Download Honours Finance (Advanced Concepts in Finance)

Honours Finance (Advanced Topics in Finance:
Nonlinear Analysis)
Lecture 1: Introduction
The Dual Price Level Analysis
What is Finance?
• The branch of economics concerned with the behaviour
of money and the markets for claims on physical assets
• 2 approaches:
– money and financial assets are no different to other
commodities except that time preference is involved
• they are stable equilibrium systems subject to external
shocks
– money and financial assets are
different to standard commodities
fundamentally
• they are unstable far from equilibrium systems (also
subject to external shocks)
What is Finance?
• First approach (Modern Portfolio Theory [MPT] or
“Modern Finance”) dominates finance literature; but...
– Is acknowledged by almost all finance professionals to
be clearly wrong
• If true
– asset prices should follow a “random walk”
– The numbers generated by any finance market should
be “independently and identically distributed” (iid)
• Both conditions are manifestly falsified by the data
• So second approach has at least prima facie grounds for
being correct, but
– sporadically developed by tiny minority of profession
– theoretical linkages not well known
Subject Overview
• Broadly this subject covers:
– (1) Foundations of “endogenous instability” approach to
analysing finance markets
– (2) Essential mathematical techniques for analysing
endogenous instability, covering topics
• taught in Maths 1.3 but not put into economic context
(polynomial series expansions of functions, matrix
algebra)
• taught by maths department in 3rd year (ordinary
differential equations [ODEs])
• not taught at all at this University (systems of ODEs,
introductory chaos theory)
– (3) Behavioural approach to Finance
Subject Overview
• Critique of Efficient Markets Hypothesis
• The Dual Price Level theory of Finance
• Techniques for analysis of deterministic nonlinear
systems
– Ordinary Differential Equations
– Block Diagram Techniques
• A non-standard quantitative approach to Portfolio
Analysis
• Nonlinear computer approaches to Portfolio Analysis
– Neural networks
– Genetic Algorithms
• Recent advances
– Econophysics; nonextensive statistical mechanics
Subject Overview
• Necessarily technical mathematical approach, but
– attempt to keep focused on purpose behind techniques
– material learnt will help understand basis of different
approaches to finance
• Dual Price level theory
– never collated before
– necessarily more “macro” in flavour because
• unlike MPT, argues finance does have macroeconomic
impact
• developed by leading critical macroeconomists: Marx,
Fisher, Keynes, Kalecki, Minsky
– has both philosophic and mathematical aspects
– But first, recap on CAPM…
The Capital Assets Pricing Model
• Problem: How to “predict the behaviour of capital
markets”
• Solution: extension of economic theories of investment
under certainty...
– to investment under conditions of risk
• Based on neoclassical utility theory
• Investor maximises utility subject to (s.t.) constraints
• Utility is a:
– Positive function(+ive fn) of expected return ER
– -ive fn of risk (standard deviation) sR
• Constraints are available spectrum of investment
opportunities
The Capital Assets Pricing Model
Z inferior
to C
(lower ER)
and B
(higher
sR)
Investment
opportunities
“Efficient”
opportunities
on the edge
Indifference
curves
Increasing utility:
Higher expected
returns & lower risk
Optimal
combination
for this
investor
Border (AFBDCX) is Investment Opportunity Curve (IOC)
The Capital Assets Pricing Model
• Sharpe assumes riskless asset P with ERP=pure interest
rate, sRP=0.
• Investor can form portfolio of P with any other
combination of assets
• One asset combination will initially dominate all others:
The Capital Assets Pricing Model
Efficiency: maximise expected return
& minimise risk given constraints
Only asset combination
which can efficiently
be combined with
riskless asset P in
a portfolio
The Capital Assets Pricing Model
• Assume limitless borrowing/lending at riskless interest
rate = return on asset P
• Investor can move to anywhere along PfZ line by
borrowing/lending
• Problem:
– P the same for all investors (“simplifying assumption”)
– But investor perceptions of expected return, risk,
investment correlation will differ
• Solution:
– assume “homogeneity of investor expectations” [OREF
II]
– utterly unrealistic assumption, as is assumption of
limitless borrowing by all borrowers at riskless
interest rate. So...
The Capital Assets Pricing Model
• Defended by appeal to Friedman’s “Instrumentalism”:
– “the proper test of a theory is not the realism of its
assumptions but the acceptability of its implications”
• Consequence of assumptions:
– spectrum of available investments/IOC identical for
all investors
– P same for all investors
– PfZ line same for all investors
– Investors distribute along line by borrowing/lending
according to own risk preferences:
The Capital Assets Pricing Model
Thrill seeker...
Highly
risk-averse
The Capital Assets Pricing Model
• Next, the (perfect) market mechanism
– Price of assets in f will rise
– Price of assets not in f will fall
– Price changes shift expected returns
– Causes new pattern of efficient investments aligned
with PfZ line:
The Capital Assets Pricing Model
Capital market line
Range of
efficient asset
combinations
after market
price
adjustments:
more than just
one efficient
portfolio
The Capital Assets Pricing Model
• In order to derive conditions for equilibrium in the capital
market we invoke two assumptions. First, we assume a common
pure rate of interest, with all investors able to borrow or lend
funds on equal terms. Second, we assume homogeneity of
investor expectations: investors are assumed to agree on the
prospects of various investments–the expected values, standard
deviations and correlation coefficients described in Part II.
Needless to say, these are highly restrictive and undoubtedly
unrealistic assumptions. However, since the proper test of a
theory is not the realism of its assumptions but the
acceptability of its implications, and since these assumptions
imply equilibrium conditions which form a major part of classical
financial doctrine, it is far from clear that this formulation
should be rejected–especially in view of the dearth of
alternative models leading to similar results. (Sharpe 1964
[1991]; emphasis added)
• But Sharpe later admits to some qualms with this:
The CAPM: Reservations
• “People often hold passionately to beliefs that are far from
universal. The seller of a share of IBM stock may be convinced
that it is worth considerably less than the sales price. The
buyer may be convinced that it is worth considerably more.”
(Sharpe 1970)
• However, if we try to be more realistic:
– “The consequence of accommodating such aspects of reality
are likely to be disastrous in terms of the usefulness of the
resulting theory... The capital market line no longer exists.
Instead, there is a capital market curve–linear over some
ranges, perhaps, but becoming flatter as [risk] increases over
other ranges. Moreover, there is no single optimal
combination of risky securities; the preferred combination
depends upon the investors’ preferences... The demise of the
capital market line is followed immediately by that of the
security market line. The theory is in a shambles.” (Sharpe
1970 emphasis added)
Within Economics: Instrumentalism
– Logical consistency of assumptions has been challenged
(Sraffa), not just realism
– Sciences do attempt to build theories which are
essentially descriptions of reality
– Musgrave (1981) argues Friedman’s “significant theory,
unrealistic assumptions” position invalid
– Classifies assumptions into 3 classes
• Negligibility assumptions
• Domain Assumptions
• Heuristic Assumptions
Within Economics: Instrumentalism
• Negligibility Assumptions
– Assert that some factor is of little or no importance in
a given situation
• e.g., Galileo’s experiment to prove that weight does not
affect speed at which objects fall
– dropped two different size lead balls from Leaning
Tower of Pisa
– “assumed” (correctly) air resistance “negligible” at
that altitude for dense objects, therefore ignored
air resistance
• Domain assumptions
– Assert that theory is relevant if some assumed
condition applies, irrelevant if condition does not apply
Within Economics: Instrumentalism
• e.g., Newton’s theory of planetary motion “assumed”
there was only one planet
– if true, planet follows elliptical orbit around sun.
– if false & planets relatively massive, motion
unpredictable. Poincare (1899) showed
• there was no formula to describe paths
• paths were in fact “chaotic”
• planets in multiple planet solar systems therefore
have collisions
• present planets evolved from collisions between
proto-planets
• “evolutionary” explanation for present-day
roughly elliptical orbits
Classes of assumptions
that this result … cannot be
maintained; in other words, the
law that we have just written
down does not hold in reality. For
the time being, however, we shall
assume its correctness.”
(Einstein 1916)
0.9 c
train
• Heuristic
– assumption known to be false, but used as stepping
stone to more valid theory
– e.g., in developing theory of relativity, Einstein
assumes that distance covered by person walking
across a train carriage equals trigonometric sum of
• forward movement of train
• sideways movement of passenger
+passengerThen says: “We shall see later
+ 0.9 c
Just where are markets efficient?
• The Efficient Markets Hypothesis: assume
– All investors have identical accurate expectations of
future
– All investors have equal access to limitless credit
• Negligible, Domain or Heuristic assumptions?
• Negligible? No: if drop them, then according to Sharpe
“The theory is in a shambles” (see last lecture)
• Heuristic? No, EMH was “end of the line” for Sharpe’s
logic: no subsequent theory developed which
– replaced risk with uncertainty, or
– took account of differing inaccurate assumptions,
different access to credit, etc.
• Basis of eventual empirical failure of CAPM
The CAPM: Evidence
• Sharpe’s qualms ignored & CAPM takes over economic
theory of finance
• Initial evidence seemed to favour CAPM
– Essential ideas:
• Price of shares accurately reflects future earnings
– With some error/volatility
• Shares with higher returns more strongly correlated to
economic cycle
– Higher return necessarily paired with higher
volatility
• Investors simply chose risk/return trade-off that
suited their preferences
– Initial research found expected (positive) relation
between return and degree of volatility
– But were these results a fluke?
