This document provides an overview of stock-flow consistent (SFC) modeling. It discusses the justification and origins of the SFC approach, key features of post-Keynesian SFC models, and some problems and solutions related to SFC modeling. Specifically, it covers: 1) The background and motivation for SFC modeling from an accounting perspective. 2) Main features of post-Keynesian SFC models, including the use of balance sheet matrices, transaction flow matrices, and portfolio decisions. 3) Some challenges with SFC modeling, such as dealing with redundant equations, closures, calibration, and the possibility of multiple equilibria. It also discusses potential solutions to these challenges

1. Stock-flow consistent
modeling
Marc Lavoie

2. SFC MODELING
ISN’T ALWAYS EASY!
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3. Outline
1. Justification, background and origins of the
SFC approach
2. Main features of the PK SFC approach
3. Problems (and solutions) with the SFC
approach
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4. Justification,
background and
origins of the SFC
approach
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5. 1.1 The financial crisis: those that saw it
coming
• « „Accounting‟ (or flow-of-funds) models of the
economy turn out to be the shared mindset of a large
subset of those analysts who worried about a credit-
cum-debt crisis followed by recession, before the
policy and academic establishment did.»
• « They are „accounting‟ models in the sense that they
represent households‟, firms‟ and governments‟
balance sheets and their interrelations, and that
accounting identities play a major role in the model
structure and outcomes.» (Bezemer, 2010)
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6. 1.2 … and those who will see it coming
• « By building an accounting framework that follows the
circulation of money through the economy, we can therefore
ensure that we account for all the critical flows of financing that
lead to the stocks of assets and liabilities in which financial
fragility can build….Looking ahead, we hope that using a
framework that draws out the linkages between activity and
balance sheets of the financial sectors can make a contribution
towards the detection of growing financial fragilities.» (Barwell
and Burrows, 2011, Bank of England).
 See also Bê Duc and Le Breton 2009, ECB
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7. 1.3 Standard accounting matrix in
macro
Meschede July 2013
+ Sources of funds; – Uses of funds

8. 1.4 Drawbacks of standard macro
• What form does personal saving take?
• Where does personal saving go?
• Where does the finance for investment come from?
• How are government budget deficits financed?
• Which sector provides the counterparty to every
transaction in assets?
• Standard macro relies on the 1953 presentation of
the UN system of national accounts (SNA).
• But there has been a fully integrated SNA version
since 1968 (revised in 1993 and 2008)!
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9. 1.5 SFC redefined
• Many models and traditions can claim to be
provide consistency between stocks and
flows.
• Perhaps a more appropriate name would
have been:
– Post-Keynesian stock-flow consistent
approach
– Real stock-flow monetary model
– Financial stock-flow coherent approach
– Sectoral stock-flow coherent approach
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10. Cambridge Growth
Project
R. Stone
Input-Output Growth
Model
L. Johansen
New Cambridge
Models
W. Godley – F. Cripps
Yale General
Equilibrium Models
J. Tobin – W. Brainard
Fixed-Price
Multiplier Models Harvard CGE Models
G. Pyatt – E. Thorbecke L. Taylor / S. Robinson
SFC Models KMG Models CGE Models
AS/AD Growth
Models
S. Turnovsky / T. Sargent
StructuralistModels
NeoclassicalModels
1.6 A family-tree of accounting-based
macromodels
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Flaschel, Semmler,
Chiarella, Franke

11. 1.7 Network of SFC models (Caversazi
and Godin, 2013)
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12. Main features of
the PK SFC
approach
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13. Balance sheet matrix of the Lavoie and Godley
(2001-02) model
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Households Firms Banks ∑
Fixed
capital
+K +K
Deposits +Dh −D 0
Loans −Bf +B 0
Shares +s∙ps −s∙ps 0
Balance −Vh −Vh 0 −K
∑ 0 0 0 0

14. 2.1 Features of the transaction matrix
• All rows sum to zero (counterparties)
• All columns sum to zero (budget constraint)
• Everything comes from somewhere and everything goes
somewhere.
• There should be no « black holes ».
• The matrix can be made as complicated as needed.
• The flow matrix, along with a revaluation matrix (capital
gains and losses, not shown here) must be linked to the
stock matrix, to find the evolution of stocks.
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15. UMKC March 2014
Households Firms Banks
Account Current Capital Current Capital ∑
Consumption − C + C 0
Investment + I −I 0
Δinventory stocks + ΔIN − ΔIN 0
Wages + wL − wL 0
Net profits + PD −(PND +PD) + PND 0
Interest on loans − iB∙B(−1) + iB ∙B(−1) 0
Interest on deposits + iD ∙D(−1) iD ∙D(−1) 0
Δ in loans + ΔB − ΔB 0
Δ in deposits − ΔD + ΔD 0
Shares − psΔs + psΔs 0
∑ 0 0 0 0 0 0
A transactions-flow matrix in a closed economy
without government

