Posts Tagged Equilibrium
This is the second part of my response to criticisms of Keen’s Debunking Economics. In my previous post* I covered some of the fundamental objections Keen had to neoclassical theory. Here, I will cover Keen’s exploration of alternatives: first, a brief note on dynamics and chaos theory; then a discussion of Keen’s own models; finally, his dismissal of the Marxist Labour Theory of Value (LTV).
Dynamics and Equilibrium
Many economists have argued that Keen’s contention that economists do not study dynamics is false. I agree. Keen does not really address the DSGE conception of equilibrium, which is highly different to the typical conception of a steady state. An equilibrium in an economic model occurs when all agents have specific preferences, endowments etc. and take the course of action which suits them best based on this. This can be subject to incomplete information, risk aversion or various other ‘frictions.’ These agents intermittently interact in market exchanges, during which all markets clear. Basically, ‘solving for equilibrium’ means you specify the actions and characteristics of economic agents, then see what happens when markets clear. It’s entirely possible that the subsequent model could exhibit chaotic behaviour.**
Now, there are obviously many problems here. The fact is that the overwhelming majority of people who learn economics will not touch this. They will instead be faced with static-style equilibrium models, which they have been told are unrealistic but ‘elucidate certain principals.’ This is nonsense – they elucidate nothing, and simply need to be thrown out. Nevertheless, many policymakers, regulators and business economists are working under this framework. Furthermore, even those economists who have gone beyond this level seem to have the concepts deeply ingrained into their minds, and regard them as useful.
However, even the more advanced ‘dynamic’ equilibrium clearly has problems. First, the presence of irreducible uncertainty – which, as far as I can see, is a concept entirely misused by economists – means that it is virtually certain not all expectations will be fulfilled, while equilibrium assumes they will be. Second, ‘fulfilled expectations’ is far stronger than economists seem to think – for example, it eliminates the possibility of default! Third, the assumption that all markets clear is obviously false, otherwise supermarkets wouldn’t throw out old food. Anyway, I digress: Keen could easily address all of these criticisms, but for some reason he doesn’t. This is indeed a shortcoming of his book.
First, a brief note on Keen’s model of firm behaviour: it seems to make the error of maximising the growth rate of profits, rather than profits themselves. I am not sure if this has been fixed. Nevertheless, I regard it as subsidiary to Keen’s main criticisms. His most important model is the Minsky Model of banking and the macroeconomy.
Keen recently had a debate over his Minsky Model with the Cambridge economist Pontus Rendahl. Andrew Lainton has a post on this, along with a contentious discussion with Rendahl, over on his blog. In my opinion, Rendahl – though overly dismissive in tone, and not causing as many problems for Keen as he seemed to think – highlighted a number of issues with Keen’s model in its current form:
(1) Say’s Law holds. In Keen’s model, income is simply a function of the capital stock, and there is no role for demand.
(2) In what was generally a model set in continuous time, which used ODEs, there is an equation which uses discrete time intervals. Such equations cannot be solved in the same way, so Keen’s methodology is inconsistent.
(3) There is, as of yet, no role for expectations in Keen’s model.
(4) Rendahl argues that DSGE models are also Stock Flow Consistent (SFC). I think he is correct – see, for example, his own paper, which has agents accumulating stocks of money from previous periods. The major differences between SFC and DSGE appear to be: a lack of micro foundations; continuous functions; use of classes; market clearing; fulfilled expectations; and, of course, with Keen’s, the role of banks and private debt.
In terms of assumptions, I’d say Keen’s model is in the ‘heuristic’ stage – it’s not completely right and needs development. The criticisms are essentially things that have not yet been added to the model, rather than conceptual or logical problems (save the inconsistent equation). This means they can be added as it develops. However, if the model makes good predictions, it may prove to be useful, even though that should never serve as a barrier to making it more realistic and comprehensive.
Labour Theory of Value
If neoclassical economists want a lesson in how to respond to a critique you strongly disagree with without being vitriolic and dismissive, then they need look no further than the marxist responses to Keen’s critique of the LTV. This is all the more ironic given said economist’s willingness to dismiss marxists as illogical and dogmatic.
Keen’s critique is threefold, so I will discuss it briefly, followed by the marxist responses.
The first critique is Bose’s commodity residue. The idea is that no matter how far you go back in time, disaggregating a commodity into what was required to produce it, there will always be a commodity residue left over. Hence, no commodity can be reduced to merely labour-power. The problem here is the projection of capitalism into all of history. For Marx, a commodity only resulted from capitalist production. However, if you go back in time you will find non-capitalist production, and eventually you will be able to reduce everything into land/natural resources and labour, which Marx never defined as commodities. Having said this, one question remains: can the natural resources or land not be a source of surplus value? Could this surplus value not have been transferred into capitalist commodities?
