Financial Economics Lecture Eleven

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Financial Economics Lecture Eleven

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Title: Financial Economics Lecture Eleven

1
Financial Economics Lecture Eleven

More on Minsky
Modelling endogenous money/debt deflation

2
Brief HET of Minsky

Parents met at a Communist Party social function
No prizes for guessing early formative
influences!
Fought in US Army in WWII, decamped post-war to
do a degree
Educated during McCarthyist communist witch
hunt periodno mention ever of Marx in his
research, for obvious reasons
Began with degree in mathematics, attempted to
build mathematical model of trade cycle based on
Hickss difference equation model, extended by
Kaleckis principle of increasing risk (last
lecture)

3
Brief HET of Minsky

Kalecki argued investment restrained by
increasing risk (uncertainty-style!) as capital
grows
Minsky used this at macro level to give an
otherwise explosive model of trade cycle a
turning point
Model was

Where Minsky made b a variable dependent on
financial conditions
b declines as economy grows, thus giving turning
point to upward explosive movement
"the accelerator coefficient ... is in part based
on the productive efficiency of investment, but
it is also related to the willingness of
investors to take risks and the terms in which
investors can finance their endeavours..."
(Minsky 1965 261)

4
Brief HET of Minsky

Model went nowhere, but Minsky began to explore
implications of finance for economic behaviour
Initially tried to do this from conventional
understanding of Keynes
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)
Also got nowhere
Then, one day, by chance, he read Keyness 1937
papers

5
Brief HET of Minsky

In 1969, Minsky states that his own ideas about
uncertainty "seem to be consistent with those of
Keynes" (1969a, 1982 191, footnote 6), citing
Keynes 1937
Eventually concludes
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. (Minsky 1969b 224)

6
Brief HET of Minsky

Basic model outlined in previous lecture from
now on, consider how to produce economic
(mathematical) model of process Minsky describes
First, some mathematical preliminaries
Minskys model essentially dynamic, and therefore
cannot be modelled either using equilibrium tools
or static drawings
Basic tool of dynamic analysis is the
differential equation
Quick introduction to this, then
Graphical tools for simulating dynamic processes
Insights from endogenous money argument

7
Dynamic modellingan introduction

Dynamic systems necessarily involve time
Simplest expression starts with definition of the
percentage rate of change of a variable
Population grows at 1 a year
Percentage rate of change of a variable x is
Slope of function w.r.t. time (dx/dt)
Divided by current value of variable (x)
So this is mathematically

This can be rearranged to

Looks very similar to differentiation, which you
have done but essential difference rate of
change of x is some function of value of x itself.

8
Dynamic modellingan introduction

Dependence of rate of change of variable on its
current value makes solution of equation much
more difficult than solution of standard
differentiation problem
Differentiation also normally used by economists
to find minima/maxima of some function
Profit is maximised where the rate of change of
total revenue equals the rate of change of total
cost (blah blah blah)
Take functions for TR, TC
Differentiate
Equate
Easy! (also wrong, but thats another story)
However differential equations

9
Dynamic modellingan introduction

Have to be integrated to solve them

Rearrange
Integrate
Solve
Take exponentials

Constant is value of x at time t0

10
Dynamic modellingan introduction

Simple model like this gives
Exponential growth if agt0
Exponential decay if alt0
But unlike differentiation technique (most
functions can be differentiated)
Most functions cant be integrated no simple
solution can be found and also
Models can also be inter-related
x can depend on itself and y
y can depend on itself and x
Models end up much more complicated

11
Dynamic modellingan introduction

Simple example relationship of fish and sharks.
In the absence of sharks, assume fish population
grows smoothly
The rate of growth of the fish population is a
p.a.