16. 2.2 The main purpose
• The Holy Grail of economics is the ability to
integrate the real economy with the financial
economy.
• The purpose is « to show how the whole system fits together
and cast banks in a realistic role » (Godley 1996).
• “The structure of an economic model that is relevant for a
capitalist economy needs to include the interrelated balance
sheets and income statements of the units of the economy”
(Minsky 1996).
• SFC models integrate money seen as a flow with money
seen as a stock.
• SFC models also provide a link, or fill the gap, between
short-run analysis and long-run analysis.
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17. 2.3 THE SFC APPROACH I
• The three matrices (flows, stocks, revaluation) and
their links (the stock-flow coherent (SFC) approach)
help pin down the evolution of whole economic
systems, which is what macroeconomics is.
• The claim here is that stock-flow consistent models
(SFC models), inspired in particular by the work of
Wynne Godley, are the likely locus of some form of
post-Keynesian consensus in macroeconomics, as it
allows to entertain both monetary and real issues
within a single model, by dealing both with tangible
and financial capital.
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18. 2.4 THE SFC APPROACH II
• The SFC approach is a response to the critics who, as reported
by Chick (1995, p. 20), believe that PKE is « not coherent, not
scientific, not formal, not logical »
• « The fact that money stocks and flows must satisfy accounting
identities in individual budgets and in an economy as a whole
provide a fundamental law of macroeconomics, analogous to
the principle of conservation of energy in physics » (Godley and
Cripps 1983, p. 18).
• SFC restrictions « remove many degrees of freedom from
possible configurations of patterns of payments at the macro
level, making tractable the task of constructing theories to close
the accounts into complete models » (L. Taylor 2004, p. 2).
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19. 2.5 The quadruple entry principle
• « Because moneyflows transactions involve two transactors, the
social accounting approach to moneyflows rests not on a
double-entry system but on a quadruple-entry system »
(Copeland, 1949)
• « The principle of double entry bookeeping, where financial
assets are liabilities on another balance sheet and where every
entry on a balance sheet has a dual in another entry on the
same balance sheet, means that every transaction in assets
requires four entries » (Minsky, 1996)
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20. UMKC March 2014

