Behavioural Finance
Lecture 09 Part 2
Modelling Endogenous Money
Behavioural Finance and
Economics
Basic Circuitist Dilemmas solved
• Need one more account:
– “Household Deposit” HD
– Table now has 4 columns:
Type of Account
Name
Asset
• & 2 new activities
– Workers paid wages
– Consumption
Liability (Deposits by nonbank public)
Income
Firm Loan
Firms
Households
Bank
Symbol
FL
FD
HD
BD
Compound Interest
A
Deposit Interest
Pay Interest
-A
Pay Wages
-B
-A
+A
-C
Wages
+C
+D
Workers
Bankers
consume
consume
Interest on HH
Consume
Sum of flows
+B
0
-D
E+F
-E
-F
B+E+F-(A+C)
C+D-E
A-(B+D+F)
Basic Circuitist Dilemmas solved
• Bank accounts will stabilise if flows in equal flows out:
Type of Account
Name
Asset
Liability
Income
Firm Loan
Firms
Households
Bank
Symbol
FL
FD
HD
BD
Compound Interest
A
Deposit Interest
Pay Interest
-C(=-A)
Pay Wages
+B
-B
-C
+C
-D
HH Interest
Consume
Sum of flows
0
+D
+E
-E
F+G
-F
-G
B+F+G-(C+D)
D+E-F
C-(B+E+G)
• Loans stable since repayments=compounding
• Firm deposit stable if B+F+G=C+D
– Deposit Interest + Sales = Loan Interest + Wages
• Household deposit stable if D+E=F
– Worker Consumption = Wages + Interest on HH Deposits
• Bank deposit stable if C=B+E+G
– Loan interest = Deposit Interest + Banker Consumption
Basic Circuitist Dilemmas solved
• Doesn’t sound too difficult
– unlike Graziani’s arguments that constant economic
activity requires rising debt levels to pay interest…
"Type"
1
1
1
0




"Name"
"Firm Loan" "Firm Deposit" "Household Deposit" "Bank Deposit" 
• New system is:


"Symbol"
FL( t)
FD( t)
HD( t)
BD( t )



• New parameters
A
0
0
0
 "Compound Interest"

S2   "Deposit Interest"

0
B
0
B


C
0
C
– w: rate of flow of  "Pay Loan Interest" C

0
D
D
0
 "Pay Wages"

funds from firms
 "Household Interest"

0
0
E
E


0
FG
F
G
 "Consumption"

to workers as
Related to balances in accounts
D  w FD( t)
E  rD HD( t)
F  w HD( t)
G  b  BD( t)
wages for working
in factories
• System equations are…
– w: consumption

d

FL( t) 0


dt


rate of workers
 d F ( t ) b  B ( t )  w H ( t )  r  F ( t )  r  F ( t )  w  F ( t ) 
D
D
D D
L L
D 
 dt D
SystemODEs  S2  

– b: consumption
d


HD( t) rD HD( t)  w HD( t )  w  FD( t)
dt


rate of bankers


d


dt
BD( t)
rL FL( t)  rD FD( t)  b  BD( t)  rD HD( t)


Basic Circuitist Dilemmas solved
• Simulating this with trial values:
– w=3; w=26; b=1
– What do we get?
Parameters
rL  5% rD  1%
Years  25
Loan  100
w  3
w  26 b  1
Given
Account Balances
120
100
FL2( t ) 80
FD2( t )
H D2( t )
d
FL( t )
dt
0
d
FD( t)
dt
b  BD( t )  w HD( t)  rD FD( t)  rL FL( t)  w  FD( t)
d
HD( t)
dt
rD HD( t)  w HD( t)  w  FD( t )
d
BD( t)
dt
FL( 0)
Loan
60
40
BD2( t )
20
rL FL( t )  rD FD( t )  b  BD( t)  rD HD( t)
• Simulation results:
• All accounts stabilise
at positive values…
FD( 0)
Loan
HD( 0)
0
BD( 0)
0
0
 FL2( Years ) 

