-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Three examples of new approaches tomacroeconomic modelling
M. R. Grasselli
Professor and Chair, Mathematics and Statistics - McMaster
UniversityDirector, Centre for Financial Industries - Fields
InstituteLeader, Systemic Risk Analytics Lab - Fields/CQAM
Based on joint work with Aditya Maheshwari, Patrick Li, Gael
Giraud andAlex Lipton
New Analytical Tools and Techniquesfor Economic Policy
Making
OECD-NAEC and Baillie GiffordApril 16, 2019
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Goodwin model
Keen model
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Dynamic Stochastic General Equilibrium (DSGE)
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.
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.
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Goodwin model
Keen model
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
SMD theorem: something is rotten in GE land
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Goodwin model
Keen model
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
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.
Accommodate a number of behavioural assumptions in away that is
consistent with the underlying accountingstructure.
Reject the RARE individual (representative agent withrational
expectations) in favour of SAFE (sectoral averagewith flexible
expectations) modelling.
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Goodwin model
Keen model
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
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 ]
Depreciation −pδK +pδK 0
Wages +W −W 0
Sum 0 Sf p(I − δK ) 0
Flow of Funds
Change in Capital +p(I − δK ) p(I − δK )
Sum 0 Sf p(I − δK )
Change in Net Worth 0 Sf + ṗK pK̇ + ṗK
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Goodwin model
Keen model
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Trajectories in the Goodwin model
0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76
0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92Wage Share
0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
Employment Rate
Boom Recession
DepressionRecovery
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Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Goodwin model
Keen model
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Testing the Goodwin Model
Figure: Grasselli and Maheshwari (2017) and (2018)
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Goodwin model
Keen model
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Stochastic orbits of a Goodwin model withproductivity shocks
Figure: Figure 3 in Nguyen Huu and Costa Lima (2014)
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Goodwin model
Keen model
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
SFC table for Keen (1995) model
Balance Sheet HouseholdsFirms
Banks Sum
current capital
Deposits +∆ −∆ 0
Loans −Λ +Λ 0
Capital +pK pK
Sum (net worth) Xh 0 Xf Xb pK
Transactions
Consumption −pC +pC 0
Investment +pI −pI 0
Acct memo [GDP] [pY ]
Wages +W −W 0
Depreciation −pδK +pδK 0
Interest on deposits +rd∆ −rd∆ 0
Interest on loans −rΛ +rΛ 0
Sum Sh Sf −p(I − δK ) Sb 0
Flow of Funds
Change in Deposits +∆̇ −∆̇ 0
Change in Loans −Λ̇ +Λ̇ 0
Change in Capital +p(I − δK ) pI
Sum Sh 0 Sf Sb p(I − δK )
Change in Net Worth Sh (Sf + ṗK ) Sb ṗK + pK̇
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Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Goodwin model
Keen model
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Convergence to the good equilibrium in a Keenmodel
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)
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Goodwin model
Keen model
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
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)
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
SFC table for the dual Keen model
Workers Investors Firms Banks Sum
Balance sheetCapital stock +pK pKDeposits +Mw +Mi +Mf −(Mw + Mi
+ Mf ) 0Loans −Lw −Li −Lf +(Lw + Li + Lf ) 0Equities +peE −peE 0Sum
(Net worth) Xw Xi Xf Xb X
Transactions Current CapitalConsumption −pCw −pCi +pC −pCb
0Investment +pI −pI 0Accounting memo [GDP] [pY ]Wages +w` −w`
0Depreciation −pδK +pδK 0Interest on loans −rLw −rLi −rLf +r(Lw +
