Paul Romer continues to display his confusion. In reverse chronological order, you can look here, here, here, here, and so on. Also see Noah Smith.

Romer continues to put forward ever more false dichotomies and other simple-minded logical fallacies. For example, he seems to say economics has a choice between talky, non-scientific political advocacy or rigorous mathematical economics. And he gets his history wrong:

"Over the five decades from 1890 to 1940 (a time when physicists developed mathematical theories of statistical mechanics, quantum mechanics and both special and general relativity) economists avoided the use even of calculus and spent 50 years mired in the confusion spawned by the talky, market-by-market, supply-and-demand-ish approach to economic analysis codified in 1890 in Alfred Marshall'sPrinciples of Economics." -- Paul Romer

I suppose one can be generous and take Romer to be confining himself to Anglo-American economics. Obviously, economists such as Leon Walras, Gustav Cassel, and Frederick Zeuthen were analyzing mathematical models. (As I understand it, Zeuthen was the first to formulate the Walras-Cassel model with inequalities.) And, I guess in this tradition, Abraham Wald, in 1935, provided the first rigorous proof of the existence of a general equilibrium.

But even when restricted to Anglo-American economics, Romer is not quite correct. J. R. Hicks, with his 1939 edition of *Value and Capital* and earlier papers with R. G. D. Allen, reintroduced General Equilibrium theory into Anglo-American economics, with as many derivatives, matrices, etc. as you please.

Romer's comments about "talkiness" are silly. I would be embarrassed to dismiss a scholar like Fernand Braudel on the grounds that he did not put forth mathematical models, as in physics.

Romer is just as silly on the other side of his false dichotomy. He's seems to think that as long as a model is put forth in terms of valid mathematics, it is rigorous. Here's what he writes about Solow's growth model:

"Robert Solow (a close colleague of Samuelson's at MIT) ... showed how to describe the behavior of an economy in which things did change. By restricting attention to a single type of output, Solow developed a workable framework for talking about changes in wages, the return to capital, and total output." -- Paul Romer

When I read that in context, I thought Romer was just expressing himself badly. This is in the midst of a short overview about Paul Samuelson's contributions to economics, a task I would find Herculean. Maybe Romer knows that Solow's model is, at best, a non-rigorous, rough-and-ready framework for empirical work. But he really does think otherwise, that Solow's model is rigorous:

"Solow's explicit dynamic model of growth based on an aggregate production function was a solid piece of SAGE [Simple, Applied General Equilibrium] theory. After all, if new Chicago and the rest of the profession agree on one part of good theoretical practice, this has to signal something." -- Paul Romer

The above is just false. The rest of the profession do not agree.

What would have to be the case for Solow's model to apply in a world in which more than one commodity is produced? One set of assumptions is that, in some sense, effectively one commodity is produced. At any given time, the capital stock could be disassembled and costlessly transmuted into either any consumption good or any other collection of capital goods, and vice versa. Then, the historical cost of capital goods, the current prices of capital goods, and their present value would not diverge. On the other hand, these costs do diverge in actual economies set in historical time. The above is a summary of a substantive argument from Joan Robinson, who jokingly claimed that neoclassical economists thought of capital goods as meccano sets or ectoplasm.

Romer resolutely refuses to address the substance of either side of the Cambridge Capital Controversy. (And there are other points than the above. Is Romer even aware of the existence of Piero Sraffa or Pierangelo Garegnani?) Instead, he whines about Robinson's tone:

"...the sarcasm and put-downs that were a part of British intellectual life that Solow had to confront in his exchanges with Joan Robinson." -- Paul Romer

And he attacks Joan Robinson's motives:

"In so doing, he used the same techniques that economists from Cambridge England used to attack his model of output as a function of a stock of capital. Joan Robinson probably had the same concern. What will young Samuelson and Solow do with all their maths? Because an aggregate production function might lend support for a marginal productivity theory of the distribution of income, perhaps we should strangle it in the crib." -- Paul Romer

The above is simply ad hominem. Apparently, some have sent email to Romer with similar points. He then cites Roger Backhouse as an authority, while doubling down on the ad hominem.

I suppose I cannot complain about Romer's treatment of Robinson. Romer's knowledge of General Equilbrium theory seems to be lacking, and he treats Frank Hahn and Robert Solow's objections to macroeconomics after Lucas no more seriously. He complains about their tone, but pretends they had no substance to their complaints. Is Romer even aware of Hahn's attempts to integrate money into the Arrow-Debreu model and his outline of the difficulties? Is Romer even aware of the existence of Hahn and Solow's 1995 monograph? To be generous to Romer, I suppose one could say the latter is only of retrospective importance when considering the controversies in macroeconomics in the 1970s.

