Complexity economics is the application of ideas from complex systems to economics. But what is a complex system?

In my physics courses at Stanford, I learned a great deal about motion, force and energy. My courses took a reductionist approach: The goal was to understand the fundamental rules that determine the interactions of simple things – like masses on springs or elementary particles – and study them in simple contexts. In celestial mechanics, for example, we learned how to calculate the orbits of two bodies, such as a single planet and the sun. But more complicated situations, such as the orbits of three such bodies, were omitted because the equations couldn’t be solved.

I couldn’t help but ponder the big questions that my courses were not addressing. I wanted something that was the opposite of reductionism. Given that all the fundamental forces of nature are simple interactions between relatively simple physical things, how can this lead to phenomena such as life and intelligence? How did matter spontaneously organize itself in the origin of life? How did evolution create such a remarkable thing as the human brain?

When I was in graduate school at the University of California (Santa Cruz), I discovered cybernetics, which was the precursor of complex-systems theory. My friends and I read and discussed Norbert Wiener’s ideas about feedback and control, Claude Shannon’s theory of information, John von Neumann’s self-reproducing automaton and Erwin Schrödinger’s reflections about life and the mind. The big question we pondered more than all others was the mystery of self-organization: how can disorganized configurations of matter spontaneously become organized?

Later, at Los Alamos, I organized conferences and workshops on “Cellular Automata,” “Evolution, Games and Learning” and similar topics, and invited leading scholars who were thinking about these things to visit, creating a hub of activity. The senior fellows at Los Alamos decided that this kind of work needed its own institution, free from the taint of a weapons laboratory. So, in 1984, the Los Alamos physical chemist George Cowan cofounded (with theoretical physicist Murray Gell-Mann) the Santa Fe Institute, and shortly afterward the phrase “complex systems” entered our vocabulary.

I became affiliated with SFI, and, in 1988, I started the Complex Systems Group at Los Alamos and recruited several outstanding postdoctoral researchers who later became leaders in the field. There are now thousands of scientists devoted to the study of complex systems scattered across almost every discipline in the physical, natural and social sciences, including economics.

What is a complex system? By definition, a system is complex if it has “emergent properties.” I’ve already mentioned the example of the brain. We humans don’t just think – we are conscious, with a sophisticated model of ourselves, the world around us and how we fit into it. Consciousness isn’t present in the individual building blocks – it emerges from the interaction of billions of neurons. In human brains and other complex systems, emergence happens when building blocks are connected to give rise to behavior qualitatively different from what any of the building blocks can do alone.

Ant colonies are another classic example. Individual ants are simple creatures with only about 250,000 neurons, so the reasoning power of individual ants is extremely limited. But ants communicate through chemical signals and touch. This gives a colony of ants computational powers that individual ants lack, and through their collective interactions they can do surprisingly sophisticated things. Ant colonies cultivate fungi, raise aphids, and fight wars. Individual ants can’t do these things. There is no Super Ant directing the colony – the queen is just an egg factory. Instead, these sophisticated collective behaviors emerge from the interactions of many ants.

Emergent behavior can be counterintuitive. The idea that thought and consciousness are purely mechanical processes that can be explained from the bottom up is so radical and difficult to fathom that it was not widely accepted until the 20th century. Given that farming was not invented by Homo sapiens until what we term the agricultural revolution of about 10,000 years ago, how could simple creatures like ants have been doing something similar for millions of years?

Complex systems like the brain or an ant colony are called “adaptive complex systems.” They are distinguished from ordinary complex systems with simpler emergent behaviors by the fact that their properties have evolved over time through a process of selection. Consciousness doesn’t emerge by simply hooking up neurons at random; they have to be connected in just the right way. It took evolution billions of years of trial and error to invent the human brain.

Thinking in evolutionary terms is essential for understanding adaptive complex systems. And evolution is not just about biology; it applies to a broad range of adaptive complex systems including economics and the other social sciences. Firms, for example, have to make profits or they quickly go out of business, illustrating that selection underlies the essence of how capitalist economies function. The study of adaptive complex systems has helped clarify the basic principles of evolution so that they can be applied more generally outside of biology.

Can We Make Better Economic Predictions?

