The stock-flow consistent
approach: background,
features, and objectives
Marc Lavoie
University of Ottawa
Outline
1.
2.
3.
4.
5.
Background of the SFC approach
Main features of the SFC approach
Main features of the post-Keynesian SFC
approach
Limits of the SFC work
Applied SFC spirit: The fundamental
identity and the Levy model
Background
1.1 Keynesian and modern (Barro
GDE) macroeconomics
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Y = C+I+G = W+P
There is no room or no role for banks
What about the central bank, where does it fit?
Individuals and firms are often netted out (representative
agent)
Where does personal saving go?
What are the liability counterparts of this saving?
What sector provides the counterparty to the transaction?
How are government deficits financed?
What role play financial stocks?
1.2 National accounting and flow of
funds analysis 1940s-1950s
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Macroeconomics is based on the system of national
accounts of the UN 1953 (Richard Stone) (flow national
income and product accounts)
This system left out flow-of-funds and balance sheets
French and Dutch national accountants bitterly complained
then (Denizet: irony)
“When total purchases of our national product increase,
where does the money come from to finance them? When
purchases of our national product decline, what becomes
of the money that is not spent?” (Copeland 1949)
The 1968 new System of National Accounts (SNA)
remedies to all this (and again in SNA 1993). But to no
avail, despite the introduction of Social Accounting Matrices
(SAM).
1.3 James Tobin 1960s - 1982
► The
New Haven, or pitfalls, school
► Introduces balance sheets, with several
distinct assets and liabilities
► Behavioural equations defining portfolio
decisions, based on rates of return
► The debts of a sector are the assets of
another sector: Financial interdependence
► Adding-up portfolio conditions: if you desire
less of an asset, you want more of another
1.4 A Wall Street view: the American
Post-Keynesians 1960s-1970s
► Paul
► One
Davidson and Hyman Minsky
must at least distinguish between money and
equities
► PK economics in the 1960s is like Hamlet without
the Prince
► Debts generate flow commitments
► “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, p. 77).
1.5 Godley and Cripps 1983 and the New
Cambridge
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A response to monetarism
Keynesians did not pay enough attention to money and
other financial assets
Keynesians did not pay enough attention to inflation
accounting
Need to introduce the constraints which adjustments of
money and other financial assets impose on the economy.
Money stocks and flows must satisfy accounting identities
in sectoral budgets, most notably
The NAFA of private sector (net financial saving of private sector) =
PSBR + current account balance
1.6 Eichner 1989 textbook
► Eichner
(1987, pp. 810-838) devotes nearly 30
pages to flow of funds analysis in the chapter on
money and credit of his main book, with more
than a dozen tables reproducing flow of funds
consequences of various decisions by economic
agents.
► The very first of these tables (Eichner 1987, p.
811) illustrates the quadruple accounting entry
principle first put forth by Morris Copeland, the US
creator of flow-of-funds analysis.
1.7 Providing a traverse: Godley in the
1990s at the Levy Institute
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Ironically, both the Tobin and the Godley research
programs had to be abandoned in 1983, when their
funding was cut off.
 For ideological reasons (Thatcher)
 Econometric performance, due to collinearity problems, was a
mixed success at best (Buiter 2003)
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In the 1990s, W. Godley makes a link between his
previous work
 which tracks income flows and the money/debt stock through
time,
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and the work of James Tobin
 which focuses on portfolio choice and rates of return.
Godley 1996 Levy Institute working paper, with equities,
but still without growth
► Godley uses simulations to describe his models and
tracks variables through time.
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1.8 Similar proposals elsewhere
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Various authors propose, at some point or another, to put together
NIPA and flow-of-funds.
Bain, A.D. “Survey in applied economics: Flow of funds analysis”,
Economic Journal, December 1973.
Roe, Alan R. “The case for flow of funds and national balance sheet
accounts”, Economic Journal, June 1973.
Davis, E.P. “A stock-flow consistent macro-econometric model of the
UK economy – Part I”, Journal of Applied Econometrics , April 1987.
