Sraffians are actually debating about non-problems. The standard GE model is a strict generalisation of the classic one. They simply don't get it, as they have proven at a conference on this very issue. The people who are really into aggregation problems are theorists like Kirman and Hildenbrand.I find Petri (2004) cogent and well-argued. But given the references in the introduction to my draft paper, "A Model for Exploring Manifestations of Capital-Theoretic 'Paradoxes' in Temporary Equilibria", would I learn anything new by reading the proceedings in the volume edited by Petri and Hahn? This paper also shows why I don't find it convincing to say dynamic equilibria (which I take to be the same as temporary equilibria) are immune from Sraffian criticisms.

6 years ago

## 9 comments:

There are equilibrium models with a infinite time horizon, and there are existence proofs and proofs of the welfare theorems out there. None of the arguments depends on a "last period". One can certainly treat Sraffian models as such equilibrium models.

The problem with equilibrium models is not that they are inable to produce some effects, the problem ist that almost every effect can be produced (but it is probably impossible to generalize the MSD results to a model with a infinite commodity space and finitely many agents).

Michael,

Thanks for commenting. Unfortunately, I am unable to see how anything much in your comment relates to anything in my post or linked paper.

You may be saying that Sraffian models can be viewed as the limit, as time increases without bound (when such a limit exists) of paths in short period temporary equilibrium models. If so, I agree that that is a mainstream perspective on such models.

I consider it an open question whether capital-theoretic "paradoxes" can tell us something about such models. For example, do they help us examine (in)stability of paths in such models? Do they tell us something about tatonnement stability?

In canonical expressions of such models, is it useful to formulate a condition that, along an equilibrium path, the value quantity of capital goods at each point in time is willingly held by somebody? Does this provide an avenue for exploring Cambridge capital aspects?

And what about the impermanence problem, as put forth by Petri? Even in theory, are these models capable of providing empirical claims?

These questions are all addressed somewhat at an advanced level, including by Sraffians, in the literature.

I don´t think there is any worth in analysing tatonnement stability. The minimal Arrow-Debreu model tells almost nothing empirically (Donald Brown has shown that it has some empirical content though). I do think that one can get more out of it by taking distributions of characteristics of individuals into account.

The A-D-model allows for completely disaggregated capital, and one can reproduce things like reswitching in such models.

I don't know what the impermanence problem is.

I show, in footnote 5 of my draft paper linked to in the post, that I am quite aware of the view that the Arrow-Debreu "model allows for disaggregated capital". So Michael is not telling me anything I do not already know, while I am also aware of the view expressed in Parrinello (2005, also referenced in the linked paper). I have already tried to explain what I understand Petri's impermanence problem to be, in responses to a lying coward.

I agree with Michael in thinking some papers by Alan Kirman well worth reading. But I have to conclude that Michael was just talking when he said that Sraffians "simply don't get it".

Wether you "know" ia already doesn't matter. The point is that this renders the critique of the Sraffians irrelevant as a criticism of modern GET.

In your response to the person you termed a "coward" (why, if I may ask), you argued that the AD model takes all capital goods as original endowments which is clearly wrong.

I still don´t see the problem. The work of Alfred Marshall is basically irrelevant to modern Walrasian GET.

The people who don´t get it are the ones still attacking Frank Hahn and the like. The book I mentioned gives ample evidence.

Michael,

Thanks for sharing your reactions. And I did find it interesting to be pointed to Donald Brown's work.

Anonymously commenting on blog posts with repeated falsehoods about the contents of those posts, even after the author points out the falsehoods, seems like the opposite of bravery to me.

Maybe I phrased my description there of the Arrow-Debreu model badly. The original endowments of capital goods, i.e., at the start of the modeled time period, are given (elements of a vector). I'm quite aware that the quantities of capital goods vary after the original instant and that these quantities are endogenous variables.

My point is that the draft paper I link to shows that I am quite aware of the point of view that Michael is putting forth.

I don't know where I argue that the work of Alfred Marshall is relevant to neo-Walrasian GE models or why Michael thinks he is responding to something I say. I do think that the GE models do not support "intuitive" findings often put forward in partial equilibrium models and applied work. I believe Michael agrees, based on his prior statements.

Certainly, Sraffians have responded to Frank Hahn's 1982 CJE piece, as I document in my linked draft paper. The fact that Sraffians have another point of view does not show that the Sraffians "don't get it". I don't see how one can show that unless one engages their arguments.

Anonymously commenting on blog posts with repeated falsehoods about the contents of those posts, even after the author points out the falsehoods, seems like the opposite of bravery to me.What falsehoods?

Maybe I phrased my description there of the Arrow-Debreu model badly. The original endowments of capital goods, i.e., at the start of the modeled time period, are given (elements of a vector).In any sensible model that takes time into account, capital is fixed at some point in time. But that doesn't imply that such a model is a "very-short-run" model as you claimed: "The Arrow-Debreu model of intertemporal equilibium shold actually be referred to as 'very short run'. In the model, quantities of all capital goods, both fixed and variable are taken as given."

