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Bridging the gapbetween Kaleckis words

and the modelingof a monetary macroeconomy

Gerard DUMENIL and Dominique LEVYCNRS and PSE-CNRS

Article prepared for a special issue of Metroeconomica dedicated to MichalKalecki.

Address all mail to: PSE-CNRS, 48 bd Jourdan, 75014 Paris, France.Tel: 33 1 43 13 62 62, Fax: 33 1 43 13 62 59E-mail:, gerard.dumenil@u-paris10.frWeb Site:

The focus of this study is the treatment of monetary and credit(monetary for short) mechanisms within macro models of busi-ness-cycle fluctuations. The analysis is introduced in relation toMichal Kaleckis work in the broader context of Marxian and Key-nesian economics (section 1). Kaleckis words on investment echoMarxs approach of accumulation in terms of financing out of pre-viously garnered profits and borrowing. Independently of Keynes,Kalecki developed a framework of analysis hinging around the prin-ciple of effective demand (in Keyness formulation) or, equivalently,a short-term equilibrium by quantities, the pillar of Keynesian andpostKeynesian ((post)Keynesian for short) economics. Kaleckismethodology is, however, thoroughly distinct from those of Marxand Keynes. In his analysis of the business cycle, Kalecki devotedconsiderable energy to the investigation of what he, himself, calledeconomic dynamics (the mathematical study of cyclical changes)to build a theory of business-cycle fluctuations. The study of sucheconomic dynamics requires the definition of a framework in whichdisequilibrium around short-term equilibrium may prevail. Despitesuch promising inroads, however, the models presented by Kalecki donot actually lay the foundations of what could be seen as a commonground within heterodox economics. The ambition of this study isto bridge this gap.

1 - Kalecki between Marx and Keynes

This preliminary section defines the overall project and intro-duces the general outline. Three contemporary frameworks specifi-cally relevant to the present investigation are, then, contrasted.

1.1 General outline

Section 2 discusses financing in reference to Kaleckis statementsconcerning the financing of investment out of income and borrow-ing. The analysis is conducted within the postKeynesian frameworkof transaction-flow matrices extended to the dynamics toward short-term equilibrium. A relationship follows, the straightforward expres-sion of Kaleckis explicit statements concerning investment, in which

2 The modeling of a monetary macroeconomy

demand is financed out of income and the variation of the net debtsof economic agents. Only in a situation of equilibrium the variationof the net debt of households is null.

Section 3 focuses on (in)stability, a central theme in the presentstudy. The stability of short-term equilibrium is always subject toconditions. The section contends that, if abstraction is made of theaction of monetary authorities, the behaviors of economic agents aresuch that short-term equilibrium is unstable, a built-in instability.This fundamental property of capitalism makes of the stabilizing ac-tion of central institutions a basic requirement. This action is, how-ever, not always successful. Thus, a central aspect of the businesscycle is the succession of phases in which the stability of short-termequilibrium is ensured or not.

Section 4 is devoted to the modeling of monetary mechanisms.The principle of co-determination is put forward. Not only realand monetary variables (for example, respectively, investment andborrowing) are determined jointly, but both the behaviors of nonfi-nancial and financial agents are involved. For example, householdsmake projects that only materialize in the negotiation with banks.The action of the central bank is finally crucial. The behaviors ofhouseholds concerning real and financial variables, and the actionsof commercial banks and of the central bank are modeled in a singlefunction, the co-determined monetary function. This approach in our opinion, the cornerstone of monetary macroeconomics mustbe substituted for the postKeynesian perspective of accommoda-tive money. In our framework, money is neither endogenous norexogenous.

A set of possible models of a monetary macroeconomy are intro-duced in section 5. Alternative stabilizing mechanisms the controlof the level of indebtedness, the control of inflation, the manipulationof interest rates, and fiscal policy are considered.

Section 6 focuses on the explanatory power of the (in)stability ofshort-term equilibrium in the analysis of business-cycle fluctuations.A link is, finally, established with Hyman Minsky financial instabilityframework, in which business-cycle fluctuations are approached interms of instability and the emphasis is on financial mechanisms.

