Behavioural Finance
Lecture 10 Part 1
Extending Endogenous Money
Recap
• Last week we built model of pure credit economy
– Model of a pure credit, paper money economy in QED:
• Right-click on zip file to download QED
• Expand to QED subdirectory on your computer to run
Recap
• Terms in model:
Recap
• Flow diagram and graphs
Recap & This Lecture
• Pure credit economy can be self-sustaining
– Single initial loan causes sustained economic activity
– Positive bank balances, incomes
• This lecture:
– Extending model to include production
– Explaining values of parameters
– Expanding model to include growth
– Applying the model:
• Why lenders tend to create too much debt
• Modelling a “credit crunch”
Production
• Actual production involves
– Multiple commodities used to produce each other
– Factories (fixed capital); Machinery that
• Transforms inputs
– E.g, blast furnace
• Iron Ore + Coal in, Steel out
• Depreciates (wears out over time) in use
– “Circulating” capital (Marx’s term)
• Goods used up entirely in producing output
– Raw materials, energy, intermediate goods (e.g.,
rivets become part of car)
– Many types of labour (skilled, unskilled, supervisors)
Modelling Production
• Economic models of production
– Basic Neoclassical: “factors of production”
• Labour & Capital In—Goods Out
• Numerous problems with this
– Shown to be invalid in “Cambridge Controversies”
over the nature of capital
– Weaknesses in model ignored (or not even
known) by most neoclassical economists
• See History of Economic Thought lecture;
• Chapter 6 of Debunking Economics
Modelling Production
• Advanced Neoclassical
– General Equilibrium
• Multiple goods as inputs, multiple goods as outputs
• Better than “Factors of production” fallacy
– But problems with assumption that economy in
continuous equilibrium
– See History of Economic Thought lecture;
• Chapter 8 of Debunking Economics
• Post-Keynesian
– Most are dynamic (good!)
– Use abstraction of single commodity output, &
constant ratio between labour input & GDP output (not
so good, but not as bad as neoclassical “factor of
production” models)
Modelling Production
• “Sraffian”
– Based on work of Piero Sraffa
• Developer of critique of neoclassical “factor of
production” model
– Model production as multiple goods as inputs producing
multiple goods as output (very good)
– But work in equilibrium (very bad)
• Model of production used here
– Dynamic (Very good)
– With abstraction of single commodity (Not so good)
• Labour in—GDP out (Not so good)
– But later expanded to multiple goods in, multiple
goods out…
Absolutely Basic Modelling of Production
• Start with:
– Single Output (Q or “GDP”)
– Labour input L
– Constant labour productivity (a) so that
• Q = a.L
– Constant money wage W
• Link between monetary model developed last lecture
• And physical output
• Is Price (P)
• Have to work out a dynamic equation for price…
Absolutely Basic Modelling of Production
• In equilibrium, price must just enable flow of demand to
purchase flow of output
– Flow of output is
– Q = a.L
– L equals flow of wages divided by wage rate
• From last week’s lecture, flow of wages is
Worker’s share of
surplus generated in
production
1s
Time lag between
financing production
and receiving sales
revenue
S
 FD
Balance in Firm
sector’s deposit
account
Absolutely Basic Modelling of Production
• So Labour employed L is this flow divided by the wage
rate W:
F
L
1s
S

D
W
• Physical output Q is then labour employed L multiplied
by labour productivity a:
1  s FD
Q  a L  a 

S W
• Physical demand (D) is the monetary flow of demand
divided by the price level P
F
• Monetary flow of demand is D
S
Absolutely Basic Modelling of Production
• So demand in physical units per year is this divided by
price level P:
F
D
D
S
P
• When economy is in equilibrium, flow of supply will equal
flow of demand:
DEq 
FD
Eq
S
1  s FDEq
 PEq  QEq  a 

S W
• We can now solve for what Price would be in equilibrium:
FD
Cancel
Eq
FD
1  s Cancel
Eq
PEq 
a 

S
S W
Cancel
Cancel
1 W
PEq 
1s a
Absolutely Basic Modelling of Production
• So in equilibrium, price is a markup on the monetary cost
of production:
Money wage per worker
Markup: 1/(1-s) is
divided by units of
bigger than 1
output per worker is
1 W
PEq 
the cost of production
1s a
per unit produced
• Price as a markup on cost of production means that
– Prices convert the physical surplus into a monetary one
• Basic dynamic price equation consistent with this is:
Relation in Equilibrium
Time lag in price setting
Rate of
change of
dP
1 
1 W 
prices
  P 

dt
P 
1s a 
Absolutely Basic Modelling of Production
• Minimum production system is therefore:
Q  a L
• Monetary-production model is
1  s FD
– This physical system
L