The CAPM: Evidence
• Volatile but superficially exponential trend
– As it should be if economy growing smoothly
12000
DJIA 1920-2001
10000
8000
6000
4000
2000
0
11/25/1921
-2000
8/4/1935
4/12/1949
12/20/1962
8/28/1976
5/7/1990
1/14/2004
The CAPM: Evidence
• Sharpe’s CAPM paper published 1964
• Initial CAPM empirical research on period 1950-1960’s
– Period of “financial tranquility” by Minsky’s theory
• Low debt to equity ratios, low levels of speculation
– But rising as memory of Depression recedes…
• Steady growth, high employment, low inflation…
• Dow Jones advance steadily from 1949-1965
– July 19 1949 DJIA cracks 175
– Feb 9 1966 DJIA sits on verge of 1000 (995.15)
• 467% increase over 17 years
– Continued for 2 years after Sharpe’s paper
• Then period of near stagnant stock prices
The CAPM: Evidence
• Dow Jones “treads water” from 1965-1982
– Jan 27 1965: Dow Jones cracks 900 for 1st time
– Jan 27 1972: DJIA still below 900! (close 899.83)
• Seven years for zero appreciation in nominal terms
• Falling stock values in real terms
– Nov. 17 1972: DJIA cracks 1000 for 1st time
• Then “all hell breaks loose”
– Index peaks at 1052 in Jan. ‘73
– falls 45% in 23 months to low of 578 in Dec. ’74
– Another 7 years of stagnation
– And then “liftoff”…
The CAPM: Evidence
• Fit shows average exponential growth 1915-1999:
• index well above or below except for 1955-1973
4.5
Log of Dow Jones Industrial Average 1915-1999
4
3.5
Crash of ’73: 45%
fall in 23 months…
Sharpe’s paper published
Jan 11 ’73: Peaks at 1052
Log Closing Value
3
y = 6E-05x + 1.4228
R2 = 0.9031
Dec 12 1974: bottoms at 578
2.5
Bubble takes off in ‘82…
2
1.5
1
Steady above trend growth 19491966: Minsky’s “financial tranquility”
CAPM fit to this data looks pretty good!
0.5
0
7/5/1914
CAPM fit doesn’t look
so hot any more…
4/13/1926
1/20/1938
10/29/1949
8/7/1961
5/16/1973
Date
2/22/1985
12/1/1996
9/9/2008
6/18/2020
The CAPM: Evidence According to Fama 1969
• Evidence supports the CAPM
– “This paper reviews the theoretical and empirical
literature on the efficient markets model… We shall
conclude that, with but a few exceptions, the efficient
markets model stands up well.” (383)
• Assumptions unrealistic but that doesn’t matter:
– “the results of tests based on this assumption depend
to some extent on its validity as well as on the
efficiency of the market. But some such assumption is
the unavoidable price one must pay to give the theory
of efficient markets empirical content.” (384)
The CAPM: Evidence According to Fama 1969
• CAPM good guide to market behaviour
– “For the purposes of most investors the efficient
markets model seems a good first (and second)
approximation to reality.” (416)
• Results conclusive
– “In short, the evidence in support of the efficient
markets model is extensive, and (somewhat uniquely in
economics) contradictory evidence is sparse.” (416)
• Just one anomaly admitted to
– Large movements one day often followed by large
movements the next—“volatility clustering”…
The CAPM: Evidence According to Fama 1969
• “one departure from the pure independence assumption
of the random walk model has been noted … large daily
price changes tend to be followed by large daily changes.
The signs of the successor changes are apparently
random, however, which indicates that the phenomenon
represents a denial of the random walk model but not of
the market efficiency hypothesis… But since the
evidence indicates that the price changes on days follow
ing the initial large change are random in sign, the initial
large change at least represents an unbiased adjustment
to the ultimate price effects of the information, and this
is sufficient for the expected return efficient markets
model.” (396)
• 35 years later, picture somewhat different…
The CAPM: Evidence According to Fama 2004
• “The attraction of the CAPM is that it offers powerful
and intuitively pleasing predictions about how to measure
risk and the relation between expected return and risk.
• Unfortunately, the empirical record of the model is
poor—poor enough to invalidate the way it is used in
applications.
• The CAPM's empirical problems may reflect theoretical
failings, the result of many simplifying assumptions…
• In the end, we argue that whether the model's problems
reflect weaknesses in the theory or in its empirical
implementation, the failure of the CAPM in empirical
tests implies that most applications of the model are
invalid.” (Fama & French 2004: 25)
The CAPM: Evidence According to F&F 2004
• Clearly admits assumptions dangerously unrealistic:
– “The first assumption is complete agreement given
market clearing asset prices at t-1, investors agree on
the joint distribution of asset returns from t-1 to t.
And this distribution is the true one—that is, it is
the distribution from which the returns we use to test
the model are drawn. The second assumption is that
there is borrowing and lending at a risk free rate,
which is the same for all investors and does not
depend on the amount borrowed or lent.” (26)
• Bold emphasis: model assumes all investors know the
future
• Assumptions, which once “didn’t matter” (see Sharpe
earlier) are now crucial…
The CAPM: Evidence According to F&F 2004
• “The assumption that short selling is unrestricted is as
unrealistic as unrestricted risk-free borrowing and
lending… But when there is no short selling of risky
assets and no risk-free asset, the algebra of portfolio
efficiency says that portfolios made up of efficient
portfolios are not typically efficient. This means that
the market portfolio, which is a portfolio of the
efficient portfolios chosen by investors, is not typically
efficient. And the CAPM relation between expected
return and market beta is lost.” (32)
• Still some hope that, despite lack of realism, data might
save the model…
The CAPM: Evidence According to F&F 2004
– “The efficiency of the market portfolio is based on
many unrealistic assumptions, including complete
agreement and either unrestricted risk-free
borrowing and lending or unrestricted short selling of
risky assets. But all interesting models involve
unrealistic simplifications, which is why they must be
tested against data.” (32)
• Unfortunately, no such luck…
– 40 years of data strongly contradict all versions of
CAPM
• Returns not related to betas
• Other variables (book to market ratios etc.) matter
• Linear regressions on data differ strongly from risk
free rate (intercept) & beta (slope) calculations from
CAPM
The CAPM: Evidence According to F&F 2004
• Tests of the CAPM are based on three implications…
– “First, expected returns on all assets are linearly
related to their betas, and no other variable has
marginal explanatory power.
– Second, the beta premium is positive, meaning that the
expected return on the market portfolio exceeds the
expected return on assets whose returns are
uncorrelated with the market return.
– Third, … assets uncorrelated with the market have
expected returns equal to the risk-free interest rate,
and the beta premium is the expected market return
minus the risk-free rate.” (32)
The CAPM: Evidence According to F&F 2004
• “There is a positive relation between beta and average
return, but it is too "flat." … the Sharpe-Lintner model
predicts that
– the intercept is the risk free rate and
– the coefficient on beta is the expected market return
in excess of the risk-free rate, E(RM) - R.
– The regressions consistently find that the intercept is
greater than the average risk-free rate…, and the
coefficient on beta is less than the average excess
market return” (32)
The CAPM: Evidence According to F&F 2004
• Average Annualized Monthly Return versus Beta for Value
Weight Portfolios Formed on Prior Beta, 1928-2003
• “the predicted return on the portfolio with the lowest beta is 8.3
percent per year; the actual return is 11.1 percent. The predicted
return on the portfolio with the highest beta is 16.8 percent per
year; the actual is 13.7 percent.” (33)
The CAPM: Evidence According to F&F 2004
• The hypothesis that market betas completely explain
expected returns …
– Starting in the late 1970s… evidence mounts that
much of the variation in expected return is unrelated
to market beta…” (34)
– Fama and French (1992) update and synthesize the
evidence on the empirical failures of the CAPM… they
confirm that size, earnings-price, debt equity and
book-to-market ratios add to the explanation of
expected stock returns provided by market beta.” (36)
– Best example of failure of CAPM as guide to building
investment portfolios: Book to Market (B/M) ratios
provide far better guide than Beta…
The CAPM: Evidence According to F&F 2004
• “Average returns on the B/M portfolios increase almost
monotonically, from 10.1 percent per year for the lowest
B/M group to an impressive 16.7 percent for the highest.
• But the positive relation between beta and average
return predicted by the CAPM is notably absent… the
portfolio with the lowest book-to-market ratio has
the highest beta but the lowest average return.
• The estimated beta for the portfolio with the highest
book-tomarket ratio and the highest average return is
only 0.98. With an average annualized value of the
riskfree interest rate, Rf, of 5.8 percent and an average
annualized market premium, Rm - Rf, of 11.3 percent, the
Sharpe-Lintner CAPM predicts an average return of 11.8
percent for the lowest B/M portfolio and 11.2 percent
for the highest, far from the observed values, 10.1 and
16.7 percent.”
The CAPM: Evidence According to F&F 2004
• Average Annualized Monthly Return versus Beta for
Value Weight Portfolios Formed on B/M, 1963-2003
• Simple regression gives opposite relationship to CAPM:
return rises as beta falls! High returns with low volatility
The CAPM: Evidence According to F&F 2004
• End result: CAPM should not be used.
– “The … CAPM … has never been an empirical success…
The problems are serious enough to invalidate most
applications of the CAPM.