Second is Ian Steedman’s Sraffian interpretation of Marx. Simply put, it seems Steedman had his interpretation wrong – Marx’s is not a physical, equilibrium system based on determining factor prices. This is something that actually struck me on the first read of Keen’s LTV chapter: Steedman simply converts Marx into Sraffian form without much justification. If Marx did not intend this to be the case, the criticism is defunct from the outset.Hence, it follows that Steedman’s model is simply a misinterpretation of Marx, and it is not even necessary to go into the maths. There is, of course, a possibility that this is an overly superficial interpretation and I am mistaken.
The third criticism is that Marx’s treatment of use-value and exchange-value is inconsistent: properly applied, it implies that a commodity’s use-value can exceed its exchange value, and hence be a source of surplus value. Now, I remain unsure of this area so I might be wrong in my exposition, but here is my attempt to explain the Marxist response: (warning: the following paragraph will contain a vast overuse of the word ‘value’ in what is already a necessarily convoluted explanation).
Marxists contend that Keen’s is a misinterpretation of use-value, which is simply a binary concept and not quantifiable. Something may have any number of uses which give it a use-value, which is a necessary condition for it to have an exchange-value. However, the exchange-value cannot ‘exceed’ the use-value, because the use-value cannot be measured. It is in this sense that labour is unique in Marx’s conception of capitalism: its specific use-value is the production of surplus for capitalists. It is the only ‘factor of production’ that can do this – after all, capital ultimately reduces to past labour value. If production could take place without labour, prices would fall to zero and, while Marx would be refuted, nobody would care because the problem of economic scarcity would vanish. Hence, surplus production and profits depend on labour producing more than it is rewarded.
I remain neither convinced of the LTV, nor of its critics.*** For me, most discussion of the LTV appears to rest on the LTV as a premise. The debate is split into people who accept the LTV and people who not only reject it, but see no need for it. For this reason, critics seem to misrepresent and misinterpret it continually – a common theme is to try and abstract from historical circumstance, when it’s clear Marx emphasised that his analysis only applied under capitalism, which he saw as a particular social relation. For me, the main issue remains the same as it is for other theories: what is the falsification criteria for the LTV?
Overall, a couple of points stand out for post-Keynesians for their own theories, both of value and economic systems. The first is that DSGE models are probably not that different to some heterodox models, and identifying the actual differences is crucial to opening up a dialogue between mainstream and heterodox economists.
The second is that I would caution left-leaning economists not to be too hasty to dismiss Marxism as dogmatic (in my experience marxists are anything but), or avoid it simply out of fear of being dismissed themselves. In my opinion, the LTV – while not entirely convincing – is a cut above the neoclassical ‘utility’ conception of value, and I’d sooner be equipped with Marxist explanations of a crisis when trying to understand capitalism. This isn’t to say post-Keynesians haven’t thought about Marx; moreso that the issue is often approached with a degree of bias. At the very least, the distinction between use-value and exchange-value is something that befits post-Keynesian analysis well.
So, as far as theory goes, this is the last post on Keen’s book. I will, however, do some closing notes from a more general perspective. As I said before, if there are any other criticisms of Keen that I have not covered, feel free to discuss them in the comments.
*It is worth noting that in my previous post I was somewhat – thought not totally – off the mark with my discussion of Keen on demand curves. The Gorman conditions for the existence of a representative agent do indeed have many similarities to the SMD theorem and conceptually they are dealing with the same issue: aggregation of preferences. Nevertheless, Keen weaves between the two, when it would have been more accurate to note economists have used two (main) different methods to get around the problem, and critiqued them separately. Similarly, though Keen’s quote from MWG was incorrect, it is true that economists such as Samuelson have used the assumption of a dictator to aggregate preferences. However, the specific one Keen presented was not right.
**However, that does not make it the same as chaos theory.
***For me, claims that worker ownership of production would be desirable don’t really rest on the LTV; instead, the simple point is that workers could employ capital themselves.
Chapter 9 of Steve Keen’s Debunking Economics criticises economist’s reliance on static models in a clearly dynamic system. He first shows both Walrasian equilibrium and Gerard Debreu’s related models to be highly questionable – this is, of course, not difficult, and will be met with ‘we have improved on those!’ However, the real message of the chapter is that static analysis is fairly worthless, and dynamic analysis does not simply ‘fill in the gaps’ between different equilibria.
If you are not familiar with Walras or Debreu, prepare to be amazed at how clearly unlike the real economy these models are.
Walrasian equilibrium supposes that an auctioneer has control over the buying and selling of every commodity, and determines the ‘market clearing’ price – where supply equals demand for every commodity – before any trade takes place. Walras suggested that the auctioneer start with a random guess, which would probably be wrong. They’d then go on to adjust prices until equilibrium was reached, at which point trade would take place.
