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Barro and Grossman’s Dynamic Disequilibrium

Macroeconomics1

Abstract

During the 1970s, most macroeconomists developed “fixed-price” equilibrium models. Such

models featured equilibria with rationing on markets. Not the dynamic of non-clearing markets.

However, this was the original project. “Fixed-price” equilibrium models emerged out of Don

Patinkin ([1956] 1965), Robert Clower (1965), and Axel Leijonhufvud’s (1968) interpretation

of the General Theory (1936). All three considered that John Maynard Keynes (1936) was

concerned with the dynamic of markets when individuals behaved under rationing constraints.

From there, they all tried to provide microfoundations to a model capable of portraying

disequilibrium adjustment processes occurring in capitalist economies. The question is whether

“fixed-price” theorists abandoned this project. My paper shows that Robert Barro and Herschel

Grossman did not. When elaborating the seminal “fixed-price” model (1971), they had a second

step in mind. It was to build a dynamic disequilibrium model. It turns out to be very much in

the spirit of Patinkin ([1956] 1965) and Clower’s (1965). I present its main features and discuss

its scope. By doing so, I account for the richness and limits of the research line that Patinkin

([1956] 1965) and Clower (1965) initiated but barely explored.

JEL Codes: B13, B21, B22, D45, D5, E12.

Keywords: dynamics, disequilibrium, microfoundations of macroeconomics, Barro and

Grossman.

1 Duke University, Department of Economics, Center for the History of Political Economy, e-mail: romain.plassard@duke.edu

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Introduction

During the 1970s, most macroeconomists, including Robert Barro and Hershel

Grossman (1971), Jean-Pascal Bénassy (1975), Jacques Drèze (1975), Jean-Michel Grandmont

and Guy Laroque (1976), and Edmond Malinvaud (1977), developed “fixed-price” equilibrium

models. Such models featured equilibria with rationing on markets. Not the dynamic of non-

clearing markets. However, this was the original project. “Fixed-price” equilibrium models

emerged out of Don Patinkin ([1956] 1965), Robert Clower (1965), and Axel Leijonhufvud’s

(1968) interpretation of the General Theory (1936). All three considered that John Maynard

Keynes (1936) was concerned with the dynamic of markets when individuals behaved under

rationing constraints. From there, they all tried to provide microfoundations to a model capable

of portraying disequilibrium adjustment processes occurring in capitalist economies. The

question is whether “fixed-price” theorists abandoned this project. My paper shows that Barro

and Grossman did not.2

While presenting the seminal “fixed-price” equilibrium model, Barro and Grossman

(1971) showed a concern for disequilibrium dynamics. They argued that their “analysis did

have implications for the appropriate specification of the forces making for changes in prices

and wages” (1971: p. 84); they considered “a parenthetical example concerning the cyclical

behavior of real wages” (1971: p. 84); and they referred to an article in which Grossman (1971)

addressed “in details (…) the disequilibrium behavior of prices and interest” (1971: p. 85). All

these remarks suggest that the 1971 model was just a stage in the process of developing a

dynamic disequilibrium model. A conjecture which becomes even more plausible when reading

the contents of Money, Employment, and Inflation (Barro and Grossman, 1976). Section 2.5

offered a “Dynamic analysis in the absence of recontracting”, Section 4.4.3 analyzed the

“Dynamic effects of monetary policy”, Chapter 5 explored the dynamic of “Inflation and

unemployment”, and Chapter 6 focused on “The Dynamics of aggregate demand” (1976: vi-

vii).

The challenge is to place dynamics at the heart of Barro and Grossman’s disequilibrium

program of microfoundations. This requires to show that when writing the 1971 article, Barro

and Grossman had a dynamic approach to disequilibrium economics. Then, I have to determine

how Barro and Grossman modeled the operation of economic activities during the adjustment

2 Matthieu Renault, Goulven Rubin, and I express a similar viewpoint in a recent working paper, centered on French “fixed-price” theorists.

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of markets. To overcome these difficulties, I place their disequilibrium program of

microfoundations in its intellectual context. Emphasis is given to two sources of inspirations:

disequilibrium macroeconomics à la Patinkin ([1956] 1965) and Clower (1965), and non-

tâtonnement economics à la Frank Hahn and Takashi Negishi (1962). Besides, I analyze in

depth “Market Disequilibrium in a Macro-Economic Context”, an unpublished manuscript

written by Grossman in 1968, and Money, Employment, and Inflation (1976).3

In that process, two interpretations of Barro and Grossman’s microfoundational

program are challenged. The first one asserts that Barro and Grossman either marginalized or

abandoned Patinkin ([1956] 1965), Clower (1965), and Leijonhufvud’s (1968) project to model

the dynamic of non-clearing markets. The extreme position is supported by Michel de Vroey

(2016), in A History of Macroeconomics from Keynes to Lucas and Beyond. Whilst

acknowledging that Barro and Grossman “found inspiration in reading Patinkin, Clower, and

Leijonhufvud”, De Vroey argue that like other “fixed-price” theorists, they “were striving to

produce an equilibrium result, a radically different project” (2016: p. 124). Roger Backhouse

and Mauro Boianovsky (2013) are more nuanced in Transforming Modern Macroeconomics:

Exploring Disequilibrium Microfoundations, 1956-2003. They acknowledge that Barro and

Grossman (1976) extended their “[1971] model to encompass dynamics” (2013: p. 78). But this

is not presented as a central element of their disequilibrium program of microfoundations. The

treatment of “wage and price dynamics” would be just one extension “amongst” others of the

1971 model (2013: p. 72). The second interpretation concerns the analytical proximity between

Patinkin ([1956] 1965), Clower (1965), and Barro & Grossman’s models. The three historians

consider that it is limited. Barro and Grossman would use simply Patinkin ([1956] 1965) and

Clower’s (1965) foundations – i.e., the spillover effect and the dual-decision hypothesis.

By contrast, I argue that just like Patinkin ([1956] 1965), Clower (1965), and

Leijonhufvud (1968), Barro and Grossman’s project was to model disequilibrium adjustment

processes. They completed it by elaborating a disequilibrium model very much in the spirit of

Patinkin ([1956] 1965) and Clower’s (1965). I present its main features and discuss its scope.

By doing so, I account for the richness and limits of the research line that Patinkin ([1956]

1965) and Clower (1965) initiated but barely explored.

3 Juan Carlos Acosta found this manuscript in Franco Modigliani’s Papers, at Duke University. I would like to thank him for giving me access to it.

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1. A dynamic approach to disequilibrium economics

Just like Patinkin ([1956] 1965) and Clower (1965) or Hahn and Negishi (1962), Barro and

Grossman adopted a dynamic approach to disequilibrium economics. They considered

disequilibrium as a phenomenon occurring only during the market-clearing process. From there,

the challenge was to provide microfoundations to a dynamic theory of spillover and to study

the stability properties of Walrasian equilibrium.

