Notes on the Stock-Flow Consistent Approach to Macroeconomic Modeling

8/22/2019 Notes on the Stock-Flow Consistent Approach to Macroeconomic Modeling

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1 - Notes on the Stock-Flow Consistent Approach to Macroeconomic Modeling

Introduction

The aim of this paper is to present and discuss the general features of the Stock-

Flow Consistent Approach to Macroeconomic Modeling (SFCA, from now on).

Although the SFCA is still not widely adopted, its our contention that (i) it is crucial for

sound macroeconomic reasoning in general1 and, therefore, (ii) its widespread adoption

would increase both the transparency and the logical coherence of most macro models2.

In order to support our claims, we chose to divide these notes in four parts. The

first describes what exactly we mean by the stock-flow consistent approach to

macroeconomic modeling. As the distinguishing features of the SFC approach are

perhaps clearer when its contrasted to other approaches, we decided to dedicate the next

two parts of the paper to such comparisons. Therefore, the second part attempts to relate

the SFC approach to current mainstream macroeconomics, while the third (briefly) relates

it to conventional Post-Keynesian macroeconomics. The fourth and last part of this paper

attempts to summarize the state-of-the-art of this line of research as we see it and,

hopefully, share with the reader some of the excitement felt by SFCA authors about the

possibilities of this line of research. A couple of concluding remarks is presented in the

end of the paper.

1 The same opinion is expressed, for example, in Tobin (1980 and 1982), Godley and Cripps

(1983), Taylor (1997) and Godley and Shaikh (2002).

2The same opinion is expressed, for example, in Lavoie and Godley (2001-02).


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1.1 - Stock-Flow Consistent Macroeconomic Models: An Introduction

Although the 1970s marked the end of its hegemony in macroeconomics,

Keynesian thought showed vitality in that period. Indeed, in a series of seminal articles, a

distinguished group of economists at Cambridge (UK), MIT and Yale developed an

entirely new family of models very different in nature from the popular textbook version

of Keynesianism3. The 1981 Nobel Prize lecture by James Tobin one of the main

architects of this new family of models is perhaps the most well known and clear

exposition of the Keynesian frontier at that time. In the second page of that lecture,

Tobin (1982) writes that:

Hickss IS-LM version of keynesian [theory]() has a number of defects that have limited its

usefulness and subjected it to attack. In this lecture, I wish to describe an alternative framework, which tries

to repair some of those defects. (). The principal features that differentiate the proposed framework from

the standard macromodel are these: (i) precison regarding time (); (ii) tracking of stocks (); (iii) several

assets and rates of return (); (iv) modeling of financial and monetary policy operations (); (v) Walrass

Law and adding-up constraints.

This alternative framework mentioned above is probably one of the best

definitions of SFCA4,5. This approach has been continuously developed in the last twenty

3 See Brainard and Tobin (1968), Tobin (1969), Foley and Sidrauski (1971), Blinder and Solow

(1973 and 1974), Foley (1975), Cripps and Godley (1976), Tobin and Buiter (1976), Turnovsky

(1977), Backus et.al. (1980), Tobin (1982), and Godley and Cripps (1983), among others. Most of

these papers aimed to address issues raised by Ott and Ott (1965) and Christ (1967, 1968).

4Even though Tobin himself didnt call it that way. Yale people (like Fair, 1984, for example)

called it the pitfalls approach, in a reference to the seminal paper by Brainard and Tobin (1968).

The expression stock-flow consistent is commonly associated with the works of Wynne Godley

[though used also by Davis (1987a and 1987b) and Patterson and Stephenson (1988), among

others], but it seems to us that it can and should be applied more generally. Moudud (1998), for

example, preferred to use the term Social Accounting Matrix (SAM) approach - also widely


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years, especially by a relatively small group of macroeconomists associated with the

Bank of England, the University of Cambridge, the Levy Economics Institute-NY, the

New School for Social Research and the University of Ottawa6, and despite its Keynesian

origins, its regarded as indispensable for sound macroeconomic reasoning in general7.

Most authors in this tradition would probably agree with Solow (1983, p.164) that

perhaps the largest theoretical gap in the model of the General Theory was its relative

neglect of stock concepts, stock equilibrium and stock-flow relations. It may have been a

used by Taylor - but that doesnt emphasize enough the crucial importance these authors give to

the coherent and explicit treatment of the inter-relationships between macroeconomic stocks andflows at a given moment and through time. Indeed, Taylor himself (1990) provides examples of

SAMs in which only flows are taken into consideration and, therefore, the fact that a

macroeconomic model is SAM-based does not mean that it is stock-flow consistent. On the

other hand, the original version of the Godley and Crippsmodel (1983) is an example of a stock-

flow consistent model not presented in a SAM. The SFCA is also, clearly, a subset of what Taylor

(1997, chapter 1, p.1) calls the structuralist approach to macroeconomics.

5 Although the neoclassical concept of Walrass Law is considered unnecessary by most SFC

authors.6

See Rosensweig and Taylor (1984), Anyadike-Danes et al. (1987), Davis (1987a and 1987b),

Patterson and Stephenson (1988), Godley and Zezza (1989), Taylor (1990), Godley (1996, 1999a

and 1999b), Alemi and Foley (1997), Taylor (1997, 1998a, 1998b, 1999 and 2001), Moudud

(1998), Lavoie and Godley (2001-2002) and Godley and Shaikh (2002), among many others.

Godleys intelectual debt to Tobin is explicit, for example, in Anyadike-Danes et.al. (1987) and

Godley (1996), while Taylors is explicit in Taylor (1990, chapter 1) and Foleys in Foley and

Sidrauski (1971).

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Godley and Cripps (1983, p.44), for example, argue that the SFCA is what() [they] mean bymacroeconomic theory. Taylor (1997, ch.1, p.1) expresses a similar opinion stating that

macroeconomic frameworks which constrain sectoral and micro level social and economic

actors and their actions are the topic of() [macroeconomics]. For SFC models in the tradition

of the classical economists and Marx, see Moudud (1998). Foleys formalizations of Marxs


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necessary simplification for Keynes to slice the time so thin that the stock of capital

goods, for instance, can be treated as constant even while net investment is systematically

positive or negative. But those slices soon add up to a slab, across which stock

differences are perceptible. Besides, it is important to get the stock-flow relationships

right; and since flow behavior is often related to stocks, empirical models cannot be

restricted to the shortest of the short runs8. Note, however, that explicit recognition of

stock-flow relationships Tobins item (ii) above - necessarily implies a dynamic

approach to modeling and this is in sharp contrast with conventional Keynesian

economics, which generally assumes a static short run equilibrium. Indeed, in a SFC

model current flows - which are in part determined by past stocks end up changing

(either increasing or decreasing) current stocks and, through this channel, future flows as

well9. This point is made very clearly by Tobin (1982, p.189), according to whom, a

model of short run determination of macroeconomic activity must be regarded as

referring to a slice of time, whether thick or paper thin, and as embedded in a dynamic

process in which flows alter stocks, which in turn condition subsequent flows.

The dynamic context necessarily implied by the explicit recognition of the stock-

flow relationships creates, by its turn, two related needs. First, one needs to be precise

circuit of capital (Foley, 1982, 1986a and 1986b) also have many elements in common with the

SFCA.8

Tobin (1980, p.75 and 1982, p.188) and Godley (1983, p.170), at least, express essentially the

same opinion. Well have more to say about this issue in section 1.1.3 below.

9 As Turnovsky (1977, p.xi) puts it [SFC] relationships necessarily impose a dynamic structure

on the macroeconomic system, even if all the underlying behavioural relationships are static.

Turnovsky calls this SFC dynamics the intrinsic dynamics of the macroeconomic system.


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about how one treats the passage of time Tobins item (i) above. In practice, as put by

Tobin himself (1982, p.189) most SFC models:

() count time in discrete periods of equal finite length. Within any period each variable assumes one and

only one value. (). From one period to the next asset stocks jump by finite amounts. Therefore, the

demands and supplies for these jumps affect asset prices and other variables within the period, the more so

the greater the length of the period. They will also, of course, influence the solutions in subsequent

periods.