Rearrange
Integrate
Solve
Exponentials
12
Dynamic modellingan introduction

Simulating gives exponential growth if agt0

13
Dynamic modellingan introduction

Same thing can be done for sharks in the absence
of fish
Rate of growth of shark population equals c p.a.
But here c is negative

But we know fish and sharks interact
The rate of change of fish populations is also
some (negative) function of how many Sharks there
are

The rate of change of shark population is also
some (positive) function of how many Fish there
are

14
Dynamic modellingan introduction

Now we have a model where the rate of change of
each variable (fish and sharks) depends on its
own value and the value of the other variable
(sharks and fish)

This can still be solved, with more effort (dont
worry about the maths of this!)

15
Dynamic modellingan introduction

But for technical reasons, this is the last level
of complexity that can be solved
Add an additional (nonlinearly related)
variablesay, seagrass levelsand model cannot be
solved
But there are other ways
Mathematicians have shown that unstable processes
can be simulated
Engineers have built tools for simulating dynamic
processes.

16
Dynamic modellingan introduction

Express model as vector equation

Provide values for constants a,b,c,d, initial
values for Fish, Shark numbers (ratio a/b gives
equilibrium for sharks, c/d for fish)

17
Dynamic modellingan introduction

Express as vector differential equation and
simulate using Runge-Kutta algorithm (like
sophisticated Taylors expansion)

18
Dynamic modellingan introduction

Graph results

A far from equilibrium model with just 2
variables and constant coefficients
System will never reach equilibrium
(What odds that the actual economy is in
equilibrium)

19
Dynamic modellingan introduction

Thats the hard way now for the easy way
Differential equations can be simulated using
flowcharts
The basic idea
Numerically integrate the rate of change of a
function to work out its current value
Tie together numerous variables for a dynamic
system
Consider simple population growth
Population grows at 2 per annum

20
Dynamic modellingan introduction

Representing this as mathematics, we get

Next stage of a symbolic solution is

Symbolically you would continue, putting dt on
the RHS but instead, numerically, you integrate

As a flowchart, you get

Read it backwards, and its the same equation

Feed in an initial value (say, 18 million) and we
can simulate it (over, say, 100 years)

21
Dynamic modellingan introduction

MUCH more complicated models than this can be
built

22
Dynamic modellingan introduction

Models can have multiple interacting variables,
multiple layers for example, a racing car
simulation

23
Dynamic modellingan introduction

System dynamics block has these components

And this block has the following components

24
Dynamic modellingan introduction

This is not toy software engineers use this
technology to design actual cars, planes,
rockets, power stations, electric circuits

25
Dynamic modellingan introduction

Lets use it to build the Fish/Shark model
Start with population model, only
Change Population to Fish
Alter design to allow different initial numbers

This is equivalent to first half of

To add second half, have to alter part of model
to LHS of integrator

26
Dynamic modellingan introduction

Sharks just shown as constant here

Sharks substract from fish growth rate

Now add shark dynamics

27
Dynamic modellingan introduction

Shark population declines exponentially, just as
fish population rises
(numbers obviously unrealistic)
Now add interaction between two species

28
Dynamic modellingan introduction

Model now gives same cycles as seen in
mathematical simulation.

Now to apply this to endogenous money!

29
Dynamic modellingan introduction

Some general principles
Dynamic models can (usually do) have unstable and
multiple equilibria
Systems often remain in permanent but changing
disequilibrium
Nonlinear relations essential for interesting
results (cycles without breakdown), but
Nonlinearity can arise naturally (e.g., price
times quantity gives nonlinear results) rather
than out of arbitrary assumed nonlinear
behaviours

30
Recap on principles of endogenous money

(1) Kydland and Prescott rule out deterministic
causes of business cycles on grounds that
"Theories with deterministic cyclical laws of
motion may a priori have had considerable
potential for accounting for business cycles but
in fact they have failed to do so. They have
failed because cyclical laws of motion do not
arise as equilibrium behaviour for economics with
empirically reasonable preferences and
technologiesthat is, for economies with
reasonable statements about people's ability and
willingness to substitute." (KP 5)
BUNKUM! Cant rule out far-from-equilibrium model
on basis of behaviour of a different equilibrium
model!
On the othe hand