1.1 Background

Barro and Grossman initiated their disequilibrium program of microfoundations

between 1968 and 1971, at Brown University.4 In 1968, Grossman wrote “Market

Disequilibrium in a Macro-Economic Context”. In this research project (submitted to the

National Science Foundation), he argued that the “existing macro-economic literature” (i.e.,

Walrasian macroeconomics à la Hicks) was inappropriate for “explaining and predicting the

behavior of the actual economy.5 For the actual economy may rarely, if ever be in equilibrium”

(1968: p. 5). According to Grossman, the bulk of actual exchange took place while individuals

would like to buy and/or to sell more, given market prices. Hence the need to “analyze explicitly

the behavior of macro-economic systems which [were] not necessarily or even typically

characterized by market equilibrium” (1968: p. 5). Such an approach to macroeconomics

already attracted Barro’s interest while he was in graduate school at Harvard (Backhouse and

Boianovsky, 2013: p. 67). Thus, when arriving at Brown University in 1968, he engaged with

Grossman.6 This resulted in a collaboration which culminated in the publications of “A General

Disequilibrium Model of Income and Employment” (1971) and of Money, Employment, and

Inflation (1976).

4 In the preface of Money, Employment, and Inflation (1976), Barro and Grossman explained that their “monograph [was] the outgrowth of ideas developed while [they] were colleagues at Brown University from 1968 to 1971. During that period, [they] became aware that [they] shared similar reservations about the weak foundations of conventional macro-economic analysis. [They] both felt the need for a substantial restructuring of these foundations, especially to deal adequately with the problem of exchange under non-market-clearing conditions” (1976: xi). 5 “The existing macro-economic literature deals primarily with analysis of the characteristics and stability properties of market equilibrium: that is, the condition of equality between aggregate supply and demand. The classic example is the Hicksian comparative static analysis of the values of dependent variables consistent with market equilibrium” (1968: p. 5). 6 In “Money, Interest, and Prices in Market Disequilibrium” (1971), Grossman acknowledged that his article “benefited from extensive discussions with Robert Barro” (1971: p. 943).

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Initially, the research program was designed as a synthesis between disequilibrium

macroeconomics and non-tâtonnement economics. According to Grossman:

The Hahn and Negishi, Patinkin, and Clower models should be regarded as

complementary. Future fruitful work might be based on development of a

synthesis (1969: p. 479).

The aforementioned models addressed the behavior of markets when exchange took place out

of Walrasian equilibrium. But not in the same way. Grossman (1969) indicated that Hahn and

Negishi (1962) focused on distribution effects, i.e., how excess supplies or excess demands are

distributed among individuals during the exchange process. Effects ignored by Patinkin ([1956]

1965) and Clower (1965). On their side, what mattered was to account for spillover effects, i.e.,

how a firm or a household is forced to revise its plans when failing to sell (or buy) what it

desires given market prices. Effects ignored by Hahn and Negishi (1962). However,

“distribution and spillover effects [were the] “two distinct channels [through which] trades

carried out at non-clearing prices should affect” the functioning of markets. Hence the project

to elaborate a disequilibrium model synthesizing the Hahn and Negishi (1962), Patinkin ([1956]

1965) and Clower’s (1965).

1.2 A common approach to disequilibrium economics

What is common to these four economists is a dynamic approach to disequilibrium

economics. Hahn and Negishi’s was adopted in reaction to contemporaneous developments in

general equilibrium theory – in particular, Herbert Scarf’s (1960) examples of global instability

of competitive equilibrium. Scarf’s examples showed that it was not possible to demonstrate

that Walrasian equilibrium was stable in general, i.e., very special assumptions were necessary

to prove that individuals found common grounds to exchange. Hahn and Negishi concluded

that the tâtonnement hypothesis did not provide a satisfactory representation of market

economies. Accordingly, they started studying the stability properties of competitive

equilibrium, under an alternative rationalization of exchange (Hahn’s non-tâtonnement

process).7 Around the same period, Patinkin ([1956] 1965) and Clower (1965) were also

concerned with the dynamic of non-clearing markets. But in their case, this reflected how they

7 In “The Stability of the Competitive Economy: A Survey Article”, Negishi (1962) claimed that: “It is possible to interpret [Scarf’s] examples as showing [that] the tâtonnement process does not provide a correct representation of the dynamics of markets. See Hahn (1960). The failure of the general stability of the tâtonnement process suggests the study of the stability of the non-tâtonnement process” (1962: p. 659).

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addressed the microfoundations of the General Theory. Neither Patinkin ([1956] 1965) nor

Clower (1965) considered the existence of an equilibrium featuring involuntary unemployment.

In their market models, the sole equilibrium position was the full-employment. This resulted in

the association between involuntary unemployment, disequilibrium, and the dynamic of

markets. The central issue was whether price and quantity adjustments were stabilizing when

firms and/or households failed to realize their Walrasian optimizing plans.

Just like Patinkin and Clower or Hahn and Negishi, Barro and Grossman adopted a

dynamic approach to disequilibrium economics.8 They viewed disequilibrium as a dynamic

phenomenon; asserted the need to study the stability of Walrasian equilibrium; and in turn, set

a roadmap for a dynamic disequilibrium model. All these aspects are emphasized through a

combination of arguments found in Grossman’s (1968) research project and in other articles

written with or without Barro, in the early 1970s.

A dynamic conception of disequilibrium phenomena

While “analyzing the causes of market disequilibrium in a macro-economic context”

(1968: p. 3), Grossman argued that:

sluggish market clearing in either the product market or the debt market [was]

responsible for disequilibrium in the sense of nonzero notional excess demand

(1968: p. 12).

Quite similarly, in “Suppressed Inflation and the Supply Multiplier”, Barro and Grossman

explained that disequilibrium situations such as:

suppressed inflation and suppressed deflation both [resulted] from the inability

of wages and prices to adjust instantaneously, in response to shifts in aggregate

demand or supply, to satisfy the conditions for general market clearing (1974: p.

87).

Taken together, these two quotations show that in Barro and Grossman’s view, disequilibrium

occurred only during the market-clearing process. There was only one equilibrium. It featured

full market clearing, and was stationary. That explains why Barro and Grossman always

8 The same is true for much of the economists who furthered researches on disequilibrium and non-tâtonnement economics. Among these economists, some drew Barro and Grossman’s attention when developing their disequilibrium program of microfoundations. Let me mention Peter Frevert (1968, 1971), Axel Leijonhufvud (1968), Donald Tucker (1966, 1968), Robert Solow and Joseph Stiglitz (1968), and Emiel Veendorp (1975).

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considered the same experiment when undertaking a disequilibrium analysis. Grossman

summed it up in “Money, Interest, and Prices in Market Disequilibrium” (1971):

The experiment begins with particular values of r and P [market prices] which

are not consistent with general equilibrium. An ‘instantaneous-multiplier’

process then determines […] ‘fixed-price-equilibrium’ quantities, in the sense

that they would have no tendency to change so long as P and r did not change.

[…] At the same time, but as a conceptually distinct operation, P and r are being

adjusted (Grossman, 1971: p. 958).

Initially, the economy was supposed to be at full-employment. An exogenous shock disturbed

this equilibrium position (e.g., downward shift of aggregate demand). Since prices and wages

varied too slowly to ensure an instantaneous return to full-employment equilibrium,

disequilibrium analyses were undertaken. The goal was to explain the determination of output

and employment at given non-clearing market prices, and the dynamic of markets.