– For example, finance textbooks often recommend
using the … CAPM risk-return relation to estimate the
cost of equity capital… [But] CAPM estimates of the
cost of equity for high beta stocks are too high … and
estimates for low beta stocks are too low…
– The CAPM … is nevertheless a theoretical tour de
force. We continue to teach the CAPM as an
introduction to the fundamental concepts of portfolio
theory and asset pricing…
– But we also warn students that despite its seductive
simplicity, the CAPM's empirical problems probably
invalidate its use in applications.” (F&F 2004: 46-47)
The Dual Price Level theory of Finance
• If even the “true believers” have abandoned CAPM, a new
theory is needed
• However “everything old is new again”:
– Many contributions to economics & finance neglected
because of CAPM dominance
– These contributions provide philosphical/theoretical
basis for emerging nonlinear theories of finance:
• Smith, Fisher, Keynes, Schumpeter, Kalecki, Minsky,
Marx
• First some preliminary visual statistics
The archetypal financial series: the DJIA
104
7
6
5
4
3
2
DJIA
103
7
6
5
4
3
2
102
7
6
5
4
3
2
101
1/1/33
9/2/43
5/3/54
1/1/65
DAY
9/2/75
5/3/86
1/1/97
The cyclical DJIA? Deflate by CPI and…
The Dow Jones Index Deflated by the CPI, 1933-1997
60
DJIA CPI Deflated
50
• Similar
cyclical
patterns
evident
in
interest
rates,
inflation
40
30
20
10
0
4/30/38
4/12/49
10/21/43
3/25/60
10/3/54
3/8/71
9/15/65
Day
2/18/82
8/28/76
1/31/93
8/11/87
30/08/96
30/08/94
30/08/92
30/08/90
30/08/88
30/08/86
30/08/84
30/08/82
30/08/80
30/08/78
30/08/76
30/08/74
30/08/72
30/08/70
30/08/68
WW
II
30/08/66
-10
30/08/64
30/08/62
30/08/60
30/08/58
15
30/08/56
Great
Depression
30/08/54
30/08/52
30/08/50
30/08/48
30/08/46
30/08/44
30/08/42
30/08/40
30/08/38
30/08/36
-15
30/08/34
30/08/32
30/08/30
30/08/28
30/08/26
20
30/08/24
30/08/22
30/08/20
30/08/18
USA Interbank Lending Rate
25
Interbank Rate
Real Rate
Inflation Rate
Linear (Real Rate)
Poly. (Real Rate)
10
5
0
-5
Post-War
Recovery
-20
Pre-capitalist perspective on money
• Contrary to majority opinion, capitalism has not existed
forever
• Capitalist economy evolved out of feudal systems of
Europe
• Feudal systems based on social hierarchy determined by
birth
– King at top ruled kingdom
– Lords beneath controlled “fiefs” (large estates)
• effective owners of land, but title legally with king
• paid tribute to king, provided knights for armies, etc.
– Serfs worked the land
• bonded to land
• system of mutual obligation between serfs and lord
Pre-capitalist perspective on money
– Disparate systems of artisans constituted industry
• normally organised in guilds
– No formal financial system
• wealth in physical terms (goods, gold) rather than money
• Dominant ideology of feudal system religious
– social order ordained by God
• “The rich man at his castle, the poor man at his gate;
God made one high, one lowly, and ordered their estate”
– Main religion Catholicism
• Major minority Jewish, tiny minority Muslim
– Religious attitude to moneylending censorious: an evil
From Usury to Utility
• During pre-capitalist era, money regarded as
fundamentally different to normal commodities because
– “barren”: Normal commodity sold at profit by
tradesman
– profit represents labour of tradesman: “a man may ...
seek gain, not as an end, but as payment for his
labor” (Aquinas)
– No labour involved in money exchange “To take
interest for money lent is unjust in itself, because
this is to sell what does not exist, and this evidently
leads to inequality which is contrary to justice.”
(Aquinas)
– Intended only for circulation, not accumulation
– Usury (lending of money at secured rate of return)
banned
From Usury to Utility
• In practice usury undertaken
• not prohibited from one religion to another (in
Christian/Jewish religions), so fictional chains (see HET
lectures) used to lend from Christian to Christian
• But legislative prohibitions until 1624
– UK Act Against Usury of 1571 prohibited usury
absolutely, but penalties depended on rate of interest
charged:
• If less than ten per cent, the usurer forfeited the
interest
• If greater, usurer forfeited the interest plus three
times the principal (half going to the Crown, half to the
informer) (Jones 1989: 62-64, 92).
From Usury to Utility
• Religion basis of anti-usury ideology
– 1571 Act prohibited usury absolutely on the basis that
the role of Parliament was “to apply the word of God
to an issue on which God had expressed Himself”
(Jones 1989: 1)
– theoretical prohibition dominant until late 17th
century but absolute prohibition repealed in 1624
• Usury still a sin but practice now an issue for usurer and
God, not the Law
• Legal Usury now defined in terms of the interest rate:
greater than 8 per cent was “usurious”
From Usury to Utility
• Pre-1571, rates of interest
– varied between 12 and 500 per cent per annum
– majority between 15 and 50 per cent, but quite
unsystematic; sample from time of Elizabeth I:
Loans made by Thomas Manners to John Wilde
Duration
Rate p.a
Date
Amount (months)
Interest
(%)
11-Apr
33s. 6d. 10
13s. 4d.
46
14-Apr
26s. 8d. 9
12s.
60
23-Apr
£5
9
36s.
48
24-Apr
46s. 8d. 12
12s. 8d.
27
27-Apr
£12
2
17s. 4d.
43
30-Apr
40s.
2
4s.
60
27-Aug
£6 l0s. 6
18s.
27
2-Jan
£3 l0s. 8
18s.
36
15-Jan
30s.
8
18d
7.5
(Jones 1989: 78)
Little
wonder
that
“usurer”
was a
dirty word!
From Usury to Utility
• Pre-capitalist rates clearly unsustainable
– Little wonder that religions protected borrower:
• “And if the debtor is in straitened circumstances, then
(let there be) postponement to (the time of) ease; and
that ye remit the debt as almsgiving would be better for
you if ye did but know. ” (Qu’ran , Al-Baqara 2.280)
• As capitalist era commences, legislative pressure reduces
maximum rate of interest:
– Post 1571, 10 per cent; 1624, 8 per cent; 6 per cent
during 17th century
– 5 per cent in late 18th century
From Usury to Utility
• Actual rate tended to be just below legal maximum
– 3 to 4.5 per cent versus 5 per cent ceiling (Smith
1776: Book 1, Ch 9)
• Lending of money at interest common commercial
practice by dawn of capitalist era, but still “prohibited”
by religious ideology. Alternative theory needed to
justify it
• Utilitarianism the eventual alternative theory, but not
the first perspective of economists
• Instead, Smith
– criticised prohibitions on usury; but
– supported legal limits to the rate of interest
From Usury to Utility
• The complete prohibition of interest taking “like all
others of the same kind, is said to have produced no
effect, and probably rather increased than diminished
the evil of usury” (Smith, 1776: Book I, Ch. 9).
• Laws prohibiting lending “increase the evil of usury; the
debtor being obliged to pay, not only for the use of the
money, but for the risk which his creditor runs by
accepting a compensation for that use. He is obliged, if
one may say so, to insure his creditor from the penalties
of usury.” (Smith, 1776: Book II, Ch. 4)
• But control over the rate of interest a good thing:
From Usury to Utility
• “In countries where interest is permitted, the law, in
order to prevent the extortion of usury, generally fixes
the highest rate which can be taken without incurring a
penalty. This rate ought always to be somewhat above the
lowest market price... In a country, such as Great Britain,
where money is lent to government at three per cent and
to private people upon a good security at four and four
and a half, the present legal rate, five per cent, is
perhaps as proper as any.” (Smith, 1776: Book II, Ch. 4)
• The reasons?
– Better control of allocation of finance
– Higher rate of productive investment
– Prevention of exploitation
From Usury to Utility
• “The legal rate ... ought not to be much above the lowest
market rate. If the legal rate [is much higher], the greater
part of the money which was to be lent would be lent to
prodigals and projectors, who alone would be willing to give
this high interest...”
• “A great part of the capital of the country would thus be
kept out of the hands which were most likely to make a
profitable and advantageous use of it, and thrown into
those which were most likely to waste and destroy it.”
• “Where the legal rate of interest, on the contrary, is fixed
but a very little above the lowest market rate, sober people
are universally preferred, as borrowers, to prodigals and
projectors. The person who lends money gets nearly as much
interest from the former as he dares to take from the latter,
and his money is much safer in the hands of the one set of
people than in those of the other.”
From Usury to Utility
• “A great part of the capital of the country is thus thrown into
the hands in which it is most likely to be employed with
advantage.” (Smith, 1776: Book II, Ch. 4)
• Thus according to Smith, “credit controls” improve allocation
of finance
– Willingness to pay higher rates correlated with reduced
quality of lender
– Acknowledgement of speculative and wasteful employment
of credit, possibility of bankruptcy/default by borrowers,
and macroeconomic consequences (lower rate of growth)
– Distinction between normal goods, where market can set
the price, and money where a maximum should be set
• But Smith’s realism defeated by Bentham’s utilitarianism
From Usury to Utility
• “no man of ripe years and of sound mind, acting freely,
and with his eyes open, ought to be hindered, with a view
to his advantage, from making such bargain, in the way of
obtaining money, as he thinks fit... This proposition, were
it to be received, would level ... all the barriers which law,
either statute or common, have in their united wisdom set
up, ... against the crying sin of Usury.” (Bentham 1787, In
Defence of Usury)
• Bentham’s starting point was libertarianism:
– “‘You, who fetter contracts; you, who lay restraints on
the liberty of man, it is for you’ (I should say) ‘to
assign a reason for your doing so.’”
From Usury to Utility
• Bentham’s target was not prohibition, but controls on the
maximum rate (as accepted by Smith):
– “To say then that usury is a thing that ought to be
prevented, is saying ... that the utmost rate of
interest which shall be taken ought to be fixed;... A
law punishing usury supposes, therefore, a law fixing
the allowed legal rate of interest.”
• As a leading proponent of the removal of all restraints to
trade, Bentham starts by asking “why a policy, which, as
applied to exchanges in general, would be generally
deemed absurd and mischievous, should be deemed
necessary in the instance of this particular kind of
exchange ”.
From Usury to Utility
• Bentham considers and dismisses each perceived
argument in favour of controls on the maximum rate of
interest: One of the earliest statements of this concept
• Money exchange vs commodity exchange: why the
difference?
– “Much has not been done, ... in the way of fixing the
price of other commodities: and, in what little has
been done, the probity of the intention has, I believe,
in general, been rather more unquestionable than the
rectitude of the principle, or the felicity of the result.
