Of models and men


I did my Ph.D. as the only pure theoretician in a lab of experimentalists. The experiments involved breaking materials; the theory involved figuring out how and why the material broke. My colleagues would spend days setting up experiments in the lab, diligently preparing the samples and meticulously instrumenting them. The experiments themselves were anti-climactic: when a material wants to break, it does not prolong its own suffering. In fact, most of our time was spent not before the experiment or during it, but after, on the computer, combing through the gigabytes of data that collectively formed a sort of autopsy report.

In some respects, making models is easier than running experiments. The medium is much more tractable — have an idea, write down its mathematical representation, code it up, and press “Enter”. There is no need to deal with the idiosyncrasies and fragilities of physical objects. What is hard is to create a model that comports with physical reality. All models of physical phenomena, by construction, simplify those physical phenomena, so that one does not and cannot expect perfect agreement between the model and the reality it seeks to represent. That being said, my advisor at the time was generally dubious of any models I made that did not at least predict the salient trends from our experiments.

I later worked as a postdoc for an academic whose lab comprised only pure theoreticians. The difference in perspective was striking. We obtained all of our experimental results — the bases for comparison to our models — secondhand, and thus it was easier to cast aspersions on them. Perhaps the other lab prepared the samples improperly. Perhaps they instrumented them incorrectly. Perhaps the post-mortem analysis was done wrong. While it is true that there is no such thing as a “pure” experiment, and that all experimental observations are, to some extent, theory-laden, our default setting was to assume the fault was in others instead of ourselves.

I have an email on this topic from the first email conversation I ever had with my postdoctoral advisor. (We hadn’t yet met in person, and I remember being very intimidated by him.) He wrote,

The role of experiment vs. theory is interesting philosophically.  The experimentalist (and some theorists) often thinks that theory needs to be validated by experiments.  But theory plays several other roles: (i) describing something that cannot be directly measured and yet is essential in controlling some (higher-scale) observation/measurement and (ii) providing a framework within which to evaluate experiments – if the experiments don’t match the theory, then why not?  What aspect of the theory is not present in the experiments, or what aspect of the experiment/material is not actually what it is believed to be?

On the other hand, one must be careful about constructing a theory that is totally internally consistent but that makes untestable predictions or contains so many unknown variables that it can never be used for anything useful.  The theory as a theory is fine, but it exists in a vacuum. But sometimes we do have to make theoretical progress by creating such theories and then using them to understand the importance of different variables, whether some mechanism is or is not crucial, etc.

Overall, it is therefore a mistake to think that “theory” can only exist underneath “experiment”, and not as an equal partner in both discovery and understanding.  The key aspect of both types of research is in doing a good experiment (i.e. one that uncovers what you think you want to know) or creating a good theory (one that should enable predictions, explain existing experiments, and suggest new experiments).  In the latter, think “Higgs Boson” – predicted 50 years ago by theorists following the existing laws of physics to their natural consequences.

I can’t find fault with any of the particulars of his argument. But the overall message seems almost certainly wrong, if construed broadly. Too many theoreticians have convinced themselves that theory can outpace experiment, that they are like Einstein predicting Mercury’s precession, or Higgs, Englert, and others imagining the existence of the gravity particle. That might be the case in a relatively narrow realm of science. But as the reality we seek to represent becomes more complex, and as it begins to involve people as well as objects, it seems more and more important to subordinate theory to experiment, to see them less as “equal partners”. If our models fail to capture the behaviors of artificial experiments in a lab, we are permitted to blame the experiment to some extent, to ask “what aspect of the experiment/material is not actually what it is believed to be”. But if our models fail to capture the reality of systems that humans have constructed, we should not blame them for contradicting our mathematical elegances.

I have been re-reading Thomas Piketty’s masterpiece Capital in the 21st Century, after reading it for the first time shortly after its translation into English. Readers of the book focused primarily on its indictment of capitalism. As Marshall Steinbaum wrote in the Boston Review, “The book’s central tenet—that wealth grows faster than economic output, thus concentrating capital (and the income it produces) in ever-fewer hands—confirmed the public’s sneaking suspicion that the workings of the capitalist economy are malfunctioning.”

If anything, though, Piketty’s book is as much an indictment of the discipline of economics. In its introduction, Piketty reflects on his experience in American academia:

I should perhaps add that I experienced the American dream at the age of twenty-two, when I was hired by a university near Boston just after finishing my doctorate. This experience proved to be decisive in more ways than one. It was the first time I had set foot in the United States, and it felt good to have my work recognized so quickly. Here was a country that knew how to attract immigrants when it wanted to! Yet I also realized quite soon that I wanted to return to France and Europe, which I did when I was twenty-five. Since then, I have not left Paris, except for a few brief trips. One important reason for my choice has a direct bearing on this book: I did not find the work of US economics entirely convincing. To be sure, they were all very intelligent, and I still have many friends from that period of my life. But something strange happened: I was only too aware of the fact that I knew nothing at all about the world’s economic problems. My thesis consisted of several relatively abstract mathematical theorems. Yet the profession liked my work. I quickly realized that there had been no significant effort to collect historical data on the dynamics of inequality since [Simon] Kuznets, yet the profession continued to churn out purely theoretical results without even knowing what facts needed to be explained. And it expected me to do the same. When I returned to France, I set out to collect the missing data.

