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.     

Second-order ambiguous beliefs

This paper axiomatizes models of second-order ambiguous beliefs in the original domain of preferences of Anscombe and Aumann (Ann Math Stat 34:199–205, 1963) by weakening the first-stage independence postulate. The models we propose include the second-order subjective expected utility (SOSEU) of Seo (Econometrica 77:1575–1605, 2009) as a particular case. We characterize the intersection of our models of second-order ambiguity with the canonical models of (first-order) ambiguity aversion and provide a further generalization of SOSEU by relaxing the completeness axiom.     

Optimal insurance design of ambiguous risks

We examine the characteristics of the optimal insurance contract under linear transaction costs and an ambiguous distribution of losses. Under the standard expected utility model, we know from Arrow (1965) that it contains a straight deductible. In this paper, we assume that the policyholder is ambiguity averse in the sense of Klibanoff et al. (Econometrica 73(6):1849–1892, 2005). The optimal contract depends upon the structure of the ambiguity. For example, if the set of possible priors can be ranked according to the monotone likelihood ratio order, the optimal contract contains a disappearing deductible. We also show that the policyholder’s ambiguity aversion may have the counterintuitive effect to reduce the optimal insurance coverage of an ambiguous risk.     

Are the treasures of game theory ambiguous?

Goeree and Holt (Am Econ Rev 91:1402?C1422, 2001) experimentally study a number of games. In each case, they initially find strong support for Nash equilibrium; however, by changing an apparently irrelevant parameter, they find results which contradict Nash equilibrium. In this paper, we study the five normal form games from Goeree and Holt (Am Econ Rev 91:1402?C1422, 2001). We argue that their results may be explained by the hypothesis that subjects view their opponents?? behaviour as ambiguous. Ambiguity-aversion causes players to avoid strategies, which give low out of equilibrium payoffs. Similarly, ambiguity preference can make strategies with high payoffs more attractive.     

Inequality aversion and separability in social risk evaluation

This paper examines how to satisfy “independence of the utilities of the dead” (Blackorby et al. in Econometrica 63:1303–1320, 1995; Bommier and Zuber in Soc Choice Welf 31:415–434, 2008) in the class of “expected equally distributed equivalent” social orderings (Fleurbaey in J Polit Econ 118:649–680, 2010) and inquires into the possibility to keep some aversion to inequality in this context. It is shown that the social welfare function must either be utilitarian or take a special multiplicative form. The multiplicative form is compatible with any degree of inequality aversion, but only under some constraints on the range of individual utilities.     

Liquidity and asset prices in rational expectations equilibrium with ambiguous information

The quality of information in financial asset markets is often hard to estimate. Reminiscent of the famous Ellsberg paradox, investors may be unable to form a single probability belief about asset returns conditional on information signals and may act on the basis of ambiguous (or multiple) probability beliefs. This paper analyzes information transmission in asset markets when agents?? information is ambiguous. We consider a market with risk-averse informed investors, risk-neutral competitive arbitrageurs, and noisy supply of the risky asset, first studied by Vives (Rev Financ Stud 8:3?C40, 1995a, J Econ Theory 67:178?C204, 1995b) with unambiguous information. Ambiguous information gives rise to the possibility of illiquid market where arbitrageurs choose not to trade in a rational expectations equilibrium. When market is illiquid, small informational or supply shocks have relatively large effects on asset prices.     

A competitive equilibrium for a warm-glow economy

The warm-glow model (Andreoni in J Political Econ 97:1447–1458, 1989; Econ J 100:464–477, 1990) of public goods provision has received widespread interest, yet surprisingly most attention has focused on the voluntary contribution equilibrium of the model, and only very little attention has been devoted to the competitive equilibrium. In this paper, we introduce the concept of competitive equilibrium for a warm-glow economy (henceforth, warm-glow equilibrium) and establish both existence and welfare properties. The warm-glow equilibrium concept may prove to be very useful to the normative and positive theory of public goods provision. First, it is a price-based mechanism achieving efficient outcomes. Second, not only could the warm-glow equilibria outcomes serve as a point of reference to measure free-riding and welfare loss but also, as suggested by Bernheim and Rangel (Behavioral Economics and Its Applications, 2007), in large economies they may be approximated by Walrasian equilibria outcomes.     

