What is equilibrium in economics and when it is (not) useful

Equilibrium is the most widespread assumption across all subfields of economic theory. It means different things in different subfields, but all equilibrium concepts have a common meaning and purpose, with the same pros and cons. In this post I will argue that the different way in which equilibrium is treated is the distinctive feature of complexity economics, narrowly defined. (This post is mostly methodological. In this blog I will alternate actual research and methodology, always pointing to concrete examples when talking about methodology.)

What equilibrium means in economics

Before talking about what equilibrium is, it is useful to say what it is not. First, equilibrium does not necessarily imply stationarity. Indeed, many equilibrium concepts are dynamic and so for example it is possible to have chaotic equilibria. Conversely, stationary states need not be equilibria. Second, equilibrium in economics has nothing to do with statistically balanced flows, as used in many natural sciences. Third, equilibrium is independent of rationality, if rationality just means choosing the optimal action given available information (I will come back to this).

Equilibrium in economics can generally be thought of as a fixed point in function space, in which beliefs, planned actions and outcomes are mutually consistent. Let me elaborate on this. Differently from particles, economic agents can think, and so have beliefs about states of the economy. Behavioral rules that can be fully or boundedly rational map these beliefs into planned actions. Finally, outcomes resulting from the combined actions of all agents may let each agent realize their planned actions, or may force some agent to choose an action that was not planned. Equilibrium outcomes are such that agents – at least on average – always choose the action that was planned given their beliefs and behavioral rules. In other words, beliefs and planned actions match outcomes.

A few examples should clarify this concept. Perhaps the most famous equilibrium is the Walrasian one. This is usually described as demand=supply, but there is more to that. In a market with one or multiple goods, agents have beliefs about the goods prices, and through some behavioral rule these beliefs determine the quantities that agents try to buy or sell (planned actions). Aggregating up these quantities determines outcomes – the differences between demand and supply for each good. If there is excess demand or excess supply, some agents buy or sell more (or less) than what they planned. Instead, in a Walrasian equilibrium agents have beliefs on prices that make them buy or sell quantities that “clear” the market, i.e. demand=supply. In this way, all agents realize their plans.

When strategic interactions are important, economists use game theory to model interdependent choices. In game theory players have beliefs about what their opponents will do and plan actions according to these beliefs and some behavioral rule. For example, if players are fully rational their behavioral rule is to select the action that maximizes their payoff given their beliefs. In a Nash equilibrium all players’ actions and beliefs are mutually consistent, so no agent can improve her payoff by switching to another action. But agents could be boundedly rational, playing also, with some smaller probability, actions that do not maximize their payoff. In this case it is for example possible to define a Quantal Response Equilibrium, in which again beliefs and planned actions match outcomes.

All equilibrium concepts above are static, but it is straightforward to include a temporal dimension. (Beliefs over time are called expectations.) For example, in many macroeconomic models agents are forward-looking, e.g. they plan how much to consume in each future period of their life. These consumption decisions depend on future interest rates: in periods when the interest rates are high, agents may prefer saving to consuming, so to earn higher interest and afford higher consumption in the future. In a rational expectations equilibrium [1], the expectations for future interest rates are on average correct, so that again beliefs and planned actions (consumption decisions) match outcomes (interest rates). The assumption of rational expectations places no restriction on macroeconomic dynamics: this may reach a stationary state, but also follow limit cycles or chaos.

Many more equilibrium concepts have been proposed in economics, and new ones keep being introduced, but all equilibria share the same rationale. For example, search and matching models are used to go beyond the Walrasian equilibrium concept. When applied to the labor market, these models assume that workers and firms engage in costly search of a good match. This potentially difficult search process may explain involuntary unemployment, which could not be explained if labor demand=labor supply, as in Walrasian models. Yet, the equilibrium of search and matching models can still be viewed in the same way as in the examples above. Workers have beliefs about future vacancy rates, which determine how difficult it is to find a job, and firms have beliefs on future unemployment rates, determining how difficult it is to fill a vacancy. These beliefs determine which minimum wage to accept or offer, or how long to search (planned actions), typically following a rational behavioral rule. Finally, the combined decisions of workers and firms lead to outcomes, namely unemployment and vacancy rates. Again, in equilibrium beliefs, planned actions and outcomes are mutually consistent.

