General Equilibrium – Why Post-Keynsians Can’t Live Without it

Perhaps the most fundamental proposition common to all Post-Keynesian economists, irrespective of the particular group or special group to which they belong is a rejection of the Walrasian theory of general equilibrium as the micro-foundation of the macroeconomic theory.

They find the Walrasian theory quite incompatible with Keynesian economics. In the Walrasian system it is crucial to understand that no trading or exchange can take place until planned demand and planned supply match in every market.

M. Agarwal

I dont disagree – however the concept of general equilibrium is older than Walras, Arrow-Debrau or DGSE, and the dominant model of general equilibrium  from early neo-classical economics was in any event challenged by an alternative concept of equilibrium from Keynes. The problem is with the dominant current conception of general equilibrium based on perfect foresight and rational expectations,  This is a model without time, without surprise, without profit, without any feature of economic interest.

Economics cannot do without a theory of equilibrium, it is the most important component of Macroeconomics and without it we can say nothing about the general price level.  What is needed is a properly dynamic theory of equilibrium that deals with economic activity in time and continuously.

Equilibrium is by definition a state in which the relevant variables are not changing, therefore, time is not taken into consideration in equilibrium analysis”.

J.R. Hicks

No.  The concept of equilibrium was derived from economics and was fundamentally misunderstood. Laying aside issues with physics envy equilibrium is not about no change it is a balance of forces which motion takes the path of least action (energy); this is important as for example if one holds constant or varies one variable others will shift you maintain an equilibrium state. This is important when you consider intertemporal equilibrium, whereby if you maintain a path of consumption, investment must shift (though causally maintaining a path of investment and consumption shifting is more plausible empirically and theoretically) and consequential effects on income lead to  continually varying states of the key variables.  Again brownian motion is not ‘no change’ it is continuous change but when viewed at a certain macroscopic level all forces are in balance.

The familiar argument that most of the time most of the economy is in disequilibrium is no argument to abandon the concept of equilibrium.  If disequilibrium is the natural state then prices would be essentially random and economics would have nothing to say.  Empirically most prices are fairly stable or follow fairly predictable paths, except in times of crisis.

Objections to the General Equilibrium (GE) approach seemed to be based on the dominant understanding of GE in neoclassical economics – that is a walrasian intertemporal equilibrium with rational expectations (perfect foresight) where all prices are set in advance and forever which exists is stable and unique, consumers maximise utilities based on endowments and the outcome is pareto optimal.  Alongside these are several (often hidden) assumptions such as perfect competition, no production and constant returns to scale – which are incompatible with the neoclassical theory of the firm. Prices are also only relative prices unless you set the price of the unit of exchange at unity – which means the price of money is exogenous to the model.  Not helpful.

The ‘fixed’ concept of equilibrium is historically limited and unnecessary; both Adam Smith and Ricardo commented on the observation that in most places most prices are relatively stable, apart from disturbances caused by war, bad harvests and currency  debasement.

Although most students are taught this version is ‘Walrasian; in fact  this is a radically simplified version derived from Cassel (1924),  Walras’s model was complex and modular and included production, capital goods, money etc. – not always very satisfactorily.  Cassel also dropped utility functions, though in post war years this in turn was dropped in favour of Walras’s original emphasis on utility.

Almost none of these are plausible or necessary for a theory of general equilibrium. Indeed all that is necessary for a theory of GE is ‘general’ stability/price convergence under bounded conditions. Indeed prior to Walras that was the assumption of the classical competition process.

Following the SMD findings we know that because of wealth effects it is not possible to derive a well formed excess demand function for an economy as a whole, and hence there can be multiple equilibria and prices can formed fixed cycles.  This does not mean however that ‘anything goes’ anything may be possible but that does not mean it is probable.  Again the statistical analysis framework of analysis is helpful as a jump between two phases is analogous to the annealing process – whereby a system suddenly jumps from one state of minimum energy to another.  This is helpful as we have a well established mathematical structure to deal with this – simulated annealing – which does not require modelling of every agent – rather the probability of different states -see Wu and Yany (1989) for a summary . A recent paper by Campbell and Baker (2017) applies adaptive expectations to commodity speculation applies the simulated annealing approach with helpful results. This approach is useful as they can be used to analyse groups where the probability of agency effects within a group is low – hence allowing for the advantages of agency based modelling without the overheads.  Ranges of groupings of agents based on factors such as income, assets and indebtedness can be tested in models empirically against past data and the best fits used for projections.

Walras of course mathematically described what prices could be in an equilibrium,  But his simultaneous equations method does not describe how it formed.  He intuitively described how agents ‘groped’ towards prices but lacked the tools to describe a market process of swarming and arbitrage – a process clear in the classical model.  What we today see as the ‘Walrasian’  auctioneer model is where prices are set forever prior to trading by agents with perfect foresight.  As perfect competition is assumed agents cannot affect prices and so prices cannot change.  Walras was unclear about whether this process was dynamic or static.  After Cassell and of course Arrow and Debrau a static version of equilibrium was used with ‘time’ reduced to indexing goods of different vintages so ice cream at time x could be traded different from ice cream at time x+y.  This underlined the importance of expectations of future prices.  In later editions Walras seemed to conclude that all that matters was that GE could be represented by static equations, and Cassell’s indexing approach assisted this by stripping away production, money and capital goods – if all you had were ‘endowments’ and all expectations were realised then all that was needed was a pure exchange economy, and all agents could be reduced to one representative agent.

