Tuesday, July 25, 2006

Response To Comments On Steve Keen's Work

Introduction

In comments on a previous post, Radek comments on some work of Steve Keen's. Since I've let something like a week go by, I thought I ought to raise this response to a post.

I respond more to people I disagree with. But I think I ought to note that, like DSquared, I respect Solow, while disagreeing with him. My favorite polemic from the Cambridge Capital Controversy is this:
“I have long since abandoned the illusion that participants in this debate actually communicate with each other. So I omit the standard polemical introduction, and get down to business at once.” –- Robert M. Solow (1962)

But back to Keen. What I appreciate most in Keen’s book is his attempt to convey to the introductory student and common reader that good reason exists to doubt (mainstream) economics, no matter how much (mainstream) economists attempt to blind one with “science”. Keen claims very little originality for most of what he has to say. As one can see, I have some disagreements with Keen’s attempts at popularization. But the discussion in this post only concerns two out of fourteen chapters in Keen’s book. And Radek does not even concede any virtues in those chapters.

Also, I can do without accusations that Keen is a “hack”, whether “a pretty skillful hack” or not; a “charlatan”; a liar; “dishonest and embarrassing”; “engages in” “dishonest rhetorical trick[s]”. For me, Guiness stout and Monty Python fall in the same category: things I’m still unsure what I think of. But I’m fairly sure abuse is not an argument.

Profit Not Maximized When Price Equal Marginal Revenue

Chapter 4, “Size Does Matter”, seems to be the most argued about chapter of Debunking Economics. It surprised me too.

Atomistic competition, in which one has a continuum of infinitesimal agents, is a standard assumption in economics. Keen and Standish (2006) point out that the assumption of atomistic competition is that one firm does not change its level of production in reaction to another firm's variation in production levels. Keen (2001) points out that Stigler shows that, under atomistic competition, the demand curve for a consumption good faced by the firm has the same slope as the demand curve for the market. I find Keen is not original in noting that atomistic competition is incompatible with the usual textbook U-shaped average cost curves:
"Of course, global increasing returns to scale (or more modestly, situations in which efficient scale is reached at a level of output which is noninfinitesimal relative to the total size of the market) remains a problem. Also, we do not deny the descriptive reality of the latter situation." -- Duffie and Sonnenschein (1989)

Radek ignores all this motivation for Keen’s simulations, and I find it difficult to argue with Keen’s claims. And they wreck havoc on mainstream introductory textbooks in microeconomics.

I have done work with simulations in quite different contexts. In my experience with certain researchers, they wanted to see their analytical arguments confirmed by both simulations, in which they could control the environment to which their arguments are applied, and practical applications. I think Radek should welcome my simulation. If he looks, he will see that I allow the user to vary the order in which firms make decisions. So I agree with Radek in that I think Keen can be challenged here. I also seem to recall an impression that step size matters to convergence in my simulation. I still think I would need to do further work to substantiate these worries.

The Sonnenschein-Mantel-Debreu Results

Keen brings up the SMD results in Chapter 2 of Debunking Economics. Duffie and Sonnenschein (1999) characterize these results as stating that "the class of excess demand functions generated by economies has no structure beyond Walras' law and homogeneity" (p. 574). They point out the implication that "the equilibrium price set may be an essentially arbitrary subset of the set of relative prices" (p. 574).

Radek states, "SMD is not about aggregating individual utilities in the sense that Keen's talking about." I find Keen to only be echoing the professional literature on this point. Think, for example, of Kirman’s (1992) analysis of representative agent models, which are widespread in New Classical Economics. Keen’s point is that Margaret Thatcher was wrong in asserting that “There is no such thing as society”. Would Radek accept Kirman’s claims, which I think are along the same lines:
"The problem seems to be embodied in what is an essential feature of a centuries-long tradition in economics, that of treating individuals as acting independently of each other...

If we look back briefly to the result that underlies the whole problem expressed here it is clear that in the standard framework we have too much freedom in constructing individuals. The basic artifact employed is to find individuals each of whose demand behavior is completely independent of the others... making individual behavior dependent or similar may open the way to obtaining meaningful restrictions...

