Tag Archives: gennaro zezza

What Is Equilibrium?

The new paper by Gennaro Zezza and Michalis Nikiforos for the Levy Institute, surveying the literature on stock-flow consistent models has a discussion on the concept of equilibrium:

In the short run, “equilibrium” is reached through price adjustments in financial markets, while output adjustments guarantee that overall saving is equal to investment. However, such “equilibrium” is not a state of rest, since the expectations that drive expenditure and portfolio decisions may not be fulfilled, and/or the end-of-period level for at least one stock in the economy is not at its target level, so that such discrepancies influence decisions in the next period.

In theoretical SFC models, the long-run equilibrium is defined as the state where the stock-flow ratios are stable. In other words, the stocks and the flows grow at the same rate. The system converges towards that equilibrium with a sequence of short-run equilibria, and thus follows the Kaleckian dictum that “the long-run trend is but a slowly changing component of a chain of short-run situations; it has no independent entity” (Kalecki 1971: 165). The adjustment takes place because stocks and stock-flow ratios are relevant for the decisions of the agents of the economy. If stocks did not feed back into flows, the model may generate ever-increasing (or decreasing) stock-flow ratios: a result that might be stock-flow consistent, but at the same time unendurable. The convergence towards the long-run equilibrium also depends on more conventional hypotheses regarding the parameters of the model.

So equilibrium is a state where stock-flow ratios are stable.

Of course equilibrium just means that and doesn’t automatically translate to full employment, for example. One can imagine stock-flow ratios such as public debt/gdp, private debt/gdp may converge to some level such as 80%, 50% respectively but with unemployment at, say, 5%.

Also, it’s worth mentioning—especially in open economies—there is in general no automatic/market mechanism which guarantees that stock-flow norms are converging to some stable ratios.

Let me offer an alternative viewpoint for the short run.

In the short run, there’s really no concept of equilibrium because there is no heavenly Walrasian auctioneer in most markets. As pointed out by Nicholas Kaldor, there are dealers who are both buyers and sellers simultaneously. Dealers quote bid/ask prices and the quantities they are willing to buy or sell. Since there is a mismatch in demand and supply of “outside buyers” and “outside sellers”, dealers accumulate inventories or stocks. Dealers make a business out of the bid-ask spread. In non-financial markets, the terminology is slightly different. You won’t find a board with bid/ask prices at a car dealer, but the concept is similar. Here even the producer has inventories in the goods market. In the services market, whatever is demanded is supplied (or put in queue or refused if capacity is reached).

So there’s no equilibrium to be reached in the short-run. It’s always in disequilibrium. Sometimes neoclassical authors make it look like accounting identities are violated in disequilibrium and satisfied in equilibrium arranged by the Walrasian auctioneer. But in SFC models, it’s illogical to have such a thing. Accounting identities must always be respected. At all times, between all time periods, even infinitesimally small.

In real life, especially because of complications of the open economy, there is no such thing as an equilibrium or a tendency to move toward any equilibrium via market forces.

Still, the concept of equilibrium is useful even in SFC models. One can start with a state with a stable stock-flow ratios and then study what happens if some parameter or some exogenous variable is changed or a set of them are changed simultaneously. The dynamics may or may not reach equilibrium in the long run but we can study what happens in the traverse.


Stock-Flow Consistent Models: A Survey

There’s a new paper by Gennaro Zezza and Michalis Nikiforos for the Levy Institute.


The stock-flow consistent (SFC) modeling approach, grounded in the pioneering work of Wynne Godley and James Tobin in the 1970s, has been adopted by a growing number of researchers in macroeconomics, especially after the publication of Godley and Lavoie (2007), which provided a general framework for the analysis of whole economic systems, and the recognition that macroeconomic models integrating real markets with flow-of-funds analysis had been particularly successful in predicting the Great Recession of 2007–9. We introduce the general features of the SFC approach for a closed economy, showing how the core model has been extended to address issues such as financialization and income distribution. We next discuss the implications of the approach for models of open economies and compare the methodologies adopted in developing SFC empirical models for whole countries. We review the contributions where the SFC approach is being adopted as the macroeconomic closure of microeconomic agent-based models, and how the SFC approach is at the core of new research in ecological macroeconomics. Finally, we discuss the appropriateness of the name “stock-flow consistent” for the class of models we survey.

