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.     

Informational efficiency: ranking markets

Summary. The paper studies informational properties of three types of imperfectly competitive markets: a one-signal speculative market (OSS market) in which agents have only private information about the fundamental value (v) of the risky asset traded, a two-signal speculative market (TSS market) in which agents have private information about both v and the asset supply, and a market in which agents are endowed with both information about v and shares of the risky asset traded. In this last market (JA market), agents have joint activities: they trade for both speculative and hedging purposes. It is shown that (i) the JA market and the OSS market are the most and the least efficient, respectively, and (ii) the levels of informational efficiency in the three markets are inversely correlated with the intensities with which traders use their private information about the fundamental value of the asset. Received May 28, 1999; revised version: May 28, 1999     

Retailers as agents and the limits of parallel trade

The volume of retail-level parallel trade is surprisingly small despite persistent international price differences. We offer an agency-based explanation by considering competition between an original home manufacturer and a foreign retailer. The model endogenizes the role of the retailer as an agent with private information on the perceived quality of the good in its own market. The manufacturer cannot control the retailer once the latter has ordered its sales quantity but it can limit the initial offer. If parallel trade is permitted, this offer will fall if there is incomplete information, resulting in a small, or zero, volume of parallel trade. This outcome makes both the original producer and foreign consumers worse off, while offering little benefit to home consumers, compared to the case where such trade is banned.     

Information, trade and incomplete markets

The no-trade result of Milgrom and Stokey, J Econ Theory 26:17–27 (1982), states that if rational traders begin with an ex-ante Pareto optimal allocation then the arrival of information cannot generate trade. This paper allows traders to trade before and after the arrival of information. If there are enough securities to hedge against all payoff relevant risk, then the preinformation-arrival allocation is Pareto optimal and information arrival has no effect. This no-retrade result is the competitive analog of the no-trade result of (1982). However, information generically generates trade when markets are state-contingent incomplete.We thank seminar participants at Cambridge, Carnegie Mellon,Cornell, Essex, London, Maastricht, USC, and York and participants at the 2003 SITE, the 2003 SAET and the Fall 2002 Cornell–Penn State Macro Conference. We also thank Karl Shell and a referee for this journal for useful comments     

General equilibrium in economies with adverse selection

We model economies of adverse selection as Arrow–Debreu economies. In the spirit of Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we identify the consumption set of the individuals with the set of lotteries over net transfers. Thus, prices are linear in lotteries, but they may be non linear in commodity bundles. First, we study a weak equilibrium notion by viewing the economy of adverse selection as a pure exchange economy. The weak equilibrium set is non empty, but some of the allocations may be inefficient, and the equilibria indeterminate. Second, following Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we introduce an intermediary (firm) supplying feasible and incentive compatible measures. Equilibria are constrained efficient, but the equilibrium set is empty for an open set of economies containing the Rothschild and Stiglitz insurance economies. The research of A. Rustichini was supported by the NSF grant NSF/SES-0136556.     

Ex ante contracting with endogenously determined communication plans

Summary. In this paper we introduce a new model of ex ante contracting for economies with asymmetric information to examine endogenously determined communication plans for information sharing in the interim stage. In contrast to the models used in previous research, in the present model agents negotiate not only on a contract of state contingent allocations but also on a communication plan, a set of rules describing how agents will reveal part of their private information at the interim stage to execute the trade contracts. We prove a result about the nested structure of the set of allocations implementable by various communication plans and establish the existence of core strategies for this cooperative game under various regularity conditions. Received: 4 March 1998; revised version: 17 September 1999     

Joining a Queue or Staying Out: Effects of Information Structure and Service Time on Arrival and Staying Out Decisions

We study a class of single-server queueing systems with a finite population size, FIFO queue discipline, and no balking or reneging. In contrast to the predominant assumptions of queueing theory of exogenously determined arrivals and steady state behavior, we investigate queueing systems with endogenously determined arrival times and focus on transient rather than steady state behavior. When arrival times are endogenous, the resulting interactive decision process is modeled as a non-cooperative n-person game with complete information. Assuming discrete strategy spaces, the mixed-strategy equilibrium solution for groups of n = 20 agents is computed using a Markov chain method. Using a 2 × 2 between-subject design (private vs. public information by short vs. long service time), arrival and staying out decisions are presented and compared to the equilibrium predictions. The results indicate that players generate replicable patterns of behavior that are accounted for remarkably well on the aggregate, but not individual, level by the mixed-strategy equilibrium solution unless congestion is unavoidable and information about group behavior is not provided.JEL Classification: C71, C92, D81     

