Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Extensions of the Keen-Minsky Model forFinancial Fragility
M. R. Grasselli
Sharcnet Chair in Financial MathematicsMathematics and Statistics - McMaster UniversityJoint work with B. Costa Lima, X.-S. Wang, J. Wu
University of Western Sydney, August 03, 2012
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Why another talk on financial crises?
Because they are a hardy perennial.
Because macroeconomics is too important to be left at thehands of macroeconomists.
Because Carthago delenda est
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Dynamic Stochastic General Equilibrium
Overwhelmingly dominant school in macroeconomics.
Seeks to explain the aggregate economy using theoriesbased on strong microeconomic foundations.
All variables are assumed to be simultaneously inequilibrium.
The only way the economy can be in disequilibrium at anypoint in time is through decisions based on wronginformation.
Money is neutral in its effect on real variables and onlyaffects price levels.
Largely ignores the role of irreducible uncertainty.
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Hardcore (freshwater) DSGE
The strand of DSGE economists affiliated with RBCtheory made the following predictions after 2008:
1 Increases government borrowing would lead to higherinterest rates on government debt because of crowdingout.
2 Increases in the money supply would lead to inflation.3 Fiscal stimulus has zero effect in an ideal world and
negative effect in practice (because of decreasedconfidence).
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Wrong prediction number 1
Figure: Government borrowing and interest rates.
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Wrong prediction number 2
Figure: Monetary base and inflation.
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Wrong prediction number 3
Figure: Fiscal tightening and GDP.
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Meanwhile in Britain...
Figure: Office for National Statistics (UK), April 2012
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Soft core (saltwater) DSGE
The strand of DSGE economists affiliated with NewKeynesian theory got all these predictions right.
They did so by augmented DSGE with imperfections(wage stickiness, asymmetric information, imperfectcompetition, etc).
Still DSGE at core - analogous to adding epicycles toPtolemaic planetary system.
For example: Ignoring the foreign component, or lookingat the world as a whole, the overall level of debt makes nodifference to aggregate net worth one persons liability isanother persons asset. (Paul Krugman and Gauti B.Eggertsson, 2010, pp. 2-3)
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Then we can safely ignore this...
Figure: Private and public debt ratios.
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Really?
Figure: Change in debt and unemployment.
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Minskys alternative interpretation of Keynes
Neoclassical economics is based on barter paradigm:money is convenient to eliminate the double coincidence ofwants.
In a modern economy, firms make complex portfoliosdecisions: which assets to hold and how to fund them.
Financial institutions determine the way funds areavailable for ownership of capital and production.
Uncertainty in valuation of cash flows (assets) and creditrisk (liabilities) drive fluctuations in real demand andinvestment.
Economy is fundamentally cyclical, with each state (boom,crisis, deflation, stagnation, expansion and recovery)containing the elements leading to the next in anidentifiable manner.
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Minskys Financial Instability Hypothesis
Start when the economy is doing well but firms and banksare conservative.
Most projects succeed - Existing debt is easily validated:it pays to lever.
Revised valuation of cash flows, exponential growth incredit, investment and asset prices.
Beginning of euphoric economy: increased debt toequity ratios, development of Ponzi financier.
Viability of business activity is eventually compromised.
Ponzi financiers have to sell assets, liquidity dries out,asset market is flooded.
Euphoria becomes a panic.
Stability - or tranquility - in a world with a cyclical pastand capitalist financial institutions is destabilizing.
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Derivation
Example
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Goodwin Model (1967) - Assumptions
Assume that
N(t) = N0et (total labour force)
a(t) = a0et (productivity per worker)
Y (t) = K (t) = a(t)L(t) (total yearly output)
where K is the total stock of capital and L is the employedpopulation.