Putting money out at interest, is exchanging present
money for future: but why a policy, which, as applied
to exchanges in general, would be generally deemed
absurd and mischievous, should be deemed necessary
in the instance of this particular kind of exchange,
mankind are as yet to learn.”
From Usury to Utility
• Money exchange vs commodity exchange : why the
difference?
– “For him who takes as much as he can get for the use
of any other sort of thing, an house for instance,
there is no particular appellation, nor any mark of
disrepute: nobody is ashamed of doing so, nor is it
usual so much as to profess to do otherwise. Why a
man who takes as much as he can get, be it six, or
seven, or eight, or ten per cent for the use of a sum of
money should be called usurer, should be loaded with
an opprobrious name, any more than if he had bought
an house with it, and made a proportionable profit by
the house, is more than I can see.”
From Usury to Utility
• Money exchange vs commodity exchange : why a
maximum?
– “Another thing I would also wish to learn, is, why the
legislator should be more anxious to limit the rate of
interest one way, than the other? why he should set
his face against the owners of that species of
property more than of any other? why he should make
it his business to prevent their getting more than a
certain price for the use of it, rather than to prevent
their getting less? why, in short, he should not take
means for making it penal to offer less, for example,
than 5 per cent as well as to accept more?”
From Usury to Utility
• Protection of “prodigals”
– Admits prevention of prodigality of some merit:
• “That prodigality is a bad thing, and that the prevention
of it is a proper object for the legislator to propose to
himself, so long as he confines himself to, what I look
upon as, proper measures, I have no objection to allow”
– But argues that a prodigal will not, in fact, be charged
an excessive rate of interest:
• “In the first place, no man, ..., ever thinks of borrowing
money to spend, so long as he has ready money of his
own, or effects which he can turn into ready money
without loss.”
– Prodigal with money and/or liquid assets therefore
won’t borrow
From Usury to Utility
• Protection of “prodigals”
– Exceptions to above (no money) but with requisite
collateral can get a loan at the usual rate
– Those that do not have security will only be lent to by
those who like them, and these friendly persons will
naturally offer them the standard rate
• “Persons who either feel, or find reasons for pretending
to feel, a friendship for the borrower, can not take of
him more than the ordinary rate of interest: persons,
who have no such motive for lending him, will not lend
him at all.”
– So Shylock died with Shakespeare in the 16th
century?
From Usury to Utility
• Protection of the mentally unsound
– No idiot is likely to be less accurate than a legislator
• “I am by this time entitled to observe, that no
simplicity, short of absolute idiotism, can cause the
individual to make a more groundless judgment, than the
legislator, who, in the circumstances above stated,
should pretend to confine him to any given rate of
interest, would have made for him.”
– Supremacy of individual judgment, however
hampered, over legislative.
From Usury to Utility
• Protection of the mentally unsound
– Mentally unsound more in need of protection from high
prices of normal commodities than of money:
• “Buying goods with money, or upon credit, is the business
of everyday. borrowing money is the business, only, of
some particular exigency, which, in comparison, can occur
but seldom. Regulating the prices of goods in general
would be an endless task, and no legislator has ever been
weak enough to think of attempting it. ... But in what
degree soever a man's weakness may expose him to
imposition, he stands much more exposed to it, in the
way of buying goods, than in the way of borrowing
money.”
From Usury to Utility
• Bentham’s justification of a total free market for loans
– based on individual liberty and individual utility
maximisation
– asserts commonality of contracts for money with all
other commodity contracts
– introduces concept of a loan as “exchanging present
money for future”
– makes some rather questionable assumptions (only
friends lend to prodigals)
– does not address Smith’s macroeconomic arguments
(more productive investment, higher rate of growth if
maximum interest rate set by law)
From Usury to Utility
• Despite weaknesses, Bentham’s utilitarian approach
becomes basis of modern theory of finance via Fisher
Mark I:
– The rate of interest “expresses a price in the
exchange between present and future goods.” (Fisher
1930: 61),
– This price is the product of three forces
• the subjective preferences of individuals for present
goods over future goods
• the objective possibilities for profitable investment
• and a market mechanism for loanable funds which brings
these two forces into equilibrium.
From Usury to Utility
• the subjective preferences of individuals for present
goods over future goods determines supply of funds
– a low time preference:
• most likely a lender
– high time preference (prefers to consume now rather
than later)
• most likely a borrower.
– Borrowing thus means by which those with a high
preference for present goods acquire the funds they
need now, at the expense of later income.
From Usury to Utility
• The objective side of the equation
– the marginal productivity of investment or “marginal
return over cost” (1930: 182).
– willingness to borrow/lend not enough
• must also be possible for borrowed money to be invested
and earn a rate of return.
From Usury to Utility
• Market mechanism brings subjective and objective forces
into harmony
– Supply
• A high rate of interest
– even those with a very high time preference will lend
– supply of funds will be quite high
• Low rate of interest
– only those with a very low time preference will lend
– very small supply of funds
From Usury to Utility
– Demand
• High rate of interest
– most investments will be unviable
– demand for funds will be low
• Low rate of interest
– most investments have positive net present value
– demand for funds will be high
• Market mechanism
– Forces of supply and demand determine equilibrium
interest rate at which the funds demanded and the
funds supplied are equal.
From Usury to Utility
• Fisher’s analysis supports zero rate of interest during
medieval/feudal times
– Average rate of accumulation zero (all surplus
consumed by royal class)
– “Average rate of return on investment” therefore zero
– Rate of subjective time preference must therefore
also become zero:
• “Since, as we have seen, this rate must equal the rates
of preference, or impatience, and also the rate of
interest, all these rates must be zero also.” (1930: 186)
• Modern Finance thus supports prohibition on interest:
laws reflected subjective rate of time preference of
medieval society.
From Usury to Utility
• More on utility theory of finance later in course
• Now to Fisher and the alternative Dual Price Level theory
• Two conditions needed for market to perform in Fisher’s
equilibrium model
– “(A) The market must be cleared—and cleared with
respect to every interval of time.”
– “(B) The debts must be paid.” (1930: 495)
– i.e.:
• No disequilibrium
• No bankruptcy/default
– As unrealistic as Bentham on prodigals, but...
From Usury to Utility
• Fisher cognisant of
– social basis to time preference
• “the smaller the income, the higher the preference for
present over future income” (71)
– “If a person has only one loaf of bread he would not
set it aside for next year even if the rate of
interest were 1000 per cent; for if he did so, he
would starve in the meantime” (71-72)
– “the effect of poverty is often to relax foresight
and self-control and to tempt us to ‘trust to luck’ for
the future, if only the all-engrossing need of present
necessities can be satisfied” (72)
From Usury to Utility
– affect of time pattern and expectations on time
preference
• “A man who is now enjoying an income of only $5000 a
year, but who expects in ten years to be enjoying one of
$10,000 a year, will today prize a dollar in hand far more
than the prospect of a dollar due ten years hence. His
great expectations make him impatient to realize on
them in advance. He may, in fact, borrow money to eke
out this year's income and promise repayments out of
his supposedly more abundant income ten years later”
(73)
– Akin to lending to poor/lending to prodigals in Smith’s
reasons to restrain the rate of interest
– Both reasons why preconditions (A) and (B) may not be
met in the real world
From Utility to Depression
• As well as one of world’s most prominent economists,
Fisher was also a newspaper columnist (a risky business...)
• On Wednesday, October 15, 1929, Fisher
comments“Stock prices have reached what looks like a
permanently high plateau. I do not feel that there will
soon, if ever, be a fifty or sixty point break below
present levels, such as Mr. Babson has predicted. I
expect to see the stock market a good deal higher than it
is today within a few months.”
• On October 23rd, 1929, Black Wednesday: Dow Jones
loses almost 10% in a single day
• 4 years later, the broad market was 1/6th of its peak,
and Irving Fisher had lost over $10 million.
The Wall Street Crash
From 32 at its zenith
S&P 500 Composite Index
103
6
4
3
2
102
6
4
3
2
101
6
4
3
2
100
25/11/21
12/12/33
29/12/45
15/01/58
1/02/70
18/02/82
7/03/94
Week
4/12/27
21/12/39
7/01/52
24/01/64
10/02/76
27/02/88
S&P 500 Composite Index
35
30
To below
5
at its
nadir
in less than 3 years
25
20
15
10
5
0
2/01/29
2/04/30
1/07/31
Week
28/09/32
27/12/33
From Utility to Depression
• Fisher’s reputation destroyed by above prediction, but
turned to developing theory to explain the crash
– “The Debt Deflation Theory of Great Depressions”
• based on rejection of conditions (A) and (B) above
– Previous theory assumed equilibrium but real world
equilibrium short-lived since “New disturbances are,
humanly speaking, sure to occur, so that, in actual fact,
any variable is almost always above or below the ideal
equilibrium” (1933: 339)
– As a result, any real world variable is likely to be over
or under its equilibrium level--including confidence &
speculation
Debt Deflation Theory of Great Depressions
• Key problems debt and prices
– The “two dominant factors” which cause depressions
are “over-indebtedness to start with and deflation
following soon after”
• “Thus over-investment and over-speculation are often
important; but they would have far less serious results
were they not conducted with borrowed money. That is,
over-indebtedness may lend importance to overinvestment or to over-speculation. The same is true as
to over-confidence. I fancy that over-confidence seldom
does any great harm except when, as, and if, it beguiles
its victims into debt.” (Fisher 1933: 341)
– When overconfidence leads to overindebtedness, a
chain reaction ensues:
Debt Deflation Theory of Great Depressions
• “(1) Debt liquidation leads to distress selling and to
• (2) Contraction of deposit currency, as bank loans are
paid off, and to a slowing down of velocity of circulation.