S W
– Coupled with previous
monetary flows table
dP
1 
1 W 
  P 

dt
P 
1s a 
Type of Account
Name
Symbol
Asset
Bank Reserve
BR
Compound Interest
Liability
Firm Loan
Firms
Households
Bank
FL
FD
HD
BD
A
Deposit Interest
Pay Interest
-C(=-A)
Pay Wages
+B
-B
-C
+C
-D
HH Interest
Consume
F+G
Repay Debt
+H
-H
-H
Relend Reserves
-I
+I
+I
H-I
I-H
B+F+G+I-(C+D+H)
Sum of flows
Income
+D
+E
-E
-F
-G
D+E-F
C-(B+E+G)
A monetary model of production
Price
• In equations:
rL  5% rD  1%
Parameters
RR  2 a  2
2
Years  25
 P  1
Loan  100
w  3
  26   1
1
LR 
7
1.5
W  2
d
BR( t)
dt
LR FL( t)  RR BR( t)
BR( 0)
0
d
FL( t)
dt
RR BR( t)  LR FL( t )
FL( 0)
Loan
d
FD( t)
dt
  BD( t )   HD( t)  rD FD( t )  rL FL( t)  w  FD( t)  LR FL( t )  RR BR( t)
FD( 0)
Loan
d
HD( t )
dt
rD HD( t)   HD( t)  w  FD( t)
HD( 0)
0
d
BD( t)
dt
rL FL( t)  rD FD( t)    BD( t)  rD HD( t)
BD( 0)
0
Financial sector as derived
from table of flows
Q( t)
L( t)
1
P
 P( t) 


Price
system
W
Labour-based production
FD( t )
 1  s 
   W
 S 
0
0
1
2
3
Output and Employment
600
P( 0)
1
Q( 0)
600
L( 0)
• Simulation shows system
describes viable pure credit
economy:
4
t

a ( 1  s ) 
a L( t)
P 4( t ) 1
0.5
400
Output
Employment
Units & Workers
d
P( t)
dt
$/Unit
Given
400
Q 4( t )
L4( t )
200
0
0
1
2
3
t
4
A monetary model of production
• Monetary & physical systems consistent in equilibrium
– But convergence to equilibrium takes time:
Convergence to Equilibrium Over Time
Output, Prices and Revenue
100
500
1.3
Output
Revenue
Price Level (RHS)
80
40
20
0
400
1.2
300
1.1
$/Unit
Units & $
$
60
Profits from Monetary System
Revenue-Wages from Production System
0
2
• Original
monetary
flows only
model
4
 BR3( Years ) 
 FL3( Years ) 


 FD3( Years ) 
 B ( Years ) 
 D3

 HD3( Years ) 


6




93.333


  80.294 
 3.771 


 9.268 
6.667
200
0
0.5
1
• Expanded
monetary flows,
physical flows and
price model
1.5
 BR4( Years ) 


 FL4( Years ) 


 FD4( Years ) 
 B ( Years ) 
 D4

 HD4( Years ) 


 P4( Years ) 
 Q ( Years ) 
 4

 L4( Years ) 


1
 6.667 
 93.333 


 80.294 
 3.771 


 9.268 
 1.333 
 240.882 


 120.441 
A monetary model of production
• Monetary estimates of profits
– Rate of surplus (s)
– Times Firm Deposit Account (FD)
– Divided by turnover rate (S)
• Converges over time to equal physical estimate
– Price times Quantity minus Costs (Wages only here)
• Ditto monetary estimate of wages
– One minus rate of surplus (1-s)
– Times Firm Deposit Account (FD)
– Divided by turnover rate (S)
Wages 4( Years )


 240.882 
• Converges over time to




W  L4( Years )
240.882

 

Profits 4( Years )
– Wage rate times Labour:

   80.294 
 Revenue ( Years )  WageBill ( Years )   80.294 
 
4
4


4.667




Interest 4( Years )


A monetary model of production
• Taking stock so far: Combining
– Circuit insights into nature of credit money; and
– Basic approach to dynamic modelling;
• Has yielded working model of “the circular flow”
– Not just a diagram… • But working model of
monetary and physical flows
• No hassles about assuming
equilibrium, etc.
• Next stages
– Explain parameter values
– Allow for growth; and
– Beginnings of behaviour
(rather than fixed
parameters)
Parameter Values and Time Lags
• Values used for parameters may seem strange…
– =26 for workers consumption;
– =1 for bankers consumption
• Full list of values is:
 rD 
 
 rL 
 
 s 
 S 
 
  
  
