Chapter 13
THE GENERAL THEORY OF THE RATE OF INTEREST
I
We have shown in chapter 11 that, whilst there are forces
causing the rate of investment to rise or fall so as to keep the
marginal efficiency of capital equal to the rate of interest, yet
the marginal efficiency of capital is, in itself; a different
thing from the ruling rate of interest. The schedule of the
marginal efficiency of capital may be said to govern the terms on
which loanable funds are demanded for the purpose of new
investment; whilst the rate of interest governs the terms on
which funds are being currently supplied. To complete our theory,
therefore, we need to know what determines the rate of interest.
In chapter 14 and its Appendix we shall consider the answers
to this question which have been given hitherto. Broadly
speaking, we shall find that they make the rate of interest to
depend on the interaction of the schedule of the marginal
efficiency of capital with the psychological propensity to save.
But the notion that the rate of interest is the balancing factor
which brings the demand for saving in the shape of new investment
forthcoming at a iven rate of interest into equality with the
supply of saving which results at that rate of interest from the
community's psychological propensity to save, breaks down as soon
as we perceive that it is impossible to deduce the rate of
interest merely from a knowledge of these two factors. What, then, is our own answer to this question?
II
The psychological time-preferences of an individual require
two distinct sets of decisions to carry them out completely. The
first is concerned with that aspect of time-preference which I
have called the propensity to consume, which, operating
under the influence of the various motives set forth in Book III,
determines for each individual how much of his income he will
consume and how much he will reserve in some form of
command over future consumption.
But this decision having been made, there is a further
decision which awaits him, namely, in what form he will
hold the command over future consumption which he has reserved,
whether out of his current income or from previous savings. Does
he want to hold it in the form of immediate, liquid command (i.e.
in money or its equivalent)? Or is he prepared to part with
immediate command for a specified or indefinite period, leaving
it to future market conditions to determine on what terms he can,
if necessary, convert deferred command over specific goods into
immediate command over goods in general? In other words, what is
the degree of his liquidity-preference¾where
an individual's liquidity-preference is given by a schedule of
the amounts of his resources, valued in terms of money or of
wage-units, which he will wish to retain in the form of money in
different sets of circumstances?
We shall find that the mistake in the accepted theories of the
rate of interest lies in their attempting to derive the rate of
interest from the first of these two constituents of
psychological time-preference to the neglect of the second; and
it is this neglect which we must endeavour to repair.
It should be obvious that the rate of interest cannot be a return to saving or waiting as such. For if a man hoards
his savings in cash, he earns no interest, though he saves just
as much as before. On the contrary, the mere definition of the
rate of interest tells us in so many words that the rate of
interest is the reward for parting with liquidity for a specified
period. For the rate of interest is, in itself; nothing more than
the inverse proportion between a sum of money and what can be
obtained for parting with control over the money in exchange for
a debt
for a stated period of time.
Thus the rate of interest at any time, being the reward for
parting with liquidity, is a measure of the unwillingness of
those who possess money to part with their liquid control over
it. The rate of interest is not the 'price' which brings into
equilibrium the demand for resources to invest with the readiness
to abstain from present consumption. It is the 'price' which
equilibrates the desire to hold wealth in the form of cash with
the available quantity of cash;¾which
implies that if the rate of interest were lower, i.e. if the
reward for parting with cash were diminished, the aggregate
amount of cash which the public would wish to hold would exceed
the available supply, and that if the rate of interest were
raised, there would be a surplus of cash which no one would be
willing to hold. If this explanation is correct, the quantity of
money is the other factor, which, in conjunction with liquidity-preference,
determines the actual rate of interest in given circumstances.
Liquidity-preference is a potentiality or functional tendency,
which fixes the quantity of money which the public will hold when
the rate of interest is given; so that if r is the rate of
interest, M the quantity of money and L the
function of liquidity-preference, we have M = L(r).
This is where, and how, the quantity of money enters into the
economic scheme.
At this point, however, let us turn back and consider why such
a thing as liquidity-preference exists. In this connection we can
usefully employ the ancient distinction between the use of money
for the transaction of current business and its use as a store of
wealth. As regards the first of these two uses, it is obvious
that up to a point it is worth while to sacrifice a certain
amount of interest for the convenience of liquidity. But, given
that the rate of interest is never negative, why should anyone
prefer to hold his wealth in a form which yields little or no
interest to holding it in a form which yields interest (assuming,
of course, at this stage, that the risk of default is the same in
respect of a bank balance as of a bond)? A full explanation is
complex and must wait for chapter 15. There is, however, a
necessary condition failing which the existence of a
liquidity-preference for money as a means of holding wealth could
not exist.
