CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Critical Mathematical Economics
Johannes Buchner
Mathematics and Statistics, McMaster University
PhiMac Seminar, McMaster University, March 27th, 2015
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
The financial crisis and the crisis in economics
Steve Keen: Debunking Economics (2002)
The Financial Crisis and the Systemic Failure of AcademicEconomics, Dahlem Report 2008 (e.g. by Hans Foellmer)
Adair Turner: Economics after the Crisis (2012)
Institute for New Economic Thinking (INET, founded2009)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Mathematics for New Economic Thinking
MNET: Fields Institute, 2013 (organized by M. Grasselli)
Critical Mathematical Economics: Mathematics has beenpartly misused in mainstream economics to justify‘unregulated markets’ before the crisis
New approaches: e.g. Systemic Risk in Banking Systems,Revival of Keynes and Minsky in Macroeconomics
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Dynamic Stochastic General Equilibrium (DSGE)
Standard model in Macroeconomics
Seeks to explain the aggregate economy using theoriesbased on strong microeconomic foundations.
Collective decisions of rational individuals over a range ofvariables for both present and future.
All variables are assumed to be simultaneously inequilibrium.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
DSGE and ‘General Equilibrium Theory’ as aMicrofoundation
Theorem (from ‘The theory of general economic equilibrium: Adifferentiable approach’. A. Mas-Colell, 1985).
Let z : S → Rl be a C 3- vector field satisfying some boundaryconditions. Then for any ε > 0 we can find an economy E suchthat the excess demand function of E coincides with f on Sεand p is an equilibrium for E if and only if z(p) = 0
It is also known as ‘Sonnenschein-Mantel-Debreu Theorem’, or‘anything goes’ Theorem.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
SMD theorem: something is rotten in GE land
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Alternative Microfoundations: ABMs
‘Agent Based Models’ as a Microfoundation
simulate the behaviour of heterogenous agents on thecomputer numerically
Reference: e.g. ‘Handbook of Computational Economics’(Volumes 1-3, most recent 2014)
sometimes critized as ‘black box’, as until recently noanalytical solutions had been available
Idea: Use methods from statistical physics to provide thoseby a mean-field approximation (see e.g. S. Landini, 2014)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
A probabilistic Micro-/Mesofoundation ofMacroeconomics
‘The point is that precise behavior of each agent is irrelevant.Rather we need to recognize that microeconomic behavior isfundamentally stochastic.’ (Aoki and Yoshikawa 2006)
Idea:
identifying homogeneous sub-populations of agents
computing the mean-field variables (mean-fieldapproximation), on an intermediate ‘Meso-level’
master equation: study of the dynamics of the number ofagents in each cluster, i.e. the transition probabilities
Project with M.Grasselli and Patrick Li: Link this toStock-Flow-Consistent Maroeconomic Models
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Back to Macroeconomics: Dynamic StochasticGeneral Equilibrium (DSGE)
Equilibrium is only disrupted by exogenous shocks.
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.
Neoclassical economics is based on barter paradigm:money is convenient to eliminate the double coincidence ofwants. DSGE is ‘Macroeconomics without banks’ !
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Minsky’s alternative interpretation of Keynes
In a modern economy, financial institutions determine theway funds are available for ownership of capital andproduction.
Economy is fundamentally cyclical, with each state (boom,crisis, deflation, stagnation, expansion and recovery)containing the elements leading to the next in anidentifiable manner.
“Stability - or tranquility -is destabilizing” (in a world witha cyclical past and capitalist financial institutions).
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Minsky’s Financial Instability Hypothesis
Start when the economy is doing well but firms and banksare conservative. Most projects succeed -it pays to lever.
Beginning of “euphoric economy”: increased debt toequity ratios, development of Ponzi/Speculative 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.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Stock-Flow Consistent models
Stock-flow consistent models emerged in the last decadeas a common language for many heterodox schools ofthought in economics.
They consider both real and monetary factorssimultaneously.
Specify the balance sheet and transactions betweensectors.
Reject the RARE individual (representative agent withrational expectations) in favour of SAFE (sectoral averagewith flexible expectations) modelling.