The modeling of a monetary macroeconomy 3

1.2 Alternative contemporary frameworks

Elaborating on the foundations laid by Marx, Keynes, and Kaleckimuch work has now been done. The present study refers to three con-temporary frameworks:

1. The continuation of the traditional Keynesian viewpoint. A firstapproach, directly inspired by Keyness analysis, is still typical ofmany Keynesian economists. The focus is on the position of short-term equilibrium, that is, the degree to which productive capacityis used. Reference is made to the uncertainty surrounding expecta-tions in the decision to invest as in Keynes original formulations.Did Keynes himself, in the General Theory, attempt to interpret thesluggish U.K. macroeconomy of the 1920s or the sudden collapse ofoutput into the Great Depression, which suggests a lost stability?One thing is sure, the theoretical framework built by Keynes focusedon the position of short-term equilibrium, not the dynamics towardthis equilibrium. Keynes did not contemplate long-term equilibria.The same is true of traditional Keynesian economists.2. PostKeynesian economists. The main segment of contemporaryKeynesian economists studies short-term equilibria in the traditionalKeynesian perspective, but acknowledges that such positions are nec-essarily temporary equilibria. A distinction is made between flowsand stocks. Flow variables are studied in the framework of short-term equilibrium, while stock variables are gradually altered along asequence of short-term equilibria leading to a Keynesian long-termsteady state with any value of the capacity utilization rate. There istypically little interest in the stability of short-term equilibria.3. Our viewpoint. The formal framework is the same as in postKey-nesian models, with the consideration of short-term equilibria, andthe analysis of the succession of such temporary equilibria converg-ing toward a long-term equilibrium. In such a long-term equilibrium,however, prices have converged toward prices of production (with uni-form profit rates) as in Marxs analysis of competition (and outputsand capital stocks have been adjusted). This is what we denote asbeing Keynesian in the short term and classical in the long term.1Another important difference is the attention paid to the stability ofshort-term equilibrium, in our view, a crucial component in the anal-ysis of business-cycle fluctuations and the main object of the presentstudy.

1. G. Dumenil, D. Levy, Being Keynesian in the Short Term and Classicalin the Long Term: The Traverse to Classical Long-Term Equilibrium, TheManchester School, 67 (1999), p. 684-716.

4 The modeling of a monetary macroeconomy

2 - Financing demand

This section recalls Kaleckis major statements concerning thefinancing of investment out of both previously garnered profits andborrowing. The methodology of transaction-flow matrices is used tomake explicit the basic macro relationships implicit in such state-ments. A special emphasis is placed on the application of this ac-counting framework to the analysis of the dynamics of macro vari-ables out of equilibrium a truly original approach. The financingframework introduced is more general than the framework consideredby Kalecki, in which borrowing are limited to the financing of invest-ment by capitalists. The main result is the formulation of equationsthat link demands, income flows, and the variations of the net debtsof nonfinancial agents, the straightforward expression of Kaleckisformulations concerning investment.

2.1 Kaleckis words on the financing of investment

The traditional interpretation concerning investment contrasts aMarxian approach in which investment, denoted as accumulation,is financed out of previously garnered profits, and the confrontationbetween the marginal efficiency of capital and the interest rate, asin Keynes analysis. Kaleckis approach to investment is much closerto the Classical-Marxian perspective2:

How can capitalists invest more than remains from theircurrent profits after spending part of them for personal con-sumption [1]? This is made possible by the banking systemin various forms of credit inflation [2].3

(Credit inflation refers to the expansion of credit or, equivalently,the issuance of money.)

2. The quotations in this section are from M. Sawyer, Kalecki and Fi-nance, European Journal of the History of Economic Thought, 8 (2001),p. 487-508.3. M. Kalecki, Capitalism: Business Cycles and Full Employment, Col-lected Works of Michal Kalecki, Vol. I (Edited by J. Osiatynski), Oxford:Clarendon Press (1990), p. 148.

The modeling of a monetary macroeconomy 5

Not only can savings out of current profits be directly in-vested in the business [1], but this increase in the firmscapital will make it possible to contract new loans [2].4

The first parts [1] of the two statements echo the perspective ofaccumulation in the strict sense. Kalecki opens, however, the optionthat capitalists borrow [2] to finance additional investment. Thereshould be no attempt at theorizing investment and business-cyclefluctuations without this reference to credit (and, obviously, money):Business fluctuations are strictly connected with credit inflation.5

Such views suggest that real and monetary mechanisms are tightlyrelated and should not be considered autonomously. Note that bothMarx and Kalecki associate credit inflation with the rapid expansionof output.6

