Linear and non-linear price decentralization

Compendious and thorough solutions to the existence of a linear price equilibrium problem, the second welfare theorem, and the limit theorem on the core are provided for exchange economies whose consumption sets are the positive cone of arbitrary ordered Fréchet spaces—dispensing entirely with the assumption that the vector ordering of the commodity space is a lattice. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory vector orderings that are not lattices, which arise in the typical model of portfolio trading with missing options. The assumptions are on the primitives of the model. They are bounds on the marginals of non-linear prices and for ω-proper economies they are both sufficient and necessary.     

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.     

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.     

The communication requirements of efficient allocations and supporting prices

We show that any communication finding a value-maximizing allocation in a private-information economy must also discover supporting prices (in general personalized and nonlinear). In particular, to allocate L indivisible items between two agents, a price must be revealed for each of the 2^L-1 bundles. We prove that all monotonic prices for an agent must be used, hence exponential communication in L is needed. Furthermore, exponential communication is needed just to ensure a higher share of surplus than that realized by auctioning all items as a bundle, or even a higher expected surplus (for some probability distribution over valuations). When the utilities are submodular, efficiency still requires exponential communication (and fully polynomial approximation is impossible). When the items are identical, arbitrarily good approximation is obtained with exponentially less communication than exact efficiency.     

Dynamic Equilibrium with Overpriced Put Options

It is a well-known anomaly that prices of put options are too high when options are out-of-the-money. This paper presents a simple general equilibrium model of the market where European put options become substantially overpriced when they are out-of-the-money. Overpricing is due to the presence of short-sale constraints on trading stocks and derivatives, as well as the heterogeneity between investors. We confirm the predicting power of the model by comparing its implications with existing empirical results.     

Germany's New Insider Law: The Empirical Evidence after the First Year

Abstract. This paper investigates insider trading activities in German stocks during the first year following implementation of the new Insider Law on 1 July 2002. It can be observed that insiders act as contrarian investors. They buy stocks after prices have fallen and sell stocks after prices have risen. In general, insider trades are very profitable. A typical stock purchased by an insider yields an abnormal return of almost 3 per cent during the 25 days following the transaction. In contrast, a typical stock that has been sold by insiders achieves an abnormal return of nearly −3 per cent over the same time period. Outsiders who copy the transactions of insiders can achieve nearly the same abnormal returns. Abnormal returns remain substantial even after transaction costs. The results suggest that prices of stocks in which insiders trade do not seem to be semi-strong efficient.     

Internal rationality, imperfect market knowledge and asset prices

We present a decision theoretic framework in which agents are learning about market behavior and that provides microfoundations for models of adaptive learning. Agents are ‘internally rational’, i.e., maximize discounted expected utility under uncertainty given dynamically consistent subjective beliefs about the future, but agents may not be ‘externally rational’, i.e., may not know the true stochastic process for payoff relevant variables beyond their control. This includes future market outcomes and fundamentals. We apply this approach to a simple asset pricing model and show that the equilibrium stock price is then determined by investors? expectations of the price and dividend in the next period, rather than by expectations of the discounted sum of dividends. As a result, learning about price behavior affects market outcomes, while learning about the discounted sum of dividends is irrelevant for equilibrium prices. Stock prices equal the discounted sum of dividends only after making very strong assumptions about agents? market knowledge.     

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.     

Modelling the demand for housing over the life cycle

We model individual demand for housing over the life cycle, and show the aggregate implications of this behaviour. Individuals delay purchasing their first home when incomes are low or uncertain. Higher house prices lead households to downsize, rather than to stop being owners. Fixed costs (property transactions taxes) have important impacts on welfare (a wealth effect) and house purchase decisions (substitution effect). In aggregate, positive house price shocks lead to consumption booms among the old but falls in consumption for the young, and reduced housing demand; positive income shocks lead to consumption booms among the young and increased housing demand.     

Equilibrium Prices When the Sunspot Variable Is Continuous

We analyze sunspot-equilibrium prices in nonconvex economies with perfect markets and a continuous sunspot variable. Our primary result is that every sunspot equilibrium allocation can be supported by prices that, when adjusted for probabilities, are constant across states. This result extends to the case of a finite number of equally-probable states under a nonsatiation condition, but does not extend to general discrete state spaces. We use our primary result to establish the equivalence of the set of sunspot equilibrium allocations based on a continuous sunspot variable and the set of lottery equilibrium allocations. Journal of Economic Literature Classification Numbers: D51, D84, E32.     

Models of Capital Requirements in Static and Dynamic Settings

The aim of this paper is twofold. First, we generalize the notion of capital requirement, originally formulated in a regulatory framework, in order to unify other apparently diverse financial concepts. Second, we stress the interpretation of a capital requirement as a measure of risk, providing a link with the theory of coherent risk measures. We define a capital requirement as the minimal initial cost of a hedging action that makes the original position acceptable. Three basic elements are involved in such a methodology: a system of prices, a class of permitted hedging actions and a criterion of acceptability. Our approach is very general, because we construct capital requirements on vector spaces. However, we will give some concrete applications related, in particular, to the availability of a financial market, to the presence of different business units in an institution or to the fact that pay-offs are spread over different dates.     

Reserve price signaling

In a general auction model in which bidders’ signals are affiliated, we characterize the unique separating equilibrium in which the seller can use reserve prices to credibly signal her private information. When the buyers’ signals are independent, the optimal reserve price is shown to be increasing in the number of bidders under certain conditions. We also demonstrate that the probability that the item is sold at the reserve price can increase as the number of bidders increases, which indicates a more central role for reserve prices than perceived in the standard auction models.     