If we are to progress further we may well be forced to theorise in terms of groups who have collectively coherent behaviour. Thus demand and expenditure functions if they are to be set against reality must be defined at some reasonably high level of aggregation. The idea that we should start at the level of the isolated individual is one which we may well have to abandon. There is no more misleading description in modern economics than the so-called microfoundations of macroeconomics which in fact describe the behaviour of the consumption or production sector by the behaviour of one individual or firm. If we aggregate over several individuals, such a model is unjustified...

It is clear that making assumptions on the distribution of agents' characteristics amounts, in some sense, to making assumptions about the organization of society...

In conclusion, then, it is worth repeating that recent theoretical work has shown how little the Walrasian model has to say about aggregate behavior. Economists therefore should not continue to make strong assertions about this behaviour based on so-called general equilibrium models which are, in reality, no more than special examples with no basis in economic theory as it stands."-- Alan Kirman (1989)

Radek comments:
So how 'huge' are SMD results - the fact that one may have multiple equilibria. Well, here I think there's often a good bit of intellectual dishonesty among critics of GE. On one hand they criticise GE for being 'unrealistic' on the other they wave SMD theorem as proof that GE is 'untenable' (again, whatever that means). But seriously, why should you expect the Real World to have a unique equilibrium? Particularly in the presence of wealth effect, which are the driving force behind SMD theorem, and the whole point of doing GE in the first place? Personally I think the possibility of multiple equilibria is a REALISTIC feature of general equilibrium theory and a point in favor of it rather than against it.

One would be in trouble if the theorem predicted a continuum of equilibria, or that the First Theorem no longer applied but that's not the case. One can still do local comperative statics and all them multiple equilibria are still Pareto efficient.

I find the above confused. Tony Lawson is the scholar to read when it comes to “realism” and Post Keynesianism. I don’t say every Post Keynesian agrees with him. But one who wants to engage Post Keynesian discussions of realism of assumptions must read at least some of Lawson. I don’t know what it means to say “the Real World” has multiple or unique equilibria. I think equilibria are properties of models, not characteristics of actually existing capitalist economies, independently of how they are described.

I don't care for Radek’s sort of abusive attack on people who say they are echoing the experts in a field, especially when the attackers do not cite any examples of who they are talking about. I think a good appreciation of the SMD results might require a historical perspective on what (some) economists were (and still are?) claiming about General Equilibrium and what the experts in the field now claim:
"It follows from the preceding observation that the Walrasian theory and the existence theorems do not tell us how to relate tastes, technology, and the distribution of wealth to a single set of relative values. Rather, they tell us that there is at least one vector (and possibly many more) of relative values compatible with the data of the model. In the absence of uniqueness, the comparative statics of how prices and allocations will change with a change in the parameter values is not a well-defined exercise. The finiteness result alluded to above may be of some help here, but what is really needed is a completion of the Walrasian theory that describes the particular choices that are made from the equilibrium set. Such a completion will almost surely require a theory that deals explicitly with the adjustment to equilibrium. If forces are not in balance, what changes will take place in order to bring them into balance?" -- Duffie and Sonnenschein (1989)

I suggested to Keen, prior to the publication of his book, that the assumptions that all agents have identical and homothetic utility functions are merely sufficient, not necessary, conditions to get well-behaved utility functions. On this logical point, I agree with Radek. But Keen has convinced me with his book and later work that, in practice, (mainstream) economists do widely adopt these assumptions in applied work, with little justification.

