Knowledge that Transforms

We investigate the classical Anscombe–Aumann model of decision-making under uncertainty without the completeness axiom. We distinguish between the dual traits of “indecisiveness in beliefs” and “indecisiveness in tastes.” The former is captured by the Knightian uncertainty model, the latter by the single-prior expected multi-utility model. We characterize axiomatically the latter model. Then we show that, under independence and continuity, these two models can be jointly characterized by means of a partial completeness property.

We study matching and coalition formation environments allowing complementarities and peer effects. Agents have preferences over coalitions, and these preferences vary with an underlying, and commonly known, state of nature. Assuming that there is substantial variability of preferences across states of nature, we show that there exists a core stable coalition structure in every state if and only if agents' preferences are pairwise-aligned in every state. This implies that there is a stable coalition structure if agents' preferences are generated by Nash bargaining over coalitional outputs. We further show that all stability-inducing rules for sharing outputs can be represented by a profile of agents' bargaining functions and that agents match assortatively with respect to these bargaining functions. This framework allows us to show how complementarities and peer effects overturn well known comparative statics of many-to-one matching.

We investigate the welfare properties of the one-sector neoclassical growth model with uninsurable idiosyncratic shocks. We focus on the notion of constrained efficiency used in the general equilibrium literature. Our characterization of constrained efficiency uses the first-order condition of a constrained planner’s problem. This condition highlights the margins of relevance for whether capital is too high or too low: the factor composition of income of the (consumption-) poor. Using three calibrations commonly considered in the literature, we illustrate that there can be either over- or underaccumulation of capital in steady state and that the constrained optimum may or may not be consistent with a nondegenerate long-run distribution of wealth. For the calibration that roughly matches the income and wealth distribution, the constrained inefficiency of the market outcome is rather striking: it has much too low a steady-state capital stock.

This paper studies information aggregation in dynamic markets with a finite number of partially informed strategic traders. It shows that, for a broad class of securities, information in such markets always gets aggregated. Trading takes place in a bounded time interval, and in every equilibrium, as time approaches the end of the interval, the market price of a “separable” security converges in probability to its expected value conditional on the traders' pooled information. If the security is “non-separable,” then there exists a common prior over the states of the world and an equilibrium such that information does not get aggregated. The class of separable securities includes, among others, Arrow–Debreu securities, whose value is 1 in one state of the world and 0 in all others, and “additive” securities, whose value can be interpreted as the sum of traders' signals.

This paper argues that in the presence of intersectoral input-output linkages, microeconomic idiosyncratic shocks may lead to aggregate fluctuations.We show, as the economy becomes more disaggregated, the rate at which aggregate volatility decays is determined by the structure of the network capturing such linkages.Our main results provide a characterization of this relationship in terms of the importance of different sectors as suppliers to their immediate customers as well as their role as indirect suppliers to chains of downstream sectors.Such higher-order interconnections capture the possibility of "cascade effects" whereby productivity shocks to a sector propagate not only to its immediate downstream customers, but also to the rest of the economy.Our results highlight that sizable aggregate volatility is obtained from sectoral idiosyncratic shocks only if there exists significant asymmetry in the roles that sectors play as suppliers to others, and that the "sparseness" of the input-output matrix is unrelated to the nature of aggregate fluctuations.

The delta method and continuous mapping theorem are among the most extensively used tools in asymptotic derivations in econometrics. Extensions of these methods are provided for sequences of functions that are commonly encountered in applications and where the usual methods sometimes fail. Important examples of failure arise in the use of simulation-based estimation methods such as indirect inference. The paper explores the application of these methods to the indirect inference estimator (IIE) in first order autoregressive estimation. The IIE uses a binding function that is sample size dependent. Its limit theory relies on a sequence-based delta method in the stationary case and a sequence-based implicit continuous mapping theorem in unit root and local to unity cases. The new limit theory shows that the IIE achieves much more than (partial) bias correction. It changes the limit theory of the maximum likelihood estimator (MLE) when the autoregressive coefficient is in the locality of unity, reducing the bias and the variance of the MLE without affecting the limit theory of the MLE in the stationary case. Thus, in spite of the fact that the IIE is a continuously differentiable function of the MLE, the limit distribution of the IIE is not simply a scale multiple of the MLE, but depends implicitly on the full binding function mapping. The unit root case therefore represents an important example of the failure of the delta method and shows the need for an implicit mapping extension of the continuous mapping theorem.

This paper analyzes Bayesian normal form games in which players write contracts that condition their actions on the contracts of other players. These contracts are required to be representable in a formal language. This is accomplished by constructing contracts which are definable functions of the Godel code of every other player's contract. We provide a complete characterization of the set of allocations supportable as pure-strategy Bayesian equilibria of this contracting game. When information is complete, this characterization provides a folk theorem. In general, the set of supportable allocations is smaller than the set supportable by a centralized mechanism designer.

This paper studies endogenous risk-taking by embedding a concern for status (relative consumption) into an otherwise conventional model of economic growth. We prove that if the intertemporal production function is strictly concave, an equilibrium must converge to a unique steady state in which there is recurrent endogenous risk-taking. (The role played by concavity is clarified by considering a special case in which the production function is instead convex, in which there is no persistent risk-taking.) The steady state is fully characterized. It displays features that are consistent with the stylized facts that individuals both insure downside risk and gamble over upside risk, and it generates similar patterns of risk-taking and avoidance across environments with quite different overall wealth levels. Endogenous risk-taking here is generally Pareto-inefficient. A concern for status thus implies that persistent and inefficient risk-taking hinders the attainment of full equality.

I explore the equilibrium value implications of economic models that incorporate responses to a stochastic environment with growth. I propose dynamic valuation decompositions (DVD's) designed to distinguish components of an underlying economic model that influence values over long investment horizons from components that impact only the short run. A DVD represents the values of stochastically growing claims to consumption payoffs or cash flows using a stochastic discount process that both discounts the future and adjusts for risk. It is enabled by constructing operators indexed by the elapsed time between the trading date and the date of the future realization of the payoff. Thus formulated, methods from applied mathematics permit me to characterize valuation behavior and the term structure of risk prices in a revealing manner. I apply this approach to investigate how investor beliefs and the associated uncertainty are reflected in current-period values and risk-price elasticities.

I propose a new mechanism design approach to the problem of ranking standard auctions with two heterogeneous bidders. A key feature of the approach is that it may be possible to rank two auctions even if neither dominates the other for all combinations of types. The approach simplifies the analysis and unifies results in the existing literature. Roughly speaking, the first-price auction is more profitable than the second-price auction when the strong bidder's distribution is flatter and more disperse than the weak bidder's distribution. Applications include auctions with one-sided externalities. Moreover, contrary to previous work, reserve prices are easily handled. Finally, the method can be extended to some environments with many bidders.