Stability of full-employment equilibrium or the central issue for macroeconomics

In 1974, while commenting on Leijonhufvud’s (1973) article “Effective Demand

Failures”, Grossman acknowledged that the stability of full-employment equilibrium was the

central issue for macroeconomics:

According to Leijonhufvud […] the essential question for macroeconomics is

the following ‘Does the market system…tend to move automatically towards a

state where all market excess demands and supplies are eliminated? How strong

or weak are those tendencies?’ (p.29). As evidenced by my own writing – see,

for example, Grossman [1969, 1971, 1973] and Barro & Grossman [1971,

January 1974, July 1974] – I have much sympathy with Leijonhufvud’s

perspective and I agree with Leijonhufvud’s identification of the central issue

for macrotheory (1974: p. 358).

A roadmap for a dynamic disequilibrium macroeconomics

In his research project, Grossman (1968) argued that his “major objective was the

development of a theory of spillover” (1968: p. 3). This was because:

the notional excess demands generally should not be regarded as appropriate

measures of market pressures making for [price] change [out of Walrasian

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equilibrium]. As Patinkin [1952] points out, the notional excess demands

measure the ‘net amount demanded on the assumption that the individuals who

constitute the market are able to buy or sell as much as they desire at the

prevailing set of prices. But this is precisely the situation that does not obtain

under [disequilibrium] conditions; for then, by assumption there are unsatisfied

buyers and sellers. For example, suppose that the array of prices is such that the

amount demanded exceeds the amount supplied for both shoes and clothing.

Then, the pressure on the price of, say, shoes comes from two sources: first, the

buyers who have not succeeded in obtaining all the shoes they which to purchase

at the given prices; second, the buyers who have not succeeded in spending all

they intended to (at the given prices) on clothing, and who redirect part of this

unspent income to the shoe market.’ […] The second of these factors Patinkin

[1965] has called ‘spillover’ (1968: p. 10).

The development of a dynamic theory of spillover was challenging. The first challenge

was to offer a microeconomic framework adapted to market adjustment processes. According

to Grossman (1968), “Clower’s [1965] dual decision hypothesis” was a good “starting point”

(p. 15). This was because when generalized to the firms, this theory of choice could be used to

deduce effective excess-demands for all individuals (1968: p. 15). Both Barro and Grossman

considered that these functions measured properly the forces making for change in wages and

prices out of full-employment equilibrium (1971: p. 84). That said, the dual-decision hypothesis

was not sufficient to base the analysis of wages and prices adjustments on maximizing behavior.

Barro and Grossman (1971) explained why:

The inability of a firm to sell its desired output at the going price violates an

assumption of the perfectly competitive model. Kenneth Arrow has stressed this

inconsistency of perfect competition with disequilibrium. Essentially, he argues

that economic units which act as perfect competitors in equilibrium must (at least

in certain respects) perform as monopolists in disequilibrium. In this paper, we

focus on the reaction of economic units to given (equilibrium or disequilibrium)

price levels. If in addition, one wished to analyze explicitly the dynamics of price

adjustment, it would be necessary to discard the perfectly competitive paradigm

of the producer as a price taker [In this regard, see Barro] (1971: p. 85).

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Arrow emphasized the incompatibility between disequilibrium and perfect competition, in

“Toward a Theory of Price Adjustment” (1959). He argued that the existence of disequilibrium

(e.g., an excess supply of goods) contradicted the assumption that in perfect competition, firms

were supposed to face a perfectly elastic demand curve. At the same time, just like Tjalling

Koopmans’s (1957), Arrow (1959) explained that the law of supply and demand, as price

mechanism, reflected no one’s maximizing behavior. Hence the need to discard the perfect

competition framework. Reference to Barro’s (1972) article on monopolistic price adjustment

suggested that the elaboration of a microeconomic framework adapted to disequilibrium

adjustment processes was on the agenda.

The second challenge posed by the development of a dynamic theory of spillover was

to study the stability of full-employment equilibrium. In his research project, Grossman argued

that “future work on pure theory of market disequilibrium in a macro-economic context will

concentrate on […] the relationship of spillover to global stability” (1968: p. 21). In “Money,

Interest, and Prices in Market Disequilibrium”, Grossman (1971) provided a first stability

analysis. Thereafter, Barro and Grossman investigated systematically the dynamic of non-

clearing markets in Money, Employment, and Inflation (1976). By that time, they had stabilized

a dynamic disequilibrium model. It turns out to be very much in the spirit of Patinkin ([1956]

1965) and Clower’s (1965). Next section presents its main features.

2. A dynamic disequilibrium model

Barro and Grossman followed in Patinkin ([1956] 1965) and Clower’s (1965) footsteps to

elaborate their disequilibrium model. First, they focused on the behavior of aggregates, in a

competitive environment. Second, they devised a Walrasian-type technology of exchange.

Third, they assumed that market prices responded to effective excess demands.

2.1 Environment

Just like Patinkin ([1956] 1965) and Clower (1965a), Barro and Grossman “abstracted

from distribution effects” (1976: p. 9).9 Emphasis was given to the behavior of three

9 Patinkin used the “Hicks Composite-Good Theorem” to build aggregates ([1956] 1965: p. 411). Clower (1965) also did, but without mentioning it. The same is true for Barro and Grossman (1976): “when analyzing the behavior of firms, working households, and retired households, we consider the ‘representative’ unit; that is, a unit whose behavior, expect for its atomistic scale, is identical to the behavior of the aggregate of such units. The representative unit is essentially an average unit. Consequently, we are able to move freely between the individual and aggregate, and we use the same notation to represent both” (1976: p. 9).

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“representative units” (1976: p. 9): a firm, a household, and a government.10 These three

economic units were supposed to interact through two markets. The labor market, where labor

services were exchanged against money, and the market for goods, where consumable

commodities and public services were exchanged against money. Within this framework,

government provided public services by collecting taxes and/or supplying money balances; the

firm demanded labor and supplied commodities in view of maximizing profits; and the

household aimed to maximize an intertemporal utility function by choosing the quantity of

goods to demand, the quantity of labor to supply (until they retired), and the quantity of real

balances to transfer from one period to another.11

Moreover, economic units acted in a competitive environment. Barro and Grossman

assumed that on each market, an “agent” set the price and provided economic units with

information about their level of constraint on sales or purchases (1976: p. 31 and p. 95). On the

basis of these information, firms and/or households revised their plans and expressed either an

effective supply or an effective demand in the other market (dual-decision hypothesis).

2.2 A Walrasian-type technology of exchange

The technology of exchange adopted by Barro and Grossman (1976) was reminiscent

of Patinkin ([1956] 1965) and Clower’s (1965). In Chapter XIII, Patinkin drew an analogy

between the dynamic adjustment process occurring “when the level of real income [was] held

constant during the tâtonnement [and] when the level of income (and hence employment) [was]

permitted to vary” ([1956] 1965: p. 328). This suggested that the Walrasian technology of

exchange used in the microeconomic part of his book could be adapted to his disequilibrium

macroeconomics. But Patinkin did not specify how.12 By contrast, Clower (1965) rationalized

the process of exchange in a non-tâtonnement context. On the one hand, a “central market

authority” checked the validity of purchase orders and, in turn, determined the level of actual

transactions (1965: p. 51). Specifically, in situation of involuntary unemployment, workers’

purchase orders were “cancelled unless [they had] a positive balance of ‘book credit’ to cover

the entire value of the purchase order” (1965: p. 51). Hence why workers expressed an

“effective” demand for goods instead of a “notional” demand for goods. The determination of

output followed – “actual transactions [being] dominated by the “short-side” of the market”

10 Barro and Grossman treated government behavior as exogenous (1976: p. 17). 11 Once retired, households were supposed to consume until their death, by using their saving. 12 For a detailed discussion on Patinkin’s technology of exchange (the Hicksian week) and whether it was compatible with his disequilibrium macroeconomics, see Michel de Vroey (2002).