Endogenous timing in a mixed oligopoly with semipublic firms

An endogenous order of moves is analyzed in a mixed market where a firm jointly owned by the public sector and private domestic shareholders (a semipublic firm) competes with n private firms. We show that there is an equilibrium in which firms take production decisions simultaneously. This result is strikingly different from that obtained by Pal (Econ Lett 61:181–185, 1998), who shows that when a public firm competes with n private firms all firms producing simultaneously in the same period cannot be sustained as a Subgame Perfect Nash Equilibrium outcome. Our result differs from that of Pal (Econ Lett 61:181–185, 1998) for two reasons: firstly, we consider that there is a semipublic firm rather than a public firm. Secondly, Pal (Econ Lett 61:181–185, 1998) considers that the public firm is less efficient than private firms while in our paper all firms are equally efficient.     

Strategic policies and growth: an applied model of R&D-driven endogenous growth

We introduce and explore a general equilibrium model with R&D-driven endogenous growth, whose antecedents are the models of Romer (1990) [Romer, P.M., 1990. Endogenous technological change. Journal of Political Economy, 98, S71-102] and Grossman and Helpman (1991) [Grossman, G.M., Helpman E., 1991. Innovation and Growth in the Global Economy, The MIT Press, Cambridge]. Utilizing evidence from recent econometric studies on sources of growth, the model also accounts explicitly for cross-border technological spillovers. The model is specified and calibrated to data from Japan, and is solved to obtain both the transitional and the steady-state equilibria. We explore the effects of selective trade and R&D promotion policies on long-run growth and social welfare. The model results suggest that while a strategic trade policy has little effect on re-allocating resources into domestic R&D activities, it can significantly affect the cross-border spillovers of technological knowledge, which, in turn, stimulates growth. We find that trade liberalization may cause the growth rate to fall and lead to a loss of social welfare in the long-run, although it improves welfare in the short-run. R&D promotion policies stimulate growth by inducing private agents to allocate more resources to domestic R&D, as well as to take greater advantage of global R&D spillovers. Here, we find significantly high growth effects together with sizable gains in social welfare at low incidence to tax payers.     

Researching Preferences,Valuation and Hypothetical Bias

A number of recent papers in environmental economics have focused on the process of researching preferences – agents are uncertain about preferences but with effort may narrow their uncertainty. This issue has arisen in formulating bids in contingent valuation (CV) as well as the debate over the divergence between WTP and WTA. In the context of CV, it has been suggested that the hypothetical nature of the preference elicitation process biases responses. This paper provides both a theoretical model and experimental evidence to contribute to this debate. The model is a model of competitive bidding for a private good with two components that are particularly relevant to the debate. The first component is that bidders are unsure of their own value for the private good but may purchase information about their own value (researching preferences). The second component is that there is a probability that the auction is hypothetical – that the winning bidder will not get the private good and will not pay the winning bid. The experiment tests this theoretical model of bidding equilibrium and analyzes the effects of variations in the parameters (hypotheticalness, information costs and number of agents) on the endogenous variables (such as the proportion of bidders who become informed and the winning bid). Experimental results suggest that an increase in the hypotheticalness of an auction tends to decrease the likelihood that bidders pay for information on their valuation with an ambiguous effect on the winning bid.      

Feasibility Criteria in Monetary Trade

Consider the problem of how agents in a pure exchange competitive framework acquire their desired bundles of goods through a process of decentralized trade, i.e., in the absence of an auctioneer. Since the agents' wants are not mutually coincident, a medium of exchange is necessary to conduct trade. One relevant question to ask in this context is what property a commodity should possess in order for it to be eligible as a medium of exchange? This note discovers one such attribute, that the good be included in the final consumption vector of each agent. The condition is an improvement over an earlier one due to Ostroy and Starr (1974) which requires each agent to have large quantities of the medium of exchange in her/his initial endowment of commodities. JEL Classification Numbers: D50, E42.     