[The title is the link]


Levy Institute’s Strategic Analysis On The US Economy

Michalis Nikiforos and Gennaro Zezza of the Levy Economics Institute Of Bard College have published their strategic analysis report for the U.S. economy.

They discussion two scenarios — baseline scenario and scenario 1. Growth in either scenario is low. The authors argue that while equity markets have risen in recent times on expectations of a fiscal stimulus, it is unlikely. In scenario 1, it’s assumed that equity markets fall and this leads to a fall in private expenditure relative to income and this causes a fall in growth by 2020 and a rise in the budget deficit to 8.3% because of it.

It looks more likely that the Trump administration isn’t going to relax fiscal policy. Donald Trump had promised in his campaign to reduce taxes for even the middle class but is now saying that it’s dependent on numbers in the Republican healthcare plan.

At any rate, the report has a chart showing how tight fiscal policy has been since the recession. This is how real government expenditure changed after the crisis. The red line is the current recovery (2009Q2-) and other colours are for previous recoveries post recession trough.

Source: Levy Institute

[the title is the link]

Fiscal Conservatism, Weak International Trade Performance And Income Inequality Not Good For The U.S. Economy

The US economy is only 8.8 percent above the pre-crisis peak.

The Levy Institute has a new Strategic Analysis publication titled Fiscal Austerity, Dollar Appreciation, And Maldistribution Will Derail The US Economy in which they identity three main structural characteristics of the economy of the United States that stand in the way of the recovery:

(1) the weak performance of net exports, (2) pervasive fiscal conservatism, and (3) high income inequality

They show that in their baseline scenario, if the projections of the Congressional Budget Office’s outlook hold, their model simulations imply that the private sector’s net lending would turn negative by the end of 2017 and hence the private sector would be in a financial deficit, which is not sustainable.

The publication has some nice charts about the US balance of payments. One is the components of the current account of balance of payments with attention on the primary income balance:

U.S. Balance Of Payments And Components

Note how the balance on primary income has grown during the recent crisis. Another chart gives a further breakdown:

Balance On Primary Income

So direct investment income is the main component.

I like the way the authors explain this: it is a symptom of the crisis. From the article:

An interesting question is whether this improvement in net primary income receipts is sustainable or just symptomatic of the crisis. In our view, it is most likely the latter.

For more details, read the article here.

Private Indebtedness In CBO’s Forecasts

Michael Stephens of the Levy Institute highlights the recent Levy Institute Strategic Analysis: Back To Business As Usual? Or A Fiscal Boost? in a post Where Will US Growth Come From If Austerity Reigns on the Institute’s blog Multiplier Effect. 

According to the authors Dimitri Papadimitriou, Gennaro Zezza and Greg Hannsgen,

The results of our simulation are reported in Figure 4. The government deficit falls rapidly, but if we want to achieve the CBO’s projected growth path, the private sector has to start borrowing again, switching to a deficit position. Under this scenario, we would return to a situation not so different from the one we had before the 2007–09 recession.

In Figure 5 we report the path of household and non-financial business debt, relative to GDP. Both of these sectors must become more indebted, given our scenario 1 assumptions. If this is the path the US economy takes, it will not be long before another crisis hits, if only because of heavy private sector indebtedness.

Here’s private indebtedness in the assumed CBO scenario of growth and lower budget deficits.

So this implies that the United States still has cracks in the foundations of growth (as per a title of the Institute’s Strategic Analysis piece before the crisis) and policy needs to change.

The Institute’s Strategic Analysis articles have always pointed out logical inconsistencies in the CBO’s projections (from mid 1995 onward) and presented more realistic scenarios on growth with solid suggestions on how to run the economy. Here’s from April 2007 in a report titled The U.S. Economy – What’s Next:

The authors said:

In Figure 3, we translate the debt-to-GDP ratios in Figure 2 into flows of lending relative to GDP simply by subtracting from each quarter’s debt the previous quarter’s debt. One striking feature of Figure 3, not at all obvious from inspection of Figure 2, is that net lending was already falling rapidly from the beginning of 2006. The lower line for the post-2006 period shows what would happen to the net lending flow if the debt-to-income ratio were to level off: net lending would continue to fall rapidly, though not so far or fast as happened in 1980. The projections in the figure also show the enormous gap between the leveling-off scenario, in which we are inclined to believe, and the (implied) CBO scenario, in which we don’t believe at all.

