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).