sgt
where Sgt = - (l-A)82t_1 + €2t'

For estimation purposes, the dependent variable now becomes
Aloth - Aloth_1. Although the method of two stage least squares
estimation of A eliminates the correlation between AlogBt and the

error term,e e*t is still serially correlated which introduces

*

2t’ 2

inefficiency, and correlation between Alog‘Mt_1 and 8*2t introduces

inconsistency. The autocorrelation of the disturbance terms again

causes the estimates of the standard errors to be biased downward.
An alternative assumption about the form of equation (2a')

will eliminate the theoretical problems in the estimation of A. Let

us assume that Aloth assumes the following functional form

(2") Aloth = A1 +0§AlogBt + l3AlogB + e

t-l 2t

2
where O<A2,A <1 and ezébNID(0472).

3

The two stage least square estimates of the A's in equation
(2") will be consistent.
' The rate of change in the monetary base.--Let us assume that
the change in the monetary base is a random variable of the following

form

33

I .—
(3a ) ABt - ai+ th + 53t

2
where 63: 'V NID(O,03) .

The two stage least square estimates of a and b are consistent.
With the resulting estimates of ABt’ estimates of AlogBt can be computed

as is described in the derivation of equation (3) in part one above, i.e.,

£E~

(3') Aiogst - t,

B(_1) + 8 £31
i=0

 

This estimate of AlogBt is then used to get the two stage least square
estimates of equations (2') and (2").

The rate of deficit expenditure.--Equation (4b) expresses the
current deficit being determined by what happened to the price level
six months previously. When we allow Dt to be stochastic we must add
the integral of the random element of real deficit expenditure and
what is happening to the price level during the current quarter, i.e.,

l xAlogPt_2 l xAlogPt

(4b') Dt = 6 Pt_3e gidx + 6 Pt_1e eatdx

2
where €4t WNID(0gJ4). The integration yields

 

P g AlogP P AlogP
t-3 1 - .. t
t = ———(e t 2 -1) + _t__1_(e -l)e:4t or
AlogPt_2 AlogPt
Pt_3g1 AlogP _
(4') Dt = -——————-(e t 2 -l) + 6*
AlogPt“2 ' 4t
Pt-l AlogPt
where 6* = (e -l)€4t.
4t AlogPt

The least square estimate of g1 in equation (4') is unbiased and

34

consistent, but probably inefficient because EZt is almost certainly
heteroskedastic.1

Finally, to take account of seasonal effects in the endogenous
variable, a set of three seasonal (0,1) dummy variables is added to

each equation.

So for estimation, the system of equations now becomes:

 

. NP = _ l!
(1 ) Alogcfi—Jt 8y + aBAlogPt_1 + 3(1og(N)t_1
- *
logPt_1) + dliSi + Elt
' - = - *
(2 ) Aloth Alog‘Mt_1 A(AlogBt Aloth_1) + dZiSi + €2t
(3') AlogBt = t , which is derived from

B + Z ’3.
{-1) i=0 1

I ..
(3a ) AB - a + th + d3isi + e3t

Pt_3 AlogPt_2
(4') D e

g-———-————- -l) + d S. + 6*

where Si (i a l, ..., 3) is set of three seasonal dummy variables in

 

 

Ps-l AlogPS ~
1To facilitate discussion let (e ‘1) = P5.
AlogPS
So we have
* ~ ~ 2 *2
Var(€4i) — E [Pie4i - EPie4i' - O4i
and
Var(€* ) = E[P. . - EP. .]2 = 0* 2
aj J 43 J 43 4j
£48 and P3 are not independent. It is possible for Pj and
£41 to interact in the same manner in which Pj and 841 interact for

2

- *
i # j, but since most probably Pi # Pj’ then most probably 0412 # 043 .

35

each equation, and dji (j = l, ..., 4) is the set of their coefficients

to be estimated.

Conclusion

A caveat applying to the estimates of the parameters in all
the equations is apprOpriate here. Since we cannot be sure that each
equation is the true specification between the variables, there exists
the possibility of misspecification which would cause the parameter
estimates to be biased.

This danger exists on equation (1') where we assume real per
capita consumption and leisure and the rate of interest to be constant,
in equation (3a') where we assume the deficit to be the only source of
change in the monetary base, and in equation (4') where we assume the
real deficit to be constant.

Direct least square estimates are computed for equations (1')
and (4'). The resulting estimate of Dt in equation (4') is used to
compute the two stage least square estimate of equation (3a'). The
resulting estimate of ABt is uSed as indicated in equation (3') to
obtain an estimate of lflogBt. The estimate of AlogBt is used in the
two stage least square estimate of equation (2'). Alternatively we
also use the estimate of AlogBt in the two stage least square estimate

of equation

I
[llogBt_1 + d2isi +-e

H
(2 ) Aloth A1 + AzAlogBt + A

3 2t

where again S 21

i is the set of three seasonal dummy variables, and d

is the set of three coefficients to be estimated.

36

Under the stated assumptions, the estimates of the parameters
in equations (1'), (2'), (2"), (3a') and (4') have the previously

mentioned prOperties.

CHAPTER III
EMPIRICAL RESULTS

The system of equations, whose paremeters are to be estimated

is the following:

NP = _ M
(l!) A1°8(fi—)t By + (381110ng1 + B(log(«fi)t'_1

: _ _
(2 ) Alog‘Mt - Alog‘Mt_1 - MAlogBt Aloth_1) + d2isi + Sgt
I! = I *
(2 ) AlogMt Al + AZAlogBt + A3AlogBt_1 + dZiSi + €2t

' =
(3a ) ABt a + th + d3isi + €3t

Pt-3 AlogPt_2

' ._ .-
(4 ) Dt - g1 (e l) + d iSi + 6*

4 4t

[110ng2

where Si (1 = l, ..., 3) is a set of three seasonal dummy variables

in each equation, and dji (j = l, ..., 4) and d5. are the set of their
1

coefficients, which are to be estimated.

Equation (2") is an alternative formulation of equation (2').