  100 


 FD2( Years ) 
86.029 



 9.93 
 HD2( Years ) 


 B ( Years )   4.04 
 D2

 20
0
10
20
t
Firm Loan
Firm Deposit
Household Deposit
Bank Deposit
• How do we interpret this?...
– Can we derive incomes from account figures?
– Are they compatible with positive incomes for all?
Basic Circuitist Dilemmas solved
• Gross Incomes
– Bank obviously rL.FL = 5% of $100 = $5 p.a.
– Wages obviously w.FD = 3 x $86.029 = $258.088 p.a.
• Notice annual wages much larger than initial loan
– $L = $100
– But what are profits???
• Clue given by fact that wages much larger than
initial loan
• Money “turns over” several times in a year
– Turnover period (time from spending M on
production & getting M+ back in sales) one part
• Wages represent workers share in surplus of
outputs over inputs
– Share of surplus going to capitalists other part
Basic Circuitist Dilemmas solved
• Call capitalist share of surplus s
– Then workers get (1-s)
• Call turnover period tS
– Fraction of a year that it takes to go from M to M+
• Time between initial outlay (hire workers, pay
wages) & receiving money from sale of output
• So w = (1-s)/tS
– And wages are ((1-s)/tS).FD
• Profits are (s/tS).FD
• So given w=3, one possibility is
– Capitalists share of surplus from production = 25%
– Turnover period from M to M+ is 3 months= ¼ year
– Profits = 0.25/¼.FD= 1.0 x $86.029 = $86.029 p.a.
Basic Circuitist Dilemmas solved
• So Loan of $100 generates
– Equilibrium annual income of FD/tS=$344.117
• Which is split
– 75% to workers = $258.088
– 25% to capitalists = $86.029
• Banks’ gross interest ($5) a cut from this
• Both net and gross incomes positive:
Wages, Profits & Interest
Class Incomes
400
400
Wages
Profits
Interest
350
300
300
Wages 2( t )
250
HHIncome2( t )
250
Profits 2( t )
200
Capitalist 2( t )
200
Interest 2( t )
150
Banker2( t )
150
100
100
50
50
0
0
10
20
t
Workers
Capitalists
Bankers
350
0
0
10
20
t
Basic Circuitist Dilemmas solved
• What about paying back debt?
– Debt account a record of amount you owe to bank
– Can be reduced by repaying debt
• But isn’t “negative money”
• So another account needed to record debt repayment
– Bank Reserves (BR)
• Repayment goes here
– Seignorage if went into BD account
• Banks spending money they created
• Bank reduces record of outstanding debt
• 2 operations in debt repayment
– Transfer of money from Firm Deposit to Bank Reserve
– Recording of repayment on Firm Loan record.
Basic Circuitist Dilemmas solved
• Bank can also lend from its Reserves, so 2 more rows:
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
H-I
I-H
…+I-H
Sum of flows
Income
• System can be stable if
– Repayment rate=Relending rate (H=I)
• Simulating this…
+D
+E
-E
-F
-G
…
…
Basic Circuitist Dilemmas solved
• The model…
• The Account
results…
Balances
120
Parameters
rL  5% rD  1%
Years  25
Loan  100
w  3
w  26 b  1
1
LR 
7
Given
d
BR( t)
dt
LR FL( t)  RR BR( t)
BR( 0)
0
RR  2
100
BR3( t )
80
FL3( t )
FD3( t ) 60
d
FL( t)
dt
RR BR( t )  LR FL( t )
FL( 0)
Loan
d
FD( t)
dt
b  BD( t)  w 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 )  w HD( t )  w  FD( t )
HD( 0)
0
d
BD( t)
dt
rL FL( t)  rD FD( t)  b  BD( t)  rD HD( t)
BD( 0)
0
H D3( t ) 40
BD3( t ) 20
0
 20
0
10
20
t
Wages, Profits & Interest with Repayment
400
Wages
Profits
Interest
350
300
Wages 3( t )
250
Profits 3( t )
200
Interest 3( t )
150
 6.667 


 93.333 
  80.294 
 9.268 


 3.771 
• Positive bank balances & incomes
• Capitalists in pure credit
economy can borrow money &
make a profit
100
50
0
 Wages 3( Years )   240.882 




 Profits 3( Years )    80.294 
 Interest ( Years )   4.667 
3


Bank Reserves
Firm Loan
Firm Deposit
Household Deposit
Bank Deposit
 BR3( Years ) 
 FL3( Years ) 


 FD3( Years ) 
 H ( Years ) 
 D3

 BD3( Years ) 