 
L
 R
R 
 R
 0.01 
 0.05 


0.25


 0.25 


26


 1 
 0.143 


 2 
• Interest rates based on long run averages
– Loan minus deposit rates normally 4%
• Rate of surplus & turnover arbitrary
• but generate income shares close to actual data
• Other 4 parameters (, , LR, RR) are inverse time lags:
– Time lag tells how long a process would take to reach
its equilibrium if it continued linearly…
– It’s related to slope of a function at its initial point…
Parameter Values and Time Lags
• Consider just consumption
1 d

M  
• Equation for outflow from account M is
M dt
• Solve this via integration:
1 d
dM
dM

M  
   dt
    dt

M dt
M
M
ln  M    t  C
M t   M0  e  t
• Graph for M0=100,  = 26:
• Notice that tangent to curve
at t=0 crosses time axis at 2
weeks = 1/26th year = 1/
• Slope of tangent is derivative…
d t
d
d
 t
M0 
e
M t  
M0  e
M0    e  t
dt
dt
dt
Worker account with consumption outflow only ( =26)
100
Amount in Account
Tangent at t=0
90
$ in Account
80
70
M (  100 26)
60
Tangent M (  100 26)
50
40
30
20
10
0
0
2
4
6
8
10
12
14
16
18
20
22
24
  52
Weeks
• At t=0, slope of tangent is   M0  e  0    M0  2600
26
Parameter Values and Time Lags
• Equation of tangent to curve at t=0 is
• Equals M0 at t=0 M0  1   t  • Slopes away at .M0
• Equals zero at t=1/ (in workers’ case, 1/26th of a year)
Worker account with consumption outflow only ( =26)
• Point where
Amount in Account
Tangent at t=0
tangent to curve
crosses zero gives
convenient way to
describe curve:
• Tangent hits zero
at t=1/26

100
90
$ in Account
80
70
M (  100 26)
60
Tangent M (  100 26)
50
40
30
20
10
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
  52
Weeks
• “Time lag for workers’ consumption is 1/26th of a year”
• =1/26 …
• Same idea used for all other parameters:
Parameter Values and Time Lags
• Rule applies in general
• Time where tangent to curve crosses equilibrium value of
function is the time lag of the function, expressed as
fractions of the time unit (here, years)
Parameter Values and Time Lags
• Lets us interpret  as number of times a year workers
“turnover” their accounts
– “Workers spend their wages 26 times a year”
•  = 26
• And express consumption by workers as a time lag
– “Time lag for workers’ consumption is
• 2 weeks or 1/26th of a year”
• W = 1/26
• So consumption from household accounts can be shown as
d
M    M where = 26
dt
d
1
M 
 M where = 1/26
dt
W
• In practice, time lag
version used, since it
expresses behaviour
in fractions of basic
time unit of a year
Parameter Values and Time Lags
• So the various “strange” parameter values mean:
Parameter
Value
Time Lag
Meaning
S
¼
S = ¼
“Production takes ¼ year to go
from outlaying M on inputs to
getting M+ from sales”