In reaching provisional conclusions about the future growth rate of output and the future configuration of the three financial balances, we have used revised assumptions about output in the rest of the world because of lower U.S. growth than in the CBO scenario (based on the solution of a world model) and the performance of the stock market. The major conclusion is that output growth slows down almost to zero sometime between now and 2008 and then recovers toward 3 percent or thereabouts in 2009–10. However, by the end of the period, the level of output is still far (about 3 percent) below that in the CBO’s projection, which implies that unemployment starts to rise significantly and does not come down again.

(emphasis: mine)

Of course every situation is different, so to see/make some scenarios and projections, do look at Back To Business As Usual? Or A Fiscal Boost?

Seven Unsustainable Processes – Original

Of all the economists, Wynne Godley had the rarest of rare ability to model and imagine the economic dynamics of the whole world. “… a full macroeconomic model in his head, which, by some sort of subconscious process, he computed.” as his obituary from FT said.

In the recent INET conference paper, Dirk Bezemer discusses Wynne Godley’s approach (among others’) and also refers to his paper Seven Unsustainable Processes from 1999.

I obtained this original scanned copy of the paper Seven Unsustainable Processes – Medium Term Policies For The United States And The World by Wynne Godley from 1999 from the Levy Economics Institute and  thought that since this version is missing for some reason from the levyinstitute.org website, I’ll post it here (after asking them if I may post).

Click to see the pdf.

Seven Unsustainable Processes from 1999

Here’s the link to the updated version of the paper from the year 2000. The original had a typo. Two columns in Table 1 appeared with incorrect headings (should have been the reverse).

Wynne Godley at the Levy Institute

Godley warns of the private sector indebtedness:

… Moreover, if, per impossibile, the growth in net lending and the growth in money supply growth were to continue for another eight years, the implied indebtedness of the private sector would then be so extremely large that a sensational day of reckoning could then be at hand.

Wynne Godley never liked the chimerical and primitive view of economists where anything and everything is traded in the markets via supply and demand. So,

The difference between the consensus view and that put forward here could not exist without a profound difference in the view of how the economy works. So far as the author can observe, the underlying theoretical perspective of the optimists, whether they realize it or not, sees all agents, including the government, as participants in a gigantic market process in which commodities, labor, and financial assets are supplied and demanded. If this market works properly, prices (e.g., for labor and commodities) get established that clear all markets, including the labor market, so that there can be no long-term unemployment and no depression. The only way in which unemployment can be reduced permanently, according to this view, is by making markets work better, say, by removing “rigidities” or improving flows of information. The government is a market participant like any other, its main distinguishing feature being that it can print money. Because the government cannot alter the market-clearing price of labor, there is no way in which fiscal or monetary policy can change aggregate employment and output, except temporarily (by creating false expectations) and perversely (because any interference will cause inflation).

No parody is intended. No other story would make sense of the assumption now commonly made that the balance between tax receipts and public spending has no permanent effect on the evolution of the aggregate demand. And nothing else would make sense of the debate now in full swing about how to “spend” the federal surplus as though this were a nest egg that can be preserved, spent, or squandered without any need to consider the macroeconomic consequences.

The seven unsustainable processes were:

(1) the fall in private saving into ever deeper negative territory, (2) the rise in the flow of net lending to the private sector, (3) the rise in the growth rate of the real money stock, (4) the rise in asset prices at a rate that far exceeds the growth of profits (or of GDP), (5) the rise in the budget surplus, (6) the rise in the current account deficit, (7) the increase in the United States’s net foreign indebtedness relative to GDP.

As it happened, the United States went into a recession but recovered quickly because of further deregulations and low interest rates which led to more borrowing, and a fiscal stimulus which put a floor on the downfall. However, the private sector went back into deficits and its indebtedness kept rising relative to income. The current balance of payments also went deeply in deficit rising to about 6.43% at the end of 2005 – hemorrhaging the circular flow of national income at a massive scale. See the related post here: The Un-Godley Private Sector Deficit.