This contraction of deposits and of their velocity,
precipitated by distress selling, causes
• (3) A fall in the level of prices, in other words, a swelling
of the dollar. Assuming, as above stated, that this fall of
prices is not interfered with by reflation or otherwise,
there must be
• (4) A still greater fall in the net worths of business,
precipitating bankruptcies and
Debt Deflation Theory of Great Depressions
• (5) A like fall in profits, which in a "capitalistic," that is, a
private-profit society, leads the concerns which are
running at a loss to make
• (6) A reduction in output, in trade and in employment of
labor. These losses, bankruptcies, and unemployment, lead
to
• (7) Pessimism and loss of confidence, which in turn lead
to
• (8) Hoarding and slowing down still more the velocity of
circulation. The above eight changes cause
• (9) Complicated disturbances in the rates of interest, in
particular, a fall in the nominal, or money, rates and a rise
in the real, or commodity, rates of interest.” (1933: 342)
Debt Deflation Theory of Great Depressions
• Fisher thus concurs with ancient charge against usury,
that “it maketh many bankrotts” (Jones 1989: 55)
• While such a fate largely individual in a feudal system, in
a capitalist economy a chain reaction ensues which leads
the entire populace into crisis
• Theory nonequilibrium in nature
– argues that “we may tentatively assume that,
ordinarily and within wide limits, all, or almost all,
economic variables tend, in a general way, towards a
stable equilibrium”
• but though stable, equilibrium is “so delicately poised
that, after departure from it beyond certain limits,
instability ensues” (Fisher 1933: 339).
Debt Deflation Theory of Great Depressions
• Two classes of far from equilibrium events explained:
– Great Depression, when overindebtedness coincides
with deflation
• with deflation on top of excessive debt, “the more
debtors pay, the more they owe. The more the economic
boat tips, the more it tends to tip. It is not tending to
right itself, but is capsizing” (Fisher 1933: 344).
• Cycles, when one occurs without the other
– with only overindebtedness or deflation, economic
growth eventually corrects situation; it
• “is then more analogous to stable equilibrium: the more
the boat rocks the more it will tend to right itself. In
that case, we have a truer example of a cycle” (Fisher
1933: 344-345)
Debt Deflation Theory of Great Depressions
•
•
•
•
Fisher’s new theory ignored
Old theory made basis of modern finance theory
Debt deflation theory revived in modern form by Minsky
Fisher’s macroeconomic contribution (which emphasised
the need for reflation and “100% money” during the
Depression) overshadowed by Keynes’s “General Theory”
• Many similarities and synergies in Keynes and Fisher, but
different countries meant one largely unaware of others
work
Keynes and Debt-deflation
• Some consideration of debt-deflation in General Theory
when discussing reduction in money wages (neoclassical
proposal):
– “Since a special reduction of money-wages is always
advantageous to an individual entrepreneur ... a general
reduction … may break through a vicious circle of
unduly pessimistic estimates of the marginal efficiency
of capital … On the other hand, the depressing
influence on entrepreneurs of their greater burden of
debt may partially offset any cheerful reactions from
the reductions of wages. Indeed if the fall of wages
and prices goes far, the embarrassment of those
entrepreneurs who are heavily indebted may soon reach
the point of insolvency—with severe adverse effects on
investment.” (Keynes 1936: 264)
Keynes and Debt-deflation
– “The method of increasing the quantity of money in
terms of wage-units by decreasing the wage-unit
increases proportionately the burden of debt; whereas
the method of producing the same result by increasing
the quantity of money whilst leaving the wage-unit
unchanged has the opposite effect. Having regard to
the excessive burden of many types of debt, it can
only be an inexperienced person who would prefer the
former.” (1936: 268-69)
– Keynes’s focus here more physical and macro (impact
on investment) than Fisher; Keynes’s main
contributions on finance relate to
• Dual Price Level hypothesis
• Analysis of expectations and behaviour of finance
markets
Keynes and the Dual Price Level Hypothesis
• In most of General Theory, Keynes argued that
investment motivated by relationship between marginal
efficiency of investment schedule (MEI) and the rate of
interest
• In Chapter 17 of General Theory, “The General Theory of
Employment” and “Alternative theories of the rate of
interest” (1937), instead spoke in terms of two price
levels
– investment motivated by the desire to produce “those
assets of which the normal supply-price is less than
the demand price” (Keynes 1936: 228)
• Demand price determined by prospective yields,
depreciation and liquidity preference.
• Supply price determined by costs of production
Keynes and the Dual Price Level Hypothesis
• Two price level analysis becomes more dominant
subsequent to General Theory:
– The scale of production of capital assets “depends, of
course, on the relation between their costs of
production and the prices which they are expected to
realise in the market.” (Keynes 1937a: 217)
– MEI analysis akin to view that uncertainty can be
reduced “to the same calculable status as that of
certainty itself” via a “Benthamite calculus”, whereas
the kind of uncertainty that matters in investment is
that about which “there is no scientific basis on which
to form any calculable probability whatever. We simply
do not know.” (Keynes 1937a: 213, 214)
Keynes and the Dual Price Level Hypothesis
• In the midst of incalculable uncertainty, investors form
fragile expectations about the future
• These are crystallised in the prices they place upon
capital asset
• These prices are therefore subject to sudden and violent
change
– with equally sudden and violent consequences for the
propensity to invest
• Seen in this light, the marginal efficiency of capital is
simply the ratio of the yield from an asset to its current
demand price, and therefore there is a different
“marginal efficiency of capital” for every different level
of asset prices (Keynes 1937a: 222)
Keynes on Uncertainty and Expectations
• Three aspects to expectations formation under true
uncertainty
– Presumption that “the present is a much more
serviceable guide to the future than a candid
examination of past experience would show it to have
been hitherto”
– Belief that “the existing state of opinion as expressed
in prices and the character of existing output is based
on a correct summing up of future prospects”
– Reliance on mass sentiment: “we endeavour to fall back
on the judgment of the rest of the world which is
perhaps better informed.” (Keynes 1936: 214)
• Fragile basis for expectations formation thus affects
prices of financial assets
Keynes on Finance Markets
• Conventional theory says prices on finance markets
reflect net present value capitalisation of expected
yields of assets
• But, says Keynes, far from being dominated by rational
calculation, valuations of finance markets reflect
fundamental uncertainty and are driven by whim:
– “all sorts of considerations enter into the market
valuation which are in no way relevant to the
prospective yield” (1936: 152)
•
•
•
•
ignorance
day to day instability
waves of optimism and pessimism
“the third degree”
Keynes on Finance Markets
• Ignorance due to dispersion of share ownership (shades
of the Internet Bubble, Nasdaq 2000?):
– “As a result of the gradual increase in the proportion
of equity ... owned by persons who ... have no special
knowledge ... of the business... the element of real
knowledge in the valuation of investments ... has
seriously declined” (1936: 153)
• Impact of day to day fluctuations
– “fluctuations in the profits of existing investments,
which are obviously of an ephemeral and nonsignificant character, tend to have an altogether
excessive, and even an absurd, influence on the
market” (1936: 153-54)
Keynes on Finance Markets
• Waves of optimism and pessimism
– “In abnormal times in particular, when the hypothesis
of an indefinite continuance of the existing state of
affairs is less plausible than usual ... the market will be
subject to waves of optimistic and pessimistic
sentiment, which are unreasoning and yet in a sense
legitimate where no solid basis exists for a reasonable
calculation.” (1836: 154)
• “The Third Degree”
– Professional investors further destabilise the market
by attempting to anticipate its short term movements
and react more quickly
• As Geoff Harcourt once remarked, Keynes “writes like an
angel”. The next few slides are in Keynes’s own words.
Keynes on Finance Markets
• “It might have been supposed that competition between
expert professionals ... would correct the vagaries of the
ignorant individual... However,... these persons are, in
fact, largely concerned, not with making superior longterm forecasts of the probable yield of an investment
over its whole life, but with foreseeing changes in the
conventional basis of valuation a short time ahead of the
general public... For it is not sensible to pay 25 for an
investment of which you believe the prospective yield to
justify a value of 30, if you also believe that the market
will value it at 20 three months hence.” (1936: 154-55)
Keynes on Finance Markets
• “Of the maxims of orthodox finance none, surely, is more
anti-social than the fetish of liquidity, the doctrine that
it is a positive virtue on the part of investment
institutions to concentrate their resources upon the
holding of ‘liquid’ securities. It forgets that there is no
such thing as liquidity of investment for the community
as a whole. The social object of skilled investment should
be to defeat the dark forces of time and ignorance which
envelop our future. The actual, private object of most
skilled investment today is ‘to beat the gun’, as the
Americans so well express it, to outwit the crowd, and to
pass the bad, or depreciating, half-crown to the other
fellow.” (1936: 155)
Keynes on Finance Markets
• “professional investment may be likened to those
newspaper competitions in which the competitors have to
pick out the six prettiest faces from a hundred
photographs, the prize being awarded to the competitor
whose choice most nearly corresponds to the average
preferences of the competitors as a whole; ... It is not a
case of choosing those which, to the best of one's
judgment, are really the prettiest, nor even those which
average opinion genuinely thinks the prettiest. We have
reached the third degree where we devote our
intelligences to anticipating what average opinion expects
the average opinion to be. And there are some, I believe,
who practise the fourth, fifth and higher degrees.”
(1936: 156)
Keynes on Finance Markets
• “If the reader interjects that there must surely be large
profits to be gained from the other players in the long
run by a skilled individual who, unperturbed by the
prevailing pastime, continues to purchase investment on
the best genuine long-term expectations he can frame, he
must be answered, first of all, that there are, indeed,
such serious-minded individuals and that it makes a vast
difference to an investment market whether or not they
predominate in their influence over the game-players. But
we must also add that there are several factors which
jeopardise the predominance of such individuals in
modern investment markets.”
Keynes on Finance Markets
• “Investment based on genuine long-term expectation is so
difficult today as to be scarcely practicable. He who
attempts it must surely lead much more laborious days
and run greater risks than he who tries to guess better
than the crowd how the crowd will behave; and, given
equal intelligence, he may make more disastrous mistakes.
