How does the diversity of investors’ beliefs affect stock price informativeness?

A growing number of studies have investigated the role of stock prices in aggregating private information and guiding resource reallocation. However, this article may be the first attempt to study how the diversity of beliefs affects stock price informativeness. The framework of the noisy rational expectations model shows that stock informativeness is determined by both the precision and use of private information in trading. If private beliefs about the value are highly diverse, the aggregate average opinion revealed in a stock’s price will be more accurate and, thus, more informative. As the price becomes more informative, however, individual investors will rely less on their private information. When this occurs, less private information will be absorbed in price, which, in turn, reduces price informativeness. Our model shows that the relationship between belief diversity and price informativeness is U-shaped in equilibrium.     

Do Irrational Investors Destabilize?

In a financial market where all investors have valuable private information, full rationality requires that investors have an unlimited ability of figuring out the equilibrium model. Instead, I assume that due to a lack of knowledge or experience, some investors do not know the equilibrium model and use only their private information in forming their demand. By investigating the investment behavior of these “boundedly rational” investors and contrasting it with that of the rational ones, I find that in a market where the two kinds of investors coexist, it is the boundedly rational investors who contribute to price stability. The welfare implication is that, although each investor benefits from conditioning his asset demand on the information transmitted by the equilibrium price, it can happen that all investors lose by doing so because the equilibrium price becomes too volatile.     

Bargaining and markets: complexity and the competitive outcome

Rubinstein and Wolinsky (Rev. Econ. Stud. 57 (1990) 63-78) consider a simple decentralised market game in which agents meet randomly or voluntarily and bargain over the terms of trade. They show that any individually rational price can be sustained as a sequential equilibrium even though the model has a unique competitive outcome. Here, I consider Rubinstein and Wolinsky's model and show that if complexity costs of implementing strategies enter players’ preferences, together with the standard payoff in the game, then every equilibrium is stationary/Markov and induces the unique competitive price. Thus, I demonstrate that aversion to complexity may provide a justification for the competitive outcome.     

Are Rational Expectations Equilibria with Private Information Eductively Stable?

The paper derives conditions for eductive stability of rational expectations equilibria in simple linear economic models with private information. Following Guesnerie (1992; 2002), the concept of eductive stability is used. It is shown that even in a private information setting, rational expectations equilibria might be justified as a result of mental process of reasoning of the agents. The paper considers an equilibrium concept, where the agents are unable to condition their forecasts on the actual market price. It is shown that eductive stability in this case requires that a condition is satisfied that is also relevant in the symmetric information case. This condition is compared to the respective stability condition that must hold if agents are able to use the current market price as an additional source of information. It turns out that the conditions for eductive stability that emerge under both equilibrium concepts differ.revised version received September 11, 2003     

Speculative dynamics

We develop a method for solving for equilibrium outcomes in stationary strategic settings in which speculators are informationally large and understand how their actions affect the information content of prices. This allows us to characterize speculation by institutional investors who receive private long-lived information on a recurring basis, and trade strategically. When the underlying asset value process has a stationary autoregressive structure, we develop a contraction mapping argument to solve for the stationary linear equilibrium. We derive analytically and numerically how the characteristics of private information—its quantity, persistence and correlation, and division among speculators—affect trading profits, pricing and trading strategies. Our central finding is that what matters for equilibrium outcomes are the most recent signals that speculators receive. Speculators trade so much more aggressively on new information than old that the bulk of their profits come from their two or three most recent private signals. Trading on past prices drops off faster yet; effectively only the most recent price matters.     

Admissible market data structures: A complete characterization

This paper characterizes the market data which, if observed by traders in a stochastic exchange environment, will permit the general existence of (rational) expectations equilibria. It is proved that if a trader observes and conditions his expectations on some nonconstant market data, he must observe at least the equilibrium price and his own equilibrium trade. Any data which do not satisfy this requirement, such as the price alone, or the price and the volume of trade, will fail to permit the existence of an expectations equilibrium for some otherwise well-behaved stochastic environment.     

Information structure and equilibrium asset prices

In a continuous trading economy, it is shown that if information is revealed continuously and if agents' preferences are continuous in a certain topology, then equilibrium asset price processes must have continuous sample paths. Except for uninteresting cases, the sample paths of price processes will be of unbounded variation. In particular, if the information is generated by a Brownian motion,then equilibrium asset price processes are Ito integrals. When information is not revealed continuously, the times (which may be random) at which prices can have jumps are identified.     