Not only did Godley see the crisis coming, he also figured out that the United States will soon run into policy issues and will have less room to come out of a crisis. In this 2005 strategic analysis paper The United States And Her Creditors – Can The Symbiosis Last? he and his collaborators (Dimitri Papadimitriou, Claudio Dos Santos and Gennaro Zezza) pointed out that:

The range of strategic policy options for the United States is beginning to narrow … As the normal equilibrating forces (changes in exchange rates) are being subverted, it is very far from obvious what the United States can do on her own …

In his last ever article, Prospects For The United States And The World – A Crisis That Conventional Remedies Cannot Resolve (from which I got the subtitle of my blog!), Godley and collaborators (Dimitri Papadimitriou and Gennaro Zezza) said:

The prospects for the U.S. economy have become uniquely dreadful, if not frightening. In this paper we argue, as starkly as we can, that the United States and the rest of the world’s economies will not be able to achieve balanced growth and full employment unless they are able to agree upon and implement an entirely new way of running the global economy.

Stressing the need for concerted action (from which I got the title of my blog!), the authors said:

… Fiscal policy alone cannot, therefore, resolve the current crisis. A large enough stimulus will help counter the drop in private expenditure, reducing unemployment, but it will bring back a large and growing external imbalance, which will keep world growth on an unsustainable path …

… What must come to pass, perhaps obviously, is a worldwide recovery of output, combined with sustainable balances in international trade. Since this series of reports began in 1999, we have emphasized that, in the United States, sustained growth with full employment would eventually require both fiscal expansion and a rapid acceleration in net export demand. Part of the needed fiscal stimulus has already occurred, and much more (it seems) is immediately in prospect. But the U.S. balance of payments languishes, and a substantial and spontaneous recovery is now highly unlikely in view of the developing severe downturn in world trade and output … By our reckoning (which is put forward with great diffidence), if the United States were to attempt to restore full employment by fiscal and monetary means alone, the balance of payments deficit would rise over the next, say, three to four years, to 6 percent of GDP or more—that is, to a level that could not possibly be sustained for a long period, let alone indefinitely …

… It is inconceivable that such a large rebalancing could occur without a drastic change in the institutions responsible for running the world economy—a change that would involve placing far less than total reliance on market forces.

The Un-Godley Private Sector Deficit

Economists worry too much about the government’s deficit although they seem to not know about the private sector deficit.

Goldman Sachs’ chief economist Jan Hatzius came to know about the sectoral balances approach and called the difference between United States’ private expenditure and income in “The Un-Godley Private Sector Deficit”. He later included the sectoral balances approach in his forecasting models.

Here’s the sectoral balances for the United States using data from the Federal Reserve’s Z.1 Flow Of Funds Accounts Of The United States:

GDP appears in Table F.6 and sectoral balances in Table F.8 – as “Net Lending(+)/Net Borrowing(-)”. The above is using quarterly seasonally adjusted data. Easy work. Excel data is available at the Federal Reserve’s page here

It can be verified that

Private Sector Balance = Government Deficit + Current Balance of Payments

The red line is the private sector balance and is the difference between the private sector income and expenditure. When positive, the private sector is in surplus and when negative, it is in deficit.

For most of history having been positive (and back to being positive now), the private sector balance made a dramatic shift in the mid-1990s reaching as low as as -5.8% in Q1 2000 (and hence “private sector deficit”). This implied that before the recession, growth in the United States was driven by higher private expenditure relative to income. The flip side of this growth was that due  to the Un-Godley private sector deficits, the budget went into a surplus while private indebtedness continued to rise.

This was enough to cause a recession in the early 2000s and the US government had to provide a massive fiscal stimulus to prevent a severe recession. The Federal Reserve also provided stimulus by keeping interest rates low but the private sector went into a deficit again – rushing to participate in a boom. The result of all this was the increase in the current account deficit of the United States to about 6.43% of GDP at the end of 2005 – hemorrhaging the circular flow of national income at a massive scale and cracks started to appear in the foundations of growth – as warned by a series of articles from the Levy Institute.

This appears a bit like Scenario 4 in a Levy Institute paper Debt And Lending – A Cri De Coeur by Wynne Godley and Gennaro Zezza from April 2006 – the “gloomiest variant” according to the authors – where a drastic fall in private expenditure relative to income induces a recession in the United States, reducing the current account balance dramatically and increasing the budget deficit (to eventually enough to become the central debate in US politics).

And it turned out that the private sector deficit quickly went into a surplus – faster than the scenario presented above because the private sector could not handle the rise in indebtedness. The fall in private expenditure relative to income also meant – as mentioned above – that the United States went into a deep recession – from which it is still recovering.