I might as well conclude with another example of silliness from Romer. Here Romer tries to explain one of Lucas's contributions:

"Then Robert Lucas showed how to add uncertainty to a version of the Samuelson and Diamond models. This let him pin down loose conjectures from Keynes about the role of expectations." -- Paul Romer

Now, Chapter 12 in the *General Theory* is often turned to when one wants to read Keynes on expectations. And in that chapter, one finds:

"By 'very uncertain' I do not mean the same thing as 'very improbable'.Cf. myTreatise on Probability..." -- John Maynard Keynes (1936, p. 148).

Romer is equivocating. As far as I know, Lucas did not introduce uncertainty in any mathematical models in economics. (Can anybody find Lucas explicitly discussing the inconsistency between rational expectations and non-ergodic time series?) So Romer should either not reference Keynes at all (with silliness about "loose conjectures") or talk about Lucas modeling probability (also known as risk) or expand on his text to show how Lucas was actually modeling Keynes's uncertainty. That is, Romer should if he has any interest in the truth value of his statements.

I think the above is not one of my better posts. Too uniformly negative even for me and too wandering. But I think Romer should try not to commit simple logical fallacies in his complaints about lack of scholarship and rigor among economists.

**References**

- Braudel, Fernand ().
*Civilization and Capitalism, 15th - 18th Century, Volume 1: The Structure of Everyday Life.* - Hahn, Frank and Robert Solow (1995).
*A Critical Essay on Modern Macroeconomic Theory*, MIT Press. - Hicks, J. R. (1939).
*Value and Capital*(1st edition).

## 12 comments:

Cripes, now there's a Paul Romer?

Does economics really need ANOTHER Ro(e)mer?

«the first rigorous proof of the existence of a general equilibrium»

There is no such thing! And I am surprised that you fall for claims that it has been done, given your attention to the tricks of the the trade.

General equilibrium models formalizing neoclasssical Economics *cannot* be proven to have a general equilibrium because they are both mathematically and semantically broken, they have no valid solutions, they just don't work.

The various published "proofs" of the existence of general equilibrium are misleading: they are simply proofs that certain artfully constructed systems of equations are solvable.

The confusion that those systems of equations that have been specifically shaped to be solvable are proofs that general equilibrium happens in neoclassical Economics is given by simple devices like giving labels like "price", "quantity", "capital", "labor" to various quantities in them, as if the equations were a mathematical formalization of the neoclassical handwaving model.

Looking at the systems of equations that have been proven to be solvable they don't actually match the usual "talkiness" side of neoclassical economics, they describe "something" that is far simpler.

Note: I think that the first case where a rigorously well defined neoclassical model that could be meaningfully said to achieve general equilibrium was created was by P Sraffa in the "commodities by means of commodities" line, and he did that specifically to explore whether even a very simplified neoclassical model worked in the way the neoclassical claimed, stripping away the "talkiness", and the answer was that it did not.

P Romer's argument are particularly ironic given that neoclassical Economics is essentially just "talkiness", as it involves handwaving into existence imaginary things like "capital", "infinite markets", "perfect competition with one representative agent", "smooth aggregate demand functions" etc., and then creating mathy-looking systems of equations that don't actually correspond to the "talkiness".

Many thanks for spotting this in P Romer's post:

«"an aggregate production function might lend support for a marginal productivity theory of the distribution of income,"»

As it shows very clearly that P Romer is very aware that the core issue is the central truthiness of Economics, and that hallucinatory neoclassical talkiness of «an aggregate production» is meant to support that central truthiness.

«Romer's comments about "talkiness" are silly.»

Again, especially because neoclassical Economics, as in Arrow-Debreu-Lucas, is entirely "talkiness" and the "mathyness" that accompanies it does not match the "talkiness". It is all just sophistry.

«I would be embarrassed to dismiss a scholar like Fernand Braudel on the grounds that he did not put forth mathematical models, as in physics.»

There is a much bigger topic here that unfortunately seems very little known and yet is exceptionally important and an european philosopher, Chaim Perelman, has been writing about it in a good way.