Of course, nothing prevents one from using the same strategy with continuous time,

instead of with discrete time, but as Tobin (idem)10 reminds us:

Either representation of time in economic dynamics is an unrealistic abstraction. We know by common

observation that some variables, notably prices in organized markets, move virtually continuously. Others

remain fixed for periods of varying length. Some decisions by economic agents are reconsidered daily or

hourly, while others are reviewed at intervals of a year or longer except when extraordinary events compel

revisions. It would be desirable in principle to allow for differences among variables in frequencies of

change and even to make those frequencies endogenous. But at present models of such realism seem

beyond the power of our analytic tools. Moreover, many statistical data are available only for arbitrary

finite periods.

The second need, related to the first, is the need for what Wynne Godley calls an

accounting framework with no black holes [in which] every flow comes from

somewhere and goes somewhere (Godley, 1996, p.7)11. Indeed, if we want to track the

process of change of stocks by flows and the feedback of the new stocks in future flows,

we have to make sure that current stocks are exactly the result of past flow decisions. If

we dont do that, we literally have no idea of what determined current stocks and, as a

10 Foley (1975) expresses a similar opinion as well discuss in more detail below.

11The treatment of time and the appropriate accounting are related because often the second is

determined by the first.


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result, we cant say that we are modeling the process of change of stocks by flows in an

adequate way. The national accounting issue is, therefore, unavoidable to the SFCA.

In these days of neoclassical hegemony it is probably important to stress right

from the start, however, that national accounting schemes are based on a pre-conceived

view about the economically relevant sets of people and institutions () [within an

economy] (Taylor, 1990, p.3). As Godley (1996, p.3) puts it, it is a matter of

ascertainable fact that the real world is characterized by a huge and complex structure of

interdependent institutions such as governments, firms, banks and households. I do not

accept that these institutions are veils with nothing more to do than passively sponsor

or facilitate the optimizing aspirations of individual agents; and wish, rather, to start from

a conceptual framework which has cognisance of (something remotely approaching) the

real world as we know it12. Taylor (1997, p.1) expresses the same opinion as follows:

() social accounts and social relations frame macroeconomics. The social accounts are

a skeleton, and social relations change its position over real, historical time. Specifying

just which relations drive the motions is not a trivial task (). But the objects that move

the observable phenomena in macro are mostly the numbers comprising the national

income and product accounts (or NIPA) and allied systems.

Of course, a huge number of theoretical and applied macroeconomic models

probably beginning with Quesnays famous Tableau Economique were phrased as (or

12 It is conceivable, however, to think about a SFC model based on several representative agents

(like a representative household, a representative bank, a representative non-financial firm and so

forth). In general, however, SFCA authors dont use representative agents. Tobin (1989, p.18) is

probably expressing the view of most SFCA authors when he remarks that why this

representative agent assumption is less ad hoc and more defensible simplification than ()

constructs of early macro modelers () is beyond me.


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were based on) some kind of (implicit or explicit) social accounting matrix (or SAM 13)

and, therefore, one must emphasize the importance of the allied systems mentioned

above by Taylor. Indeed, most of these models are based on some sort of flow

accounting (like the NIPA) and, therefore, either focus only on flows or deal with stocks

and flows inconsistently. Although for manyapplications references to stocks and/or the

bias introduced by stock-flow inconsistency may not be relevant, SFCA authors

strongly believe that for most kinds of macroeconomic analysis it is. SFC models

(applied or theoretical), therefore, are necessarily based on sophisticated accounting

frameworks that consistently integrate flows of income and product with flows of

financial funds and a full set of balance sheets14. To put it briefly, the adjectives SAM-

based and SFC are not synonyms, although many SAM-based models are indeed

SFC15.

13Taylor (1990, p.7) traces the concept of SAMs back to Stone, R (1966), The Social Accounts

from a Consumer Point of View, Review of Income and Wealth, series 12, n.1. Although

Stones rigorous concept must be differentiated from the more generic idea that a SAM is any

kind of matrix portraying any kind of social accounting (like, for example, Quesnays Tableau

Economique), the literature not always does that. Here well use the generic meaning of the

term.

14In applied work this is achieved (or approximated) through the (non-trivial) integration of

NIPA accounts with Flow of Funds accounts. The relevance of this integration has been

increasingly emphasized by the United Nations System of National Accounts as well. Dawson

(1996) is a good source for both the details of this integration and the intellectual history of the

Flow of Funds Accounts. As Dawson makes clear, FoF authors are, in many aspects, intellectual

ancestors of the SFCA approach.

15 SAM-based (Computable General Equilibrium) models, in Stones sense (see footnote 15),

are widely used in the development literature, both by orthodox and non-orthodox economists.

Taylor (1990) and Alarcn et.al. (1991), two surveys of this SAM-based development


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It also true that a huge number of theoretical and applied macroeconomic models

discuss some sort(s) of stock-flow relation(s)16. Harrods famous analysis of a growing

economy and all the literature that followed it is one of the examples that quickly come to

mind. Harrods case is important in our argument for two reasons. First, because he was

one of the first to point out the need for intrinsically dynamic analyses of the kind

proposed by the SFCA17. Second, because even though his model explicitly theorizes

about stock-flow ratios it is not SFC, in the sense that not all macroeconomic stocks and

flows implicit in its hypotheses are accounted for. Who finances investment in Harrods

model? Given that savings are non-negative, wealth is certainly being accumulated, but

wheres the stock of wealth in Harrods model? This list could go on. In other words, a

model may very well say something about some stock-flow relation(s) without being

SFC18. And, again, even though the bias introduced by stock-flow inconsistency may be

of little relevance for the fundamental message of many macroeconomic models (as

argued by Moudud, 1998 and subsequent papers, in the case of Harrod), this has to be

proved rather than simply asserted.

literature, present many SFC and non-SFC models. Rosensweig and Taylor (1984) is often cited

as a pioneer SAM-based SFC model.

16The same is true, by the way, for microeconomic models. Obvious examples are models of real

estate markets and commodities in general.

17 As he put it it is necessary to think dynamically () once the mind is accustomed to thinking

in terms of trends of increase, the old static formulation of problems seems stale, flat and

unprofitable (Harrod, 1939, p.16).

18A survey of all the authors that have theorized about specific stock-flow ratios or relations

without presenting a formal SFC model would be a very large one, though, well beyond the scope

of this paper.


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In practice, most SFC macro models follow conventional national accounts and

assume that the economy can be adequately depicted as consisting of 5 sectors, which are

(aggregations of) (i) Households, (ii) Non-Financial Firms, (iii) Financial Sector (Banks),

(iv) Government and (v) Rest of the World19,20. Of course, further aggregation or

disaggregation of some sectors and/or the elimination of a few others are possible and, in

fact, desirable depending on the nature of the analysis and the aesthetic judgement of the

model-builder. It is our contention, however, that the choice of the appropriate (SFC)

accounting structure is far from obvious and can be seen as the first fundamental

hypothesis of a SFC model. Indeed, this choice implies a huge number of non-trivial

theoretical assumptions (explicit or not) about the players in the game and the moves

they make (Cohen, 1986, p.3) and perhaps the best way to see it is as something

equivalent to the creation of a simple artificial economy21. As a consequence, different

people will have different opinions concerning the optimum size/degree of disaggregation

of the accounting structure22 and what exactly must be accounted for23.

19Making the models especially appropriate for the discussion of items (iii) and (iv) of Tobins

passage mentioned above.

20The main exceptions are recent models (see, Godley, 1999b or Taylor, 1999, for examples) of

two interdependent economies which together make up a whole world (Godley, 1999b, p.1)

21Note that, as Brainard and Tobin (1968, p.99) remind us, [this procedure] guarantees us an

Olympian knowledge of the true structure that is generating the observations . (). [But it] ()

cannot tell us anything about the real world. You cant get something for nothing. We realize

further that the lessons derived or illustrated by simulations of our particular structure will not be

very convincing or even interesting to people who believe that the model bears no resemblance to

the process which generate actual statistical data.

22Given that, as put by Taylor (1990, p.1) any economy is a maze of structural detail more than

one could ever build into equations or use in policy design, the choice of what to include and

what to leave out of a macroeconomic model is more an art than a science.