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(1965: p. 44). On the other hand, the “central market authority” facilitated transactions by

debiting and crediting individuals’ accounts (1965: p. 51). Likewise, Barro and Grossman’s

market “agents” ensured the compatibility between individuals’ plans and realized transactions.

Barro and Grossman were only more precise about the timing of their operations. Both the

determination and the realization of transactions occurred at once. Market “agents” received

information about what individuals would like to buy and sell given market prices and their

rationing on markets. Simultaneously, market “agents” set output and employment levels

according to the principle of “voluntary exchange” – i.e., “actual total transactions of any good

will equal the smaller of the quantities supplied and demanded” (1976: p. 40). At the same time,

market “agents” ensured the realization of transactions – since the representative firm was not

supposed to hold money, receipts and disbursements had to be perfectly synchronized (1976:

p. 10). As a result, Barro and Grossman’s “market agents” acted as the Walrasian auctioneer

and as the Walrasian clearing house.

2.3 Adjustment rules

Either in Patinkin ([1956] 1965), Clower (1965) or Barro and Grossman’s (1976)

disequilibrium model, market prices responded to effective excess demands. Evidence of this

can be found in Chapter XIII, even if Patinkin ([1956] 1965) did not formalize a constrained

demand for labor. Patinkin explained that wages declined because of the excess supply

generated by firms’ decision to revise their demand for labor downward ([1956] 1965: p. 321).

The same principle underlined the dynamic model sketched by Clower in the last pages of the

“Counter-Revolution” article. He assumed that market prices varied according to effective

excess demands (1965: p. 54). An assumption made clearly by Barro and Grossman. This

resulted in the following formalization:

!"#$"$%& = 𝜆")𝑙$

+ − 𝑙-+. [1] and !/#$/$%& = 𝜆/)𝑐$

+ + 𝑔$ − 𝑦-4. [2], where 𝜆"

and 𝜆/ [are] positive constants. Relations [(1) and (2)] specify that whenever an

effective supply or demand does not coincide with the corresponding notional

supply or demand, the effective supply or demand is the relevant magnitude

influencing the speed of wage or price adjustment (1976: p. 95).

After transactions occurred, Barro and Grossman’s market “agents” observed effective excess

demands and varied market prices accordingly (1976: p. 95). For instance, they increased wages

(𝑊) and prices (𝑃) when the effective demand was higher than the effective supply in the labor

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market and in the market for goods. Otherwise, they decreased 𝑊 and 𝑃. Such variations

occurred in between periods where “fixed-price” equilibria were determined. Accordingly, the

dynamic of the economy was represented as a sequence of “fixed-price” equilibria.

To conclude, Barro and Grossman’s disequilibrium macroeconomics not only built on

the foundations laid down by Patinkin ([1956] 1965) and Clower’s (1965) analyses of

involuntary unemployment. It also built on Patinkin ([1956] 1965) and Clower’s (1965)

approach to disequilibrium economics. Considering disequilibrium as a dynamic phenomenon,

Barro and Grossman sought to elaborate a theory of adjustment processes. Its full version was

presented in Money, Employment, and Inflation (1976). Following in Patinkin ([1956] 1965)

and Clower’s (1965) footsteps, Barro and Grossman (1976) focused on the behavior of

representative economic units, in a competitive environment; they devised a Walrasian-type

technology of exchange; and they replaced “notional” excess demands by effective excess

demands in the price adjustment mechanism. Next section discusses the dynamic properties of

their disequilibrium model.

3. Dynamic properties

Just like Patinkin ([1956] 1965) and Clower (1965), Barro and Grossman (1976) were

concerned with the stability of full-employment equilibrium and the significance of monetary

exchange in the transmission of disequilibria. They showed that Walrasian equilibrium was

stable and that quantity adjustments were larger in monetary economies. At the same time,

Barro and Grossman (1976) enlarged the investigations. From a theoretical perspective, they

discussed how rapidly worked monetary policy. From a more empirical perspective, they

addressed the relation between real wage and employment variations, and the relation between

wage inflation and unemployment rate. That knowledge-building process results in a rich and

accurate picture of the explanatory power of Patinkin ([1956] 1965) and Clower (1965)-type

macroeconomics.

3.1 Stability of the full-employment equilibrium

Both Patinkin ([1956] 1965) and Clower (1965) considered that “the central question

[was] the efficiency of an automatically functioning market system with flexible money wages

in eliminating involuntary unemployment” ([1956] 1965: p. 315). The challenge for them was

to provide a formal analysis of the adjustment process. Such an ambition appears in the

correspondence that Patinkin and Clower had respectively with Nissan Liviatan and Donald

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Bushaw.13 In this context, Patinkin and Clower expressed frustration with their inability to offer

a formal stability study:

When I tried to [present spillover effects] in a mathematical way, I went through

the same problem, and that is why there is no mathematical appendix to that

chapter [XIII]!14

My problem is naturally mathematical in character. Consider a price system […]

in which the demand and supply functions depend not only on prices, but on

quantity actually exchanged, this being defined as quantity demanded if there is

excess supply in any market, as quantity supplied if there is excess demand (the

short side of the market governs it) […] I emphasize that this could be a really

significant breakthrough in economics if you can say something definite;

otherwise, I shall just be left to my own literary devices to figure out what one

can say about this.15

Like most economists, Patinkin and Clower advocated for formal analyses to facilitate the study

and exposition of economic problems. In particular, formalization would have allowed to offer

an accurate picture of the relationship between individuals’ behavior and market dynamics.

This would have resulted in the clarification of the logical properties of their disequilibrium

models. Notably whether price and quantity adjustments were stabilizing when considering

spillover effects. Given that neither Patinkin ([1956] 1965) nor Clower (1965) provided a

formal stability analysis, the issue of how individuals behaved during the adjustment process

remained opened. Just like whether the market system was self-regulating or not.16

13 Liviatan was a former student of Patinkin. He was the only economist with whom Patinkin discussed the disequilibrium model presented in Chapter XIII, before the first edition of Money, Interest, and Prices (1956) was published (Mauro Boianovsky, 2006); Bushaw was a mathematician colleague of Clower at Washington State University. At various stage of Clower’s career, Bushaw helped him to formalize his views. See Plassard (2018b) for an historical investigation on Bushaw and Clower’s ‘stock-flow’ program of microfoundations. 14 Letter from Patinkin to Liviatan (29 January 1955) – Don Patinkin Papers, Rubenstein Rare Book and Manuscript Library. Boianovsky quoted it while tracing “The Making of Chapter 13 and 14 of Patinkin’s Money, Interest, and Prices” (2006: p. 237). For a detailed exposition of the difficulties experienced by Patinkin in the process of elaborating his theory of unemployment, see Boianovsky (2006). 15 Letter from Clower to Bushaw. R.W. Clower Papers, Rubenstein Rare Book and Manuscript Library. This letter is undated. Yet it sounds like a report on a discovery: the dual-decision hypothesis. For a discussion of the difficulties experienced by Clower when trying to study the stability properties of his 1965 disequilibrium model, see Plassard (2016, chapter IV). 16 While Patinkin considered that the real-balance effect ensured the stability of the full-employment equilibrium ([1956] 1965: pp. 324-328), Clower was less clear-cut (1965: p. 55). This was because he had identified a scenario of persistent involuntary unemployment (1965: pp. 54-55).