Pros and cons of equilibrium

If equilibrium has been a key concept in economic theory for more than a century, there must be some good reasons. The first reason, I think, is that modeling out-of-equilibrium behavior is harder than modeling equilibrium behavior. What is a realistic way to model what happens when beliefs, planned actions and outcomes are systematically inconsistent? (I give a possible answer at the end.) Equilibrium is then an incredibly useful simplification, that makes it possible to abstract away from this problem. Economic theorists are often interested in adding more and more realistic features about how the economy works in their models, and by assuming equilibrium they keep their models tractable. In addition, contemporary economics is becoming more and more empirical. Many applied economists are happy to just build a model that accounts for some property of the data, and building models with equilibrium is a transparent way to highlight the relevant theoretical mechanisms.

A second reason for the success of equilibrium is that time averages of beliefs, planned actions and outcomes may approximate equilibrium, which would then be a useful point prediction. An example that comes from my research is the game of Matching Pennies. If this game is played repeatedly, under some learning algorithms the players will never converge to a Nash equilibrium. However, it is easy to show that time averaged play is close to equilibrium behavior [2]. Something similar has been observed experimentally.

A third reason is that by assuming equilibrium many variables are determined endogenously, that is within the model. This makes it possible to consider non-trivial interdependencies, called by economists general equilibrium effects. An example comes from a nice paper by Cravino and Levchenko I recently read. In this paper the authors build an equilibrium model to investigate how much multinational corporate control affects international business cycle transmission. Assuming that parent companies are hit by a “shock” in one country, the authors look at aggregate effects on other countries where affiliate companies operate. Interestingly, the effect of the shocks is amplified if workers in the other countries are less willing to change how many hours they work. This general equilibrium effect is due to the interconnections between the good and labor markets, captured by assuming equilibrium.

Despite the advantages of equilibrium assumptions, I think there are two main shortcomings. The first is that, in my opinion, little of what happens in the real world is precisely described by equilibrium. If one is interested in quantitative models, forcing the model to be in equilibrium is a strong mis-specification, even if some aspects of reality are reasonably approximated by equilibrium. Of course many equilibrium models are shown to fit the data, but most analyses are based on in-sample fitting and so could be prone to overfitting.

The second shortcoming is more practical. In some cases solving for equilibrium is technically challenging, and this prevents including some realistic assumptions and fully embracing heterogeneity. In the words of Kaplan and Violante in the Journal of Economic Perspectives “Macroeconomics is about general equilibrium analysis. Dealing with distributions while at the same time respecting the aggregate consistency dictated by equilibrium conditions can be extremely challenging.” Kaplan and Violante propose macroeconomic models named HANK (Heterogeneous Agent New Keynesian), but the way they deal with heterogeneity is extremely stylized. In addition, I think that one of the main reasons why insights from behavioral economics are not routinely added to economic models – in macroeconomics but also in other fields – is that it is technically harder to solve for equilibrium if one departs from full rationality. However, heterogeneity and bounded rationality are key to make serious quantitative models (real people are heterogenous and boundedly rational).

In sum, I think that assuming equilibrium can be really useful if models are used for qualitative reasoning, but it is an obstacle for quantitative analyses.

Complexity economics and equilibrium

My favorite narrow definition of complexity economics is making economic models that are not solved by assuming equilibrium. Rather, the modeler postulates the behavioral rules that each agent will follow and then just lets the system evolve over time. This is what happens in Agent-Based Models (ABMs), often represented as computer programs, or in Heterogenous Agent Models (HAMs), typically represented as dynamical systems. In either case, beliefs and planned actions need not match outcomes. In some cases they might, perhaps after an initial transient, but this is not a primary concern of the modeler. I think that assuming equilibrium is a strong top-down constraint imposed on the system. ABMs and HAMs let outcomes emerge in a bottom-up way without imposing equilibrium constraints, which I think is more in line with a complex systems view of the economy.

Is this useful? I think that the main advantages mirror the shortcomings of equilibrium models. Because one does not have to solve for equilibrium, it is very easy to include any form of heterogeneity and bounded rationality. If one also believes that out-of-equilibrium behavior better describes real economic agents, ABMs and HAMs seem more promising than equilibrium models for quantitative analyses. With the increasing availability of large datasets, we may be able to show this explicitly in the upcoming years. Another advantage is that not assuming equilibrium may lead to more natural descriptions of some problems: for an example, see the housing market ABM in my paper with Jean-Pierre Nadal and Annick Vignes.