See Godley and Lavoie (2007) for the full framework.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Goodwin Model - SFC matrix
Balance Sheet HouseholdsFirms
Sum
current capital
Capital +pK pK
Sum (net worth) 0 0 Vf pK
Transactions
Consumption −pC +pC 0
Investment +pI −pI 0
Acct memo [GDP] [pY ]
Wages +W −W 0
Profits −Π +Πu 0
Sum 0 0 0 0
Flow of Funds
Capital +pI pI
Sum 0 0 Πu pI
Change in Net Worth 0 pI + pK − pδK pK + pK
Table: SFC table for the Goodwin model.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Goodwin Model (1967) - Assumptions
Assume that
N(t) = N0eβt (total labour force)
a(t) = a0eαt (productivity per worker)
Y (t) = νK (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 = Φ(λ)w (Phillips curve)
K = (Y − wL)− δK (Say’s Law)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Goodwin Model - Differential equations
Define
ω =wL
Y=
w
a(wage share)
λ =L
N=
Y
aN(employment rate)
It then follows that
ω = ω(Φ(λ)− α)
λ = λ
(1− ων− α− β − δ
)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Example: Goodwin model
0.7 0.75 0.8 0.85 0.9 0.95 10.88
0.9
0.92
0.94
0.96
0.98
1
ω
λw
0 = 0.8, λ
0 = 0.9
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
SFC table for Keen (1995) model
Balance Sheet HouseholdsFirms
Banks Sum
current capital
Deposits +D −D 0
Loans −L +L 0
Capital +pK pK
Sum (net worth) Vh 0 Vf 0 pK
Transactions
Consumption −pC +pC 0
Investment +pI −pI 0
Acct memo [GDP] [pY ]
Wages +W −W 0
Interest on deposits +rD −rD 0
Interest on loans −rL +rL 0
Profits −Π +Πu 0
Sum Sh 0 Sf − pI 0 0
Flow of Funds
Deposits +D −D 0
Loans −L +L 0
Capital +pI pI
Sum Sh 0 Πu 0 pI
Change in Net Worth Sh (Sf + pK − pδK ) pK + pK
Table: SFC table for the Keen model.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Keen model - allow Investment through debt
Assume now that new investment is given by
K = κ(π)Y − δK
where κ(·) is a nonlinear increasing function of profitsπ = 1− ω − rd .
This leads to external financing through debt evolvingaccording to
D = κ(π)Y − πY
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Keen model - Differential Equations
Denote the debt ratio in the economy by d = D/Y , the modelcan now be described by the following system
ω = ω [Φ(λ)− α]
λ = λ [g(π)− α− β]
d = κ(π)− π − dg(π)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Example: convergence to the good equilibrium in aKeen model
0.7
0.75
0.8
0.85
0.9
0.95
1
λ
ωλYd
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
ω
ω0 = 0.75, λ
0 = 0.75, d
0 = 0.1, Y
0 = 100
d
λ
ω
Y
Figure: Grasselli and Costa Lima (2012)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Example: explosive debt in a Keen model
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
λ
0
1000
2000
3000
4000
5000
6000
Y
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
ω
ω0 = 0.75, λ
0 = 0.7, d
0 = 0.1, Y
0 = 100
ωλYd
λ
Y d
ω
Figure: Grasselli and Costa Lima (2012)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
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
ωλ
d
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Ponzi financing
To introduce the destabilizing effect of purely speculativeinvestment, we consider a modified version of the previousmodel with
D = κ(1− ω − rd)Y − (1− ω − rd)Y + P
P = Ψ(g(ω, d)P
where P stands for Ponzi (speculative) financing and Ψ(·) is anincreasing function of the growth rate of economic output.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Example: Destabilizing 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
λ
ω
ω0 = 0.95, λ
0 = 0.9, d
0 = 0, p
0 = 0.1, Y
0 = 100
No SpeculationPonzi Financing
Figure: Grasselli and Costa Lima (2012)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
The Great Moderation in the U.S. - 1984 to 2007
Figure: Grydaki and Bezemer (2013)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Possible explanations
Real-sector causes: inventory management, labour marketchanges, etc.
Financial-sector causes: financial innovation, deregulation,better monetary policy, etc.