37

38

. .umuumsv summon ago no uoommo Hmaommmm man

no monogamouaa on ou ma aumu unnumcoo onu A.mmV uoooxo mooaumsuo oSu mo none cH .HH noummno ca
ooHMHoomm mos uH assumes mo mmoaoumwou nowumsvo some ca sumo unnumooo m Seem muaamou one

.aOHumavo some mo mamas can an voumOHvow

ma Amgmmv monsoon unon swoon can no Amanv moumsum momma uoonfiv Hosanna .ooaumafiumo mo_oonuma
man can .Ho>oa name you o>am on» on unonmwomHm mum Mmauoumm cm Sofia emumauumm omosya

 

SH m AwHo.V H HHHo.V H HeHo.V

mHmH Ame. a «mo .m + msHeo. . msnao. . mgmeo. .
Hus HHH.V u H-.V HHHO.V u
HAOHasso. + mmoHamm. . «use. a zmoHa Hzmv

um m HmHo.V H HmHo.V H Homo.o

mHmN Ass. u may a + mg~so. u mwamo. I mammo. .
.u a HSH.V HmHo.V Hus u
HH szH . HmquvsHm. + ease. n zmoHa . smoHa H.HV
SH mHoHo.V H Homo.v H Ha~o.v
man Ase. n va o +. mooo. + mammo. + msnmo. +
H!” In 2 A¢n0.v I” . AnH.v Ammo.v z
A mmoH . H omeOHV«SH. + H aonasnm. + mace. - _mmvmoHH H.Hv

H.m=owumavo mo amummm «no mo coaumawumo sou mo muaammu «no mafiamxo Hanan 03 302

39

.Azmv pom A.Nv mcowumovo mo mmumafiumm

mumsvm ummma mwmum 03H mau ca .oHOMouoau .vomo was moaomfium> amcommmm moo usonuHB coaumsvm

one aoum vm>HHoo mmumeHumm sea .Hm>mH uoou Hon m wau um oomofimwstm mums moaomfipm> Hmoommmm

map mo muoofiofimwmoo man mo ocoz .mmHessv Hmaommmm one escapes oumefiumm onu amnu AEoeooum mo

moouwmo How omumaounoov m Hmsoa m use mm seamen m wowamam mmfieaso Hmoommmm one ouHB oumefiumo
was .mmaomfium> meson Hmmmmmow mSu unocufis pom nufis noon vamEHumm was A.mmV soaumsvm

 

 

uq m Amo.~v N Aoo.mv Haqn.~v
mqmm AaN\ u va o + maom.w I mamo.o I moo.m I
qu . .
. mmoHe Hosoo V Ann «V H
AHI.NIu av qu «Hmo. + mm.~ n o A.qv
mwoa< m
on u HHH.V HOH.NV s
mAm Ann. I my 0 + nama.a + om. u mq A.mmv

N

40

In equation (1') both the estimates of a8 and B are significant
at the 5 per cent level. An estimate of .14 for B and .35 for as
imply an estimate of 2.5 for a. The estimate of .0093 for -By is not
significant at the 5 per cent level. This estimate and the estimate
of 8 imply an estimate of -.066 for Y.

It will be remembered that the sum of the weights on the

 

l}08 . Plugging in our

estimate of a8 gives a value of 1.54. This implies a 1% increase in

Alog(%)t_i term in equation (la) is equal to

the per capita money supply will produce a 1.54% increase in the price
level after all lagged adjustments have taken place. A sustained
increase in the per capita money stock of 5.9% per quarter would then
produce a 9.1% per quarter increase in the price level. Over the period
of this study, the per capita money stock expanded at a mean rate of
5.9% per quarter while the price level increased an average of 7.5%
per quarter.

The hypothesis implies that the price level responds to an

increase in the money supply only after some lag. Our estimate of

 

08 would imply that after one quarter 65% (= 1154) of the adjustment
has taken place, after two quarters about 88% (= %4%%), after three

1.47

quarters about 96% (=

 

),and after four quarters about-98% (= %f%%),
i.e., after a year we can expect that whatever changes occurred in
the per capita money stock at the beginning of the year will have
practically no more effect on the price level.

The response of the rate of price level change to a change in
the rate of monetary expansion, other things being equal, depends on
the desires of peOple to hold real cash balances-~the response being

different with different demands for real balances. If one assumes

41

a Specific demand for money function as we have in equation (xiii),

one must be willing to accept all the logical conclusions which follow--
one being the aforementioned response of the rate of change in prices
to a sustained shift in the rate of monetary expansion. On the other
hand, if one asswmes a certain response of the rate of change in prices
to an increase in the rate of monetary expansion, one is also obligated
to abide by its logical conclusions--one being a specific form of the
demand for money function. Diz's demand for money function is similar
to the one used in this study and implies exactly the same conclusion
concerning the effect of a sustained shift in the rate of monetary
expansion on the rate of change in prices.1 He goes on to say, though,
that on theoretical grounds, other things equal, one would expect an
upward and sustained shift in the rate of monetary expansion to bring
about a similar increase in the rate of change in prices.2 He then
regresses the rate of change in prices on the current and lagged

rates of change in the money supply plus some other variables, and
argues that if all relevant lags were taken into account, the sum of
the coefficients on the variables expressing the current and lagged
rates of change in the money stock would equal one. That the sum of
the coefficients is often significantly different from one is grounds
for him to conclude that all relevant lags probably were not taken

into account.3 To argue this would be equivalent to arguing that the

demand for real balances be independent of past rates of change in

 

1Diz, pp. 39-40.
21bid., p. 63.

3Ibid., p. 67.

42

the price level, .but on the same page Diz states that his demand for
money function would imply a lower level of real cash balances to be
consistent with a new and higher rate of change in prices after the
upward and sustained shift in the rate of monetary expansion had fully
worked its effects on the rate of change in the price level. Indeed,
from equation (xiii)

8
3AlogPt_1_i

 

[log(%?)t] = -o8(l-B)i< o (1=1, 2, ...)

where Et = B. (1-8)iAlogP

1

"DGB
C)

t-l-i

from the solution of the difference equation (xiv).

Harberger argues similarly that general equilibrium theory
would tell us to expect, in a truly "ceteris paribus" situation, that
' a l per cent per annum rise in the quantity of money would produce a
1 per cent per annum rise in the general price level, and that this
would mean that in a regression of the rate of change in prices on
the current and lagged rates of change in the money stock, the sum of
the coefficients on the variables expressing the rates of change in
the money stock should equal one.1 Again this implies that the demand
for real balances is independent of past rates of change of prices.
But he assumes that peOple will attempt to reduce their real balances
with rising expected cost of holding cash--the rate of change in the
expected cost of holding cash being represented by the difference between
the rate of inflation in the past year and the rate of inflation in

the year before that.2 Since the sum of the coefficients on the

 

1Harberger, p. 222.

21bid., p. 226.

