The Solow Model: is it the GOAT?

It is probably too late to write a biography of Robert Solow. He has outlived his teachers, his peers, and even some of his students, which makes it difficult to gather material. I do think that biographies of economists can be very insightful, and I would encourage any young economist or economic journalist to search for an interesting subject. Of the living Nobel Laureates, the ones I would most like to read about are Solow, Vernon Smith, George Akerlof, and Robert Merton. Probably also Paul Romer, although there is some discussion of him in David Warsh’s Knowledge and the Wealth of Nations. From the business world, Hal Varian and Bob Litterman come to mind, although I am no doubt forgetting a number of interesting business economists.

Here, I will sketch my experiences with Solow and my impressions of him.

1976-1980

When I arrived to begin my Ph.D program at MIT, the duo of Paul Samuelson, then aged 61, and Robert Solow, then aged 52, was already a spent force. Samuelson was still trying to publish research papers, and would do so into his 90s, but by this point his strengths had turned into weaknesses. His knowledge of mathematical techniques no longer towered over that of his colleagues, and his audacity was now overshadowed by his carelessness. While I was a student, a comment on one of Samuelson’s then-recent papers appeared in a journal. The comment’s author pointed out that what Samuelson reported as the social welfare optimum in the derivation of this particular model was actually the social welfare minimum. The editor also included Samuelson’s two-word reply: mea culpa.

Solow was all but retired. He spent his summers on his sailboat, and he spent the academic year eeping up a very extensive correspondence.

Our cohort of graduate students took a one-quarter course taught by Solow, in which he used as a text Edmund Malinvaud’s The theory of unemployment reconsidered. This was an attempt to provide a “microfoundation” to Keynesian macroeconomics. It took as an assumption that prices (not just wages) failed to move sufficiently quickly to bring about full-employment equilibrium. I found this course inspiring, and for my dissertation I set out to develop an explanation for price “stickiness.”

I think that what I came up with makes sense, and it seems better than the “cost of re-publishing the restaurant menu” story that Greg Mankiw popularized. I said that habitual customers of one store would not change stores unless they heard about lower prices at the alternative store, and they would not hear about lower prices unless that store paid for advertising.

Solow supervised my dissertation, and he was very skilled at providing gentle feedback to steer me away from unhelpful ideas and toward more promising ones. But I met with him only rarely and for never more than a few minutes at a time. Most of our interaction was by mail (snail mail, of course).

Solow was of no help to me on the job market. One problem was that his praise of students was always so effusive that it was heavily discounted in the market. But the main problem was that at this point Stan Fischer and Rudi Dornbusch had essentially taken over the role of advising and placing MIT macro Ph.D’s. If you wrote a “rational expectations” dissertation under Stan or Rudi, your career got off to a good start. Not if you didn’t. My most attractive job offer–and just about my only one–came from the Fed, and that was based on connections I had made there as a research assistant prior to going to grad school.

1980 and beyond

While I was on the job market, one of the professors who came to MIT to give screening interviews was ____, then an assistant or associate professor at Amherst. I described my job market paper to ____, but he was not sufficiently interested to invite me to give a talk at Amherst.

It turned out, though, that ____ was not completely uninterested in my work. In 1982, the Quarterly Journal of Economics published an article by ____ which was my idea, including some of the terminology that I coined about it. There was no mention of me, not even a footnote. This was while my own article had not been accepted by any top journal and was scheduled for publication in a lesser journal.

I wrote a letter to Solow, and I expected him to contact the economics department at Amherst and the QJE to inform them of this plagiarism. Instead, he wrote back saying “____ is wrong, of course” but implying that neither he nor I should try to do anything about it. To this day, I am shocked and embittered by this indifferent attitude. Imagine getting mugged and having the police say “Well, the mugger is wrong, of course,” but showing no interest whatsoever in having the mugger punished or trying to recover your stolen property.

I corresponded with Solow only sporadically after that. When I collected a series of my essays for a self-published book, I asked him to write a blurb. He refused. In the first essay, I quoted Megan McArdle, then a blog-writer, now a columnist for the Washington Post. Solow wrote to me that I had quoted a blogger, and this made it impossible for him to endorse the book in any way.

Playing Amateur Psychologist

All of Solow’s correspondence was by snail mail. His resentment of personal computers must have been intense (it was Solow who in 1986 quipped that “We see computers everywhere but in the productivity statistics”).

As long as I am playing amateur psychologist, I will say that I suspect that Solow is a “disagreeable,” by which I mean that for all his geniality and popularity in the economics profession, on the Big Five personality traits he would be very low on the “agreeable” trait that measures one’s desire to please others. Another quip for which he was known was saying that whenever he listened to John Kenneth Galbraith, his thoughts turned to all of the competitive forces in the economy, and whenever he listened to Milton Friedman his thoughts turned to all of the imperfections in a market economy.

