Speculative bubble

Introduction

A speculative bubble refers to a situation where asset prices exceed the asset’s fundamental value, driven by traders’ expectations of selling at even higher prices in the future. Traditional finance theory often argues that fully rational agents with common knowledge should not engage in trades that create bubbles – by backward induction in finite horizons or transversality conditions in infinite horizons, prices shouldn’t rise above discounted fundamentals.

Yet history offers many examples of bubbles (Tulip Mania, the South Sea Bubble, the Dot-Com boom, etc.), suggesting that certain market frictions or belief differences allow bubbles to form even when individuals appear rational. Modern research has proposed various theoretical models and documented empirical evidence to explain how bubbles can arise even with rational agents, often due to private information, heterogeneous beliefs, or limits to arbitrage.

Below is a survey of key papers – both theoretical and empirical – that shed light on the nature of speculative bubbles, including cases of assets with no intrinsic value (cryptocurrencies, virtual goods) being traded at high prices. We also highlight major explanations such as the “greater fool” dynamic, asymmetric information, and constraints on arbitrage that facilitate bubbles.

Rational Bubbles in Infinite Horizons and Overlapping Generations

Early theoretical work showed that if the economic environment permits no definitive end to trading, rational bubbles can exist. In an infinite-horizon or overlapping-generations model, an asset that pays no dividends can still have positive price if each agent believes they can resell it later – essentially a rational Ponzi scheme.

Jean Tirole (1985) demonstrated that with an overlapping-generations economy, bubbles can emerge as an equilibrium: young agents buy the asset expecting future agents to buy it off them. In such models, the bubble’s price grows at the rate of interest, and it can persist indefinitely as long as new buyers enter the market.

Classic frameworks by Blanchard (1979) and Blanchard & Watson (1982) allowed for rational expectations bubbles, where price rises simply because everyone expects it to keep rising. The asset’s value has two components – a fundamental value (based on cash flows) and a bubble component purely from self-fulfilling beliefs.

A recent application is van Oordt (2024), who builds on classical rational bubble models to analyze Bitcoin. If the price of a cryptocurrency exceeds what its transactional usage can justify and instead relies on continued new investment inflows, that price excess is effectively a bubble with Ponzi-like payoffs.

Asymmetric Information and Greater-Fool Dynamics

Many influential models show that private information or heterogeneous beliefs can fuel bubbles, even in finite-horizon settings, by creating a “greater fool” dynamic.

In their foundational paper, Harrison & Kreps (1978, QJE) showed that investors are willing to pay a “speculative premium” above fundamental value because they anticipate selling the asset to others with even more optimistic beliefs. Even if an investor thinks the asset is overvalued, they value the resale option of potentially selling to a “greater fool.”

Allen, Morris & Postlewaite (1993, JET) built a finite-horizon model where all agents are rational and dividends are known, yet a bubble still arises. Traders hold private signals and recognize others might act on more optimistic beliefs, breaking common knowledge and allowing overvaluation to persist until the end.

Scheinkman & Xiong (2003, JPE) modeled overconfidence as the key driver: each trader believes too strongly in their private information, leading to heterogeneous valuations. This overconfidence, combined with short-sale constraints, creates a resale option and generates a rational bubble with high turnover and volatility.

Conlon & Liu (2018, JET) provided a minimal rational “greater-fool” bubble model. Buyers knowingly pay inflated prices because they expect someone else (a greater fool) will pay more in the near future. No one wants to be the last buyer, but all believe they can sell in time.

Heterogeneous Beliefs, Short Sale Constraints, and Bubbles

When some investors are more optimistic than others, and pessimists cannot easily short the asset, the result is price inflation – effectively a bubble.

This mechanism was introduced by Miller (1977) and supported empirically by Chen, Hong & Stein (2002, JFE), who found that stocks with limited investor participation and constrained short sales underperform later.

Ofek & Richardson (2003, JF) studied the dot-com bubble and showed that Internet stocks with extreme short-sale constraints (due to insider lock-ups) saw enormous price inflation. When constraints expired, these stocks plummeted.

Shleifer & Vishny (1997, JF) introduced the “limits of arbitrage” theory: rational arbitrageurs may avoid correcting bubbles if they manage outside capital and face liquidation risk from early losses.

Brunnermeier & Nagel (2004, JF) documented that hedge funds actually rode the dot-com bubble rather than betting against it, suggesting that rational traders sometimes choose to time the bubble rather than burst it.

Abreu & Brunnermeier (2003, Econometrica) formalized a model where arbitrageurs delay attacking a bubble due to coordination problems. Even if traders know the price is wrong, each waits for others to act first, allowing bubbles to persist.

Bubbles in Markets With No Fundamental Value (Crypto and Virtual Assets)

Perhaps the clearest examples of bubbles are in markets where the assets have no fundamental value, such as some cryptocurrencies and virtual goods.

For example, van Oordt (2024) shows that Bitcoin can be viewed as a rational bubble sustained by speculative inflows. When the price exceeds its transactional utility, the excess becomes a speculative component.

Kogan et al. (2023, NBER) show that crypto traders exhibit momentum-chasing and are often driven by extrapolative beliefs and FOMO, unlike their behavior in traditional equity markets.

In the viral “Banana” game on Steam, players bought and sold worthless virtual bananas at high prices. This market became a greater-fool game in pure form: users paid real money hoping to flip digital bananas for a profit despite their intrinsic worthlessness.

In the lab, Smith, Suchanek & Williams (1988, JPE) showed that bubbles arise even when traders know the fundamental value. Prices overshoot in early rounds due to speculative expectations, even though the asset’s value is clearly defined.

Hirota & Sunder (2007, JFE) showed that small amounts of asymmetric information or shifts in trading horizons in experimental markets increase bubble likelihood and size.

The real-world bubble in Chinese warrants analyzed by Xiong & Yu (2011, AER) involved put options that were essentially worthless, but traded at inflated prices because investors hoped to resell them. The market had no short-sale mechanism, which enabled the bubble.

Other Explanations: Herding, Narrative, and Behavioral Factors

Beyond rational models, behavioral and informational dynamics also explain bubble formation.

Avery & Zemsky (1998, AER) showed that informational cascades and herding can occur when there is uncertainty about the state of the world and what others know. Investors may rationally follow others’ trades, amplifying price movements.

Barberis, Greenwood, Jin & Shleifer (2018, JFE) presented an extrapolation-based bubble model, where investors expect recent price increases to continue. This behavior drives a positive feedback loop: rising prices boost demand, leading to even higher prices.

Greenwood & Shleifer (2014) showed that investor expectations about future returns are positively correlated with past price increases, even though rational models suggest expected returns should decline after price surges.

[Narrative-driven bubbles**, as emphasized by Robert Shiller, arise from compelling stories that justify high prices: “this time is different” or “the old rules don’t apply.” These narratives often accompany manias like the Dot-Com boom or crypto surges.

Conclusion

Modern research shows that speculative bubbles can form even in markets with rational agents, as long as there are realistic frictions: private information, heterogeneous beliefs, limits to arbitrage, and coordination problems.

Models and data consistently show how greater-fool dynamics, short-sale constraints, and herding behavior allow prices to deviate from fundamentals. Empirical cases from stock markets, crypto, video games, and lab experiments confirm that rational traders often buy overpriced assets expecting to profit from resale.

In zero-fundamental markets like crypto or virtual bananas, these dynamics are especially vivid. Bubbles form not because people are irrational, but because they rationally believe they won’t be the last one holding the bag.

Understanding these dynamics helps economists detect and study bubbles, as well as explain why markets periodically become disconnected from fundamentals despite widespread awareness of the risks.