43

variables expressing the current and lagged rates of monetary change
is very close to unity, he concludes that the lags which he introduces
fully capture the effect of money supply increases on prices.1 This
conclusion is not at all justified. Without exactly Specifying the
form of the demand for money function, which Harberger does not do,

it is impossible to say what the exact value of the sum of the
coefficients of the variables expressing the rates of monetary change
should be. All we can say, under Harbergerts assumptions about the
demand for money, is that the sum should be greater than, not equal
to, unity. .

Some discussion of the economic meaning of B and its estimate
is appr0priate. From equation (xiv) we deduce that 8 gives the speed
at which the expected rate of price change adjusts to the actual rate.
When 8 is multiplied by the difference between last period's actual
and expected rates of price change, the product gives the rate of
change of the expected rate of change in the price level.

Cagan states that % gives the "average length of each
weigMHng pattern" and "serves as a measure of the average length of
time by which expectations of price changes lag behind the actual

2

changes." Diz seems to be talking about the same thing when he

mentions the "average length of the weighting pattern," but doesn't

Specify how he arrives at it.3 The average length of the weighting

pattern as defined to be equal to.% does not appear to have any

significant meaning. If B = .14 as given by our estimate and an

 

11bid., p. 238.
2Cagan, p. 41.

3Diz, pp. 44-46, 73.

44

initial equality of expected and actual rates of price change is
assumed, and if the actual rate of price change shifted to a new and
constant level, this definition would seem to imply that the expected
rate of price change would adjust to this new and constant level in
about 7.1 (3.714) quarters.

AS mentioned above, the solution of difference equation (xiv)
is

w i
= .1- 1
Et Bi£0( B) A ogPt-l-i

Let us assume that in the initial and all previous periods the
expected rate of price change was equal to the actual, i.e.,
Eo . AlogPo, and in all subsequent periods, the actual rate of price
change was equal to C # AlogPo. For any given number of quarters, n,
from the initial period, it is now possible to compute the extent to
which the expected rate of price change, En’ has adjusted to the
actual rate, C. We merely solve for X in
n .
xc = 330 (1-B)1c

where XC = En. This reduces to

 

n+1
X = Z (1-8) = = 1 - (1-8)
1:0 1 ' (1'8)
For = .14 we have

x = 1 - (436)“1

This means that after one quarter the expected rate has adjusted to
26% of the actual rate of price change, after two quarters to 36%,

after a year to 53%, after seven quarters to 70%, and after two years

45

to 74%. Only after five years under these assumptions has the expected
rate adjusted to 96% of the actual. Note that the full adjustment
has not been made after 7.1 quarters.

Since the actual rate of price change is rarely constant,
about the only meaningful interpretation of B would seem to be that
the current quarter's expected rate of price change is revised at the
rate of 1008% of the difference between last quarter's actual and
expected rates of price change, whatever that difference might be.

Our estimate of 8 equal to .14 would imply that this rate of adjust-
ment is 14%.

In equation (2') the estimate of A is .31 and is statistically
significant at the 5 per cent level. The sum of the coefficients of
AlogBt and AlogBt_1 is equal to .50, implying that a sustained
increase in the rate of expansion of the monetary base would, after
two-quarters, cause an increase in the rate of monetary expansion of
half the magnitude. Further, the sum of the coefficients of AlogBt,
AlogB

, and AlogB is .65 with the obviously similar implication.

t-l t-2
We notice that the total sum of the coefficients of the variables
expressing rates of change in the monetary base is equal to l implying
that after all adjustments have worked themselves out, a l per cent
increase in the monetary base will affect a l per cent increase in the
money supply.

In equation (2") the estimate of AZ is not statistically
different from zero at the 5 per cent level, but the estimate of A3
is equal to .64 and is Significant at the 5 per cent level. The

implication is that a shift in the rate of change in the monetary base

does not exert any influence on the rate of change in the money supply

46

until the second quarter after the shift. Equations (2') and (2")
give similar results in that both imply a lagged response in the rate
of money expansion to changes in the rate of increase in the monetary
base. They imply different lagging patterns, however. The mean rate
of expansion of the money supply (as Opposed to the per capita money
supply considered in equation (1')) over the period of study was 6.2%
per quarter and that of the monetary base was 5.9% per quarter.

Only the estimate of b equal to 1.13 in equation (3a') is
significant at the 5 per cent level implying that a l peso increase
in the deficit is associated with a 1.13 peso increase in the monetary
base. Over the period of the study, the average quarterly increase
in the Central Bank claims on the government (used as~a proxy for the
deficit) was 10.7 billion pesos and the average quarterly increase in
the monetary base was 12.9 billion pesos. The results imply that a
10.7 peso per quarter increase in the Central Bank claims on the govern-
ment will produce an increase in the monetary base of 12.1 pesos per
quarter. Our a priori expectations would be that brbe close to unity.
Where the government finances most of its deficit by the sale of
securities to the Central Bank we would expect that after completion
of the expenditures the increase in the sum of bank reserves and

currency would be approximately equal to the amount of the deficit.1

 

1The rate of change in the monetary base can be deduced from
equation (3a') as was done with equation (3a) in Chapter II, i.e.,

t t

t
I _ a

31)

t t

B + at + b E D. + Z c .
(-1) i=0 1 i=0 3]..

47

Equation (4') calls for the price index, Pt-3’ to be expressed

as a fraction of l (e.g.,.89, 1.32, etc.) but instead, it was read

 

and therefore after dividing equation (3a') by (3b') we get

 

3" Al B -
( ) 08 t t t

B + at + b 2 D + 2 e
('1)1-o i 1- 0 31

I attempted first to estimate a and b from equation (3")

 

 

 

 

 

after taking a Taylor expansion around the points a = 0, b = l, £3t = o,
t- l
and Z €31=0 and drOpping the higher order terms. The linearized
i=0
equation is
t t
Dt 1:0D1 B(_1) - tDt + 1:0Di
(3"') AlogB - + a
t t 2 t 2
12 B + 2
(B (- -1) " $01) ( (-1) D1)
i=0
B D
- t
+b ( 1) + e'
t 2 3t
(B( + 2 Di)
-1) 130
t-1 t-l
B + 2 D D 2 e
-l
. = ' ) i=0 i E _ t i=0 31
3t t 2 3t t 2
+ B.’ + D
(B(-1)if0D1) ( {-1) :0 1)

Upon adding three seasonal dummy variables to equation (3"')
direct least squares yielded an estimate of 1.04 for "b" with standard
error .25 and an estimate of .68 for "a" with standard error 1.02.
Direct least square estimates of equation (3a') with seasonal dummies
added yielded an estimate of 1.09 for "b" with standard error .13 and
an estimate of -.076 for "a" with standard error 3.11.