Assume further that
w = ()w (Phillips curve)
K = (Y wL) K (Says Law)
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Derivation
Example
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Goodwin Model - Differential equations
Define
=wL
Y=
w
a(wage share)
=L
N=
Y
aN(employment rate)
It then follows that
= (() )
=
(1
)
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Derivation
Example
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 1: Goodwin model
Basic_Goodwin_movie.aviMedia File (video/avi)
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Derivation
Example
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 1 (continued): Goodwin model
0
1000
2000
3000
4000
5000
6000
Y
0 10 20 30 40 50 60 70 80 900.7
0.75
0.8
0.85
0.9
0.95
1
t
,
w0 = 0.8,
0 = 0.9, Y
0 = 100
Y
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Introducing a financial sector (Keen 1995)
Assume now that new investment is given by
K = (1 rd)Y K
where () is C 1(,) increasing function satisfyingcertain technical conditions.
Accordingly, total output evolves as
Y
Y=(1 rd)
:= g(, d)
This leads to external financing through debt evolvingaccording to
D = (1 rd)Y (1 rd)Y
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Keen model - Differential Equations
Denote the debt ratio in the economy by d = D/Y , the modelcan now be described by the following system
= [() ]
=
[(1 rd)
](1)
d = d
[r (1 rd)
+
]+ (1 rd) (1 )
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Good equilibrium
Define1 =
1(( + + ))
Then the following is an equilibrium for (1):
1 = 1 1 r( + + ) 1
+
1 = 1()
d1 =( + + ) 1
+
Moreover
g(1, d1) =(1 1 rd1)
= + .
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Bad equilibrium
If we rewrite the system with the change of variablesu = 1/d , we obtain
= [() ]
=
[(1 r/u)
](2)
u = u
[(1r/u)
r
]u2 [(1r/u)(1)] .
We now see that (0, 0, 0) is an equilibrium of (2)corresponding to the point
(2, 2, d2) = (0, 0,+)
for the original system.
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Local stability
Analyzing the Jacobian of (1) and (2) we obtain thefollowing conclusions.
The good equilibrium (1, 1, d1) is stable if and only if
r
[(1)
(1 (1) + ( + )
) ( + )
]> 0.
The point (0, 0, 0) is a stable equilibrium for (2) if andonly if
0 < r .
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 2 : convergence to the good equilibriumin a Keen model
Goodwin_plus_banks_movie_convergent.aviMedia File (video/avi)
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 2 (continued): convergence to the goodequilibrium in a Keen model
0.7
0.75
0.8
0.85
0.9
0.95
1
Yd
0
1
2
3
4
5
6
7
8x 10
7
Y
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
d
0 50 100 150 200 250 300
0.7
0.8
0.9
1
1.1
1.2
1.3
time
0 = 0.75,
0 = 0.75, d
0 = 0.1, Y
0 = 100
d
Y
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 3: explosive debt in a Keen model
Goodwin_plus_banks_movie_divergent_70y.aviMedia File (video/avi)
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 3 (continued): explosive debt in a Keenmodel
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
1000
2000
3000
4000
5000
6000Y
0
0.5
1
1.5
2
2.5x 10
6
d
0 50 100 150 200 250 3000
5
10
15
20
25
30
35
time
0 = 0.75,
0 = 0.7, d
0 = 0.1, Y
0 = 100
Yd
Y d
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 3 (continued): explosive debt in a Keenmodel
Goodwin_plus_banks_movie_divergent_200y.aviMedia File (video/avi)
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 3 (continued): explosive debt in a Keenmodel
0
1
2
3
4
5
6
7
8
9
10
d
7
6
5
4
3
2
1
0
1dd
/dt
0 10 20 30 40 50 60 70 80 90
0.4
0.5
0.6
0.7
0.8
0.9
1
time
0 = 0.75,
0 = 0.7, d
0 = 0.1
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Data detour: debt
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Data detour: debt and employment
Figure: Source: Keen (2009)
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Derivation
Equilibria
Examples
Stabilizinggovernment
Ponzifinancing
Model withNoise
Basin of convergence for Keen model
0.5
1
1.5
0.40.5
0.60.7
0.80.9
11.1
0
2
4
6
8
10
d
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Introducing a government sector
Following Keen (and echoing Minsky) we add discretionarygovernment spending and taxation into the original systemin the form
G = G1 + G2
T = T1 + T2
where
G1 = 1()Y G2 = 2()G2
T1 = 1()Y T2 = 2()T2
Defining g = G/Y and t = T/Y , the net profit share isnow
= 1 rd + g t,and government debt evolves according to
Dg = rDg + G T .
