Source-linked AI summary
The virtues and vices of equilibrium and the future of financial economics
J. Doyne Farmer, John Geanakoplos
TL;DR
The paper asks when equilibrium models provide empirically useful descriptions of economic and financial phenomena and when their assumptions limit their predictions. It reviews equilibrium theory’s strengths, critiques its scope, and considers non-equilibrium and alternative approaches. Its conclusion is that equilibrium models are useful in some situations but cannot adequately address others, so their applicability should be resolved empirically.
Problem
Equilibrium theory dominates economics and finance, but its empirical validity and scope remain debated, including whether some predictions are unfalsifiable.
Method
The paper evaluates equilibrium theory’s assumptions, strengths, limitations, and empirical performance, then reviews non-equilibrium and alternative approaches.
Results
Equilibrium models provide powerful financial implications, including no-arbitrage reasoning, but their usefulness varies across phenomena and their scope can be limited.
Takeaways & Limitations
Equilibrium should remain an important component of economists’ toolkits while being supplemented by non-equilibrium approaches where equilibrium is unlikely to apply.
Takeaways & Limitations
Equilibrium theory can make financial questions about future prices and investment timing effectively unanswerable within the model.
Abstract
from arXiv · showhide
The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn't be a question of dogma, but should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out, i.e., where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models. We sketch some alternative approaches and discuss why they should play an important role in future research in economics.
1 Introduction
The paper examines equilibrium theory’s dominant role in economics and finance, asking how far its predictions are empirically valid. It combines perspectives shaped by both equilibrium and time-series trading strategies to clarify where equilibrium models help and where they fall short.
- Equilibrium theory seeks parsimonious descriptions of economic phenomena while incorporating human reasoning.
- The paper evaluates equilibrium theory by contrasting theories that are empirically useful with those that are merely aesthetically pleasing.The authors draw on experience developing different trading strategies for hedge funds.
- The paper reviews equilibrium theory, market efficiency, its strengths and limitations, empirical evidence, non-equilibrium motivations, and alternative approaches.
2 What is an equilibrium theory?
Equilibrium theory models market interactions among rational agents and connects their decisions to production, consumption, and prices. Its general-equilibrium framework provides closure by linking economic components under a minimum set of assumptions.
- Market equilibrium models describe interactions among rational agents who make production, consumption, and pricing decisions.Agents are characterized by endowments, technologies, and utilities.
- The Arrow–Debreu framework assumes perfect competition, utility optimization, market clearing, and rational expectations.
- General equilibrium theory provides closure by connecting the economy’s components and specifying assumptions sufficient to obtain a solution.
- General equilibrium theory marked a transition toward a highly mathematical economics centered on quantitative explanation.
- Efficiency is identified as the most important consequence of equilibrium theory for the paper’s purposes.
2.1 Existence of equilibrium and fixed points
Equilibrium existence can be established through fixed-point reasoning, but finding or reaching equilibrium is not straightforward. Financial equilibrium extends the framework across time, uncertainty, and securities.
- Equilibrium means that agents’ plans are mutually fulfilled, with aggregate demand matching aggregate supply.
- Arrow, Debreu, and McKenzie showed that equilibrium exists under diminishing marginal utility and diminishing marginal product.
- The existence proof maps prices to prices by adjusting prices for excess demand or supply, then identifies equilibrium as a fixed point.
- Tatonnement can cycle without approaching equilibrium, so the existence of equilibrium does not ensure that markets can find it.
- General equilibrium is non-temporal, whereas financial equilibrium incorporates time, uncertainty, and financial securities.
- Financial models represent uncertainty with exogenous states of nature and extend traded goods to securities promising future deliveries.
- Agents in financial equilibrium choose action plans across future states, including contemplated trades in commodities and securities.
2.4 Rational Expectations and Utility Maximization
Rational-expectations equilibrium assumes agents optimize over complete consumption plans using detailed knowledge of future states, probabilities, and prices. The framework has been repeatedly extended and partially relaxed to address bounded rationality and information differences.
- Utility maximization requires agents to evaluate complete consumption plans, future states, their probabilities, and prices.
- Behavioral economics challenges standard utility assumptions by showing that preferences can depend on context and framing.
- Extensions range from fixed beliefs and noise traders to models with less-than-perfectly rational agents.
- The rational-expectations equilibrium model is highly idealized, motivating extensions such as overlapping generations, asymmetric information, and default.
- An equilibrium model may include boundedly rational agents if at least some agents maximize preferences and form expectations self-consistently.
3 Efficiency
Equilibrium and efficiency concepts provide powerful benchmarks for financial economics, especially through arbitrage and informational efficiency. However, incomplete markets undermine Pareto efficiency, and departures from rational expectations can make added securities destabilizing.