"I don't know where I argue that the work of Alfred Marshall is relevant to neo-Walrasian GE models or why Michael thinks he is responding to something I say."

Because your discussion with the "anonymous coward" focused entirely on dinosaur neoclassicals.

I do think that the GE models do not support "intuitive" findings often put forward in partial equilibrium models and applied work. I believe Michael agrees, based on his prior statements.No. With quasilinear preferences and separable production, every partial equilibrium model can be made into a GE model. What one can say is that properties all partial equilibrium models share may not be shared by all general equilibrium model.

Certainly, Sraffians have responded to Frank Hahn's 1982 CJE piece, as I document in my linked draft paper. The fact that Sraffians have another point of view does not show that the Sraffians "don't get it". I don't see how one can show that unless one engages their arguments.The only critical thing you write on Hahn and co. in your paper is that with non-tatonnement dynamics, one cannot rely on the equilibrium path of such economies as an actual prediction. This of course is common knowledge in GET and Hahn was on the forefront of research on non-tatonnement dynamics. So Sraffians offer exactly nothing new, other than a fetishism for steady states of linear production models.

In any sensible model that takes time into account, capital is fixed at some point in time.As Garegnani (1990a) points out in a related context, the above begs the question.

But that doesn't imply that such a model is a "very-short run" model as you claimed...As far as I am concerned, in describing certain models, in which some initial endowments of capital goods are taken as part of the givens, as "short run", I am merely following traditional neoclassical terminology (Garegnani 1976, Milgate 1979, Petri 2004). Michael, of course, provides no rationale for his proposed change in terminology.

I don't think I'll enter into Michael's odd comment about "dinosaur neoclassicals" in the referenced posts and comments.

With quasilinear preferences and separable production, every partial equilibrium model can be made into a GE model...I think I am only echoing the literature, e.g.: "This arbitrariness of excess demand implies that monotone equilibrium comparative statics and global stability of equilibria under tatonnement will only result from the imposition of a limited set of conditions on preferences and endowments" (Brown and Shannon 1998).

The only critical thing you write on Hahn and co. in your paper is that with non-tatonnement dynamics, one cannot rely on the equilibrium path of such economies as an actual prediction.I don't know why Michael takes, say, Garegnani (2000, 2005a, and 2005b) and Schefold (2005a and 2005b) to be about non-tannonement dynamics. Michael just refuses to engage the arguments put forth by Sraffians. I should think it would go without saying that I am not referring primarily to my own arguments.

This of course is common knowledge in GET and Hahn was on the forefront of research on non-tatonnement dynamics. So Sraffians offer exactly nothing new,...Pasinetti (2000) points out the non sequitur in concluding about reswitching: "as if the difficulties, when they are already known could, by this very fact, acquire a justification for being ignored, no matter whether they crop up in a different context, where they are reiterated and extended."

...other than a fetishism for steady states of linear production models.I see no "fetishism of steady states" in, e.g., Richard Goodwin (1990), Luigi Pasinetti, Barkley Rosser (1983), or Kieran Sharpe (1999). I think I'll stick with Frank Hahn (1982): "Sraffa's work shows that certain simplified routes [on which full neoclassical equilibrium is supposed to come about] are very risky and not free from logical difficulties".

As Garegnani (1990a) points out in a related context, the above begs the question.Why should I worry that Garegnani has strange views on the nature of "time".

"As far as I am concerned, in describing certain models, in which some initial endowments of capital goods are taken as part of the givens, as "short run", I am merely following traditional neoclassical terminology (Garegnani 1976, Milgate 1979, Petri 2004). Michael, of course, provides no rationale for his proposed change in terminology."

Such as Arrow? Debreu? Hahn? Lucas? Prescott? If you need a rationale why I think the data of the world (modulo some qantum effects) are fixed at a point in time requires argument? Ouch.

I think I am only echoing the literature, e.g.: "This arbitrariness of excess demand implies that monotone equilibrium comparative statics and global stability of equilibria under tatonnement will only result from the imposition of a limited set of conditions on preferences and endowments" (Brown and Shannon 1998).That´s a statement about the

classof all A-D-models not a statement about all models. Of course there are general equilibrium models with unique equilibria, nice convergence properties and so on. Maybe, you should also read the part of papers with all those symbols in it.I don't know why Michael takes, say, Garegnani (2000, 2005a, and 2005b) and Schefold (2005a and 2005b) to be about non-tannonement dynamics.I was talking about your paper. It didn't mention any other critique (citing papers is something else).

Pasinetti (2000) points out the non sequitur in concluding about reswitching: "as if the difficulties, when they are already known could, by this very fact, acquire a justification for being ignored, no matter whether they crop up in a different context, where they are reiterated and extended."Where did I say they could be ignored?

I think I'll stick with Frank Hahn (1982): "Sraffa's work shows that certain simplified routes [on which full neoclassical equilibrium is supposed to come about] are very risky and not free from logical difficulties".Nice. I was born in 1982. Of course that is long ago. This routes aren't mainstream anymore. Of course Hahn has a very different view of Sraffa and the Sraffians.

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