Incomplete markets: transverse financial structures

Summary. In a multiperiod economy with incomplete markets and assets with payoff depending on the price history (e.g., asset and derivatives), we show that in order to get endowment generic existence of an equilibrium it is not needed to alter settlement features such as when payments are made and when the asset is traded. This is non-trivial as each such characteristic introduces a non-generic subclass of financial instruments. We show essentially that expiry date payments are the only payments that one needs perturbing (if at all). For previous periods - the P&L discovery map - is the one relevant for wealth transfers. This map transfers wealth between one period and the next by associating to each portfolio next period potential profit and losses as a function of the revealed information at the node. All present values involved can in general - because of backward induction pricing structure - be appropriately controlled via expiry payoffs only. This enables us to extend two-period work and introduce Transverse Financial Structures for multiperiod economies, where one cannot identify the payoffs of financial instruments to the P&L discovery map (in other words we introduce some financial ingeneering for Transverse Financial Structures). We capitalize on that difference using unexploited “maturity payout degrees of freedom” and rolling back the uncertainty tree. As an application of this approach we prove a conjecture by Magill and Quinzii that commodity forward contracts lead to endowment generic existence of an equilibrium in a multiperiod set-up. Received: June 25, 1999; revised version: April 4, 2001     

Risky arbitrage,asset prices,and externalities

We introduce a no-risky-arbitrage price condition (NRAP) for asset market models allowing both unbounded short sales and externalities such as trading volume. We then demonstrate that NRAP is sufficient for the existence of competitive equilibrium in the presence of externalities. Moreover, we show that if all risky arbitrages are utility increasing, then NRAP characterizes competitive equilibrium in the presence of externalities. We are indebted to an anonymous referee for helpful comments on an earlier version of this paper. Page and Wooders are especially grateful to CERMSEM and EUREQua for their support and hospitality which made possible our collaboration.     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.     

Competitive prices for a stochastic input–output model with infinite time horizon

Consider a one-sector stochastic input–output model with infinite time horizon. The technology in each time period exhibits constant returns to scale on positive linear combinations of a finite number of basic input–output pairs. Furthermore, perfect information is available as a filtration generated by finite partitions of the state space. By definition, competitive prices require expected profit maximization in every time period. The Riesz representation of a sequence of competitive price functionals yields a state-price deflator with a supermartingale property. We show that there exists a competitive price system for some feasible program if and only if there is No Free Production (NFP). Furthermore, there exists a competitive price system for a particular program if and only if if NFP holds and the program is short-run efficient. This model includes a securities market model with or without convex cone trading constraints as a special case. Under these circumstances, NFP reduces to No Arbitrage and we recover a version of the fundamental theorem of asset pricing. The author expresses gratitude for the advice of two anonymous referees, one who pointed out the simple way to prove the key lemma and the other who helped integrate the conclusions into the existent literature.     

Social learning in a changing world

Summary. In the social learning model of Banerjee [1] and Bikhchandani, Hirshleifer and Welch [2] individuals take actions sequentially after observing the history of actions taken by the predecessors and an informative private signal. If the state of the world is changing stochastically over time during the learning process, only temporary informational cascades – situations where socially valuable information is wasted – can arise. Furthermore, no cascade ever arises when the environment changes in a sufficiently unpredictable way. Received: December 5, 1996; revised version: February 11, 1997     

Existence and local indeterminacy of periodic equilibrium paths in infinite horizon models with external effects

Summary. It is expected that every periodic equilibrium path may exist even under standard assumptions such as low discounting and the concavity of utility functions in infinite horizon models with external effects. Nevertheless, until now no such example has been presented. In this note we will first construct a bounded growth model that has an external effect and every periodic equilibrium path under any discount factor. Next we will study the conditions under which periodic equilibrium paths have a local indeterminacy. Received: December 23, 1998; revised version: April 19, 1999     

On locally optimal programs in the Robinson–Solow–Srinivasan model

In the context of a model due to Robinson, Solow and Srinivasan (the RSS model), we report results on the existence and characterization of locally optimal programs, a concept taken from theoretical physics. In particular, we propose a (new) transversality condition under which all locally optimal programs are good. An extended introduction places our theorems in the context of previous work on the existence question, including that on agreeable programs. It appears that there is no completely rational way to attack [the] problem without considering development programmes over an infinite horizon (Gale in Rev Econ Stud 34:1–8, 1967). The analysis of simple models is essential if we are to understand the corresponding situation for more complex models of the economy (Mirrlees and Stern in J Econ Theory 4:268–288, 1972). The technical convenience, for clear and quantitative results, of using an infinite time horizon is rather great (Hammond and Mirrlees in Models of economic growth, Wiley, New York, pp 283–299, 1973).     

