Monotone continuous multiple priors

Summary. In a multiple priors model á la Gilboa and Schmeidler (1989), we provide necessary and sufficient behavioral conditions ensuring the countable additivity and non-atomicity of all priors.Received: 25 November 2002, Revised: 24 June 2004, JEL Classification Numbers: D81.We thank Roko Aliprantis, Maristella Botticini, Erio Castagnoli, Larry Epstein, Paolo Ghirardato, Itzhak Gilboa, Luigi Montrucchio, David Schmeidler, Marciano Siniscalchi, an Associate Editor, and an anonymous referee for helpful discussions. Fabio Maccheroni and Massimo Marinacci gratefully acknowledge the financial support of MIUR and NOMOS Sistema (Milano).     

Stationary Markov equilibria for overlapping generations

Summary.  At a stationary Markov equilibrium of a Markovian economy of overlapping generations, prices at a date-event are determined by the realization of the shock, the distribution of wealth and, with production, the stock of capital. Stationary Markov equilibria may not exist; this is the case with intra-generational heterogeneity and multiple commodities or long life spans. Generalized Markov equilibria exist if prices are allowed to vary also with the realization of the shock, prices and the allocation of consumption and production at the predecessor date-event. (Stationary) Markov -equilibria always exist; as allocations and prices converge to equilibrium prices and allocations that, however, need not be stationary.Received: 2 March 2004, Revised: 2 April 2004, JEL Classification Numbers:   D50, D52, D60, D80, D90.Correspondence to: Felix KublerWe thank participants in seminars in Athens and Lund, at Penn, at IMPA and at Stanford, the 2002 CEME (NBER) General Equilibrium Conference and the 2002 SED meetings, and especially Martin Hellwig, George Mailath and an anonymous referee for very helpful comments.     

An axiomatic approach to \boldsymbol{\varepsilon}-contamination

Summary.  Suppose that an economic agent is 100% certain that uncertainty she faces is characterized by a particular probability measure, but that she has a fear that, with 100% chance, her conviction is completely wrong and she is left perfectly ignorant about the true measure in the present as well as in the future. This situation is often called -contamination of confidence. The purpose of this paper is to provide a simple set of behavioral axioms under which the decision-makers preference is represented by the Choquet expected utility with the -contamination of confidence.Received: 25 November 2002, Revised: 15 November 2004, JEL Classification Numbers:   D81. Correspondence to: Hiroyuki OzakiWe are grateful to an anonymous referee. The referees comments greatly improved the exposition of the paper. The work reported here is partially supported by a grant from the Economic and Social Research Insitute, the Cabinet Office, the Government of Japan.     

Voting in assemblies of shareholders and incomplete markets

Summary. An economy with two dates is considered, one state at the first date and a finite number of states at the last date. Shareholders determine production plans by voting - one share, one vote - and at -majority stable stock market equilibria, alternative production plans are supported by at most percent of the shareholders. It is shown that a -majority stable stock market equilibrium exists if where S is the number of states at the last date and J is the number of firms. Moreover, an example shows that -majority stable stock market equilibria need not exist for smaller s.Received: 23 December 2002, Revised: 14 June 2004, JEL Classification Numbers: D21, D52, D71, G39. Correspondence to: Hervé CrésThe authors are grateful to an anonymous referee for helpful comments and suggestions. Financial support from the Danish Research Councils and hospitality of HEC is gratefully acknowledged by Mich Tvede and support from Fondation HEC is gratefully acknowledged by Hervé Crés.     

Definitions of ambiguous events and the smooth ambiguity model

We examine a variety of preference-based definitions of ambiguous events in the context of the smooth ambiguity model. We first consider the definition proposed in Klibanoff et?al. (Econometrica 73(6):1849?C1892, 2005) based on the classic Ellsberg two-urn paradox (Ellsberg Q J Econ 75:643?C669, 1961) and show that it satisfies several desirable properties. We then compare this definition with those of Nehring (Math Soc Sci 38(2):197?C213, 1999), Epstein and Zhang (Econometrica 69:265?C306, 2001), Zhang (Econ Theory 20:159?C181, 2002), and Ghirardato and Marinacci (J Econ Theory 102:251?C289, 2002). Within the smooth ambiguity model, we show that Ghirardato and Marinacci (J Econ Theory 102:251?C289, 2002) would identify the same set of ambiguous and unambiguous events as our definition while Epstein and Zhang (Econometrica 69:265?C306, 2001) and Zhang (Econ Theory 20:159?C181, 2002) would yield a different classification. Moreover, we discuss and formally identify two key sources of the differences compared to Epstein and Zhang (Econometrica 69:265?C306, 2001) and Zhang (Econ Theory 20:159?C181, 2002). The more interesting source is that these two definitions can confound non-constant ambiguity attitude and the ambiguity of an event.     

