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April 26, 2005

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john

Five books for a Desert Island

1. Nietzsche's Beyond Good and Evil - My favorite work from Nietzsche; amazingly intellectually challenging and fascinating; so many wonderful aphorims one after another

2. Chuang-Tzu - To me, the definitive non-western statement of life and a very nice balance to Nietzsche

3. Porter's Competitive Advantage - Machiavelli for the contemporary age; I would enjoy examining different strategies

4. Now, Discover Your Strengths - It's like playing the Glass Bead Game with humans as you subject matter. I would be fasinated with building different combinations of strengths and determining what their best fit would be

5. Proust Remembrance of Things Past - With this work, I would be able to experience all the emotions of being amongst people

dsquared

"rigorous and abstract" treatments are in general as good as the axioms on which they are based, which in the case of Microeconomics is "absolutely dreadful". If you are prepared to believe that the Sonnennshein-Mantel-Debreu conditions apply, then a theorem-proof approach to economics will tell you a lot. On the other hand, if you believe that, you're mental. (The specific problem involved is that it's very difficult to get any of the basic microeconomic results off the ground in rigorous form without making assumptions which are equivalent to assuming that all consumers and all commodities are identical).

Ironically, the best rigorous economics textbooks are (I'm told) only available in Russian. Kantorovich and his gang as the Soviet Academy produced a series of texts which derived almost all of the important results of economic theory by considering properties of linear programming systems. This is a rigorous approach because it's neutral as regards psychological assumptions; it doesn't make the most ludicrous and handwaving appeals to intuition and then pretend that they're rigorous by calling them axioms.

[caveat; I haven't read Mas-Colell's textbook, but I know from having gone through the "Steve Keen Theory of the Firm Wars" on mailing lists that he does make at least one strange assumption to prove a fairly key result, which led to the joke: "How does Mas-Colell buy an ice-cream? First he buys the complete output of a continuum of infinitesimal ice-cream producers then integrates". Mas-Colell is a giant of his field and a very good economist, but I would be scared of someone whose only exposure to economics was via the extremely strong assumptions of Mas-Colell's version of Walrasian General Equilibrium]

There are good theorem-proof style textbooks in economics; Tirole's "Industrial Organization" is very good precisely because it's very specific about the empirical consequences of its assumptions and "Continuous Time Finance" is good because it's basically an engineering textbook. But a general microeconomics textbook which tries to stick to what can be proved rigorously is always going to end up taking the economics out of economics.

Abiola Lapite

"If you are prepared to believe that the Sonnennshein-Mantel-Debreu conditions apply, then a theorem-proof approach to economics will tell you a lot. On the other hand, if you believe that, you're mental."

Way to go with the charm there, hombre. FYI, I'm fully aware that the assumptions are too strong to apply in reality - one would think I'd take at least that much from reading Hayek and Stiglitz. The point is that Mas-Colell et. al. at least make clear just what their assumptions are, and what exactly does or does not follow from them, rather than engaging in hand-waving dressed up in fancy rhetoric. Intuition is a lousy guide when dealing with mathematically sophisticated concepts, and an economics which relies on it isn't worth taking seriously in my view - and this applies even if we're talking about an approach practiced by people I find ideologically sympathetic, e.g. the Austrians.

"But a general microeconomics textbook which tries to stick to what can be proved rigorously is always going to end up taking the economics out of economics."

Then perhaps there just isn't that much to economics at present - see above. If people are going to be making conjectures, it helps if they're forthright about what they're doing, rather than dressing them up as "laws", as seems all too common in economics.

Nicholas Weininger

Lang's _Algebra_ should come with the caveat: only take it to your desert island if you already know everything in it, or in any case everything that you want to know.

I'm serious. Lang is a good reference-- as you say, nothing else covers so much ground in one volume-- but about as inaccessible as you can get without actually being written in a gnostic code. Adkins and Weintraub's _Algebra: An Approach via Module Theory_ is much friendlier.