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Second, we should not forget that even if we agree on the level of aggregation of

the accounting structure and on what it must account for, the facts remain that (i) the

choice of the accounting conventions is basically theory determined24 and (ii) even within

the boundaries of a given theory, in general theres a lot of room for discretion25. This last

point is clearly put by Wynne Godley and Francis Cripps in the first paragraph of the first

chapter of their seminal book (1983, p.23): definitions of national income, expenditure

and output, although generally chosen to make it as easy as possible to reach conclusions

about major objectives of macroeconomic policy, are in last resort arbitrary. As a

consequence, different authors would very likely disagree not only on what to account

for, but also on the level of aggregation of the accounts and on how to account for what

they think is right to account for26.

Given all these degrees of freedom one might very well ask why someone would

bother to use any national accounting framework or data whatsoever. There are several

23Perhaps the clearest example of this fact is the distinction between the neoclassical accounting

of, for example, Buiter (1983) - that emphasizes future (fundamentally uncertain) revenues of

agents (like, for example, governments future tax revenue) - and the ones in, for example,

Godley (1996) and Taylor (1997) that dont even mention them.

24See Shaikh and Tonak (1994) for a thorough discussion about theoretical determinants of NIPA

accounting conventions.

25There is no terribly compelling reason, say, to consider consumption goods (like pens, or a pair

of jeans) that last longer than a year to be an investment by households as it is the current

practice in the U.S Flow of Funds accounts. NIPA accounts, for example, treat them as

consumption.

26This, by the way, helps to explain why it is almost impossible to find any two different SFCA

authors that use the same accounting framework/conventions. Of course, papers with different

goals would probably use different accounting structures but this doesnt explain all the

differences one finds in the accounting of SFC authors.


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(mutually compatible) arguments for the use of models explicitly based on such things,

though. One of them, at the same time simple and compelling, is provided by Buiter

(1990, p.2), according to whom without measurement there can be no science. Also, the

way we measure things, organize data and try to map them into their theoretical

counterparts will color our understanding of the processes we are monitoring. A second

one, perhaps more pragmatic and probably implicit in Taylors views mentioned above, is

that - despite all their possible problems - national accounts of a specific type have been

made available to the public for more than 50 years now and are, certainly, the most

comprehensive set of data available about any national economy. Most economists,

whatever their persuasion, agree that not to take advantage of such an amount of data

would not make sense, although many (like Buiter, 1983 or Shaikh and Tonak, 1994)

would argue in favor of the use of modified national accounts data.

A third argument Tobins item (v) above, first pointed out by Brainard and

Tobin (1968) and especially emphasized in the work of Wynne Godley - is that the use of

consistent accounting frameworks constrains what can be said to happen with the

economy they portray27. As Godley and Cripps (1983, p.18) eloquently put it, the fact

that money stocks and flows must satisfy accounting identities in individual budgets and

in the economy as a whole provides a fundamental law of macroeconomics analogous to

the principle of conservation in physics28. The fact that these constraints can be

presented in a concise and intuitive manner in SAMs explains why the SFC literature

27See, for example, Godley and Shaikh (2002) and Taylor (1999) for details.

28Fair (1984, p.35) also makes this point, although with considerably less enthusiasm. After

emphasizing that a macro model should try to incorporate as good micro foundations as possible


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since Tobin (see, for example, Bakus et.al., 1980) has increasingly used these matrices to

summarize the accounting framework of macroeconomic models.

Fourth, accounting frameworks provide skeletons (Taylor, 1997, p.1) that

come to life as (...) economic model(s) (Backus et.al., p. 262) when behavioral

assumptions are added to the accounting framework. As put by Taylor (1991, p.41), the

accounting serves as a basis to the definition of closures of a () macro model, to

adopt a methodology from Sen (1963) and a term from Taylor and Lysy (1979).

Formally, prescribing a closure boils down to stating which variables are endogenous or

exogenous in an equation system largely based upon macroeconomic accounting

identities, and figuring out how they influence one another. As stressed by Taylor (1990,

1991 and 1997), its often possible to phrase the views of different authors as different

closures for the same accounting framework. Note, however, that different authors are

likely to disagree also on the choice of the appropriate skeleton itself and therefore this

procedure may imply a significant bias a kind of home court advantage for some

views over the others.

1.2 - The SFCA and mainstream macroeconomics

The first thing we need to do in order to relate the SFCA to mainstream

macroeconomics is to define the later. This is not an easy task, though. As Fair (2000,

p.2) reminds us, at least since Lucass (1976) critique of macroeconometric models,

[mainstream] macroeconomics has been is a state of flux. Beginning in the 1970's,

and account for the possibility of disequilibrium, he adds that a model should also (somewhat

less importantly) account explicitly for balance sheet and flow of funds constraints.


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macroeconomic research scattered in a number of directions and many puzzled as to

whether the field is going anywhere".

So, rather than trying to accomplish the huge task of surveying all mainstream

lines of research in macroeconomics, well try here to paint a general (and impressionist)

picture of mainstream macro based on a few, widely accepted, mainstream

methodological beliefs and families of models and then compare it to the SFCA. This is

what well do in what follows.

1.2.1 - Parables and all that

As James Tobin aptly noted more than a decade ago:

In journals, seminars, conferences and classrooms macroeconomic discussion has become a babble of

parables. The parables are often specific to one stylized fact, for example the correlation of nominal prices

and real output in cyclical fluctuations. Their usual inability to fit other stylized facts appears not to bother

the authors of papers of this genre. The parables always rely on individual optimization, across time and

states of nature. They differ in the arbitrary institutional restrictions they specify on technology, markets, or

information (Tobin, 1989, p. 19)

Indeed, one of the distinguishing features of todays mainstream macroeconomics

is that it doesnt care at all to build models that look like the real world as we know it.

On the contrary, it seems that the predominant view among mainstream economists is

that any model that is well enough articulated to give clear answers to the questions we

put to it will necessarily be artificial, abstract and patently unreal (Lucas, 1980, quoted

in Hoover, 2001, p.139) and, therefore, insistence on the realism of an economic

model subverts its potential usefulness in thinking about reality (Hoover, 2001, p.139).

As a result, mainstream discourse about classic macroeconomic issues is now spread


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among different branches of the profession (i.e, labor, development, monetary,

international and public economics) besides macroeconomics proper, each of which using

their own set of nice optimizing parables to explain reality either directly or with the

help of very simplified macroeconomic models.

As it should be clear from the previous section, this trend goes against the SFCA

view. One of the main goals SFC model builders seek to achieve is to capture the

essential interdependences (Brainard and Tobin, 1968, p.99) between (real)

macroeconomic sectors, a feature of reality considered too important to be simplified

away from the analysis. This potential advantage, however, doesnt come without a cost

because a more detailed approach implies an increase in the complexity of the relevant

model. On the other hand, its undeniable that in actual economies each macroeconomic

sector interacts with all the others in many different and complex ways. Bonds issued by

the government, for example, are held and traded by firms, banks, households and

possibly also by the rest of the world, often in many differentiated markets; goods

produced by firms are also bought by all the other macroeconomic sectors as well; banks

provide loans to many other macroeconomic sectors; and the list goes on. It is also true

that a given financial asset is often issued by several different macroeconomic sectors.

For example, banks, firms and the rest of world can all issue equity, all these sectors and

the government can issue bonds, etc. In other words, each actual sectoral balance sheet

consist of a very large number of assets (which are also liabilities of other sectors) and

liabilities (which are also assets of other sectors).

