Valuation bubbles and sequential bubbles

Price bubbles in an Arrow-Debreu valuation equilibrium in infinite-timeeconomy are a manifestation of lack of countable additivity of valuationof assets. In contrast, known examples of price bubbles in sequentialequilibrium in infinite time cannot be attributed to the lack of countableadditivity of valuation. In this paper we develop a theory of valuation ofassets in sequential markets (with no uncertainty) and study the nature ofprice bubbles in light of this theory. We consider an operator, calledpayoff pricing functional, that maps a sequence of payoffs to the minimumcost of an asset holding strategy that generates it. We show that thepayoff pricing functional is linear and countably additive on the set ofpositive payoffs if and only if there is no Ponzi scheme, and providedthat there is no restriction on long positions in the assets. In the knownexamples of equilibrium price bubbles in sequential markets valuation islinear and countably additive. The presence of a price bubble indicatesthat the asset's dividends can be purchased in sequential markers at acost lower than the asset's price. We also present examples of equilibriumprice bubbles in which valuation is nonlinear but not countably additive.

Adverse selection, credit and efficiency: The case of the missing market

We analyze a standard environment of adverse selection in credit markets. In our environment,entrepreneurs who are privately informed about the quality of their projects needto borrow in order to invest. Conventional wisdom says that, in this class of economies, thecompetitive equilibrium is typically inefficient.We show that this conventional wisdom rests on one implicit assumption: entrepreneurscan only access monitored lending. If a new set of markets is added to provide entrepreneurswith additional funds, efficiency can be attained in equilibrium. An important characteristic ofthese additional markets is that lending in them must be unmonitored, in the sense that it doesnot condition total borrowing or investment by entrepreneurs. This makes it possible to attainefficiency by pooling all entrepreneurs in the new markets while separating them in the marketsfor monitored loans.

Hiring and firing costs, adverse selection and long-term unemployment

In this paper, we present a matching model with adverse selection that explains why flows into and out of unemployment are much lower in Europe compared to North America, while employment-to-employment flows are similar in the two continents. In the model,firms use discretion in terms of whom to fire and, thus, low quality workers are more likely to be dismissed than high quality workers. Moreover, as hiring and firing costs increase, firms find it more costly to hire a bad worker and, thus, they prefer to hire out of the pool of employed job seekers rather than out of the pool of the unemployed, who are more likely to turn out to be 'lemons'. We use microdata for Spain and the U.S. and find that the ratio of the job finding probability of the unemployed to the job finding probability of employed job seekers was smaller in Spain than in the U.S. Furthermore, using U.S. data, we find that the discrimination of the unemployed increased over the 1980's in those states that raised firing costs by introducing exceptions to the employment-at-will doctrine.

Improved estimation of the covariance matrix of stock returns with an application to portofolio selection

This paper proposes to estimate the covariance matrix of stock returnsby an optimally weighted average of two existing estimators: the samplecovariance matrix and single-index covariance matrix. This method isgenerally known as shrinkage, and it is standard in decision theory andin empirical Bayesian statistics. Our shrinkage estimator can be seenas a way to account for extra-market covariance without having to specifyan arbitrary multi-factor structure. For NYSE and AMEX stock returns from1972 to 1995, it can be used to select portfolios with significantly lowerout-of-sample variance than a set of existing estimators, includingmulti-factor models.

Selection of artificial hosts for oviposition by wild Anastrepha obliqua (Macquart) (Diptera, Tephritidae): influence of adult food and effect of experience

Several factors influence the selection of oviposition substrates by insects. The aim of the present work was to find answers to the following questions related to the oviposition behavior of Anastrepha obliqua. Can carbohydrates (glucose or sucrose) present in the adult diet have influence on the female preference for an oviposition substrate with similar composition? Can the previous experience with a host containing one of mentioned carbohydrates interfere in further selection of oviposition substrates? The results showed that the kind of carbohydrate present in the adult diet did not affect the female preference for an artificial oviposition substrate, neither when it was presented by itself nor in combination with brewer's yeast. The effect of experience in the oviposition behavior was observed when there was a previous contact with artificial oviposition substrates containing yeast and sucrose. The data are discussed in terms of the behavioral plasticity presented by this species in relation to feeding and oviposition behaviors.

Dynamic adverse selection and debt

This paper argues that the strategic use of debt favours the revelationof information in dynamic adverse selection problems. Our argument is basedon the idea that debt is a credible commitment to end long term relationships.Consequently, debt encourages a privately informed party to disclose itsinformation at early stages of a relationship. We illustrate our pointwith the financing decision of a monopolist selling a good to a buyerwhose valuation is private information. A high level of (renegotiable)debt, by increasing the scope for liquidation, may induce the highvaluation buyer to buy early at a high price and thus increase themonopolist's expected payoff. By affecting the buyer's strategy, it mayreduce the probability of excessive liquidation. We investigate theconsequences of good durability and we examine the way debt mayalleviate the ratchet effect.

Long-run selection and the work ethic

That individuals contribute in social dilemma interactions even when contributing is costly is a well-established observation in the experimental literature. Since a contributor is always strictly worse off than a non-contributor the question is raised if an intrinsic motivation to contribute can survive in an evolutionary setting. Using recent results on deterministic approximation of stochastic evolutionary dynamics we give conditions for equilibria with a positive number of contributors to be selected in the long run.