14

By contrast, Barro and Grossman (1976) provided a formal stability analysis. By doing

so, they clarified how behaved individuals during the adjustment process and showed that:

Changes in l and y [the levels of employment and production], as well as in W

and P [reestablished] general-market-clearing conditions (1976: p. 97).

To demonstrate that Walrasian equilibrium was stable, Barro and Grossman considered a

situation of general excess demand (1976: pp. 97-100). Let us account for the stabilization

process, starting from a general excess supply case. To this end, I need to identify how "/

vary

from one “fixed-price” equilibrium to another. Without specifying the relative speed at which

W and P fall, the variation of the real wage is ambiguous. What Barro and Grossman did was

to determine subregions (within the space created by the effective market-clearing loci) where "/

increased or decreased (1976: p. 96). This depended on whether the effective excess supply

for goods was greater than the effective excess supply for labor (1976: p. 96) – according to (1)

and (2), the more the discrepancy between effective demand and supply is large, the more W

and P vary rapidly (and conversely).17 Assume that after a shock, the economy situates in a

subregion where real wage declines. Since the labor cost is reduced, firms will hire. At the same

time, the supply of labor declines. Both because households are lower paid and because their

nonwage wealth increases (under the real-balance effect and of rising profits). As a result, price

change tends to reduce the gap between demand and supply in the labor market. In the process,

the rate of decrease of P declines, which progressively leads the real wage to rise. Under these

circumstances, consumption raises while the supply of goods tends to fall. Consequently, output

also converges towards its market-clearing level, associated to general-equilibrium values of

W, P, and "/

.

3.2 Monetary structure of exchange

When sketching their models, Patinkin ([1956] 1965) and Clower (1965) considered

that money constrained rather than facilitated transactions during economic depressions. Such

17 Barro and Grossman indicated that the stability of Walrasian equilibrium was not affected by their “arbitrary” identification of subregions where "

/ increased or declined: “had we assumed the dashed line to be upward

sloping, W would have initially risen proportionately faster than P, so that "/

would have initially risen, before

falling back to ("/)∗” (1976: p. 98).

15

an intuition underlined Patinkin’s explanation of how an excess supply in the market for goods

was transmitted to the labor market:

When firms planned the inputs of labor described by the [standard] demand

curve, they assumed that they would be able to pay for these inputs with the sales

proceeds of the resulting outputs. Therefore, when these sales fail to materialize,

firms find themselves with their funds tied up in illiquid inventories and hence

financially unable to carry out their original plans. Accordingly, […] they now

demand a smaller input ([1956] 1965: p. 320)

Firms failed to receive the proceeds they had planned because of the excess supply in the market

for goods. Without sufficient access to cash, they could not pay their wage bill. Hence why they

revised their production plans and, in turn, generated involuntary unemployment. Inspired by

chapter XIII when writing the “Counter-Revolution” article, Clower put efforts towards the

elaboration of a disequilibrium model where individuals would behave under cash constraints

(Plassard, 2017). Its microfoundations combined the dual-decision hypothesis with the

dichotomized budget constraint, presented in “A Reconsideration of the Microfoundations of

Monetary Theory” (1967). Due to the dichotomization of “income” and “expenditure”

branches, individuals would be forced to get cash to consume and to receive cash in return for

their sales. Accordingly, they had to revise their purchasing plans downward when unable to

earn a monetary income. That was why the monetary structure of exchange caused disequilibria

to spread.

To confirm the existence of this causal link, it must be shown that the effects of

disequilibrium transactions would be different if barter exchange were admitted.18 Patinkin

([1956] 1965) and Clower (1965) did not. Neither did Barro and Grossman (1976). However,

Grossman provided such a comparative analysis in his “Comment” (1974) of Leijonhufvud’s

article “Effective Demand Failure” (1973). Using the disequilibrium model elaborated with

Barro, Grossman showed that:

18 Many disequilibrium theorists worked toward resolving this theoretical problem. Let me mention Jean-Pascal Bénassy, Jean-Michel Grandmont, Axel Leijonhufvud, Guy Laroque, or Yves Younes. For a more exhaustive list, see Allan Drazen’s (1980) survey on disequilibrium macroeconomics.

16

The multiplier effects associated with a non-general-market-clearing

combination of wages and prices depend on the monetized structure of exchange

(1974: p. 365)

Grossman considered a situation of general excess supply and discussed employment and

output variations. First when money served as a medium of exchange, and then when the

consumption good played this role. In the first case, cash constraints forced firms and

households to curtail their demand for labor and commodities. As a result, the effective demand

for labor and commodities determined respectively employment and output levels (1974: p.

365). In the second case, the excess supply in the market for goods no longer forced firms to

adjust their demand for labor downward. This was because firms could pay their wage bill and

distributed profits in the form of commodities (1974: p. 364). Under these circumstances, the

notional demand for labor services and the notional supply of commodities determined

employment and output levels (1974: p. 365). This resulted in a contraction of unemployment.

But of less magnitude than when money was used as the medium of exchange. Hence why

multiplier effects depended on the monetary structure of exchange.

This demonstration concludes the first phase of knowledge-building on disequilibrium

models à la Patinkin ([1956] 1965) and Clower (1965). Let me now turn to the second phase.

Barro and Grossman’s analyses continue to be used to clarify the properties of Patinkin ([1956]

1965) and Clower (1965)-type macroeconomics. However, the analytical distance between

frameworks may increase. Moreover, emphasis is given to issues that were not discussed in

Money, Interest, and Prices or in the “Counter-Revolution” article. Barro and Grossman’s

(1976) analysis of how rapidly worked monetary policy is a case in point.

3.3 Monetary policy speed

In its basic form, Barro and Grossman’s (1976) model was not appropriate for analyzing

the effects of monetary policy. Change in the money supply could take place. But in the absence

of assets other than money, its influence on the rate of interest was not taken into account. Thus,

one of the main channels through which monetary policy was supposed to affect economic

activity was not modelled. To fill this gap, Barro and Grossman (1976) incorporated a financial

market into their framework.19 By assumption, economic units exchanged equity shares and

treasury bonds against money. The supply of equity shares came from firms; the supply of

19 See chapter 3 “Capital, financial assets, and the rate of return” (1976: pp. 101-153) for a full account of the change introduced by Barro and Grossman.

17

treasury bonds came from the government; and the demand for these two assets resulted from

households’ portfolio choice.20 Since there was no uncertainty about their rates of return,

households considered equity shares and treasury bonds as perfect substitutes (1976: p. 103).

Accordingly, the disequilibrium model included one more exchange ratio, the rate of interest

(𝑟), also determined according to the principle of “voluntary” exchange.

On that basis, Barro and Grossman offered a comparative-statics analysis to demonstrate

the efficiency of monetary policy (1976: pp. 151-153). Moreover, they “analyze[d] the exact

form of the time path of 𝑦 and 𝑟 implied by the behavior of 𝑀 [quantity of money]” (1976: p.