ALek

though my experience with different algebra texts is limited - never seen Lang - is there someting against Hungerford here? Though much of the second chapter, which deals primarily with the classification of finite groups, was skipped in my class, I'm still impressed by the immense amount of material covered in just the two chapters on groups. It is short on examples, but the exercises contain many many useful results.

radek

“If you are prepared to believe that the Sonnennshein-Mantel-Debreu conditions apply, then a theorem-proof approach to economics will tell you a lot. On the other hand, if you believe that, you're mental. … assumptions which are equivalent to assuming that all consumers and all commodities are identical).”

What the hell are “Sonnennshein-Mantel-Debreu conditions”? They’re certainly not in Mas-Collel et. al. (MWG) and I haven’t seen them anywhere else (are they in Varian?). Now there is a Sonnennshein-Mantel-Debreu THEOREM which basically says that without making some strong assumptions (gross substitution property or a version of strong axiom of RP if I remember correctly) one cannot guarantee the UNIQUENESS of Walrasian equilibrium. Basically, this is due to the fact that the aggregate excess demand function inherits only certain properties of the individual excess demand functions, which are not strong enough to guarantee that it has only one fixed point.
However:

1. Existence of equilibrium is still assured under usual conditions (basically convex preferences – even that can be relaxed)
2. The number of equilibrium(s) is finite (and odd) by the index theorem. This excludes a continuum of them, which means that comparative statics apply locally – this certainly is a ‘practical’ result.
3. The equilibrium(s) are Pareto Efficient – by the First Thm so under the assumption of no externalities etc.

radek

“[caveat; I haven't read Mas-Colell's textbook, but I know from having gone through the "Steve Keen Theory of the Firm Wars" on mailing lists…”

Ah, I see. Alright, this one's gonna be long cuz Keen is a particular nasty piece of work and a personal pet peeve of mine.

I remember you citing Keen somewhere and being really surprised. I had the unfortunate experience of reading “Debunking Economics” in the bookstore because at first glance it looked like a ‘legit’ critique of mainstream economics. It’s not. It’s crap. Keen is at best a moron and more likely a liar

BTW, for a ‘legit’ critique of mainstream economics the History of Economic Though web page at the New School is where all the hip kids go:

http://cepa.newschool.edu/het/index.htm

I’m guessing this is the Keen nonsense you’re referring to:

http://www.debunking-economics.com/overview_more.htm

I’m gonna hold my nose and quote some of it:

“In the book, I note that a number of ‘conditions’ which economists impose upon their models are actually ‘proofs by contradiction’ that their theories contain errors. The most blatant example of this are what are known as the ‘Sonnenshein-Mantel-Debreu’ conditions. These say that, in order to be able to aggregate the individual utility which different consumers derive from consuming different commodities:
(a) all consumers indifference curves must have the same slope; and
(b) the slope must be such that spending doesn’t change with income—therefore all Engels curves must be straight lines.
But condition (a) means that all consumers must be identical—so that there is really only one consumer. Condition (b) means that all commodities must be identical—so that there is really only one commodity. This means that utility can’t be aggregated across different consumers and different commodities—it is a ‘proof by contradiction’ that what economists are trying to do is impossible.”

Now like I said, I don’t know what “SMD conditions” are. What it sounds like he’s talking about is something like the Representative Consumer Thm, or the “Gorman Form” – but he even screws this up too.

First of all you can always aggregate individual utilities in some way. Just give my utility a weight of 1 and everyone else a zero and we’re done. Likewise, you can always find SOME representative consumer. Let’s see…you!, Yes you, picking your nose at the computer. Yeah, you in the red shirt. From now on you represent the preferences of everyone who’s ever visited this website.

Of course some may be less than satisfied with my choice of aggregation and of the RC. What we want is a way to aggregate which is ‘meaningful’ and a RC who can do some actual representin’.