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 4: Start with initial conditions near thelocally stable equilibrium at infinite debt . . .
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
78
d
0 10 20 30 40 50 60 70 80 90 1000
2
4
6
8
10
12
time
0 = 0.75,
0 = 0.8, d
0 = 5, g
0 = 0, t
0 = 0, r = 0.03,
max = 0.01
d
k
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 4 (continued): . . . then add governmentto drive it to the locally stable good equilibrium.
0
0.2
0.4
0.6
0.8
1
0
1
2
3
4
5
6
d
0 50 100 1500.4
0.6
0.8
1
1.2
1.4
time
0 = 0.75,
0 = 0.8, d
0 = 5, g
0 = 0.1, t
0 = 0.1, r = 0.03,
max = 0.01
0.05
0
0.05
0.1
0.15
g T
0
0.5
1
1.5
2
d G
0 50 100 1500
0.05
0.1
0.15
0.2
time
g S
dk
dG
gT
gS
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 4 (continued): But the system stillcrashes for sufficiently bad initial conditions!
0
0.2
0.4
0.6
0.8
1
0
1
2
3x 10
201
d
0 50 100 1500
2
4
6
8
time
0 = 0.3,
0 = 0.3, d
0 = 5, g
0 = 0.1, t
0 = 0.1, r = 0.03,
max = 0.01
0.05
0
0.05
0.1
0.15
g T
0
1
2
3x 10
201
d G
0 50 100 1500
1
2
3x 10
198
time
g S
dk
gT
gS
dG
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 5: Make government spending highenough, however, and the system is persistent . . .
0
0.2
0.4
0.6
0.8
1
0
2
4
6
8
10
d
0 50 100 1500
0.5
1
1.5
2
2.5
3
time
0 = 0.3,
0 = 0.3, d
0 = 5, g
0 = 0.1, t
0 = 0.1, r = 0.03,
max = 0.5
0
0.02
0.04
0.06
0.08
0.1
g T
0
1
2
3
4
d G
0 50 100 1500
0.1
0.2
0.3
0.4
time
g S
d
k
dG
gS
gT
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 5 (continued): . . . no matter how bad itstarts.
0
0.2
0.4
0.6
0.8
1
0
1000
2000
3000
4000d
0 50 100 1500
2
4
6
8
10
time
0 = 0.1,
0 = 0.1, d
0 = 5, g
0 = 0.1, t
0 = 0.1, r = 0.03,
max = 0.5
2
0
2
4
6
8
g T
60
40
20
0
20
d G
0 50 100 1500
50
100
150
time
g S
d
k
dGg
Tg
S
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Hopft bifurcation with respect to governmentspending.
0.68
0.682
0.684
0.686
0.688
0.69
0.692
OMEGA
0.28 0.285 0.29 0.295 0.3 0.305 0.31 0.315 0.32 0.325eta_max
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Ponzi financing
To introduce the destabilizing effect of purely speculativeinvestment, we consider a modified version of the previousmodel with
D = (1 rd)Y (1 rd)Y + PP = (g(, d)P
where () is an increasing function of the growth rate ofeconomic output
g(, d) =(1 rd)
.
