keynes's theory of monetary policy: an essay in historical reconstruction

KEYNES’S THEORY OF MONETARYPOLICY: AN ESSAY IN HISTORICAL

RECONSTRUCTION

EDWIN DICKENS

Saint Peter’s College

Keynes’s theory of monetary policy is composed of three concepts—namely, the

investment multiplier, the marginal efficiency of capital and the interest rate. By ana-

lyzing how these three concepts interact in the short period, Keynes explains why he

is opposed to countercyclical monetary policies. And by analyzing how they interact

in the long period, he explains why the economy tends to fluctuate around a long-

period equilibrium position that is characterized by unemployment. Keynes con-

cludes that the sole objective of the monetary authority should be to use its influence

over the interest rate to dislodge the economy from its long-period equilibrium pos-

ition that is characterized by unemployment and propel it toward a long-period equi-

librium position that is characterized by full employment.

JEL Classification: E12; E43; E52; B31; B22

I. INTRODUCTION

Perhaps a complex offer by the central bank to buy and sell at stated prices gilt-edged bondsof all maturities, in place of the single bank rate for short-term bills, is the most importantpractical improvement which can be made in the technique of monetary management(Keynes, 1936, p.206).

The purpose of this paper is to reconstruct Keynes’s theory of monetary policy, as

stated in The General Theory of Employment, Interest and Money (1936). To accom-

plish this purpose, I build upon the work of Eatwell & Milgate (1983a,b; also see

Eatwell, 1983 and Milgate, 1982). In particular, I use the classical long-period

method to model the relationships between the investment multiplier, the marginal

efficiency of capital and the interest rate—which constitute Keynes’s theory—and

I do so in such a way that the short-period fluctuations of the economy are around a

long-period equilibrium position characterized by unemployment. I conclude that

buying and selling ‘at stated prices gilt-edged bonds of all maturities . . . is the most

important practical improvement which can be made in the technique of monetary

management’, as noted above, because it would help propel the economy from a

Contributions to Political Economy (2011) 30, 1–11

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long-period equilibrium position characterized by unemployment closer to one

characterized by full-employment.1

The paper is organized as follows. In Section II, I use Keynes’s concepts of

the investment multiplier and the marginal efficiency of capital to specify the

long-period equilibrium position of the economy which is characterized by

unemployment.

In Section III, in order to explain why the economy fluctuates around a long-

period equilibrium position characterized by unemployment, I specify the difference,

as well as the relationship, between Keynes’s concepts of probability and risk and

the orthodox ones.

In Section IV, I use Keynes’s concept of the interest rate to explain the effects of

monetary policy, both in the short-period and in the long-period.

Lastly, in Section V, I provide a summary and conclusion.

II. THE INVESTMENT MULTIPLIER, THE MARGINAL EFFICIENCY

OF CAPITAL AND UNEMPLOYMENT

Let Ns be the supply of labor and Nd the demand for labor, or the actual volume of

employment (n). We can then define full-employment (no) as Nd/Ns ¼ 1; unemploy-

ment (nk) as Nd/Ns , 1; and the unemployment rate as 1 2 nk.

For Keynes (1936, pp. 25–29ff.), n is determined by the aggregate level of output

(Y) and the productivity of labor (P). That is to say, by definition P ¼ Y/Nd.

Re-arranging terms, Nd ¼ Y/P. Substituting into our definition of n, we thus get

n ¼ Y/P Ns.

For Keynes (1936, p.96ff.), Y is determined, via the investment multiplier

(defined as the reciprocal of the marginal propensity to save (s)), by the aggregate

rate of investment (I). Consequently, we can derive the determinants of the unem-

ployment rate (1 2 nk) by building upon the following counter-posing of the effects

of an aggregate rate of investment that is insufficient to generate full-employment

(Ik) with the effects of an aggregate rate of investment that is sufficient to generate

1 Ricardo (1817) first developed the classical long-period method without the concept of a long-periodequilibrium position of the economy characterized by unemployment, much less a role for monetarypolicy in determining it. In the following passage, Keynes makes clear his intention to rectify, but notabandon, Ricardo’s legacy:

Ricardo and his successors overlook the fact that even in the long period the volume of employmentis not necessarily full but is capable of varying, and that to every banking [monetary] policy therecorresponds a different long-period level of employment, so that there are a number of positions oflong-period equilibrium corresponding to different conceivable interest policies on the part of themonetary authority (Keynes, 1936, p.191).