31
Recap on principles of endogenous money

Circuitist results from Kaleckian algebra
Money prices independent of quantity of money,
etc
But Kaleckian identities presume equilibrium
while model of money formation required
disequilibrium otherwise level of money in
economy falls to zero
An assumption is therefore required for the
existence of a money stock, namely that
wage-earners spend their money incomes gradually
over time It is a necessary assumption if we do
not want money to disappear altogether from the
system. (6)
Need base model that generates cyclical,
far-from-equilibrium behaviour

32
Recap on principles of endogenous money

KP working from the data (rather than
theoretical leanings, as earlier)
"This finding that the real wage behaves in a
reasonably strong procyclical manner is counter
to a widely held belief in the literature." (KP
13-14)
Income distribution dynamics form part of the
trade cycle

33
Recap on principles of endogenous money

Model has to give credit a key role in cycles
"The fact that the transaction component of real
cash balances (M1) moves contemporaneously with
the cycle while the much larger nontransaction
component (M2) leads the cycle suggests that
credit arrangements could play a significant role
in future business cycle theory. Introducing
money and credit into growth theory in a way that
accounts for the cyclical behaviour of monetary
as well as real aggregates is an important open
problem in economics." (17)
Credit and debt go hand in hand
Credit money carries with it debt obligations
(whereas fiat or commodity money does not),
therefore debt dynamics are an important part of
the monetary system

34
Recap on principles of endogenous money

Blowout in inside to outside money ratios,
but Debt to broader money measures (M2, M3)
fairly constant
Debt a proxy for credit

(Dip in M2,3/M1 rise in Debt/M2,3 ratios due to
bailout activities in post-87/9 slump)
35
Recap on principles of endogenous money

Empirical work by Fama and French (Efficient
Markets Hypothesis proponents) finds
Debt seems to be the residual variable in
financing decisions. Investment increases debt,
and higher earnings tend to reduce debt. (1997)
The source of financing most correlated with
investment is long-term debt These correlations
confirm the impression that debt plays a key role
in accommodating year-by-year variation in
investment. (1998)

36
Recap on principles of endogenous money

Key activity in capitalist system is
accumulation
Marx sees market economy as dominated by desire
of capitalists to accumulate wealth
Accumulate! Accumulate! That is Moses and the
prophets! (Capital I, Ch 24.3 p. 558 Progress
Press)
Store of value and unit of account crucial here
what matters to capitalists is not consumption
per se, but accumulation. Abstract unit by which
to measure accumulation therefore vital
Accumulation of assets (bank balances, productive
capital) key activity in capitalism

37
Recap on principles of endogenous money

Key Circuitist insight cannot collapse banks and
firms into one sector
Banks and firms must be considered as two
distinct kinds of agents. Firms are present in
the market as sellers or buyers of commodities
and make recourse to banks in order to perform
their payments banks on the other hand produce
means of payment, and act as clearing houses
among firms. In any model of a monetary economy,
banks and firms cannot be aggregated into one
single sector. (Graziani 4)
Need to separate bank activities accumulation
from firm activities accumulation

38
Recap on principles of endogenous money

Fisher key role of excessive debt and falling
prices on economic processes
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).
Key roles of accumulation of debt and price
dynamics out of equilibrium

39
Recap on principles of endogenous money

Minsky on impact of Big Government?
Anti-cyclical spending and taxation of government
enables debts to be repaid
Renewal of cycle once debt levels reduced
Stability is not avoidance of cycles, but
avoidance of complete breakdown

40
Recap on principles of endogenous money

Can blend all these insights into model of
financial instability
Cyclical model of real economy Goodwins
predator-prey model
Driven by Phillips curve
Add debt as source of investment credit (a la
Fama French)
Debt as proxy for credit (endogenous money
component, accommodating as per Moore)
Government counter-cyclical spending as
stabiliser a la Minsky
Markup price dynamics (commodities) and
expectation price dynamics (assets) as further
destabilisers