Keen refrains from commenting substantially on the realism of this approach, instead taking his usual route of accepting economist’s logic, then showing that the model still can’t work. The maths is somewhat over my head, but Keen channels John Blatt, who uses a theorem of matrices – a mathematical system by which a Walrasian auction can be explained – to show that the auctioneers prices will not converge towards equilibrium.
Simply put, there are two conditions required to Walras’ auction to ‘work:’
- The system must be able to reproduce itself e.g. produce enough iron for the required inputs of iron in the next period.
- The prices must be ‘feasible;’ basically, they cannot be negative.
According to Blatt, these two conditions require the matrix and its inverse to have the same properties. In English, this means that something and its opposite have to have the same properties, which is obviously logically impossible. Hence, the auction will not converge to equilibrium.
Debreu did not worry about whether an economy would converge to equilibrium, but simply whether or not an equilibrium existed. However, the same conditions outlined above – not to mention the incredibly restrictive assumptions of Debreu’s model, such as virtually identical, prophetic actors – showed that even if equilibrium were achieved, it would be unstable.
Keen concludes that the elusive search for equilibrium is a dead end, and moves on to chaos theory, in which equilibria are unstable and rarely or never, reached, but clear patterns emerge:
The two ‘eyes’ here are the equilibria, and as you can see they are quite clearly not worth studying – what is instead needed are differential equations that describe the dynamic evolution of the system. Economists do have a more advanced definition of equilibrium, which states the time path for the economy, but it involves restrictive assumptions similar to Debreu’s, and is not on the same level of dynamism as chaos theory. Anyone untainted by neoclassicism will be able to see that the above pattern is similar in type to the cyclical behaviour of a capitalist economy, and that applying chaos theory to economics is surely an idea with potential.
Keen ends the chapter by giving a couple of examples of attempted dynamic (though not chaotic) analysis – the Goodwin model, based on Marx’s analysis of the relationship between wages, investment and capital, and A .W. Phillip’s ill-fated attempts to bring dynamic modelling into economics. Contrary to popular belief, Phillips was well aware of expectations and how they changed, and incorporated this into his model. Both of these models produced realistic business cycles, as do Keen’s similar model (which we will come to in a later post).
But economists reject this type of analysis because…engineers don’t know what they are doing? The empirically successful microfoundations project? Assumptions don’t matter but do when they aren’t ours? I honestly just don’t understand.
Simon Wren-Lewis discusses the large gap between mainstream and heterodox economics, and asks why the heterodox economists are so willing to throw out almost every aspect of neoclassical theory. Allow me to offer an explanation.
The reason heterodox economists remain dissatisfied with mainstream economics, no matter how many modifications the latter adds to its core framework, is that there is always an implication that, in the absence of various real world ‘frictions’, the economy would function like a smoothly oiled machine. That is: assuming perfect information, mobility, ‘small’ firms, no unions, flexible prices/wages and so forth, the economy would achieve full employment, with near perfect utilisation of resources, and stay there, perhaps buffeted by mild external shocks.
New Keynesians and New Classicals sometimes act like bitter rivals, but mainly they only differ on which ‘frictions’ should be present or not (this is an oversimplification of the disagreement, of course). The original New Classical models started with economies that are always in equilibrium, preferences are constant, and competition is perfect. New Keynesian models add imperfect competition, sticky prices, transaction costs and so forth. The newest papers go further and add heterogeneous agents (which generally means two), changing preferences, and other ‘frictions.’ However, it is assumed that if the economy were rid some specific features/characteristics, it would function similarly to one of the core Walrasian or Arrow-Debreu style formulations.
So is it not true that real world mechanics prevent things from going as smoothly as they might do in absence of those mechanics? Well, partially. But according to heterodox economists, capitalism has inherent tendencies to crisis, unemployment and misallocation anyway.
A key example of where this is evident is finance. Generally the mainstream analyses of why finance is unstable focus on irrationality, imperfect information, externalities and other such modifications. If only everyone had access to information, if transactions were cost less, and if people were rational self maximisers, then finance would be stable.
Minskyites, on the other hand, argue that this isn’t the real problem. Even if the economy starts stable, the resultant strong returns on investments will cause capitalists/investors to take more risk. This process will continue and the economy will endogenously destabilise itself as higher returns are sought and more risk is taken on, until eventually the capacity to make a return on these risks is outrun and we face a collapse. There is no need to invoke a specific ‘friction’ for this process to occur.*
Another prominent example is the labour market. Generally, economists presume that without ‘search costs’, oversized firms/unions and sticky wages, the economy would achieve full employment. But heterodox economists disagree on a number of counts: the Marginal Value Product Theory is faulty, so higher wages will not necessarily cause unemployment to rise; wages are also an essential component of aggregate demand, so reducing them may well be counterproductive. In fact, Keynes argued that sticky wages were far from a barrier to full employment; they actually stabilised aggregate demand. Steve Keen’s model also produces less severe business cycles when sticky wages and prices are added.