My purpose in this paper is to concretize this passage. See D’Orlando (2007) for a recent appraisal of theclassical long-period method.

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full-employment (Io) (see Shaikh, 2004 for a similar formalization):

Yk ¼Ik

s; Yo ¼

Io

sð1Þ

or

nk ¼Ik

s P N s; no ¼

Io

s P N sð2Þ

where, ceteris paribus, 1 2 nk is determined by Ik , Io.

For Keynes (1936, pp. 135–137), I is determined by the net present value of pro-

spective investment projects (NPV):2

NPV ¼ �Sp þE1

1þ rs

þ E2

ð1þ rsÞ2þ � � � þ Et

ð1þ rsÞtð3Þ

where Sp is the supply price of prospective investment projects; E is the profit

expected from operating them for t periods; and rs is the ‘safe’ interest rate (see

Section IV for an explanation of it). If NPV . 0, I increases. If NPV , 0, I

decreases. If NPV ¼ 0, I is in equilibrium.

Assume that t ¼ 1 and Sp and rs are given. Then the expected profit (Eo) in equili-

brium that induces investors to undertake the full-employment aggregate rate of

investment (Io) and the expected profit (Ek) in equilibrium that induces them to

undertake the less-than-full-employment aggregate rate of investment (Ik) can be

distinguished as follows:

NPV ¼ �Sp þEk

1þ rs

¼ 0; NPV ¼ �Sp þEo

1þ rs

¼ 0 ð4Þ

Equations (1–4) apply to both the long-period and the short-period, depending

upon whether Ek and Eo denote long-term expectations or short-term expectations.

Ceteris paribus, long-term expectations determine the volume of investment

projects undertaken and short-term expectations determine the pace of their

implementation.

III. PROBABILITY, RISK, AND LONG-TERM EXPECTATIONS

Let A be the payoff required to induce entrepreneurs to undertake the full-

employment rate of investment (Io). Then, following Dickens (2008, pp. 225–226

and 229), the difference between the long-term Eo and the long-term Ek can be

2 Keynes applies equation (3) to capital assets rather than investment projects, and thereby obtains hisconcept of the marginal efficiency of capital. As Garegnani (1983) demonstrates, this application isincorrect because it implies that capital is a factor of production that yields a marginal product whenplugged into a (aggregate) production function. However, as Pasinetti (1974, pp. 37–38) demonstrates,equation (3) still applies to investment projects. To make clear that I am using equation (3) in the validsense of applying to investment projects, I drop the concept of the marginal efficiency of capital in favor ofthe concept of net present value.

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analyzed in terms of the following formulation of the difference between Keynes’s

concepts of probability and risk and the orthodox ones:

Ek ¼ pkA; Eo ¼ poA ð5Þpo ¼

m

zð6Þ

pk ¼2w

ð1þ qÞð1þ wÞ

� �po ð7Þ

where m is the number of occurrences of an outcome; z is the number of possible

occasions for the outcome to occur; w is the weight of arguments; and q ¼ 1 2 po.

Equation (6) is derived from the law of large numbers and incorrectly assumes

that the underlying causal structure that determines the outcome of investment pro-

jects is known in the same way that the underlying causal structure that determines

the outcomes of coin tosses or turns of the roulette wheel is known. In fact, the

underlying causal structure that determines the outcome of investment projects is

either knowable but unknown or, as Keynes (1937a,b,c) argues, unknowable.

Following Markowitz (1959, p. 39ff.), orthodox economists take this fact into

account by interpreting equation (6) in terms of the principle of non-sufficient

reason.