Endogenous population with human and physical capital accumulation

This paper proposes an economic growth model with population growth and physical and human capital accumulation. The physical capital accumulation is built on the Solow growth model (Solow in Q J Econ 70:65–94, 1956). The education and human capital accumulation is influenced by the Uzawa–Lucas model (Uzawa in Int Econ Rev 6:18–31, 1965; Lucas in J Monet Econ 22:3–42, 1988). The population dynamics are influenced by the Haavelmo population model (Haavelmo in a study in the theory of economic evolution. Haavelmo, Amsterdam, 1954) and the Barro–Becker fertility choice model (Barro and Becker in Econometrica 57:481–501, 1989). We synthesize these dynamic forces in a compact framework, applying an alternative utility function proposed by Zhang (Econ Lett 42:105–110, 1993). The model describes a dynamic interdependence between population change, wealth accumulation, human capital accumulation, and division of labor. We simulate the model to demonstrate the existence of equilibrium points and to plot the motion of the dynamic system. We also examine the effects of changes in the propensity to have children, the mortality rate parameter, the propensity to receive education, the human capital utilization efficiency, and the mortality rate elasticity of human capital upon dynamic paths of the system.     

The effects of the take-option in dictator-game experiments: a comment on Engel’s (2011) meta-study

In this paper, we report a replication of Engel’s (Exp. Econ. 14(4):583–610, 2011) meta-study of dictator game experiments. We find Engel’s meta-study of dictator game experiments to be robust, with one important exception: the coding of the take-option (List in J. Polit. Econ. 115(3):482–493, 2007; Bardsley in Exp. Econ. 11(2):122–133, 2008; Cappelen et al. in Econ. Lett. 118(2):280–283, 2013). While Engel reports this as having no statistically significant effect, in our replications, we find an economically and statistically significant negative effect on giving in line with the relevant literature.     

Bargaining over productivity and wages when technical change is induced: implications for growth, distribution, and employment

I study a model of growth and income distribution in which workers and firms bargain à la Nash (Econometrica 18(2):155–162, 1950) over wages and productivity gains, taking into account the trade-offs faced by firms in choosing factor-augmenting technologies. The aggregate environment resulting from self-interested, objective function-maximizing decision rules on wages, productivity gains, savings and investment, is described by a two-dimensional dynamical system in the employment rate and output/capital ratio. The economy converges cyclically to a long-run equilibrium involving a Harrod-neutral profile of technical change, a constant rate of employment of labor, and constant input shares. The type of oscillations predicted by the model is qualitatively consistent with the available data on the United States (1963–2003), replicates the dynamics found in earlier models of growth cycles such as Goodwin (A growth cycle, in C.H. Feinstein (ed). Socialism, Capitalism and Economic Growth. Cambridge University Press, Cambridge 1967. Cambridge University Press, Cambridge, 1967); Shah and Desai (Econ J 91:1006–1010, 1981); van der Ploeg (J Macroecon 9:1–12, 1987); Flaschel (J Econ: Zeitschrift für Nationalökonomie 44:63–69, 1984) and Sportelli (J Econ: Zeitschrift für Nationalökonomie 61(1):35–64, 1995), and can be verified numerically in simulations. Institutional change, as captured by variations in workers’ bargaining power, has a positive effect on the long-run rate of growth of output per worker but a negative effect on long-run employment. Economic policy can also affect the growth and distribution pattern through changes in the unemployment compensation, which also have a positive long-run impact on labor productivity growth but a negative long-run impact on employment. In both cases, employment can overshoot its new equilibrium value along the transitional dynamics.     