The estimates of "a" in both equations are not statistically
significant at the 5 per cent level, but both the estimates of "b"
are significant and of similar magnitudes. This experience was a
testimony to me of the usefulness of a Taylor expansion in empirical
work.

48

 

 

 

 

 

 

 

 

40 -
Deficit in billions of pesos.
------- Estimated deficit in billions of pesos.
35 -
’ I
I
30 . I
I
H
' I
I
‘25-
20 r
15 .
I
. I‘,
I \
I E\ I \
10 . I\ I I \
I‘\ I\ I
I I
. r . \ I :
, I‘\,' I
5 I " I " \‘J
I\ I \ I \ :
t '\ l \'
I \ I V
l‘,
\
0 ; \ ,
\l
L I ‘
D\‘
‘l
lJlllJa IJJAlAALLRLL‘JlllllllJIJJ
58 59 60 61 62 63' 64 65 66

Fig. 2.--Actual and Estimated Deficit

49

into the computer as a fraction of 100 (e.g., 89, 132, etc.). It is
therefore necessary to multiply the estimate of gi in equation (4')
by 100 to get the estimate of the real government deficit (increase
in Central Bank claims on the government). This estimate is 3.1
billion pesos per quarter and is significant at the 5 per cent level.

The assumption of a constant real deficit is not a good one,
but for lack of a better one describing the time path of real deficit
expenditures, it was chosen. Even under this stringent assumption, it
was possible to explain the quarterly deficit (increase in Central
Bank claims on the government) with an R2 - .71. Figure 2 shows the
actual and estimated deficit (increase in Central Bank claims of the
government).

Summagy.--In this chapter, we have presented the results of
the estimation of the parameters of the model.

The parameter estimates of equation (1') imply that a 1%
increase in the per capita money supply will produce a 1.54% increase
in the price level after all lagged adjustments have taken place, and
that it takes about five years for the expected rate of price change
to adjust to within 96% of some constant actual rate of price change.

The estimates of the parameters in equations (2') and (2")
imply that after two quarters, a 1% increase in the monetary base will
have caused the money stock to increase by .50% (equation (2')) or by
.64% (equation (2")).

The estimate of 1.13 for b in equation (3a') supports our
expectation that a one dollar increase in Central Bank claims on the
government will lead to a one dollar increase in the monetary base.

The estimate of 1.13 is reasonably close to the estimate of one which

50

we would expect. If we had used deficit data instead of increases in
Central Bank claims on the government, we would have expected our
estimate of b to be less than one.

Equation (4') was reasonably good in estimating the actual
deficit (increase in Central Bank claims on the government) even with
the assumption of a constant real deficit (constant increase in
Central Bank claims on the government per quarter) which was estimated

to be 3.1 billion pesos per quarter in 1958 prices.

CHAPTER IV
DATA AND HISTORICAL SKETCH, 1958-1966

pg

The period of this study was the second quarter of 1958 through
the fourth quarter of 1966. Because of the relevant lags, the data
cover the period from.the third quarter of 1957 through the fourth
quarter of 1966.1

All of the data are end of quarter figures, and all of the
data except that for pOpulation came from International Financial
Statistics, a publication of the International Mbnetary Fund. The
population data is from.the Statistical Bulletin for Latin America,
Vol. III, No. 7, Feb. 1966, United Nations.

Pgigg§.--The "cost of living" price index was used.

Authorized by the Supply Law of 1964, the government relied
quite heavily on direct price controls during 1964 and 1965 in an
attempt to limit the rate of increase in the price level. The price
controls were partially relaxed during 1966 and totally after the

repeal of the Supply Law in November, 1966.2

 

1This beginning period was chosen because deposits were
returned to commercial banks in October, 1957 from the Central Bank
where they had been Since 1946. There is, therefore, no data for
commercial bank reserves from the end of the first quarter, 1946 to
the end of the third quarter, 1957. Diz, pp. 5, 7.

2International Monetary Fund, pp. 13-15.

51

52

The estimates of the parameters in equation (1') presented in
Chapter III, will be somewhat biased because of this fact.

Money Supply.--The sum of currency outside banks ("a residual

 

series obtained by subtracting commercial banks' holdings of Central
Bank notes and coin from the total amounts issued. The figures in
this series include currency held by the government and semi-fiscal
agencies.")1 plus demand deposits held by the nonbanking public.
"This series excludes interbank deposits, government deposits, and
"2

items in process of collection.

Monetary Base.--The sum of bank reserves ("amount of reserves

 

held by commercial banks in the form of gold, currency, and deposits
with the Central Bank.")3 plus currency outside banks.
Deficit.--Expenditures of the central government minus tax
receipts. I was unable to find quarterly data for this series.
Annual data was available, but the two series which I checked were
seemingly quite unrelated to each other. Since the central govern-
ment relied heavily on the Central Bank for the financing of its
deficit, I used the series of quarterly increases in the Central
Bank's claims on the government as a proxy for the quarterly deficit.
As a result of this substitution, we would expect the estimate
of b in equation (3a') to be very close to one, since a one dollar
increase in Central Bank claims on the government would mean a one dollar
increase in the monetary base. As we noted in Chapter III, the

estimate of b is very close to unity.

 

1Diz, p. 81.

ZIbid.

31bid., p. 82.

53

However, the estimate of g1 in equation (4') would not be the
esthmate of planned real fiscal deficit, but rather the estimate of
planned real deficit financing through the Central Bank. The
evidence suggests that deficit financing through the Central Bank
and the deficit move together; therefore, this substitution probably
won't affect the validity of our results.

Population.--The quarterly series was constructed by linearly

 

interpolating the annual series of mid-year estimates.

Historical Sketch

Since the model outlined in Chapter II, has been used to
describe the Argentine case, a brief history of the inflation over
the period will be of interest.

Since the beginning of 1958, Argentina has experienced a
substantial amount of inflation. Near the end of 1958, the government
initiated a stabilization plan aimed at, among other things, reducing
the rate of price increase. "The chief points of this plan were the
abandonment of price controls and subsidies, a tight money policy, a
balanced budget, wage controls, a further devaluation of the peso and
thereafter a stabilization of the foreign exchange market."1 Prices
increased greatly in 1959 ". . . reflecting merely corrective price
adjustments."2

An examination of Table 1 below indicates that a tight money
policy was not followed in 1959 since the money supply increased by

40.5 per cent. In fact, the rate of monetary expansion was not

 

1Villaneuva, p. 17.

2International Monetary Fund, p. 13.

