There is a new paper in Journal of Economic Perspectives. Its author, Dan Sichel, studies the price of nails since 1695 (image below). Most of you have already tuned off your attention by now. Please don’t do that: the price of nails is full of lessons about economic growth.

Indeed, Sichel is clear in the title in the subtitle about why we should care — nail prices offer “a window into economic change”. Why? Because we can use them to track the evolution of productivity over centuries.

Take a profit-maximizing firm and set up a constrained optimization problem like the one below. For simplicity, assume that there is only one input, labor. Assume also that a firm is in a relatively competitive market so as to remove the firm’s ability to affect prices so that, when you try to do your solutions, all the quantity-related variables will be subsumed into a n term that represent’s the firm share of the market which inches close to zero.

If you take your first order conditions and solve for A (the technological scalar). You will find this this identity

The table above showcases the strength of Sichel’s application of a relatively simple tool. Consider for example the period from 1791 to 1820. Real nail prices declined about 0.4 percent a year even though the cost of all inputs increased noticeably. This means that total factor productivity played a powerful role in pushing prices down (he estimates that advances in multifactor productivity pulled down nail prices by an average of 1.5 percentage points per year). This is massive and suggestive of great efficiency gains in America’s nail industry! In fact, this efficiency increases continued and accelerated to 1860 (reinforcing the thesis of economic historians like Lindert and Williamson in Unequal Gains that American had caught up to Britain by the Civil War).

I know you probably think that the price of nails is boring, but this is a great paper to teach how profit-maximizing (and constrained optimization) logic can be used to deal with problems of data paucity to speak to important economic changes in the past.

I had the title of this post sitting in “Drafts” for a couple months now, but Kris and Paul have given me good reason to actually write about it. These thoughts are largely off the cuff, but they do come from experience.

What is Agent-Based Modeling?

This is not actually as straight-forward question as one might think. If you define it broadly enough as, say, any model within which agents make decisions in accordance with pre-defined rules and assigned attributes, then the answer to the overarching question posed by this post becomes: well, actually, economics has been producing agent-based models for decades, but that answer is as annoying as it is useless.

Instead, let’s start with a minimal definition of an agent-based model:

1. They are composed of n >3 agents making independent decisions
2. Agents are individually realized within the model.
3. Decisions are made in accordance with pre-defined rules. These rules may or may not evolve over time, but the manner in which they evolve are themselves governed by pre-defined rules (e.g. learning, mutation, reproduction under selective pressures, etc).

If we stop at this minimalist definition, then the answer becomes only marginally less trivial, as essentially any dynamic programming/optimal control model within macroeconomics would meet the definition. This leads to what I consider the minimal definiton of an agent-based model as a distinct subclass of computational model:

1. Agents within the model are characterized by deep heterogeneity.
2. Agents exist within a finite environment which serves as a constraint in at least one dimension (lattice, sphere, network, etc).
3. Decisions are made sequentially and repeatedly over time

Now we’re getting farther into the weeds and beginning to differentiate from whole swaths of modern macroeconomics that either employ a “representative agent” or collapse agent attributes to the 1st and 2nd moments of distributions. But that doesn’t eliminate all of modern macro. If embracing heterogeneous agents in your models of macroeconomics, banking, etc, are of interest to you, there are scholars waiting to embrace you with open arms.

Which brings me to the final attribute that I believe fully distinguishes the bulk of the agent-based models and their advocates from modern economics:

1. Agent-based models exist as permanently dynamic creations, absent any reliance on equilibria as a final outcome, characterization, or prediction.

The departure from general or partial equilibria as outcomes or predictions is where the schism actually occurs and, I suspect, is where many purveyors found themselves with a research product they had a hard time selling to economists. Economics, perhaps more than any other social science, demands that theoretic predictions be testable and falsifiable. Agent-based models (ABMs) don’t always produce particularly tidy predictions that lend themselves to immediate validation. Which doesn’t preclude them from making a scientific contribution, but it puts them on unsteady footing for economists who are used to having a clear path from the model to the data.

OK, but really, why didn’t agent-based modeling happen?