Keen’s “condition (b)” is just plain nonsense. I’m being generous here and assume he’s taking about homothetic preferences – so it’s not that spending doesn’t change as income changes, but the share spend on each good doesn’t change. He still fucks it up. Take a Cobb-Douglas utlity (x^a)(y^b). As income changes the share spent on x is always a and share spent on y is always b. Why the hell does Keen seem to think that this means that x is y and y is x?. What it does say is that how you allocate your income between DIFFERENT goods, is independent of how rich you are. Certainly a strong assumption but not an error on anyone’s part, except for Keen’s (if it’s an error and not a conscious misrepresentation).

I can’t remember if homotheticity is necessary for the Gorman Thm and also specifically about condition (a). I’m sure that homotheticity + (a) are sufficient. The Gorman Thm though says that a Representative Consumer that is better than the red shirted nose picker exists, if indirect utility can be written in linear form with the same intercept across individuals and with slopes which can vary. Maybe vice versa – can’t remember – probably not – at any rate, one of the coefficients is indexed by i so obviously consumers CAN be different. So whatever the hell SMD conditions are, they cannot say that in order to aggregate utilities (and get a RC) there’s only one type of consumer and one type of good, as that’s just plain not true.

Now, there’s some reason for his criticism (as Ratzinger says, every successful lie is based on a grain of truth) – you get a RC when people’s preferences, if they differ, do so in systematic tractable ways. Basically this means aggregatin’ is a tricky business. Doesn’t mean you can never do it or that you don’t learn anything from studying the problem itself.

As an aside, to further emphasize the fact that he don’t know what he’s talking about, there’s some extensions of the theorem. If the wealth distribution is not too crazy then we can relax the linear form and admit more general utilities (since, as always, it's the wealth effects which are making trouble). Also if we can’t aggregate meaningfully because consumers are not similar enough we can aggregate when … they’re different enough. The intuition for this is that the various idiosyncrasies offset each other – just like if you add up a bunch of kinky functions together, as long as the kinks are in different places, you get something that approximates a nice smooth function and the kinks don’t matter much. Anyway, there’s a bunch of work on this and it’s not like economists are ignorant of problems posed by aggregation (though some topics cannot be tackled without brave assumptions of some kind).

 razib

i like lynch's book too. i had a good friend who worked in his lab when he was at oregon...for someone as prominent as he is (he get's mentioned in popularizations like mark ridley's the cooperative gene) he couldn't get funding and moved to indiana.

dsquared

Radek; you're picking on simplified pedagogical assumptions here. As I say, I've lived through this flamewar on mailing lists and Keen, IMO did a pretty good job of defending a more rigorous version of the same critique.

On the subject of Engels curves, I think you have a point that Keen oversimplified, but less of one than you perhaps think. With Cobb-Douglas preferences or constant shares of spending, then the "differences" between commodities are differences which don't make a difference along the income axis. You might as well lump all the commodities together and call it a single commodity, because the consumer doesn't change the proportions in the portfolio as income changes. Obviously relative price movements affect demand for the different components, so it is wrong of Keen to make this exaggerated "only one commodity" remark (and, I suppose, wrong of me to repeat it), but there is an important point here about the differences between commodities not being modelled in a realistic manner.

On the representative consumer issue, I have much more sympathy for Keen's point. Any model which has a representative consumer is a model in which it doesn't matter who gets a marginal dollar of income. That's not realistic.

[aggregatin’ is a tricky business. Doesn’t mean you can never do it ]

No? My understanding of the import of the Gorman theorems is that it *does* mean that you can never do it; or at least that you cannot do it on the basis of realistic assumptions about consumers and commodities and get anything like the Walrasian results that you want. Btw, the problem with placing a weight of 1 on a single consumer and 0 on everyone else is not that it is not "representative", it is that it is not "aggregation".

[we can aggregate when … they’re different enough]

But what you mean here is "if they're different enough, in the right way". If consumers are different in ways which depend on their position in the wealth and income distribution, then it will matter who gets an extra dollar of income, and this is always going to pose problems for a representative consumer model. The correct conclusion to draw from this is that representative consumer models aren't worth bothering with.