Equilibrium selection through incomplete information in coordination games: An experimental study

We perform an experiment on a pure coordination game with uncertaintyabout the payoffs. Our game is closely related to models that have beenused in many macroeconomic and financial applications to solve problemsof equilibrium indeterminacy. In our experiment each subject receives anoisy signal about the true payoffs. This game has a unique strategyprofile that survives the iterative deletion of strictly dominatedstrategies (thus a unique Nash equilibrium). The equilibrium outcomecoincides, on average, with the risk-dominant equilibrium outcome ofthe underlying coordination game. The behavior of the subjects convergesto the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that subjects do not apply through"a priori" reasoning the iterated deletion of dominated strategies.Instead, they adapt to the responses of other players. Thus, the lengthof the learning phase clearly varies for the different signals. We alsotest behavior in a game without uncertainty as a benchmark case. The gamewith uncertainty is inspired by the "global" games of Carlsson and VanDamme (1993).

Optimal contracts, adverse selection and social preferences: An experiment

It has long been standard in agency theory to search for incentive-compatible mechanisms on the assumption that people care only about their own material wealth. However, this assumption is clearly refuted by numerous experiments, and we feel that it may be useful to consider nonpecuniary utility in mechanism design and contract theory. Accordingly, we devise an experiment to explore optimal contracts in an adverse-selection context. A principal proposes one of three contract menus, each of which offers a choice of two incentive-compatible contracts, to two agents whose types are unknown to the principal. The agents know the set of possible menus, and choose to either accept one of the two contracts offered in the proposed menu or to reject the menu altogether; a rejection by either agent leads to lower (and equal) reservation payoffs for all parties. While all three possible menus favor the principal, they do so to varying degrees. We observe numerous rejections of the more lopsided menus, and approach an equilibrium where one of the more equitable contract menus (which one depends on the reservation payoffs) is proposed and agents accept a contract, selecting actions according to their types. Behavior is largely consistent with all recent models of social preferences, strongly suggesting there is value in considering nonpecuniary utility in agency theory.

KIT mutations and dose selection for imatinib in patients with advanced gastrointestinal stromal tumours.

A recent randomized EORTC phase III trial, comparing two doses of imatinib in patients with advanced gastrointestinal stromal tumours (GISTs), reported dose dependency for progression-free survival. The current analysis of that study aimed to assess if tumour mutational status correlates with clinical response to imatinib. Pre-treatment samples of GISTs from 377 patients enrolled in phase III study were analyzed for mutations of KIT or PDGFRA by combination of D-HPLC and direct sequencing of tumour genomic DNA. Mutation types were correlated with patients' survival data. The presence of exon 9-activating mutations in KIT was the strongest adverse prognostic factor for response to imatinib, increasing the relative risk of progression by 171% (P<0.0001) and the relative risk of death by 190% (P<0.0001) when compared with KIT exon 11 mutants. Similarly, the relative risk of progression was increased by 108% (P<0.0001) and the relative risk of death by 76% (P=0.028) in patients without detectable KIT or PDGFRA mutations. In patients whose tumours expressed an exon 9 KIT oncoprotein, treatment with the high-dose regimen resulted in a significantly superior progression-free survival (P=0.0013), with a reduction of the relative risk of 61%. We conclude that tumour genotype is of major prognostic significance for progression-free survival and overall survival in patients treated with imatinib for advanced GISTs. Our findings suggest the need for differential treatment of patients with GISTs, with KIT exon 9 mutant patients benefiting the most from the 800 mg daily dose of the drug.

A characterization of sequential rationalizability

A choice function is sequentially rationalizable if there is an ordered collection of asymmetric binary relations that identifies the selected alternative in every choice problem. We propose a property, F-consistency, and show that it characterizes the notion of sequential rationalizability. F-consistency is a testable property that highlights the behavioral aspects implicit in sequentially rationalizable choice. Further, our characterization result provides a novel tool with which to study how other behavioral concepts are related to sequential rationalizability, and establish a priori unexpected implications. In particular, we show that the concept of rationalizability by game trees, which, in principle, had little to do with sequential rationalizability, is a refinement of the latter. Every choice function that is rationalizable by a game tree is also sequentially rationalizable. Finally, we show that some prominent voting mechanisms are also sequentially rationalizable.

Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

A simple randomized algorithm for consistent sequential prediction of ergodic time series

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if thesequence is a realization of a stationary and ergodic random process then the average number of mistakes converges, almost surely, to that of the optimum, given by the Bayes predictor.

Revealed preference and indifferent selection

It is shown that preferences can be constructed from observed choice behavior in a way that is robust to indifferent selection (i.e., the agent is indifferent between two alternatives but, nevertheless, is only observed selecting one of them). More precisely, a suggestion by Savage (1954) to reveal indifferent selection by considering small monetary perturbations of alternatives is formalized and generalized to a purely topological framework: references over an arbitrary topological space can be uniquely derived from observed behavior under the assumptions that they are continuous and nonsatiated and that a strictly preferred alternative is always chosen, and indifferent selection is then characterized by discontinuity in choice behavior. Two particular cases are then analyzed: monotonic preferences over a partially ordered set, and preferences representable by a continuous pseudo-utility function.

Sequential screening

We present a model of price discrimination where a monopolistfaces a consumer who is privately informed about thedistribution of his valuation for an indivisible unit ofgood but has yet to learn privately the actual valuation.The monopolist sequentially screens the consumer with amenu of contracts:the consumer self-selects once by choosing a contract andthen self-selects again when he learns the actual valuation. A deterministic sequential mechanism is a menu of refundcontracts, each consisting of an advance payment and a refundamount in case of no consumption, but sequential mechanismsmay involve randomization.We characterize the optimal sequential mechanism when someconsumer types are more eager in the sense of first-orderstochastic dominance, and when some types face greatervaluation uncertainty in the sense of mean-preserving-spread.We show that it can be optimal to subsidize consumer typeswith smaller valuation uncertainty (through low refund, as inairplane ticket pricing) in order to reduce the rent to thosewith greater uncertainty. The size of distortion depends bothon the type distribution and on how informative the consumer'sinitial private knowledge is about his valuation, but noton how much he initially knows about the valuation per se.