The main problems of not assuming equilibrium also mirror the main advantages of doing so. First, being forced to model out-of-equilibrium behavior in each submodule of the model makes ABMs computationally very expensive. Second, it is easy to overlook interdependencies and to take too many variables as exogenous. Third, if beliefs, planned actions and outcomes are systematically inconsistent this may lead to mechanistic behavior that is as unrealistic as equilibrium. For example, in this very nice paper by Gualdi et al., for some parameter settings the ABM economy undergoes a sequence of booms and busts determined by consumers and firms systematically failing to coordinate on equilibrium prices (see first paragraph of Section 5.2). While this may be a realistic description of some economic crises, it seems unlikely that economic agents would systematically fail to recognize the discrepancy between beliefs and outcomes.

I think that the problem of what happens when beliefs and planned actions systematically do not match outcomes can be tackled in ABMs by modeling learning in a sensible way, perhaps including models of agents learning how to learn. In this way, agents may systematically be wrong but in many different ways, and so be unable to find the equilibrium. This view, I think, best describes economic reality.

In sum, complexity economics models are not solved by assuming equilibrium, and this also has its pros and cons. We will see over the upcoming years if the pros outweigh the cons.

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I would like to thank everyone for your interest in this blog: my first post received way more online attention than I expected. Hope you will find my posts interesting! And please give me feedback — I wrote this post with the hope that a natural scientist with just a vague knowledge of economics could understand the basic idea; if you are such a scientist, let me know if I succeeded!

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[1] I find the name “rational expectations” very misleading. Rational expectations equilibria have nothing to do with rationality, rather with the assumption that expectations match outcomes, which does not necessarily imply rationality.

[2] It is not always true that time averages correspond to equilibrium behavior. For example, if the players learn using fictitious play this is not true. And one always has to check ergodicity when using time averages.

Complexity Economics

Welcome to my research blog! I have always found reading other people’s research blogs tremendously useful, as blogs give unique perspectives on aspects of research that do not show up in papers. This blog is my perspective as a junior scientist on the research topics I am passionate about – economics and complex systems – as well as on general topics in science and on careers in research.

My blog is about complexity economics, broadly defined as the application of complex systems methods in economics. In complex systems the whole is more than the sum of its parts, and complex systems scientists investigate how collective behavior emerges from interactive individual components. Practically speaking, complex systems science is a collection of computational and mathematical methods that are applied across the natural and social sciences.  This leads to the broad characterization of complexity economics as a theoretical and empirical focus in economics on networks, non-linear dynamics, adaptation, learning and heterogeneity.

I favor a narrower definition that applies to economic theory. According to this definition, complexity economics is economic modeling without equilibrium. I will write a separate blog post about what equilibrium means in economics, why economists make equilibrium assumptions and what building non-equilibrium models means. Here I only want to stress that equilibrium is a top-down constraint imposed on the economic system. A complex systems view of economics would rather suggest to take a bottom-up approach, for example using agent-based models. This is what makes the (narrowly-defined) complexity economics approach non-mainstream in economics, and perhaps “heterodox”.

I aim my blog at both complex systems scientists – mathematicians, physicists, biologists, computer scientists, etc. – and economists. To this end, I will try to avoid jargon and explain basic things that may be obvious in a field but not clear in others. This for example applies to my research. Every time I publish a paper I plan to write a blog post that describes the paper’s contribution in general terms. But my goal is also to discuss other people’s research, and general topics across economics and science. I would also like to give my opinion as a PhD student and (in the future) postdoc about careers in research, e.g. whether interdisciplinarity pays off or whether the economics job market chokes risky and innovative research.

I will not talk about politics. While I am deeply worried about recent trends across the world, I want to keep this blog only about science, and will only discuss political issues in a positive way (jargon alert: see link). I will also probably not talk about technical aspects of research such as coding and visualization. While this is my day-to-day job and I like having good code and good figures, I am neither a professional developer nor a visual designer, so other people would do a better job at talking about this.

I hope to write a blog post on average every month/two months. There are excellent blogs in economics and in complex systems, I hope this blog will contribute linking the two fields – making economists more aware of what it practically means to take a complex systems approach to economics, and making interdisciplinary scientists more aware of what economists are really doing and why they do it the way they do. This blog will not be the usual critique of economics from a natural sciences perspective, but will rather illustrate mainstream economists’ point of view while promoting an alternative approach.