According to the principle of non-sufficient reason, if investors do not have a

reason to assign different probabilities to a set of possible outcomes, they must

assign them equal probabilities. Therefore, if qualms about factors that are knowable

but unknown or unknowable undermine the confidence of investors in their calcu-

lations of the outcome of prospective investment projects, orthodox economists

instruct them to assign equal probabilities to the outcomes they fear may result from

these factors, with the sum of assigned probabilities being equal to one. Orthodox

economists thus interpret the expected profit (Eo) in equation (5) as the mathemat-

ical mean of the sum of the products of all possible outcomes of investment projects

and their probability. They then interpret the risk of investment projects as the varia-

bility (or standard deviation), of the sum of the products of all their possible out-

comes and their probability, around the mathematical mean.

The orthodox concept of risk is obviously incorrect, since it includes the possi-

bility that the actual profit of investment projects will exceed the expected profit.

Risk (R) only results from the possibility that the actual profit will fall short of the

expected profit, a fact that Keynes (1921, p. 348) formulates as follows:

R ¼ ð1� poÞEo

or

R ¼ qEo ð8ÞAs such, R represents the cost of insurance against catastrophic loss of the money

waged on investment projects. The cost of re-insurance to the insurer (R1) would

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then be qR ¼ q2Eo. If the re-insurance company buys re-insurance (R2), and

that re-insurance company gets re-insurance, and so on, then the risk of loss

is eliminated, but so is the expected profit (Eo). That is,

Eo þ R1 þ R2 þ � � � ¼ Eoð1 þ q þ q2 þ � � �Þ ¼ Eo=1 � q ¼ Eo=po ¼ A. In

short, Keynes formulates equation (8) in such a way that it is only by bearing some

risk of loss that potential investors can expect to profit.

Less obviously, for Keynes (1936, p. 152; 1921, p. 77–80), the orthodox concept

of expected profit (Eo) ‘leads to absurdities’3 because it ignores the weight of argu-

ments (w). Following Dickens (2008, p. 227–228), w can be explained as follows:4

pk ¼ wðajh � poÞ ð9Þ

where a is the proposition that A, as formulated in equation (5), will be the payoff

from undertaking the full-employment aggregate rate of investment (Io); h is the set

of propositions that constitute the premises of the argument for undertaking Io; po,

as formulated in equation (6), is the proposition that dominates h; and w measures

the extent of po’s dominance.

Equation (9) can be read as ‘proposition a on the hypothesis h . po has a prob-

ability pk’. Alternatively, it can be read as ‘the conclusion a can be inferred from the

evidence h . po with a probability of pk’.

If w(ajh . po) ¼ 1, then the hypothesis h . po implies the conclusion a with certainty.

If w (ajh . po) ¼ 0, then hypothesis h implies that the conclusion a is impossible.

If 0 , w(ajh . po) , 1, then there is a probability relation of degree pk between

a and h . po.

In short, Keynes’s concept of probability (pk), as formulated in equation (9),

encompasses the orthodox concept of probability (po), as formulated in equation

(6), and the relationship between the two is mediated by Keynes’s concept of the

weight of arguments (w).

For Keynes (1921, p. 77–80), w measures the vague but pervasive sense of inade-

quacy that investors feel when they compare what they know with what they think

they ought to know in order to make informed investment decisions. If w ¼ 1, then

the interpretation of equation 6 in terms of the principle of non-sufficient reason has

quelled investors’ sense of inadequacy, po is completely dominate and equation (9),

and pk ¼ po. If 0 , w , 1, then investors do not suppress the fact that setting w

equal to one leads to absurdities (see Dickens (2008, p. 224–225) for an expla-

nation of why), and the factors making the underlying causal structure determining

the outcome of investment projects knowable but unknown or unknowable take the

form of propositions in h which weigh against po’s dominance, so that pk , po.

3 Dickens (2008, pp. 224–225) draws upon the literature in behavioral finance to explain why theorthodox concept of expected profit (Eo) leads to absurdities.

4 The formulation of Keynes’s concept of probability (pk) in equation (9) differs from its formulationin equation (7) because, at this point in the argument, we are abstracting from the concept of risk, asformulated in equation (8). As shown below, equation (7) results from the combination of equations (8)and (9).