As a consequence, as put by Godley and Zezza (1989, p.3), the simplest realistic

[SFC] model requires a relatively large number of accounting equations. Most SFCA


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authors deal with this problem by imposing simplifying assumptions to the accounting

structure like, say, only domestic firms issue equity, or only banks buy bonds from the

rest of the world and, while its true that in many real economies some holdings of

assets by sectors can indeed be neglected, the choice of simplifying assumptions is bound

to be controversial. As put by Taylor (1990, p.4) the degrees of freedom available to any

actor depend on institutions and history of the economy at hand; incorporating them in a

convincing fashion is part of the model-building art29. The bottom line is that, although

29The issue at hand is somewhat analogous to the specification problem in econometrics. We can

either underestimate or overestimate the importance of sectoral interdependence (by analogy to

underparametrize/overparametrize a regression). In the first case, well probably get biased

results in the sense that our model fails to capture essential interdependences between sectors

and, therefore, gives us a distorted picture of reality. In the second case we lose precision, in the

sense that the relevant causal mechanisms are obscured by the irrelevant ones. In order to fully

understand what is involved in over-aggregating a SFC model, one has to (i) have in mind that

sectoral accounts are obtained by simply adding up the individual accounts of the members of the

sector; and (ii) note that by following this procedure one loses trace of all intra-sectoral

transactions. If, for example, a bank repays a loan to another bank, this transaction will not appear

in the accounts of the banking sector as a whole (since the payment of one bank will cancel out

with the receipt of the other). The fact that these transactions are neglected in SFC macromodels

is not supposed to mean, of course, that they are not relevant per se, but that they are not crucial

to the understanding of the behavior of the economy as a whole. The risk of working with an

over-aggregated model is therefore to neglect differences among sub-sectors which are

indeed important to the understanding of the economy as a whole. Note also that over-

aggregation is not the only possible form of under-parametrization Another important kind is

the omission of relevant kinds of transactions among sectors. If, for example, the households

sector is responsible for a significative part of the aggregate demand for, say, bank loans, its

clear that an assumption like households dont have access to credit will add a bias to the

model. The case of overparametrization is somewhat easier to analyze. No qualitative detail is

likely to be added if we disaggregate the households in, say, basketball lovers, football lovers

or neutral, but the increased number of equations/variables in the model will certainly make the


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SFCA authors have no problems acknowledging the trivial fact that all models are

unrealistic in some degree, ceteris paribus they prefer more realism to less.

1.2.2 - Isnt the current mainstream SFC, after all?

The mainstream emphasis on unrealistic parables is not enough to characterize it

as stock-flow inconsistent. The very fact that SFC requirements are not even mentioned

by most mainstream practitioners implies they are considered either trivial or irrelevant.

It might, indeed, be the case that, as unrealistic as they are, mainstream models would

perform well in all Tobins five items above. In order to address these issues we must dig

a little deeper and thats what well do in what follows. Of course, as both the number of

neoclassical parables available in the market and the number of possible mainstream

macroeconomic models based on these parables (or combinations of these parables) are

very big, well have to deal here only with the ones we deem more important and/or

popular.

We shall begin with the most rigorous neoclassical model, i.e, Arrow-Debreus

general equilibrium model with perfect markets for all present and contingent

commodities. This model is relevant not only because of its intellectual prestige, but

because in this situation each individual knows all future prices in all contingencies, and

these future prices actually occur. Each firm or household can choose a path for

investment or consumption, and the choice of path simultaneously implies a portfolio of

analysis of its properties more difficult. Indeed, given that its often impossible to find analytic

solutions even for relatively simple systems of difference/differential equations, the comparative

statics/dynamics properties of most SFC models can only be studied by means of repeated

computer simulations, a procedure that gets more complicated as models grow in size.


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assets at each instant. Under these strong hypotheses there is no need to distinguish ()

between stock decisions and flow decisions, because they are always mutually

consistent (Foley and Sidrauski, 1971, p.4). So, assuming a competent auctioneer, we

can be sure that flows increase/decrease stocks exactly as they must. The problem here,

as is well known, is that this model has clear problems with at least two features of

Tobins definition, i.e, the careful treatment of time (since its static) and the explicit

modeling of monetary operations (because it has no obvious place for money).

This difficulty in dealing with money is also present in the mainstream

workhorses, i.e, the Ramsey and OLG models

30

. This is not to say that money cannot be

included in these models, but that this inclusion is somewhat artificial. One way to do it

that brings the models closer to the SFC paradigm is through the introduction of the so-

called Clower constraint condition (or cash in advance constraint), i.e, the fact that

money buys goods and goods buy money but goods do not buy goods (Blanchard and

Fischer, 1989, p.165)31. A good example of such models is David Romers OLG-Cash in

advance model (idem, p.165-180), which does get reasonably good grades in many of

Tobins items, even if one considers that it simplifies things a little too much assuming

that the government creates money by giving it to newborn babies as transfers (even

though there are banks in the model!). This problem isnt that important, though, since

Romers model could conceivably be adapted to provide a better treatment of financial

30 See, for example, the textbook expositions of Blanchard and Fischer (1989, ch.4) and Romer

(1996,ch.2).

31Another is the inclusion of money in the utility function of agents. The Clower constraint is

somewhat problematic because credit also buys goods. The money in the utility function

hypothesis is problematic because people in general derive utility from goods not from painted

pieces of paper. See Blanchard and Fischer (1989, ch.4) for a discussion.


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and monetary operations and improve its SFC grade32. What is relevant to our point

and will be further discussed in the next section - is that, even though its possible to

make most mainstream models SFC, most mainstream macroeconomists simply dont

care to do it.

Before discussing some possible reasons for this last fact, it must be mentioned

that despite all their academic predominance, the mainstream workhorses are rarely, if

at all, used in practice by applied macroeconomists. As put by John Taylor (2000, p. 90,

quoted in Fair, 2000, p.2), at the practical level, a [new] common view of

macroeconomics is now pervasive in policy-research projects at universities and central

banks around the world. According to Fair (2000, p.3) this view, summarized in Clarida,

Gal, and Gertler (1999), is based on three basic equations, which are: (i) an interest rate

rule: The Fed adjusts the real interest rate in response to inflation and the output gap

(deviation of output from potential)33. The real interest rate depends positively on

inflation and the output gap. Put another way, the nominal interest rate depends positively

on inflation and the output gap, where the coefficient on inflation is greater than one; (ii)

a price equation: Inflation depends on the output gap, cost shocks, and expected future

inflation; and (iii) an aggregate demand equation: aggregate demand (real) depends on

the real interest rate, expected future demand, and exogenous shocks. The real interest

32As Blanchard and Fischer (1989, p.179) put it, the model gives a flavor of the complexity of

money flows in an actual economy. SFCA authors expect models to do much better than that,though.

33 As put by Blinder (1998, p.27-28) ferocious instabilities in estimated LM curves in the U.S,

U.K, and many other countries, beginning in the seventies and continuing to the present day, led

economists and policy makers alike to conclude that money-supply targeting is simply not a


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rate effect is negative. In empirical work the lagged interest rate is often included as an

explanatory variable in the interest rate rule. This picks up possible interest rate

smoothing behavior of the Fed (Fair, 2000, p.2-3).

Although the model described above looks pretty much like a conventional

AD/AS model with endogenous money, the authors take great pride in the fact that these

equations are based on a general equilibrium model with optimizing representative

agents. For us what is important to note is that - like its distant cousin, the old IS/LM

equilibrium - the new consensus leaves aside important stock-flow relations34. As Fair

(2000, p.28-29) points out, this view is unrealistically simple, among other things

because all stock effects are omitted (including wealth effects) as well as the interest

income effect that arises from the undisputed fact that households hold a large amount

of short term securities of firms and the government, and when short term interest rates

change, the interest revenue of households changes.

We finish this quick (and partial) survey of current mainstream macroeconomic

models based on rigorous microfoundations, reminding the reader that a a variety of

ad-hoc models have played, and continue to play, important roles in influencing the way

[mainstream] economists, and perhaps more importantly, policy-makers, think about the

role of monetary policy (Walsh, 1998, p.3)35. The same point is made by Krugman (2000,

p.42), according to whom ()microfounded models have not lived up to their promise

(in the particular sense that they didnt add noticeably to our ability to match the

viable option. () As Gerry Bouey, a former governor of the Bank of Canada put it: we didnt

abandon the monetary aggregates, they abandoned us.

34 For details about the New Consensus view, see Taylor, J.B (2000), Clarida, Gali and Gertler

(1999) and Fair (2000).


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phenomena, ibid, p.39) and, therefore, after 25 years of rational expectations,

equilibrium business cycles, growth and new growth, and so on, when the talk turns to

the next move by the Fed, the European Central bank, or the Bank of Japan, when one

tries to see a away out of Argentinas dilemma, or ask why Brazils devaluation turned

out relatively well, one almost inevitably turns to the sort of old-fashioned () [IS-LM]

model macro ().