As much as big, irreconcilable differences in scientific philosophy would make for a satisfying explanation, I suspect the most salient reasons are less sexy and, in turn, less flattering of the day-to-day realities of grinding out research in the social sciences. Here are a few.

Economics was already a “model” social science

One of the reasons mobile phones caught on faster in Africa than North America was an absence of infrastructure. The value add of going from “no phones” to “mobile phones” is far larger than going from “reliable land lines in every edifice” to “mobile phones”, making it easier to justify both investments in relevant infrastructure and bearing of personal costs. Such a thing occurred across the social sciences with regards to ABMs.

Rational choice and mathematical sociology always had a limited following. Evolutionary biologists were often alone in their mathematical modeling, computational biology barely existed, and cultural anthropologists were more excited about Marx’s “exchange spheres” than they were about formal models of any kind. For a PhD student in these fields, the first time they saw a Netlogo demonstration of an agent based model, they were seeing something never previously available to their field: the ability to formalize their own theories in a way fully exogenous to themselves. There would be no fighting about what their words actually meant, whose ideas they were mischaracterizing, what they were actually predicting. Their critics, be it journal referees or thesis committee members, would have no choice but to confront their theory as an independent entity in the world.

This advantage of formality, of independent objectivity, in agent-based modeling was not something new to economics. While critics have many (often correct) complaints about modern economics, it’s rare to air concerns that economics is insufficiently formal or mathematized.

Too many “thought leaders”, not enough science

Axtell and Epstein wrote their landmark book “Growing Artificial Societies” in 1996. In it they produced a series of toy simulation models within which simple two-good economies emerged. This wasn’t revolutionary in it’s predictions by any means (whole swaths of macro models were able to make comparable predictions for two decades prior), but the elegance through which minimalist computer code could produce recognizable markets emergent from individual agent decisions was just incredible. The potential to readers was immediately obvious: if we can produce such things from 100 lines of code, what could we simulate the fully realized power of modern programming?

What came next was…still more people evangelizing and extolling the power of ABMs to revolutionize economics. What didn’t come were new models. Forget revolutionary, its hard to even find models that were useful or at least interesting. The ratio of “ABMs are gonna be great” books and articles to actual economic models is disappointing at best, catastrophic to the field at worst.

There were a couple early models that got attention (the artificial Anastazi comes to mind), but after a few years everyone noticed that same 2-3 models were still be brought up as examples by evangelists, and none of them had meaningful economic content. As for the new models that did end up floating out there, there was also an oversupply of “big models”, with millions (billions) of agents and gargantuan amounts of code that intended to make predictions about enormous chaotic systems. Models, such as the Santa Fe Artificial Stock Market, tried to broadly replicate the dynamics of actually stock markets across a large number of dimensions. Such ambitions were greeted with skepticism by economics for a variety of reasons, not least of which the “curse of dimensionality”, which limits what you can learn about underlying mechanisms when the number of modeler choices exceeds your ability to test them or, for that matter, verify their internal coherence. For better or worse, these models felt akin to amateurs trying to predict a town’s weather 30 days out.

Bad models drove out good

The problem of too few good models was closely followed by the over-supply of bad models. Agent-based modeling, for good and for ill, is not a technique with high entry costs. A successful macroeconomic theorist is effectively a Masters-level mathematician, bachelors level computer programmer, and PhD economist. Netlogo programming can be learned in a week. You can get really good at programming agent-based models in a dedicated summer.

This isn’t unto itself a problem, but I can tell you this: in my first 5 years as an assistant professor, I was asked to review at least 100 papers built around agent-based models. I’m not sure if any of them were any good. I am sure that many of them were extremely bad. Most concerning is that I don’t think I learned anything from any of them. The costs of producing bad ABM papers is much lower than the costs of producing bad theory papers based on pure math. Bad science is often evolutionarlily selected for in modern science, a dynamic that in the case of ABMs was only amplified by a lower cost supply curve.