There is no clear evidence from experience that the
investment policy which is socially advantageous coincides
with that which is most profitable. It needs more
intelligence to defeat the forces of time and ignorance
than to beat the gun.”
Keynes on Finance Markets
• “Moreover, life is not long enough;--human nature desires
quick results, there is a peculiar zest in making money
quickly, and remoter gains are discounted by the average
man at a very high rate. The game of professional
investment is tolerably boring and over-exacting to
anyone who is entirely exempt from the gambling instinct;
whilst he who has it must pay to this propensity the
appropriate toll.”
• “Furthermore, an investor who proposes to ignore nearterm market fluctuations needs greater resources for
safety and must not operate on so large a scale, if at all,
with borrowed money...”
Keynes on Finance Markets
• “Finally it is the long-term investor ... who will in practice
come in for most criticism, wherever investment funds
are managed by committees or banks. For it is in the
essence of his behaviour that he should be eccentric,
unconventional and rash in the eyes of average opinion. If
he is successful, that will only confirm the general belief
in his rashness; and if in the short run he is unsuccessful,
which is very likely, he will not receive much mercy.
Worldly wisdom teaches us that it is better for
reputation to fail conventionally than to succeed
unconventionally.” (Keynes 1936: 156-58)
Keynes plus Fisher plus Kalecki
• Keynes thus augments Fisher
– Fisher explains the dynamic consequences of
overindebtedness and deflation
– Keynes explains how expectations formation can lead
to excessive valuations being placed upon financial
assets
• Kalecki explains the link between finance and real
investment with “The Principle of Increasing Risk”
(Kalecki 1937, 1990: 285-293)
– Rejects argument that conditions of production
(relation of marginal cost to marginal revenue)
determine level of investment
The Principle of Increasing Risk
• Consider entrepreneur with capital k to invest, given
method of production, expected stream of returns and
hence an expected internal rate of return e. These can be
combined to yield the prospective gross profit
  k e
• Prospective net gain g derived by deducting market
rate of return r, and allowance for riskiness, s.
g    r  s  k
The Principle of Increasing Risk
• Micro theory assumes
– expected gain g is a function of capital employed k
– function has a single maximum turning point
(diminishing returns again)
– the second differential of g with respect to k is
negative.
– The zero of first differential therefore tells us the
optimal amount of capital to invest
– condition for the maximum prospective gain is
dg d d

  r  s   k 
dk dk dk
dg d
 dr ds 

 r  s   k  

0
dk dk
 dk dk 
The Principle of Increasing Risk
• Conventional micro
– expected profit  increasing but diminishing
function of capital k
– no relationship between capital and the interest
rate or capital and risk:
dr ds
dk

dk
0
• So that optimal investment condition is
dg d
Firm invests until rate of change

  r  s   k  0  0  0
of profit wrt capital equals sum
dk dk
of market return plus risk
d
 r  s 
premium for investment
dk
The Principle of Increasing Risk
• Colloquial explanation: amount of investment is
constrained either by diseconomies of scale as k rises, or
by imperfect competition (or similar real barriers to
expansion).
• Kalecki rejects both
– “True, every machine has an optimum size, but why not
have 10 (or more) machines of this type?”,
– not relevant when an investor can put his funds into a
portfolio of projects across a range of industries.
• d/dk therefore constant
• no effective real (non-monetary) barrier to the optimal
size of k for a single investor (Kalecki 1937: 286-287)
The Principle of Increasing Risk
– Instead to expand k, investor must borrow
– the more he borrows the greater is his risk s.
– If investor not cautious, then “it is the creditor who
imposes on his calculation the burden of increasing
risk, charging the successive portions of credits above
a certain amount with a rising rate of interest” (1937:
288).
– Thus
either
dr
ds
d
 dr ds 
 0 or
 0 and
 k 

0
dk
dk
dk
 dk dk 
– for maximum profitable size of investment
– so increasing risk (and conditions of finance)
restrains the size of an individual capitalist’s
investment, not physical yield of investment.
The Principle of Increasing Risk
• Principle of Increasing Risk provides a link between
finance and investment
• Finance thus limits entrepreneur’s investment.
• Same conclusion reached by Keynes in 1937:
– “it is, to an important extent, the `financial’ facilities
which regulate the pace of new investment”
– Not a lack of savings which inhibits investment, but a
lack of finance consequent upon “too great a press of
uncompleted investment” (Keynes 1937b: 247)
– Causal loop is thus FinanceInvestmentSavings
rather than InvestmentSavings as in GT or
SavingsInvestment as in neoclassical economics
• Schumpeter also emphasises importance of finance in
theory of entrepreneurial change:
Schumpeter’s model: money has real effects
• Schumpeter’s finance-real economy link
– Schumpeter
– Entrepreneurs must borrow to finance innovations
– Credit thus plays essential role in economy’s
boom/bust cycle
Schumpeter’s model: money has real effects
• In Schumpeter’s model, entrepreneurs start new firms
– No retained earnings, capital, workers
• “…the carrying out of new combinations takes place
through the withdrawal of services of labor and land
from their previous employments…
• this again leads us to … the heresy that money, and …
other means of payment, perform an essential function,
– hence that processes in terms of means of payment
are not merely reflexes of processes in terms of
goods.
• In every possible strain, with rare unanimity, even with
impatience and moral and intellectual indignation, a very
long line of theorists have assured us of the opposite.”
(Schumpeter p. 95)
Schumpeter’s model: money has real effects
• Conventional interpretation of money emphasises
– Money simply a “veil over barter”
– Money plays no essential role
• Double all prices & incomes, no-one better or worse off
• Schumpeter accepts above as true for existing products,
production techniques, etc., in general equilibrium
• But new products, new methods, disturb “the circular
flow”. Money plays essential role in this disequilibrium
phenomenon
– Affects the price level and output
– Doubling all prices & incomes would make some better
off, some worse
• Those with debts would be better off
– Including entrepreneurs…
Schumpeter’s model: money has real effects
• Conventional theory suffers from “barter illusion”
– Existing producers using existing production methods
exchanging existing products
• “Walras’ Law” applies
• Major role of finance is initiating new products /
production methods etc.;
• For these equilibrium-disturbing events, classic “money a
veil over barter” concept cannot apply.
– “From this it follows, therefore, that in real life total
credit must be greater than it could be if there
were only fully covered credit. The credit structure
projects not only beyond the existing gold basis, but
also beyond the existing commodity basis.” (101)
• “Walras’ Law” therefore false for growing economy…
Schumpeter’s model: credit has real effects
• “[T]he entrepreneur needs credit …
• [T]his purchasing power does not flow towards him
automatically, as to the producer in the circular flow, by
the sale of what he produced in preceding periods.
• If he does not happen to possess it … he must borrow it…
He can only become an entrepreneur by previously
becoming a debtor…
• his becoming a debtor arises from the necessity of the
case and is not something abnormal, an accidental event
to be explained by particular circumstances. What he
first wants is credit. Before he requires any goods
whatever, he requires purchasing power. He is the
typical debtor in capitalist society.” (102)
Schumpeter’s model: credit has real effects
• In normal productive cycle, income from production
finances purchases; credit can be used, but not essential
– “[T]he decisive point is that we can, without
overlooking anything essential, represent the process
within the circular flow as if production were currently
financed by receipts.” (104)
• Effectively, Say’s Law applies: “supply creates its own
demand”
• Aggregate demand equals aggregate supply (with maybe
some sectors above, some sectors below)
– But credit-financed entrepreneurs very different
• Expenditure (demand) not financed by current receipts
(supply) but by credit
• Aggregate Demand exceeds Aggregate Supply
Schumpeter’s model: credit has real effects
• Credit finance for entrepreneurs thus endogenous: not
“deposits create loans” but “loans create deposits”:
– “[I]n so far as credit cannot be given out of the
results of past enterprise … it can only consist of
credit means of payment created ad hoc, which can be
backed neither by money in the strict sense nor by
products already in existence...
– It provides us with the connection between lending and
credit means of payment, and leads us to what I
regard as the nature of the credit phenomenon.” (106)
Schumpeter’s model: credit has real effects
• “[G]iving credit involves creating purchasing power, and
newly created purchasing power is of use only in giving
credit to the entrepreneur,… credit is essentially the
creation of purchasing power for the purpose of
transferring it to the entrepreneur, but not simply the
transfer of existing purchasing power.
• The creation of purchasing power characterises, in
principle, the method by which development is carried out
in a system with private property and division of labor.
• By credit, entrepreneurs are given access to the social
stream of goods before they have acquired the normal
claim to it.” (106-107)
• Credit irrelevant to equilibrium economics, but essential
to disequilibrium process of economic development:
Schumpeter’s model: credit has real effects
• “… credit is not essential in the normal circular flow, because …
it can be assumed there that all purchases of production goods
by producers are cash transactions or that in general whoever
is a buyer previously sold goods of the same money value…”
• However “it is certain that there is such a gap to bridge in the
carrying out of new combinations. To bridge it is the function
of the lender, and he fulfils it by placing purchasing power
created ad hoc at the disposal of the entrepreneur.