Market power, survival and accuracy of predictions in financial markets

In a standard General Equilibrium framework, we consider an agent strategically using her large volume of trade to influence asset prices to increase her consumption. We show that, as in Sandroni (Econometrica 68:1303–1341, 2000) for the competitive case, if markets are dynamically complete and some general conditions on market preferences are met then this agent’ long-run consumption will vanish if she makes less accurate predictions than the market, and will maintain her market power otherwise. We thus argue that the Market Selection Hypothesis extends to this situation of market power, in contrast to Alchian (J Pol Econ 58:211–221, 1950) and Friedman (Essays in Positive Economics, University of Chicago Press, Chicago, 1953) who claimed that this selection was solely driven by the competitiveness of markets. I would like to thank T. Hens, A. Kirman and A. Sandroni for many stimulating conversations and encouragements. Two anonymous referees also provided very valuable comments.     

Utility representation of continuous preferences

Summary.  By generalising the Arrow-Hahn approach, we give new conditions under which a preference relation on a metric space can be represented by a continuous utility function. Received: December 11, 1995; revised version July 29, 1996     

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.     

Generalized method of moments and present value tests of the consumption-capital asset pricing model under transactions costs: evidence from the UK stock market

In this paper we test for the inclusion of the bid–ask spread in the consumption CAPM, in the UK stock market over the time period of 1980–2000. Two econometric models are used: first, Fisher’s (in J Appl Econometrics 9:S71–S94, 1994) asset pricing model is estimated by GMM. We obtain plausible values of all the structural parameters and transactions costs. We subsequently test the robustness of our results by extending the VAR approach proposed by Campbell and Shiller (in Rev Financ Stud 1:195–228, 1988). This is achieved with the inclusion of the normalised bid–ask spread as an independent variable in the pricing equation. Overall, the statistical tests are unable to reject the bid–ask spread as an independent explanatory variable in the C-CAPM. In addition, in the VAR specification we find that both the normalised and the absolute bid–ask spread is a significant predictor of the dividend to price ratio. The paper’s main conclusion is that transaction costs should be included in asset pricing models, as they possess independent explanatory power.      

Asset price bubbles in Arrow-Debreu and sequential equilibrium

Summary. Price bubbles in an Arrow-Debreu equilibrium in an infinite-time economy are a manifestation of lack of countable additivity of valuation of assets. In contrast, the known examples of price bubbles in a sequential equilibrium in infinite time cannot be attributed to the lack of countable additivity of valuation. In this paper we develop a theory of valuation of assets in sequential markets (with no uncertainty) and study the nature of price bubbles in light of this theory. We define a payoff pricing operator that maps a sequence of payoffs to the minimum cost of an asset holding strategy that generates it. We show that the payoff pricing functional is linear and countably additive on the set of positive payoffs if and only if there is no Ponzi scheme, provided that there is no restriction on long positions in the assets. In the known examples of equilibrium price bubbles in sequential markets valuation is linear and countably additive. The presence of a price bubble means that the dividends of an asset can be purchased in sequential markets at a cost lower than the asset's price. We present further examples of equilibrium price bubbles in which valuation is nonlinear, or linear but not countably additive.     

Fiat money and the value of binding portfolio constraints

We establish necessary and sufficient conditions for the individual optimality of a consumption-portfolio plan in an infinite horizon economy where agents are uniformly impatient and fiat money is the only asset available for intertemporal transfers of wealth. Next, we show that fiat money has a positive equilibrium price if and only if for some agent the zero short sale constraint is binding and has a positive shadow price (now or in the future). As there is always an agent that is long, it follows that marginal rates of intertemporal substitution never coincide across agents. That is, monetary equilibria are never full Pareto efficient. We also give a counter-example illustrating the occurrence of monetary bubbles under incomplete markets in the absence of uniform impatience.     