Now, here’s the thing: there was probably huge selection effects into what I interacted with. I doubt I was getting the best papers sent to me for review given my status in the field. But the quantity of bad papers was astonishing. They were just too easy too churn out. I suspect that some decent papers were lost in haystack of ad hoc pseudoscience and, in turn, some decent scientific careers probably got lost in the shuffle. More than once I had the thought “Editors are going to start rolling their eyes every time they see the term agent-based modeling if this what keeps coming across their desks.” Combined with the fact that ABMs are tricky to evaluate because you really need to go through the code to know what is driving the results, I think a lot good modelers got lumped in with the dreck.

[Not for nothing, it wasn’t uncommon for ABM papers to spend the bulk of the paper describing model outputs, while having nearly nothing about model inputs (i.e. rules, code, math, etc). These models were essentially black boxes that expected you to take their coherence on faith. I should note here that I haven’t really kept up with the field in the past few years. Hopefully transparency norms have improved, particularly in biological, ecological, and anthropological modeling, where ABMs have thrived to a far greater extent.]

The empirical revolution took hold of economics

I’ve save the biggest reason for last, but honestly I think it dwarfs the others.

The same rise in cheap computational power that gave rise to other forms of computational modeling, including ABMs, came along with the plummeting cost of data creation, storage, analysis, and access. By 2010 it was already increasingly clear that theory was taking a backseat in economics. Not because we were becoming an a-theoretic discipline (far from it), but because the marginal contribution of theory against the body of broadly accepted economic framings was small compared to those made by empirically testing the predictions of the existing body of theories against real data. The questions were no longer “How do we mentally organize and make sense of the world”, but instead “What is the actual measured effect of X on Y?” Theory gave way to statistical identification. Modeling technique gave way to causal inference.

Agent-based models are hard to empirically evaluate and test

Which gives way to a sort of subsidiary problem. It is more difficult for agent-based models to take advantage of the new data-rich world we live in. They don’t produce neatly direct predictions the way that microeconomic theories do, nor do they lend themselves to measured empirical validation in the same way as general equilibrium predictions of macroeconomic models. Empirical validation is by no means impossible, but it requires the matching of observed dynamics or patterns, which is generally a taller order. In this way, agent-based computational models are a bit of a throwback to the days of “high theory”, making for interesting discussion but of secondary importance when it comes to the assigning of journal real estate that makes and breaks careers.

Bonus story

I once presented my ABM paper on emergent religious divides, only to have an audience member become extremely upset, closing with the denouncement that “This isn’t agent-based modeling, this is economics!” That was my first exposure to the theme of ABMs as “antidote” to the hegemony of economics and all of its false prophecies. The idea that the destiny of ABMs was to unseat economics as the queen of the social sciences was probably an effective marketing strategy in many hallways, but not so much in economics departments (well, maybe at The New School).

So why should economists give agent-based modeling another shot?

That’s another post for another day. If you’re curious though, I did write about how and why ABMs are useful for economists interested in the study of religious groups and movements. The logic of that piece applies to anyone interested in studying the macroscopic dynamics characterizing social norms, group formation and decay cycles, and how social outliers can pull entire populations in interesting directions.

UPDATED 1/2/2026

I finally got around to writing the promised sequel post. If you got this far, decent chance you’ll find it interesting.

The Kyiv department of economics has created what appears to be a vetted and relatively efficient channel for donating to the care of the Ukraine people during this crisis. You can donate via credit card or crypto. This is very much one of those cases where I believe every little bit helps. Consider:

1. Russia planning and logistical failures mean a continuing heavy invasion may not be sustainable, leading instead to a long runing siege. If this is the case, then it becomes all the more important to get basic humanitarian resources in now in order to minimize the suffering caused by the siege and minimize the odds of Russian success.
2. Ukrainian resistance depends as much on morale as it does lethal resources. Knowing their families are fed and receiving basic healthcare is critical.
3. If the micro-returns protecting a Ukrainian soldier or feeding a Ukrainian family aren’t enough for you, here’s a macro one: if the autocratic leader of an increasingly fascist regime with the strategic advantage of a nuclear arsenal is rebuffed in the Ukraine by a heroic local resistance partnered by global economic sanctions, it will serve as a signal to every leader with similar aspirations that success is less likely than they previously estimated. If your donation can help force a Bayesian update on dangerous autocrats and strongmen everywhere, that seems like nothing less than a perfectly rational act of utility maximization to me.