Grydaki and Bezemer (2013): growth of debt in the realsector.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Bank credit-to-GDP ratio in the U.S
Figure: Grydaki and Bezemer (2013)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Modelling the Great Moderation I: Keen modelwith Ponzi financing
Story: high debt → growth with low volatility → evenhigher debt → explosive volatility
Idea: choose initial conditions that are close to the basinof attraction of the equilibrium point with finite debt, butnot inside it
Result: long period of very low volatility, followed byexplosion and collapse
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Example: strongly moderated oscillations
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
λ
0
500
1000
1500
2000
2500
3000
3500
Y
0
20
40
60
80
100
120
140
160
180
d
0
2
4
6
8
10
12p
0 10 20 30 40 50 60 70 80 90 1000.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
time
ω
ω0 = 0.9, λ
0 = 0.91, d
0 = 0.1, p
0 = 0.01, Y
0 = 100, κ’(π
eq) = 20
ωλYdp
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Example (cont): Shilnikov bifurcation
0.450.5
0.550.6
0.650.7
0.750.8
0.850.9 0.7
0.75
0.8
0.85
0.9
0.95
1
0
2
4
6
8
10
12
λ
ω0 = 0.9, λ
0 = 0.91, d
0 = 0.1, p
0 = 0.01, Y
0 = 100, κ’(π
eq) = 20
ω
d
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Modelling the Great Moderation II: Debt Dynamics
Joint with M.R. Grasselli (McMaster University and TheFields Institute) and Y. Choi (Montclair State University)
Consider the following Debt Dynamics of firms andhouseholds, where df = Df
Y and dh = DhY is the debt share:
Df = I − (1− ω − rf df )Y (investment - profits)
Dh = Ch + Qh − (ω − rhdh)Y (purchases - disp. income)
Ch is households’ consumption, and Qh their demand forreal estate
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Modelling the Great Moderation II: Consumption
Household consumption Ch is a multiple of wage lessinterest payment, plus a function of wealth:
Ch = γ1(W − rhDh) + γ2Xh
the wealth of households is given by
Xh = Mh + phEh − Lh,
where ph is the unit price of real estate and Eh is the totalstock of real estate (i.e the number of houses)
for the evolution of prices of houses, assume the followingsupply and demand relationship:
ph = η(Qh − phfhEh),
where η, fh are constants.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Modelling the Great Moderation II: Boom
high demand Qh (which can be financed by householddebt) can push prices up.
the overall wealth of households goes up, leading to higherconsumption
the increase in house prices ph also leads to high returnson real estate, which pushes demand Qh up as well.
So while house prices are going up, both consumption anddemand for houses go up.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Modelling the Great Moderation II: Crisis
eventually there is too much debt and consumption drops.
this brings overall demand Y down, together with profitsfor firms, leading to lower employment and lower wagesthrough the Philips curve mechanism.
this also negatively affects the demand for houses Qh,leading to lowers house prices, lower wealth, and evenlower consumption.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Modelling the Great Moderation II: Conclusion
the work on the model has just started :)
Note: This model is ‘demand-led’ in the sense thatinvestment is the accommodating variable (in the sameway that consumption was the accommodating variable inthe original Keen model)
In other words, we let consumption be determined by theequation above and then use the relations
K = I − δK , Y =K
ν, Y = C + I
to derive the necessary level of investment as
I =K
ν− C .
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Pseudo-Cycles and wage-led vs. profit-led
Goodwin / Keen models: ‘profit-led’ or ‘investment-driven’(investment is modelled, depends positively on profits, andconsumption adjusts)
Debt-Dynamics model: ‘wage-led’ or ‘consumption-driven’(consumption is modelled, depends positively on wages,and investment adjusts)
Research Question: Could there be a model that ‘lookslike’ profit-led (e.g. by showing Goodwin-Cycles), but it isindeed wage-led?