Through science, things that appear to be random can be rendered predictable. Prediction is enormously useful because it allows us to make sensible decisions. We tend to take for granted the myriad ways that science has fundamentally changed our view of the world. The Trojan War from Greek mythology provides an example.

After Agamemnon gathered his troops to fight Troy, the wind refused to blow, so his fleet could not set sail. He consulted Calchas, the seer, who told him that he must sacrifice his beloved daughter Iphigenia to appease the goddess Artemis. He had his daughter killed, and the winds began to blow.

Modern science casts a different light on this story. Unlike the ancient Greeks, we see no conceivable causal connection between Iphigenia’s sacrifice and whether or not the wind blows. Today, a father who acted as Agamemnon did would be regarded as utterly mad. A modern Agamemnon would simply consult the weather forecast, note the high-pressure zone hovering over Argos and tell his men to wait a few days until the wind started to blow again. Physics has transformed something formerly believed to depend on the whims of the gods into a predictable event whose causal mechanisms are well understood.

Fast forward to contemporary Greece where an example shows that we still lack broad agreement about essential cause-and-effect relationships in economics. Since 2008, the Greeks have suffered one of the worst depressions in modern times. Greek GDP dipped by 30 percent from its peak, unemployment reached 27 percent, and in 2021 almost half of Greek young people (aged 15-24) were still out of work. Paul Krugman and many others have argued that all this suffering could have been avoided if only Germany had not forced Greece to adopt a policy of austerity (budgetary belt-tightening) just when economic stimulus was most needed. In contrast, Wolfgang Schäuble, the German finance minister, along with a host of prominent economists, insisted that austerity was unavoidable and the only way for Greece to become solvent again.

Who was right? There is no widely agreed-upon economic model that can answer that question. This is not unusual: while the majority of economists agree on some things, in many cases an array of different models make divergent predictions, leaving people free to choose the model they like best, based on ideology, politics and self-interest. We can break out of this stalemate only by finding models whose predictions are consistently good enough to gain a wide level of credibility.

My goal in this book is to set out a vision for how we can build models that make better economic predictions. Surprisingly, many economists do not agree on the importance of this goal. To quote two prominent Harvard economists, David Laibson and Xavier Gabaix:

Predictive precision is infrequently emphasized in economics research. … In this sense, economic research differs from research in the natural sciences, particularly physics. We hope that economists will close this gap. Models that make weak predictions (or no predictions) are limited in their ability to advance economic understanding of the world.

When I emphasize this in my talks, economists often respond that the central goal of economics is to provide a conceptual framework for thinking about the world and evaluating policy choices. I wholeheartedly agree that having a conceptual framework is central. But in my view, this only makes the quest for better predictions even more important. If we can’t make reliable predictions, how do we know if the conceptual framework is correct?

It is easy to forget that prediction is interwoven into everything we do. To pick up a glass of water, your brain has to predict how your muscles need to be stimulated to get your hand to move to the glass and grasp it, then predict how to compensate for the weight of the glass as you bring it to your lips to drink. Similarly, every policy decision represents a prediction that the economy is likely to do better if that choice is made.

I should be clear about what I mean by the word “prediction.” Niels Bohr is said to have declared that “prediction is very difficult, especially if it’s about the future.” This remark seems ironic: Aren’t all predictions about the future?

Actually, no, not at all. Consider Boyle’s Law. In 1662, Robert Boyle invented a device that allowed him to control the volume of air inside a container and showed that the air pressure is inversely proportional to the volume. In other words, if you know the volume, you can predict the pressure, and vice versa. This is scientific prediction, true at any point in time – present, past or future.

Of course, many predictions are explicitly about the future. For instance, central banks and treasury departments use models to make predictions about GDP and unemployment. Models provide a sandbox where they can test policy options to understand how well they work and how they might be revised to work better. What happens if we raise interest rates? What happens if we require banks to hold more capital? What happens if we raise the minimum wage? Implement a universal basic income? Decrease taxes? Leave everything as it is? Bad models lead to bad decisions.

Predictions are also important because they test models and tell us whether we can trust them. Does the model we’re using capture cause-and-effect relationships well enough? If the model fails to make accurate predictions about the world as it is now, we can’t trust it to correctly answer the “what-if” questions we need to pose when contemplating a change in policy. Unfortunately, even after decades of hard work by several generations of macroeconomists, Nobel Laureates in economics like Paul Romer question whether the effectiveness of macroeconomic forecasting has improved at all.