Patterson, K.D. and Stephenson, M.J. “Stock-flow consistent
accounting: A macroeconomic perspective”, Economic Journal,
September 1988.
Dawson, John C. (ed.), Flow-of-Funds Analysis: A Handbook for
Practionners. M.E. Sharpe: Armonk, 1996.
Klein, L. “Some potential linkages for input-output analysis with
flow-of-funds”, Economic Systems Research, September 2003.
Recent paper at European Central Bank.
1.9 Recent work and research teams
Lavoie – Godley, JPKE 2001-2002
Godley – Lavoie, “Monetary Economics”, 2007
Godley, Lavoie, Zhao, Daigle, Greenwood (Leeds) on open
economy models
► Jacques Mazier and students (Paris 13): open economy
models
► Lance Taylor, Barbosa-Filho etc. on SFC models and the
business cycle
► Cripps, Izurieta etc. on world model
► Van Treeck, Mouakil, Le Héron, Clévenot, on
financialization
► Zezza – Dos Santos, growth models
► Gennaro Zezza, SFC and housing
► Macedo e Silva and Dos Santos, methodology of SFC
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1.10 Other related SAM work
► Flaschel,
Semmler, Chiarella, Franke, Charpe and
others (2000s) with differential equations (KeynesMeltzer-Goodwin-Tobin model)
► Harvard Structuralist General Equilibrium Model
(Easterly and L. Taylor) and Computable general
equilibrium models (S. Robinson, World Bank)
► Financial computable general equilibrium models
(Bourguignon, OECD)
Main features of the SFC
approach
2.1 No black holes
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“The fact that money stocks and flows must satisfy
accounting identities in individual budgets and in an
economy as a whole provides a fundamental law of
macroeconomics analogous to the principle of
conservation of energy in physics”. (Godley and Cripps
1983)
Everything must add up.
The simplest way to make sure that nothing has been
forgotten is to construct matrices.
This consistency requirement is particularly important
and useful in the case of portfolio choice with several
assets, where any change in the demand for an asset,
for a given amount of expected or end-of-period wealth,
must be reflected in an overall change in the value of
the remaining assets which is of equal size but opposite
sign (cf. Tobin)
2.2 The quadruple entry principle
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This principle is attributed to Copeland (1949).
Any change in the sources of funds of a sector must be
compensated by at least one change in the uses of funds
of the same sector.
But any transaction must have a counterparty. Therefore
the above two changes must be accompanied by at least
two changes in the uses and sources of funds of another
sector.
« Because moneyflows transactions involve two
transactors, the social accounting approach to moneyflows
rests not on a double-entry system but on a quadrupleentry system » (Copeland, 1949)
2.2A The quadruple entry principle
Sources of funds: + sign; Uses of funds: minus sign
2.2B The quadruple entry principle
2.2C The quadruple entry principle
and Minsky
2.3 Transactions flow, stock, and
revaluation matrices: Full integration
► Three
matrices are needed to track flows
and stocks.
► A stock matrix (balance sheet)
► A matrix of transactions (flows)
► A revaluation matrix (capital gains)
► Each stock can be tracked by taking into
account both the transactions matrix and
the revaluation matrix (full integration)
2.4 An example, a closed economy
with capital gains (Model LP)
The transactions-flow matrix LP
Assessing capital gains in discrete time
A full-integration matrix, households
only
2.5 Portfolio equations and the
adding-up conditions
… In matrix form
First (Tobin) vertical condition:
Other vertical adding-up conditions
Horizontal (Godley) adding-up conditions
The effect on demand for the asset in question of an increase in its own
rate of interest, with all the other rates remaining constant, should not be
any different from that of a fall, of the same size, in all the other rates, with
the own rate staying put.
Symmetry (B. Friedman) conditions
An increase in the expected rate of return on bonds will generate a drop in
the holdings of bills that will be of the same magnitude as the drop in the
holdings of bonds generated by a similar increase in the rate of interest on bills.