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].     

Tari–tax reforms and market access

Reducing taris and increasing consumption taxes is a standard IMF advice to countries that want to open up their economy without hurting government finances. Indeed, theoretical analysis of such a tari–tax reform shows an unambiguous increase in welfare and government revenues. The present paper examines whether the country that implements such a reform ends up opening up its markets to international trade, i.e. whether its market access improves. It is shown that this is not necessarily so. We also show that, comparing to the reform of only taris, the tari–tax reform is a less efficient proposal to follow both as far as it concerns market access and welfare.     

Efficient markets and Bayes’ rule

Summary. A series of financial anomalies motivated the development of new theories that modify the rational expectations ideal. Two possibilities have been systematically explored. The literature on behavioral finance relaxes the assumption that agents form beliefs according to the laws of probability and assume, instead, that simpler heuristic rules are used. Another stream of the literature assumes that agents process information according to Bayes rule, but do not posses sufficient information to know the true data generating process. In this paper, Bayesian and Behavioral agents coexist and trade in a standard dynamic asset pricing model. A long-standing conjecture is demonstrated. It is shown that, under suitable assumptions, Bayesian agents drive Behavioral, non-Bayesian agents out of the market. Hence, asset prices are eventually determined under the Bayesian paradigm.Received: 3 June 2004, Revised: 17 September 2004, JEL Classification Numbers: D83.Preliminary versions have circulated under the titles Markets Favor Bayesian Models and Market Selection of Empirical Models under Limited Information. I thank Larry Blume, David Easley, Larry Epstein, Armando Gomes, Bruce Hansen, Lars Hansen, Richard Kihlstrom, Grace Koo, George Mailath, Werner Ploberger, Andrew Postlewaite and Shakeeb Khan for useful comments. I also thank participants at the NBER GE meetings, Evolutionary Finance conference in Zurich, Latin American Meetings of the Econometric Society, Stanford Institute for Theoretical Economics, the Instituto de Matematica Pura e Aplicada, the theory seminar at Brown, Chicago, Harvard-MIT, Minnesota, Penn and Wisconsin. I gratefully acknowledge the financial support from the National Science Foundation Grant SES 0109650.     

Mistaken self-perception and equilibrium

Summary. Motivated by real-world information economics problems and by experimental findings on overconfidence, this paper introduces a general epistemic construction to model strategic interaction with incomplete information, where the players self-perception may be mistaken. This allows us to rigorously describe equilibrium play, by formulating appropriate equilibrium concepts. We show that there always exist objective equilibria, where the players correctly anticipate each others strategies without attempting to make sense of them, and that these outcomes coincide with the equilibria of an associated Bayesian game with subjective priors. In population games, these equilibria can also be always introspectively rationalized by the players, despite their possibly mistaken self-perception.Received: Received: May, 12, 2003; revised version: 3 December 2004, Revised: 3 December 2004, JEL Classification Numbers: J31, D82, D83.I thank Massimiliano Amarante, Eddie Dekel, Massimo Marinacci, Jean Francois Mertens, Giuseppe Moscarini, Paolo Siconolfi, Marciano Siniscalchi, Joel Sobel, and an anonymous referee.     

Two new proofs of Afriat’s theorem

Summary. We provide two new, simple proofs of Afriats celebrated theorem stating that a finite set of price-quantity observations is consistent with utility maximization if, and only if, the observations satisfy a variation of the Strong Axiom of Revealed Preference known as the Generalized Axiom of Revealed PreferenceReceived: 12 June 2003, Revised: 9 October 2003, JEL Classification Numbers: D11, C60.Correspondence to: A. Fostel     

Theoretical conditions under which monetary policies are effective and practical obstacles to their verification

Summary. We derive (i) necessary and sufficient and (ii) sufficient conditions for monetary policies to conform to what the literature characterizes as good policies. We show that the biasing effects of omitted variables, measurement errors, and misspecifications of true functional forms on the coefficients of monetary-policy reaction functions present practical obstacles to verifying such conditions.Received: 30 September 2003, Revised: 6 February 2004, JEL Classification Numbers: E52, E58. Correspondence to: George S. TavlasWe thank Charalambos Aliprantis, Peter von zur Muehlen and an anonymous referee for helpful comments on an earlier version of this paper. The views expressed in this paper are the authors own and do not represent those of their respective institutions.     