54

TABLE 1

PERCENTAGE CHANGE (CONTINUOUS OOMPOUNDING)
IN THE PRICE LEVEL AND MONEY STOCK

 

 

 

Cost of Living Money
Year Price Index Stock
1958 27.4 22.6
1959 76.1 40.5
1960 24.0 28.6
1961 12.8 16.1
1962 24.6 5.5
1963 21.8 16.1
1964 20.0 34.2
1965 25.1 27.9
1966 27.7 25.9

 

Source: International Financial
Statistics by the International Monetary
Fund.
stabilized until 1962. The rate of price increase reached its minimum
in 1961, at which time the government decided to gradually abandon
the stabilization plan.

The plan was criticized because it did not eliminate the
inflation.1 One should ask just how deflationary the plan really
was. Between 1959 and 1962, the money supply more than doubled and
the government achieved neither a substantial rise in taxation nor a
significant reduction in expenditures.2

The period since 1962 has been characterized by substantial

increases in prices and the money stock and large government deficits.3

 

1Ferrer, p. 198.

2Villaneuva, p. 22

3International Monetary Fund, p. 20.

CHAPTER V

THE DYNAMIC PROPERTIES OF THE MODEL

It is of interest to note the time path of the rate of change
in the price level in the absence of any external constraints or
shocks. Although the model implies a self generating inflation, we
still don't know just how self generating it is. That is, if the
system is left alone, will successive periods generate the same rate
of inflation, a lesser rate, a greater rate, or will the rate of
inflation oscillate in some manner? To consider these questions, let
us look at the model again in its deterministic form as presented in

the first section of Chapter II.

 

_ - H
(l) AlogPt - BY + Alog(N)t + oBAlogPt_1
+ 8(10 (5) - 10 P )
g N t-l g t-l
(2) Alog‘Mt = lAlogBt + (l-A)Alog‘Mt_1
a +th
(3) AlogB =
t t
B(_1) + at +1.37: Di
i=0
PI:-381 AlogPt_2
(4) D = ———(e -1)
AlogPt_2

From equation (3) we note that the rate of change in the base

decreases as time increases, all other things equal. We also note that

55

56

 

 

t-l
3 AlogBt - B(_1) + 8(t-1) + b lgoDi
ant t 2
(B(_1) + at + b .2 Di)

i=0

which is probably always positive since the D are almost always

i
positive. Therefore, AlogBt decreases with time and increases with
increases in the deficit, all other things constant. We cannot judge
a priori which will dominate. If the net effect is an increase in
AlogBt as time passes, the rate of change in the price level could
increase without limit depending on the magnitudes of a, B, and Y.

To get some idea, we solve the reduced form for AlogPt. To do
this, it is neceSsary to linearize equation (3) and equation (4).
Equation (3) was linearized by taking_a Taylor expansion around D,
the average of all the D's, around tilDi (t = 35, the number of
quarters during the study), the average of all the sums of the D's
from the initial period to one period before the final period, and
around E, the average of the number of quarters. Equation (4) was
linearized by taking a Taylor expansion around TESEPE:E, the average
of the rates of change in the price level from two quarters before
the initial one to two quarters before the final one, and around
P::;, the average of the price level from three quarters before the
initial one to three quarters before the final one. The system of

equations now becomes

_ _ - M
(l) AlogPt - BY'+ Alog(N)t + aBAlogPt_1
+ B(1og(M) - logP )
N t-l t-l
A = .. '
(2) logMt AAlogBt + (l A)Aloth_1

57

 

 

 

 

 

 

t-l
(3) AlogBt = A + BDt - cc - .1 1:0 Di
(4) Dt -- - G + FPt_3 + @10ng2
_ _ FT _
(a‘+ bD)A - b(B(_1) + a(t-l) + b( 2 D1))D
where A = 2 —-*
A
2 ._._ __ IT?
(a +abD)t - b(a + bD)(: 2 D1)
+
A2
_ 13.-1'
A2
C a2 + abD
A2
b(a + b5)
J = ---———
A2
AlogPt_2
g. Pt-3 AlogP _ (e ~l)
K ='-l——-——- (e t 2 - )
AlogPt_2 AlogPt“2
AlogP
t-Z
(8 -1)
F = g1 ________
AlogPt“2
AlogP
-——————— t-2
AlogPt_2 (e -1) __
G = g (e - ) P
1 ———————- t-3
AlogPt_2
ET?
and A = B

+ E b5+b
(_1) a + ( 2 Di)

58

By plugging in the estimated values of the parameters and
the values of the other constants, we can solve for the coefficients

in the structural equations. We get a value of 19.39 x 1010 for A

and consequently a value of 375.792 x 1020 for A2. The coefficients
A, B, C, and J are essentially equal to zero, because a A2 appears in
the denominator of each of them.and the highest magnitude in any one
of the numerators is of order 1010. The reduced form for the rate
of change in prices is then simply derived from equations (1) and

(2) after setting AlogBt - 0 in equation (2). This gives
(5.1a) AlogPt = -BY + oBAlogPt_1 + (l-A)Aloth_1

+ 8(loth_1 - logPt_1 - logNt_1) - AlogNt

By lagging (5.1a) one quarter and subtracting the result from

(5.1a) we get

(5.1b) AlogPt = (1+aB-B)AlogP - aBAlogPt_

t-l 2

+ (l-A-+B)Alog'Mt_1 - (l-A)Aloth_2 - AlogNt

- BAlogNt_1

which becomes upon substituting in the estimated values of the

parameters

(5.1) AlogPt = 1.21AlogP - .35AlogP + .83Alog‘Mt_1

t-2 t-2

.69Alog‘Mt_2 - 1.14AlogN

where we let AlogNt AlogNt 1 = AlogN = the average rate of increase

in the p0pulation per quarter.

59

From equation (2), we note that the reduced form for the rate

of increase in the money stock is

(5.2a) Aloth = (l-A)AlogM.t_1

which becomes, upon substituting in the estimated value of A

(5.2) Aloth = .69Alog‘Mt_1

Now we can simulate the time path of the rate of change in
the price level. To evaluate the magnitudes of both endogenous
variables for quarter t we insert into equations (5.1) and (5.2) the
values for quarter (t-l) and for preceeding quarters, as required,
along with the rate of change in the pOpulation. Using the values
of the endogenous variables for quarter t thus obtained, we generate
values of the endogenous variables for quarter (t+l) in like manner.
We continue the process until we have proceeded far enough into the
future to satisfy our curiosity.