- Financial equilibrium: Complete markets make financial equilibrium Pareto efficient, whereas incomplete markets are almost never Pareto efficient.Complete markets require securities that offset every future state-specific risk; without them, intervention may improve everyone’s welfare.
- Limits: Financial equilibrium’s efficiency implications depend on strong assumptions about market completeness, information, and expectations.These assumptions distinguish allocative efficiency claims from the more limited price properties used when allocative efficiency fails.
- Informational efficiency: Informational efficiency treats security prices as unpredictable, with the strongest form stating that prices follow a martingale.Under this property, current prices are the best predictions of future prices and incorporate available economic information.
- Limits: When agents depart from rational expectations, adding securities can destabilize prices, suggesting market completeness may sometimes reduce utility.The cited example assumes agents use reinforcement learning rather than rational expectations.
- Arbitrage efficiency: Arbitrage efficiency supports major financial results, including Black-Scholes pricing, without requiring explicit assumptions about utility.The option-pricing derivation relies on random-walk behavior for the underlying asset and the absence of risk-free profits.
4 The virtues of equilibrium
Equilibrium theory offers a unified, parsimonious way to model reasoning, evaluate institutions, and make conditional forecasts. Its usefulness is nevertheless constrained by unrealistic rationality assumptions, equilibrium-selection problems, and the risk that standardization suppresses radically different approaches.
- Agent Based Modeling: Equilibrium theory explains aggregate relationships through individual actions, allowing policy conclusions to depend on agents’ incentives and responses.The Phillips curve example shows that workers may initially respond to rising wages, but later recognize that prices rise too, weakening the proposed output channel.
- Rationality: Rational expectations provide a parsimonious, self-consistent benchmark, but modeling bounded rationality requires additional assumptions about cognition or learning.The paper presents rational expectations as potentially useful in some settings, while acknowledging that perfect rationality is unattainable for individuals.
- Succinctness: Equilibrium theory supplies a standardized framework and language for deriving and comparing conclusions across economic problems.This common structure can support specialized models and extensions such as asymmetric information or default, but may stultify radically new approaches.
- Normative purpose: Equilibrium models connect institutional evaluation to utility, whereas purely phenomenological models require an additional ad hoc criterion for recommending institutions.The normative comparison depends on evaluating the benefits each person receives from the resulting equilibrium.
- Normative purpose: The rationality assumption is indispensable to standard proofs that free-market incentives produce Pareto-efficient outcomes.Misinformation about future production or whimsical behavior can make free-market decisions socially poor.
- Models and markets: Equilibrium models can influence future behavior, as users’ trading on model-implied mispricing may move markets closer to the model’s predictions.The paper gives Black-Scholes as an example of a model that became more descriptively accurate as traders used it.
- Conditional forecasting: Conditional forecasts organize uncertainty by computing equilibrium outcomes across possible future states rather than issuing unconditional predictions.Equilibrium trees are most useful when states are imaginable, computationally manageable, and associated with reliable probabilities.
- No-arbitrage: The no-arbitrage hypothesis reduces the state space and can help traders infer probabilities, making tree-based calculations feasible.Traders use conditional analysis to search for riskless arbitrages, although such opportunities are rare in practice.
5 Difficulties and limitations of equilibrium
Equilibrium models are parsimonious but difficult to test and use because their assumptions are hard to observe, their predictions are often qualitative, and equilibrium cannot describe its own deviations. Their rationality, stability, and completeness assumptions therefore impose important limits on financial and economic analysis.
- Equilibrium should remain part of the economist’s toolkit, but its dangers and limitations require explicit attention.
- Equilibrium models are difficult to test because they simplify dynamics and institutions, require auxiliary assumptions, and often yield few sharp predictions.
- Utility functions and rational preferences lack firm empirical foundations, while behavioral evidence motivates alternatives such as prospect theory that remain incompletely integrated.
- Expectations are difficult to measure because researchers observe only one potentially atypical historical path through future states.
- Perfect rationality demands omniscience and excessive computation, while equilibrium existence does not guarantee stability or convergence from disequilibrium.
- Equilibrium cannot model deviations from itself, limiting questions about efficiency violations, and its financial implications can become powerful but nearly empty.
6 Empirical evidence for and against
Empirical evidence for equilibrium models is mixed: some applications have practical success, but many predictions remain qualitative, fail to match observed prices or trading, or lose support as specialized models are tested. The evidence therefore leaves room for both useful equilibrium applications and extensions or alternatives.
- Equilibrium theory has produced practical suggestions and applications, including diversification, index funds, Black-Scholes pricing, and utility-based explanations of prime-mortgage prepayment.