On the impact of leverage constraints on asset prices and trading volume

Abstract. Researchers have used stylized facts on asset prices and trading volume in stock markets (in particular, the mean reversion of asset returns and the correlations between trading volume, price changes and price levels) to support theories where agents are not rational expected utility maximizers. This paper shows that this empirical evidence is in fact consistent with a standard infinite horizon – perfect information – expected utility economy where some agents face leverage constraints similar to those found in todays financial markets. In addition, and in sharp contrast to the theories above, we explain some qualitative differences that are observed in the price-volume relation on stock and on futures markets. We consider a continuous-time economy where agents maximize the integral of their discounted utility from consumption under both budget and leverage constraints. Building on the work by Vila and Zariphopoulou (1997), we find a closed form solution, up to a negative constant, for the equilibrium prices and demands in the region of the state space where the constraint is non-binding. We show that, at the equilibrium, stock holdings volatility as well as its ratio to stock price volatility are increasing functions of the stock price and interpret this finding in terms of the price-volume relation. We would like to thank the editor and two anonimous referees for valuable substantive comments. Our gratitude also to Franklin Allen, Kerry Back, Domenico Cuoco, Xavier Freixas, Sanford Grossman, Michel Habib, Lutz Hendricks, Richard Kihlstrom, Fernando Restoy, Mary Thomson, Jean-Luc Vila, participants to seminars at Birkbeck College, Carnegie-Mellon, Columbia, ESSEC, HEC, IAE, INSEAD, London Business School, London School of Economics, McGill, Michigan, National University of Singapore, Pompeu Fabra, North Carolina, Washington-St-Louis, Wharton, the Jornadas de Economía Financiera BBV, and the Meetings of the Society for Economic Dynamics and Control and the American Finance Association. Special thanks are due to Süleyman Basak for his enthusiastic support and many helpful suggestions. The usual disclaimer applies. We gratefully acknowledge the support of the BBV and Caja de Madrid Foundations and CREF (both authors) and of the Spanish Ministry of Education under DGICYT grant no. PB93-0388 (first author).     

General equilibrium models of monopolistic competition: A new approach

We analyze a class of ‘large group’ Chamberlinian monopolistic competition models by applying different concepts of functional separability to the same set of first-order conditions for utility maximization. We show that multiplicatively quasi-separable (MQS) functions yield ‘constant relative risk aversion’ (CRRA), and, therefore ‘constant elasticity of substitution’ (CES), functions, whereas additively quasi-separable (AQS) functions yield ‘constant absolute risk aversion’ (CARA) functions. We then show that the CARA specification sheds new light on: (i) pro-competitive effects, i.e., profit-maximizing prices are decreasing in the mass of competing firms; and (ii) a competitive limit, i.e., profit-maximizing prices converge to marginal costs when the mass of competing firms becomes arbitrarily large.     

Observable restrictions of general equilibrium models with financial markets

This paper examines whether general equilibrium models of exchange economies with incomplete financial markets impose restrictions on prices of commodities and assets given the stochastic processes of dividends and aggregate endowments. We show that the assumption of time-separable expected utility implies restriction on the cross-section of asset prices as well as on spot commodity prices. However, a relaxation of the assumption of time separability will generally destroy these restriction.     

The α-MEU model: A comment

In Ghirardato et al. (2004) [7], Ghirardato, Macheroni and Marinacci propose a method for distinguishing between perceived ambiguity and the decision-maker?s reaction to it. They study a general class of preferences which they refer to as invariant biseparable. This class includes CEU and MEU. They axiomatize a subclass of α-MEU preferences. If attention is restricted to finite state spaces, we show that any α-MEU preference relation, satisfies GMM?s axioms if and only ifα=0 or 1, that is, the preferences must be either maxmin or maxmax. We show by example that these axioms may be satisfied when the state space is [0,1].     

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.     

Imperfect financial integration and asymmetric information: competing explanations of the home bias puzzle?

Abstract This paper shows that imperfect financial integration and informational asymmetries are not competing theories but rather complementary ideas to a single explanation of the home bias puzzle. We develop a rational expectations model of asset prices with investors that face informational constraints and find that informational advantages arise endogenously as a response to small financial frictions. We also present empirical evidence that (i) international financial frictions are correlated to observed patterns of US investors’ attention and that (ii) the attention US investors allocate to foreign stocks helps explain home bias towards those countries, even after controlling for financial integration levels.     

Art market inefficiency

Art is often used as an investment vehicle. Given the importance of market efficiency in finance, we use a large auction-based index to test whether the art market is weakly efficient. Evidence reveals that returns on artworks exhibit high positive auto-correlation. We attribute this result to price truncation resulting from unobservable reserve prices in auctions. We conclude that the art market is not efficient, mainly because price formation is opaque to outsiders who lack information on unsold artworks.     

Asset price fluctuations without aggregate shocks

We analyze the pricing of a productive asset in a class of dynamic exchange economies with heterogeneous, infinitely-lived agents, and self-enforcing intertemporal trades. Individual incomes fluctuate and are correlated; preferences, dividends and aggregate income are fixed. Almost all economies in this class have a unique stationary Markovian equilibrium with fluctuations in asset prices. As the set of unrationed households changes over time and states, excess demand functions shift, asset returns fluctuate, and some households are shut out of asset markets. Examples suggest that the amplitude of these movements is negatively correlated with the productivity of the asset and with the penalty for default.