214). What was at stake was whether monetary policy worked slowly, an issue explored by

taking into account “various structural lags”. For instance, Barro and Grossman assumed

gradual adjustments of money balances (1976: pp. 211-217), of the demand for goods (1976:

pp. 217-223), and a gradual clearing of the financial market (1976: pp. 230-237).

They showed that “the existence of structural lags [did] not necessarily imply a lag in

the response of 𝑦 to change in 𝑀” (1976: p. 221). In other words, monetary policy could have

instantaneous effects on economic activity while some components of aggregate demand

reacted slowly to stimuli.21 To explain why, let me focus on one of the cases studied in chapter

6 of Money, Employment and Inflation, “The dynamics of aggregate demand”. By assumption,

the economy was in a situation of general excess supply. Accordingly, output and employment

levels were determined by the effective demands in the respective markets. Then, throughout

the analysis, p remained fixed, and r ensured effective clearing of the financial market (1976:

p. 211). Therefore, Barro and Grossman considered only quantity adjustments in the market for

goods, and the time path of r was somehow pre-determined. Lastly, Barro and Grossman

assumed that households adjusted gradually their money balances and their demand for goods

according to target levels (1976: p. 220). Under these circumstances, they claimed that:

the gradual adjustment of money balances causes a more exaggerated response

of 𝑟 to changes in 𝑀, which in turn tends to produce a more exaggerated

movement in 𝑦. At the same time, the gradual adjustment of effective

20 To “rationalize the holding of money and the diversification of wealth between money and earning assets”, Barro and Grossman introduced transactions costs into the analysis (1976: p. 104). Households had to pay a financial service when buying assets. Thus, they would seek to minimize the number of financial transactions. Hence the accumulation of saving in the form of money and assets. 21 Barro and Grossman (1976) acknowledged that Tucker had already obtained this result in two articles: “Dynamic Income Adjustment to Money Supply Change” (1966) and “Credit Rationing, Interest Lags, and Monetary Policy Speed” (1968). See Money, Employment and Inflation (1976: p. 220; p. 232)

18

commodity demand tends to dampen the response of 𝑦 to any change in 𝑟. The

net result can be either a greater or lesser response of 𝑦 to 𝑀 in the short-run

than in the long-run (1976: p. 221).

Due to the gradual adjustment of money balances, an immediate change in the target level of

money balances was the condition for individuals to demand the new money put into circulation

(1976: p. 215). Such a change would take place if individuals had an incentive to sell assets

against money. And the incentive needed to be strong, because of the cost of financial

transactions. Hence the “exaggerated” decrease in the rate of interest. From there, aggregate

demand and production increased mechanically – according to the principle of “voluntary

exchange”, the representative firm kept 𝑦 equal to 𝑦$4. Accordingly, monetary policy had

immediate effects on economic activity. Barro and Grossman only indicated that the magnitude

of the rise in production depended on how rapidly households adjusted their demand for goods

to the new target level of effective commodity demand.

3.4 Empirical content

Until now, no attention was paid to the empirical content of Barro and Grossman’s

disequilibrium model. However, Barro and Grossman were concerned with its capacity to fit

the data. They focused on two empirical issues. The relation between real wage and

employment variations, and the relation between wage inflation and unemployment rates.

Real wages and employment fluctuations

When addressing the relation between real wages and employment fluctuations, Barro

and Grossman referred to two empirical studies. Edwin Kuh’s, in “Unemployment, Production

Functions and Effective Demand” (1966), and Ronald Bodkin’s in “Real Wages and Cyclical

Variations in Employment: A Re-Examination of the Evidence” (1969).22 In both articles, Kuh

and Bodkin reopened the debate over whether real-wages were positively or negatively related

to the rate of unemployment. They obtained two results. First, no strong statistical evidence

supported the view that employment increased when real-wages decreased. Second, some of

the cases studied (e.g., USA during the post-second World War period) showed that real-wages

were related negatively and significantly to the rate of unemployment.

22 For an explicit reference to Kuh (1966) and Bodkin (1969), see “A General Disequilibrium Model of Income and Employment” (1971: p. 83). See also Money, Employment, and Inflation (1976: p. 2).

19

Already in the 1971 article, Barro and Grossman highlighted the gap between these two

results and the assumptions underlying the “conventional” theory of the firm. In standard

models, entrepreneurs’ demand for labor was inversely and uniquely related to the real-wage.

Accordingly, “cyclical variations in the quantity of labor demanded and the amount of

employment must imply countercyclical variations in real wage rates” (1971: p. 82). By

contrast, Barro and Grossman’s model of the labor market could replicate the positive relation

between real-wage and employment variations:

To the extent that real wages decline in response to this excess supply, a fall in

real wages toward 𝑤=will accompany (follow upon) the decline in employment.

If, at point 𝐶 or at some intermediate point between 𝐵 and 𝐶, some action is

taken to restore effective commodity demand, excess demand for labor (or at

least reduced excess supply) will result. In that case, a rising real wage may

accompany the recovery of output an employment. Thus, disequilibrium analysis

of the labor market suggests that real wages move procyclically (1971: p. 87).

Here was the scenario considered by Barro and Grossman (1971). Initially, a decline in

commodity demand forced entrepreneurs to revise their demand for labor downward. This

resulted in a situation of involuntary unemployment. Given the excess supply in the labor

market, real-wages declined. Just before real-wages reached the level which cleared the labor

market, the government implemented a fiscal policy. The resulting increase in aggregate

demand led entrepreneurs to hire more. Given the low level of real-wages, entrepreneurs might

be constrained in the labor market. Barro and Grossman concluded that a rise in real-wages

followed upon a rise in employment, and vice versa.

Wage Inflation and unemployment rate

When addressing the relation between wage inflation and unemployment rate, Barro

and Grossman (1976) considered one empirical study. Alban William Phillips’, in “The

relationship between unemployment and the rate of change of money wage rates in the United

Kingdom, 1862-1957” (1958). According to Barro and Grossman, Phillips established two

empirical regularities which characterized the experience of most developed countries until the

end of the 1950s. First, on average, the higher the unemployment rate the lower the rate of wage

inflation. Conversely, the lower the unemployment rate the higher the rate of wage inflation.

Moreover, the unemployment rate was positive when the rate of inflation was zero. Second,

when wage inflation started increasing, unemployment rate increased over a short period of

20

time and eventually decreased. Conversely, when wage inflation started decreasing,

unemployment rate decreased over a period of time and eventually increased. This resulted in

what Barro and Grossman described as a “counterclockwise cycle” around the average relation

between unemployment and wage inflation (1976: p. 201). On top of these two empirical

regularities, Barro and Grossman observed the phenomenon of “stagflation” (1976: p. 206). It

was related to a change in the cyclical pattern of unemployment and wage inflation. While

analyzing data from the U.S. Bureau of Labor Statistics (1973), Barro and Grossman realized

that when wage inflation accelerated, unemployment could decrease for a short period of time.

Conversely, when wages started decreasing, unemployment could increase for a short-period

of time. But eventually, an acceleration of the wage inflation led to a rise in the unemployment

rate, and vice versa. This resulted in a “clockwise cycle” around the average relation between

unemployment and wage inflation (1976: p. 201).