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Even if w ¼ 1, pk is still less than po once we add Keynes’s concept of risk, as for-

mulated in equation (8), to w as a mediating factor between pk and po, and thereby

obtain equation (7). Keynes (1921, p. 348) formulates equation (7) in such a way

that two conditions are met: If po ¼ 1 and w ¼ 1, then pk ¼ 1; and if po ¼ 0 and w ¼

0, then pk ¼ 0. It follows that, if 0 , w , 1 and/or 0 , po , 1 (so that q ¼ 1 2 po has

a value between zero and one), then pk , po. Of course, po ¼ m/z ¼ 1 only if there is

apodictic certainty about the underlying causal structure that determines the

outcome of investment projects, in the way that there is apodictic certainty about

the outcome of tossing a two-headed coin—hardly a relevant case to evaluating

prospective investment projects.

If pk , po, then we know from equations (5), (4), (1), and (2), respectively, that

Ek , Eo! Ik , Io! Yk , Yo! 1 2 nk . 0. In short, if Keynes’s concepts of prob-

ability and risk are correct, the long-period equilibrium position of the economy is

characterized by unemployment.

IV. MONETARY POLICY AND THE SAFE INTEREST RATE

The monetary authority directly controls the short-term interest rate.5 With ‘a

modest measure of persistence and consistency of purpose,’ Keynes (1936, p. 204)

asserts that the monetary authority can also influence the long-term interest rate.6

Orthodox economists (see, for example, Ingersoll, 1989, pp. 173–178) have

accepted Keynes’s assertion, taking it to mean that the long-term interest rate is the

mathematical mean of the sum of the products of all possible outcomes of the short-

term interest rate and their probability. For example, the yield on the 10-year bond

allegedly equals the mathematical mean of the expected yields on 3-month securities

for the next 10 years, plus an illiquidity premium which reflects the orthodox

concept of risk. Unfortunately, orthodox economists ignore the difference between

Keynes’s concepts of probability and risk and the orthodox ones, and reject the clas-

sical long-period method, which Keynes uses to distinguish between the long-period

equilibrium values of variables and their short-period values. To reconstruct

Keynes’s theory of monetary policy, these oversights must be rectified.

For Keynes (1936, pp. 144–145, 222–229 and 240), the long-term interest rate

is ‘a duplication of a proportion of entrepreneur’s risk,’ modified to take into

account the weight of arguments (w). Consequently, the long-period equilibrium

value of the long-term interest rate—what Keynes’s calls the safe long-term interest

rate (rs)—and its relationship to the actual long-term interest rate (ra), as determined

5 This proposition preempts the analysis of the determination of interest rates by the schedule ofliquidity preference and the supply of money.

6 ‘The short-term interest rate’ denotes an index of all market yields on high-quality securities of shortmaturity and ‘the long-term interest rate’ denotes an index of all market yields on high-quality bonds oflong maturity. Using such indexes is legitimate because all short-term market yields move in tandem, asdo all long-term market yields. However, the short-term interest rate and the long-term interest rate donot move in tandem. Sometimes the yield curve is positively sloped, sometimes inverted, and sometimesflat.

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in the bond market, can be represented as follows:7

rs ¼ g 1� 2w

ð1þ qÞð1þ wÞ

� �� ð10Þ

NPV ¼ �Sp þEk

1þ rs

¼ 0; NPV ¼ �Sp þEa

1þ ra

¼ 0 ð11Þ

where 0 , g , 1 (i.e. g measures the proportion of the entrepreneur’s risk that is

duplicated); the bracketed expression in equation (10) takes into account both entre-

preneur’s risk and w, as they are formulated in equation (7); and Ea is the actual

expected profit from investment projects, as determined in the stock market.8

Equation (11) reformulates equation (4) to specify the relationship between rs and

ra. In the same way, equations (1) and (2) can be reformulated as follows to specify

the relationship between the long-period equilibrium aggregate rate of investment

(Ik) and the actual aggregate rate of investment (Ia), and thus the relationships

between the long-period equilibrium aggregate level of output (Yk) and the actual

aggregate level of output (Ya), and between long-period equilibrium employment

(nk) and actual employment (na), respectively are as follows:

