Milton Friedman

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Research Papers in Economics

This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research
Volume Title: A Theoretical Framework for Monetary Analysis
Volume Author/Editor: Milton Friedman
Volume Publisher: UMI
Volume ISBN: 0-87014-233-X
Volume URL: http://www.nber.org/books/frie71-1
Publication Date: 1971
Chapter Title: Some Dynamic Implications of the Monetary Theory of Nominal Income
Chapter Author: Milton Friedman
Chapter URL: http://www.nber.org/chapters/c0919
Chapter pages in book: (p. 40 - 43)40 / MONETARY ANALYSIS
(9)' and (11), real income. The price level would then be given by
the ratio of the nominal income obtained from equations (31) and wi (33) to the real income given by equations (9)', (10)', (11), and T
(34). The two sets of equations combined would be a complete system th
of. seven equations in seven variables determining both real and nominal H
magnitudes.
Such a combination, ifit were acceptable, would be intellectually
very appealing. Over a decade ago, during the early stages of our com-
parison of the predictive accuracy of the quantity theory and the in-
come-expenditure theory, my hopes were aroused that such a corn-
liD
bination might correspond with experience. Some of our early results
were consistent with the determination of the real variables by the mul-
tiplier, and the nominal variables by velocity. However, later results p
shattered the hope for this outcome (Friedman and Meiselman 1963).
The unfavorable empirical findings, moreover, are reinforced by the-
oretical considerations.
C
The major theoretical objections are twofold. First, it seems entirely
satisfactory to take the anticipated real interest rate (or the difference t
between the anticipated real interest rate and the secular rate of growth)
as fixed for the demand for money. There, the real interest rate is at
best a supporting actor. Inflation and deflation are surely center stage.
Suppressing the variations in the real interest rate (or the deviations of
the measured real rate from the anticipated real rate)is unlikely to
introduce serious error. The situation is altogether different for saving
and investment. Omitting the real interest rate in that process is to leave
out Hamlet. Second, the consumption function (9)' is highly unsatis-
factory, especially once we take inflation and deflation into account.
Wealth, anticipations of inflation, and the difference between per-
manent and measured income are too important and too central to be
pushed off stage completely.
Hence for both empirical and theoretical reasons, I am inclined to
reject this way of marrying the real and the nominal variables and to
regard the saving-investment sector as unfinished business, even on the
highly abstract general level of this paper.
9. Some Dynamic Implications of the Monetary Theory
of Nominal Income
In equation (31), which determines r,wehave so far taken [(1/Y)
(dY/dt)]* asa predetermined variable at timetand not looked
closely at its antecedents. It is natural to regard it as determined by
past history. If it is, we can write equation (33) as41 / MONETARY ANALYSIS
Y(t) =V[Y(T)1.M(t),T < , (35)
where V is now a functional of the past history of income, Y(T) for
T < t. However, the past history of income in its turn is a function of
the past history of money, thanks to equation (33) for earlier dates.
Hence, we can also write equation (33) as
Y(t) =F[M(T)].M(t),1' < t, (36)
where F is a functional of the past history of money. There is also
imbedded in these equations the value k0, i.e., the assumed fixed value
of the difference between the anticipated real interest rate and the secu-
lar rate of growth of output. So equations (35) and (36) must be inter-
preted as depicting the movements of nominal income around a long-
term trend on which k0, and its components, p"andg*, adjust to more
basic long-term forces—fundamentally for both, changes in the quantity
of resources available (human and nonhuman) and in technology.
A specific example may help to bring out the dynamic character of
this simple model. Take logarithms of both sides of equation (33) and
differentiate with respect to time. This gives
1 dY_ idV1 dM
YdtV dt+Mdt
ldVdr1dM
—Vdr dt+Mdt
Replace (1/V) (dV/dr) by s (to stand for the slope of the regression
of log V on r), and dr/dt by the derivative of the right-hand side of
equation (31):
ldYdrldyl*1dM -= s.L?-jJ +--. (38)
Assume that the anticipated rate of growth of income is determined
by a simple adaptive expectations model:
d ridYl*El dY(i dY*
dEL?J — — 'zij (39)
Substitute equation(39)in equation(38) and solve for (l/Y)
(dY/dt). The result is
1 dY—(idY\* 1[1 dM(i dY*1
