Knowledge that Transforms

This paper is about measuring state dependence in dynamic discrete outcomes. I develop a nonparametric dynamic potential outcomes (DPO) model and propose an array of parameters and identifying assumptions that can be considered in this model. I show how to construct sharp identified sets under combinations of identifying assumptions by using a flexible linear programming procedure. I apply the analysis to study state dependence in unemployment for working age high school educated men using an extract from the 2008 Survey of Income and Program Participation (SIPP). Using only nonparametric assumptions, I estimate that state dependence accounts for at least 30–40% of the four‐month persistence in unemployment among high school educated men.

We analyze financial markets in which agents face differential constraints on the set of assets in which they can trade. In particular, the assets available to each agent span a partition of the state space that can be strictly coarser than the partition spanned by the assets available in the market. We first show that the existence of differential constraints has an impact on prices and allocations as compared to a complete financial market with unconstrained agents. We consider the implications for survival, taking the work of Blume and Easley (2006) as a starting point. We show that whenever agents have identical correct beliefs and equal discount factors, and their partitions are nested, all agents survive. When agents have heterogeneous beliefs, differential constraints may allow agents with wrong beliefs to survive. Provided constraints are relevant (in a sense we define more precisely), the condition for an agent to survive is that his survival index is at least as large as that of the agents with finer partitions. We also study the impact of deregulation (an increase in the set of assets available to some agents). Unless the agent can adopt beliefs that are closer to the truth on the newly refined partition than those of less constrained agents, increasing his opportunities for trade might harm his chances for survival.

Making inferences about aggregate business cycles from regional variation alone is difficult because of economic channels and shocks that differ between regional and aggregate economies. However, we argue that regional business cycles contain valuable information that can help discipline models of aggregate fluctuations. We begin by documenting a strong relationship across U.S. states between local employment and wage growth during the Great Recession. This relationship is much weaker in U.S. aggregates. Then, we present a methodology that combines such regional and aggregate data in order to estimate a medium‐scale New Keynesian DSGE model. We find that aggregate demand shocks were important drivers of aggregate employment during the Great Recession, but the wage stickiness necessary for them to account for the slow employment recovery and the modest fall in aggregate wages is inconsistent with the flexibility of wages we observe across U.S. states. Finally, we show that our methodology yields different conclusions about the causes of aggregate employment and wage dynamics between 2007 and 2014 than either estimating our model with aggregate data alone or performing back‐of‐the‐envelope calculations that directly extrapolate from well‐identified regional elasticities.

We study the interactions between sovereign debt default and maturity choice in a setting with limited commitment for repayment as well as future debt issuances. Our main finding is that, under a wide range of conditions, the sovereign should, as long as default is not preferable, remain passive in long‐term bond markets, making payments and retiring long‐term bonds as they mature but never actively issuing or buying back such bonds. The only active debt‐management margin is the short‐term bond market. We show that any attempt to manipulate the existing maturity profile of outstanding long‐term bonds generates losses, as bond prices move against the sovereign. Our results hold regardless of the shape of the yield curve. The yield curve captures the average costs of financing at different maturities but is misleading regarding the marginal costs.

A general selection theorem is presented constructing a measurable mapping from a state space to a parameter space under the assumption that the state space can be decomposed as a collection of countable equivalence classes under a smooth equivalence relation. It is then shown how this selection theorem can be used as a general purpose tool for proving the existence of measurable equilibria in broad classes of several branches of games when an appropriate smoothness condition holds, including Bayesian games with atomic knowledge spaces, stochastic games with countable orbits, and graphical games of countable degree—examples of a subclass of games with uncountable state spaces that we term purely atomic games. Applications to repeated games with symmetric incomplete information and acceptable bets are also presented.

We revisit the Nash bargaining model and axiomatize a procedural solution that maximizes the probability of successful bargaining. Our characterization spans several known solution concepts, including the special cases of the Nash, egalitarian, and utilitarian solutions. Using a probability‐based language, we offer a natural interpretation for the product operator underlying the Nash solution: when the bargainers' individual acceptance probabilities are independent, their product recovers the joint acceptance probability.

We study economies in which agents face Knightian uncertainty about state prices. Knightian uncertainty leads naturally to nonlinear expectations. We introduce a corresponding equilibrium concept with sublinear prices and prove that equilibria exist under weak conditions. In general, such equilibria lead to Pareto inefficient allocations; the equilibria coincide with Arrow-Debreu equilibria only if the values of net trades are ambiguity-free in the mean. In economies without aggregate uncertainty, inefficiencies are generic. We introduce a constrained efficiency concept, uncertainty-neutral efficiency, equilibrium allocations under price uncertainty are efficient in this constrained sense. Arrow-Debreu equilibria turn out to be non-robust with respect to the introduction of Knightian uncertainty.

This paper provides nonparametric identification results for a class of latent utility models with additively separable unobservable heterogeneity. These results apply to existing models of discrete choice, bundles, decisions under uncertainty, and matching. Under an independence assumption, such models admit a representative agent. As a result, we can identify how regressors alter the desirability of goods using only average demands. Moreover, average indirect utility (“welfare”) is identified without needing to specify or identify the distribution of unobservable heterogeneity.

An Equivalence Theorem between geometric structures and utility functions allows new methods for understanding preferences. Our classification of valuations into “Demand Types” incorporates existing definitions (substitutes, complements, “strong substitutes,” etc.) and permits new ones. Our Unimodularity Theorem generalizes previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a “demand type.” Contrary to popular belief, equilibrium is guaranteed for more classes of purely‐complements than of purely‐substitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalition‐formation, and the “Product‐Mix Auction” introduced by the Bank of England in response to the financial crisis.

We revisit prominent learning models in which a sequence of agents make a binary decision on the basis of both a private signal and information related to past choices. We analyze the efficiency of learning in these models, measured in terms of the expected welfare. We show that, irrespective of the distribution of private signals, learning efficiency is the same whether each agent observes the entire sequence of earlier decisions or only the previous decision. In addition, we provide a simple condition on the signal distributions that is necessary and sufficient for learning efficiency. This condition fails to hold in many cases of interest. We discuss a number of extensions and variants.