Joint with Charlie Brummit (Columbia), Torsten Heinrich(Bremen), Engelbert Stockhammer (Kingston)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
A simplified ‘toy’ Goodwin Model
We follow [Stockhammer, Mitchel 2014]. They consider thefollowing ‘toy’ Goodwin model
y = y(1− w)
w = w(−c + ry)
Note: This corresponds to the Goodwin model discussed abovewith parameters α = β = δ = 0 and ν = 1, where we havechosen a linear Phillips curve Φ(λ) = −c + rλ
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Example: ‘Goodwin Cycles’
outputy(t)
wagew(t)
2 4 6 8 10t
0.5
1.0
1.5
2.0
(A)
-0.5 0.0 0.5 1.0 1.5 2.0 2.5
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
outputy(t)
wagesharew(t)
(B)
Figure: Sample orbit of the toy Goodwin model for r = c = 1 andinitial condition y(0) = 0.6,w(0) = 0.5.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Recall: Minsky’s FIH - a Minsky Cycle
Start when the economy is doing well but firms and banksare conservative. Most projects succeed -it pays to lever.
Beginning of “euphoric economy”: increased debt toequity ratios, development of Ponzi/Speculative 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.
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
A toy 2d Minsky Model
Let’s consider the following ‘ toy Minsky Model’ model
y = y(1− f ) (1)
f = f (−1 + py) (2)
Note: f stands for ‘financial fragility’ (think debt), and playsthe role of the wage-share in the Goodwin model (the modelabove is equivalent to the toy Goodwin model for c=1, w=f,and renaming r to p)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Example: ‘Minsky Cycles’
outputy(t)
frag.f (t)
2 4 6 8 10t
0.5
1.0
1.5
2.0
(A)
-0.5 0.0 0.5 1.0 1.5 2.0 2.5
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
outputy(t)
financialfragilityf(t)
(B)
Figure: Sample orbit of the 2d Minsky model showing a ‘MinskyCycles’ (for p = 1 and initial condition y(0) = 0.6, f (0) = 0.5).
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
A 3d Minsky Model with wage share
Finally, consider the following 3d Minsky Model, by adding awage share variable (3) to equations (1) and (2):
y = y(1− f )
f = f (−1 + py)
w = w(−c + ry − w) (3)
A pseudo-Goodwin cycle is a counterclockwise closed orbit in(y(t),w(t)) such that y and w form a master-slave system(i.e. there is a feedback from y to w , but not vice-versa).
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Example: ‘Pseudo Goodwin Cycles’
0.5
1.0
1.5
2.0
2.5
(C)
outputy(t) wagew(t) frag. f (t)
01
2outputy(t)
0
1
2wagew(t)
0
1
2
frag. f (t)
(D)
Figure: Sample orbit in 3d Minsky model: ‘Pseudo Goodwin Cycle’(for p = 2, r = 5, c = 3/2 and y(0) = 0.6, f (0) = 0.5,w(0) = 0.4).
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
General Pseudo-Cycles
Goal 1: Try to find Pseudo Goodwin Cycles in a wage-ledMinsky model and make it rigorous
Goal 2: Generalize the ‘Pseudo-Cycles’ idea and relate todiscussion on observational equivalence
Note: Discussion if economy is profit-led’ or ‘wage-led’ isvery relevant for economic policy!
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Concluding remarks
We discussed stock-flow macro-models and theirmicro-/meso-foundations.
Applications included modelling the Great Moderation andthe identification of Pseudo-Cycles
The modelling framework is an alternative to the dominantmicrofounded DSGE paradigm in macroeconomics.
Our approach opens up new avenues for the application ofmodern mathematical techniques to economics
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Outlook
Complexity and the Art of Public Policy (Colander, 2014):
‘Complexity science - made possible by modern analyticaland computational advances - is changing the way wethink about social systems and social theory’
‘Unfortunately, economists policy models have not kept up’
Work has just begun . . . new collaborators welcome :)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
And now to something completely different...
... my research before I came to Canada :)
CriticalMathematicalEconomics
JohannesBuchner
Introduction
Micro-/Meso-foundations
Goodwin andKeen models
The GreatModeration
Pseudo-Cycles
Conclusions
Ancient Dynamics of the Einstein Equationsand the Tumbling Universe
The Einstein Field Equations
Ric(g)− 12Scal(g)g = T
geometry of space-time matter content
Bianchi Cosmological models
Spatially homogeneous but anisotropic
Spatial hypersurfaces: 3-dimensional Lie group,classification [Bianchi 1898]
the Einstein Equations reduce to ODEs, with chaoticoscillations towards the big bang: A Tumbling Universe