Construction of a state space for interrelated securities with an application to temporary equilibrium theory

Summary We construct an endogenous state space in an exchange economy with possibly infinite horizon. Every period agents trade securities whose payoffs depend on future dividends and asset prices. We reject the perfect foresight assumption on the ground that agents have not only limited knowledge of other individuals' endowments and preferences, but also limited capacity to compute equilibria. We choose instead absence of arbitrage as the principle which allows agents to determine if a system of future prices is possible. We give an alogrithm to compute the set of nonarbitrage prices every period, with both finite and infinite horizon. We then apply this endogenous structure of uncertainty to an infinite horizon temporary equilibrium model.I would like to thank Professor Donald Brown for his constant help and guidance. I have also greatly benefited from helpful discussions with Professors Jacques Drèze, Bernard Dumas, Mordecai Kurz, Carsten Nielsen, Jan Werner, and Ho-Mou Wu.     

Competitive equilibrium with unawareness in economies with production

This paper investigates an extension of the GEI-unawareness framework by Modica et al. (Econ. Theory 12 (1998) 259) to economies with entrepreneurial production. Existence of equilibrium is guaranteed given decreasing returns to scale. Firm's value and investment decision in equilibrium are characterized. An example of commodity innovation shows that the effect of different degrees of awareness on investment decisions depend upon the degree of risk aversion. In the case of log preferences unawareness may not matter for commodity innovation, although this depends on other preference features.     

Unawareness and bankruptcy: A general equilibrium model

Summary. We present a consistent pure-exchange general equilibrium model where agents may not be able to foresee all possible future contingencies. In this context, even with nominal assets and complete asset markets, an equilibrium may not exist without appropriate assumptions. Specific examples are provided. An existence result is proved under the main assumption that there are sufficiently many states that all the agents foresee. An intrinsic feature of the model is bankruptcy, which agents may involuntarily experience in the unforeseen states. Received: April 23, 1997; revised version: May 19, 1997     

Multiplicity in general financial equilibrium with portfolio constraints

This paper explores the role of portfolio constraints in generating multiplicity of equilibrium. We present a simple financial market economy with two goods and two households, households who face constraints on their ability to take unbounded positions in risky stocks. Absent such constraints, equilibrium allocation is unique and is Pareto efficient. With one portfolio constraint in place, the efficient equilibrium is still possible; however, additional inefficient equilibria in which the constraint is binding may emerge. We show further that with portfolio constraints cum incomplete markets, there may be a continuum of equilibria; adding incomplete markets may lead to real indeterminacy.     

Coordination and correlation in Markov rational belief equilibria

Summary This paper studies the effect of correlation in the rational beliefs of agents on the volatility of asset prices. We use the technique of generating variables to study stable and non-stationary processes needed to characterize rational beliefs. We then examine how the stochastic interaction among such variables affects the behavior of a wide class of Rational Belief Equilibria (RBE). The paper demonstrates how to construct a consistent price state space and then shows the existence of RBE for any economy for which such price state space is constructed. Next, the results are used to study the volatility of asset prices via numerical simulation of a two agents model. If beliefs of agents are uniformly dispersed and independent, we would expect heterogeneity of beliefs to have a limited impact on the fluctuations of asset prices. On the other hand, our results show that correlation across agents can have a complex and dramatic effect on the volatility of prices and thus can be the dominant factor in the fluctuation of asset prices. The mechanism generating this effect works through the clustering of beliefs in states of different levels of agreement. In states of agreement the conditional forecasts of the agents tend to fluctuatetogether inducing more volatile asset prices. In states of disagreement the conditional forecasts fluctuatein diverse directions tending to cancel each other's effect on market demand and resulting in reduced price volatility.This research was supported, in part, by the Fondazione Eni Enrico Mattei of Milan, Italy, and by the Research Incentive Fund of Stanford University. The authors thank Carsten K. Nielsen and Ho-Mou Wu for valuable discussions on an earlier draft. Carsten K. Nielsen also made an important contribution to the development of Section 3.     

Sorting equilibrium in a multi-jurisdiction model

This paper analyzes a general model of an economy with heterogeneous individuals choosing among two jurisdictions, such as towns or political parties. Each jurisdiction is described by its constitution, where a constitution is defined as a mapping from all possible population partitions into the (possibly multidimensional) policy space. This study is the first to establish sufficient conditions for existence of sorting equilibria in a two-jurisdiction model for a policy space of an arbitrary dimension.     

Evolutionary stability of social norms in a socioeconomic equilibrium model

A hybrid of a model of economic equilibrium in two markets and a social game is formed. The link between the two is established through a social norm that conditions correct social behavior on economic variables and therefore distorts the economic equilibrium allocation. The initial endowment of an individual determines whether she gains from a social norm. The evolution of norms is examined in a dynamic model where norms are more likely to persist if they deliver higher utility to their believers. Also it is assumed that norms lose importance when they are disobeyed by their believers. Optimally coordinating norms are not necessarily evolutionarily stable, and a suboptimal norm can be the outcome of the evolutionary process.     

Resource allocation in a general equilibrium model of production under uncertainty

The purpose of this paper is to examine the implications of uncertainty for resource allocation, real income, and income distribution in terms of a simple two-sector general equilibrium model of a small country where uncertainty is introduced by assuming that production in one sector occurs in a stochastic environment. Assuming decreasing risk aversion, we show that an increase in uncertainty causes the movement of the resources away from the uncertain sector, a decline in expected real income, and a shift in the distribution of income against the factor employed intensively by the uncertain sector.     