Can we do better? Many argue that this is impossible for several reasons. As I’ve already explained, economics is about people, and because people can think their behavior is hard to predict. Or there may be fundamental limits: The economy may have intrinsic properties, such as market efficiency or chaos, that defy accurate prediction by any model, no matter how good. We will never be able to predict the economy perfectly – far from it – but we can do much better than we are doing now.

In the last few years the concept of self-organizing systems – of complex systems in which randomness and chaos seem spontaneously to evolve into unexpected order – has become an increasingly influential idea that links together researchers in many fields, from artificial intelligence to chemistry, from evolution to geology. For whatever reason, however, this movement has largely passed economic theory by. It is time to see how the new ideas can be applied to that immensely complex, but indisputably self-organizing system we call the economy. — Paul Krugman (1996)

Twenty-five years ago, the distinguished economist Paul Krugman proposed that the time had come to study the economy as a complex system. Unfortunately, his call largely went unheeded by the mainstream, whose conceptual models and mathematical toolkit were not well suited to take advantage of complexity theory, and Krugman himself went on to pursue other things, such as becoming a columnist for The New York Times.

The remarkable evolution of civilization, from the early days of Homo sapiens until now, is a dramatic illustration of Krugman’s point that the economy is a self-organizing complex system. The economy is just a name for the process of specialization, cooperation and competition that supports us. The sustainable human population has grown by several orders of magnitude due to technological progress and advances in social organization, which underpin our evolving economy – without it, most of us would not exist.

Because of the emergent properties of the economy, most of our lives are far more prosperous and secure than they would be if we were Robinson Crusoes acting on our own. The economy’s organization of our collective behavior enables us to create vaccines, predict the weather, go to the moon and do all sorts of other things that none of us could ever accomplish alone.

Because the economy is an adaptive complex system, biological concepts such as metabolism, ecology and evolution are very useful for thinking about it. These are more than just metaphors; they contain general principles that help us understand how the economy is organized and how it works.

How Concepts from Biology Help Us Understand the Economy

The idea that economics could profit from concepts in biology has been around a long time. In 1890, in his Principles of Economics, Alfred Marshall, a key founder of neoclassical economics, famously wrote, “The Mecca of the economist lies in economic biology.” Writing in the 1940s, the Austrian American political economist Joseph Schumpeter emphasized that capitalism can be understood only as an evolutionary process of continuous innovation and creative destruction.

In 1982, Richard Nelson and Sidney Winter’s An Evolutionary Theory of Economic Change made a compelling argument that the evolutionary perspective is essential for understanding how innovation drives economic growth and alters the structure of the economy over time. But Nelson and Winter were prescient when they wrote, “We expect that many of our economist colleagues will be reluctant to accept the second premise of our work – that a major reconstruction of the theoretical foundations of our discipline is a precondition for significant growth in our understanding of economic change.” Ideas from biology have not, so far, led to quantitative theories making useful, falsifiable predictions. Complexity economics is starting to change this.

Adam Smith’s 1776 book The Wealth of Nations, widely regarded as the foundation of economics, describes the economy as a complex system: “In the lone houses and very small villages which are scattered about in so desert a country as the Highlands of Scotland,” he wrote, “every farmer must be butcher, baker and brewer for his own family.” In towns and cities, however, it was far more efficient for butchers to sell meat, brewers to make beer and bakers to bake bread than for each citizen to make all their own provisions. Trade enabled people to specialize in what each did best, and the promise of a good income motivated them not only to do things well but also to innovate.

Smith understood that the economy as a whole behaves very differently from the individuals who comprise it. Stated in modern terms, he saw the economy as an emergent phenomenon.

We can restate Smith’s key insight in ecological terms: The economy is organized as an ecosystem of specialists. In biology, the word ecosystem refers to a collection of species who interact with and affect each other. Each is a specialist, with its own unique strategy for extracting energy from the environment in order to survive and reproduce.

Species eat one another, compete with one another, cooperate with one another and collectively alter the environment. Understanding the interactions between species is essential. If you want to understand grass, you must also think about lions. Lions protect grass: If the lions go extinct, the zebra population will rise and grass will decline. To make sense of the biosphere, it’s not enough to study species in isolation. We must understand how they affect each other and alter their shared environment.