The issue he describes is that the rise of cartesian rationalism has created a situation where all discussions that cannot be handled with the cartesian method as pure talk. That is the assumption that either a topic can be discussed "scientifically" or it is complete bullshit.

Which means that "scientifically" becomes a big talking point, and that discussions that are not purely bullshit but are not purely scientific either get lumped in with those that are mostly or entirely bullshit.

That means surrendering too many topics that cannot be conclusively proven to deliver "scientific truth" to purely irrational discussion.

The solution he describes is to resurrect "rhetoric" as a philosophical device, rather than a propaganda tool: that is to admit that there is a third category between the "provable truth" of the scientific method, and the "worthless bullshit" at the other end, and it is what I would call "persuasive even if not conclusive arguments".

Rhetoric is then the set techniques that allow of constructing persuasive arguments where possible, even if the conclusions are uncertain, because *action* cannot be simply always guided by proven scientific truth, and should not be guided by arbitrary irrationality in every other case.

The arguments of F Braudel as to history are an example of "rhetoric" well deployed: he does not write mathematical models, he does not prove the truth of his explanations, but supports them with persuasive interpretations and corroborating evidence he presents. His conclusions are uncertain for sure but they are not arbitrary, and it is then a call of judgement of the audience reading them as to how much to believe them.

Put another way, Chaim Perelman makes the seemingly obvious argument that between hard scientific truth that can be proven with some accuracy, and arbitrary irrational bullshit about which nothing can be said either way, there should be a recognized category of well-founded persuasive judgement to which assign different weights of applicability.

That is a very important argument.

This Romer is often suggested as being eligible for a Nobel prize, for his work on endogenous growth, particularly Romer (1990). I'll be amused when and if he gets it.

I find that Paul Romer was, at once time, that Hahn and Solow had backed upped their derision for macro following Lucas with solid analysis, as mathematical as you please. That is, Romer wrote a cover blurb for Hahn and Solow (1995).

A prove of the existence of an equilibrium is not a statement about actually existing economies. It merely says that a certain set of equations, inequalities, or whatever is consistent.

Von Neumann provided such a proof shortly after Wald. And Von Neumann's model had certain family resemblances to Sraffa's.

Thanks for the reference to Chaim Perelman. I probably will not read it, since I think Romer's scientism is not argued for much these days among philosophers of science. Those who agree with me that there's room among scholars for non-fully arguments are probably on Simon Wren-Lewis side here, at least for this point.

«A prove of the existence of an equilibrium is not a statement about actually existing economies. It merely says that a certain set of equations, inequalities, or whatever is consistent.»

But the question is not whether the proof is of equilibrium of actually existing economies, it is whether the proof is of equilibrium in actually existing neoclassical theories. The equations in the various "proofs" of equilibrium are not those for recognizable neoclassical theories, but for very simplified versions of them. Since the solvability of the equations depends critically on many subtle assumptions, proving those equations have a solutions does not imply that any or most neoclassical theories have an equilibrium...

Said differently, the various people who "proved" that "the neoclassical theory" has a unique optimal equilibrium under which income is determined solely by productivity did not take "the neoclassical theory" and wrote it up in equations and then proved that.

That's far too hard :-).

What they did is something that you by now should be familiar with, as it is a standard technique in Economics (and other subjects) to get a paper out with big sounding (until one looks at the assumptions) results: they kept adjusting a set of equations clipping away the "hard" bits until they could find a set of equations for which they could prove "equilibrium".

The resulting equations are not a model for "the neoclassical theory", unless it is decided to redefine the term "the neoclassical theory" as the theory described by that set of equations, but that's even bigger sophistry.

Quite a collection of morons you've assembled here, Bob.

Thank you for your craven expression of interest in the opinions of commentators.

«Many thanks for spotting this in P Romer's post:

«"an aggregate production function might lend support for a marginal productivity theory of the distribution of income,"»

As it shows very clearly that P Romer is very aware that the core issue is the central truthiness of Economics, and that hallucinatory neoclassical talkiness of «an aggregate production» is meant to support that central truthiness.»

«Looking at the systems of equations that have been proven to be solvable they don't actually match the usual "talkiness" side of neoclassical economics, they describe "something" that is far simpler.»

Note that here I was just repeating what P Samuelson and F Hahn and other neoclassicals acknowledged during the Cambridges Capital Controversy, as I have summarized by quotes in my comments to a later post:

http://robertvienneau.blogspot.co.uk/2015/11/herbert-scarf-1930-2015.html

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