You're on firmer ground with your first point (that the nonaggregability of preferences is less of a killer blow than Keen thinks it is). John Quiggin made the same point in his review of the book, although I think he is a bit harsh on Keen because the Arrow-Debreu assumptions are if anything more ludicrous than those needed for representative agents. I don't think that the existence of local equilibria is either an important or a practical result; under realistic assumptions about consumer preferences there is nothing pushing us in the direction of any one of those equilibrium, so I don't think that this validates comparative statics at all - unless one is prepared to make the unwarranted assumption that we are in an equilibrium right now.

radek

To point out that the Gorman form, or Arrow-Debreu relies on some strong assumptions is one thing. To talk silly a la Keen is another. Having scoured his website - other's stupidity always gives a cheap boost to one's ego - these non existant SDM conditions are not the only place where he talks nonsense. Somewhere in there is another of his deep complaints: "Economists never put numbers on their graphs!". Well, gee, I guess I'm busted. I could go on pickin' on him with other examples but it feels like kicking a passed out drunk after you've robbed him.

Also. First the initial argument was about theorem-proof economics. Well, the SDM theorem is theorem-proof economics which tells us that equilibrium may not be unique, and by extension that there may not be stable tatonnment dynamics which get you to a particular one - a point you allude to above (though roughly half of them would be stable). That's the value of theorem-proof economics right there - we learn something that otherwise might have escaped us.

Second, you said you liked Tirole. It's a great book. But if you're worried about strong assumptions, this should have you screaming. The "economics makes crazy assumptions" folks should be marching in the street with a puppet of Tirole. For one thing consumer surplus is used to evaluate welfare through out. This implicitly assumes that utility is quasi-linear. If you think CobbDogoulas is unrealistic then quasi-linear is just bunkers. Second, linear demand means that the non-numeraire portion of the quasi-linear utility is quadratic. This is bunkers squared. On the other hand, from Mas-Collel you can learn that consumer surplus is a good approximation to other, more sophisticated measures of welfare and likewise quadratic utility under most conditions (bliss point is high) does a good job. In fact the continued popularity of CobbDouglas is partly due to that it can be derived as a second order Taylor approximation to pretty much any reasonable function. So in the end, crazy assumptions, but who cares. They're used to make excellent points.

And you can't do ANY kind of macro without some kind of representative agent, whether you're talking RBC or old fashioned Keynesian consumption functions, or Austrians and Post-Keynsians writing literary economics with the lucidity of Samuel Beckett. The only difference is whether you explicitly acknowledge that you're assuming a representative agent or not. (Ok, I might leave Austrians out of it - but then what they can say is severly limited). Macro means you got to aggregate means you run into the same damn problems no matter which way you go - folks is different, their wealth levels are different and the relationship between goods is not straightforward but an ugly mix of substitution and complementarities. If you're gonna be intellectually honest and you say "I am very much against that representative consumer fellow" then I don't want to hear words like "inflation", "unemployment", and "economic growth" coming out of your mouth or keyboard.
On the other hand, like with Tirole, you can say, yeah representative consumer is based on some strong assumptions, but it allows us to actually say something about how the world works.

To me the whole thrust of the anti-RC theory is basically to say that the "new" macro (that is of the 80's) does not have any better "microfoundations" than the old macro with the Keynsian cross and linear consumption functons, if microfoundations are a sort of thing you loose sleep over.

dsquared

See, this is a great example of how people can appear to be talking the same language, but actually not be. As far as I can see, you're hopelessly confused here; you presumably think I am. Going through the card:

1. Consumer surplus is a concept which makes sense. It represents the surplus value which accrues to consumers; the amount that consumers in aggregate might have been prepared to pay but did not have to. It's also a quantity which it is better to have more of than less, and that's where the analysis should stop. It's the attempt to use extraordinary transformations of the consumer surplus as if they were in some way better measures of something that is precisely what I object to.