Li + Lf ) 0Interest on deposits +rMw +rMi +rMf −r(Mw + Mi + Mf )
0Dividends +rkpK + ∆b −rkpK −∆b 0Financial balances Sw Si Sf −pI +
pδK Sb 0Flows of fundsChange in capital stock +p(I − δK ) p(I − δK
)Change in deposits +Ṁw +Ṁi +Ṁf −(Ṁw + Ṁi + Ṁf ) 0Change in
loans −L̇w −L̇i −L̇i +(L̇w + L̇i + L̇f ) 0Change in equities +pe Ė
−pe Ė 0Column sum Sw Si Sf Sb p(I − δK )Change in net worth Ẋw =
Sw Ẋi = Si + ṗ
eE Ẋf = Sf − ṗeE + ṗK Ẋb = Sb Ẋ = ṗK + pK̇
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Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Bounded oscillations with stable income ratios
Figure: Giraud and Grasselli (2019)
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Explosive debt and increasing inequality
Figure: Giraud and Grasselli (2019)
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
SFC table for Keen model with monetary policy
Households Firms Banks Gov Sum
Balance SheetCapital stock +pK +pKDeposits +∆ −∆ 0Loans −Λ +Λ
0Bills +B −B 0Sum (net worth) Xh Xf Xb Xg pK
Transactions current capitalConsumption −pC +pC 0Gov Spending
+pG −pG 0Capital Investment +pI −pI 0Accounting memo [GDP] [pY
]Wages +W −W 0Taxes −pT +pT 0Depreciation −pδK +pδK 0Interest on
deposits +rd∆ −rd∆ 0Interest on loans −rΛ +rΛ 0Interest on Bills
+rgB −rgB 0Dividends +Πb −Πb 0Financial Balances Sh Sf −p(I − δK )
Sb Sg 0Flow of FundsChange in Capital Stock +p(I − δK ) +p(I − δK
)Change in Deposits +∆̇ −∆̇ 0Change in Loans −Λ̇ +Λ̇ 0Change in
Bills −Ḃ +Ḃ 0Column sum Sh Sf Sb Sg p(I − δK )Change in net worth
Sh Sf + ṗK Sb Sg ṗK + pK̇
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Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Convergence in a Keen model with monetary policy(moderate
initial debt)
Figure: `0 = 0.6, g = 0.2, t = 0, δr = 0.03, ηr = 0.1 and ηg =
0.2.
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Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Stabilizing monetary policy (high initial debt)
Figure: `0 = 6, g = 0.2, t = 0, δr = 0.03, ηr = 0.1 and ηg =
0.2.
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Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
A model with two types of firms and two types ofhouseholds
Let z = 1, 2 denote aggressive and conservative firms
withinvestment for firm n given by
int+1 = (αznt π + β)p · qnt − γ · bnt ,
where αz ≥ 0, β ≥ 0, λ ≥ 0 are known parameters, andα1 > α2,
and π is the profit share (see next page).
Consider also two types of households, workers andinvestors,
characterized by their consumption
ch1,t+1 = (1− sy1 )y
ht+1 + (1− sv1 )vht
ch2,t+1 = (1− sy2 )y
ht+1 + (1− sv2 )vht
Assume that sy1 ≤ sy2 and s
v1 ≤ sv2 , which implies that
workers save less than investors.
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Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Mean-Field approximation
Consider the ansatz
Xt = Nm(t) +√Nst ,
where m(t) = E [Xt ] and st is a stochastic spread.
Expanding the Master Equation and collecting terms oforder N−1/2
and N−1 lead to the following system ofcouple equations
dm
dτ= λ− (λ+ µ)m
∂Q
∂τ= (λ+ µ)
∂
∂s[sQ(s, τ)] +
λ(1−m) + µm2
∂2Q(s, τ)
∂s2
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Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
ABM versus MF - number of firms
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Example 1: stable stock market
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Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Example 2: unstable stock market
-
Threeexamples of
newapproaches tomacroeco-nomic
modelling
M. R. Grasselli
Introduction
Inequality
NegativeInterest Rates
Mean-Fieldand ABM
Conclusions
Concluding remarks
Macroeconomics is too important to be left
tomacroeconomists.
Banking, money, and finance should not be treated asfrictions in
an ideal barter system.
Intermediation between saving households and
borrowingentrepreneurs is only a small portion of banking
andfinancial activity.
Equilibrium models are based on ludicrous assumptions,have
serious problems of internal consistency (see SMDtheorems) and poor
empirical performance.
SFC-ABM models, complemented by networks,
mean-fieldapproximations and other techniques (including
mean-fieldgames), have the potential to redefine the role
ofmathematics in macroeconomics.
IntroductionGoodwin modelKeen model
InequalityNegative Interest RatesMean-Field and
ABMConclusions