More equal but not so fair: an analysis of Brazilian income distribution from 1995 to 2009

This study measures unfair inequality in Brazil between 1995 and 2009. To achieve that, we used the statistical tool developed by Almås et al. (J Public Econ 95:488–499, 2011) and the concept of “responsibility-sensitive” fairness proposed by Bossert (Math Soc Sci 29:1–17, 1995), Konow (J Econ Behav Organ 31(1):13–35, 1996) and Cappelen and Tungodden (Fairness and the proportionality principle, Discussion paper SAM 31/2007. Norwegian School of Economics and Business Administration, 2007). The results indicate that the fairness level in Brazil remained unchanged throughout the analyzed period.     

Taxation without commitment

This paper considers a Ramsey model of linear capital and labor income taxation in which a benevolent government cannot commit ex-ante to a sequence of policies for the future. In this setup, if the government is forced to keep budget balance in every period, then it may not be able to sustain zero capital taxes in the long run, as shown in Benhabib and Rustichini (J Econ Theory 77:231–259, 1997) and Phelan and Stachetti (Econometrica 69:1491–1518, 2001). However, (Dominguez in J Econ Theory 135:159–170, 2007) shows that if the government is allowed to borrow and lend to households, the optimal capital income tax still converges to zero in the long run, as long as the value of defaulting is independent of the level of government debt. This paper provides a game theoretic setup with government debt where the value of the worst equilibrium only depends on the initial level of capital and can be determined in advance. This implies that under our assumptions the best sustainable equilibrium has zero capital taxes in the long run, even in the absence of government commitment.     

Cobb-Douglas preferences under uncertainty

This paper axiomatizes Cobb-Douglas preferences under uncertainty. First, we extend the original Trockel (Econ Lett 30:7–10, 1989)’s axiomatic foundation to a general state space framework based on the Strong Homotheticity Axiom, obtaining also the incomplete case a la Bewley (Decis Econ Financ 25:79–110, 2002). We show that this key axiom for the Cobb-Douglas expected utility specification is refuted by Ellsberg’s uncertainty aversion behavioral pattern. Our main result provides a set of meaningful axioms characterizing Cobb-Douglas min-expected utility preferences, an important class of uncertainty averse preferences for studying the consequences of ambiguity in finance and other fields. Finally, we present briefly how to obtain more general representations like the variational case.     

Finitely repeated games with social preferences

A well-known result from the theory of finitely repeated games states that if the stage game has a unique equilibrium, then there is a unique subgame perfect equilibrium in the finitely repeated game in which the equilibrium of the stage game is being played in every period. Here I show that this result does in general not hold anymore if players have social preferences of the form frequently assumed in the recent literature, for example in the inequity aversion models of Fehr and Schmidt (Quartely Journal of Economics 114:817–868, 1999) or Bolton and Ockenfels (American Economic Review 100:166–193, 2000). In fact, repeating the unique stage game equilibrium may not be a subgame perfect equilibrium at all. This finding should have relevance for all experiments with repeated interaction, whether with fixed, random or perfect stranger matching.     

The visible hand: finger ratio (2D:4D) and competitive bidding

In an experiment using two-bidder first-price sealed bid auctions with symmetric independent private values and 400 subjects, we scan also the right hand of each subject. We study how the ratio of the length of the index and ring fingers (2D:4D) of the right hand, a measure of prenatal hormone exposure, is correlated with bidding behavior and total profits. 2D:4D has been reported to predict competitiveness in sports competition (Manning and Taylor in Evol. Hum. Behav. 22:61–69, 2001, and H?nekopp et al. in Horm. Behav. 49:545–549, 2006), risk aversion in lottery tasks (Dreber and Hoffman in Portfolio selection in utero. Stockholm School of Economics, 2007; Garbarino et al. in J. Risk Uncertain. 42:1–26, 2011), and the average profitability of high-frequency traders in financial markets (Coates et al. in Proc. Natl. Acad. Sci. 106:623–628, 2009). We do not find any significant correlation between 2D:4D on either bidding or profits. However, there might be racial differences in the correlation between 2D:4D and bidding and profits.     