Similarly, the economy is a complex ecosystem of specialized organizations populated by workers who belong to households, whose members are consumers. In developed countries, consumption choices vary enormously – many of the products I consume are likely substantially different from those you consume. There are thousands of different kinds of firms making products, which can either be goods, like Pop-Tarts or screwdrivers, or services, like legal advice and caregiving. Each firm tends to be highly specialized, because the production of most of the goods and services in the modern economy requires specific knowledge that takes a great deal of time and effort to acquire, and it is more useful and rewarding to specialize than to try doing many different things.

The know-how embodied in firms and other organizations is the result of specialized occupations, each with its own unique knowledge and set of skills. Other types of organizations, such as governments and schools, play an important role in the economy. Understanding this ecosystem means thinking about the economy in terms of networks, which provide a universal language describing the operations of complex systems.

Economics = Accounting + Behavior

Networks are one of the core ideas in complex systems. For example, your extended social network describes your friends, your friends’ friends and so on. You can visualize your extended social network by thinking of the people in it as nodes, which you can represent by dots, with links between friends, which you can represent by lines. If you want to be introduced to someone you don’t already know, knowledge of your extended social network allows you to understand who could introduce you, or who could introduce you to someone who could introduce you. As famously shown by Stanley Milgram, we can reach almost anyone with only six degrees of separation.

Networks identify the essential building blocks of a complex system and supply a schematic view of their interactions. In a transportation network, the nodes might be cities and highways might be links. In a schematic of the financial system, the nodes might be banks and the links might be loans or investments. I say “might” because there are usually many possible choices for nodes and links, depending on what one wants to understand. For example, the links between cities could also be based on trade, and the links between banks could be based on their common asset holdings.

The skeleton of the modern economy is a vast network of balance sheets. Each balance sheet is a list of assets and liabilities, which can be physical goods and services or contracts (money, for example, is a contract). The nodes in the network correspond to organizations – households, corporations, governments or any organization that might have a balance sheet either explicitly or implicitly. Since contracts are by definition agreements between two or more parties, they link balance sheets together. My home-insurance policy is an asset on my balance sheet, but it is a liability for the company that issued it. Balance sheets are also linked by transactions, which cause goods and contracts to flow from one balance sheet to another.

The network of balance sheets underlying the modern economy is truly vast. Globally there are roughly two billion households and 200 million firms, as well as governments and other types of organizations that are consumers and suppliers of goods and services. Members of households are employed by firms, governments and other nonprofit organizations. And households (especially in developed countries) consume thousands of different products, creating many trillions of links between households and firms. In addition, there are trillions of active contracts – so many it is difficult to count. The global network of balance sheets is constantly in flux. Every transaction causes something to leave one balance sheet and appear on another. There is constant turnover, causing some nodes to disappear and new nodes to be added. Innovation creates new types of goods and new contracts. The network of balance sheets in the modern world is vastly more complicated and interconnected than it was 10,000 years ago.

We can think about the economy schematically as an interaction of accounting and human decision-making. Accounting is represented by the network of balance sheets, which continually changes as people make economic decisions.

These decisions take many forms: What product to consume? What product to offer? Whom to hire? When to borrow? How much and from whom? All these decisions constitute economic activity. To understand the economy, we have to understand human behavior as it relates to economic decision-making, and we need to understand how this interacts with the underlying network of balance sheets.

Accounting and decision-making both pose difficult problems, but in very different ways. Accounting is complicated but well understood, whereas decision-making requires an understanding of human nature that is still incomplete.

Accounting consists of a mechanical set of rules that measure economic activity. Accounting has a central conservation law, “equity equals assets minus liabilities,” much like the conservation laws for energy, momentum and other quantities that play a central role in physics. Tracking and understanding the vast, complicated, interconnected balance sheets of the real global economy is challenging. We now have enough computer power that this is possible, but we aren’t taking full advantage of this capability.

Because people don’t follow simple mechanical rules, modeling human decision-making is an even bigger challenge. Understanding how people make decisions, both as individuals and in groups, is an important goal of the disciplines of psychology, sociology, anthropology and political science. The past 50 years have seen the emergence of behavioral economics, which draws on insights from other social sciences to study how we make decisions that affect balance sheets. But we still lack a comprehensive theory of economic decision-making.