2.2 Accounting relationships

During the recent years, the consideration of monetary and fi-nancial variables made important progress within the postKeynesianliterature.7 Real and monetary variables are carefully articulatedwithin tables inspired by national accounting frameworks, denotedas transaction-flow matrices as, notably, in Wynne Godleys andMarc Lavoies work.8 These matrices are used to account for the

4. M. Kalecki, Capitalism: Economic Dynamics, Collected Works of MichalKalecki, Vol. II (Edited by J. Osiatynski), Oxford: Clarendon Press (1991),p. 277-278.5. M. Kalecki, Capitalism: Business Cycles and Full Employment, op. cit.note 3, p. 148-149, emphasized by Kalecki.6. Kalecki noted that there is an increased demand for money in circu-lation [in the upswing of the business cycle] in connection with the rise inproduction and prices. (Kalecki, CWI, p. 93). (M. Sawyer, Kalecki andFinance, op. cit. note 2 p. 491).7. The analysis of the circuit of capital and reproduction schemes in MarxsVolume II of Capital also expresses such a network of stock/flow relation-ships as in national accounting frameworks (G. Dumenil, Marx et Keynesface a la crise, Paris: Economica (1977); D. Foley, Understanding Capital,Marxs Economic Theory, Cambridge: Harvard University Press (1986);G. Dumenil, D. Levy, The Analytics of the Competitive Process in aFixed Capital Environment, The Manchester School, LVII (1989), p. 34-57 and The Real and Financial Determinants: The Law of the TendencyToward Increasing Instability, in W. Semmler (ed.), Financial Dynamicsand Business Cycles: New Perspectives, Armonk: Sharpe (1989), p. 87-115).8. W. Godley, M. Lavoie, Monetary Economics. An Integrated Approachto Credit, Money, Income, Production and Wealth, London: Palgrave(2007).

Table 1. Equilibrium transaction-flow matrix Wage-

earners Capitalists Enterprises

(current) Banks

Demand and production -Dw -Dk D 0 Income paid out W -Y 0 Change in loans Lw Lk -L 0 Change in deposits -Mw -Mk 0 M 0 0 0 0 0

Table 2. Dynamic transaction-flow matrix for period t+1 Wage-

earners Capitalists Enterprises

(current) Banks

Demand and production -Dwt+1 -Dkt+1 Dt+1 0 Income paid out Wt t -Yt 0 Change in loans Lwt+1 Lkt+1 -Lt+1 0 Change in deposits -Mwt+1 -Mkt+1 -Met+1 Mt+1 0 0 0 0 0

6 The modeling of a monetary macroeconomy

macroeconomics of a monetary economy. The objective is to makeexplicit necessary accounting relationships linking real flow variables(consumption, investment, income) to the variations of stocks (tan-gible assets, loans, and so on) generated in each period. The linkis, thus, established with the matrix in the following period. Thesedynamics are those of the sequence of temporary equilibria.

The technical aspects of the method depend on the frameworkof analysis. Various categories of agents can be introduced: house-holds (wage-earners and capitalists), enterprises, banks (commercialand central), and government. The current and capital accounts ofenterprises are distinguished. Current refers to production, sales,and the distribution of income, and capital to the variations of theaccounts of the balance sheet of enterprises. A period, typically oneyear, is considered.

A simple form of such matrices is used in tables 1 and 2. Fouragents are considered, capitalists, wage-earners, enterprises, and banks.(In the commentary of the tables, capitalists and wage-earners arejointly denoted as households, and households and enterprises, asnonfinancial agents.) There is no government. In addition to tradi-tional macro variables income, consumption, or investment twocategories of financial variables are involved, loans, L, and deposits inbank accounts, M . Only the variations of these monetary variables,L and M , are represented in the table jointly with the abovemacro variables. The analysis of financing here uses the notion of thenet debt, N , of economic agents, the difference between their loansand deposits, N = L M . The emphasis is on the variation N ofthis net debt.

The following additional commentaries can be made:

1. Money is taken in the strict sense of deposits. Thus, there is nodistinction between monetary and financial mechanisms. Thisframework abstracts from securities, such as bonds and equities, andthe payment of interest or dividends. A strict correspondence existsbetween the two categories of variables as money is issued, M , bynew bank loans, L, to wage-earners and capitalists, and destroyedwhen these loans are paid back (column Banks). Thus, M = L.Since only households borrow and banks are the unique lenders, thetotal loans of banks, L, are equal to the debts of households: Lh =Lk+Lw. Total deposits in the accounts o...


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