In Chapter 5 of Money, Employment, and Inflation (1976), Barro and Grossman showed

that their disequilibrium model could account for these three empirical observations. The

condition was to make some change to its basic version:

Section 5.2 developed a basic model of the average inverse relation between 𝑢

and (1 𝑊B )(𝑑𝑊 𝑑𝑡B ). Equation (5.2), )1 𝑊B .#𝑑𝑊 𝑑𝑡B & = 𝜆"𝐻, and equation

(5.9), 𝑢 = 𝐺(𝐻), summarized this model. Section 5.4 introduced partial

adjustment into the relation between 𝑢 and 𝐻. This modification generated

equation (5.16), 𝑑G 𝑑%B = 𝜆H[𝐺(𝐻) − 𝑢], as a generalization of (5.9). With 𝜆H less

than infinite, the model, summarized by equations (5.2) and (5.16), predicted a

counterclockwise cyclical pattern. Section 5.5 introduced adaptive expectations

into the relation between (1 𝑊B )(𝑑𝑊 𝑑𝑡B ) and 𝐻. This modification generated

equation (5.21), $(! "B

$"$%B )

$L= 𝜆"(𝜃N𝐻 +

$O$L), as a generalization of equation

(5.2). With 𝜃N greater than zero, the model summarized by equations (5.9) and

(5.21), predicted a clockwise cyclical pattern (1976: p. 209).

Barro and Grossman’s analysis started with the wage adjustment relation (1976: p. 189). Wages

were supposed to vary according to the effective excess demand for labor (𝐻). They increased

when the effective excess demand for labor increased, and vice versa. Equivalently, wages

decreased when the effective excess supply of labor increased, and conversely. This resulted in

21

an inverse relation between wage variations and unemployment. However, its features “[were]

counter to empirical evidence” (1971: p. 192). Zero wage inflation was associated to zero

unemployment. Moreover, there was an inverse relation between wage variations and

unemployment only when wages declined (1971: p. 192). Hence the need to change the basic

framework. Barro and Grossman made three modifications. They introduced heterogeneity into

labor services, considered that the unemployment rate reacted with a lag to change in 𝐻, and

introduced expectations into the wage adjustment relation. The first modification allowed to

generate Phillip’s average relation between unemployment and wage inflation. Coupled with

the gradual adjustment of the unemployment rate, the model also generated Phillips’ second

empirical regularity. Lastly, a disequilibrium model involving heterogeneous labor services and

inflationary expectations could portray “clockwise cycle” around the average relation between

unemployment and wage inflation.

To conclude, while studying the dynamic properties of their disequilibrium model,

Barro and Grossman (1976) showed how rich the research line opened in Chapter XIII and in

the “Counter-Revolution” (1965) article was. Both from a theoretical and a more empirical

perspective. That said, Barro and Grossman also identified the flaws of their disequilibrium

model (1976: pp. 4-6). Next section questions its capacity to explain satisfactorily the dynamic

of actual economies.

4. Flaws

Patinkin ([1956] 1965), Clower (1965), and Barro & Grossman’s (1976) approach to

disequilibrium dynamics was deficient. First, their adjustment rule reflected no one’s

optimizing behavior. Second, the process of exchange was centralized. Third, the intertemporal

dimension was either ignored or insignificant. These flaws called into question the capacity of

their models to portray the dynamic of actual economies. To explain why, emphasis is given to

arguments formulated by Barro and Grossman (1976), by Howitt (1977) in his review of

Money, Employment, and Inflation, or by Clower and Leijonhufvud.

4.1 Ad hoc adjustment process

Unlike effective supply and demand functions, the law of supply and demand was not

deduced from agents’ optimizing behavior. Barro and Grossman made this point in the

introduction of Money, Employment, and Inflation:

22

Although the discussion stresses the implication of exchange at wages and prices

which are not consistent with general market clearing, we provide no choice-

theoretic analysis of the market-clearing process itself. In other words, we do not

analyze the adjustment of wages and prices as part of the maximizing behavior

of firms and households. Consequently, we do not really explain the failure of

markets to clear, and our analyses of wage and price dynamics are based on ad

hoc adjustment equations (1976: p. 6).

The law of supply and demand was an adjustment rule fixed exogenously. This posed two

“embarrassing” problems (1976: p. 6). On the one hand, no rational argument justified why

market prices varied slowly. Accordingly, Barro and Grossman’s project to provide

microfoundations to macroeconomics remained incomplete. On the other hand, the results of

their dynamic analyses had to be read with care. This was because they depended on an “ad

hoc” specification of the dynamic process. This caution was all the more important since

effective excess demands may not reflect properly individuals’ behavior. Howitt (1977) made

this point in his review of Money, Employment, and Inflation. He argued that “under conditions

of excess supply in the labor market, [Barro and Grossman] assumed that the effective supply

of labor [was] the same as if at the same real wage there were excess demand for labor, which

[amounted] to a highly implausible independence of labor force participation rates from

unemployment rates” (1977: p. 125). As a result, “it was not clear that prices ought to respond

to the effective excess demands that the authors [defined]” (1977: p. 124).

4.2 Unrealistic process of exchange

The need to provide realistic microfoundations to macroeconomics prompted Barro and

Grossman’s research program. As a reminder, Grossman (1968) observed that in the real-world,

prices varied slowly and individuals not always succeeded in selling or buying what they

desired given exchange ratios (p. 5). Hence the need to depart from the perfect price flexibility

assumption underlying tâtonnement economics. Instead, Barro and Grossman assumed perfect

quantity flexibility. As a result, their disequilibrium model was based on an unrealistic

technology of exchange:

As we have formulated the analysis, the convergence to output and employment

levels 𝑦 and 𝑙 would be instantaneous. [This] assumes a simultaneous

determination of the actual transactions carried out in both markets by each

economic unit and of the effective demands of each economic unit in both

23

markets. Realistically however, households would not obtain information about

actual transactions in the labor market until the firms had expressed their

demands, while the firms would not obtain information about actual transactions

in the commodity market until the household had expressed their demands.

Furthermore, the profit income of households would not be determined until both

𝑦 and 𝑙 were determined. The actual effective demands which determine output

and employment according to the [principle of voluntary exchange] could only

emerge in practice from a recursive interaction (1976: p. 58).

In reality, individuals made decisions and then transactions occurred. Due to this sequence,

individuals would start formulating their plans with a minimum level of information about their

constraints on markets. Several sequences would be necessary before firms and households

identified the levels of output and employment which ensured the consistency of their plans –

i.e., a balance budget equal to zero for all individuals. Barro and Grossman concluded that “in

practice”, a “fixed-price” equilibrium could emerge only after a “recursive” process. Yet, they

did not model it. Instead, Barro and Grossman (1976) assumed perfect quantity flexibility. This

reduced the “recursive” process into an instantaneous interaction and so, ruled out any exchange

which did not ensure the coordination of individuals’ plans. Consequently, their sequence of

“fixed-price” equilibria offered a distorted picture of market dynamics.

Neither Patinkin ([1956] 1965) nor Clower (1965a) assumed perfect quantity flexibility.