I think that below the surface humor there was a layer of intense anger. I find it frustrating when I see people I regard as intellectual inferiors strutting across the public stage, brandishing awards and credentials. I imagine Solow suffering from that same resentment.

The “rational expectations revolution” that dominated the profession for two decades was, in my view as well as Solow’s, an intellectual dead end. He, of course, stuck with the Keynesian views of his youth. I went in a different direction, mostly because of my hands-on experience with macroeconometrics. See my science of hubris essay and my memoirs essay.

Solow’s intellectual disdain extended to his Harvard teachers, including Schumpeter. In a review of McCraw’s biography, Solow ends with “The man was all problems, and one very important idea.”

After helping Wassily Leontief fill out input-output-tables, Solow went on to make a career out of insisting on the importance of substitution effects that Leontief assumes away. In the 1970s, Solow (correctly) denounced as nonsense the “limits to growth” propounded by the Systems Dynamics group at MIT.

Prior to that, Solow made the contributions that won him the Nobel Prize in part by showing that the instability inherent in a model of economic growth known as the Harrod-Domar model was due to its failure to allow for substitution between capital and labor. With such substitution allowed for, a stable model of economic growth emerged.

This was, of course, the famous Solow model. As far as mathematical models go, the Solow model is a candidate for what in contemporary sports lingo is know as The GOAT (Greatest of All Time). What other model makes such simple, appealing assumptions, gets such intriguing results, and has resulted in so much empirical application?

Having said that, I think that the Solow model should be taken down a peg, or several. My concern is that I do not believe in the notions of “aggregate labor” or “aggregate capital.” Solow was always cognizant of this issue, if anything more sensitive to it than anyone who has followed in his footsteps. In his Nobel lecture, Solow said

One can not do macroeconomics without aggregative relationships; and at least for the moment there is no substitute for macroeconomics.

Economists want to do macroeconomics, and when they discuss economic growth they want to say things that are precise (or at least sound that way). Ergo, they will use aggregate production functions. But I don’t think that they work.

The road to sociology

Another humorous phrase that comes from Solow is “amateur sociology.” He had derived useful knowledge from a simple mathematical model. He saw that the attempts to derive useful knowledge from more complex mathematical models, such as “rational expections” macro, were ill-advised. He thought that better answers might come indeed from sociology, but he also evidently thought that economists should make as little use as possible of the methods of sociologists. So “amateur sociology” can be seen as expressing humility, implying that there are some questions that economists cannot answer with the mathematical rigor that is their pride and joy.

My own view is that we should embrace the fact that economics is embedded in sociology. My main concern with the “road to sociology” is that is paved with the intentions of social justice activists rather than truth-seekers.

7 thoughts on “The Solow Model: is it the GOAT?

  1. Vernon Smith’s autobiography, recently republished as two volumes, is good. There is so much specialization now, is the problem. So many academics specialize early and don’t have broad interests, so they are not that interesting to write about.

  2. Do you think the theft of your ideas was done intentionally? That’s incredibly brash, and if I were in your shoes, I’m not sure I could remain silent about it. Thanks for sharing the story.

  3. Perhaps the Solow model and the Cobb-Douglas function can serve some useful purpose in the very short term when culture is assumed to be static or useful for describing a period in history when technological progress was slower.

    When I first saw the Cobb-Douglas function I assumed that everybody would keep in mind that the real world doesn’t have smooth functions so everybody understands that what you predict is not exactly what is going to happen.

    Software can have arbitrary functions that aren’t smooth so if we ever get the data to design jerky functions we will. In the meanwhile these functions are kind of amusing because they are telling you we don’t have the data we want or if we do have the data we don’t have the right software. Universities teach other math things and not math things that are the best that could be created at the time in history when they were. If we know that education is not wholly practical then we know that there will be some education that is merely historically interesting. If ideas that need to be taken down a peg are taken down a peg then buyers of education will be better served. Hopefully low and middle income families know what they are paying for when they pay for a young person’s education.

  4. I don’t what prompted Arnold’s reminiscence, but in the current issue, MIT’s Technology Review is devoting a good deal of print revisiting Solow’s career at MIT — a hagiography, especially compared to what you may read here. I am looking forward to seeing Dr. Kling’s review of that review.

      • That is the “Main” article I was referring to, which appears in both the online and print edition. But there was also another supplemental one included in the “alumni insert” that went on about his role as a mentor and highlighted a “prediction” that capitalism only has about two or so decades to do. And something about then we are all Marxists. As you can tell, I did not read it that carefully…

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