References
  • Duffie, Darrell and Hugo Sonnenschein (1989). "Arrow and General Equilibrium Theory", Journal of Economic Literature, V. 27, N. 2 (June): 565-598.
  • Keen, Steve (2001). Debunking Economics: The Naked Emperor of the Social Sciences, Zed Books.
  • Keen, Steve and Russell Standish (2006). "Profit Maximization, Industry Structure, and Competition: A Critique of Neoclassical Theory", Physica A
  • Kirman, Alan (1989). "The Intrinsic Limits of Modern Economic Theory: The Emperor has No Clothes", Economic Journal, V. 99, N. 395: 126-139.
  • Kirman, Alan P. (1992). "Whom or What Does the Representative Individual Represent?" Journal of Economic Perspectives, V. 6, N. 2 (Spring): 117-136.
  • Solow, Robert M. (1962). “Substitution and Fixed Proportions in the Theory of Capital”, Review of Economic Studies, V. 29, N. 3 (Jun): 207-218.

1 comment:

radek said...

I apologize for not responding earlier - I had to finish my work and am currently engaged in moving across the countries. But anyways:

“But the discussion in this post only concerns two out of fourteen chapters in Keen’s book. And Radek does not even concede any virtues in those chapters.

Also, I can do without accusations that Keen is a “hack”, whether “a pretty skillful hack” or not; a “charlatan”; a liar; “dishonest and embarrassing”; “engages in” “dishonest rhetorical trick[s”

Calling Keen a “hack” etc., while not nice, is no different and in similar spirit as your “making fun of the Austrians”, “disrespecting Hazlitt” or the “so much for Solow’s “Nobel” (sic)”. It’s not like I called him a hack without substantiating it. To reiterate, I showed two instances (really, you don’t expect me to go nitpicking through the whole book? Two out of fourteen oughta be representative enough in this context) where Keen claims to have done something that he really hasn’t. He either misrepresents the work he is critisizing or he misrepresents what it is he himself is doing. Since I believe that he’s technically and intellectually competent enough, I have to conclude that he’s trying to pull a fast one (and yes, the whole book has that unpleasant feel of someone trying to sell you a replica Rolex). More specifically:

With regard to the DMS theorem I explained that:
1. Keen’s confusing (perhaps not on purpose) the DMS theorem with what looks like a version of the Gorman Polar Form theorem.
2. He misrepresents the assumptions that underly the GPF theorem making them much more stronger then need be. (He also seems to be confusing indifference curves with indirect utility functions but whatever).
3. Even under the extra strong assumptions for the wrong theorem he claims to prove something (by contradiction) that actually doesn’t follow. I mean, ok, let’s get crazy. Let’s pretend the GPF theorem really is the DMS theorem, let’s pretend that in order to “aggregate preferences” (not exactly the same thing as a represantative consumer existing, but at this point, hey, it’s too much to get into) all individuals have to have identical and homothetic preferences (which they don’t) – it still doesn’t follow that there is only one good and only one individual! You and I can have same preferences – that doesn’t make Robert Radek and Radek Robet. Simplest counter example is anything with externalities. Even without externalities the fact that we have different wealth levels could make things interesting. So identical preferences := 1 person. Also linear Engel curve, while admitadelly empirically unrealistic, do not mean there’s only one good. If spend 20% of my income on food and 80% on everything else regardless of my income level that doesn’t mean there’s only food and food. No, there’s still food and everything else. This should be blindlingly obvious.
Conclusion: Keen either doesn’t know what the hell he’s talking about or he’s lying.
Note that this holds regardless of what one thinks the implications of DMS theorem are on viability of GE models – that’s a different discussion.

“Think, for example, of Kirman’s (1992) analysis of representative agent models, which are widespread in New Classical Economics. Keen’s point is that Margaret Thatcher was wrong in asserting that “There is no such thing as society”. Would Radek accept Kirman’s claims, which I think are along the same lines: (quote)”

Man, I’m really starting to think that Kirman’s paper (BTW, first thing we read in our grad Macro class – so it’s not like this is outside the mainstream) is the most over cited and misunderstood paper by folks who want to kick around “mainstream” economics. It is a good and important paper. But again it’s mostly concerned with the Gorman Form theorem, not DMS or “representative agent” in the Ramsey sense (essentially the one in all the RBC models – not the same as the Gorman RA). I have some issues with Kirman but take his points. To say that “aggregation is hard”, which is what Kirman does, is fine – insightful even. But Keen goes much farther beyond that.
And BTW I would interpret the Gorman/Kirman point in a way precisely opposite to yours – the fact that a Representative Agent doesn’t exist in general means exactly that there is no such thing as society. After all, the whole point of constructing an RA is to talk about “society” rather than an washed multitude of individual agents.