Generally, when you do your microeconomics class you get to see isoquants. I mean, I hope you get to see them (some principles class dont introduce them and are left to intermediate classes). But when you do, they look like this:

Its a pretty conventional approach. However, there is a neat article in History of Political Economy by Peter Lloyd (2012) titled “the discovery of the isoquant“. The paper assigns the original idea, rather than to the usual suspect of Abba Lerner in 1933, to W.E. Johnson in 1913 as A.L. Bowley was referring to his “isoquant” in a work dated from 1924 (from which the image is drawn). But what is more interesting that the originator of the idea is how the idea has morphed from another of its early formulations. In the 1920s and 1930s, Ragnar Frisch was teaching his price theory classes in Norway and depicted isoquants in the following manner in his lectures notes.

Do you notice something different about Frisch’s 1929 (or 1930) lectures relative to the usual isoquants we know and love today? Watch the end of each isoquant. They seem to “arc” do they not? How could an isoquant have such a bent? Most economists are probably so used to using isoquants that do not bend (except for perfect complements) that it will take a minute to answer. Well, here is the answer: its because Frisch was assuming that the production function from which the isoquant is derived had a maximum which means that the marginal product of an input could become negative. This is in stark contrast with our usual way to assume production functions as smoothly declining (but never negative) marginal products. This is why Frisch includes an arc to this shape (a backward bend).

Why did we move away from Frisch’s depiction? Well think about the economic meaning of a negative meaning marginal product. It means that a firm would be better off scaling down production regardless of anything else. Its a straightforward proposition to understand why in all settings, a firm would automatically from such an “uneconomic” zone. In other words, we should never expect firms to continually operate in a zone of negative marginal product. Ergo, the “bend”/”arc” is economically trivial or irrelevant. Removing it simplifies the discussion and formulation but also does something subtle — it sneaks in a claim rationality of behavior from firmowners and operators.

This is a good setup for a question to ask your students in an advanced microeconomics class that isnt just about the mathematics but about what the mathematical formulations mean economically!

The Ukraine is as of this writing holding its ground and cities against the invading Russian army. There are a host of reasons, from incredible Ukrainian bravery, unmatched global sanctions clamping down on the Russian economy, to tactical and military failure on the part of Russia. There is nothing I can contribute beyond the linked sources or the constant flow of information coming out in real time. What I would like to add is one bit of broad economic context.

Baumol’s famous “cost disease” idea works like this: as a society gets richer the opportunity cost of everyone’s time increases. This makes certain services, like getting a haircut, more expensive because there is no substitute for a person’s time, no technology to increase labor efficiency, when it comes to cutting hair. Economists never stop speaking of the opportunity cost of time, but I sometimes think we undersell the importance of the concept. Lives are finite, time is the only thing that matters. To say that the opportunity cost of time has increased is to say that lives have been made better. Baumol’s cost disease restated: Anything that improves a person’s life makes claims on their time more dear.

The same logic applies to risk and to armies. Military technology continues to advance, but there as yet remains no substitute for soldiers, particularly if you want to occupy territory (there are plenty of superior substitutes if you just want to take lives and scorch the earth, but thats a different story). While the “labor productivity” of soldiers as occupying forces has remained relatively stagnant, the lives of the soldiers themselves has improved with everyone else’s. As their lives improve, the bar for what they are willing to risk their lives (and their conscience) for gets higher. For Ukrainians defending their homes and families from invaders, the risk is more than worth it and they are awing the world with their bravery everyday. Russian soldiers, on the other hand, are surrendering, scrolling Tinder, and abandoning tanks.