1.2.3 - Why should one care about SFC issues? A mainstream perspective

Considering that many neoclassical authors stressed the importance of SFC issues

in the sixties and seventies36, the careless approach of current mainstream concerning

these issues may strike some as surprising. Foley (1975), however, offers an elegant

explanation of this apparent paradox. Indeed, well before the rational expectations

hypothesis became hegemonic in the mainstream, Foley proved that, under the

assumption of perfect foresight on average37, the distinction between stock and flow

equilibria in asset markets is non-existent. In other words, under the assumption of

rational expectations theres no logical problem in phrasing macroeconomic models just

in terms of flows (or stocks), since a flow (stock) equilibrium would necessarily imply a

35For a detailed account of central banking in practice, see Blinder (1998).

36 See, for example, Christ (1967, 1968), Foley and Sidrauski (1971), Foley (1975), Turnovsky

(1977) and Buiter (1980, 1983).

37 Foley uses the term perfect foresight without the qualification on average, but explains that

in more complex models of where expectations are represented as probability distributions, ()

[my] notion of perfect foresight corresponds to the assumption that the mean of that distribution

is correct (Foley, 1975, p.315). We decided to include the qualification to avoid confusion with

the more intuitive notion of perfect foresight as a synonym of zero expectational error. We

also made a couple of (convenient and harmless) small changes in Foleys notation.


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stock (flow) equilibrium as well. Given that Foleys reasoning touches a series of

important methodological points of the SFC literature well discuss it in some detail in

what follows38. Although this section is slightly more technical than the others, non-

technical readers can skip it without any major loss in continuity.

It seems convenient for our purposes to start from Foleys views on the treatment

of time in macroeconomic modeling. On this issue, he (p.310) agrees with Hahn that

while in reality people may take decisions discontinuously, not all people take decisions

at the same time and, therefore, that both continuous time models (that assume decisions

made continuously) and period models (that assume that all transactions of a certain

class occur in some synchronized rhythm) are unrealistic abstractions. Having

established that, Foley (p.311) then concludes that a theorist using a period model must

either establish a natural period in which decisions of many different agents are

synchronized or accept the position that a period model is, like a continuous time model,

an approximation of reality in which case outcomes of the macroeconomic model should

not depend in any important way of the period used. Indeed, it seems natural to think

that if one has no knowledge at all about the actual timing of the decisions of the

aggregate of the agents, then one simply should not propose models that depend crucially

on this timing. This conclusion has non-trivial implications, though. If the extent of the

period (implicit in a period model) doesnt matter, then we must be able to decrease it,

say, from a quarter to a week, or a day, or even a second without changing the qualitative

outcomes of the model. What this means in practice is that a sound period model in

38Even though we will not be particularly interested in the details of Foleys mathematical proof.

For those, see Foley (1975) and Buiter and Woglom (1977).


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Foleys sense can always be transformed into a continuous time model by taking the limit

of the size of the period equal to zero.

A second important point made by Foley is that, even if we limit ourselves to

period models, we still have at least two different concepts of equilibrium in asset

markets, i.e, the beginning-of-period and the end-of-period equilibria39. In order to

illustrate these concepts Foley assumes an economy with just two assets, money (M) and

capital (K). If we also assume, a la Tobin and Foley, that the aggregate demands for these

assets depend on both the aggregate wealth and their expected rates of return, well have

the following equations:

Md(t)=[1/pm(t)]* L{W(t), [(pm(t+t)-pm(t))/tpm(t)], [r(t)/pk(t) + (pk(t+t)-pk(t))/tpk(t)]}

Kd(t)=[1/pk(t)]* J{W(t), [(pm(t+t)-pm(t))/tpm(t)], [r(t)/pk(t) + (pk(t+t)-pk(t))/tpk(t)]}

where,

Md(t) and Kd(t)= aggregate demands for money and capital at time t.

pm(t) and pm(t+t) = expected price of money (i.e, the inverse of the price of goods) in

times t and t+t

L{}and J{}= real functions

W(t) = expected aggregate wealth

r(t) = expected profit rate at time t

pk(t) and pk(t+t) = expected price of capital in times t and t+t

and, of course,

[(pm(t+t)-pm(t))/tpm(t)] = real rate of return on M

39 And, he adds that, although these two distinct characterizations () have quite different

theoretical consequences (p. 307), the () literature does not always recognize the distinction

between () [them] and occasionally confuses them (p.304)


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and

[r(t)/pk(t) + (pk(t+t)-pk(t))/tpk(t)] = real rate of return on K

In the end-of-period equilibrium, according to Foley (p.309), demands and

supplies [of assets] are offered as of the end of the period. Agents can offer to sell K, for

instance, which does not exist at the trading moment but which they plan to produce

during the period. Contracts are made for labor and capital services and consumption

during the period and asset deliveries at the end. So, in this case we have that the

relevant supplies of assets are the supplies available at the end of the period (i.e, the

supplies available in the beginning of the period, M(0) and K(0), plus the additions

created within the period, M and K) and the relevant demands for assets take into

consideration the portfolio the agents will want to have in the beginning of the next

period (and, therefore, are functions of the expected returns two periods ahead).

Formally:

M(0)+M=[1/pm(t)]*L{W(t),[(pm(2t)-pm(t))/tpm(t)],[r(t)/pk(t)+(pk(2t)-

pk(t))/tpk(t)]}

K(0)+K=[1/pk(t)]*J{W(t),[(pm(2t)-pm(t))/tpm(t)],[r(t)/pk(t)+(pk(2t)-

pk(t))/tpk(t)]}

In the beginning-of-period equilibrium, on the other hand, trading in and

delivery of assets are assumed to take place at the same time, that is, the beginning of the

period. Within period consumption is contracted for but within-period production is done

on a kind of speculation (Foley, p.310). So, in this case we have that the relevant

supplies of assets are the supplies available at the beginning of the period (M(0) and

K(0), i.e, the stocks inherited from the previous period) and the relevant demands for


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assets take into consideration the portfolio the agents will want to have in the beginning

of the period (and, therefore, are functions of the expected returns one period ahead).

Formally:

M(0)= [1/pm(0)]* L{W(0), [(pm(t)-pm(0))/tpm(0)], [r(0)/pk(0) + (pk(t)-pk(0))/tpk(0)]}

K(0)=[1/pk(0)]* J{W(0), [(pm(t)-pm(0))/tpm(0)], [r(0)/pk(0) + (pk(t)-pk(0))/tpk(0)]}

After having defined both kinds of asset equilibrium in period models, Foley then

checks if they are indeed sound taking the limits of both sets of equilibrium conditions as

t tends to zero40. By doing that, Foley is able to find two different continuous time

types of equilibrium in asset markets (i.e, the different limit versions of the two

different concepts of equilibrium in period models). Foley calls the continuous time

analogue of the beginning-of-period equilibrium the stock equilibrium, since it

equates an instantaneous demand to hold a stock of an asset with an instantaneous

demand supply(p.315). The continuous time analogue of the end-of-period

equilibrium, on the other hand, is called by Foley flow equilibrium, since it equates

instantaneous flow demand[s] for () asset[s] with instantaneous flow () [supplies]

(p.314). Foley then is able to prove that these two kinds of equilibrium have very

different qualitative properties despite the subtlety of their differences and, in fact, are

only equivalent under the perfect foresight on average hypothesis (and, therefore, under

rational expectations as well). Foleys result, therefore, may explain why new classical

macroeconomists often use flow and stock equilibria as perfect substitutes in rational

expectations models.

40Foley actually modifies a little bit the concept of end-of-period equilibrium, but well skip

the technicalities here. For details, see Foley (1975) and Buiter and Woglom (1977).


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1.3 - The SFCA and Post Keynesian Macroeconomics

The aim of this part of the paper is to discuss in an introductory and non-

exhaustive way - the case for the wide adoption of the SFCA by Post-Keynesians as

presented by Lavoie and Godley (2001-02, p.131). According to these authors:

Post Keynesian economics, as reported by Chick (1995), is sometimes accused of lacking coherence,

formalism, and logic. (). The stock-flow monetary accounting framework provides (...) an alternative

[logical] foundation [for Post-Keynesian macroeconomic modeling] that is based essentially on two

principles. First, the accounting must be right. All stocks and all flows must have counterparts somewhere

in the rest of the economy. The watertight stock flow accounting imposes system constraints that have

qualitative implications. This is not just a matter of logical coherence; it also feeds into the intrinsic

dynamics of the model.