0
10
20
t
Basic Circuitist Dilemmas solved
• Loan of $L causes much more than $L turnover per year
• Profits and Wages earned from flows initiated by loan
– Easily exceed Loan itself
• $321 annual incomes from $100 loan
– So payment of interest easy
• Just $4.67 gross from profits of $80.30
– Repayment also easy
• And a discovery: not only “Loans create Deposits”
• But “Loan Repayment creates Reserves”
– Reserves stabilise at $6.67 from zero start
• A pure credit economy “works”
– No necessity for a financial crisis
– But they do occur—can we work out why?
• Next week. For now, QED…
Modelling the Circuit in QED
• A new program for modelling dynamics
– Free for UWS students—download from vUWS
• Initial screen will be like this:
• Right-click to bring up menu for adding rows and columns
Modelling the Circuit in QED
• Add several new columns and rows
• Label columns FL, FD, BD
• Overwrite “INTEREST” with “Compound debt”
• Put “A” in FL column
Modelling the Circuit in QED
• Now click on Actions/C.O.D. Equations:
• Define A as rL * FL(t):
• Now click on Actions/Var/Equations
Modelling the Circuit in QED
• Define rL to be 0.05 (5%)
Modelling the Circuit in QED
• Shut C.O.D. And Var windows & go back to Godley Table
• Make the initial value of FL & FD 100 (“initial loan = $100”)
• Now click on “Phillips Diagram/View...
• Erase any diagram already there and generate a new one
Modelling the Circuit in QED
• Diagram starts off cluttered...
• Drag objects to make it neater
Modelling the Circuit in QED
• Get something like this:
• Now click on “Show Player” and “Play”
Modelling the Circuit in QED
• Complete rest of model
– B = rL * FL(t) (Firm sector pays interest)
– C = rD * FD(t) (Bank pays interest on deposit)
• Regenerate Phillips Diagram
Modelling the Circuit in QED
• Rearrange
• Play...
• All money
transfers from FD
to BD; FL remains
constant
• What if we add in
next stage of
Circuit model?:
• Firms hire workers
• Worker and banks
consume output of
factories…
• Is the system
viable???
Modelling the Circuit in QED
• One extra column for workers
– Rows for wage payment, interest, and consumption:
• Define D to F
and give them
values
• Regenerate and redesign Phillips Diagram
Modelling the Circuit in QED
• Minimum complete system is:
• Click Play and
see what
happens...
• All accounts
settle down to
equilibrium
levels over
time...
• “Revolving
fund of
credit” works
as Keynes
described
QED: A tool for modelling financial dynamics
• Most models in this subject built using Mathcad
– Great program, but minimum price for students A$170
• QED: “Quesnay Economic Dynamics”
– Alternative free program for dynamic modelling
– Built by UK computer programmer/collaborator
– Implements my tabular approach to dynamic modelling
– Seamlessly integrates this with flowchart modelling
– Name honours pioneer of economic dynamics
• Francios Quesnay: founder of “Physiocratic School”
• 18th Century physician to French King
• Inspired by autopsies (recent practice) showing
human circulation system
• Modelled economic flows in “Tableau Economique”
Quesnay and the “Tableau Economique”
PRODUCT IVE
EXPENDIT URE OFT HE
EXPENDITURE
relative to
agriculture, etc.
REVENUE
after deduction of taxes, is divided
between productive expenditure
STERILE
EXPENDITURE
relative to
industry, etc.
and sterile expenditure
Annual advances
required to produce a
revenue 0f 600l are 600l
• See my History of
Economic Thought
Lecture 02 for
explanation
• QED—modern
version of Quesnay’s
dynamics
Annual
revenue
Annual advances
for the works of sterile
expenditure are
QED
• Download from vUWS or my blog; Expand Zip File
(anywhere on your computer) to create “QED”
subdirectory
• Doubleclick on
QED.exe
to launch
program
QED
• Core menu function is “Actions”
– PS Interface and functions will change over time
– Program still evolving
•
•
•
•
•
Key functions
Godley Table
Var/Equations
COD Equations
Click on Godley
Table to start
building model:
QED
• Commemorates Wynne Godley
– Leading Post Keynesian economist
– Pioneer of “Social Accounting Matrix” approach
• This window will appear:
QED
• Right-click on table to
bring up control menu:
• Insert columns & rows...
QED
• Enter/Edit financial flow operations in first column
• Using this to build a model of 19th century “Free Banking”:
• US private banks allowed to issue own paper currency
if lending backed by substantial assets (normally land)
of bank founders
• Some typical bank notes:
QED
• Free banking system ultimately failed
• Succumbed to temptation of seignorage
• But basic system could have worked...
• Bank issues set number of notes (say “N”)
• Stores notes in its vault (BV: Bank Vault)
• Lends to firms (FD: Firms Deposit)
• Records debt of firms (FL: Firms Loan)
• Firm pay wages to hire workers (WD: Worker Deposits)
• Banks
– receive interest from firms
• in income/transactions account
• Pay interest to firms & workers
– From Bank Transactions account (BT)
QED
• Modelling this using QED:
– Enter variable names in top row
• Click on cell and type (use F2 to edit)
– Enter initial conditions (N notes) on next row
– Enter financial flows on subsequent rows...
QED
• Enter formulas
for flows in COD
Equations window
• Enter values for
parameters or
functions in
Variables/
Equations window
QED
• Program generates flowchart diagram
– Forrester Diagram
• Like conventional “systems engineering” programs
– Phillips Diagram
• In honour of Bill Phillips (of “Phillips Curve” fame)
– Tried to introduce economists in 1950s to
engineering techniques
– Derided and misunderstood as “hydraulic
Keynesianism”
• Both can be run dynamically
– Phillips Diagram generates simulation “reservoir/pump”
analogy of flows/stocks in model
QED
• Diagrams (after reformatting)
QED
• Can also be graphed dynamically as model runs
Next week
•
•
•
•
•
Extending model to include production
Explaining values of parameters
Working out why lenders like lending too much money
Expanding model to include growth
Modelling a “credit crunch”
– One possible reason why Australia’s outcome better
than USA’s
• USA followed “money multiplier” model & “rescued
banks”
• Australia took a punt and “rescued households”
– Which worked better?
– Is the financial crisis over???