Unawareness of theorems

This paper provides a set-theoretic model of knowledge and unawareness. A new property called Awareness Leads to Knowledge shows that unawareness of theorems not only constrains an agent’s knowledge, but also can impair his reasoning about what other agents know. For example, in contrast to Li (J Econ Theory 144:977–993, 2009), Heifetz et al. (J Econ Theory 130:78–94, 25 2006) and the standard model of knowledge, it is possible that two agents disagree on whether another agent knows a particular event. The model follows Aumann (Ann Stat 4:1236–1239, 1976) in defining common knowledge and characterizing it in terms of a self-evident event, but departs in showing that no-trade theorems do not hold.     

Pluralism(s) in economics: lessons from complexity and innovation. A review paper

My analysis focuses on two main observations. First, many competing schools of thoughts are currently present in economics with no predominant paradigm. We are experiencing an era of pluralism (Davis J Econ Methodol 14(3):275–290, 2007, Camb J Econ 32:249–366, 2008; Colander 2000; Colander et al. J Polit Econ 16(4):485–499, 2004). The term ‘pluralism’ is extremely interesting since, as I will show, it has different dimensions to it. These offer insights into interpreting the tangled universe of the economics. Second, there is a progressive intertwining of innovation economics with complexity economics, which I argue provides an instance of the above-described shift toward pluralism.     

Niche products, generic products, and consumer search

We endogenize product design in a model of sequential search with random firm-consumer match value à la Wolinsky (Quart J Econ 96:493–511, 1986) and Anderson and Renault (RAND J Econ 30:719–735, 1999). We focus on a product design choice by which a firm can control the dispersion of consumer valuations for its product; we interpret low-dispersion products as “generic” and high-dispersion products as “nichy.” Equilibrium product design depends on a feedback loop: when reservation utility is high (low), the marginal customer’s match improves (worsens) with more nichy products, encouraging high (low) differentiation by firms. In turn, when firms offer more nichy products, this induces more intense search; depending on search costs, this could raise or lower consumers’ reservation utility. Remarkably, when the match distribution satisfies a hazard rate condition, firm and consumer interests align: equilibrium product design always adjusts to the level that maximizes utility. When this condition is not met, either multiple equilibria (one nichy, the other generic) or one asymmetric equilibrium (generic and nichy firms coexist) can arise; we argue that the former is more likely for common specifications of consumer preferences.     

Optimality of impulse harvesting policies

We explore the link between cyclical and smooth resource exploitation. We define an impulse control framework which can generate both cyclical solutions and steady-state solutions. Our model can admit convex and concave profit functions and allows the integration of different stock-dependent profit functions. We show that the strict concavity of the profit function is only a special case of a more general condition, related to submodularity, that ensures the existence of optimal cyclical policies. We then establish a link with the discrete-time models with cyclical solutions by Benhabib and Nishimura (J Econ Theory 35:284–306, 1985) and Dawid and Kopel (J Econ Theory 76:272–297, 1997). For the steady-state solution, we explore the relation to Clark’s (1976) continuous control model.     

Liquidity and the marginal value of information

We revisit Kyle’s (Econometrica 53:1315–1335, 1985) model of price formation in the presence of private information. We begin by using Back’s (Rev Financ Stud 5(3):387–409, 1992) approach, demonstrating that if standard assumptions are imposed, the model has a unique equilibrium solution and that the insider’s trading strategy has a martingale property. That in turn implies that the insider’s strategies are linear in total order flow. We also show that for arbitrary prior distributions, the insider’s trading strategy is uniquely determined by a Doob $h$ -transform that expresses the insider’s informational advantage. This allows us to reformulate the model so that Kyle’s liquidity parameter $\lambda $ is characterized by a Lagrange multiplier that is the marginal value or shadow price of information. Based on these findings, we can then interpret liquidity as the marginal value of information.