With regard to the Cournot simulations:
1. I showed that Keen makes the thing work by sneaking in a particular assumption whereas he claimed explicitly that this was not an assumption he was making.
2. The assumption completely changes the context making Keen’s comments irrelevant
3. Keen seems to be confused with the meaning of “convergence”. Cournot theorem says that as number of firms goes to infinity quantity converges to competitive level and p converges to mc. Keen takes “converge” to mean that as TIME goes to infnity, given N, p and q converge to some level. Cournot: t fixed, N ->inf, p ->mc. Keen, N fixed, t ->inf, p->? Again, different model and one should be upfront about it.

Furthermore, after reading the Keen and Standish paper I’d like to add that

4. The “rich variety” of results they obtain have nothing to do with the “Keen equation (you know, it’s really obnoxious and pompous to name formulas after yourself ”, even if you did write them down - usually others do it for you) or the structure of competition. Nah, it all comes from the ridiculously complicated COST function they assume. I mean third-order polynomial cost function? They say that they do it in order to get increasing MC, but you only need a quadratic for that. But hey, with the quadratic you get ‘regular results’ not ‘rich results’. N (number of firms) as part of the total cost function? In quadratic form? Now you’re talking some serious spillovers between firms. No wonder it’s sensitive to the step parameter. This is looking NOTHING like a Cournot model, nevermind the fact that it’s not even a one shot game. Again, this type of exercise in and of itself can be interesting and illuminating, but they really need to leave the “Cournot was wrong” and all other ideological BS out of it.

As far as your simulation – you seem to have constant MC so step size shouldn’t matter except for the speed of convergence – this is the simulation I wrote above, you can solve it mathematically without the need for a computer. And the link to the paper don’t work.

Finally with respect to the “Stigler’s formula”, and the rest of the Keen and Standish paper which I didn’t get to before.

1. In Stigler’s paper the forumla is just a footnote – he’s writing down what he thinks everyone already knows, so it’s silly (misinformative) to name the formula after Stigler since it’s obviously common knowledge in the profession by 1952.
2. It applies to COURNOT competition, not perfect competition.
3. I wish the word “atomistic” wasn’t brought into it. It’s at best unneccesary, definetly confusing and probably falls in the “I don’t think that means what you think it means” category. The references with regard to “atomism” in K and S are to Mas-Collel. But to just parts in Mas-Collel which deal with perfect competition. The word “atomistic” doesn’t appear anywhere on those pages. And perfect competition ASSUMES price taking behavior. Price taking behavior automatically IMPLIES that a firm believes itself to be facing a flat demand schedule, even if market demand is downward sloping.
This is principles stuff. But maybe a technical explanation will make more sense. Suppose you have a continuum of firms of length “whatever”. Each firm is a point on this continuum, produces some amount of output and total market output is given by the integral over the continuum. Market price is a downward sloping function of this integral. Now, if you change any one’s firm’s output the integral doesn’t change so market quantity doesn’t change, so price doesn’t change. Consequently each firm regards price as given, acts as if it can sell all it wants at the going market price and doesn’t see itself as affecting total supply. But if each firm acts this way of course, then the total integral will change and hence market price will change. So flat demand faced by firms, downward sloping market demand. So there you go, I have no idea what Keen’s talking about - he's taking the wrong derivative I think. Wait, yes, I do, he’s talking about Cournot, go back above.

Oh yeah, your quote about increasing returns to scale is true – in general perfect competition is not compatible with increasing returns and it’s a pretty well known fact that in those cases no competitive equilibrium exists and you’re gonna get either a monopoly or a duopoly (again, Cournot). But this is a different issue. Oh and, increasing returns is downward sloping average cost curves. Perfect competition is perfectly fine with U-shaped ones.

Alright, that's it for now. Debate what DMS really means and all the other stuff some other time.