In Table 2 below, we begin with the actual rate of price
change in the third quarter of 1966, 3.49% per quarter. This rate of
price change generates a 3.53% rate for the succeeding quarter. After
three quarters, the rate of price increase has dr0pped to .41% per
quarter,and all rates of price change after one year are then negative.
We note that the time path of the rate of change in the price level
is one of damped oscillation which reaches an equilibrium rate of
-3.26% per quarter after 6.25 years.

These results follow from the fact that in the process of
linearization of equation (3) the link between the deficit and the

money supply is broken, so that the rate of monetary expansion falls

60

TABLE 2

TIME PATH 0F QUARTERLY RATE OF CHANGE
IN THE PRICE LEVEL

 

 

 

Quarters Since Rate of Quarters Since Rate of
Initial Period Price Change Initial Period Price Change
0 .0349 15 -.0346
1 .0353 16 -.0342
2 .0185 17 -.0339
3 .0041 18 -.0336
4 -.0141 19 -.0334
5 -.0242 20 -.0332
6 -.0306 21 -.0330
7 -.0342 22 -.0329
8 -.0360 23 -.0328 q-
9 -.0367 24 -.0327
10 -.0367 25 -.0326
11 . -.0364 26 -.0326
12 -.0360 .‘ 27 -.032§
13 -.0355 28 ‘ -.0326

14 -00350 ’29 -00326

 

to zero after 4.75 years. The most dominant determinants of the current
rate of price change become the two previous periods' rates of price
change after the rate of monetary expansion has sufficiently diminished.
After about a year, the rate of monetary expansion will have diminished
sufficiently so that this will be the case.

This gives us an idea of what we might expect if the deficit

were eliminated and the expansion of the money supply were halted.

61

If the rate of price increase were greater than 3.49% per
quarter in the quarter in which these restrictive policies were
initiated, it would take longer for the rate of price increase to
fall to zero. This would also be the case if the rate of increase
in the money stock were larger than the 6.28% per quarter in the
initial period and the 5.26% in the period before that, which we used
as initial conditions. It is clear that the system seeks a stable
equilibrium, but the length of time that it takes to achieve that
equilibrium depends upon the initial conditions.

For these results to hold, it is necessary that the coefficient
of expectation, 8, does not change. It is probable, though, that
under protracted restrictive policies and diminishing rate of price

increase that B would change.

CHAPTER VI
CONCLUSIONS

The purpose of this study was to formulate a model to explain
inflation in a country whose institutions are such as to make the
inflation self generating in nature. The model is designed to describe
situations where there is a high rate of price increase, a high rate
of monetary expansion and a large deficit which is financed partially
or wholly through the Central Bank. Also, where tax collections,
whose nominal value is fixed at the time of assessment, lag behind
government expenditures so that the rising price level over the period
in itself produces a deficit. That is, expenditures rise with the
rising price level over the period, but tax collections do not.
Argentina, being such a country, was chosen and its data were used
to test the model.

The model comprises four equations. Equation (1) shows the
relationship of the rate of change in the price level to the rate of
change in the money stock. Equation (2) depicts the relationship
between the rate of monetary expansion and the rate of increase of
the monetary base (bank reserves plus currency outside banks).
Equation (3) shows how the rate of fiscal deficit per period and the
rate of change in the monetary base are related. Equation (4) shows
the link between the rate of change in the price level and the rate

of deficit expenditure per period.

62

63

From.the theory of consumer behavior, it was shown that under
specific assumptions, the aggregate demand for real per capita money
balances can be expressed as a function of the expected rate of price
change. Then a specific demand for money function similar to the one
Phillip Cagan used in his study of hyperinflation was chosen and
then transformed to express the rate of change in the price level as
the dependent variable. This was labeled equation (1).

From a simple theory of banking behavior and consumer response
to an increase in their currency holdings, the response in the rate of
change in the money supply to variations in the rate of change in the
monetary base was shown in equation (2).

Equation (3) explains the somewhat mechanical relationship
between the rate of fiscal deficit per period and the rate of change
in the monetary base.

In deriving equation (4) we indicated how the institutional
structure of the fiscal mechanism establishes a link between the rate
of change in the price level and the rate of fiscal deficit per
period.

Estimates of the parameters of the model were obtained, most
of which seem to be quite reasonable. The estimate of .35 for QB in
equation (1) implies that a 1% increase in the per capita money supply
will produce a 1.54% increase in the price level after all lagged
adjustments have taken place. This result is implied by the specific
demand for money function used in this study. The estimate of .14
for 8 implies that the expected rate of price level change would
adjust to within 96% of a new and constant actual rate of price change

only after five years.

64

The estimate of .31 for A in equation (2) implies that a 1%
increase in the monetary base will have produced a .5% increase in
the money stock after two quarters.

The estimate of 1.13 for b in equation (3) implies that a
one dollar increase in Central Bank claims on the government (proxy
for the deficit) will cause a 1.13 dollar increase in the monetary
base.

A constant real increase in Central Bank claims on the govern-
ment (proxy for the deficit) of 3.1 billion pesos per quarter was
obtained as the estimate of 31 in equation (4).

The dynamic analysis of the model indicates that the time
path of the rate of change in the price level free of any external
constraints or shocks, is one of damped oscillation which seeks an
equilibrium.rate of -3.26% per quarter. The length of time which it
takes to achieve this equilibrium depends upon the initial conditions,
i.e., the initial rates of change in the price level and the initial
rates of monetary expansion.

We can conclude that the system.of four equations does
reasonably well in describing the inflationary process in Argentina
for the period 1958 to 1966. It is seen to be self generating in
nature.

The analysis shows that a government plan to halt the inflation
by eliminating its deficit thereby reducing the increase in the
monetary base and the rate of increase in the money stock will have
the desired effect only after some time lag. Elimination of the
deficit will have its full impact on the monetary base within the

current period. The adjustment process takes about a year, however,

65

for a 1% reduction in the monetary base to cause a 3/4% reduction in
the money stock. It takes another year for a 1% reduction in the
money stock to bring about a 1% reduction in the price level. The
results indicate that no less than two years would be required to
feel the effects of such a plan. A reduction in the rate of increase
in the monetary base to zero would produce quicker results, however.
If such a measure were taken, it seems possible to reduce the rate of
price increase from about 3.5% per quarter to 0.0% per quarter in
about a year. But, barring such a strong measure, it is not surprising
then that so many hold the view that a stabilization plan is ineffective
when it is tried only for a short period and then abandoned because
it did not halt the inflation. Results can be seen only if resolution
and patience are exercised.