The network of global balance sheets can’t be studied in literal detail – it is too huge and complicated, and much of the necessary information is opaque due to confidentiality. We have to simplify the problem by dividing the network of balance sheets up into pieces and aggregating each piece. We take averages for countries or regions and study their interactions. GDP, for example, is a measure of economic activity. Macroeconomics studies the interactions of aggregate quantities, like GDP, unemployment, inflation and interest rates, within and between nations. Microeconomics studies the interactions of balance sheets on a finer scale, but without trying to look at the whole economy. In Chapters 5 and 6 we will discuss how traditional economics understands the network of balance sheets from the top down, while complexity economics understands it from the bottom up.

Understanding the Metabolism of Civilization

The labor process … is purposeful activity aimed at the production of use-values. It is an appropriation on what exists in nature for the requirements of man. It is the universal condition for the metabolic interaction between man and nature … common to all forms of society in which human beings live. — Karl Marx (1867)

Back in the 1980s, in the early days of complex-systems science, the main focus was on the problem of self-organization. How do organized configurations of matter, like life or the brain, spontaneously emerge from the disorganized background following the creation of the universe? While important and fascinating, this is a problem that will likely take centuries if not millennia to solve, and so far we have made only incremental progress.

As the science of complex systems matured, it branched out to tackle easier problems with more immediate practical applications. Some of the most important early successes involved networks. The pioneering sociologist Mark Granovetter introduced the concept of social networks, as discussed earlier, in which the nodes are people or firms and the links between them can take many different forms. He showed how the economic relationships between people or firms are “embedded” in social networks, making them behave differently than they would in an abstract market setting.

Complex-systems scientists such as Mark Newman, my colleague at SFI, embraced the idea of networks and developed new mathematical methods for applications to data. They showed how networks could be used to understand and improve many different real-world systems, such as how to structure connections between internet hubs to make them more reliable and less prone to sabotage, or how to allocate vaccines to ensure the maximum effect in reducing the spread of disease.

Network modeling is one of the few complex-systems ideas that has made its way into mainstream economics. Stanford economist Matthew Jackson (like me, an external faculty member of SFI) has produced a body of
insightful work on the role of networks in economics, showing, for example, how social networks influence employment and inequality.

Representing a system as a network begins by identifying its building blocks and their interactions, asking, “What are the most important nodes?” and “Are there communities? If so, what are they?” (Mathematically speaking, a community is a set of nodes that interact with one another much more strongly than they do with other nodes.)

Websites provide a good example. The most important websites are not necessarily those with the most traffic or those that are linked to the largest number of other websites. Rather, they are the websites that are linked to the largest number of other important websites. Although this sounds circular, network theory provides a way to unravel this conundrum and identify the websites that are the most important.

To see how the algorithm works, imagine a “random walker” who starts at a random node (website) in the network. The walker then randomly jumps to one of the websites that the starting website is linked to. This process is repeated many times as the walker wanders through all the nodes. The importance of any one of these websites is proportional to the frequency with which it is visited. This algorithm, which is called PageRank, was patented by Larry Page and Sergey Brin and is used in the Google search engine.

Network analysis is also useful for understanding lending between banks. In the interbank-lending network, banks are nodes and loans between banks are links. If a bank cannot pay back its lenders, this may cause the lenders to default as well, setting off a chain reaction.

Suppose you’re a regulator and want to keep the financial system from collapsing. Which banks are most important? If you can prop up only a few, which should you choose? The biggest banks? The banks that lend to the largest number of other banks? In fact, the answer turns out to be similar to the story for websites: the most important banks are those connected to the largest number of other important banks.

The same PageRank algorithm that was invented for web pages can be used to identify the banks whose collapse would cause the most harm. This makes it possible to identify the best banks to support during a financial crisis, and has been used by organizations such as the European Central Bank to identify what they call Systemically Important Financial Institutions. That the same basic idea can be used to understand systems as different as banks and the internet (and many others) illustrates the value of complex-systems thinking.

