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and the Marginal Propensity to Consume
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Grand theoretical safaris are usually organized around the
hunt for some quiddity with which to epitomize an entire field of
study. The last time this happened in economics, John Maynard
Keynes bagged a certain Marginal Propensity to Consume. SFEcon's entrant in this game is
a reconsideration on L,
the financial analyst's familiar notion of a price for one value
unit purchased now, but for delivery in one year.
Keynesians have made elaborate treatments of the income/ consumption
problem in order to establish bone fides for the marginal
propensity; and these have, in passing, disparaged attempts to
epitomize income/consumption relations in simple structures such as
the delay mechanisms controlling things financial in the SFEcon
system. This page is a counterargument on the premise that a
delay calibrated by L
is the proper structure for understanding income/consumption
relations, with an implicit corollary that delay mechanisms are
likely to be as effective in controlling economic dynamics as they
are in controlling dynamic systems generally.
The Marginal
Propensity to Consume
The functional relation between income and consumption was defined in
rather non-negotiable terms by our late Baron of Tilton in 1936:
"Granted, then, that the
propensity to consume is a fairly stable function so that, as a rule,
the amount of aggregate consumption mainly depends on the amount of
aggregate income (both measured in terms of wage-units), changes in the
propensity being treated as a secondary influence, what is the normal
shape this function?
The fundamental psychological law, upon which
we are entitled to depend with great confidence both a priori
from knowledge of human nature and from the detailed facts experience,
is that men are disposed, as a rule and on the average, to increase their
consumption as their income increases, but not as much as the increase
in their income. That is to say if Cw is the amount of consumption and
Yw is income (both measured in wage-units) Cw has the same sign as
Yw,
but is smaller in amount, i.e. Cw/Yw, is positive and less than
unity."
[The emphasis and interjections are Keynes']
Unfortunately Lord Keynes never revealed how this "fundamental law" came
to be impressed upon his thinking; and his followers have been left to
wonder just what "facts" and what inferences he placed at the center of
his theory.
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The Defense
Gardner
Ackley, in his standard text, accomplishes the most sympathetic
treatment that the constant marginal propensity to consume MPC is ever
likely to receive. His announced purpose is to make a clear
statement of as much basic theory as can be generally agreed to.
He requires three chapters and 99 pages to make a
graduate level exposition of the decision to consume in the presence of
an income stream.
The initial chapter on
consumption theory establishes that 50 or so years of income versus consumption data
will plot out to a fairly
solid line with a slope just less than unity. It is, however,
". . .
when we push somewhat deeper below the surface that problems of
interpretation continue to raise their ugly heads."
"
In many if not most of the
contexts in which we wish to apply the consumption function to
questions of economic policy, it is the short run behavior of
consumption in which we are interested."
By the end of his third
chapter on the Keynesian Consumption Theory, Professor Ackley's
exposition of the marginal propensity to consume has degenerated through
qualification, to compromise, and finally to apology. His
conclusion is as follows:
"In this chapter we have
demonstrated that the very short-run fluctuations of consumer spending
cannot be explained by income changes. On a quarter-to-quarter
basis, consumption change as likely to cause income change as to be
the passive result of change in income."
This conclusion is from
twenty-two computations of the marginal propensity to consume, based on
the consumption and income data from 1948 to 1956. In another
reference to these same data Professor Ackley observes that in
"
.
. . only seven cases is the 'marginal propensity to consume', as here measured, both
positive and less than one. To be sure, the irregularities tend
to disappear if we take the movement of six-month or nine-month
periods, but not in all cases."
Here Professor Ackley is more generous than we can be on the basis of
the empirical compilation below.
This pedestrian analysis
of the marginal propensity to consume MPC is
based on yearly series; and it seems the MPC is at best indifferent as to staying within the range anticipated by
Keynes. Keynes'
rule is established insofar as these data are serially unbiased,
i.e.: the series is symmetric about the expected value for MPC;
and deviations from the norm occur randomly in the dimension of
time. But we should also note the data to be rather widely
dispersed outside the range (shaded) anticipated by Keynes . In
this respect, Keynes' "secondary influences" would
seem to contain as much of consumers' behavior as what he identifies as
the primary tendency.
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The Delay Model of
Income and Consumption
In his 1985 Newtonian Economics, Kurt Roemer (Obiwan Knobe of the SFEcon saga) revisited the Income/Consumption
conundrum for the sake of exhibiting
the virtues of dynamic
systems analysis. Professor Ackley's performance
was appropriated for this purpose because it is shot through with one
rejection after another of a simple model wherein consumption is a delay on income.
Credit is given to Professors James Duesenberry and D. H. Robertson for
attempting to explain the "erratic" short-run behavior of the
consumption function through various formulations of mathematical delay,
but the conclusion is that
". . . no simple lag
function appears to improve the explanation of short run consumer
behavior."
Professor Ackley also
credits Professor Pigou, Professor Dan Patinkin, and others for introducing
the wealth variable as a partial explanation for intransigent nature of
consumer's behavior. The last words, however, given to Professors
Thomas Meyer and Alvin Hansen:
"
. . . the Pigou effect is
in practice of little empirical significance."
If consumption were a simple lag on
income, its behavior could be modeled by the presentation below.
Pigou's wealth variable W is represented by the level
of a fluid reservoir. Income Y is the rate at which the reservoir
is filled. The fill rate would be controlled by analogy to a real historical series
of income data, i.e.: so many gallons per minute representing some
number of dollars per year. A simple delay
on the income series Y is effected when the reservoir's effluent rate C
is regulated in proportion to the wealth level W:
The proportion between C and
W would correspond to the L
by which an economic system might, in the most general sense, propel its
stocks of
value.