2. You absolutely can do macro without any representative agent. Who's the representative agent in a good old-fashioned Leontief input-output table? For that matter, where's the representative agent in a set of flow-of-funds accounts? There is all the difference in the world between aggregating transactions and aggregating individuals. To add together a load of transactions is to measure a quality that has a physical analogue in the world; the extra (and incorrect) step is to reify the aggregate as being a property of a (nonexistent) representative agent. Saying that 1000 apples were consumed is something that can easily be checked - you just count the cores. Saying that a representative agent with a budget of 1/1000 of the economy consumes a bundle which includes 1 apple, is the bit that is correctly objected to. Similarly with unemployment (a head count of actual individuals) and even inflation (a weighted average of prices, with serious but soluble problems in constructing the weighting function). I can't believe that you mean what you say; it's obvious that the unemployment rate is the number of people out of work, not the extent to which one person is unemployed.

All the aggregate entities of macroeconomics, apart from "capital", measure real physical quantities. They are consistent with any or no microfoundations because they are facts, not theories. The whole problem is the attempt to give "microfoundations" to macroeconomics when it doesn't need them.

radek

"Consumer surplus is a concept which makes sense."

As long as wealth effects of price changes can be ignored - here again are those wealth effects causin' trouble just like they do in GE. In most cases it's a perfectly good approximation (like I said) but you are missing a lot - the whole interconnection of various markets.

"It's also a quantity which it is better to have more of than less, and that's where the analysis should stop"

Ummm, so what you're saying is that it's just an ordinal but not a cardinal measure? (can I add two consumer surpluses, say from two different periods, to measure welfare?) But then why do we need it in the first place? As long as there's no Giffen goods if a price falls we know the consumers who consume that good are better off. It's precisely that consumer surplus is supposed to be a 'real' measure that makes it both very useful and reliant upon strong assumptions.

"You absolutely can do macro without any representative agent. Who's the representative agent in a good old-fashioned Leontief input-output table?"

There's no representative consumer in Leontief's linear model because there's no consumers. Everything's determined by the production side of the economy. Very Ricardian. Also very very unrealistic. As an aside, the Leontief input output model is a good illustration of the interplay between assumptions on technology (fixed coefficients - linear) with assumptions on preferences. So yeah, one can get rid of consumers and pretend to have gotten around the problem of aggregating preferences, by making particularly unrealistic assumptions on production technology.

But you're right, I did overstate my case. You can do macro without consumers. You can't make statements about folk's well being though. If the compostion of output changes we can't say anything about who, not even a representative consumer, is better off. We can't even say that unemployment or lower output is bad, because it could just mean that more leisure is being produced.
(As an aside, I've never seen a linear programming GE model with money and inflation - I would be very interested to see one - so I'm not sure how that answer can get addressed in this setting either).

BTW, this stuff is in MWG (although in one of the 'optional' sections) - which is what prompted this whole argument. It's also theorem-proof economics. Your original statement said that theorem-proof economics are only useful if one accepts some fictional SMD conditions in which case one's nuts. Now you yourself are providing some nice counter examples to your original contention.

"There is all the difference in the world between aggregating transactions and aggregating individuals"

Yeah of course. But if you don't aggregate individuals somehow then you are very very limited in what you can say. Lesotho produces a lot of diamonds. France produces a lot of cheese. And.....


"I can't believe that you mean what you say; it's obvious that the unemployment rate is the number of people out of work, not the extent to which one person is unemployed."

Whoa! I can't believe you're serious either. It's not obvious. My 12 year old sister is out of work, does that mean she's unemployed? If so then that measure of unemployment is completly useless and why worry about it. If not, then we might also consider other cases. The guy who inherited money and now sits on his couch all day smoking weed, is he unemployed? A grandma working as a greeter at WalMart for 5 hours a week? Is she employed, unemployed or somewhere in between? Do we give her the same weight as the guy who works 50 hours at chicken processing factory? The problem is that unemployment is NOT just a headcount of individuals - it's a headcount of individuals who meet a certain, very amorphous and subjective definition. My point was that without specifying preferences of some type (here over income and leisure) you can't say anything about whether 'unemployment' is bad or good, much less of how various policies may affect it - and that's what motivates the definition of who's unemployed that we use. And that gets us back to individuals and all the messy problems they represent...

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