The results also show that a necessary part of any plan to
halt the inflation is either elhnination of the government deficit
or the financing of the deficit by borrowing directly from the papula-
tion. If the deficit is not eliminated, then it must not be financed
through the Central Bank, i.e., this is necessary if it is desired to
maintain a stable flow of bank credit to the private sector. If the
monetization of the deficit were to continue, the money supply could
be reduced by sufficiently restricting private credit, but this is
probably not very desirable. This is what was done in 1959-1960,
however, which was another criticism of the stabilization plan.

We have shown that a linear regression of the rate of change
in prices on the current and lagged rate of changethnthe money stock,
as Diz and Harberger do, introduces a simultaneous equation bias

into the estimates of the coefficients. This is so because the equation

66

for the rate of change in prices is only one in a system of equations
wherein the current rate of money expansion is also an endogenous
variable.

We have shown that the one equation models of inflation,
when applied to countries like Argentina, leave much of the process
yet to be explained. This study was an attempt, even though in a

quite simplified manner, to explain the process.

APPENDIX A

In Chapter III, the results of the estimation of equations
(1'), (2'), (2"), (3a'), and (4') were presented where equations
(1') and (4') were estimated by the method of direct least squares
and equations (2'), (2") and (3a') were estimated by the method of
two stage least squares.

During the sequence of many computer runs, I obtained direct
least square estimates of equations (2'), (2") and (3a') as well as
their two stage least square estimates. The following are the
results of those least square estimations. Partially for review
and to maintain continuity the direct least square estimates of
equations (1') and (4') are presented again as well.

Those parameter estimates with an asterik are significant

at the five per cent level.

67

68

N m aNHo.V N Amao.v
3a SN. n N5 .u + 93°. .. 938. u
a “Nflo.c a-“ ANH.V u ANH.V AHHo.c u
mewno. . macaqum. + mmoflegos. + «Nno. a zuONq Ach
N m fiNHo.V N Amao.v
man Aom. u Nev a + manna. - msmNc. .
H Asao.v Hus u Ammo.v Aamoo.v Hus u
mamNo. u A zuoNq n mmoqugNm. + «Nee. u zmoae . zwoaq A.NV
H nasNo.v N AONo.V ANNo.V
man Ase. a Nev m + mesa. + menmo. + ngNmo. +
a-“ a-“ isms.c a-» Ana.c Ammo.v u z
A amoa I Amvmodai. + .302 «mm. + 88. _- wmvmoz b:

69

man AaN. u Nev

mun Ann. I may

n

HAeN.NV
moo.m u Aa- Nuu
mmoaq

Ass.nv Nst.mv

mmmN.m + mom.

a +

e Amo.~v Aoo.uv
o + mmeom.w I «memo.o u

N-umwose Aosoo.v Ann.Ne

av m-um same. + NN.N .u

 

sacs.mc u ANH.V Asa.mV
I mom.~ + memo.a + 050.1 I

u

U

a

m<

A.qv

A.mv

APPENDIX B

ANNUAL MODEL

An attempt was made to explain the annual averages of the
variables introduced in this study, i.e., the annual rates of price
increase, money supply expansion, growth of the monetary base, and
the annual deficit expenditures.

The annual model was develOped along similar lines as the
quarterly model but with some different assumptions. I was unable to
specify a demand for money function and a function which specifies
how price expectations are formed in such a way as to give, upon
transformation of the demand function, reasonable estimates of the
parameters. The other three equations gave quite reasonable estimates
in comparison with the quarterly model.

The following is the deve10pment of the model in the framework
of Chapter II. Then the results of direct least square estimation
of the individual equations are given.

The rate of price change.--Let us assume that the demand for

 

average annual per capita real money balances is expressed as a
function of the expected annual rate of price change and is a random

variable.
. !_ a _ _ a
(1) log(NP)t - Y aEt + elt

Where E: is the expected annual rate of price change in year t,

2
a > 0, and alt “aNID(0,o ).

70

71

Assume that

q

a
(11) Et 3 Et

where E: is the expected annual rate of price change in the first

quarter of year t. Let E: be revised quarterly according to the

following rule.

(111) A22 = 3(4A1ogpq 1 - Eq 1)
t‘z t-z

where 0 < B < 1 and AlogP2_l is the quarterly rate of price change in

q 1 is the annual rate of

C'—
4

q . sq - Eq 1

4

4
the last quarter of year t-l, so that 4AlogP

price change during the last quarter of year t-l. AE

and AlogPE = logP: - logP:_l. The solution of the difference equation

4
(iii) gives
. q T i q .
(1v) E = 48 2 (1-8) AlogP 1+1
1: t-_..__
i=0 4
Now upon substituting this for E2 = E: into the demand for money

function we get

°° i
(v) log(M ): = y - 4aBZ (l-B) AlogPt_ i+l + E

NP i=0 4 1t

By lagging equation (v) four quarters and subtracting the
lagged value from equation (v) and multiplying through by -l we

get

72

(vi) AlogP: - Alog(§)a - 4aBAloqu 1 + 4oB(l-B)Aloqu 2
N t t-4 t-4

+ 4o8(1'8)2AlogPE 3 + 4u8(1-B)3AlogP2_ 4

+ 4a8[(1'8)4 41111031915
4

-€

5 <1
+ (maul-B) - (1-8)]AlosPt__6_ + + elt-l 1t

4
By lagging equation (vi) by one quarter and multiplying by
(1-8) and subtracting the result from equation (vi) we get upon

rearranging

a 8 M a g gga
(vii) AlogPt Alog(-§)t + (AlogPt-% - Alog(N)t_} )

a M a
- 8(AlogPt_l]:- Alog(fi)t_21_)

+ 4018(Alongnl - AlogP:_ j) + £1
4 4 t‘l

' e1: ' (l'melt-i ' alt-l)
4 4
The annual rate of price change in year t is then expressed as a
function of the current annual rate of per capita money change, the
annual rate of price and per capita money change lagged one quarter,
and the one quarter and five quarter lagged quarterly rates of price

change.

73

For estimating equation (vii) becomes

(1) AlogP:

21.8- a - 31‘
A1og(N)t (AlogPt__% Alog(N)t_.i

'

a - M a
8(AlogPt_l]: A1°8(fi)t_ 1)
4

q - q *
+ 4a8(AlogPt__1_ AlogPt_ _2) +e 1t

where 5* 6
It

112']. all: ' (1-8)(€1t_ 25: ' E

The rate of change in the money stock.--Let us assume that the
rate of change in the money stock is a stochastic variable of the
following form.

a w i a
(2a) AlogM = A Z (l-A) AlogB, + e
t 180 t‘i 2t

a 2
where 0<x<1, A 2(1-1)1 . 1, and e t m NID(0,oZ).