Well discuss this claim in two steps. First, well present the SFC critique of the

Keynes/Kalecki conventional short run macroeconomic equilibrium, still widely used by

Post-Keynesians in general41. Second well discuss in more general terms what may go

wrong when one doesnt take SFC requirements into consideration. While the arguments

that follow are hardly new, we hope they will convince the reader of the crucial

importance of the issue at hand.

1.3.1 - Stock-flow inconsistency in the GT

As mentioned in the first part above, the SFC critique of the Keynes/Kalecki

notion of short run equilibrium was the reason why the SFCA appeared in the first place.

We chose to discuss it here for three reasons. First because it is an important particular

example of the general point that Lavoie and Godley are trying to make, i.e, that the

41See, for example, Davidson (1994), Lavoie (1992) and Palley (1996).


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adoption SFCA offers more insight than (and may correct logical problems of) current

practices. Second because, as mentioned before, versions of the Keynes/Kalecki short run

equilibrium are still widely used today despite their logical problems. Third, because we

strongly believe that Keynes and Kalecki were essentially right in their particular

formulations and we hope this will highlight the constructive nature of the SFC critique42.

One of the reasons why the discussion of Keyness short run equilibrium is useful

to highlight the distinguishing features of the SFCA though certainly not the most

important is that the exact meaning of this particular concept has been the object of

intense controversy over the years

43

. SFC authors, on the other hand, use formal models

of the whole economy that enable the reader to pin down exactly why the results come

out as they do, as opposed to other writings on monetary theory that rely solely on a

narrative method which puts a strain on the readers imagination and makes

disagreements difficult to resolve (Godley, 1999, p.394). Be that as it may, well avoid

here all the discussion about what Keynes really meant and follow chapter XVIII of the

General Theory as closely as possible.

As it is well known, in chapter XVIII Keynes divide the variables in his model in

three groups, i.e. given, independent and dependent. He called the first two groups

the deteminants of the economic system (the third comprises his endogenous variables)

and added:

42Even though the following discussion will focus on Keynes, we hope it will be clear that the

critique is valid for both authors.

43 For two of the many different interpretations of the exact meaning of Keyness short run

equilibrium, see Amadeo (1989) and Asimakopulos (1991). Many others exist and we dont want

to imply here that none of them is SFC.


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the division of the determinants of the economic system into two variables is, of course, quite arbitrary

from any absolute standpoint. The division must be made entirely on the basis of experience, so as to

correspond on the one hand to the factors in which the changes seem to be so slow or so little relevant to

have only a small and comparatively negligible short term influence in our quaesitum [i.e, the given

variables]; and on another hand to those factors in which the changes are found in practice to exercise a

dominant influence in our quaesitum [i.e, independent variables]. (Keynes, GT, ch. XVIII, p.247)

As is also well known, Keynes explicitly listed the stock of capital and labor

among the given variables and, therefore, as noted by Hicks and Asimakopulos,

Keyness short run represents an interval of time sufficiently brief so that changes

during this interval in productive capacity, that occur continuously in any economy with

positive net investment, are small relative to the initial productive capacity so that they

can be legitimately ignored. This interval, however, must also be sufficiently long for

most of the multipliers effects of a change in investment to have been completed within

that period (Asimakopulos, 1991, p.68).

But what about other macroeconomic stocks? What did Keynes have to say in the

GT, for example, about macroeconomic stocks like the public debt, private wealth or the

economys foreign debt? Not much, really. However, as Tobin (1980, p.75) points out,

though Keynes was not explicit about assets other than capital, the spirit of the approach

is presumably the same: the time span for which the model is intended is too short for

flows to make noticeable changes in stocks (Tobin, 1980, p.75).

At this point, we must be ready to understand the SFC critique of Keyness notion

of short run equilibrium as described in chapter XVIII of the GT. The problem to put it

briefly is that if one thinks about stocks in general (and not only the stock of capital),

especially financial stocks, it doesnt really make sense to think of them as given


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variables. As noted by Tobin in his Nobel Conference, thats precisely why "the

interpretation of the solution to a Keynesian short-run macroeconomic system has always

been ambiguous. () Is the solution an equilibrium in the sense of a position of rest?

This can hardly be the case for a model whose very solution implies changes in the stocks

of capital, wealth, government debt, and other assets. Since the structural equations of the

model depend on those stocks, they will not replicate the solution when the stocks are

moving. Keynes himself recognized the problem but excused himself for ignoring the

dynamics of accumulation by defining the horizon of the analysis as short enough so that

flows make insignificant difference to the size of stocks. The excuse makes tolerable

sense for the stocks of physical capital and total wealth, but unbalanced government

budgets, monetary operations and external imbalances can alter the corresponding asset

stocks quite rapidly. A model whose solution generates flows but completely ignores

their consequences may be suspected of missing phenomena important even in a

relatively short-run, and therefore giving incomplete or even misleading analyses of the

effects of fiscal and monetary policies". (Tobin, J, 1982, p. 188).

1.3.2 - What exactly are the problems? - A Summary

A lot of things happen when one takes explicitly into account all stock-flow

relations implicit in Keyness equilibrium. First, as mentioned before, Keyness static

system turns into a dynamic one. Second, one gets a series of new variables to explain.

Clearly, for example, the flow of net investment adds to the size of capital stock. What is

then the influence of this increased stock in the subsequent flows of investment and

income? Any explicit theoretical answer to this question, whatever it might be,


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necessarily involves an assertion about stock(of capital)-flow(of investment or of income)

ratios. Stock-flow ratios are at the core of most of current policy-relevant issues. How

does the size of government debt affect interest rates (and through this channel) GDP?

Whats the optimum external debt to exports ratio for under-developed countries? How

does the private stock of wealth (including the stock market part of it) affect the flows of

consumption and imports? What does conventional Post Keynesian (or Keynesian, for

that matter) economics have to say about these crucial issues? The first general point to

be made here is precisely that stock-flow ratios play a crucial role in modern capitalist

economies and, therefore, models of these economies must necessarily include them.

Surely one cant do that without theorizing about them. The need for this continuing

theorizing effort is a second general point being made here.

To state that Post-Keynesians in general dont know much about stock-flow ratios

doesnt mean, of course, to state Post-Keynesians dont now anything at all about them.

There are, of course, many Post-Keynesian models dealing with stock-flow issues44. The

problem here is that it is not clear how much their conclusions are affected by the stock-

flow inconsistency bias. So, the third general point being made here is precisely the one

made by Tobin about Keynes. If a model generates flows it has to deal with all their

consequences, otherwise it may very well give misleading analyses.

The fourth and last point we want to make here related to the third above - is

that, as well discuss below, when one explicitly takes into consideration all the flow-

flow, stock-flow and stock-stock relations implicit in a given macroeconomic model of

44 Again, a detailed list would be beyond the scope of this paper. Two examples are Thirwalls

growth model (see, for example, McCombie and Thirwall, 1994, ch.3) and Davidsons

interpretation of chapter 17 of the G.T (see, for example, Davidson, 1972, ch.4).


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hypotheses (that is, if one works with a closed system in which every flow comes from

somewhere and goes somewhere), one gets to know all the (often non-trivial) system-

wide logical requirements implicit in the system at hand and these impose a lot of

structure in the models.

1.4 - Some notes on the state-of-the-art of SFC work

SFC model building has gone a long way in the last two decades, especially since

the second half of the 1990s45. A common SFC methodology based on the pioneering

work by Brainard and Tobin (1968) and refined by Wynne Godley in a long series of

papers has been established and its application to a series of socially relevant policy

issues has shed light on many previously dark areas. Yet, the SFCA is still relatively

recent and a lot remains to be done. In what follows well attempt to summarize the main

features of the recent SFC literature. Hopefully, this summary will convince the reader

that this line of research is a clear and progressive alternative to current mainstream

macroeconomics.

