Existence of adaptively stable sunspot equilibria near an indeterminate steady state

We examine the nonlinear model x_t=E_tF(x_t+1). Markov stationary sunspot equilibria (SSEs) exist near an indeterminate steady state, , provided . Despite the importance of indeterminacy in macroeconomics, earlier results have not provided conditions for the existence of adaptively stable SSEs near an indeterminate steady state. We show that there exist Markov SSEs near x? that are E-stable, and therefore locally stable under adaptive learning, if .     

Monotonic and implementable solutions in generalized matching problems

We consider one-to-one matching problems when preferences are weak orders and search for (Maskin-)monotonic and implementable solutions. We show that for any coalition structure , the strong -core is monotonic if and only if it is the individually rational solution. We introduce a solution, which we call the “union strong -core”, and show that this solution is the minimal way to expand the strong -core recovering monotonicity. We also show that the union strong -core is implementable.     

Almost budget-balanced VCG mechanisms to assign multiple objects

Subsidy-free VCG mechanisms assign p identical objects to n agents. The efficiency loss is the largest ratio of budget surplus to efficient surplus, over all profiles of non-negative valuations. The smallest efficiency loss satisfies . If is bounded away from , converges to zero exponentially in n.Participation is voluntary in the optimal mechanism achieving if p=1, but not if p?2. Among voluntary mechanisms, the optimal efficiency loss is not significantly larger than if . But it does not converge to zero in n if .     

Rates of information aggregation in common value auctions

We study the rates at which transaction prices aggregate information in common value auctions under the different information structures in Wilson (Rev. Econ. Stud. 44 (1977) 511) and Pesendorfer and Swinkels (Econometrica 65 (1997) 1247). We consider uniform-price auctions in which k identical objects of unknown value are auctioned to n bidders, where both n and k are allowed to diverge to infinity, and k/n converges to a number in [0,1). The Wilson assumptions lead to information aggregation at a rate proportional to , but the price aggregates information at a rate proportional to in the PS setting. We also consider English auctions, and investigate whether the extra information revealed in equilibrium improves convergence rates in these auctions.     

Buy-price English auction

Consider an English auction for a single object in which there is an option for a bidder to guarantee a purchase at a seller-specified buy price b at any time. We show that there exist and (), such that a bidder purchases at the buy price immediately if his valuation v is no less than or and at least one other bidder is participating in the auction. If , he purchases at the buy price once the current bid reaches a strategically chosen threshold price. A properly set buy price increases expected social welfare and the expected utility of each agent when either buyers or seller are risk-averse.     

Uniform payoff security and Nash equilibrium in compact games

We introduce a condition, uniform payoff security, for games with compact Hausdorff strategy spaces and payoffs bounded and measurable in players’ strategies. We show that if any such compact game G is uniformly payoff secure, then its mixed extension is payoff secure. We also establish that if a uniformly payoff secure compact game G has a mixed extension with reciprocally upper semicontinuous payoffs, then G has a Nash equilibrium in mixed strategies. We provide several economic examples of compact games satisfying uniform payoff security.     

Apportioning of risks via stochastic dominance

Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable dominates via ith-order stochastic dominance for i=M,N. We show that the 50-50 lottery dominates the lottery via (N+M)th-order stochastic dominance. The basic idea is that a decision maker exhibiting (N+M)th-order stochastic dominance preference will allocate the state-contingent lotteries in such a way as not to group the two “bad” lotteries in the same state, where “bad” is defined via ith-order stochastic dominance. In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher-order risk effects, such as precautionary effects and tempering effects.     

Non-existence of recursive equilibria on compact state spaces when markets are incomplete

This paper analyzes one-good exchange economies with two infinitely lived agents and incomplete markets. It is shown that there are no recursive (Markov) equilibria for which borrowing (debt) constraints never bind if the state space of exogenous and endogenous variables is a compact subset of . Moreover, for large enough (but finite) borrowing limits, no recursive equilibrium with compact state space exists. These non-existence results hold for any economy satisfying the following standard assumptions: preferences are additively separable across time and states; the one-period utility function is time- and state-independent and unbounded from below; endowments are bounded and follow a Markov chain with stationary transition matrix; there is some idiosyncratic risk and no aggregate risk.     

Set-rationalizable choice and self-stability

Rationalizability and similar notions of consistency have proved to be highly problematic in the context of social choice, as witnessed by a range of impossibility results, among which Arrow?s is the most prominent. We propose to rationalize choice functions by preference relations over sets of alternatives (set-rationalizability) and introduce two consistency conditions, and , which are defined in analogy to Sen?s α and γ. We find that a choice function satisfies if and only if it is set-rationalizable and that it satisfies and if and only if it is self-stable, a new concept based on earlier work by Dutta. The class of self-stable social choice functions contains a number of appealing Condorcet extensions.     

Innovation and spillovers in regions: Evidence from European patent data

This paper estimates the effect of research externalities in generating innovation. We use R&D and patent data for European Regions in the 1977-1995 period. We find that spillovers are very localized and exist only within a distance of . The estimates are robust to simultaneity, omitted variable bias, different specifications of distance functions, country and border effects. However the size of these spillovers is small. Doubling R&D spending in a region would increase the output of new ideas in other regions within only by 2-3%, while it would increase the innovation of the region itself by 80-90%.     