When historians point to generals making the mistake of fighting the “previous war”, they are usually referring to the obsolescence of tactics by new military technology. What I would like to consider is the possibility of Putin trying to fight a war with the previous soldiers. The last time the Russian army marched into a country prepared to offer significant resistance was the Soviet invasion of Afghanistan (Crimea, to my understanding, was never in a position to offer significant miltary resistance). Russian soldiers and their families today have very different lives. Only a quarter are conscripts, and none are facing a life without options outside of the army. The state is not the sole means of earning a living. The Russian market may be fractured and corrupted by a kleptocratic regime, but it’s still a market, one which has led to tremendous improvements in the quality of life enjoyed by citizens. These aren’t men and women enlisted into a religious or philosophical crusade, let alone ordinary men and women fighting to keep their homeland. Soldiers have lives they don’t just hold dear for the sake of survival – they have lives in the modern world they actively enjoy.

There have been no shortage of pundits who, in the form of cliched memes and cosplay masculinity, have speculated that nations of the developed world would not sufficiently come to the aid the Ukraine, or any country invaded by a foreign power, for the simple reason that we have, in our modern decadence, grown soft. What they consistently fail to appreciate is that this is a great outcome. People holding their lives with greater value is the very definition of progress. What is most perplexing, however, is why this idea of softness born of wealth is not applicable to Russians. (As for the theory that the Ukraine would fold overnight because it doesn’t make enough babies, that theory looks less viable, even if Russia achieves any of their goals.)

Working down the supply chain

Now, let’s be clear: soldiers are soldiers, and they are still more likely than not to obey orders and carry out their duties, if nothing else then out of a sense of obligation to one another. The opportunity cost effects of improved private lives are no doubt dampened. But armies depend on a lot more than just soldiers.

Russia remains, relative to the West, a poorer country in terms of GDP per capita, but nonetheless a modern economy where individuals enjoy the luxuries of a developed economy: mobile phones, heat in the winter, food security, transportation, etc. History is filled with stories of wars won and lost because of lack for boots, gasoline, and coats. In the Soviet Union, the army may have been underprovisioned relative to their counterparts from wealthier market economies, but they weren’t beholden to the rules of a market economy. Exclusion from a global system of payments wouldn’t be able to immediately choke off resources. Even if the soldiers marching are entirely severed from their lives in the private market, the supply chains they depend on are not, and the civilians in that supply chain expect to get paid.

Did Putin expect that supplies would arrive while the Ruble plummeted? Did he expect middlemen to incur losses as the entire economy was frozen by global sanctions? Did he expect reliable logistical support from soldiers and civilians while their spouses lined up at ATMs during bank runs? You know what? Maybe he did. Or at least, maybe he thought that the Ukraine would capitulate before sanctions could become salient to the supplying of his army. I have no idea. What I want us to consider is that modern armies depend on more than soldiers to function. Without a monopoly on means for supporting a family or an omnipresent threat of the Gulag, armies depend on citizens who can look at the physical and economic risk they are taking on, and coming to the conclusion that “this is worth it.” I have a hard time believing any Russian citizen, wage earner or oligarch, is looking at what is already an economy-enveloping sinkhole borne of greed for historical infamy, and thinking this is worth it for anyone but Putin himself.

This context of war in a time of better lives places economic sanctions as a geopolitical tool in a new light. Most countries cannot hope to put together an irresistible military force without the resources of a modern developed economy. A modern developed economy will invariably lead to wealthier citizens with a greater opportunity cost of time and risking their lives. The military will, in turn, become more dependent on private citizens to provision their armies. Sanctions in this new world don’t just punish citizens and encourage some form of open revolt, they actually choke off the military from the economies they remain entirely coupled to and dependent on.

If Putin is repelled, it will more than anything be because of the bravery of 44 million Ukrainians who stood their ground and protected their homes. But the military lesson, the historical lesson, may very well be that men and women with good lives make for poor invaders. The best, most peaceful future might just be one where we all have too much too lose.

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Brief Addenum: How this “cost disease” effect would impact the probability of a nuclear strike is complex and in no way clear to me. On the one hand, if Putin believes that he has no possibility of victory without a credible threat of a strike, then it raises the possibility of war, if only through greater chance of error admidst readiness. On the other hand, it’s not like there are no middlemen between Putin and “the button.” Each link in that chain may be more likely to be insubordinate if they view their modern life as too great a sacrifice. I just don’t know.