Y dt\Y dtl+1 —Lidt\Y dtl j
(40)42 /MONETARYANALYSIS
Subtract (l/M)(dM/dt) from both sides, and equation (40) can also
be written de
1 dV—5sr 1dM 1dY4
41 V dt —1—LMdtY dt
Assume that 0 </3s<1.24 Equations (40) and (41) give a very th
simple and appealing result. If the rate of change of money equals the S
anticipated rate of change of nominal income, then nominal income P
changes at the same rate as money—we are in the simple quantity
equation world. If the rate of change of money exceeds the anticipated S
rate of change of nominal income, so will the actual rate of change of
nominal income, which will also exceed the rate of change of money— e
velocity is increasing in a "boom." Conversely for a "contraction" or
"recession," interpreted as a slower rate of growth in the actual than
in the anticipated rate of growth of income.
Note that this way of introducing a procyclical movement in velocity
is an alternative or complement to the approach I suggested in an earlier
article (Friedman 1959 and 1969). There the procyclical movement
of velocity was explained by the difference between measured and
permanent income. The two approaches are not mutually exclusive—
as I indicated in my earlier article, when I left room for interest rate
effects on velocity (Friedman 1969, pp. 130—136). In the present
context, the simplest way to introduce both effects would be to rewrite
(12b) as
MD =y*l(r), (l2c)
where Y''is permanent nominal income. To complete the system,
equation (14) must be replaced with a more sophisticated adjustment
mechanism involving Y—otherwise the system, with Y4 treated as
determined by the past history of Y, would be overdetermined. Such
a more sophisticated mechanism is discussed in section 12 below.
In summary, the key elements of the monetary theory of nominal
income are:
(a) A unit elasticity of the demand for money with respect to real
income.
(b) A nominal market interest rate equal to the anticipated real rate
plus the anticipated rate of change of prices, kept at that level by
speculators with firmly held anticipations.
(c) A difference between the anticipated real interest rate and the
real secular rate of growth determined outside the system.
'Thisis the condition for dynamic stability of the system. See Cagan 1956.43 /MONETARYANALYSIS
(d) Full and instantaneous adjustment of the amount of money
demanded to the amount supplied.
)
Theseelements are borrowed mostly from Irving Fisher and John
Maynard Keynes. Together they yield a simple two-equation system
that determines the time path of nominal income but has nothing to
say directly about the division of changes in nominal income between
prices and quantity.
This simple model for analyzing short-term economic fluctuations
seems to me more satisfactory than either the simple quantity theory
which takes real output as determined outside the system and regards
economic fluctuations as a mirror image of changes in the quantity of
money or thesimple Keynesian income-expenditure theory which
takes prices as determined outside the system and regards economic
fluctuations as a mirror image of changes in autonomous expenditures.
10. Comparison of the Three Approacbes
None of the three simple theories—the simple quantity theory, the
simple income-expenditure theory,thesimple monetary theoryof
nominal income—professes to be a complete, fully worked out analysis
of short-term fluctuations in aggregate economic magnitudes. All are
to be interpreted rather as frameworks for such analyses, establishing
the broad categories within which further elaborations will proceed.
The simple quantity theory puts in center stage the relation at each
point in time between a particular flow—the flow of spending or in-
come—and a particular stock—the quantity of money. The simple in-
come-expend iture theory emphasizes the relation at each point in time
between two components of the flow of income—autonomous and
induced spending. The simple monetary theory of nominal income
emphasizes the relation between the flow of income at each point in
time and the past history of the quantity of money.
The simple quantity theory and the simple income-expenditure theory
have six common elements, in addition to sharing the same six-equation
model, that deserve emphasis because they indicate what are the main
unresolved problems.
1. Both analyze short-run adjustments in terms of shifts from one
static equilibrium position to another.
2. Both implicitly regard each equilibrium position as characterized
by a stable level of prices or output. Neither explicitly introduces
changing prices or changing output into the formal theoretical analysis.

A Theoretical Framework for Monetary Analysis

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