- Most equilibrium predictions remain qualitative and are rarely quantitatively verified while also excluding nonequilibrium alternatives.
- CAPM initially received empirical support but later unraveled, although alternative specializations or extensions involving default and collateral might improve fit without making the theory unfalsifiable.
- Prices and fundamental values differed by more than a factor of two over periods as long as decades in U.S. stock-market evidence.
- Global financial trading is roughly one hundred times global production, appearing inconsistent with equilibrium predictions about how much people should trade.
- Large market movements often occur without discernible news, weakening the rational-expectations prediction that price changes respond primarily to new information.
7 Motivation for non-equilibrium models: a few examples
The paper highlights market phenomena that equilibrium models have not explained well, motivating non-equilibrium approaches that capture volatility, structural change, and transitions over time.
- Empirical motivations: Clustered volatility—strong temporal correlation in the size of price movements—remains unexplained by many equilibrium models.Non-equilibrium models can generate clustered volatility, and equilibrium as a special case may eliminate it.
- Empirical motivations: Power laws are widely associated with clustered volatility and other economic phenomena, though identifying them empirically is difficult because the tail’s starting point is unknown.Extreme-value formulations use a slowly varying function to describe tail behavior more precisely.
- Market efficiency: Equilibrium theory cannot address persistent efficiency violations or the time required for profitable strategies to degrade, making these inherently disequilibrium phenomena.The authors frame this limitation as a major motivation for developing non-equilibrium theory.
- Market efficiency: Estimating progression toward efficiency requires accounting for model learning and capital acquisition after a structural change creates a new inefficiency.The paper uses statistical detection and live-trading track-record requirements to motivate the relevant time scale.
- Market efficiency: Signal 2’s predictive power grew for more than a decade after a 1983 structural change, contrary to the standard expectation that market inefficiencies quickly disappear.The authors attribute the persistence partly to newly available information and the slow discovery of profitable strategies.
- Theory and scope: Nonequilibrium theory can explain transitions between equilibrium states and help determine when equilibrium models are valid.The paper argues that economics lacks a comparable disequilibrium theory for identifying those boundaries.
8 If not equilibrium, then what?
The paper argues that equilibrium theory should remain useful but should no longer dominate economics, which needs a broader toolbox that includes alternative and dynamical approaches.
- Motivation: The paper presents the future of economics as open-ended rather than centered on a single dominant theoretical path.It contrasts the apparent confidence of equilibrium economics around 1970 with the later uncertainty about the field’s direction.
- Motivation: The authors reject discarding equilibrium theory and instead recommend treating it as one among many tools in economics.They argue that excessive emphasis on equilibrium has left many economists trained in little else.
- Prior alternatives: Disequilibrium models have a history in economics, but influential Keynesian models failed when their assumed inflation-output trade-off collapsed during 1970s stagflation.The paper uses this history to show why alternatives require empirical scrutiny rather than automatic acceptance.
8.1 Behavioral and experimental finance
Behavioral and experimental economics address the unrealistic agent assumptions of rational-expectations equilibrium, but human behavior remains difficult to formalize and may change when its regularities become known.
- Behavioral and experimental approaches: The paper identifies the lack of realism in the rational-expectations agent model as a principal problem motivating behavioral and experimental economics.It notes the mainstream recognition of these fields through the work of Kahneman and Smith.
- Behavioral and experimental approaches: Experimental economics may help categorize and predict context-dependent human behavior, although its findings are difficult to reduce to quantitative mathematical form.The authors regard accurate characterization of human behavior as essential but challenging.
- Scope distinction: Econometrics remains an important exception because its models are not founded on a priori assumptions about agent behavior and are not theories in the paper’s defined sense.This distinction separates econometric practice from the theoretical approaches under discussion.
- Behavioral and experimental approaches: Behavioral finance has documented many empirical regularities, but newly discovered rules may be violated as people learn about them and adapt.The paper illustrates this concern with overconfidence and investors’ incentives to compensate for known biases.
8.2 Structure vs. strategy
The paper argues that economic models should balance strategic behavior against institutional structure, because aggregate outcomes can often be explained by interaction rules and dynamics rather than strategy alone.
- Structure and strategy: Economic models should distinguish structural properties of institutions and interactions from strategic properties of agents’ behavior.The paper argues that economics has relied too heavily on game-theoretic and equilibrium approaches relative to other factors.
- Examples: Traffic models show that physical analogies and structural constraints can dominate equilibrium reasoning despite drivers’ strategic interactions.Traffic states are modeled analogously to phases of matter, from gas-like flow to liquid-like congestion and solid-like jams.