Dynamic variational preferences

We introduce and axiomatize dynamic variational preferences, the dynamic version of the variational preferences we axiomatized in [F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity aversion, robustness, and the variational representation of preferences, Mimeo, 2004], which generalize the multiple priors preferences of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141-153], and include the Multiplier Preferences inspired by robust control and first used in macroeconomics by Hansen and Sargent (see [L.P. Hansen, T.J. Sargent, Robust control and model uncertainty, Amer. Econ. Rev. 91 (2001) 60-66]), as well as the classic Mean Variance Preferences of Markovitz and Tobin. We provide a condition that makes dynamic variational preferences time consistent, and their representation recursive. This gives them the analytical tractability needed in macroeconomic and financial applications. A corollary of our results is that Multiplier Preferences are time consistent, but Mean Variance Preferences are not.     

Satisficing behavior, Brouwer’s Fixed Point Theorem and Nash Equilibrium

Summary. We show that Nash Equilibrium points can be obtained by using response maps or reply functions that simply use better responses rather than best responses. We demonstrate the existence of a Nash Equilibrium as the fixed point of a better response map and since the better response map is continuous the fixed point can be established by simply using Brouwers fixed point theorem. The proof applies to games with a finite number of strategies as well as to games with a continuum of strategies. In case the games have a continuum of strategies the payoff functions have to be continuous on the action sets and quasi concave on the players action set.Received: 22 September 2003, Revised: 31 March 2004, JEL Classification Numbers: C72, D00, D40. Correspondence to: Robert A. BeckerWe have benefited from comments on an earlier draft made by participants at Indiana Universitys Microeconomics workshop (October 2002) and the Midwest Economic Theory Conference held at the University of Pittsburgh (May 2003). We also thank Roy Gardner for comments on earlier versions. We thank the Associate Editor, Mark Machina, for his detailed comments and suggestions. This project began when Subir Chakrabarti was a visitor in the Department of Economics, Indiana University, Bloomington in the Spring of 2002. He thanks that department for its support.     

From “tax state” to “debt state”

The paper is motivated by Joseph A. Schumpeter's The Crisis of the Tax State. It inquires whether the buildup of government debt in peacetimeprosperity is a threat to the stability, existence or creation of viable tax states. The paper begins by setting out Schumpeter's conception of the tax state and the nature of recent political-economic events which have reinvigorated the concept. Next the paper sets out some simple debt dynamics and sketches a debt-induced business cycle arising from heavy reliance on debt finance in peacetimeprosperity. Finally, the paper assesses threats to the tax state in light of recent work on path dependence and positive feedback. An attempt is made to throw some light on whether the plethora of new, and often small, states spawned by the demise of communism can be viable tax states.Essay on Government, the Tax State and Economic Dynamics submitted to the Third Schumpeter Prize Competition.     

Ambiguous events and maxmin expected utility

We study the properties associated to various definitions of ambiguity [L.G. Epstein, J. Zhang, Subjective probabilities on subjectively unambiguous events, Econometrica 69 (2001) 265-306; P. Ghirardato et al., Differentiating ambiguity and ambiguity attitude, J. Econ. Theory 118 (2004) 133-173; K. Nehring, Capacities and probabilistic beliefs: a precarious coexistence, Math. Soc. Sci. 38 (1999) 197-213; J. Zhang, Subjective, ambiguity, expected utility and Choquet expected utility, Econ. Theory 20 (2002) 159-181] in the context of Maximin Expected Utility (MEU). We show that each definition of unambiguous events produces certain restrictions on the set of priors, and completely characterize each definition in terms of the properties it imposes on the MEU functional. We apply our results to two open problems. First, in the context of MEU, we show the existence of a fundamental incompatibility between the axiom of “Small unambiguous event continuity” (Epstein and Zhang, 2001) and the notions of unambiguous event due to Zhang (2002) and Epstein and Zhang (2001). Second, we show that, in the context of MEU, the classes of unambiguous events according to either Zhang (2002) or Epstein and Zhang (2001) are always λ-systems. Finally, we reconsider the various definitions in light of our findings, and identify some new objects (Z-filters and EZ-filters) corresponding to properties which, while neglected in the current literature, seem relevant to us.     

