Stock-flow consistent modeling

Marc Lavoie

SFC MODELING ISN’T ALWAYS EASY!

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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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Justification, background and

origins of the SFC approach

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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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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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1.3 Standard accounting matrix in macro

Meschede July 2013

+ Sources of funds; – Uses of funds

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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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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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

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1.6 A family-tree of accounting-based macromodels

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Flaschel, Semmler, Chiarella, Franke

1.7 Network of SFC models (Caversazi and Godin, 2013)

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Main features of the PK SFC approach

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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 0Loans   −Bf +B 0Shares +s∙ps −s∙ps   0Balance −Vh −Vh 0 −K∑ 0 0 0 0

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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  Households Firms Banks

Account   Current Capital Current Capital ∑

Consumption − C + C       0

Investment   + I −I     0Δinventory stocks   + ΔIN − ΔIN     0

Wages + wL − wL       0Net 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 0Δ 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

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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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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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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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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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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2.7 Porfolio equations, 3 assets

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2.8 Porfolio conditions

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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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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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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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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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Problems (and possible solutions) of

the SFC approach

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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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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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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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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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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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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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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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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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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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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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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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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

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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