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.     

Corrigendum to “On randomized matching mechanisms” [Economic Theory 8(1996)377–381]

Ma (in Econ. Theory 8, 377–381, 1996) studied the random order mechanism, a matching mechanism suggested by Roth and Vande Vate (Econometrica 58, 1475–1480, 1990) for marriage markets. By means of an example he showed that the random order mechanism does not always reach all stable matchings. Although Ma's (1996) result is true, we show that the probability distribution he presented – and therefore the proof of his Claim 2 – is not correct. The mistake in the calculations by Ma (1996) is due to the fact that even though the example looks very symmetric, some of the calculations are not as “symmetric.” We thank two anonymous referees for their helpful comments. B. Klaus’s and F. Klijn’s research was supported by Ramón y Cajal contracts of the Spanish Ministerio de Ciencia y Tecnología. The work of the authors was also partially supported through the Spanish Plan Nacional I+D+I (BEC2002-02130 and SEJ2005-01690) and the Generalitat de Catalunya (SGR2005-00626 and the Barcelona Economics Program of CREA).     

Market crashes,speculation and learning in financial markets

A natural conjecture is that if agents’ beliefs are almost correct then equilibrium prices should be close to rational expectations prices. Sandroni (J Econ Theory 82:1–18, 1998) gives a counterexample in an economy with sunspots and complete markets. We extend Sandroni’s result by showing that the conjecture is generically true for economies with complete markets. We consider a standard General Equilibrium model with large but finite horizon and complete markets. We show that, for almost every such economy, if conditional beliefs eventually become correct along a path of events then equilibrium prices of assets traded along this path converge to rational expectations equilibria in the sup-norm. Moreover, we establish that, generically, there exist along any such path local diffeomorphisms between individual beliefs and equilibrium prices. I would like to thank C. Ewerhart and A. Kirman for their comments, as well as the seminar participants at the University of Minho, the General Equilibrium Workshop 2005 in Zurich, and the 15th Asian General Equilibrium Conference 2007 in Singapore. An anonymous referee also provided very valuable comments.     

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.      

Testing for cointegration using the Johansen methodology when variables are near-integrated: size distortions and partial remedies

We investigate the properties of Johansen’s (J Econ Dyn Control 12:231–254, 1988; Econometrica 59:1551–1580, 1991) maximum eigenvalue and trace tests for cointegration under the empirically relevant situation of near-integrated variables. Using Monte Carlo techniques, we show that in a system with near-integrated variables, the probability of reaching an erroneous conclusion regarding the cointegrating rank of the system is generally substantially higher than the nominal size. The risk of concluding that completely unrelated series are cointegrated is therefore non-negligible. We suggest ways of identifying the problem and different approaches to reduce the size distortions of the tests.     

On purification of measure-valued maps

This paper presents new methods to obtain purification results for continuum games, which don’t make use of the “many more players than strategies” assumption (Yannelis in Econ Theory (in press) 2007) or of Loeb spaces (Loeb and Sun in Illinois J Math 50, 747–762, 2006). The approach presented doesn’t use nonstandard analysis; it is based on standard measure theory and in particular on the super-nonatomicity notion introduced in Podczeck (J Math Econ (in press) 2007). Thanks to Erik Balder, Peter Loeb, Yeneng Sun, and Nicholas Yannelis for helpful comments.     

Evolution, bargaining, and time preferences

I include a role for time preferences within a version of the Young (J Econ Theory 59:145–168, 1993b) evolutionary model of bargaining. With or without time preferences, the stochastic stable convention yields a generalized version of the Nash (Econometrica 18:155–162, 1950) Bargaining Solution. When time preferences are added to the model, agents’ discount factors enter into the stochastically stable convention in a natural manner. That is, an agent’s discount factor acts as a bargaining weight within the Nash Bargaining Solution. By taking appropriate limits, an evolutionary foundation for the Rubinstein (Econometrica 50:97–110, 1982) Bargaining Solution is provided. I thank Lew Evans, Jack Leach, Collin Starkweather, Aaron Strong, a referee and associate editor. All errors are my own.     

