Knowledge that Transforms

We analyse a two-player game of strategic experimentation with two-armed bandits. Either player has to decide in continuous time whether to use a safe arm with a known pay-off or a risky arm whose expected pay-off per unit of time is initially unknown. This pay-off can be high or low and is negatively correlated across players. We characterize the set of all Markov perfect equilibria in the benchmark case where the risky arms are known to be of opposite type and construct equilibria in cut-off strategies for arbitrary negative correlation. All strategies and pay-offs are in closed form. In marked contrast to the case where both risky arms are of the same type, there always exists an equilibrium in cut-off strategies, and there always exists an equilibrium exhibiting efficient long-run patterns of learning. These results extend to a three-player game with common knowledge that exactly one risky arm is of the high pay-off type.

Quantile regression (QR) is an increasingly important empirical tool in economics and other sciences for analysing the impact a set of regressors has on the conditional distribution of an outcome. Extremal QR, or QR applied to the tails, is of interest in many economic and financial applications, such as conditional value at risk, production efficiency, and adjustment bands in (S,s) models. This paper provides feasible inference tools for extremal conditional quantile models that rely on extreme value approximations to the distribution of self-normalized QR statistics. The methods are simple to implement and can be of independent interest even in the univariate (non-regression) case. We illustrate the results with two empirical examples analysing extreme fluctuations of a stock return and extremely low percentiles of live infant birthweight in the range between 250 and 1500 g.

We offer an explanation for the forward premium puzzle in foreign exchange markets based upon investor overconfidence. In the model, overconfident individuals overreact to their information about future inflation, which causes greater overshooting in the forward rate than in the spot rate. Thus, when agents observe a signal of higher future inflation, the consequent rise in the forward premium predicts a subsequent downward correction of the spot rate. The model can explain the magnitude of the forward premium bias and several other stylized facts related to the joint behaviour of forward and spot exchange rates. Our approach is also consistent with the availability of profitable carry trade strategies.

We analyse information aggregation in a stopping game with uncertain pay-offs that are correlated across players. Players learn from their own private experiences as well as by observing the actions of other players. We give a full characterization of the symmetric mixed strategy equilibrium, and show that information aggregates in randomly occurring exit waves. Observational learning induces the players to stay in the game longer. The equilibria display aggregate randomness even for large numbers of players.

We study competitive market outcomes in economies where agents have other-regarding preferences (ORPs). We identify a separability condition on monotone preferences that is necessary and sufficient for one's own demand to be independent of the allocations and characteristics of other agents in the economy. Given separability, it is impossible to identify ORPs from market behaviour: agents behave as if they had classical preferences that depend only on own consumption in competitive equilibrium. If preferences, in addition, depend only on the final allocation of consumption in society, the Second Welfare Theorem holds as long as any increase in resources can be distributed in a way that makes all agents better off. The First Welfare Theorem generally does not hold. Allowing agents to care about their own consumption and the distribution of consumption possibilities in the economy, the competitive equilibria are efficient given prices if and only if there is no Pareto-improving redistribution of income.

Assortative matching between workers and firms provides evidence of the complementarities or substitutes in production. The presence of complementarities is important for policies that aim to achieve the optimal allocation of resources, e.g. unemployment insurance. We argue that using wage data alone, it is virtually impossible to identify whether assortative matching is positive or negative. Even though we cannot identify the sign of the sorting, we can identify the strength, i.e. the magnitude of the cross-partial and the associated welfare loss. We first show that the wage for a given worker is non-monotonic in the type of his employer. This is due to the fact that in a sorting model, wages reflect the opportunity cost of mismatch. We analytically show that this non-monotonicity prevents standard firm fixed effects to correlate with the true type of the firm. We then propose an alternative procedure that measures the strength of sorting in the presence of search frictions. Knowing the strength of sorting facilitates the measurement of the output loss due to mismatch.

Whether campaign advertising influences election outcomes is an open question; a paradox given the amount spent on campaigning in general and TV advertising in particular. We argue that such “absence of documentation” is due to the focus of the empirical literature on the United States, in which the allocation of campaign spending and advertising is decentralized. We explore a quasinatural experiment that enables us to mitigate the omitted variables and reverse causality problems caused by decentralized allocation. In Brazil, gubernatorial elections work in a two-round system. In the first round, candidates’ TV time shares are determined by their coalitions’ share of seats in the National Parliament. In the second round, TV time is split equally between the first-round winner and runner-up. Using differences between rounds as a source of variation, we find a large causal effect of TV advertising on election outcomes.

We propose a computationally feasible way of deriving the identified features of models with multiple equilibria in pure or mixed strategies. It is shown that in the case of Shapley regular normal form games, the identified set is characterized by the inclusion of the true data distribution within the core of a Choquet capacity, which is interpreted as the generalized likelihood of the model. In turn, this inclusion is characterized by a finite set of inequalities and efficient and easily implementable combinatorial methods are described to check them. In all normal form games, the identified set is characterized in terms of the value of a submodular or convex optimization program. Efficient algorithms are then given and compared to check inclusion of a parameter in this identified set. The latter are illustrated with family bargaining games and oligopoly entry games.

While there is an extensive literature on how economic agents bargain to divide an asset, little is known about the decision to initiate bargaining and how the initiation affects the outcome of bargaining. We address these questions in the context of high-stakes poker tournaments in which the last few players often negotiate the division of the remaining prize money rather than risk playing the tournament to the end. In 63% of the tournaments in our sample players enter into negotiations, and in 31%, they successfully reach an agreement. We find that the identity of the player who initiates bargaining affects whether a deal is completed but does not affect the terms of the eventual deal. The initiator tends to have a weaker than average position at the table, but the likelihood that a deal will be completed increases in the initiator's strength in the game and history of winning past tournaments. These findings indicate that initiating negotiations conveys information that is relevant to whether a deal will emerge. Nevertheless, initiating bargaining does not affect the initiator's pay-off in a completed deal. Lastly, we find strong evidence that bargaining tends to be initiated and is more likely to be successful when participants' stakes are about equal, consistent with the theoretical work of Cramton, Gibbons and Klemperer (1987, “Dissolving a Partnership Efficiently”, Econometrica, 55, 615–632).

We study a market model in which competing firms use costly marketing devices to influence the set of alternatives that boundedly rational consumers perceive as relevant. Consumers in our model apply well-defined preferences to a “consideration set”, which is a subset of the feasible set and subject to manipulation by firms. We examine the implications of this behavioral model on otherwise competitive markets. In our model, the market equilibrium outcome is not competitive, yet firms earn competitive payoff because the strategic use of costly marketing devices wears off the collusive impact of consumers’ bounded rationality. Equilibrium behavior satisfies an “effective marketing property”: if a consumer considers a firm only because of a marketing device it employs, he ends up buying from that firm.