Wage and price controls in the equilibrium sequential search model

In this paper, we study the effects of wage and price controls on employment, output, and welfare in a simplified version of the Bénabou (J. Econom. Theory 60 (1993) 140) equilibrium sequential search model with bilateral heterogeneity. We show that a price ceiling increases output but the change in welfare depends on three effects: the reduction in aggregate search costs, the increase in surplus due to increased output, and the transfer of production to the least efficient firm. The model is formally identical to a standard equilibrium search model of the labor market so analogous results hold for the minimum wage.     

A public firm in a model of spatial duopoly with price discrimination

We visit the role of privatization in the location decision of firms in an industry where no firm can produce all varieties demanded. We demonstrate that the Nash equilibrium locations are socially optimal, in the presence of a publicly owned firm, notwithstanding the degree of privatization.     

Asymmetric adjustment costs in simple general equilibrium models

This paper demonstrates that the introduction of asymmetric adjustment costs in a simple general equilibrium framework establishes a meaningful link between factor price determination and output determination, breaking the analytically convenient dichotomy of the Heckscher-Ohlin-Samuelson model. The possibility of trade between seemingly similar countries that differ in their adjustment technologies is visited.     

How equilibrium prices reveal information in a time series model with disparately informed, competitive traders

Accommodating asymmetric information in a dynamic asset pricing model is technically challenging due to the problems associated with higher-order expectations. That is, rational investors are forced into a situation where they must forecast the forecasts of other agents. In a dynamic setting, this problem telescopes into the infinite future and the dimension of the relevant state space approaches infinity. By using the frequency domain approach of Whiteman [Linear Rational Expectations Models: A User's Guide, University of Minnesota Press, Minneapolis, 1983] and Kasa [Forecasting the forecasts of others in the frequency domain, Rev. Econ. Dynam. 3 (2000) 726-756], this paper demonstrates how information structures previously believed to preserve asymmetric information in equilibrium, converge to a symmetric information, rational expectations equilibrium. The revealing aspect of the price process lies in the invertibility of the observed state space, which makes it possible for agents to infer the economically fundamental shocks and thus eliminating the need to forecast the forecasts of others.     

Reporting bias in incomplete information model

Company financial reports are likely to be systematically biased. In this paper, we extend the Duffie and Lando (2001) model with a skewness correction which can account for both random and directional components of reporting noise.     

Optimal tranching with diverse beliefs

In this paper, we consider the optimal selling strategy for an asset securitization originator (the issuer) when the potential buyers hold diverse beliefs. We find that the tranching process is beneficial to the issuer because it increases the total sale price. We also consider the optimal tranching strategy that maximizes the revenue of the issuer. This helps explain the widespread use of the tranching technique in the asset securitization practice. Our findings are also enlightening to understand the price bubble problem when the junior tranche is interpreted as a collateral.     

A term structure model with preferences for the timing of resolution of uncertainty

Summary In this paper we present a model of the term structure of interest rates with imperfect information and stochastic differential utility, a form of non-additive recursive utility. A principal feature of recursive utility, that distinguishes it from time-separable expected utility, is its dependence on the timing of resolution of uncertainty. In our model, we parametrize the nonlinearity of recursive utility in a way that corresponds to preferences for the timing of resolution. This way we show explicitly the dependence of prices on the rate of information, as a consequence of the nature of utilities. State prices and the term structure of interest rates are obtained in closed form, and are shown to have a form in which derivative asset pricing is tractable. Comparative statics relating to the dependence of the term structure on the rate of information are also discussed.We thank Bob Hodrick and Matt Jackson for their comments. Darrell Duffie is grateful for support from the National Science Foundation under NSF SBR-9409567. This paper presents the first model of an earlier, preliminary working paper titled: Two models of price dependence on the timing of resolution of uncertainty.     

Bertrand equilibrium with subadditive costs

We show here, in contrast to recent results, that if firms have different cost functions (that are strictly subadditive), such that the ‘monopoly breakeven prices’ are different, then in a homogeneous product duopoly there is always a Bertrand equilibrium (either in pure strategies or in mixed strategies).     

Market for Information and Identity Disclosure in an Experimental Open Limit Order Book

This paper analyses the effects of pre‐trade transparency on market quality in an experimental open limit order book preceded by a market for information. The design of the trading game is akin to the system in use in an increasing number of financial markets. We find that the disclosure of traders' identities reduces the incentive to acquire information, liquidity and volatility. We also show that a positive relation exists between the proportion of traders buying information and liquidity. The results are consistent with a standard model of price formation where the number of informed traders is endogenous .     

Consumer search with asymmetric price sampling

We explore asymmetries in the way consumers sample prices in a simple sequential search framework. In equilibrium, the price distribution of a firm catering to more local consumers first-order stochastically dominates that of its rival. Prices rise in the degree of asymmetry.     

The dynamics of efficient asset trading with heterogeneous beliefs

This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibrium when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and significant fluctuations in individual portfolios may be correct but it needs some qualifications. We consider an infinite horizon stochastic endowment economy populated by many Bayesian agents with heterogeneous priors over the stochastic process of the states of nature. Our approach hinges on studying the portfolios that decentralize Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents believe that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed generate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the true process consists of i.i.d. draws from a common distribution and the support of some agent's prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d.     

Buyer search and price dispersion: a laboratory study

We study markets with costly buyer search in which sellers simultaneously post prices. Buyers costlessly observe one or (with probability 1−q) two of the posted prices, and can accept one or pay to search again. The experiment varies q, the search cost, and the number of buyers. Equilibrium theory predicts a unified very low (high) price for q=0 (q=1) and predicts specific distributions of dispersed prices for q=1/3 and 2/3. Actual prices conform closely to the predictions in some treatments. Buyers’ reservation prices are biased away from the extremes, however, and sellers’ prices have positive autocorrelation and cross-sectional correlation.