But just like Barro and Grossman (1976), they sought to analyze how actual economies behaved

in models minimizing change to Walras’ technology of exchange. The question is whether it

was a relevant research strategy. In the mid-1970s, Clower and Leijonhufvud realized that it

was not:

We don’t as yet have an acceptable paradigm for analyzing price-quantity

behavior in decentralized markets. Most of the work that has been done thus far

on disequilibrium trading behavior starts with a Walrasian auctioneer who

merely adds to his traditional price-adjustment jobs the additional task of

conveying current information to transactors about their sales and purchases at

current (not necessarily market-clearing) prices […] My own attempt to provide

some kind of general foundation for disequilibrium analysis started within the

Walrasian framework and got me nowhere. Grossman and others (Tucker at

C.E.A, Crouch at Santa Barbara, and Frevert at Kansas) have tried to make

24

something of this beginning – the dual-decision hypothesis – but I am not

impressed by that work. All of this seems to me to attempt to squeeze into a

Walrasian paradigm phenomena that don’t belong there.23

Now, at long last, I know it in my bones – and realize that my defense to date of

having taken a Walrasian price-theory approach in my [1968] book won’t do.

It’s a good reason up to a point, but necessarily leaves damaging blind spots

(which become traps for the unwary – Grossman et al.).24

Clower and Leijonhufvud came to conclude that whatever the change made to the Walrasian

framework (e.g., rejection of the tâtonnement hypothesis and introduction of income

constraints), the resulting model would remain inappropriate for analyzing actual economies.

This was because Walrasian-type macroeconomics portrayed centralized economies, not

decentralized economies. Barro and Grossman’s (1976) disequilibrium model was a case in

point. For instance, Barro and Grossman (1976) ruled out the information problems that

occurred in decentralized systems. In their model, individuals did not have to make decision

with few information about the constraints they will face on markets. Market “agents” provided

individuals information about prices and their levels of rationing. Besides, Barro and Grossman

considered that market “agents” ensured at no cost and without delay the coordination of

economic activities. A role that no institution (either banks or traders) performs in actual

economies.

4.3 Inter-temporality without uncertainty

When discussing the dynamic of involuntary unemployment, Patinkin ([1956] 1965)

and Clower (1965) abstracted from intertemporal choice. In their models, individuals made

decision without looking beyond their current economic situations. They were not supposed to

expect future market prices, future quantity constraints, or the change in key variables such as

the stock of capital. This resulted in a deficient analysis of market dynamics. Notably because

Patinkin and Clower considered that disequilibrium situations could last long, as was the case

during the Great Depression.

23 Letter from Clower to Bernt Stigum (06/29/1970). R.W. Clower Papers, Box 1, Rubenstein Rare Book and Manuscript Library. 24 Letter from Leijonhufvud to Clower (07/10/1973). Axel Leijonhufvud Papers, Box 1, Rubenstein Rare Book and Manuscript Library.

25

In contrast to Patinkin ([1956] 1965) and Clower (1965), Barro and Grossman (1976)

introduced intertemporal choice into their disequilibrium analysis. They assumed that

individuals expected market prices and their levels of rationing. To be more specific, Barro and

Grossman (1976) separated the planning horizon of economic units into a constrained and an

unconstrained sub-period. Moreover, they assumed that firms and households expected market

prices to be fixed over time. Accordingly, Barro and Grossman did not consider any

probabilistic distribution on the evolution of market prices and of quantity constraints. Rather,

expectations “were held with certainty” in their disequilibrium model (1976: p. 4).

Despite addressing expectations, Barro and Grossman did not refer to intertemporal

choice when analyzing the stability properties of their disequilibrium model. This suggests that

their approach to intertemporal choice was inappropriate for analyzing the dynamic of markets.

At least one problem can be stressed. Barro and Grossman (1976) abstracted from uncertainty

and so, did not take into account the effects of speculation. In their disequilibrium model,

individuals did not bother about future price variations or about their capacity to buy or sell at

a reasonable price. Hence doubts about its capacity to portray the dynamic of actual economies.

Conclusion

My paper aimed to show that Barro and Grossman developed a dynamic disequilibrium

program of microfoundations. Given their role in the emergence of “fixed-price” equilibrium

macroeconomics, this raised three difficulties: to prove that they had a dynamic approach to

disequilibrium economics; to determine how they modeled the dynamic of non-clearing

markets; and to discuss the scope of their model. Two documents were central to the resolution

of these difficulties. “Market Disequilibrium in a Macro-Economic Context” (1968), and

Money, Employment, and Inflation (1976).

Just like Patinkin ([1956] 1965) and Clower (1965) or Hahn and Negishi (1962), Barro

and Grossman considered that disequilibrium phenomena occurred during the market-clearing

process. Thus, the challenge was to model the operation of economic activities throughout the

adjustment of markets. At first, a synthesis between Patinkin, Clower, and Hahn and Negishi’s

models was considered. But eventually, Barro and Grossman elaborated a model à la Patinkin

([1956] 1965) and Clower (1965). They considered the behavior of aggregates, in a competitive

environment; they assumed that market “agents” performed the coordination of individuals’

plans and synchronized transactions; and they substituted “effective” excess demands for

26

“notional” excess demands in the price adjustment mechanism. On that basis, Barro and

Grossman addressed theoretical and more empirical issues. They showed that Walrasian

equilibrium was stable, that multiplier effects depended on the monetary structure of exchange,

and that monetary policy had instantaneous effects on economic activity. On the more empirical

side, Barro and Grossman replicated a negative relationship between the real-wage and the rate

of unemployment. Besides, they replicated Phillips’ statistical regularities and stagflation. All

this showed how rich the modeling strategy initiated by Patinkin ([1956] 1965) and Clower

(1965) was. Yet at the same time, Barro and Grossman also identified the flaws of their model.

They stressed that the adjustment rule was not based on microfoundations. This forced to read

their results with care and to admit that their microfoundational program was incomplete. Then,

Barro and Grossman pointed out that their technology of exchange model was too centralized

to be realistic. An argument formulated by Clower and Leijonhufvud to explain why Walrasian-

type macroeconomics could not explain how actual economies behaved. Lastly, intertemporal

choice was either ignored or unimportant in Patinkin ([1956] 1965), Clower (1965), and Barro

and Grossman’s (1976) models. This led to put aside salient features of actual economies.

Notably the effects of speculation. Hence another reason why their approach to disequilibrium

dynamics remained unsatisfactory.

During the 1970s, several “fixed-price” theorists intended to fill these gaps. In his

doctoral dissertation, Disequilibrium Theory, Bénassy (1973) argued that “the traditional

assumption of prices moving in response to excess demand [was] not very satisfying”.

Therefore, he planned to “study more realistic models where firms [would] control the price of

some markets” (1973: abstract). This resulted in a dynamic disequilibrium model where the

exchange process was decentralized and the price adjustment mechanism reflected firms’

optimizing behavior. It was developed in “Regulation of the Wage-Profit Conflict and the

Unemployment-Inflation Dilemma in a Dynamic Disequilibrium Model” (1976) and in “Cost

and Demand Inflation Revisited: A Neo-Keynesian Approach” (1978). Other “fixed-price”

theorists addressed intertemporal choice without neglecting uncertainty, in dynamic models.

For instance, John Muellbauer and Richard Portes (1978), Volker Bohm (1980), or Pierre

Dehez (1980) formalized firms’ decision to accumulate or reduce stocks of goods, depending

on their expectations about future demand constraints. Besides, Edmond Malinvaud (1980)

focused on how firms determined their productive capacity in the future, depending on expected

demand. All this indicates that like Barro and Grossman, most “fixed-price” theorists neither

27

abandoned nor marginalized Patinkin ([1956] 1965) and Clower’s (1965) dynamic

disequilibrium program of microfoundations.

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