Sensitivity analysis of job-training effects on reemployment for Korean women

The main difficulty in treatment effect analysis with matching is accounting for unobserved differences (i.e., selection problem) between the treatment and control groups, because matching assumes no such differences. The traditional way to tackle the difficulty has been “control function” approaches with selection correction terms. This paper examines relatively new approaches: sensitivity analyses—sensitivity to unobservables—in Rosenbaum (Biometrika 74:13–26, 1987), Gastwirth et al. (Biometrika 85:907–920, 1998) and Lee (J Appl Econ 19:323–337, 2004). These sensitivity analyses are applied to the data used in Lee and Lee (J Appl Econ 20:549–562, 2005) to see how the assumption of no unobserved difference in matching affects the findings in Lee and Lee, to compare how the different sensitivity analyses perform, and to relate the “sensitivity parameters” in the different sensitivity analyses to one another. We find (i) the conclusions in Lee and Lee are weakened in the sense that only the “strong” ones survive, (ii) the sensitivity analysis in Rosenbaum (Biometrika 74:13–26, 1987) is too conservative (and inferior to Gastwirth et al.’s), and (iii) Gastwirth et al.’s and Lee’s approaches agree on some findings to be insensitive, but the two approaches also disagree on some other findings. The authors are grateful to the Editor and anonymous reviewers for their constructive and helpful comments.     

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.     

Agreeing on generalised Darwinism: a response to Pavel Pelikan

Pelikan (J Evol Econ 21:341–366, 2011) develops an interesting conceptual framework that adds to prior work on generalised Darwinism. Despite claims to the contrary we show that it is similar to the approach developed by Hodgson and Knudsen (J Evol Econ 16(4):343–366, 2006a, J Econ Behav Organ 75(1):12–24, 2010a, b), Aldrich et al. (J Evol Econ 18(5):577–596, 2008) and others. Pelikan also mischaracterises the Hodgson–Knudsen position over Lamarckism. We show why the term is misleading (rather than strictly wrong) when applied to social evolution.     

Keynes and Wagner on government expenditures and economic development: the case of a developing economy

This paper investigates the Keynesian view and the Wagner’s Law on the role of public expenditure on economic growth for Malaysia (1970–2004). The empirical results using the Auto-Regression Distributed Lag (ARDL) model and the ‘bounds test’ (Pesaran et al. in J Appl Econ 16:289–326, 2001) showed evidence of a long run relationship between total expenditures (including expenditures on defense, education, development and agriculture) and Gross National Product. The results also show that with the structural break in 1998, the long run causality is bi-directional for GNP and expenditures on administration and health, supporting both Keynes view and Wagner’s Law. For all other expenditure categories the long run causality runs from GNP to the expenditures, which supports Wagner’s Law. An erratum to this article can be found at     

A modified yardstick competition mechanism

This paper expands Shleifer’s (Rand J Econ 16:319–327, 1985) theory of yardstick competition and develops a modified yardstick competition mechanism (MYC), where the yardstick employed consists of a tariff basket and total costs. This mechanism has a significant information advantage: the regulator “only” needs to observe total costs, prices and output of all firms. The MYC mechanism can ensure a socially optimal outcome when allowing for spatial and second degree price discrimination. We also introduce regulatory lags to the model. In addition, we compare the two approaches for the case of unobserved firm heterogeneity, and provide numerical estimations of the effects. The MYC mechanism fares better in the case of unobserved heterogeneity, and may thus be a useful extension of Shleifer’s yardstick mechanism.      

A competing risks analysis of firms’ exit

Firms may exit the market in several ways and each form of exit is likely to be caused by different factors (Schary in RAND J Econ 22:339–353, 1991). This paper explores the determinants of different exit routes. Using a sample of Spanish manufacturing firms for 1990–2000, we estimate a competing risks proportional hazards model to identify the factors leading firms to exit the market through (the mutually precluding events of) liquidation/bankruptcy and acquisition/merger. Our results show the existence of a sharp difference between the determinants of these two exit routes in terms of firm and industry characteristics.     

Differentiating ambiguity: an expository note

Ghirardato et al. J Econ Theory 118:133–173, 2004 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. This note presents some examples which illustrate their results. Research supported by ESRC grant no. RES-000-22-0650. For comments and discussion we would like to thank Klaus Nehring and a seminar audience at ESEM, Vienna 2006.     