1-0 2

Applying the Koyck transformation to equation (2a) we get

a
AlogM: - (l->\)Aloth”1 = AAlogB: - (l-A)62t_1 + €2t

or for estimation we write

a a a a
2 A10 - Alo = A Alo B - Alo )‘+ 6*
( ) th th_1 ( s t th_1 2t

6* = - -A e e .
where 2t (1 ) 2t-l + 2t

The rate of change in the monetary base.--Let us assume that
the change in the monetary base is a random variable of the following

form.

74

a a
(3a) ABt . a + th + €3t

2
where €3t “INID(0,03).
With the resulting estimates of AB:, estimates of AlogB: can

be computed as described in the derivation of equation (3) in Chapter II

above, but with annual data, i.e.,

 

/“x
’,/’\\z A38
(3) AlogBt - t
t./“\
B + 2 AB“
(-1) 1.0 1
where B:_1) is the average level of the monetary base in the year

preceeding year zero.

The rate of deficit expenditure.--We assume here that the
current deficit is determined by the price level at the beginning of
the year, the rate of change in prices over the year, and the level
of real deficit expenditures over the year, which again we assume to
be constant. We will recall from Chapter I that the deficit results
because the tax assessments are based on the price level at the
beginning of the year, but the taxes are paid later on in the year
when prices are higher. Expenditures increase with the price level,
but tax collections do not, so a deficit results which is larger than
was planned. The function expressing the level of deficit expenditure
assumes the following form.

8 a
l xAlogPt l a xAlogPt

(4b) D = f P e 8 dx + f P e 6 dx
1 0 t-l 4t

where g1 is the constant level of real deficit expenditure and

75

64!: W NID(0,0Z). The integration yields

a a a A a
a g1Pt-1 AlogPt Pt-l logPt
Dt - ---1;-(e -1) +—-—--5-(e -l)€
AlogPt AlogPt 4t

So for estimation we have

a a
a a gIPt-l AlogP

(4) n a (e t -1) + 2*
AlogPt 4t
- 13:1 AlogPa
- t
where 6* = -—-————(e -l)€ .
4t AlogPa 4t
t

Summary.--Now to rewrite the four equations to be estimated in

the annual model we have

a ‘—a= - a - r8
(1) Alogrt Alos(:)t <1 8><A1ogrt_ .1 A1°3(N)t-l)
4 4
q q
+ 4018(AlogP 1 - AlogP 5) + 6*
t- - t- — 1t
4
a a a a
- A = A - i-
(2) Alog‘Mt loth-1 (AlogBt Aloth_1) + €2t
a a
(3a) ABt = a + th + 63t
a glP:_1 Mag?8
(4) nt = —T(e t -1) + 5*
AlogPt 4t

Empirical results of estimation.--Direct least squares yields
the following estimates. Those estimates with an asterisk are

significant at the five per cent level.

(1)

(2)

(3a)

(4)

76

a a
AlogPt - Alog(%)t - 3.15*(AlogP:_1_ - May-E):
4

(.47)

q

- q -
.10(AlogPt_ l AlogPt_ '2') + e1

4

a a . a a
- = * -
£110th Aloth_1 . 77 (AlogBt Aloth_1)

(.12)
+ 82
a 3
at = 7.80 + .92*Dt + e
(14.18) (.25) 3
1>al 2110311:
I): = .107* __t'_1_(e -1) + e4

(.0118) AlogP:

2

(R

(R

(R

(R2

.91) DLS

. 86) DLS

. 69) DLS

.78) DLS

BIBLIOGRAPHY
Books

Ackley, Gardner. Macroeconomic Theory. New York: The Macmillan
Company, 1964.

Beer, Werner and Kerstenetzky, Isaac (eds.). lnflation and Growth
in Latin America. Homewood, 111.: Richard D. Irwin, Inc.,

Bailey, Martin J. National Income and the Price Level. New York:
McGraw-Hill Book Company, Inc., 1962.

Bronfenbrenner, Martin and Holzman, Franklin D. 9A Survey of
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York: The Macmillan Co., 1966.

Cagan, Philip. "The Monetary Dynamics of Hyperinflation." Studies
in the Quantity Theory of Money. Edited by Milton Friedman.
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Ferret, Aldo. The Argentine Economy. Berkeley:‘ University of
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Friedman, Milton. A Theory of the Consumption Function. Princeton:
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"The Quantity Theory of Money--A Restatement." Studies
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Chicago: The University of Chicago Press, 1956.

Harberger, Arnold C. "The Dynamics of Inflation in Chile."
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Carl F. Christ. Stanford, California: Stanford University
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Henderson, James M. and Quandt, Richard W. Microeconomic Theory, A
Mathematical Approach. New York: McGraw-Hill Book
Company, 1958.

Keynes, John Maynard. How to Pay for the War. New York: Harcourt,
Brace and Company, 1940.

77

78

Lerner, Eugene M. "Inflation in the Confederacy 1801-65." Studies
in the Quantity Theory of Money. Edited by Milton Friedman.
Chicago: The University of Chicago Press, 1956.

Pesek, Boris P. and Saving, Thomas R. ‘Money, Wealth and Economic
Theory. New York: The Macmillan Company, 1967.

Selden, Richard T. "Monetary Velocity in the united States." Studies
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Chicago: The University of Chicago Press, 1956.

Warburton, Clark. "The Misplaced Emphasis in Contemporary Business
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Articles and Periodicals

Adelman, Irma and Adelman, Frank L. "The Dynamic_Pr0perties of the
Klein-Goldberger Model. Econometrica, XXVII; No. 4,
October, 1959, pp. 596-625.

Friedman, Milton. "The Demand for Money: Some Theoretical and
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Griliches, Zvi. "Distributed Lags: A Survey." Econometrica, XXXV,
No. 1, January, 1967, pp. 16-49.

 

Kmenta, Jan and Smith, Paul E. "Autonomous Expenditures Versus
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Econometrics WorkshOp Papers. Workshop Paper No. 6604.
Michigan State University, 1957.

Kmenta, Jan. "An Econometric Model of Australia, 1948-61." SSRI
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Surrey, Stanley S. and Oldman, Oliver. "Report of a Preliminary
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Villanueve, Javier. The lpflationary Process in Argentina, 1943-60.
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79

Reports

International Monetary Fund. "Argentina-1966; Article XIV Consulta-
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Unpublished‘Materials

Diz, Adolfo Cesar. "Money and Prices in Argentina, 1935-1962."
Unpublished Ph.D. dissertation, Department of Economics,
The University of Chicago, 1966.

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