Books In Honour Of Wynne Godley

There are two new books in honour of Wynne Godley and they are out now

The first one – edited by Marc Lavoie and Gennaro Zezza – has selected articles and papers by Wynne Godley, and carefully chosen.

It’s available at amazon.co.uk, but not yet on amazon.com

Here’s the book’s website on Palgrave Macmillan. The book also contains the full bibliography of Godley’s papers, books, working papers, memoranda (such as to the UK expenditure committee), magazine/newspaper articles, letters to the editor etc.

Here’s a picture I took of Marc at Levy Institute in May when he was deciding on the cover.

The is second book written in honour of Wynne Godley contains proceeding of the conference held in May at the Levy Institute (the same place the above photograph was taken)

The publisher’s website for the book is here.

Dimitri says:

The death of Wynne Godley silences a forceful and very often critical voice in macroeconomics. Wynne’s own strong view, that although his work was representative of the non-mainstream Keynesian approach to economics and especially economic policy was important nevertheless, has been confirmed time and time again as evidenced in the fortunes of the UK, US and Eurozone economies. His writings, reflecting the sharpness of his mind and intellectual integrity, have had a considerable impact on macroeconomics and have aroused the interest of scholars, economic journalists and policymakers in both mainstream and alternative thought. In a review of Wynne’s last book with Marc Lavoie (2007), Lance Taylor had this to say: ‘Wynne’s important contributions are foxy – brilliant innovations… that feed into the architecture of his models’

I also like Wynne’s stand on the current account imbalance of the United States:

Bibow finds that Godley’s diagnosis of the looming economic and financial difficulties ahead of their occurrence was prescient with regard to US domestic developments – a theme that came up in the chapters by Wray and Galbraith. But Bibow takes issue with Wynne’s assessment of the US external balance being unsustainable. He notes that the US investment position and income flows are more or less in balance and he attributes this phenomenon to the safety of the US Treasury securities and the dollar functioning as the reserve currency.

Dimitri then says

Even if this is so, it cannot continue indefinitely, Wynne would have replied.

The conference page is here

r < g Or DEF < g ?

It is frequently asserted by some economists and even some Post-Keynesians that as long as the effective interest rate paid on stocks of debt is less than the growth rate, stock-flow-norms do not keep rising forever. That is, ratios such as public debt/gdp, external debt/gdp do not rise forever at full employment if this condition is maintained, implying thereby that fiscal policy can be used to achieve a higher output and there is nothing one needs to do about the external sector.

It is the purpose of this post to clear such misconceptions.

Fiscal Policy

What can fiscal policy achieve and what are its limitations? In an essay from the centenary conference of 1983, Wynne Godley wrote [1]:

How did Keynes think the economy worked? Any time between 1950 and 1970 1 would have confidently attributed to Keynes, as preeminently important, the following views about economic policy:

(a)    Real demand, output and employment are determined via a multiplier process by the fiscal and   monetary operations or the government and by foreign trade performance.

(b)    Inflation, though influenced by the pressure of demand, is largely indeterminate in terms or economic variables and therefore, if it is to be controlled, requires some kind of direct political intervention.

(c)    Fiscal and monetary policies in any one country are potentially subject to important external constraints.

While there is reasonable support for these views about economic policy in Keynes’s writings, there is no warrant for them at all in the General Theory. Indeed it is strange, seeing how commonly the view is attributed to Keynes that fiscal policy is crucial to real output determination, that the General Theory is concerned with an economy in which neither a government nor for that matter a foreign sector exist at all.

Notwithstanding this I still think, not only that the propositions can be correctly attributed to Keynes, but that they are, themselves, essentially correct. I have however been forced to the conclusion that Keynes was a long way from achieving a coherent theoretical basis for maintaining them, and largely for this reason, his ideas have proved very vulnerable to the attacks from many different directions to which they have been subjected, particularly in the last fifteen years.

To points (a), (b) & (c) above, let me add

(a(i))  Higher output is also possible when the private sector expenditure is higher than private sector income.

This was highlighted by Godley himself in the late 90s, when the US economy expanded in spite of a tight fiscal stance and he was the first to write that this process is unsustainable!