To put it bluntly, the discipline of economics has yet to get over its childish passion for mathematics and for purely theoretical and often highly ideological speculation, at the expense of historical research and collaboration with other social sciences. Economists are all too often preoccupied with petty mathematical problems of interest only to themselves. This obsession with mathematics is an easy way of acquiring the appearance of scientificity without having to answer the far more complex questions posed by the world we live in. There is one great advantage to being an academic economist in France: here, economists are not highly respected in the academic and intellectual world or by political and financial elites. Hence they must set aside their contempt for other disciplines and their absurd claim to greater scientific legitimacy, despite the fact that they know almost nothing about anything.

(Although Piketty is obviously a French chauvinist, I appreciate his very American use of the phrase “university near Boston” to refer to MIT.)

Piketty’s investigation in Capital is dense and wide-ranging. He covers topics including the historical evolution of the capital/income ratio, inequality in labor and capital, the role of inheritance and “merit” in modern capitalism, and the progressive taxation of income and wealth. For each topic, two facts are immediately apparent. First is the dearth of economic literature. As Steinbaum writes,

[P]erhaps the greatest rebuke of Piketty to be found among academic economics is not contained in any of these overt or veiled attacks on his scholarship and interpretation, but rather in the deafening silence that greets it, as well as inequality in general, in broad swathes of the field—even to this day. You can search through the websites of several leading economics departments or the official lists of working papers curated by federal agencies and not come across a single publication that has any obvious or even secondary bearing on the themes raised by Capital in the Twenty-First Century, even in order to oppose them. It is as though the central facts, controversies, and policy proposals that have consumed our public debate about the economy for three years are of little-to-no importance to the people who are paid and tenured to conduct a lifetime’s research into how the economy works.

Second, though, is that among the economic literature that does exist, its pertinence to the realities of modern capitalism is laughably tenuous. I can’t do the entire book justice, but I will focus on a couple of interesting examples.

In his discussion of the importance of inheritance “flows” (gifts from living persons to their relatives, or transfers of estate from dead persons to those relatives), he notes the “life-cycle theory of consumption” that originated with Franco Modigliani in the 1950s. Modigliani later won the Nobel Prize in 1985, in part for this work. According to Piketty,

[In] Modigliani’s life-cycle theory, the primary reason for amassing wealth, especially in aging societies, is to pay for retirement, so that older individuals should consume most of their savings during old age and should therefore die with little to no wealth. This is the famous “Modigliani triangle,” taught to all students of economics, according to which wealth at first increases with age as individuals accumulate savings in anticipation of retirement and then decreases…But this theory of capital and its evolution in advanced societies, which is perfectly plausible a priori, cannot explain the observed facts — to put it mildly. Clearly, saving for retirement is only one of the many reasons — and not the most important reason — why people accumulate wealth: the desire to perpetuate the family fortune has always played a central role.

When I read this passage, my mind boggled. How does someone win a Nobel Prize for developing a theory that is so risibly at odds with the facts? I guess all of the billionaires giving money to Mitch McConnell to repeal the estate tax are simply irrational. If they had read Modigliani’s theory, they would have realized that there wouldn’t be any wealth at the end of their lives to tax.

I’ll close with an excerpt from Capital about Simon Kuznets, who was, indirectly and perversely, the main driving force behind the creation of the book. Kuznets studied inequality in the post-war period (he was one of the few economists to do so), and developed a “Kuznets curve” that described the evolution of inequality in industrializing societies.

According to [his] theory, inequality everywhere can be expected to follow a “bell curve.” In other words, inequality should first increase and then decrease over the course of industrialization and economic development. According to Kuznets, a first phase of naturally increasing inequality associated with the early stages of industrialization, which in the United States meant, broadly speaking, the nineteenth century, would be followed by a phase of sharply decreasing inequality, which in the United States allegedly began in the first half of the twentieth century.

Kuznets’ 1955 paper is enlightening. After reminding readers of all the reasons for interpreting the data cautiously and noting the obvious importance of exogenous shocks in the recent reduction of inequality in the United States, Kuznets suggests, almost innocently in passing, that the internal logic of economic development might also yield the same result, quite apart from any policy intervention or external shock. The idea was that inequalities increase in the early phases of industrialization, because only a minority is prepared to benefit from the new wealth that industrialization brings. Later, in more advanced phases of development, inequality automatically decreases as a larger and larger fraction of the population partakes of the fruits of economic growth.

The “advanced phase” of industrial development is supposed to have begun toward the end of the nineteenth or the beginning of the twentieth century in the industrialized countries, and the reduction of inequality observed in the United States between 1913 and 1948 could therefore be portrayed as one instance of a more general phenomenon, which should theoretically reproduce itself elsewhere, including underdeveloped countries then mired in postcolonial poverty. The data Kuznets had presented in his 1953 book suddenly became a powerful political weapon. He was well aware of the highly speculative nature of his theorizing. Nevertheless, by presenting such an optimistic theory in the context of a “presidential address” to the main professional association of US economists, an audience that was inclined to believe and disseminate the good news delivered by their prestigious leader, he knew that he would wield considerable influence: thus the “Kuznets curve” was born. In order to make sure that everyone understood what was at stake, he took care to remind his listeners that the intent of his optimistic predictions was quite simply to maintain the underdeveloped countries “within the orbit of the free world”. In large part, then, the theory of the Kuznets curve was a product of the Cold War.

It is difficult to divorce the construction of models and theory from self-serving and ulterior motives. When my postdoctoral advisor maintained that theory should be an equal partner to experiment, I assumed that that was his genuine belief, but a more cynical interpretation would not be unwarranted: where would there be room in academia for theoreticians like himself if experiments always had primacy? When reading Piketty’s dismal history of capitalism, and, in parallel, the dismal history of economics in explaining capitalism, I return to this thought: that if the models are so poor, it is because the motives behind their construction were too.


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