Network theory also offers a conceptual framework that helps us analyze ecologies of specialists in the economy. This approach has practical applications, like making better predictions about economic growth or understanding how quickly the job force can adapt to technological change. In this chapter, I present a static network model for production networks that was developed in mainstream economics and discuss how my collaborators and I modified it to successfully predict economic growth. This was a key step in constructing the model that successfully predicted the economic impact of the Covid pandemic.

My introduction to networks came about because of my interest in the origin of life. My early papers on networks in the mid-1980s were written in collaboration with Norman Packard. We developed the concept of meta-dynamical systems – networks that could change in response to their environment and also evolve over time.

In one of the papers, we teamed up with Stuart Kauffman, a remarkably creative medical doctor and developmental biologist who joined SFI’s faculty a few years later, to make a model for the prebiotic origin of life. We used networks to ask whether metabolisms might have existed even before the origin of life as we know it on the earth now. In other words, we posited the existence of a possible simpler form of life that you might call “proto-life,” which might have been a precursor to prokaryotes, the earliest of Earth’s life forms.

Richard Bagley, a chemistry graduate student at UC San Diego, came to Los Alamos to work with me and wrote his thesis there under my supervision. Rick’s thesis was a model for the origin of proto-life. It built on the abstract chemical networks that Stuart, Norman and I had developed, going beyond our schematic efforts and explicitly simulating polymer nodes and the chemical reactions linking them. His work showed that our hypothesis of the spontaneous emergence of a prebiotic metabolism was indeed plausible.

The simulated metabolism that Rick built is closely analogous to the way goods and services are produced in the economy. But before I can explain why this analogy holds, it’s helpful to describe the way the economy produces things in network terms. Economic activity in the modern economy is highly specialized. The production network reflects the division of labor in producing goods and services. The nodes are companies that provide those goods and services, and the links are the transactions among companies or between companies and households – households can be thought of as a special kind of industry that consumes the products of the other industries and provides them with labor.

Although we often take it for granted, the production network forms the backbone of the economy. It is the delocalized engine that creates the goods and services that populate and flow through the network of balance sheets.

To see how the production network functions, let’s examine how it produces a laptop. Many different specialized products are needed to manufacture a laptop. The nodes in the network are these products and the links connect each product to its constituents.

To produce a laptop, raw materials are extracted from every continent except Antarctica, transported to other locations and processed to make composite materials. These in turn are used to make the individual parts that are then combined and assembled elsewhere to create the laptop.

The process involves many firms in different industries. Each industry makes its product and sells it to another industry further downstream. The final product, the laptop, is both a consumer good and an intermediate item used to make other products. Engineers use laptops to design many things, including new laptops. This is one of many loops in the production network. Though we often refer to pieces of the production network as supply chains, this is a bad metaphor: the production network is full of branches and is more like a tangled web than a chain.

The physical inputs for laptop production are only part of the story. A laptop is designed by engineers, who work for companies that get started by raising capital, which comes from investors, including bankers and other financiers. Once it’s made, a laptop must be transported, distributed and marketed. The engineers, fabrication facilities and computer stores are all housed in buildings, so we must include the construction industry among the inputs. The buildings sit on land, so we must include real-estate companies. Manufacturing requires energy, so we have to include that, too – not to mention the janitors, cooks in the company cafeterias, accountants and lawyers, the occasional plumber to unclog a toilet. Every industry is connected to many other industries, and the connections loop back on themselves: accountants, real-estate agents and engineers all use laptops to do their jobs.

The making of a laptop illustrates how the economy operates like a big metabolism. The production network has a structure similar to the proto-life model described earlier. Their definitions are the same except for a change in noun phrases: A metabolism is a network of chemical reactions that transforms a food set of chemical inputs into other chemicals that provide energy and raw materials for living cells. A production network is a network of firms that transforms natural resources and labor into goods and services for consumers. The economy coordinates the labor of billions of people, so that each network component is available when and where it is needed.

There is an essential difference between production networks and biological metabolisms: In biology, metabolisms are localized within each organism and ecologies are built from the interactions between organisms. But the economy is structured as if it were one big superorganism, with a single metabolism. The metabolism of this superorganism operates through the actions of an ecology of specialists, each of whom the metabolism supports. This remarkable circular process thrives on the specialization of its goods and services and the specialization of the labor required to produce them.