- Examples: Crowd dynamics similarly demonstrates that aggregate behavior can be studied through physical and quantitative methods even when individuals pursue strategic goals.Analysis of the Hajj crowd contributed to modifications in crowd-control methods and a safer pilgrimage the following year.
- Examples: Income distributions provide another example where persistent empirical regularities have been most successfully modeled with random-process approaches rather than strategic equilibrium reasoning.The upper tail of income is better approximated by a power law.
- Financial markets: Tests of the Glosten equilibrium model do not match reality well, whereas zero-intelligence models can derive some empirically supported relations between order flow and prices.These relations include connections between order placement and cancellation rates and price volatility and bid-ask spreads.
- Financial markets: Zero-intelligence models may predict volatility distributions without satisfying market efficiency, suggesting that auction structure can matter more than efficiency for that outcome.Relevant structural features include transaction rules, order removal and deposition, and their interaction with price formation.
- Modeling strategy: Equilibrium and zero-intelligence models are complementary parsimonious tools for studying bounded rationality, despite their differing and sometimes unrealistic assumptions.The paper presents them as ways to isolate different aspects of economic problems.
- Modeling strategy: Good modeling may require combining structural and strategic arguments, as in explanations linking spreads, price impact, and volatility in transaction time.The authors emphasize finding the appropriate compromise rather than choosing structure or strategy universally.
8.3 Bounded rationality, specialization, and heterogeneous agents
Boundedly rational heterogeneous-agent models address financial phenomena that equilibrium theory has not explained by representing diverse strategies and their changing populations. Simulations generate several observed market patterns, but quantitative realism, parsimony, and the conditions producing these phenomena remain unresolved.
- Boundedly rational heterogeneous-agent models were developed to explain bubbles, crashes, clustered volatility, excess volatility, excess trading, and heavy-tailed returns.
- These models represent heterogeneous agents either by assigning classes of traders in advance or by generating heterogeneity through learning.
- Simulations naturally generate clustered volatility, heavy tails, bubbles, crashes, and excess trading, often through shifting strategy populations and feedback from fundamentals.
- More developed models make testable predictions while allowing information arrival to affect volatility without treating it as the sole source of volatility.
- Capital reallocation can produce arbitrage-efficient strategies and eliminate price autocorrelations after sufficient simulation time.
- Many models remain non-parsimonious, lack quantitative predictions, and leave the necessary and sufficient conditions for generating target phenomena unresolved.
8.4 Finance through the lens of biology
A biological lens treats financial strategies as evolving, interacting populations and motivates taxonomies and ecologies grounded in trader and brokerage data. This framework offers mechanisms for strategy interaction and efficiency, but its empirical foundation remains incomplete.
- Biology provides a complementary lens for BRHA models because both study specialized agents and their interactions.
- Financial economics lacks comprehensive empirical data on real trading strategies, despite evidence that strategic diversity matters for price formation.
- Market taxonomy would classify financial strategies, potentially using electronic records containing information about agents’ identities.
- Market ecology models strategies as species and invested capital as population, with prices mediating feedback between strategy activity and price formation.
- Market impact measures how a trade changes prices and can characterize the strength and ecological type of interactions between strategies.
- The gain matrix Gij = ∂ρi/∂Cj classifies pairwise strategy relationships through how strategy j’s capital affects strategy i’s returns.
- New investor- and brokerage-level datasets make ecological models more testable, but an empirical foundation linking changing ecologies to price formation is still needed.
- Financial ecologies follow descent, variation, and selection, with successful strategies proliferating and unsuccessful strategies disappearing.
8.5 The complex systems viewpoint
The complex-systems viewpoint studies how simple components interacting through simple rules can generate complex emergent behavior. In economics, general equilibrium can be viewed as an effort to simplify this interactional complexity.
- Complex systems are composed of simple components whose interactions through simple rules produce complex emergent behavior.
- General equilibrium theory can be regarded as an attempt to cut through the complexity of individual interactions.
9 Conclusion
The paper urges both physicists and economists to use equilibrium models with greater judgment: equilibrium is valuable in tractable settings but limited in complex ones. It therefore advocates empirically grounded exploration of alternatives.
- The authors seek to help physicists appreciate why equilibrium emerged while encouraging economists to recognize circumstances where it is inappropriate.
- The paper encourages physicists to incorporate equilibrium when appropriate and economists to explore alternatives informed by other fields.
- Rational-expectations equilibrium is likely to work when the cognitive task is simple, information is good, and estimation is tractable, including option pricing, hedging, and mortgage-backed securities.
- Equilibrium theory is a parsimonious but potentially crude simplification, so economics must develop foundations that can go beyond it.