This necessary condition is the existence of uncertainty as
to the future of the rate of interest, i.e. as to the complex of
rates of interest for varying maturities which will rule at
future dates. For if the rates of interest ruling at all future
times could be foreseen with certainty, all future rates of
interest could be inferred from the present rates of
interest for debts of different maturities, which would be
adjusted to the knowledge of the future rates. For example, if 1dr
is the value ln the present year 1 of £1 deferred r years
and it is known that ndr will
be the value in the year n of £1 deferred r years
from that date, we have
1dn + r
ndr = ¾¾¾¾ ;
1dn
whence it follows that the rate at which any debt can be
turned into cash n years hence is given by two out of the
complex of current rates of interest. If the current rate of
interest is positive for debts of every maturity, it must always
be more advantageous to purchase a debt than to hold cash as a
store of wealth.
If, on the contrary, the future rate of interest is uncertain
we cannot safely infer that ndr
will prove to be equal to 1dn + r / 1dn when
the time comes. Thus if a need for liquid cash may conceivably
arise before the expiry of n years, there is a risk of a
loss being incurred in purchasing a long-term debt and
subsequently turning it into cash, as compared with holding cash.
The actuarial profit or mathematical expectation of gain
calculated in accordance with the existing probabilities¾if it can be so calculated, which is
doubtful¾must be sufficient to
compensate for the risk of disappointment.
There is, moreover, a further ground for liquidity-preference
which results from the existence of uncertainty as to the future
of the rate of interest, provided that there is an organlsed
market for dealing in debts. For different people will estimate
the prospects differently and anyone who differs from the
predominant opinion as expressed in market quotations may have a
good reason for keeping liquid resources in order to profit, if
he is right, from its turning out in due course that the 1dr's
were in a mistaken relationship to one another.
This is closely analogous to what we have already discussed at some length in connection with the marginal
efficiency of capital. Just as we found that the marginal
efficiency of capital is fixed, not by the 'best' opinion, but by
the market valuation as determined by mass psychology, so also
expectations as to the future of the rate of interest as fixed by
mass psychology have their reactions on liquidity-preference;¾but with this addition that the
individual, who believes that future rates of interest will be
above the rates assumed by the market, has a reason for keeping
actual liquid cash, whilst the individual who differs from the market in the other
direction will have a motive for borrowing money for short
periods in order to purchase debts of longer term. The market
price will be fixed at the point at which the sales of the
'bears' and the purchases of the 'bulls' are balanced.
The three divisions of liquidity-preference which we have
distinguished above may be defined as depending on (i) the
transactions-motive, i.e. the need of cash for the current
transaction of personal and business exchanges; (ii) the
precautionary-motive, i.e. the desire for security as to the
future cash equivalent of a certain proportion of total
resources; and (iii) the speculative-motive, i.e. the object of
securing profit from knowing better than the market what the
future will bring forth. As when we were discussing the marginal
efficiency of capital, the question of the desirability of having
a highly organised market for dealing with debts presents us with
a dilemma. For, in the absence of an organised market,
liquidity-preference due to the precautionary-motive would be
greatly increased; whereas the existence of an organised market
gives an opportunity for wide fluctuations in liquidity-preference due
to the speculative-motive.
It may illustrate the argument to point out that, if the
liquidity-preferences due to the transactions-motive and the
precautionary-motive are assumed to absorb a quantity of cash
which is not very sensitive to changes in the rate of interest as
such and apart from its reactions on the level of income, so that
the total quantity of money, less this quantity, is available for
satisfying liquidity-preferences due to the speculative-motive,
the rate of interest and the price of bonds have to be fixed at
the level at which the desire on the part of certain individuals
to hold cash (because at that level they feel 'bearish' of the
future of bonds) is exactly equal to the amount of cash available
for the speculative-motive. Thus each increase in the quantity of
money must raise the price of bonds sufficiently to exceed the
expectations of some 'bull' and so influence him to sell his bond
for cash and join the 'bear' brigade. If, however, there is a
negligible demand for cash from the speculative-motive except for
a short transitional interval, an increase in the quantity of
money will have to lower the rate of interest almost forthwith,
in whatever degree is necessary to raise employment and the
wage-unit sufficiently to cause the additional cash to be
absorbed by the transactions-motive and the precautionary-motive.
As a rule, we can suppose that the schedule of
liquidity-preference relating the quantity of money to the rate
of interest is given by a smooth curve which shows the rate of
interest falling as the quantity of money is increased. For there
are several different causes all leading towards this result.