Empirical investigation of the
delay model requires application of numerical
methods techniques to integrate the wealth
variable W's response as it is driven by an actual income stream Y:
The investigation would compare the model's consumption stream C
with actual consumption.
Roemer performed this investigation
on the same 22 data points
that Ackley compiled for his highly equivocated defense of
Keynes. The result was presented in the income vs.
consumption plot below.
Correlations between actual and
model-predicted consumption are 0.891 for the 1948-51 period and 0.966
for 1953-56. (Ackley eliminated data for the Korean War period,
1951-53.)
As this result was both
statistically appealing and derived from a very simple idea, Roemer went
on to test the delay formulation on data from earlier and later
periods. His results for the 1961-70 period yielded a 0.982
correlation between actual and predicted consumption. Using a
somewhat different formulation to express his notions about depression
economics, Roemer was able establish a 0.931 correlation for
1929-38. In all these experiments L
was kept constant at 0.95.
Thus was created the straw man for
Roemer to demolish in his argument for an economics that is more
attentive to right religion in the analysis of dynamic phenomena:
Creditable opinion discredits the delay model of income
vs. consumption, even though its empirical reliability approaches that of
its referent data.
Economics thereby deprives itself of a simple, familiar
formulation (two equations and one parameter) in favor of 99 pages, organized in three chapters, for the sake of a marginal
propensity consume that is 'constant' in the degree portrayed above.
How can this happen?
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How the Keynesians
Got It Wrong
Roemer's
experiments with the delay formulation worked because he (unlike Pigou,
Patinkin, Duesenberry,
Robertson et
al.?) paid proper attention to the interval by which the income and
consumption data were organized:
Roemer came to the experiment with a prejudice
that the proper setting of the delay parameter L
would be approximately 0.95 per year, a typical value now of a
monetary unit to be delivered in one year:
This
commonplace of financial analysis references -n,
the interest rate (n
is a negative quantity in the SFEcon system).
SFEcon posits further meaning in the unitary values of this
equation, which we identify with V0 = 1.0/year, the velocity of
value itself. Imagine multiplying both the numerator and
denominator of the L
ratio by the value of all assets whose flow must command a
return: this reveals L
to be a ratio of 'asset values consumed' to the 'value of what those
assets produce'; or, a ratio of an economy's 'cost of sales' to
'cost of sales plus profit'.
This dimensionless ratio
is the most general indicator of an economy's 'turnover of value'
within the yearly period of financial analysis for which V0 and n
are defined. It was Roemer's guess for the most likely delay
parameter with which to validate Pigou's model of income and
consumption. The failure of reasonable correlations in such
models, as reported by
the Keynesians would, if correct, falsify the essential premises of
SFEcon.
Having concluded as to a working estimate of L
= 0.95/year, Roemer therefore knew that simulating a delay on
income Y would only be worthwhile if the discrete elements of the Y series
were refreshed at a rate of 10 per year or greater (1/10 or less of 1/L,
according to a dynamicist's rule of thumb). Since the Y series
was only reported at
quarterly or yearly intervals, the raw data had to be disaggregated into a
monthly series for the sake of keeping the experimental machinery from
resonating with the data.
Anyone adequately trained in simulation techniques would have taken this
precaution. It is analogous to choosing the film speed of a moving
picture camera. If the period of the camera's shutter opening and
closing approaches that of any natural frequency in the action being filmed,
then the resulting portrayal of motion will have nothing to do with what was
before the camera. This phenomena is visible in moving pictures of
turning wagon wheels or accelerating propellers. And it would account
for the dismal reports as to the delay-on-income model's
validity: the Keynesians might well be emphasizing
artificially induced experimental noise over Pigou's perfectly valid
theoretical insight.
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What the Marginal
Propensity Really Conveys
Having posited considerable importance with the inherent frequencies of data
series, Roemer then proceeded to a novel conclusion for this long out-worn
discussion. He began by fitting a simple logarithmic function to
the long series of income Y and consumption C data used above
in examining the MPC's constancy. This result is portrayed
below:
.
When these series originate at
the bottom of the last depression (where income and consumption are
ostensibly equal) the
regression equations are calibrated as follows:
The most suggestive
observation yielded from these regression parameters would be that both series are governed by the same growth factor, 0.024 per
year. This result is strongly indicative of C being a delay on
Y: whenever a delay is driven by an exponentially growing function,
its outflow will assume an exponential form governed by the same
time-constant as the driving function.
To the extent
that all the realities of income and consumption might be contained in these
two regression equations, the marginal propensity to consume can be computed
as a constant with a value just less than unity:
.
This conclusion references no "fundamental psychological law" nor any (yet to be elaborated)
"detailed facts experience". An
MPC with a constant value of 0.92 only presumes that
an economic order:
1. Somehow achieves
real, exponential growth in income Y; and
2. That consumption C is a delay on Y, where the parameter
governing the delay computes to the typical value of L.
The conclusion is reinforced by
comparing the error series of the regression analysis with series reported
above
for the MPC: where the
data tend to get away from the regression model, the MPC gets away from its attributed value.
To the extent that such observations persuade,
the Keynesian premise, which has ruled so much economic thinking and
political action, should collapse. If economic
growth, i.e. the exponential rate of income Y's increase, is to be merely
subsumed in economic theory, then what can ever be wrong and in need of theoretical
guidance for correction?
Viewed in this way, Keynes' theory is
far from the "depression ridden doctrine" described by Schumpeter.
Where the MPC is constant at its ordained value, income and
consumption are growing exponentially at their long-term average
rate. Thus Keynesian theory is a direct presumption of economic
well-being; one that presumably functions
to inform those still-mysterious deities of economic causation as to our
longing for improved economic conditions - an instrument of homeopathic magic.
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