26
W= 1/26
“Workers turnover their account
balances every 2 weeks or 1/26th
of a year”

1
B = 1
“Bankers turnover their accounts
every year”
LR
0.143
LR = 7
“Loans are repaid every 7 years”
RR
2
RR = ½
“Banks relend reserves every 6
months or ½ year
• Time lags used from now on to better specify models
Growth
• Model so far shows that
– Keynes was right: sustained economic activity can be
maintained with fixed stock of money as “revolving
fund of finance”
– Capitalists can borrow money & make a profit
– Debt easily repaid…
– Circuit conclusions about viability of economy without
rising injections of money based on errors in dynamics
• Next stage: how does money grow endogenously?
– Insight from Basil Moore:
• Firms finance operations by “lines of credit”
– Create new money if access line of credit
– AND debt grows by same amount
Growth
• Easily incorporated by new row
– Both debt and firm deposits grow by same amount:
Type of Account
Name
Symbol
Asset
Liability
Bank Reserve
Firm Loan
Firms
Households
Bank
BR
FL
FD
HD
BD
Compound Interest
A
Deposit Interest
Pay Interest
-C(=-A)
Pay Wages
+B
-B
-C
+C
-D
HH Interest
Consume
F+G
Repay Debt
+H
-H
-H
Relend Reserves
-I
+I
+I
+J
+J
I-H+J
B+F+G+I+J-(C+D+H)
New Money
Sum of flows
Income
H-I
+D
+E
-E
-F
-G
D+E-F
C-(B+E+G)
• Both assets and liabilities of banking sector expand…
Growth
• Relate to level of Firm Deposits:
– J = FD/NM
• Set NM = 20; “Money doubles every 20 years”
• Outcome is self-sustaining growth:
Account Balances
Wages, Profits & Interest with Growth
300
Bank Reserves
Firm Loan
Firm Deposit
Household Deposit
Bank Deposit
BR5( t )
F L5( t ) 200
600
Wages 5( t )
F D5( t )
H D5( t )
Wages
Profits
Interest
Profits 5( t )
400
Interest 5( t )
100
BD5( t )
200
0
0
0
10
20
t
0
10
20
t
Growth
• Ditto for physical economy:
Convergence to Equilibrium Over Time
Output, Prices and Revenue with Growth
600
500
1.3
400
1.2
$
$/Unit
Units & $
100
50
Output (Units)
Revenue ($)
Price Level (RHS)
300
200
0
5
10
1.1
Profits from Monetary System
Revenue-Wages from Production System
1
0
0
2
4
• Circuitist insight that money and banking must be
included in a model of capitalism
• Combined with dynamics
• Could be the “Holy Grail” that enables capitalism to be
modelled accurately…
• Next extension—variable wages & employment
6
Variable wages
• Raises the vexed issue of the “Phillips Curve”…
– Alleged statistical relationship between
• Level of unemployment and
• Rate of change of money wages
• Massively misinterpreted in literature & textbooks
– Phillips was actually a systems engineer
• Using 1950s version of technology shown here
• Tried to introduce these methods to economics
– Misinterpreted and derided as “Hydraulic
Keynesianism”
• Objective: to introduce dynamics into economics!
The Phillips Model…
• “RECOMMENDATIONS for stabilising aggregate production
and employment have usually been derived from the analysis of
multiplier models, using the method of comparative statics.
• This type of analysis does not provide a very firm basis for
policy recommendations, for two reasons.
• First, the time path of income, production and employment
during the process of adjustment is not revealed. It is quite
possible that certain types of policy may give rise to undesired
fluctuations, or even cause a previously stable system to
become unstable, although the final equilibrium position as
shown by a static analysis appears to be quite satisfactory.
• Second, the effects of variations in prices and interest rates
cannot be dealt with adequately with the simple multiplier
models which usually form the basis of the analysis.” (Phillips
1954: 290)
The Phillips Model…
• Phillips built a dynamic model using flowchart: showed
one variable (e.g., unemployment) affecting rate of
change of another (e.g., money wages…)
Level of D
Rate of change of P
• As part of
model,
postulated
nonlinear
relationship
between
output and
wage/capital
price
inflation:
The Phillips Model…
• “We may therefore postulate a relationship between the
level of production and the rate of change of factor
prices, which is probably of the form shown in Fig. 11…”
(308)
• Did research
that led to
Phillips curve to
justify this part
of his dynamic
model, using 19th
century UK
data…
The Phillips Curve
• Found a “clear tendency” for
– inverse relation between U and rate of change of
money wages (Dwm)
– Dwm above curve when U falling, and vice-versa
• Fitted exponential curve to data:
y  a  b. x
Dwm
c
Unemployment
log y  a   log b  c.log( x )
log y  0.9 .984  1394
. .log( x )
The Phillips Curve
Deviations from trend because of:
Fitted through average wage
change & U for 0-2,2-3,3-4,
4-5,5-7,7-11% unemployment
Wage-price spiral
due to wars; falling U
Rising unemployment
The Phillips Curve fitted to 1913-1948 data
War-induced
rise in M
prices
Rapid rise in U;
13% fall in M prices;
“cost of living” agreements
The Phillips Curve
• Economists didn’t comprehend Phillips on dynamics
– Instead, latched onto “trade-off”, static
interpretation of unemployment-wage rise relationship
– Proposition that policy makers could choose an
unemployment-inflation pair became part of orthodox
Keynesianism…
• Unfortunately, static relation didn’t seem to hold
• Keynesian economics discredited by this
• But employment-wage change relation common to all
schools of economics
– Still used in neoclassical static models
– Here introduced as Phillips intended—as part of
dynamic model
• In 2nd half of lecture…