Optimal pricing of a two-sided monopoly platform with a one-sided congestion effect

This paper studies the optimal pricing of a two-sided monopoly platform when one side is affected by congestion. We show that the divide-and-conquer pricing strategy (or skewed pricing) depends not only on the relative magnitude of the sides’ price elasticities of demand but it also depends on the marginal congestion cost that an agent imposes on the others. Compared with the no-congestion case, this pricing strategy gives rise to some interesting features that violate the results of Rochet and Tirole (J Eur Econ Assoc 1:990–1029 in 2003, Rand J Econ 37:645–667 in 2006). In the case of equal price elasticities of demand, the no-congested side is charged the highest price. On the other hand, in the case of different price elasticities, the platform congestion pricing depends on a certain threshold of the marginal congestion cost. We show, under some conditions, that the divide-and-conquer pricing strategy is reversed. In the social context, the Rochet and Tirole’s (J Eur Econ Assoc 1:990–1029 in 2003) cost allocation condition is modified by the congestion cost. We show that the congestion does not only affect the buyers’ contribution to the sellers’ surplus, but it also affects the sellers’ contribution to the buyers’.     

Understanding some recent existence results for discontinuous games

We introduce a new condition, weak better-reply security, and show that every compact, locally convex, metric, quasiconcave and weakly better-reply secure game has a Nash equilibrium. This result is established using simple generalizations of classical ideas. Furthermore, we show that, when players’ action spaces are metric and locally convex, it implies the existence results of Reny (Econometrica 67:1029–1056, 1999) and Carmona (J Econ Theory 144:1333–1340, 2009) and that it is equivalent to a recent result of Barelli and Soza (On the Existence of Nash Equilibria in Discontinuous and Qualitative Games, University of Rochester, Rochester, 2009). Our general existence result also implies a new existence result for weakly upper reciprocally semicontinuous and weakly payoff secure games that satisfy a strong quasiconcavity property.     

A Note on Clean Technology Adoption and its Influence on Tradeable Emission Permits Prices

In this paper, we give an example in which the price of tradable emission permits increases despite firms’ adoption of less polluting technology, a result that is in contrast with Montero (J Environ Econ 44:23–44, 2002) and Parry (J Regul Econ 14:229–254, 1998), among others. If two Cournot players switch to a cleaner technology, the price for permits may increase due to an increase in the net demand for permits and a decrease in the net supply of permits after the clean technology is adopted. This is only the case when output demand is quite elastic.     

Monotone imitation

We analyze the social learning process of a group of individuals who have limited information about the payoff distributions of each action. We say that a behavioral rule is first-order monotone (FOM) if the number of individuals who play actions with first-order stochastic dominant payoff distributions is expected to increase in any environment. We provide a characterization of FOM rules. Both Imitate if Better and Schlag’s (J Econ Theory 78:130–156, 1998) Proportional Imitation rule are FOM. No FOM rule is dominant in the sense of having the best performance in every environment.     

Large economies with differential information and without free disposal

We consider exchange economies with a continuum of agents and differential information about finitely many states of nature. It was proved in Einy et al. (Econ Theory 18, 321–332, 2001) that if we allow for free disposal in the market clearing (feasibility) constraints then an irreducible economy has a competitive (or Walrasian expectations) equilibrium, and moreover, the set of competitive equilibrium allocations coincides with the private core. However when feasibility is defined with free disposal, competitive equilibrium allocations may not be incentive compatible and contracts may not be enforceable (see e.g. Glycopantis et al. in Econ Theory 21, 495–526, 2002). This is the main motivation for considering equilibrium solutions with exact feasibility. We first prove that the results in Einy et al. (Econ Theory 18, 321–332, 2001) are still valid without free-disposal. Then, motivated by the issue of contracts’ execution, we adapt the incentive compatibility property introduced in Krasa and Yannelis (Econometrica 62, 881–900, 1994) and we prove that every Pareto optimal exact feasible allocation is incentive compatible, implying that contracts of competitive or core allocations are enforceable. We would like to thank two anonymous reviewers and the Associate Editor for their valuable suggestions and remarks. This work was partially done while V.F. Martins-da-Rocha was visiting the Dipartimento di Matematica e Informatica of the Università degli Studi di Perugia. We thank the audience of the First General Equilibrium Workshop at Rio. Section 6 dealing with contract enforcement and coalitional incentive compatibility has benefited from discussions with J. Correia-da-Silva, W. Daher, F. Forges, C. Hervès-Beloso, E. Moreno-García, K. Podczeck, Y. Vailakis and N.C. Yannelis.