41
Modelling Minsky Endogenous Money

First stage Goodwins predator-prey model of
Marxs cyclical growth theory provides
foundation of cyclical economy with
far-from-equilibrium dynamics (Fishers
Circuitist insights)
a rise in the price of labor resulting from
accumulation of capital implies ... accumulation
slackens in consequence of the rise in the price
of labour, because the stimulus of gain is
blunted. The rate of accumulation lessens but
with its lessening, the primary cause of that
lessening vanishes, i.e. the disproportion
between capital and exploitable labour power. The
mechanism of the process of capitalist production
removes the very obstacles that it temporarily
creates. The price of labor falls again to a
level corresponding with the needs of the
self-expansion of capital, whether the level be
below, the same as, or above the one which was
normal before the rise of wages took place...

42
Modelling Minsky Endogenous Money

Marxs model
High wages--gtlow investment--gtlow growth--gtrising
unemployment--gtfalling wage demands--gtincreased
profit share--gtrising investment--gthigh
growth--gthigh employment--gtHigh wages cycle
continues
Goodwin draws analogy with biology
predator-prey models
Rate of growth of prey (fish--gtcapitalists!)
depends ively on food supply and -ively
interactions with predator (shark--gtworkers)
Rate of growth of predator depends -ively on
number of predators and ively on interactions
with prey
OK now lets build it. First, the maths

43
Modelling Minsky Endogenous Money

First stage Goodwins predator-prey model of
Marxs cyclical growth theory
Causal chain
Capital (K) determines Output (Y)
Output determines employment (L)
Employment determines wages (w)
Wages (w?L) determine profit (P)
Profit determines investment (I)
Investment I determines capital K
chain is closed

accelerator
Chain is closed
productivity
Rate of change terms vital
Phillips curve
Investment function
Depreciation
44
Modelling Minsky Endogenous Money

So how does that look in flowcharts?
Lets do the rates of change first
If we stick to Goodwins capitalists invest all
their profits, the investment to capital relation
is easy

45
Modelling Minsky Endogenous Money

Next step is easyoutput is capital stock divided
by the accelerator

Output divided by labour productivity gives the
necessary employment level
Employment divided by the available workforce
gives us the rate of employment
So we need a productivity component and a
population component

46
Modelling Minsky Endogenous Money

Constant rate of growth of productivity means
exponential growth over time

Ditto for population

47
Modelling Minsky Endogenous Money

Output divided by labour productivity gives
needed number of workers

48
Modelling Minsky Endogenous Money

Workforce divided by population gives rate of
employment

Now things get a bit messy, so we hide bits we
know about in compound blocks

49
Modelling Minsky Endogenous Money

The same model, with internal complexity
simplified by compound blocks

Now we need a wage change blockemployment rate
determines rate of change of wages
Wage change function more complicated because
involves Phillips curve (Phillips researched
the stats in the first place to build a model
like this)
Next component is generalised exponential
function set to reproduce same fit as Phillips
curve

50
Modelling Minsky Endogenous Money

Feed in
minimum rate of change (-4)
(x,y) coordinates for one point (.96,0)
Slope at this point (2)
And you get the exponential curve that fits these
values

In flowchart form, this is

51
Modelling Minsky Endogenous Money

Sometimes an equation is easier to read, isnt it?

Nonetheless, if we feed the employment rate in
one end, we get the wage change out the other

Now we need to multiply this by the current wage
to get the rate of change of wages

52
Modelling Minsky Endogenous Money

Wage change function

So now the whole system is

53
Modelling Minsky Endogenous Money

Now we need to work out profit
Profit Output Wages
Wages Wage Rate times Employment

54
Modelling Minsky Endogenous Money

Since in the simple Goodwin model, capitalists
invest all their profits, we simply need to link
profit to capital (whose input is investment) and
we have built the model

55
Modelling Minsky Endogenous Money