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 4: effect of Ponzi financing
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 = 0.95,
0 = 0.9, d
0 = 0, p
0 = 0.1, Y
0 = 100
No SpeculationPonzi Financing
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 4 (continued): effect of Ponzi financing
0 20 40 60 80 100 120 140 160 180 2000.2
00.20.40.60.8
t
d
0 = 0.95,
0 = 0.9, d
0 = 0, p
0 = 0.1, Y
0=100
0 20 40 60 80 100 120 140 160 180 2000246810
x 104
d w
ith P
onziNo Speculation
Ponzi Financing
0 20 40 60 80 100 120 140 160 180 2000
2
4
6
8x 10
5
t
Y
0 20 40 60 80 100 120 140 160 180 2000
100
200
300
400
Y w
ith P
onziNo Speculation
Ponzi Financing
0 20 40 60 80 100 120 140 160 180 2000
5
10
p
t
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Stock prices
Consider a stock price process of the form
dStSt
= rbdt + dWt + tdt dN(t)
where Nt is a Cox process with stochastic intensityt = M(p(t)).
The interest rate for private debt is modelled asrt = rb + rp(t) where
rp(t) = 1(St + 2)3
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 6: stock prices, explosive debt, zerospeculation
0 10 20 30 40 50 60 70 80 90 1000
0.5
1
0 10 20 30 40 50 60 70 80 90 1000
1
2
0 10 20 30 40 50 60 70 80 90 1000
500
1000
pd
0 10 20 30 40 50 60 70 80 90 1000
50
100
150
200
St
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 6: stock prices, explosive debt, explosivespeculation
0 10 20 30 40 50 60 70 80 90 1000
1
2
3
0 10 20 30 40 50 60 70 80 90 10002468
10
0 10 20 30 40 50 60 70 80 90 10002004006008001000
pd
0 10 20 30 40 50 60 70 80 90 1000
5000
10000
St
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Example 6: stock prices, finite debt, finitespeculation
0 10 20 30 40 50 60 70 80 90 1000.7
0.8
0.9
1
0 10 20 30 40 50 60 70 80 90 1000.009
0.01
0.011
0 10 20 30 40 50 60 70 80 90 1000.5
0
0.5
pd
0 10 20 30 40 50 60 70 80 90 1000
100
200
300
400
St
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Stability map
0.5
0.5
0.55
0.55
0.55
0.55
0.55
0.55
0.55
0.550.550.
55
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.65
0.65
0.65
0.65 0.65
0.65
0.65
0.65
0.7
0.7
0.7
0.7
0.7
0.75
0.75
0.8
0.8
0.85
0.85
0.5
0.55
0.55
0.55
0.6
0.6
0.55
0.6
0.55
0.5
0.6
0.6
0.5
0.6
0.65
0.55
0.9
0.55
0.6
0.7
0.5
0.55
0.55
0.65
0.6
0.65 0.60.7
0.7
0.65
0.8
0.6
0.6
0.6
0.60.6
0.6
0.45 0.
5
0.45
0.6
0.55
0.7
0.5
0.8
0.65
0.5
0.6
0.7
0.5
0.5
0.6
0.6
d
Stability map for 0 = 0.8, p
0 = 0.01, S
0 = 100, T = 500, dt = 0.005, # of simulations = 100
0.7 0.75 0.8 0.85 0.9 0.950
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Next steps
Investigate the effects of austerity versus deficit spendingfor depressed economies
Model prices for capital goods Pk and commodities Pcexplicitly (Kaleckian mark-up theory, inflation, etc)
Extend the stochastic model (stochastic interest rates,monetary policy, correlated market sectors, etc)
Extend to an open economy model (exchange rates,capital flows, etc)
Calibrate to macroeconomic time series
Extensions ofthe
Keen-MinskyModel forFinancialFragility
M. R. Grasselli
Introduction
Goodwinmodel
Keen model
Stabilizinggovernment
Ponzifinancing
Model withNoise
Concluding thoughts
Solow (1990): The true test of a simple model is whetherit helps us to make sense of the world. Marx was, ofcourse, dead wrong about this. We have changed theworld in all sorts of ways, with mixed results; the point isto interpret it.
Schumpeter (1939): Cycles are not, like tonsils, separablethings that might be treated by themselves, but are, likethe beat of the heart, of the essence of the organism thatdisplays them.
IntroductionGoodwin modelDerivationExample
Keen modelDerivationEquilibriaExamples
Stabilizing governmentPonzi financingModel with Noise