Debt Convergence Analysis

Let us now turn to the question on convergence/divergence of stock-flow norms. In what follows, I simply use debt to denote the public debt or the external debt. Assuming away complications arising from revaluations, we have the identities [2]

Uppercase is for stock of debts, and lower case for debt-to-gdp ratio and g is the growth rate. Note: DEF is primary deficit and excludes interest payments. We will turn to complications added by interest payments soon. Whenever

the stock of debt keeps rising.

Note, when the debt-to-gdp ratio is less than 1 (100%), the sustainability condition is strong on the deficit. The condition DEF < g is at at a debt-to-gdp ratio is 1. Beyond 100%, the condition on the deficit is a bit weaker than DEF < g because the deficit can be between g and g·d.

This argument is sometimes presented differently by some Post Keynesians by including the effective interest rate r. The equation looks like the following when it is included: It is argued that the third term on the right hand side can be set to be greater than the second term (which is to say that r < g is sufficient to ensure sustainability).

This argument (r < g guaranteeing problems are solved) has no substance. This is because rearranging the terms in the way done above, shows more clearly that the stock-flow ratio rises faster than the case where the analysis was done without the interest rate term!

There is one more complication. It may be argued that growth can only bring down the deficit (the deficit here being the public sector deficit). This is true for the case of a closed economy. The convergence of the public debt-to-gdp ratio is also achieved in the case of a closed economy because interest payments by the government is income for the private sector and they will consume it (although the capitalist class’s propensity to consume is less than that of the worker class). Higher consumption leads to higher national income and hence higher taxes, bringing down the deficit.

Wynne Godley and Marc Lavoie [3] showed how this happens precisely in the case of a closed economy:

This paper deploys a simple stock-flow consistent (SFC) model in order to examine various contentions regarding fiscal and monetary policy. It follows from the model that if the fiscal stance is not set in the appropriate fashion—that is, at a well-defined level and growth rate—then full employment and low inflation will not be achieved in a sustainable way. We also show that fiscal policy on its own could achieve both full employment and a target rate of inflation. Finally, we arrive at two unconventional conclusions: (1) that an economy (described within an SFC framework) with a real rate of interest net of taxes that exceeds the real growth rate will not generate explosive interest flows, even when the government is not targeting primary surpluses, and (2) that it cannot be assumed that a debtor country requires a trade surplus if interest payments on debt are not to explode.

Also, they create some very special scenarios, where the external debt stays sustainable.

However, making the above work is difficult for the case of an open economy in general. This was what the essential argument of the New Cambridge School. 

So is there a way to achieve convergence of the stock-flow norm? To achieve that, the external sector deficit (more precisely, the primary balance in the current balance of payments) should be less than the growth rate times the external debt. This creates tensions for demand-management because if the external deficit grows higher than the growth rate, it is usually brought back to a sustainable path by deflating demand.  This is because the balance of payments deficit itself will grow if growth is high! (unless exports improve).

There are of course some scenarios which can lead to the convergence of the external debt (if the markets allow it). A more careful treatment will always lead one to studying income and price elasticities of imports, growth in the rest of the world etc.

Other scenarios which could lead to the improvement of the external sector are:  promotion of exports leading to more success abroad and luck – market forces miraculously achieving the required depreciation to improve the external sector. Since the latter is mere wishful thinking, we see nations trying to depreciate their currencies because it makes their exports more competitive.

To bring the balance of payments deficit back into balance, there is also the option of restricting imports but in the world of “free trade”, it can create tensions between nations.

There are two more options. The first is to ask your trading partners to appreciate their currencies if they have pegged them but this has to go through negotiations because they want you to do the same! The second (which includes the previous option) is what this blog is about. Since, the external sector creates problems for demand management, one can only think of coordinated efforts by institutions running the world economy, working to achieve higher world demand instead of contracting it.


  1. Wynne Godley, Keynes And The Management Of Real Income And Expenditure, p135, Keynes And The Modern World: Proceedings Of The Keynes Centenary Conference, ed.  David Worswick and James Trevithick, Cambridge University Press, 1983.
  2. Gennaro Zezza, Fiscal Policy And The Economics Of Financial Balances, Levy Institute Working Paper 569, 2009. Available at http://www.levyinstitute.org/publications/?docid=1161
  3. Wynne Godley and Marc Lavoie, Fiscal Policy In A Stock-Flow Consistent Model, p 79, Journal of Post Keynesian Economics / Fall 2007, Vol. 30, No. 1. Draft version available at http://www.levyinstitute.org/publications/?docid=911