Symmetry conditions + vertical conditions imply horizontal conditions
The importance of adding-up conditions
2.6 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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2.7 Constructing the model
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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2.8 Closures
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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
Main features of the PostKeynesian SFC approach
3.1 Market-clearing vs buffers
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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:
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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
3.2 Supply-led vs demand-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
3.3 Optimization vs reaction to
disequilibria
► In
neoclassical economics, rules are based
on constrained optimization.
► 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
3.4 Contributions of the SFC
approach to PK theory
►A
coherent formalization of Minsky’s financial
fragility hypothesis (formalizing the current crisis?)
► A coherent formalization of the stock market
► A systematic introduction of stock-flow norms
► The full integration of real and financial analyses
► The integration of money as a flow (as in circuit
theory) and as a stock (Keynes, portfolio choice)
► The ability to consider historical time, as in Joan
Robinson, by tracking variables through time
Limits of current SFC
work
4.1 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
4.2 The need for calibration
► In
our book (Godley and Lavoie 2007), we
made (nearly) no attempt at calibration.
► More effort could 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?
The Levy model and the
fundamental identity
5.1 Financial balances
In
Godley’s approach, the analysis of financial
balances – the fundamental identity – gives clues to
where the economy is going in the medium term.
The
NAFA of private sector (net financial saving of
private sector) = PSBR + current account balance =
government deficit plus funds lent abroad
(S – I) = (G – T) + (X – IM + NFY)
This equation is at the heart of the so-called Modern
Monetary theory (neo-chartalism, Wray, Mitchell)
5.2 The “New Cambridge
hypothesis”
In
the 1970s, Godley and his group used this identity as the basis for a
model of the UK economy. For the private sector as a whole, the
difference between saving and investment is equal to the net acquisition
of financial assets (NAFA), which in turn are equal to (the increase in)
liabilities of the government or of the rest of the world
NAFA = GD + CAB
This approach was unconventional, since it merged households and
business analyzing the private sector as a whole.
The “New Cambridge hypothesis” was that NAFA was stable, relative to
GDP, and this gave rise to a theory for “twin deficits”, i.e. any imbalance
in the foreign account was matched by an imbalance in the government
account.
In the face of a crisis which called for an expansionary fiscal policy on
Keynesian lines, it was thus necessary to adopt measures to counter the
implied widening of the current account imbalance (some kind of
protectionism).
5.3 The revised hypothesis”
The
“New Cambridge hypothesis” was based on empirical
grounds (see Mata, 2006 for a nice reconstruction of the
debate at the time), and the evidence in favor of the stability
of NAFA/GDP vanished after some years, so that the
approach was progressively neglected.
This
approach is still at the heart of Godley’s empirical work.
It is not, however, grounded in the stability of NAFA, but
rather on how financial balances are moving, with a strong
emphasis on boundaries for balances.
Since
each balance also measures the net increase in a
sector net debt, values of the balances above a given level
point to instability in stock-flow ratios which may trigger
either some adjustment or a crisis.
Similar
assessment, Bê Duc and Le Breton 2009, ECB
5.4 The fundamental identity in a closed economy
(Krugman 2009, via GoldmanSachs, via Levy):
(S – I) = (G – T)
Private Public
Surplus Deficit
Less investment
More saving
Private Financial
Balance
B
D
R
GDP
E
Public
Balance
Private
Deficit
Public
Surplus
E starting point
D without automatic stabilizers (1930s)
R with automatic stabilizer
B also with stimulus plan
5.5 Fundamental identity in open economy
Fiscal surplus
NAFA = -2%
NAFA = 0
NAFA = +2%
+2%
Current account deficit
-2%
Current account surplus
+2%
-2%
Fiscal deficit
5.6 Conclusions and policies
►Fiscal
policy is needed to close the gap in
aggregate demand generated by the collapse in
private sector borrowing
►All countries cannot simultaneously have a current
account surplus; at the world level, the current
account surplus is zero, so at the world level we
have: (S – I) = (G – T)
►A huge fiscal stimulus will imply a rising
government debt relative to GDP. However, within
an SFC framework, debt and deficit ratios converge
in the long run, even with high interest rates.