• Then those who supply production goods need not "wait" and
yet the entrepreneur need advance them neither goods nor
existing money. Thus the gap is closed which would otherwise
make development extraordinarily difficult, if not impossible in
an exchange economy where private property prevails.” (107)
• So process of innovation & change breaches Say’s Law: in
growing, changing economy
– Demand exceeds receipts from current sales
– Difference financed by credit (debt) to entrepreneurs
Schumpeter’s model: credit has real effects
• Say’s Law & Walras’ Law apply in circular flow, but not
entrepreneurial credit-financed activity:
– “In the circular flow, from which we always start, the
same products are produced every year in the same
way. For every supply there waits somewhere in the
economic system a corresponding demand, for every
demand the corresponding supply. All goods are dealt
in at determined prices with only insignificant
oscillations, so that every unit of money may be
considered as going the same way in every period. A
given quantity of purchasing power is available at any
moment to purchase the existing quantity of original
productive services, in order then to pass into the
hands of their owners and then again to be spent on
consumption goods.” (108)
Aside: “Marx with different adjectives”
• Schumpeter’s thinking here very similar to Marx
– Marx argued there were two “Circuits of Capital”
• Commodity—Money—Commodity
– Equivalent to Schumpeter’s “circular flow”
– Essentially Say’s Law applies
• Sellers only sell in order to buy
• Money—Commodity—Money
– Equivalent to Schumpeter’s entrepreneurial function
•Schumpeter’s
– Say’s Law doesn’t apply: “The capitalist throws less
value in the form of money into the circulation than
point:
•Capitalist “throws he draws out of it... Since he functions ... as an
in” borrowed money industrial capitalist, his supply of commodity-value is
always greater than his demand for it. If his supply
•Succeeds if can
and demand in this respect covered each other it
repay debt and
would mean that his capital had not produced any
pocket some of the surplus-value... His aim is not to equalize his supply
gap
and demand, but to make the inequality between
them ... as great as possible.” (Marx 1885: 120-121)
Schumpeter’s model: credit has real effects
• “If now credit means of payment … are created and
placed at the entrepreneur's disposal, then … his
purchasing power [takes] its place beside the total
previously existing.
• Obviously this does not increase the quantity of
productive services existing in the economic system. Yet
"new demand" becomes possible in a very obvious sense.
• It causes a rise in the prices of productive services.
From this ensues the "withdrawal of goods" from their
previous use…” (108)
– Aggregate Demand exceeds Aggregate Supply; Say’s
Law violated in move from stationary state
• Sum of excess demands negative (not zero as in Walras’
Law)
– Credit-financed demand a source of price inflation…
Schumpeter’s model: credit has real effects
• “Just as when additional gas streams into a vessel the
share of the space occupied by each molecule of the
previously existing gas is diminished by compression, so
the inflow of new purchasing power into the economic
system will compress the old purchasing power.
• When the price changes which thus become necessary
are completed, any given commodities exchange for the
new units of purchasing power on the same terms as for
the old, only the units of purchasing power now existing
are all smaller than those existing before and their
distribution among individuals has been shifted.” (109)
• This inflation
– Isn’t necessarily a bad thing
– Can be reversed by dynamics of economic development
Schumpeter’s model: credit has real effects
• “credit inflation .. is distinguished from … inflation for
consumptive purposes by a very essential element…
• The entrepreneur must not only legally repay money to
his banker, but he must also economically repay
commodities to the reservoir of goods …
• after a period at the end of which his products are on
the market and his productive goods used up - he has, if
everything has gone according to expectations, enriched
the social stream with goods whose total price is greater
than the credit received and than the total price of the
goods directly and indirectly used up by him.
• Hence the equivalence between the money and commodity
streams is more than restored, the credit inflation more
than eliminated, the effect upon prices more than
compensated for.” (110)
Schumpeter’s model: credit has real effects
• “Furthermore, the entrepreneur can now repay his debt
(amount credited plus interest) at his bank, and normally
still retain a credit balance (= entrepreneurial profit)
that is withdrawn from the purchasing-power fund of the
circular flow.” (111)
• So dynamic view of economy
– Overturns “money doesn’t have real effects” bias of
neoclassicals/monetarists
– Breaches “supply creates its own demand” Say’s Law
view of self-equilibrating economy
– Breaches Walras’ Law “if n-1 markets in equilibrium, nth
also in equilibrium” general equilibrium analysis
– Links finance and economics: without finance there
would not be economic growth, but
– Finance can affect economic growth negatively as well
as positively (if entrepreneurial expectations fail)…
Integration: Financial Instability Hypothesis
• Concepts of
– Fisher: debt deflationary mechanism, role of
commodity price inflation
– Schumpeter: entrepreneurial role of credit
– Keynes: two price levels, expectations formation under
uncertainty, behaviour of financial markets,
FinanceInvestmentSavings causal loop
– Kalecki: Finance as one of two limits on amount of
investment
– Marx:
• Tendency to cycles & crisis in capitalism
• Blended by Minsky to produce Financial Instability
Hypothesis
Integration: Fisher
• Fisher’s distinctly non-equilibrium reasoning appears in
Minsky 1962
– “However, for any unit, capital losses and gains are not
symmetrical: there is a ceiling to the capital losses a
unit can take and still fulfil its commitments. Any loss
beyond this limit is passed on to its creditors by way
of default or refinancing of the contracts. Such
induced capital losses result in a further contraction
of consumption and investment beyond that due to the
initiating decline in income. This can result in a
recursive debt-deflation process.” (1963, 1982: 6-7)
Integration: Keynes
• Pre-’68, Minsky’s view of Keynes is IS-LM:
– “If we make the Keynesian assumption that
consumption demand is independent of interest rates,
but assume that investment demand, and hence the b
coefficient, depends on interest rates, then a rising
set of interest rates will lower the b coefficient.”
(Minsky 1965, 1982: 262)
• 1968: “The General Theory of Employment” (Keynes 1937) turns up in
Minsky’s bibliography
– Uncertainty, expectations, dual price level start to enter Minsky’s
theory
– Keynesian aspects of Minsky’s thought well-known. But his “endpoint appears more Marxian:
Integration: Marx
• In simple terms, Marx says:
– “If we observe the cycles in which modern industry
moves—state
of
inactivity,
mounting
revival,
prosperity, over-production, crisis, stagnation, state
of inactivity, etc.,… —we shall find that a low rate of
interest generally corresponds to periods of
prosperity … a rise in interest separates prosperity
and its reverse, and a maximum of interest up to a
point of extreme usury corresponds to the period of
crisis…” (Marx 1894: 360-61)
• But more generally:
Integration: Marx
• “As concerns the circulation between capitalists, a period
of brisk business is simultaneously, a period of most
elastic and easy credit.”
– But easy credit leads to a crisis in which “prices fall,
similarly wages; the number of employed labourers is
reduced, the mass of transactions decreases” (Marx
1894: 448)
• “It is by no means the strong demand for loans which
distinguishes the period of depression from that of
prosperity, but the ease with which this demand is
satisfied in periods of prosperity, and the difficulties it
meets in times of depression.” (Marx 1894: 450)
Integration: Marx
• Finally, the perils of letting bankers take over capitalism:
– “...The credit system, which has its focus in the socalled national banks and the big money-lenders and
usurers surrounding them, constitutes enormous
centralisation, and gives this class of parasites the
fabulous power, not only to periodically despoil
industrial capitalists, but also to interfere in actual
production in a most dangerous manner—and this gang
knows nothing about production and has nothing to do
with it." (Marx 1894: 544-45)
Integration: Financial Instability Hypothesis
• “capitalism is inherently flawed, being prone to booms,
crises and depressions. This instability, in my view, is due
to characteristics the financial system must posses if it
is to be consistent with full-blown capitalism. Such a
financial system will be capable of both generating signals
that induce an accelerating desire to invest and of
financing that accelerating investment.” (1969: 224)
• A Marxian view of crises in capitalism
– Inherent, not exogenous
– Cyclical, not equilibrium
• The overall thesis in precis:
Financial Instability Hypothesis
• Economy in historical time
• Debt-induced recession in recent past
• Firms and banks conservative re debt/equity ratios, asset
valuation
• Only conservative projects are funded
• Recovery means conservative projects succeed
• Firms and banks revise risk premiums
– Accepted debt/equity ratio rises
– Assets revalued upwards
The Euphoric Economy
• Self-fulfilling expectations
– Decline in risk aversion causes increase in investment
• Investment expansion causes economy to grow faster
– Asset prices rise, making speculation on assets
profitable
– Increased willingness to lend increases money supply
(endogenous money)
– Riskier investments enabled, asset speculation rises
• The emergence of “Ponzi” (Bondy?) financiers
– Cash flow from “investments” always less than debt
servicing costs
– Profits made by selling assets on a rising market
– Interest-rate insensitive demand for finance
The Assets Boom and Bust
• Initial profitability of asset speculation:
– reduces debt and interest rate sensitivity
– drives up supply of and demand for finance
– market interest rates rise
• But eventually:
– rising interest rates make many once conservative
projects speculative
– forces non-Ponzi investors to attempt to sell assets to
service debts
– entry of new sellers floods asset markets
– rising trend of asset prices falters or reverses
Crisis and Aftermath
• Ponzi financiers go bankrupt:
– can no longer sell assets for a profit
– debt servicing on assets far exceeds cash flows
• Asset prices collapse, drastically increasing debt/equity
ratios
• Endogenous expansion of money supply reverses
• Investment evaporates; economic growth slows or
reverses
• Economy enters a debt-induced recession ...
• High Inflation?
– Debts repaid by rising price level
– Economic growth remains low: Stagflation
– Renewal of cycle once debt levels reduced
Crisis and Aftermath
• Low Inflation?
– Debts cannot be repaid
– Chain of bankruptcy affects even non-speculative
businesses
– Economic activity remains suppressed: a Depression
• Big Government?
– Anti-cyclical spending and taxation of government
enables debts to be repaid
– Renewal of cycle once debt levels reduced
Weaknesses in Dual Price Level Analysis
• Fisher, Keynes, Minsky originate in
Marshallian/neoclassical tradition
• Micro theory based on utility maximisation, marginal cost
pricing, equilibrium
• Difficult to explain two price levels on this analysis
• Different theoretical foundation needed for price
analysis:
– Back to Marx
• Direct inspiration only for Kalecki of above
• But Marx’s dialectical theory provides a
“microfoundation” for Dual Price Hypothesis
– At least two price levels in capitalism
• Commodities: markup on cost of production
• Labour: “class struggle” wage setting
• Assets: expectations of uncertain future gain
• And other dynamics (new products…)
Marx and the Dual Price Level Hypothesis
• Marx’s early theory of value based on labour
• Value is socially necessary labour-time
– An effort theory of value vs utility theory as per
neoclassicals
• Labour the source of all value
– Equilibrium exchange value of all commodities reflects
socially necessary labour--time contained in them
• Analysis of money an extension of this
– gold the money commodity
– price of gold reflects socially necessary labour-time
required to produce gold
– Fairly pedestrian analysis; however…
Marx and the Dual Price Level Hypothesis
• Alternative monetary analysis exists in Capital I after
Chapter 7, and throughout Grundrisse and Theories of
Surplus Value.