So the reason heterodox economists want to throw the proverbial baby out with the bath water (and also redecorate the bathroom and possibly even move house, or something), is that they think the core of mainstream economics has dug itself too deep into a ditch. The inevitable ad hoc modifications of ‘perfect’ models sometimes have so many ‘frictions’ introduced that the supposed ‘deep’ mechanics that underlie them become questionable. But they are still never abandoned. Heterodox economics is not just about adding a few real world mechanics here and there; it’s about throwing out the entire core and starting over.
*It could be said that this might not occur if Knightian uncertainty were not a factor in the real world, but I think calling this a ‘friction’ jumps the gap between friction and fundamental reality.
I like to question almost every aspect of economic orthodoxy. However, I am also interested in forming a coherent view of what is actually wrong with economics, rather than a caricature. So it pains me to see misguided criticisms such as Suzanne Moore’s piece a few weeks back, whose characterisations of economic theory will only serve to misguide the uninformed and elicit dismissive reactions from economists themselves. So here I present a list of things not to highlight when attacking neoclassical economics, in the hope of assisting would-be critics of the discipline.
Criticising early assumptions
Don’t get me wrong, criticising economist’s perversion of the use of assumptions is fair game. However, critics often go down the path of criticising ‘pure rationality’ or ‘perfect information.’ Whilst these are elements of core models (and these models should be attacked because of this, but with the caveat that the core models are the target), they are generally not found in the higher echelons of economics. Many of these assume imperfect information, bounded rationality, and can also incorporate other biases.
Most specifically, idea that economic theory assumes everybody is a selfish, emotionless self-maximiser is common trope, but as Chris Dillow noted in the link above, it’s not entirely true. More importantly, it is also defensible as an assumption – a heuristic by which to approximate behaviour, at least until something better comes along. It is important to distinguish between good and bad assumptions from a scientific standpoint, rather than how absurd they appear to be at first glance.
Many critics of economics, including well-informed ones, make the mistake of arguing that economics always assumes the economy is in equilibrium, tending to equilibrium, oscillating closely around equilibrium, or something along these lines. It is true that many economic models do this; it is also true that economic models start from the assumption that the economy is in equilibrium, and see what happens from there. However, economists generally mean something very different to other scientists when they say equilibrium. From the horse’s mouth:
An equilibrium in an economic model is characterized by two basic conditions which hold in all of the model’s time periods: i) all agents in the model solve the maximization problems implied by their preferences, resource constraints, information sets, etc; and ii) markets for all goods in the model “clear.” An equilibrium is not a snapshot of the model economy at one point in time. Instead, it is the model’s entire time path.
Even on first inspection, this type of equilibrium clearly has problems of its own, but I will save them for another post. The important thing to remember is that this, rather than a stable state, is what economists often mean when they talk about equilibrium.
Economist’s Political Beliefs
Economists are not all free marketeers – in fact, they generally lean to the left. Neoclassical economics, broadly speaking, concludes that we should: regulate oligopolies, monopolies and banking; do more to protect the environment and intervene in the case of other externalities; have some public provision of health, education and welfare; and as that survey shows, economists are generally approving of things such as safety regulations.
As I have said before, I think economic theory as taught lends itself to being used by free marketeers, because of the way the ‘market’ is presented as natural and the government ‘intervenes.’ I also object to the fact that economics applies the same analysis to every market from apples to education to labour. And it is true that the market is presented as generally equilibrating and efficient, except in a few choice cases. However, the impact of these things is not that all economists support ‘right wing’ policy prescriptions, but that neoclassical theory can generally be coopted to provide justification for them.
Naturally, I sympathise with many who try to criticise economics, as they correctly notice that the field’s empirical record (at least in macro) is not great; that many of the policy prescriptions seem to favour the rich whilst hurting the poor; that some of the models taught in economics are unintuitive and perverse. Economists are also partly to blame for not communicating their discipline well to the public, seemingly preferring to dismiss critics as ignorant and revel in their mastery of (what I consider a wholly useless) field.
Having said this, it’s important that in order to engage economists properly, the right questions are asked – ones that economists find difficult to answer. Economists have stock responses to many of the ‘pop’ criticisms of their discipline, so using them will only serve to reinforce economist’s belief in their own knowledge and create further barriers to engagement.
Of course, failing all of this, you can just repeat ‘why didn’t you see the crisis coming?’ over and over.