With Lucas the assumptions of perfect foresight, equilibrium and perfect foresight became conjoined.   The assumption was that the economy was in equilibrium all of the time which requires as an a priori assumption rational expectations /perfect foresight etc. The problem here is not the indexing approach – it is valid and goes back to Torrens and Malthus – rather it is the combination of the indexing approach with perfect foresight – which in an ironic attempt to meet the ‘lucas critique’ removes agency and time from economics and hence all microfoundations.

What all of this demonstrates is how historically narrow GE theory has become and the need to look for more realistic and broader models. All one has to do to start with is to relax the assumption of perfect foresight, that all expectations of price are correct.  That immediately brings capital goods and production back in as the expected price at the time of investment can be different than at the time of valorisation.

If expectations can be wrong, with agents adapting there expectations based on past events and ever changing them according to emerging information then we are firmly in the realm of temporary and approximate equilibrium, where the ‘state’ of the set of prices that would be formed in GE is momentary and ever changing. We are also within the realm of ‘corridor stability’  of Leijonhufvud (1973) providing expectations stay within a range.

The Analogy here is with brownian motion, stability produced by ever changing and temporary sates. Of course economic agents are not passive particles they form expectations which can be wrong. The creation of false expectations however creates information and the potential for profit. If agents have liquidity to act on false expectations we have, like brownian motion, a series of infinitely many temporary equilibrium following one another maintaining system stability. When agents dont have liquidity because so many plans are wrong at the same time we have a phase shift and a rapid change in prices.  We can also draw on the massive legacy in finance theory of martingale (brownian) processes and valuation.

Roy Radners work on the importance of unrealised expectations and information to GE theory has been recently highlighted in a post by David Glasner 

The two differences that are most relevant in this context are the existence of stock markets in which shares of firms are traded based on expectations of the future net income streams associated with those firms, and the existence of a medium of exchange supplied by private financial intermediaries known as banks. In the [Arrow-Debrau-NcKensie] ADM model in which all transactions are executed in time zero, … and since, through some undefined process, the complete solvency and the integrity of all parties to all transactions is ascertained in time zero, the probability of a default on any loan contracted at time zero is zero. As a result, each agent faces a single intertemporal budget constraint at time zero over all periods from 1 to n. Walras’s Law therefore holds across all time periods for this intertemporal budget constraint, each agent transacting at the same prices in each period as every other agent does.

Once an equilibrium price vector is established in time zero, each agent knows that his optimal plan based on that price vector (which is the common knowledge of all agents) will be executed over time exactly as determined in time zero. There is no reason for any exchange of ownership shares in firms, the future income streams from each firm being known in advance.

[If] agents have no reason to assume that their current plans, …will remain optimal and consistent with the plans of all other agents. New information can arrive or be produced that will necessitate a revision in plans. {If} plans are subject to revision, agents must take into account the solvency and credit worthiness of counterparties … The potentially imperfect credit-worthiness of…enables certain financial intermediaries (aka banks) to provide a service by offering to exchange their debt, which is widely considered to be more credit-worthy than the debt of ordinary agents, …. Many agents seeking to borrow therefore prefer exchanging their debt for bank debt, bank debt being acceptable by other agents at face value. In addition, because the acquisition of new information is possible, there is a reason for agents to engage in speculative trades of commodities or assets

i see this as the interaction of two parallel systems.  The first is the calculation of the optimum production system given a schedule of demand.  This is like a Sraffa/Sinha linear production system – showing an infinitely thin slice of time – and can be modeled as a chaining together of such systems using the principle of least action necessary to reproduce this physical system.

The second being the set of information produced by this system and the difference between this information set and the information set held by agents – which again can be modeled by the principle of least action in its form of maximum information (least entropy).

It is the interaction between these two dynamic equilibrium systems that drives change in the economy.

An economics without assumptions of perfect competition, perfect foresight and pareto optimality of markets would be a very different one from that taught today, and largely lacking in unthinking a priori normative support for untrammelled markets.  It will all depend on the model and the evidence  But this is unnecessary and unhelpful baggage, it is not needed and indeed is counterproductive to a modern general equilibrium theory.

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2 thoughts on “General Equilibrium – Why Post-Keynsians Can’t Live Without it

  1. Equilibrium is an economic obsession and Disequilibrim might become the same. As Wisdom is a dynamic integration of opposites I think that equilibrium as a goal of economic theory is valid and correct, but it undoubtedly requires the integration of policies characterized by what I refer to as “the higher disequilibrium”…..in order to accomplish such.
    wisdomicsblog.com

  2. Pingback: The Economy is Like A Marble on a Ladle – A Friendly Reply to @ProfSteveKeen | Decisions, Decisions, Decisions

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