1.4.1 - The Tobin-Godley methodology for theoretical work in macroeconomics

In somewhat schematic terms, the consensual methodology implicit or explicit in

the recent SFC literature consists of three steps, which are: (i)do the (SFC) accounting

first; (ii)establish the relevant behavioral relationships after that; and then (iii) perform

comparative dynamics exercises (generally with the help of computer simulations) to

see how the model behaves. As this description makes clear, as does our interpretation of

45See footnote 6 for a representative sample of recent SFC work.


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the SFCA as a natural development of the Keynesian research program, this Tobin-

Godley methodology has close similarities to the one implicit in the old Keynesian

models. As this fact may give the reader the wrong impression that theres nothing really

new being said in the recent SFC literature, it seems appropriate to emphasize here the

differences between these two methodologies46.

Beginning with the first point, we mentioned before several reasons why SFCA

authors rely so much on consistent accounting frameworks. In practice this means that the

first thing a SFC theorist must do in order to analyze a given issue is to make sure he or

she has an adequate SFC accounting framework to deal with it

47

. There are no

exceptions to this rule, no matter the kind of issue being analyzed. If no such accounting

framework exists, the SFC theorist has to design it herself. Data availability is, in fact,

irrelevant in this first step. What the theorist gets from this accounting exercise is the

whole set of system-wide logical requirements that are relevant to the issue at hand.

These come in three kinds. First, there is the intrinsic SFC dynamics of the system, i.e,

the fact that flows necessarily increase or decrease stocks and these, by their turn,

influence future flows. Second, there are the sectoral budget constraints, i.e, the fact

that in each accounting period the decisions of economic agents alone and in the

aggregate are constrained by what they have in the beginning of the period 48, what they

earn during the period and their access to credit. Third, there are the adding up

46 See, for example, Klein and Young (1980) for a nice example of an old neoclassical

Keynesian flow macroeconometric model. Modern expositions of the Cowles Commission

approach (like Fair, 1984) are very close to the Tobin-Godley methodology, though.

47We dont want to imply that the choice of the adequate accounting framework is independent

of theoretical considerations, though. The contrary is true, as argued in the first part of this paper.

48Subject also to liquidity constraints, as Keynes would have emphasized.


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constraints, i.e, the fact that accounting identities imply that the whole must necessarily

equal the parts and certain (combinations of) stocks and flows must necessarily equal

others. Concentrated attention on these logical requirements differentiates SFC macro

models from conventional Keynesian ones. Many authors explored some implications of

some of these logical requirements in the past, but very few of them realized/emphasized

the importance of always trying to explore all the implications of all of them.

A careful analysis of these requirements has important implications also for the

choice of the behavioral equations of the model, the second step of the Tobin-Godley

approach

49

. First, the use of SFC accounting frameworks makes clear the necessity to

theorize about stock-flow ratios (since they have non-trivial dynamic implications).

Second, and perhaps more obvious, the use of any accounting framework implies a given

number of degrees of freedom to the system and this limits the number of possible

model closures as discussed in the first part of this paper. Note, however, that in

complex accounting structures the nature of these degrees of freedom may not be obvious

at first sight. In particular, the use of a water-tight SFC accounting framework implies

that in an economy with n sectors, the financial flows of the nth sector are completely

determined by the financial flows of the other n-1 sectors of the economy50. This fact has

nothing to do with the neoclassical concepts/assumptions such as Walrass Law, utility

maximizing individual agents, market equilibrium and etc. It happens simply because

what sectors 1 to n-1 (in the aggregate) pay to sector n is equal to what sector n receives

from these sectors and vice-versa.

49 Along, of course, with other theoretical considerations and more traditional concerns with the

structure of the economy at hand (that are also present in the choice of the accounting itself).

50See Godley, 1996 and 1999.


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After the first two steps what one generally gets is a complicated system of non-

linear difference/differential equations. The third step, naturally, is to perform a series of

comparative dynamics exercises to evaluate the sensitivity of the model dynamics to

changes in parameters and key exogenous variables. Given that analytic solutions to these

systems are seldom available, SFC practitioners often must use computer simulations to

try to approximate them. As Godley (1996, p 22) puts it, this approximation is often good

in practice:

() with numerical solutions (), we can gain insights into how the system as a whole functions, by first

obtaining a base solution and then changing one exogenous variable at a time to see what difference is

made. It might seem as a though any particular model run depends so much on the particular numbers

used that the results are completely arbitrary and have no general application at all. However, it is my

experience that repeated simulation, combined with iterative modification of the model itself, does

progressively lead to improved understanding, for instance, of what the stability of the system turns on,

what combinations of parameters are plausible and how the whole thing responds when subjected to

shocks.

The schematic presentation above should not lead the reader to believe the three

steps are taken independently. There is a lot of back and forth movement between them

and, as mentioned before, a lot of art is involved in the model building process.

However, SFCA authors strongly believe that this methodology provides a logical and

coherent way to approach macroeconomic issues.

1.4.2 - Recent Developments and Unknown Territory

The recent SFC literature has both destructive and constructive sides. In fact,

many recent papers have used the SFCA to find inconsistencies in existing

macroeconomic models. So Taylor (1998a, 1999 and 2002), for example, has argued that


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the famous Mundell-Fleming model is logically inconsistent because when full SFC

accounting is respected it can be shown that it has one fewer independent equation than

one usually thinks, while Godley and Shaikh (2002) have argued that the standard (neo)

classical macroeconomic model is also stock-flow inconsistent and, although it can be

fixed with minor changes, the consequences of these changes are far from minor.

One must not overemphasize this destructive side of the SFCA literature, though.

Indeed, not only does the use of the SFCA help to identify inconsistencies in existing

macroeconomic models, but it also (almost simultaneously, in fact) helps to fix them. So

all the papers mentioned above offered SFC alternatives to the previously inconsistent

models they criticized.

Also on the constructive side, the SFCA has recently been used to shed light on a

number of policy relevant issues. So, while Taylor (1998b) has used it to criticize the

plausibility of current mainstream models of speculative attacks and financial crises and

propose a new one, Godley and Lavoie (2002) have used it to study complex monetary

arrangements like, for example, the European Monetary Union and Izurieta (2002) has

used it to analyze the consequences of dollarization schemes. As mentioned before,

new SFC work sometimes requires the construction of new SFC accounting

frameworks. Indeed, both Taylor (in his critique of the Mundell-Fleming model) and

Godley and Lavoie(2002) and Izurieta (2002) (in their analyses of the EMU and

dollarization schemes), for example, used versions of Godleys original accounting of

two interdependent economies which together form the whole world in their papers51.

51See Godley (1999b) for details.


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The frontier of the SFCA is not limited to finding inconsistencies in existing

macroeconomic models and developing new SFC accounting frameworks and models for

new problems, though. Although a discussion of empirical SFC models would have

extended this paper far too long, these models have continuously been used for policy

analysis in the last decades52. Empirical specifications of SFC models involve a large

number of unsettled issues related to the transition from theoretical to empirical

macroeconomic models. Theres no consensus, for example, about applied issues such

as the choices of (i) the size of models, (ii) their degree of aggregation, (iii) the relevant

accounting period, (iv) the relevant econometric techniques and etc. Research on SFC

models, therefore, can conceivably benefit from current research in selected fields of the

mainstream, like those related to computer simulated agent-based models (that might

illuminate issues related to aggregation), application of optimal control theory to policy

analysis and advances in macroeconometric techniques, for example.

1.5 - Conclusion

Stock-Flow consistency can be seen from different angles. As we tried to argue,

people that strongly believe in the efficiency and speed of the self-adjusting properties of

markets tend to see it as a mere detail that can be trivially met and probably can be

ignored without it causing any major problems. People that dont believe that markets

and agents are (or even can be) so rational and informed, on the other hand, tend to

52See, for example, Davis (1987a and 1987b), the SFC papers in Taylor (1990) and Alarcon et.al.

(1991) and the series of applied papers by Wynne Godley both at the Department of Applied

Economics of the University of Cambridge and at the Levy Economics Institute (like, for

example, Godley, 1999c).


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believe (or, at least, should admit the possibility) that SFC requirements impose a great

deal of structure in an otherwise extremely unpredictable economic environment.

Therefore, although both sets of economists are advised to pay careful attention to these

requirements and issues, this paper tried to argue that the second set has much more

reasons to do so than the first.