On economic disequilibrium and free lunch

There is a sharp disagreement between mainstream economists and advocates of energy efficiency as regards the potential for free lunches or no regrets policies to cut greenhouse gas emissions. From an economics perspective, the critical question is whether the economic system is — or is not — close to a Pareto-optimum equilibrium state. If so, it follows that most technological systems now in place are optimum, or nearly so, from an economic perspective. If not, there may be many sub-optimal technologies in place, with corresponding opportunities for very high returns on appropriate investments. This paper presents some of the evidence supporting the latter thesis.     

Bankruptcy games and the Ibn Ezra’s proposal

Summary. This paper explores an old solution for bankruptcy problems, described by Ibn Ezra in the XII century. Particularly, we introduce a new way of extending the Ibn Ezras proposal, the Generalized Ibn Ezra solution, by imposing that the general distribution principle from which it is inspired remains fixed. In this context, we follow the interpretation of bankruptcy problems in terms of TU games given in ONeill (1982), and propose the analysis of the Transition Game associated to bankruptcy problems to provide a characterization for the Generalized Ibn Ezra solution.Received: 14 October 2003, Revised: 26 May 2004, JEL Classification Numbers: C71, D63, D71. Correspondence to: José Alcalde: alasur@merlin.fae.ua.esWe are grateful to Carmen Herrero, Juan de Dios Moreno, William Thomson and an anonymous referee for helpful comments. Authors work is partially supported by the Institut Valenciá dInvestigacions Económiques. Alcalde and Silva acknowledge support by FEDER and the Spanish Ministerio de Educación y Cultura under project BEC 2001-0535. Marco acknowledges support by the Fundación Séneca, and the Spanish Ministerio de Educación y Cultura under projects SEC2000-0838 and BEC 2001-0781.     

Combining Keynes and Schumpeter. Ingvar Svennilson’s contribution to the Swedish growth school and modern economics

In a study of European growth in the interwar period, the Swedish economist Ingvar Svennilson integrated a Keynesian theory of demand-led cumulative growth with a Schumpeterian analysis of transformation. Today, Svennilson is seen, together with the Schumpeterian economists Johan Åkerman and Erik Dahmén, as members of a unique Swedish growth school. A combination of Keynes and Schumpeter with Svennilson as a mediator has been facilitated by neo-Schumpeterian theories of demand-led innovations. But it has been obstructed by a hypothesis in the Schumpeterian tradition that productivity growth is stimulated by low aggregate demand and by Svennilsons strong commitment to Verdoorns Law which actually is Svennilsons Law. However, Svennilsons analyses of the importance of short-run imbalances for economic growth and the existence of imperfect capital markets discriminating progressive new firms have direct equivalences in modern macroeconomics. Svennilsons main contributions to economics of today are his syntheses between macroeconomic and structural analysis, short and long run theoretical perspectives and, more basically, between theoretical and empirical research.JEL Classification: B25, E32, L6, N14, O11, O14, O31, O4A Swedish version of the paper was presented at the 7th Nordic Conference on the History of Economic Thoughts in Molde (Norway), May 2-4, 2003 and at the Ratio institute (Stockholm), May 8, 2003. I thank participants, Rolf Henriksson and two anonymous referees for valuable comments.     

Productivity and Employment in the Information Economy: What Kaldor’s and Verdoorn’s Growth Laws Can Teach the US

During the last decade of the 20th century the US economy experienced the longest economic boom since World War II. Information and communication technologies (ICT) are seen as one of the main reasons for this development and it is still an open question how ICT will affect growth and employment in the future. To evaluate this process Kaldors growth laws, especially Verdoorns law are reconsidered. It will be discussed which changes in the Verdoorn-Coefficient (VC) and the employment threshold (ET) can be expected due to ICT. Induced technical progress and increasing returns to scale could make future economic growth to be less labor-intensive. A simple OLS estimation using data for the US non-farm sector indicates that the VC increased in the second half of the 1990s. Thus, more output growth is required to keep employment constant.The author gratefully acknowledges the most valuable comments from two anonymous referees and the participants of the Annual Meeting of the Austrian Economic Association (NOeG) at the Vienna University of Economics (WU), May 21–22, 2004. Any remaining errors are my own.