Collective choice under dichotomous preferences

Agents partition deterministic outcomes into good or bad. A mechanism selects a lottery over outcomes (time-shares). The probability of a good outcome is the canonical utility. The utilitarian mechanism averages over outcomes with largest “approval”. It is efficient, strategyproof, anonymous and neutral.We reach an impossibility if, in addition, each agent's utility is at least , where n is the number of agents; or is at least the fraction of good to feasible outcomes. We conjecture that no ex ante efficient and strategyproof mechanism guarantees a strictly positive utility to all agents, and prove a weaker statement.     

Duality of welfare and profit maximization

Many economists are aware that the conditions for the efficiency and monopolization in a partial equilibrium framework are the extremes of the Ramsey–Boiteux formula when the Lagrange multiplier for the budget varies. We formalize the duality existing between the welfarist and monopolist constrained maximization programs by proving the following “folk theorem”:      

Contagion and efficiency

We consider a population of agents, either finite or countably infinite, located on an arbitrary network. Agents interact directly only with their immediate neighbors, but are able to observe the behavior of (some) other agents beyond their interaction neighborhood, and learn from that behavior by imitating successful actions. If interactions are not “too global” but information is fluid enough, we show that the efficient action is the only one which can spread contagiously to the whole population from an initially small, finite subgroup. This result holds even in the presence of an alternative, -dominant action.     

Poverty trap and global indeterminacy in a growth model with open-access natural resources

In this paper we use global analysis techniques to analyze an economic growth model with environmental negative externalities, giving rise to a three-dimensional dynamic system (the framework is the one introduced by Wirl (1997) [53]). The dynamics of our model admits a locally attracting stationary state , which is, in fact, a poverty trap, coexisting with another stationary state possessing saddle-point stability. Global dynamical analysis shows that, under some conditions on the parameters, if the initial values of the state variables are close enough to the coordinates of , then there exists a continuum of equilibrium trajectories approaching and one trajectory approaching . Therefore, our model exhibits global indeterminacy, since either or can be selected according to agent expectations. Moreover, we prove that conditions guaranteeing the attractivity of also imply the saddle-point stability of . However, when is not attractive, numerical simulations show the possible existence of one or two limit cycles: an attractive one surrounding and one endowed with a two-dimensional stable manifold surrounding .     

The swing voter's curse with adversarial preferences

We analyze voting behavior in a large electorate in which voters have adversarial state-contingent preferences with incomplete information about the state of the world. We show that one type of voter can suffer from the swing voter's curse à la Feddersen and Pesendorfer [The swing voter's curse, Amer. Econ. Rev. 86 (1996) 408-424], and go on to characterize the symmetric Nash equilibria of this model under different parameter values. We prove that unlike settings with nonadversarial preferences, there are equilibria in which in one state of the world, a minority-preferred candidate almost surely wins the election and thus the election may fail to correctly aggregate information. Indeed, we show that the fraction of the electorate dissatisfied with the result can be as large as .     

The impact of minimum wages on youth employment in Portugal

On January 1, 1987, the legal minimum wage for workers aged 18 and 19 in Portugal was raised by 49.3%. This shock is used as a “natural experiment” to evaluate the impact of the minimum wage change on teenagers’ employment. The method is to compare, based on firm-level microdata, the employment growth of 18-19-year-old workers with employment growth of older workers. The main findings are that the increase in the minimum wage significantly reduced employment of 18 and olds, but increased employment of 20- olds.     

Hope springs eternal: learning and the stability of cooperation in short horizon repeated games

This paper considers learning rates in finitely repeated prisoners’ dilemmas. If players think their opponents might be relatively cooperative (e.g., tit-for-tat or grim types), they will cooperate in finitely repeated prisoners’ dilemmas (see Kreps et al., J. Econom. Theory 27 (1982) 245). However, if there are actually no cooperative types, players will eventually learn this and cooperation will break down. This paper shows that this learning is extremely slow, so it will take an extremely long time for cooperation to break down.Thus, suppose the world is either “good” or “bad.” The probability of a grim type is δ>0 if the world is good, and zero if the world is bad. Successive generations pair up to play finitely repeated prisoners’ dilemmas. Players observe play in previous generations and use Bayes’ rule to update their prior, π, that the world is good. We show that, if the world is really bad, then π falls per generation on average. Thus, if δ is small, there is less cooperation if the world is good, but cooperation may become more stable. For a representative 19 period repeated prisoners’ dilemma, beliefs fall one percentage point on average after a thousand generations.To derive these learning rates, we must refine existing results on the sensitivity of repeated games to Kreps et al. (1982) type perturbations. Specifically, we show cooperation is possible in perturbed prisoners’ dilemmas repeated O(log(1/δ)) times. This improves significantly on the O(1/δ) results in previous work. The paper thus provides two new reasons why cooperation tends to be stable, even in short horizon repeated games.     

Non-marketed options, non-existence of equilibria, and non-linear prices

This paper presents a surprising example that shows that the lattice theoretic properties in Mas-Colell's (1986) seminal work are relevant to the existence of equilibrium even when the commodity space is finite dimensional.The example is a two-period securities model with a three-dimensional portfolio space and two traders. The paper identifies a non-marketed call option that fails to have a minimum cost super-replicating portfolio. Using this option, we construct an economy that satisfies all of Mas-Colell's assumptions, except that the three-dimensional commodity space is not a vector lattice. In this economy, there is no Walrasian equilibrium and the second theorem of welfare economics fails.Our example has important finite- as well as infinite-dimensional implications. It is also an example of a “well behaved” economy in which optimal allocations that are not supported by linear Walrasian prices are decentralized by the non-linear prices studied in Aliprantis-Tourky-Yannelis (2001).