21. UMKC March 2014

22. 2.6 Portfolio decisions
• SFC integrates money as a flow (the monetary circuit
theory) and money as a stock.
• The implicit assumption is that financial assets are
imperfect substitutes.
• The framework is inspired by the work of James
Tobin (1969).
• This was slighty modified and corrected in Godley
(1996).
• It does have some resemblance with the asset
pricing model proposed by Peter Skott (1989) and
Randy Wray (1992).
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23. 2.7 Porfolio equations, 3 assets
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24. 2.8 Porfolio conditions
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25. 2.9 Buffers vs market-clearing
• In neoclassical economics, markets clear through
price changes.
• In post-Keynesian economics, markets clear either
because quantities supplied are assumed to adjust to
demand within the period or because of buffers. The
price mechanism in our models only plays a clearing
role for stock market equities.
• SFC models normally have a buffer for each sector:
– Stocks of inventories and loans for producing firms
– Money deposits for households
– Bills held, or advances from the central bank, for private
banks
– Bills issued for the government
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26. 2.10 Buffers again
• “In the model every column sums to zero, and then it
follows that once every variable in a column bar one
has been determined that last variable is logically
implicit. This logical constraint on the sum of a
sector‟s activities has a causal interpretation,
because, with all decisions having to be made in an
uncertain world, there has to be, for every sector,
some component of the sum of their transactions
which flexibly takes on the character of a residual,
and which, as Godley and Lavoie emphasize, cannot
be directly controlled.” (Godin, Tiou and Kinsella
2012)
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27. 2.11 Main features: Demand-led
vs supply-led models
• Our models are essentially demand-led.
• It is possible to introduce supply-led effects
(Phillips curves, and so on)
• One could also introduce other supply effects,
such as reduced capacity when producing
firms default on some of their loans
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28. 2.12 Optimization vs reaction to
disequilibria
• In neoclassical economics, it‟s all optimization under
constraints.
• In PK SFC models, economic agents often have
stock-flow targets (inventories to sales ratio, wealth to
disposable income ratio, capital adequacy ratios, …).
• Economic agents react to these disequilibria by trying
to close the discrepancy.
• Several different closures are possible.
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29. Problems (and
possible solutions)
of the SFC
approach
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30. 3.1 SFC models: counting equations
and the redundant equation
• Each variable must be defined by one equation (a behavioural
equation, a definitional equation, or an identity equation).
• To track variables (in large models), it is best to put each variable on
the left-hand side of one and only one equation.
• Each column of the transaction-flow matrix provides an identity, that
can be used to define one variable (say m).
• Each row that contains more than two terms also provides an
identity (say n) {If there are only two terms, the identity is “ordinary”,
i.e., obvious, and the two terms need not be distinguished (Gs, Gd)}.
• One of these identities must be removed from the simulation model,
for otherwise the software will tell you that the model is over-
determined. This last equation is the “redundant” or “hidden”
equation.
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31. 3.2 Closures
• The same model can be closed in several different ways.
• This can involve bumping and inversing several
equations
• For instance, a 2-country model can be closed with the
assumption of a fixed exchange rate, which is held
constant because:
– A central bank accepts to purchase/sell any foreign asset at the
constant exchange rate (endogenous foreign reserves)
– Interest rates are let to move freely to keep the exchange rate
constant, while foreign reserves stay constant
– Government expenditures are let to move freely to keep the
exchange rate constant, while foreign reserves stay constant
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32. 3.3 Traditional construction of models
• Start by assuming that all stocks of the balance sheet
add up.
• Make sure that the row identities of the transactions-
flow matrix are fulfilled.
• Make sure the adding-up conditions of the
parameters of the portfolio component are verified.
• There is no need to start from the equilibrium.
• Running the model will get you there, if the
equilibrium is stable.
• In complex models, it may be quite long and difficult
to find a steady state (start from a simple model, and
add feedback relations afterwards)
• Once an equilibrium has been found, parameters can
be modified to examine what happens.
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33. 3.4 Limits of SFC: It can be
cumbersome
• As soon as more realistic models are being considered, the
number of equations rises very quickly.
• A partial way out has been suggested by Mouakil (2006), by
ignoring all “ordinary” identities.
• But still, models remain large.
• Continous time vs discrete time or differential equations vs
difference equations
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34. 3.5 Limits of SFC: controversies
remain
• While the identities of the model constrain the type of
results that we can obtain, behavioural equations still
play a crucial role.
• SFC modeling cannot remove all controversies in
macroeconomics or monetary economics.
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35. 3.6 Limits of SFC: The need for
calibration and empirically-based work
• In our book (Godley and Lavoie 2007), we made
(nearly) no attempt at calibration.
• More effort needs to be put in calibration
• More effort could be put into empirical work.
• Are new time series techniques adequate to deal with
the old problems of collinearity encountered by Tobin
and his associates?
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36. 3.7 Calibration and real-world data
• “Finding stock flow norms is, at present, a black art, and more
error than trial is involved in finding them as Taylor (2008)
argues. This is unsatisfactory intellectually, but also raises a
practical concern over the stability of these models. If they are
sensitive to small changes in the values of simple parameters
like the propensity to consume out of past income by
households, say, then how valid are they as representations of
reality? The contribution of our paper, and indeed the effort of
our research program, is to provide the missing link between the
simulated worlds described by Godley and Lavoie to a
coherently estimated model built from real world data.”
• (Godin, Tiou and Kinsella, 2012)
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37. 3.8 Solution
• Godin, Tiou and Kinsella (2012) propose a method and an
algorithm to move, within a model which is known to be SFC,
from either assumed or real-world stock and flow data to an
estimate of the parameter values.
• Even for a model as simple as the chapter 3 model of G&L
(model SIM), which can be solved analytically, the method does
well for some parameters (e.g., the tax rate) but not for others
(the propensities to consume out of current income and out of
wealth), because these parameters are undetermined (too many
parameters, not enough equations).
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38. 3.9 Limits of SFC: The possibility of
multiple equilibria
• “Using SFC models for theoretical analysis is made rather
complicated by the fact that these models become complex and
hence intractable once they seek to incorporate more features of
reality. Thus analytical solutions are difficult to obtain, if at all.
This is true in particular once non-linearity is introduced in the
model and hence the possibility of multiple equilibria emerges.
• Solving the model numerically for preselected parameter values
can therefore help to overcome the first problem and this
approach is therefore frequently used by modellers. Accordingly,
the researcher selects one or several sets of parameter values
which are economically plausible and then evaluates the model
using these values for both short and long-run equilibria.”
(Biagio Ciuffo, 2014)
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39. 3.10 How do we know the model
behaves identically for all plausible
parameter values?
• “Alas, this approach leads to another difficulty: how should
parameters be selected in the first place? After all, for most
parameters there exists a host of economically plausible values
and, by implication, there is also an infinite number of (in that
sense) plausible parameter combinations in the n-dimensional
hyperspace of assumptions. Picking just one such combination
would therefore seem rather arbitrary while the properties of the
model for other parameter configurations would remain basically
un-known.” (Ciuffo, 2014)
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40. 3.11 Solution: Monte-Carlo simulations
• “First, an economically/logically plausible range is determined
for each parameter. We then use a Monte Carlo approach to
examine which combinations of parameters and starting values
(feasibility regions) produce economically meaningful equilibria
for the short and long-run and whether the long-term equilibria
thus identified are in fact stable. In addition we undertake a
sensitivity analysis for all parameters which allows us to gauge
the extent to which model results are driven by certain
parameters and starting values.” (Ciuffo, 2014)
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41. The Dos Santos Zezza (2008) model in
Monte-Carlo experiments
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a = prop to
consume
out of wealth
vh = wealth to
income ratio
of households
vh
a

42. Conclusion
• Still lots to do.
• There are now papers mixing agent-based
modeling with the stock-flow consistent
approach.
• Everybody does not need to do SFC models !
• Draw of G&L !!!!
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