Yk ¼Ik

s; Ya ¼

Ia

sð12Þ

nk ¼Ik

s P N s; na ¼

Ia

s P N sð13Þ

7 Keynes (1936, p. 235) argues that, ‘in the absence of money . . . the rates of interest would only reachequilibrium when there is full employment.’ Following Harrod (1947) and Chick (1983), this passage,and others like it, is interpreted to mean that it is only an inflexibly high interest rate, when combinedwith the schedule of the marginal efficiency of capital, which causes long-period unemployment. Mythesis is that this would only be the case if the expected profit (Eo) is formulated in terms of equation (6)and the long-term interest rate in the way proposed by orthodox economists—and this case is precludedby the formulation of the expected profit (Ek) in terms of equation (7) and the long-term (safe) interestrate in terms of equation (10). The following passage substantiates my thesis:

The owners of wealth will then weigh the lack of ‘liquidity’ of different capital equipments . . . as amedium in which to hold wealth against the best available estimate of their prospective yields afterallowing for risk [Eo]. The liquidity-premium, it will be observed, is partly similar to the risk-premium[understood as the variability (or standard deviation), of the sum of the products of all possible out-comes and their probability, around the mathematical mean] but partly different;–the difference cor-responding to the difference between the best estimates we can make of probabilities and theconfidence with which we make them.* When we are dealing, in earlier chapters, with the estimationof prospective yield, we did not enter into detail as to how the estimation is made: and to avoid com-plicating the argument, we did not distinguish differences in liquidity from differences in risk proper.It is evident, however, that in calculating the own-rate of interest we must allow for both (Keynes1936, p.240).

*’Cf.the footnote to p. 148 above’ (i.e., ‘By ‘very uncertain’ I do not mean the same thing as ‘very improb-

able.’ Cf. my Treatise on Probability, chap. 6, on ‘The Weight of Arguments’.’)8 Tobin’s q proposes that the expected profit from investment projects, as determined in the stock

market (Ea), influences long-term expectations (Ek), and thus the aggregate rate of investment undertakenin long-period equilibrium (Ik). In contrast, as formulated in equation (11), Ea influences short-termexpectations, and thus the pace at which Ik is implemented in the short-period.


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In equation (11), rs is the center of gravitation of the short-period fluctuations of ra;

in the same way that, in equations (12) and (13), Ik, Yk, and nk are the centers of

gravitation of the short-period fluctuations of Ia, Ya, and na, respectively.

For Keynes (1936, pp. 202, 206 and 313–320), the short-period fluctuations of raaround rs are strictly limited to ‘the difference between the[ir] squares’.9 In contrast,

since the stock market determines the actual expected profit (Ea) in the short-

period, the short-period fluctuations of Ia and Ya around Ik and Yk are unlimited.10

Therefore, efforts by the monetary authority to stabilize the short-period fluctu-

ations of the economy are futile for two reasons. First, any drastic changes that the

monetary authority makes in the short-term interest rate simply cause a more

steeply sloped yield curve as ra reaches the limits of its variability around rs. Second,

such drastic changes in the short-term interest rate threaten to shatter the confi-

dence of investors in their calculations of Ea. If drastic enough, such changes may

thus cause a severe recession as investors contemplate trillions of dollars of losses on

their bets in the stock market.

More importantly, Keynes (1936, pp. 119, 206, 301–304 and 321–322) argues

that the monetary authority, rather than attempting to stabilize the short-period fluc-

tuations of the economy around a long-period equilibrium position characterized by

unemployment, should attempt to reduce the amount of unemployment that charac-

terizes the long-period equilibrium position, which can be done by making a cred-

ible commitment ‘to buy and sell at stated prices gilt-edged bonds of all maturities’.

To see why, equations (9), (5), and (10) can be reformulated as follows:

pk1 ¼ w1ða1jh1 � poÞ . pk2 ¼ w2ða2jh2 � poÞ ð14ÞEk1 ¼ pk1A . Ek2 ¼ pk2A ð15Þ

rs1 ¼ g 1� 2w1

ð1þ qÞð1þ w1Þ

� �), rs2 ¼ g 1� 2w2

ð1þ qÞð1þ w2Þ

� �)((ð16Þ

where, in equation (14), h1 includes the proposition that ‘the monetary authority

has made a credible commitment to buy and sell at stated prices gilt-edged bonds of

all maturities’ and h2 includes instead the proposition that ‘the monetary policy is

committed to changing the short-term interest rate in an effort to stabilize short-

period fluctuations of the economy’.