This paper also attempted to present a summary of the current state-of-the art of

the SFCA research. Although its impossible to make justice to both the breadth and the

potential implications of current research in a couple of pages, we hope to have given

enough evidence of the continuous progress made by SFC authors in the last two decades

and of the possibilities of this line of research.


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2 - Cambridge and Yale on Stock-Flow Consistent Macroeconomic Modeling

Introduction

The last 5 years have witnessed a revival of the stock-flow consistent approach to

macroeconomic modeling (SFCA) that was at the frontier of Keynesian research in the

seventies and eighties53. SFC models didnt receive proper attention at that time

dominated by the endless debates that followed the so-called New Classical counter-

revolution and, with notable exceptions, practically disappeared from the literature for

a while. However, with most of the profession now convinced that New Classical

economics doesnt offer convincing explanations for the dynamics of actual economies in

historical time, macroeconomists of all sorts are increasingly rediscovering old truths.

This process is not an easy one, though. Its just symptomatic that the modern New

Keynesian consensus has been criticized precisely for neglecting the stock-flow

relations emphasized by the SFCA54.

Part of the problem is that, given their emphasis on water tight accounting

frameworks, SFC authors and models are often perceived as either national accountants

(accounting) or applied economists (economics). This is a truth, but only a half-truth55.

Proper stock-flow consistent accounting imposes a great deal of structure to

macroeconomic models by making their system-wide logical implications clear to the

analyst. It also makes explicit the need for theorizing about a whole lot of forgotten

53 As discussed in section 1.4.2 above.54

As seen in section 1.2.2 above.

55Its true, in particular, that SFC macro models are often used (as any good macro theory

should) in applied research and are based on national accounting schemes. E.P Davis (1987a and

1987b), L.Taylor (1990), Alarcn et.al. (1991) and Godley (1999b) provide many examples of

applied SFC macro models.


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variables (i.e., the ones that do not appear in stock-flow inconsistent models, though

logically implied by their hypotheses), especially stock-flow ratios56. These are all

theoretical issues, not applied ones. Of course, we dont want to imply here that there

hasnt been any economic theorizing about stock-flow ratios in the past. What we do

want to imply is that most people that did this theorizing either assumed problems away

with strong hypotheses about rationality of agents and instantaneous market-clearing57 or

didnt care to phrase their arguments in a proper SFC model 58. Although the later group is

clearly more interesting than the first, their message is at best incomplete. As put by

Tobin (1982, p.188), a model whose solution generates flows but completely ignores

their consequences may be suspected of missing phenomena important even in a

relatively short-run, and therefore of giving incomplete or even misleading analyses

().

Indeed, even though the number of possible closures for any reasonably

realistic SFC accounting framework is huge59, very few authors have written reasonably

complete SFC models in the proper sense of the term and one can clearly distinguish in

these writings a Yale (or Brainard-Tobin-type)and a (New) Cambridge (or Godley-

56 Which, by the way, are at the core of many unresolved policy issues. Just to mention two

among many other possible examples, what policy-makers think about the public debt to gdp

ratio and the external debt to exports ratio will probably determine to a good extent the supply of

public and imported goods that will be made available to the people. Its symptomatic that most

Keynesian macro has focused only on static variables like the public debt or the rate of inflationand (to a reasonable extent) neglected dynamic ones.

57See Foley (1975) for a proof that stock and flow equilibria are indistinct under rational

expectations.

58This is the case of heavy-weights like Friedman, Harrod, Hicks, Meltzer and Modigliani,

among many others.


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type) types of closures60. As mentioned before, most of these ideas were written in the

seventies and eighties and, yet, we hope to demonstrate in what follows that they deal in a

careful and profound way with many theoretical issues that are still open as of today. In

fact, a second goal of this paper is precisely to provide a context for the current SFC

discussion.

Note, however, that SFC authors have written extensively about issues so

different as the behavior of banks, financial markets in general, industrial pricing, wage

determination and open-economy macroeconomics. Although all these issues can be seen

as part of the broad SFCA research program, we will restrict ourselves here to the

discussion of what these authors had to say about macroeconomic models of closed

economies with Fixprice goods market and Flexprice financial markets61. This decision

means that one must regard this paper as an introductory effort. In particular, most SFC

discussion in the seventies and eighties (especially at Cambridge) dealt with inflation

accounting and open-economy issues and these are neglected here.

In what follows we do four things. First, we present the (SFC) accounting

framework of the closed artificial economy that will be used in this paper and a couple

59 As stressed by Taylor (1990, p.46)

60Examples of Yale-type models are Brainard and Tobin (1968), Foley (1975), Tobin and Buiter

(1976), Braga de Macedo and Tobin (1979), Backus et.al. (1980) and Tobin (1982). The British

team is represented by Cripps and Godley (1976), Godley and Cripps (1983), Anyadike-Danes

et.al. (1987) and Godley and Zezza (1989), among others. We dont want to imply, of course,that other authors didnt write related material at that time. Fair (1974, 1984 and 1994) is an

obvious example from Yale, but note that, as he put it himself, what is commonly referred as

Yale macro is quite different in emphasis from () [his] own work (Fair, 1984,

acknowledgments).


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of generic theoretical issues related to the SFCA. After that, we discuss formally the

characteristics of both our (somewhat stylized) Yale-type (in section 2.2) and (New)

Cambridge-type (in section 2.3) closures of the accounting framework presented

before. The fourth section discusses briefly some recent work by Godley (1996, 1999)

and Lavoie and Godley (2001-2002) that propose a synthesis of the two pure models

presented in the previous parts.

2.1 - The Accounting framework and its implications

This part of the paper is divided in two sections. Section 2.1.1 below presents the

artificial economy we will use as a neutral theoretical court in which the arguments

of both schools can be presented and compared62. Section 2.1.2 discusses a couple of

theoretical issues that usually arise in such discussions.

2.1.1 - The artificial economy

In our artificial economy there are (a) four macroeconomic sectors, i.e.,

households, government, (non-financial) firms and banks, (b) six assets, i.e., high-

powered money (currency and bank reserves), demand deposits, time deposits,

government bonds, business equity and business loans and (c) one produced good63.

Table 1 below summarizes the main characteristics of the economy at hand.

61 In other words, well be reducing important theoretical issues either to specific behavioral

hypotheses or to specific parameters of a macro model of a closed economy.

62We leave to the reader the task of judging the neutrality of our framework, though.

63This one good economy hypothesis is characteristic of Yale-type models (see Backus et.al.,

1980, p.263). Cambridge economists, on the other hand, have always tried to theorize directly

about aggregates. For convenience, we chose here to phrase Cambridge models in terms of Yale


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Beginning with the households, our simplifying assumptions made only for

convenience - are that (i) they dont have access to credit, (ii) they dont invest, (iii) their

wealth is divided among five possible assets (i.e., cash, money and time deposits, equity

and government bonds), (iv) they dont pay taxes, and (v) their total income consists of

wages, dividends and interest payments on bonds and time deposits. A close look at

Table 1 below is probably more informative than any written description, though. The

upper part of the table accounts for the current transactions made in the economy64, so

hypotheses (ii), (iv) and (v) should be obvious just by inspection of the upper part of the

households column (note that a plus sign before a variable indicates that money is being

earned, while a minus indicates that money is being spent). The lower part of the table

accounts for the consequences of the transactions in the first part over the total wealth of

the sectors (summarized by the current savings of the sectors) and the capital

transactions, i.e., the changes in the composition of these stocks of wealth (a plus sign in

this case indicates a source of funds, while a negative sign indicates a use of funds).

Again, it takes only a look at the lower part of the households column to get assumptions

(i) and (iii) right.

ones. The alternative unavoidable in empirical work would have forced us to deal with

complicated price and volume indexes.

64 With the exception of purchases of capital and inventory accumulation by firms. These are

both current receipts (from the point of view of firms that sold them) and capital expenditures

(from the point of view of firms that acquired them).


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Table 1: Flows of funds at current prices in our artificial economy

Sectors Households Firms Government Banks

Transactions Current Capital Current Capital Cur

Notes on the Stock-Flow Consistent Approach to Macroeconomic Modeling

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