Credibility costs in the monetary integration game*

Euro candidates are expected to maintain the value of their currency within the fluctuation band of the new exchange rate mechanism for at least two years. This paper highlights some unpleasant macroeconomic effects that could occur during this interval. The problem is cast as a two‐stage sequential game between private agents and the government of the applicant country. The policy‐maker decides whether to devaluate the domestic currency or not at two distinct dates; it makes a last choice just before accession to the monetary union. Under an assumption of incomplete information of private agents about the government's priorities on inflation and economic activity, the game presents a hybrid perfect Bayesian equilibrium. In the pooling configuration, an initial policy of zero devaluation does not signal the final devaluation decision. As private agents cannot completely rule out the risk of a ‘last devaluation’, a premium adds to interest rates and entails a systematic output loss.     

Note on the non-existence of sunspot equilibrium

In this note, we emphasize the role of consumers’ risk aversion in the non-existence of sunspot equilibria in incomplete market economies. We prove that there are no sunspot equilibria if the fundamentals of the underlying economy admit a unique equilibrium for any distribution of endowments. This substantiates Mas-Colell’s (Economic analysis of markets and games: essays in honor of Frank Hahn. MIT, Cambridge, 1992) conjecture. We also prove that, in a two-consumer economy, no sunspot equilibrium exists under the more relaxed condition that the underlying economy admits a unique equilibrium for the initial endowment. This is a generalization of Corollaries 1 and 2 of Hens and Pilgrim (Econ Theory 24:583–602, 2004).      

Evolution of Walrasian equilibrium in an exchange economy

We study the stochastic stability of a dynamic trading process in an exchange economy. We use a simplified version of a trading model à la Shapley and Shubik (J Polit Econ 85:937–968, 1977). Two types of agents equipped with Leontief preferences trade goods in markets by offering endowments, and actual trades occur at market clearing prices. Better behavior tends to spread through the same type of agents by imitation, and agents also make mistakes occasionally. We provide a sufficient condition for the perturbed dynamic process to have a unique stochastically stable state that is a Walrasian equilibrium allocation. In this sense, we give a rationale for Walrasian behavior.     

Political Commodities and Sovereignty Management: Cigarette Smuggling across Brazil’s Southern Borders

Cigarette smuggling across Brazil’s borders with Paraguay, Uruguay and Argentina involves large amounts of merchandise and money. The public in Brazil associates this activity with images of war, contamination and other threats to state sovereignty. This article assesses the political meaning and uses of smuggling in order to challenge the assumption that smuggling threatens the sovereignty of the Brazilian state. With the help of a literature review, fieldwork at the border, interviews with practitioners, a cartographic analysis of news coverage of seizures, the tobacco production and consumption, the market and its regulation, actors, routes and networks were mapped and analysed. In the Southern Cone of South America, an integrated transborder territory emerges where tobacco is cultivated, prepared and distributed, and cigarettes are manufactured, transported, sold and smoked. These flows cross distinct legal framings and lead to an increase in danger and profit. Thus, the market is segmented between national legal products and imported cigarettes that are cheaper and illegal but easily obtainable. The concepts of political commodities understood as the acts of powerful agents who barter advantages related to their authority and sovereignty management, understood as the use of legal (state-managed) structures according to private interests at different scale levels, provide useful theoretical tools to examine the territorialisation of the cigarette smuggling and its control by the state and private agents. We conclude that tobacco production and trade, as well as cigarette smuggling, are connected via agents who use the border to build the legal market and, consequently, to increase the trade value of national tobacco. Cigarette smuggling across the state borders of the Southern Cone combines networks and places in such a way that is integrated into the legal economy and the national territories, and it does not defy state’s sovereignty.     