If the monetary authority has the discretion to change the short-term interest rate,

investors must take into account the possibility that future investment projects, with

lower financing costs, will compete against investment projects undertaken today at

9 For example, if the safe long-term interest rate (rs) is 4%, then the actual long-term interest rate (ra) islimited to a range of 0.04 2 (0.04)2 ¼ 3.84% to 0.04 þ (0.04)2 ¼ 4.16%. If rs is 2%, then ra is limited to arange of 0.02 2 (0.02)2 ¼ 1.96% to 0.02 þ (0.02)2 ¼ 2.04%.

10 The short-period fluctuations of na around nk have an upper bound, given by the supply of labor.However, this does not limit the short-period fluctuations of Ia and Ya around Ik and Yk; it simply definesthe point at which those fluctuations cause what Keynes (1936, pp.119 and 303) calls ‘true inflation’. Inother words, for Keynes, inflation is a short-period phenomenon.

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higher financing costs. As a result, h2 weighs more heavily than does h1 against the

dominate proposition for undertaking investments projects (po). That is to say, w1 .

w2. It follows from equation (15) that pk1 . pk2! Ek1 . Ek2; and from equation

(16) that rs1 , rs2.

We are now in a position to complete Keynes’s theory of monetary policy by

building as follows upon equations (11), (1), and (2):

NPV1 ¼ �Sp þEk1

1þ rs1

¼ 0 . NPV2 ¼ �Sp þEk2

1þ rs2

¼ 0 ð17Þ

Yk1 ¼Ik1

s. Yk2 ¼

Ik2

sð18Þ

nk1 ¼Ik1

s P N s. nk2 ¼

Ik2

s P N sð19Þ

In equation (17), NPV1 . NPV2 because Ek1 . Ek2 and rs1 , rs2. Therefore, in

equations (18) and (19), respectively, Yk1 . Yk2 and nk1 . nk2. In short, the change

from a discretionary monetary policy to one committed to buying and selling at

stated prices gilt-edged bonds of all maturities reduces the unemployment rate that

characterizes the long-period equilibrium position of the economy from 1 2 nk2 to

1 2 nk1.

V. SUMMARY AND CONCLUSION

Looking backward, we observe long-run trends shaping economic events. The confi-

dence to undertake investment projects depends upon our ability to project these

trends into the future. The problem is that we know these trends are not governed

by natural laws but are instead the result of the series of investment projects under-

taken by forward-looking investors in the past. In every short-period situation in

which such investment projects were undertaken, the long-run trends of the

economy would have taken off in a different direction, if those investment projects

had not been undertaken.

For this reason, investors take a two-step approach to the evaluation of prospective

investment projects. First, they project long-run trends into the future by assigning

probabilities to the likelihood of their continuance, and thereby calculate the

expected profit (Eo).11 Second, they contemplate the degree to which the principle

of non-sufficient reason captures their uncertainty about the degree to which know-

able but unknown or unknowable factors may cause the future trends of the

economy to differ from past ones, and thereby calculate the expected profit (Ek).

Monetary policy is a factor that has shaped the long-run trends of the economy. It

is thus necessary for investors to assign a probability to the likelihood that the

11 D’Orlando (2005) also argues that probabilistic, as opposed to deterministic, dynamic models arecompatible with the classical long-period method.


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monetary authority will continue to act in the same way that it has in the past, and

incorporate it into the calculation of Eo. If the monetary authority has the discretion

to act differently in the future than it has in the past, investors are compelled to con-

template monetary policy itself as a knowable but unknown or unknowable factor

that may cause future trends of the economy to differ from past ones, and thus take

it into account as a factor that makes Ek , Eo. If the monetary authority would

make a credible commitment to buying and selling at stated prices gilt-edged bonds

of all maturities, this element of uncertainty would be alleviated, thereby reducing

the difference between Ek and Eo. The purpose of this paper has been to show that,

as a result, the long-period equilibrium position of the economy would be character-

ized by less unemployment.

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keynes's theory of monetary policy: an essay in historical reconstruction

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