energy, finance, and macroeconomics - fields institute€¦ · energy, finance, and macroeco-nomics...

Energy,Finance, andMacroeco-

nomics

M. R. Grasselli

Introduction

Keen modelwithoutgovernment

Destabilizing astable crisis

Introducinggovernment

Ponzifinancing

Model withNoise

Energy sectorand ELR

Energy, Finance, and Macroeconomics

M. R. Grasselli

McMaster UniversityJoint work with B. Costa Lima, X.-S. Wang, J. Wu

Fields Institute Focus Program on Commodities, Energy,and Environmental Finance

Program Visitor Seminars, August 06, 2013


nomics

M. R. Grasselli

Introduction




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.


nomics

M. R. Grasselli

Introduction




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).


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Wrong prediction number 1

Figure: Government borrowing and interest rates.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise



Figure: Monetary base and inflation.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise



Figure: Fiscal tightening and GDP.


nomics

M. R. Grasselli

Introduction




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 person’s liability isanother person’s asset.” (Paul Krugman and Gauti B.Eggertsson, 2010, pp. 2-3)


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Then we can safely ignore this...

Figure: Private and public debt ratios.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Really?

Figure: Change in debt and unemployment.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Minsky’s 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.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Minsky’s 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”.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Much better economics: SFC models

Stock-flow consistent models emerged in the last decadeas a common language for many heterodox schools ofthought in economics.

Consider both real and monetary factors from the start

Specify the balance sheet and transactions between sectors

Accommodate a number of behavioural assumptions in away that is consistent with the underlying accountingstructure.

Reject silly (and mathematically unsound!) hypothesessuch as the RARE individual (representative agent withrational expectations).

See Godley and Lavoie (2007) for the full framework.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


An example of a (fairly general) Godley table


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Godley table for monetary Keen model


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Accounting relations for monetary Keen model

From the first, second and third columns of thetransactions and flow of funds matrices we obtain that

W + rMMh − C = Sh = Mh, (1)

C −W + rMMf − rLL = Ffu − I = Mf − L (2)

rLL− rMM = Sb = L− M. (3)

An example of firm behaviour satisfying (1)–(3) is

L = I − R (4)

Mf = I − R + C −W + rMMf − rLL (5)

for chosen levels of investment I and repayment R.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Special case: Keen (1995)

Let D = L−Mf and assume that p = p0, rM = rF = r .

Supposing further that Φ = Φ(λ) and I = κ(π)Y , whereπ = 1− ω − rd , leads to

ω = ω [Φ(λ)− α]

λ = λ

[κ(1− ω − rd)

ν− α− β − δ

](6)

d = d

[r − κ(1− ω − rd)

ν+ δ

]+ κ(1− ω − rd)− (1− ω)


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Equilibria

The system (6) has a good equilibrium at

ω = 1− π − rν(α + β + δ)− π

α + β

λ = Φ−1(α)

d =ν(α + β + δ)− π

α + β

withπ = κ−1(ν(α + β + δ)),

which is stable for a large range of parameters

It also has a bad equilibrium at (0, 0,+∞), which is stableif

κ(−∞)

ν− δ < r (7)


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Example 1: convergence to the good equilibrium ina Keen 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


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Example 2: 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

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

ω

ω0 = 0.75, λ

0 = 0.7, d

0 = 0.1, Y

0 = 100

ωλYd

λ

Y d

ω


nomics

M. R. Grasselli

Introduction




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

ωλ

d


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Godley table for model with government


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Modified Keen model with government

Following Keen (and echoing Minsky) we modelgovernment spending and taxation as

G = Γ(λ)Y

T = Θ(π)Y

and add government subsidies to firms as

Gs = Γs(λ)Gs

Defining g = G/Y , gs = Gs/Y and τ = T/Y , the netprofit share is now

π = 1− ω − rd + gs − τ,

and government debt evolves according to

B = rBB + G + Gs − T .


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Good equilibrium

The system (??) has a good equilibrium at

ω = 1− π − rν(α + β + δ)− π

α + β− Θ(π)

α + β

λ = Φ−1(α)

π = κ−1(ν(α + β + δ))

g s = 0

and this is locally stable for a large range of parameters.The other variables then converge exponentially fast to

d =ν(α + β + δ)− π

α + β

g =Γb(λ)

α + β

τ =Θ(π)

α + β


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Bad equilibria - destabilizing a stable crisis

Recall that π = 1− ω − rd + gs − τ .

The model has bad equilibria of the form

(ω, λ, gs , π) = (0, 0, 0,−∞)

(ω, λ, gs , π) = (0, 0,±∞,−∞)

If gs(0) > 0, then any equilibria with π → −∞ is locallyunstable provided Γs(0) > r .

On the other hand, if gs(0) < 0 (austerity), then theseequilibria are all locally stable.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Persistence

Proposition 1: Assume gs(0) > 0, then the model is eπ-UWPprovided Γs(0) > r .

Proposition 2: Assume gs(0) > 0, then the model is λ-UWPif either of the following conditions is satisfied:

1 Γs(0) > max{r , α + β}2 r < Γs(0) ≤ α + β and−r(κ(x)− x) + (1− x)µ(x) + Γ(0)−Θ(x) > 0 forµ(x) ∈ [Γs(0), α + β].