Asset trading volume in a production economy

Judd et al. (J Finance 63: 2203–2217, 2003) show that the stationary Lucas tree model cannot generate nontrivial asset trading: Heterogenous agents will optimally choose a fixed portfolio after initial rebalancing. This paper explores asset trading volume in production economies with heterogeneous agents and dynamically complete market structures. We establish a recursive version of the Negishi approach to prove the existence of a competitive equilibrium. Furthermore, we develop a general method to solve for equilibrium portfolios in production economies within a fairly general set of complete market structures. We thus establish the theoretical reasons why production economies in general generate a nontrivial volume of asset trading even if heterogeneity of the agents is kept to a minimum. We would like to thank W. Brock, D. DeJong and, especially, H. Ennis for comments and suggestions. We also thank seminar participants at Di Tella and San Andrés Universities (Argentina), the Institute for Advanced Studies (Austria), SED Meetings 2005 (Budapest) and SAET Conference 2005 (Vigo).     

Economic theory and econometric dynamics in modelling wages and prices in the United Kingdom

We show that a “competing claims” model of imperfect competition can explain the movements of wages and prices in the United Kingdom, using quarterly data covering 1976–93. We argue that careful attention both to economic theory and to the interaction between dynamics and identification is crucial in the building of the model and to dynamic econometric models in general. We use a small numerical example with simulated cointegrated data to illustrate the potential pitfalls. First version received: January 1998/final version received: November 1998     

Welfare-improving financial innovation with a single good

Summary. We show that at any equilibrium of almost every single-good incomplete markets economy, it is possible to find an asset which when introduced makes every agent better-off. Diamond (1967) has shown, however, that such economies are constrained suboptimal, so it is of course impossible to find a new asset which makes all agents worse-off. This contrasts with the case of multiple consumption goods, for which Cass and Citanna (1995) and Elul (1995) demonstrate that equilibrium utilities may be arbitrarily perturbed via financial innovation. Proving our result requires us to exploit not changes in equilibrium prices, but rather the gains to trading the new asset. In particular, we find an asset which when introduced does not change the existing asset prices even though it is traded by every agent – by a revealed preference argument it must therefore make everyone better-off. Received: May 28, 1997; revised version: July 1, 1997     

Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games

The implications of evolutionarily stable behavior in finite populations have recently been explored for a variety of aggregative games. This note proves an intimate relationship between quasi-submodularity and global evolutionary stability of strategies for these games, which – apart from being of independent interest – accounts for a number of results obtained in the recent literature: we show that any evolutionarily stable strategy of a quasi-submodular aggregative game must also be globally stable. That is, if one mutant cannot successfully invade a population, any number of mutants can do so even lessThe author is grateful to Ana Ania and Carlos Alōs-Ferrer for comments on an earlier version     

Moments of truncated <Emphasis Type="Italic">t</Emphasis> and <Emphasis Type="Italic">F</Emphasis> distributions

Truncated distributions commonly arise in economics and related areas, see, for example, Lee (Econ Lett 3:165–169, 1979), Lien (Econ Lett 19:243–247, 1985; Econ Lett 20:45–47, 1986), Burdett (Econ Lett 52:263–267, 1996), Sercu (Insur: Math and Econ 20:79–95, 1997), Abadir and Magdalinos (Econom Theory 18:1276–1287, 2002), and Horrace (J Econom 126:335–354, 2005). In this note, we consider the most commonly encountered truncated distributions with heavy tails: the truncated t distribution and the truncated F distribution. For each of these distributions, we derive explicit expressions for the moments and estimation procedures by the method of moments and the method of maximum likelihood. An application is illustrated to a popular data set in the econometric literature.      

Arrow-Debreu equilibria with asymptotically heterogeneous expectations exist

Summary. In infinite horizon economies only local equivalence of beliefs is needed to ensure the existence of an Arrow–Debreu equilibrium. In fact, agents can even disagree completely in the long run in the sense that asymptotically, their beliefs are singular. Received: November 3, 2000; revised version: February 13, 2002     

What determines simultaneous asset bubbles? An empirical analysis

The recent global financial crisis demonstrated that the simultaneous collapse of asset bubbles in different countries is a major challenge for monetary policy. In order to evaluate determinants of these simultaneous asset bubbles, we detect rational asset bubbles in corporate equity and real estate markets worldwide using forward recursive right-sided ADF tests. Then we create dummy variables for simultaneous asset bubbles and analyse potential determinants using gravity models and spatial economics. Our empirical analysis suggests that simultaneous asset bubbles depend positively upon potential asset demand, capital account openness, monetary conditions, cultural similarities and negatively upon informational frictions and exchange rate flexibility. These findings imply that monetary policy can impede the probability of simultaneous asset bubbles by ensuring sound monetary conditions and choosing a flexible exchange regime.