On optimality in intergenerational risk sharing

Summary. This paper defines and studies optimality in a dynamic stochastic economy with finitely lived agents, and investigates the optimality properties of an equilibrium with or without sequentially complete markets. Various Pareto optimality concepts are considered, including interim and ex ante optimality. We show that, at an equilibrium with a productive asset (land) and sequentially complete markets, the intervention of a government may be justified, but only to improve risk sharing between generations. If markets are incomplete, constrained interim optimality is investigated in two-period lived OLG economies. We extend the optimality properties of an equilibrium with land and give conditions under which introducing a pay-as-you-go system at an equilibrium would not lead to any Pareto improvement. Received: October 5, 1998; revised version: April 3, 2001     

On the dynamics of inequality

The dynamics of inequality are studied in a model of human capital accumulation with credit constraints. This model admits a multiplicity of steady state skill ratios that exhibit varying degrees of inequality across households. The main result studies equilibrium paths. It is shown that an equilibrium sequence of skill ratios must converge monotonically to the smallest steady state that exceeds the initial ratio for that sequence. Convergence is “gradual" in that the steady state is not achieved in finite time. On the other hand, if the initial skill ratio exceeds the largest steady state, convergence to a steady state is immediate.This paper is based on unpublished notes from 1990; see http://www.econ.nyu.edu/user/debraj/DevEcon/Notes/incdist.pdf. Two considerations suggest that these results may be worth reporting in print. First, the existence of a sizeable recent literature indicates that these relatively early notes may have value outside a filing cabinet or a private webpage. Second, Mukul Majumdar’s own research on economic growth with a nonconvex technology is an even earlier precursor to some of this literature, so the current outlet – a special issue in his honor – seems appropriate. Conversations with Glenn Loury simplified the proof of the main result. I thank Dilip Mookherjee for many useful discussions, and two anonymous referees for helpful comments on an earlier draft. Funding from the National Science Foundation under grant number 0241070 is acknowledged. This paper is dedicated with much affection and warm admiration to Mukul Majumdar – or to Mukulda, as I always think of him – on the occasion of his 60th birthday.     

Debreu’s social equilibrium theorem with asymmetric information and a continuum of agents

We provide several different generalizations of Debreu’s social equilibrium theorem by allowing for asymmetric information and a continuum of agents. The results not only extend the ones in Kim and Yannelis (J Econ Theory 77:330–353, 1977), Yannelis and Rustichini (Stud Econ Theory 2:23–48, 1991), but also new theorems are obtained which allow for a convexifying effect on aggregation (non-concavity assumption on the utility functions) and non-convex strategy sets (pure strategies). This is achieved by imposing the assumption of “many more agents than strategies” (Rustichini and Yannelis in Stud Econ Theory 1:249–265, 1991; Tourky and Yannelis in J Econ Theory 101:189–221, 2001; Podczeck in Econ Theory 22:699–725, 2003). To the memory of Gerard Debreu. A preliminary draft was presented in Paris, in April of 2005. I have benefited from the discussion, comments and questions of Erik Balder, Jean-Marc Bonnisseu, Bernard Cornet and Filipe Martins Da-Rocha and Conny Podczeck. A careful and knowledgeable referee made several useful comments and rescued me from a mishap.     

Takeoffs

This paper identifies factors associated with takeoff—a sustained period of high growth following a period of stagnation. Countries that experience takeoffs average 2.3% annual growth following their stagnation episodes, while those that do not average 0%. Using probit, we find that de jure trade openness is positively and significantly associated with takeoffs. A one‐standard‐deviation increase in de jure trade openness is associated with a 55% increase in the probability of a takeoff in our default specification. Capital account openness encourages takeoff responses, but measures of de facto trade openness are found to be poor predictors of takeoffs. We also examine the determinants of nations achieving “sustained” takeoffs; i.e. those lasting eight years or longer. Takeoffs in countries with more commodity‐intensive output bundles are less likely to be sustained, suggesting that adverse terms‐of‐trade shocks may play a role in ending long‐term high growth episodes.     

Implementation without incentive compatibility: Two stories with partially informed planners

We consider two stories, Typhoon by Conrad and Traveler's Dilemma by Basu, 1994, Basu, 2007, as implementation problems under incomplete information without incentive compatibility, but where the planner has some private information regarding the state. If social choice functions do not satisfy incentive compatibility, full implementation is unattainable via existing approaches. For each story, we construct a direct mechanism that relies on the planner's private information. We provide a sufficient condition on players' beliefs regarding the state under which every player has a unique rationalizable action, namely, telling the truth. Thus, in these stories, the planner's information can bypass the lack of incentive compatibility.