Knowledge that Transforms

Dynamic models of ambiguity aversion are increasingly popular in applied work. This paper shows that there is a strong interdependence in such models between the ambiguity attitude and the preference for the timing of the resolution of uncertainty, as defined by the classic work of Kreps and Porteus (1978). The modeling choices made in the domain of ambiguity aversion influence the set of modeling choices available in the domain of timing attitudes. The main result is that the only model of ambiguity aversion that exhibits indifference to timing is the maxmin expected utility of Gilboa and Schmeidler (1989). This paper examines the structure of the timing nonindifference implied by the other commonly used models of ambiguity aversion. This paper also characterizes the indifference to long-run risk, a notion introduced by Duffie and Epstein (1992). The interdependence of ambiguity and timing that this paper identifies is of interest both conceptually and practically—especially for economists using these models in applications.

We study repeated Bayesian games with communication and observable actions in which the players' privately known payoffs evolve according to an irreducible Markov chain whose transitions are independent across players. Our main result implies that, generically, any Pareto-efficient payoff vector above a stationary minmax value can be approximated arbitrarily closely in a perfect Bayesian equilibrium as the discount factor goes to 1. As an intermediate step, we construct an approximately efficient dynamic mechanism for long finite horizons without assuming transferable utility.

Recurrent intervals of inattention to the stock market are optimal if consumers incur a utility cost to observe asset values.When consumers observe the value of their wealth, they decide whether to transfer funds between a transactions account from which consumption must be financed and an investment portfolio of equity and riskless bonds.Transfers of funds are subject to a transactions cost that reduces wealth and consists of two components: one is proportional to the amount of assets transferred, and the other is a fixed resource cost.Because it is costly to transfer funds, the consumer may choose not to transfer any funds on a particular observation date.In general, the optimal adjustment rule---including the size and direction of transfers, and the time of the next observation---is state-dependent.Surprisingly, unless the fixed resource cost of transferring funds is large, the consumer's optimal behavior eventually evolves to a situation with a purely time-dependent rule with a constant interval of time between observations.This interval of time can be substantial even for tiny observation costs.When this situation is attained, the standard consumption Euler equation holds between observation dates if the consumer is sufficiently risk averse.

This paper proposes a symmetry-breaking model of trade with a (large but) finite number of (ex ante) identical countries and a continuum of tradeable goods, which differ in their dependence on local differentiated producer services. Productivity differences across countries arise endogenously through free entry to the local service sector in each country. In any stable equilibrium, the countries sort themselves into specializing in different sets of tradeable goods, and a strict ranking of countries in per capita income, TFP, and the capital-labor ratio emerges endogenously. Furthermore, the distribution of country shares, the Lorenz curve, is unique and analytically solvable in the limit, as the number of countries grows unbounded. Using this limit as an approximation allows us to study what determines the shape of distribution, to perform various comparative statics, and to evaluate the welfare effects of trade.

We characterize and prove the existence of Nash equilibrium in a limit order market with a finite number of risk-neutral liquidity providers. We show that if there is sufficient adverse selection, then pointwise optimization (maximizing in p for each q) in a certain nonlinear pricing game produces a Nash equilibrium in the limit order market. The need for a sufficient degree of adverse selection does not vanish as the number of liquidity providers increases. Our formulation of the nonlinear pricing game encompasses various specifications of informed and liquidity trading, including the case in which nature chooses whether the market-order trader is informed or a liquidity trader. We solve for an equilibrium analytically in various examples and also present examples in which the first-order condition for pointwise optimization does not define an equilibrium, because the amount of adverse selection is insufficient.

This paper constructs an e cient, budget-balanced, Bayesian incentive-compatible mechanism for a general dynamic environment with private information.As an intermediate result, we construct an e cient, ex post incentive-compatible mechanism, which is not budget balanced.We also provide conditions under which participation constraints can be satis ed in each period, so that the mechanism can be made self-enforcing if the horizon is in nite and players are su ciently patient.In our dynamic environment, agents observe a sequence of private signals over a number of periods (either nite or countable).In each period, the agents report their private signals, and make public (contractible) and private decisions based on the reports.The probability distribution over future signals may depend on both past signals and past decisions.The construction of an e cient mechanism hinges on the assumption of \private values" (each agent's payo is determined by his own observations).Balancing the budget relies on the assumption of \independent types" (the distribution of each agent's private signals does not depend on the other agents' private information, except through public decisions).

This paper proposes a new approach to equilibrium selection in repeated games with transfers, supposing that in each period the players bargain over how to play. Although the bargaining phase is cheap talk (following a generalized alternating-offer protocol), sharp predictions arise from three axioms. Two axioms allow the players to meaningfully discuss whether to deviate from their plan; the third embodies a “theory of disagreement”—that play under disagreement should not vary with the manner in which bargaining broke down. Equilibria that satisfy these axioms exist for all discount factors and are simple to construct; all equilibria generate the same welfare. Optimal play under agreement generally requires suboptimal play under disagreement. Whether patient players attain efficiency depends on both the stage game and the bargaining protocol. The theory extends naturally to games with imperfect public monitoring and heterogeneous discount factors, and yields new insights into classic relational contracting questions.

We model a dynamic, competitive market, where in every period, risk-neutral traders trade a one-period bond against an infinitely lived asset, with limited short-selling of the long-term asset. Traders lack structural knowledge and use different “incomplete theories,” all of which give statistically correct beliefs about next period's market price of the long-term asset. The more theories there are in the market, the higher is the equilibrium price of the long-term asset. Investors with more complete theories do not necessarily earn higher returns than those with less complete ones, who can earn above the risk-free rate. We provide two necessary conditions for a trader to earn above the risk-free rate.

We derive the analogue of the classic Arrow-Pratt approximation of the certainty equivalent under model uncertainty as de…ned by the smooth model of decision making under ambiguity of Klibano¤, Marinacci and Mukerji (2005).We study its scope via a portfolio allocation exercise that delivers a tractable mean-variance model adjusted for model uncertainty.In a problem with a risk-free asset, a risky asset, and an ambiguous asset, we …nd that portfolio rebalancing in response to higher model uncertainty only depends on the ambiguous asset's alpha, setting the performance of the risky asset as benchmark.In addition, the portfolios recommended by our model are not systematically conservative on the share held in the ambiguous asset: indeed, in general, it is not true that greater ambiguity reduces the optimal demand for the ambiguous asset.The analytical tractability of the enhanced Arrow-Pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of ambiguity aversion on equilibrium asset prices."Crises feed uncertainty.

Few microfinance-funded businesses grow beyond subsistence entrepreneurship. This paper considers one possible explanation: that the structure of existing microfinance contracts may discourage risky but high-expected-return investments. To explore this possibility, I develop a theory that unifies models of investment choice, informal risk-sharing, and formal financial contracts. I then test the predictions of this theory using a series of experiments with clients of a large microfinance institution in India. The experiments confirm the theoretical predictions that joint liability creates two potential inefficiencies. First, borrowers free-ride on their partners, making risky investments without compensating partners for this risk. Second, the addition of peer-monitoring overcompensates, leading to sharp reductions in risk-taking and profitability. Equity-like financing, in which partners share both the benefits and risks of more profitable projects, overcomes both of these inefficiencies and merits further testing in the field.