One-Shot Public Mediated Talk

We show that any correlation device with rational coefficients can be generated by a mechanism, where each player sends a private message to a mediator who in turn makes a public deterministic announcement. It is then shown that the mechanism can be adapted also to situations with differential information, where the correlation device itself depends on the players' private messages that may vary with their realized types. All the mechanisms suggested are immunized against individual deviations. Therefore, by using them, players can implement any correlated or communication equilibrium.Journal of Economic LiteratureClassification Number: C72.     

Direct sale of information when precision is unobservable

Abstract.  This paper studies the incentives of an information seller to provide precise information when precision is not observable and investors with rational expectations can extract information from the equilibrium asset price. I show that the seller can verify her precision by employing a non‐linear contract. I derive the equilibrium fee for information as a function of the seller's incentives, the sales volume, and buyers' trading intensity. I also analyse the implications of allowing the seller to trade on her own account for truthfulness and precision choice. JEL Classification: G11, G14, D42     

Bid–Ask Price Competition with Asymmetric Information between Market-Makers

This paper studies the effect of asymmetric information on the price formation process in a quote-driven market. One market-maker receives private information on the value of the quoted asset and repeatedly competes with market-makers who are uninformed. We show that despite the fact that the informed market-maker's quotes are public, the market is never strong-form efficient with certainty until the last stage. We characterize a reputational equilibrium in which the informed market-maker influences and possibly misleads the uninformed market-makers' beliefs. At this equilibrium, a price leadership effect arises, the informed market-maker's expected pay-off is positive and the rate of price discovery increases in the last stages of trade.     

An equilibrium analysis of information aggregation and fluctuations in markets with discrete decisions

This paper shows how the interaction between decentralized information gathering and discreteness of investment decisions at the individual level can generate random fluctuations in aggregate investment that involve occasionally large allocation errors. This interaction is illustrated in a model in which private information is costly to acquire and prices reveal information. The unique rational expectations equilibrium outcome of the model is shown to always be noisy and characterized by investment levels which may be high simply because uninformed investors are buying under the impression that the high price is a signal of good investment opportunities.     

Asymmetric information in bilateral trade and in markets: An inversion result

I consider bilateral trade between a seller and a buyer with private valuations. The seller makes a take-it-or-leave-it price offer. If the seller observes the buyer?s valuation (symmetric information), bilateral trade is trivially efficient. If the seller cannot observe the valuation (asymmetric information), bilateral trade is inefficient. This bilateral trading game is embedded into a large matching market. In the steady-state equilibrium of the market game, the relation between the informational regime and efficiency is inverted: With small frictions efficiency obtains if information is asymmetric. If information is symmetric, however, the trading outcome can be very inefficient—even if frictions vanish.     

Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium

In general rational expectations equilibrium (REE), as introduced in Radner (Econometrica 47:655–678, 1978) in an Arrow–Debreu–McKenzie setting with uncertainty, does not exist. Moreover, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayesian equilibrium of an extensive form game (Glycopantis et al. in Econ Theory 26:765–791, 2005). The lack of all the above properties is mainly due to the fact that the agents are supposed to predict the equilibrium market clearing price (as agent’s expected maximized utility is conditioned on the information that equilibrium prices reveal), which leads inevitably to the presumption that agents know all the primitives in the economy, i.e., random initial endowments, random utility functions and private information sets. To get around this problematic equilibrium notion, we introduce a new concept called Bayesian–Walrasian equilibrium (BWE) which has Bayesian features. In particular, agents try to predict the market-clearing prices using Bayesian updating and evaluate their consumption in terms of Bayesian price estimates, which are different for each individual. In this framework agents maximize expected utility conditioned on their own private information about the state of nature, subject to a Bayesian estimated budget constraint. Market clearing is not an intrinsic part of the definition of BWE. However, both in the case of perfect foresight and in the case of symmetric information BWE leads to a statewise market clearing; it then becomes an ex post Walrasian equilibrium allocation. This new BWE exists under standard assumptions, in contrast to the REE. In particular, we show that our new BWE exists in the well-known example in Kreps (J Econ Theory 14:32–43, 1977), where REE fails to exist. This work was done in the Spring of 2005, when EJB was a visiting professor at the University of Illinois.     