In the first place, as the rate of interest falls, it is
likely, cet. par., that more money will be absorbed by
liquidity-preferences due to the transactions-motive. For if the
fall in the rate of interest increases the national income, the
amount of money which it is convenient to keep for transactions will be increased more or less
proportionately to the increase in income; whilst, at the same
time, the cost of the convenience of plenty of ready cash in
terms of loss of interest will be diminished. Unless we measure
liquidity-preference in terms of wage-units rather than of money
(which is convenient in some contexts), similar results follow if
the increased employment ensuing on a fall in the rate of
interest leads to an increase of wages, i.e. to an increase in
the money value of the wage-unit. In the second place, every fall
in the rate of interest may, as we have just seen, increase the
quantity of cash which certain individuals will wish to hold
because their views as to the future of the rate of interest
differ from the market views.
Nevertheless, circumstances can develop in which even a large
increase in the quantity of money may exert a comparatively small
influence on the rate of interest. For a large increase in the
quantity of money may cause so much uncertainty about the future
that liquidity-preferences due to the precautionary-motive may be
strengthened; whilst opinion about the future of the rate of
interest may be so unanimous that a small change in present rates
may cause a mass movement into cash. It is interesting that the
stability of the system and its sensitiveness to changes in the
quantity of money should be so dependent on the existence of a variety
of opinion about what is uncertain. Best of all that we
should know the future. But if not, then, if we are to control
the activity of the economic system by changing the quantity of
money, it is important that opinions should differ Thus this
method of control is more precarious in the United States, where
everyone tends to hold the same opinion at the same time, than in
England where differences of opinion are more usual.
III
We have now introduced money into our causal nexus for the
first time, and we are able to catch a first glimpse of the way
in which changes in the quantity of money work their way into the
economic system. If, however, we are tempted to assert that money
is the drink which stimulates the system to activity, we must
remind ourselves that there may be several slips between the cup
and the lip. For whilst an increase in the quantity of money may
be expected, cet. par., to reduce the rate of interest,
this will not happen if the liquidity-preferences of the public
are increasing more than the quantity of money; and whilst a
decline in the rate of interest may be expected, cet. par.,
to increase the volume of investment, this will not happen if the
schedule of the marginal efficiency of capital is falling more
rapidly than the rate of intere~t; and whilst an increase in the
volume of investment may be expected, cet. par., to
increase employment, this may not happen if the propensity to
consume is falling off. Finally, if employment increases, prices
will rise in a degree partly governed by the shapes of the
physical supply functions, and partly by the liability of the
wage-unit to rise in terms of money. And when output has
increased and prices have risen, the effect of this on
liquidity-preference will be to increase the quantity of money
necessary to maintain a given rate of interest.
IV
Whilst liquidity-preference due to the speculative-motive
corresponds to what in my Treatise on Money I called 'the
state of bearishness', it is by no means the same thing. For
'bearishness' is there defined as the functional relationship,
not between the rate of interest (or price of debts) and the
quantity of money, but between the price of assets and debts,
taken together, and the quantity of money. This treatment, however, involved a
confusion between results due to a change in the rate of interest
and those due to a change in the schedule of the marginal
efficiency of capital, which I hope I have here avoided.
V
The concept of hoarding may be regarded as a first
approximation to the concept of liquidity-preference.
Indeed if we were to substitute 'propensity to hoard' for
'hoarding', it would come to substantially the same thing. But if
we mean by 'hoarding' an actual increase in cash-holding, it is
an incomplete idea¾and seriously
misleading if it causes us to think of 'hoarding' and
'not-hoarding' as simple alternatives. For the decision to hoard
is not taken absolutely or without regard to the advantages
offered for parting with liquidity;¾it
results from a balancing of advantages, and we have, therefore,
to know what lies in the other scale. Moreover it is impossible
for the actual amount of hoarding to change as a result of
decisions on the part of the public, so long as we mean by
'hoarding' the actual holding of cash. For the amount of hoarding
must be equal to the quantity of money (or¾on
some definitions¾to the quantity of
money minus what is required to satisfy the
transactions-motive); and the quantity of money is not determined
by the public. All that the propensity of the public towards
hoarding can achieve is to determine the rate of interest at
which the aggregate desire to hoard becomes equal to the
available cash. The habit of overlooking the relation of the rate
of interest to hoarding may be a part of the explanation why
interest has been usually regarded as the reward of not-spending,
whereas in fact it is the reward of not-hoarding.