• Based on philosophy of Dialectics
– Philosophy of Dynamics, developed by Hegel
• Sought to explain processes of social change
• Provides dynamic explanation of behaviour of prices for
financial assets
Marx and the Dual Price Level Hypothesis
• Essence of Dialectical social analysis:
– Any Unity (person, thing, etc.) exists in society
• Society focuses on some aspects of unity; brings to
foreground
• Forces other aspects into background
• But unity cannot exist without background aspects
• Dynamic tension created between
foreground/background aspects
• Tensions can transform unity/society itself
Dialectics
S o c ie ty
U n ity
Dialectical Tension
F o reg round
B ackg round
(But early on,
Marx’s philosophy
dominated by
reading of classical
economics)
Marx and the Dual Price Level Hypothesis
• “Discovery” of central application of dialectics to
economics by Marx somewhat tortuous
• “Revelation” occurs while writing Grundrisse, the “rough
draft” of Capital, after chance re-reading of Hegel
• Considering classical economists (Smith, Ricardo)
discussion of use-value and exchange-value and dismissal
of use-value
– “Utility then is not the measure of exchangeable value,
although it is absolutely essential to it.” (Ricardo 1819:
5-6)
– Price set solely by exchange-value (cost of
production), use-value a necessary pre-requisite but
irrelevant to price (contrast with neoclassical price
determination)
Marx and the Dual Price Level Hypothesis
• Before the Grundrisse and 1857, Marx accepted
Smith/Ricardo on use-value & exchange-value
– No role for use-value beyond pre-requisite to
exchange
• During drafting of Grundrisse, Marx realises these have
a dialectical form
– unity value
– capitalism brings exchange-value into foreground
– pushes use-value into background
– “A dialectic between use-value and exchange-value”,
muses Marx:
Marx and the Dual Price Level Hypothesis
• “Is not value to be conceived as the unity of use-value
and exchange-value? ... is value as such the general form,
in opposition to use-value and exchange-value as
particular forms of it? Does this have significance in
economics? ... If only exchange-value as such plays a role
in economics, then how could elements later enter which
relate purely to use-value... This is not in the slightest
contradicted by the fact that exchange-value is the
predominant aspect… In any case, this is to be examined
with exactitude in the examination of value, and not, as
Ricardo does, to be entirely abstracted from, nor like the
dull Say, who puffs himself up with the mere
presupposition of the word ‘utility’.” (Marx 1857: 267-68)
Marx and the Dual Price Level Hypothesis
• Dialectic between use-value and exchange-value becomes
Marx’s fundamental concept
• Believed (erroneously) that this supported preceding
labour theory of value
• Used to consider numerous other issues in economics,
including pricing of money (rate of interest) and capital
assets
• Provides a sound basis for two price level theory
• Bu first, application to labour and source of profit, wages
Marx and the Dual Price Level Hypothesis
• In capitalist, Exchange-Value of work brought to
foreground
– Exchange-Value of worker=subsistence wage
• Use-Value of worker in background: irrelevant to wage
– But Use-Value of worker to capitalist purchaser of
labour-time=ability to produce commodities for sale
• Gap between (objective, quantitative) UV and EV of
worker is source of surplus-value (SV)
– “The past labour that is embodied in the labour power,
and the living labour that it can call into action; the
daily cost of maintaining it, and its daily expenditure in
work, are two totally different things. The former
determines the exchange value of the labour power,
the latter is its use-value.” (Marx 1867: 199)
Marx and the Dual Price Level Hypothesis
• Exchange-Value of machine: cost of production
• Use-Value of machine: ability to produce commodities for
sale, as with worker
• As with worker, gap between Use-Value & ExchangeValue: machine a source of Surplus Value
• Contradicts Labour Theory of Value
– All commodity inputs to production potential source of
profits
• As an aside:
– No “transformation problem”
– No tendency for rate of profit to fall
– No inevitability of socialism
Marx and the Dual Price Level Hypothesis
• Dialectical method extended by Marx when considering
“peculiar” commodities labour-time and money
• Labour-time and money are both commodities and noncommodities
– Commodities: bought and sold on the market
– Non-commodities: not produced for profit; not
produced by means of other commodities
– Commodity/non-commodity dialectic additional to usevalue/exchange-value dialectic
Marx and the Dual Price Level Hypothesis
• Worker both a commodity (labor-power) and noncommodity (person)
• Capitalism focuses on commodity aspect, pushes noncommodity aspects into background
– Pure commodity—paid subsistence wage only
– Non-commodity—demands share in surplus
• Dialectical tension:
– struggle over minimum wage, social wage, etc.
– Wage normally exceeds subsistence; subsistence wage
a minimum (when commodity aspect dominant and
worker power minimal)
Marx and the Dual Price Level Hypothesis
• Money a commodity/non-commodity
– Exchanged, and essential for exchange,
– Not produced by means of commodities
“What ... is … the price of the loaned capital?... What
the buyer of an ordinary commodity buys is its usevalue; what he pays for is its value. What the borrower
of money buys is likewise its use-value as capital; but
what does he pay for? Surely not its price, or value, as
in the case of ordinary commodities.” (Marx 1894:
352)
• Dialectic of money: Exchange-value set by use-value
Marx and the Dual Price Level Hypothesis
• Rate of interest (“price” of a loan) set
– not by cost involved in issuing a loan
– but by the use-value of the loan itself, and
– “Its use-value, however, lies in producing profit”
(1892: 355. See also Marx 1861 Part III: 457-58).
• Result extended to assets (1861 III: 458-459; 1861II:
249; 1894: 353-356)
– Ricardo explains the price of minerals in situ on the
basis of their "value”
• but no labor (or capital) has gone into their production,
therefore they contain no value
• mining rights free if could purchase for cost of
production
Marx and the Dual Price Level Hypothesis
• But mining rates have obvious potential quantitative usevalue:
– Quantitative use-value of minerals in situ:
• expected sale price of the estimated quantity of ore
• As with loaned capital, exchange-value of assets is
determined not by their costs of production, but by
their perceived use-value
– that of being a potential source of exchange-value
– But uncertainty fundamental aspect of price
• Thus two broad classes of commodities
– Standard commodities, price determined by exchangevalue (cost of production)
– Non-commodities, determined in part by use-value
Marx and the Dual Price Level Hypothesis
• Non-commodities include
– Labour-time (Hence struggle over distribution of
income)
– Money (Hence interest rate for loans)
– Capital assets (Hence speculative and cyclical prices
for shares, companies, etc.)
– Capital equipment (Hence machinery prices procyclical; Also claimed by Minsky 1982: 64, 80))
– New products (Not yet part of input-output scheme,
hence not yet full commodities)
Marx and the Dual Price Level Hypothesis
• Hence Marx provides a firm basis for 2 price level
analysis of Fisher, Keynes, Minsky
– commodities cost-price
• profits made as realisation of surplus generated in
production
– with problem of effective demand, etc.
– assets speculative
• prices rise and fall with trade cycle
• debt accumulation a necessary component of asset
dynamics
Developing the Dual Price Level Analysis
• Minsky’s Financial Instability Hypothesis (FIH) most
developed state of Dual Price Level Analysis of finance
– But models of FIH very basic compared to models of
MPT
• Related references include Andresen, T., 1996; Asada,
1989; Isaac, A.G., 1991; Jarsulic, M., 1989; Keen, S.,
1995; Semmler, W., 1986; Skott, P., 1989
– Complete model still not developed
• To develop such models
– cannot use equilibrium methodology of simultaneous
algebraic equations, since processes are far from
equilibrium
– Instead must use Differential Equations and related
dynamic techniques
Mathematical essentials
– Essential component of Minsky’s theory is proposition
that expectations rise when economic activity is
stable.
– Can express this as
• % rate of growth of expectations = function(rate of
economic growth, or level of profit)
• % rate of growth of X = dX/dt divided by X
• we get
1 dE
 1 dY 

 f 

E dt
 Y dt 
– A Ordinary Differential Equation (ODE)
Mathematical essentials
• ODEs related to differentiation (as done in Maths 1.3)
• But added complication that an ODE is normally a
function of itself plus the underlying variable.
• E.g., above Minskian relation (this time with level of
profit  rather than rate of growth of output as
argument) is
1 dE

 f  
E dt
• This rearranges to
dE
 E  f    g E t ,  t 
dt
• This is a function of E and  (which are functions of
time t)
Mathematical essentials
• ODEs are thus more complex than differentiation per se
– vast majority of ODEs cannot be solved
– but
• can simulate numerically
• model using block diagrams
• ODEs only a partial rendition of real world systems
– use only one underlying determining variable (time),
thus pretend that all events happen in the same place
• Partial Differential Equations (PDEs) used for > 1
variable, but more complex (and more limited)
mathematics
– ignore change in parameter values over time, but real
world processes involve changing parameters
(evolution)
Mathematical essentials
• However understanding of ODEs needed as basis to
understand all other techniques
• Building block for analysis needed to model conventional
approach that finance markets are stable processes
subject to external shocks
• Tomorrow, introductory ODEs Part One.
– Bring a pad and pen/pencil for some tutorials on
differentiation, solving sample problems, etc.
– Necessarily a mini-maths course, but I will try to keep
the focus on the main game of attempting to model the
real world process of debt deflation.