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Example 3: Good initial conditions

0

0.2

0.4

0.6

0.8

1

λ

0

0.1

0.2

0.3

0.4

0.5d K

0 50 100 150 200 250 3000

0.2

0.4

0.6

0.8

1

time

ω

ω(0) = 0.9, λ(0) = 0.9, dk(0) = 0.1, g

b(0) = 0.05, g

s(0) = 0.05, τ

b(0) = 0.05, τ

s(0) = 0.05, d

g(0) = 0, r = 0.03, η

s(0) = 0.02

Keen Model+ Unified Government

0.05

0.06

0.07

0.08

0.09

0.1

τ B+

τ S

0

2

4

6

8

10

d g

0 50 100 150 200 250 3000.05

0.1

0.15

0.2

0.25

time

g B+

g S


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Example 4: Bad initial conditions

0

0.2

0.4

0.6

0.8

1

λ

0

0.5

1

1.5

2d K

0 50 100 150 200 250 3000

50

100

150

200

250

300

time

ω

ω(0) = 0.7, λ(0) = 0.7, dk(0) = 0.5, g

b(0) = 0.05, g

s(0) = 0.05, τ

b(0) = 0.05, τ

s(0) = 0.05, d

g(0) = 0, r = 0.03, η

s(0) = 0.02


0.04

0.05

0.06

0.07

0.08

0.09

0.1

τ B+

τ S

0

2

4

6

8

10

d g

0 50 100 150 200 250 3000

0.1

0.2

0.3

0.4

time

g B+

g S


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Example 5: Really bad initial conditions with timidgovernment

0

0.2

0.4

0.6

0.8

1

λ

0

0.5

1

1.5

2

2.5x 10

5

d K

0 50 100 150 200 250 3000

5

10

15

20

25

time

ω

ω(0) = 0.5, λ(0) = 0.3, dk(0) = 5, g

b(0) = 0.05, g

s(0) = 0.05, τ

b(0) = 0.05, τ

s(0) = 0.05, d

g(0) = 0, r = 0.03, η

s(0) = 0.02


−400

−300

−200

−100

0

100

τ B+

τ S

0

1

2

3

4

5

6x 10

7

d g

0 50 100 150 200 250 3000

100

200

300

400

500

600

time

g B+

g S


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Example 6: Really bad initial conditions withresponsive government

0

0.2

0.4

0.6

0.8

1

λ

0

500

1000

1500d K

0 50 100 150 200 250 3000

10

20

30

40

time

ω

ω(0) = 0.5, λ(0) = 0.3, dk(0) = 5, g

b(0) = 0.05, g

s(0) = 0.05, τ

b(0) = 0.05, τ

s(0) = 0.05, d

g(0) = 0, r = 0.03, η

s(0) = 0.2


−8

−6

−4

−2

0

2

τ B+

τ S

0

100

200

300

400

500

d g

0 50 100 150 200 250 3000

5

10

15

20

25

30

time

g B+

g S


nomics

M. R. Grasselli

Introduction




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


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


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 Ψ(·) is an increasing function of the growth rate ofeconomic output

g(ω, d) =κ(1− ω − rd)

ν− δ.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Example 7: 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


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Stock prices

Consider a stock price process of the form

dStSt

= rbdt + σdWt + γµtdt − γdN(µt)

where Nt is a Cox process with stochastic intensityµt = M(p(t)).

The interest rate for private debt is modelled asrt = rb + rp(t) where

rp(t) = ρ1(St + ρ2)ρ3


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Example 8: stock prices, explosive debt, zerospeculation

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

ωλ

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


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Example 9: stock prices, explosive debt, explosivespeculation

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

ω

λ

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


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Example 10: stock prices, finite debt, finitespeculation

0 10 20 30 40 50 60 70 80 90 1000.7

0.8

0.9

1

ωλ

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 90 100−0.5

0

0.5

pd

0 10 20 30 40 50 60 70 80 90 1000

100

200

300

400

St


nomics

M. R. Grasselli

Introduction




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

0.50.6

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

λ

d

Stability map for ω0 = 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


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


A model with the energy sector (Godin 2012)

Consider 3 productive sectors (widgets, capital goods,energy), 2 household sectors (wage earners andcapitalists), a government, and banks.

All sectors consume energy; wage earners and capitalistsconsume widgets; all productive sectors by capital goodsand pay wages; all firms and banks are owned bycapitalists.

Government collects taxes on households, paysemployment benefit, and issues bonds.

Banks make loans and accept deposits.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Flows in the Godin model


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Behavioural assumptions in the Godin model

Consumption for wage earners and capitalists depend onpreferences for energy and widgets and current wealth.Income not consumed is saved in bonds (depending onwealth and interest rate) and the rest in cash.

Investment depend on current and target capacityutilization.

Prices are given by a mark-up factor further subdividedinto retained and distributed profits.

Retained profits depend on target leverage and expectedunit costs, which in turn determine possible prices.

Investment in excess of retained profits is financed byloans.

Banks accept all demand for loans and use governmentbonds as residual.


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Guaranteed Employer of Last Resort: Green Jobs

Government intervenes by hiring all unemployed workers ata minimum age to work in energy saving projects.

Unemployment benefit is replaced by wages.

Energy consumption by government and householdschanges to

Cg ,e = (1− ξgu)Cg ,e,−1

βh = (1− ξhu)βh−1


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Results in the Godin model


nomics

M. R. Grasselli

Introduction




Ponzifinancing

Model withNoise


Concluding thoughts

Opportunities abound to add more structure and detail toSFC models with an explicit energy sector, including othertypes of investment functions, more realistic financialmarkets, commodities prices, derivatives, etc.

For example, the effect of inventories in forward curvesmentioned by G. Swindle this morning is a prime exampleof the interaction between real and financial sectors thatcan be model in a SFC way.

This innovative way of macroeconomic modelling has justbegun and has the potential to be a paradigm shiftingdevelopment that, together with complementary work onincomplete knowledge, radical uncertainty, network theory,and agent-based models, can redefine the role ofmathematics in economic theory.

energy, finance, and macroeconomics - fields institute€¦ · energy, finance, and macroeco-nomics...

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