ADVERSE SELECTION WITH HETEROGENEOUSLY INFORMED AGENTS

A model of over-the-counter markets is proposed. Some asset buyers are informed in that they can identify high-quality assets. Sellers with private information choose what type of buyers they want to trade with. When the measure of informed buyers is low, a unique equilibrium exists, and interestingly, price, trading volume and welfare typically decrease with more informed buyers. When the measure of informed buyers is intermediate, multiple equilibria arise. A switch from one equilibrium to another can lead to large drops in liquidity, price, trading volume, and welfare, like a financial crisis. Implications of an endogenous measure of informed buyers are also studied.     

Multidimensional Bargaining Under Asymmetric Information

A buyer with private information regarding marginal valuation bargains with a seller to determine price and quantity of trade. Depending on parameter values, a high‐valuation buyer wants either to reveal information to create value or to conceal it to capture value. In the first case, equilibrium trades are efficient. In the second case, the low‐valuation buyer purchases less than her efficient quantity, and there can be a one‐period delay in trade. The quantity distortion is the only inefficiency that persists when time between offers approaches zero. There exist equilibria that are independent of the seller's prior beliefs.     

Competition and confidentiality: Signaling quality in a duopoly when there is universal private information

We model non-cooperative signaling by two firms that compete over a continuum of consumers, assuming each consumer has private information about the intensity of her preferences for the firms' respective products and each firm has private information about its own product's quality. We characterize a symmetric separating equilibrium in which each firm's price reveals its respective product quality. We show that the equilibrium prices, the difference between those prices, the associated outputs, and profits are all increasing functions of the ex ante probability of high safety. If horizontal product differentiation is sufficiently great then equilibrium prices and profits are higher under incomplete information about quality than if quality were commonly known. Thus, while signaling imposes a distortionary loss on a monopolist using price to signal quality, duopolists may benefit from the distortion as it can reduce competition. Finally, average quality is lower since signaling quality redistributes demand towards low-quality firms.     

Auction and the informed seller problem

A seller possessing private information about the quality of a good attempts to sell it through a second-price auction with announced reserve price. The choice of a reserve price transmits information to the buyers. We characterize the equilibria with monotone beliefs of the resulting signaling game and show that they lead to a reduced probability of selling the good compared to the symmetric information situation. We compare the unique separating equilibrium of this signaling game to the equilibrium of a screening game in which an uninformed monopoly broker chooses the trading mechanism. We show that the ex ante expected probability of trade may be larger with a monopoly broker, as well as the ex ante total expected surplus.     

Distributional Effects of Tariff Reduction in the Transforming Chinese Economy

A general equilibrium trade model is constructed to study the issue of income redistribution between the state sector and the private sector induced by a tariff reduction in the transforming Chinese economy. The analysis is conducted in the presence of price control, tariff protection, and the coexistence of state and private sectors. It is shown that the way in which income levels of the two sectors are affected by the tariff reduction depends on (i) the way in which the price of nontradables is affected, (ii) the degree of privatization, and (iii) the extent of price control.     

Convergence to perfect competition of a dynamic matching and bargaining market with two-sided incomplete information and exogenous exit rate

Consider a decentralized, dynamic market with an infinite horizon and incomplete information in which buyers and sellers' values for the traded good are private and independently drawn. Time is discrete, each period has length δ, and each unit of time a large number of new buyers and sellers enter the market. Within a period each buyer is matched with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, the seller and winning buyer exit with their realized utility. Traders who fail to trade either continue in the market to be rematched or exit at an exogenous rate. We show that in all steady state, perfect Bayesian equilibria, as δ approaches zero, equilibrium prices converge to the Walrasian price and realized allocations converge to the competitive allocation.     

Market Crashes and Informational Avalanches

This paper analyses a security market with transaction costs and a sequential trading structure. Transaction costs may prevent many traders from revealing their private information if they trade in a sequential fashion. Due to the information aggregation failure, hidden information gets accumulated in the market which may be revealed by a small trigger, yielding a high volatility in the absence of an accompanying event. The paper first characterizes the optimal trading strategy of the agent which constitute the unique equilibrium. Further properties of the price sequence are obtained using the concepts of informational cascade and informational avalanche.
The results are applied to the explanation of market crashes. In particular, the dynamics of market crashes are illustrated as evolving through the following four phases: (1) boom; (2) euphoria; (3) trigger; and (4) panic; where the euphoria corresponds to the informational cascade and the panic corresponds to the informational avalanche.