**Abstract:**An issuer seeks to liquidate all or part of a portfolio of heterogeneous assets about which she has private information. In contrast with the single-asset case, greater optimism may lead her to sell more of a given asset. But if assets can be ranked by their informational sensitivity then the issuer first liquidates her least sensitive assets, which, under weak assumptions, are her more senior assets (following Myers’s pecking order hypothesis). When the issuer can design new securities after learning her information then she has two equivalent, optimal strategies. She may design and sell, *ex post*, a single standard debt security whose face value is decreasing in her information. Or she may pool and tranche her assets *ex ante* into many prioritized debt securities and sell, *ex post*, those tranches whose seniority exceeds a threshold that is increasing in her information. In each case, the issuer retains more of her cash flow when information asymmetries are greater, as has been found in the case of no-documentation loans.

*This paper studies a cheap policy that can avoid costly bailouts of too-big-to-fail firms. The basic ideas are set out in layperson's terms in this 5-minute narrated slide show.*

**Abstract:**Distressed firms are vulnerable to inefficient panic-based runs of their workers, suppliers, and customers. A policymaker may try to prevent such a run by pledging to protect the interests of these stakeholders should a firm cease to do business. However, this promise also enables the firm to demand better terms of trade from its stakeholders, which blunts the policy's effectiveness. We show how to avoid such an adverse response by the use of partial, countercyclical insurance. Under certain conditions, such a scheme costlessly implements the first-best outcome in the limit as the stakeholders' information becomes precise. We also identify least-cost efficient schemes in the cases of large noise, learning, and duopoly.

**Abstract:**We study the effects of securitization on interbank lending competition. An applicant's observable features are seen by a remote bank, while her true credit quality is known only to a local bank. Without securitization, the remote bank does not compete because of a winner's curse. With securitization, in contrast, ignorance is bliss: the less a bank knows about its loans, the less of a lemons problem it faces in selling them. This enables the remote bank to compete successfully in the lending market. Consistent with the empirical evidence, remote and securitized loans default more than observationally equivalent local and unsecuritized loans, respectively.

**Abstract:** Global games have unique equilibria in which aggregate behavior changes sharply when an underlying random fundamental crosses some threshold. This property relies on the existence of dominance regions: all players have a highest and lowest action that, for some fundamentals, is strictly dominant. But if the fundamental follows a random walk, it eventually spends nearly all of its time in these regions: crises gradually disappear. We obtain recurring crises by adding a single large player who lacks dominance regions. We also show that in order to obtain recurring crises, one must either relax dominance regions or restrict to fundamentals that continually return to or cross over a fixed region.

**Abstract:** Using only ordinal axioms, we characterize several multigroup school segregation indices: the Atkinson Indices for the class of school districts with a given fixed number of ethnic groups and the Mutual Information Index for the class of all districts. Properties of other school segregation indices are also discussed. In an empirical application, we document a weakening of the effect of ethnicity on school assignment from 1987/8 to 2007/8. We also show that segregation between districts within cities currently accounts for 33% of total segregation. Segregation between states, driven mainly by the distinct residental patterns of Hispanics, contributes another 32%.

**Abstract:** A theory is developed that explains how the stock market can crash in the absence of news about fundamentals, and why crashes are more common than frenzies. A crash occurs via the interaction of rational and naive investors. Naive traders believe in a simple (but reasonable) statistical model of stock prices: that prices follow a random walk with serially correlated volatility. They predict future volatility adaptively, as a weighted average of past squared price changes. We assume an initial round of trading that establishes a baseline price for the stock. In the next round, the price either remains near the baseline level or, with a small probability, "crashes" to a lower level. If the price crashes, the naive traders lower their demand in response to the apparent increase in volatility. This lowers the risk bearing capacity of the market, so that the lower crash price clears the market. Unlike other explanations of market crashes, this mechanism is fundamentally asymmetric: the stock price cannot rise sharply, so frenzies or bubbles cannot occur.

**Abstract:** A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique equilibrium if there are payoff shocks of any size. This equilibrium still has the desirable property that recessions and expansions can occur without any large exogenous shocks. We give an algorithm for computing the equilibrium and study its comparative statics properties. This work generalizes Burdzy, Frankel, and Pauzner (2000) to the case of endogenous frictions and seasonal and mean-reverting shocks.

**Abstract:** We study games with strategic complementarities, arbitrary numbers of players and actions, and slightly noisy payoff signals. We prove *limit uniqueness*: as the signal noise vanishes, the incomplete information game has a unique strategy profile that survives iterative dominance. This generalizes a result of Carlsson and van Damme for two player, two action games. The surviving profile, however, may depend on fine details of the structure of the noise. We provide sufficient conditions on payoffs for there to be noise-independent selection.

**Abstract:** We study the role of expectations in neighborhood change, assuming two groups with a preference for segregation and frictions that prevent agents from moving simultaneously. In a stationary environment, there can be multiple equilibria; a neighborhood's ethnic character may change if and only if it is expected to do so. In contrast, there is a unique equilibrium in an initially segregated neighborhood that is subject to a deterministic, exogenous trend that makes the neighborhood progressively less appealing to its current residents. The other group begins to move in at the first date at which the anticipation of this transition would be self-fulfilling. If the neighborhood is not initially segregated, there may still be multiple equilibria with a deterministic trend. However, if the exogenous trend follows a stochastic process with certain properties, a unique equilibrium is obtained for any initial conditions.

**Abstract:** We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk dominant equilibrium. More precisely, a continuum of fully rational players are randomly matched to play a symmetric 2*2 game. The payoff matrix changes according to a random walk. Players observe these payoffs and the population distribution of actions as they evolve. The game has frictions: opportunities to change strategies arrive from independent random processes, so that the players are locked into their actions for some time. As the frictions disappear, each player ignores what the others are doing and switches at her first opportunity to the risk dominant equilibrium. History dependence emerges in some cases when frictions remain positive.

**Abstract:** This paper studies the effects of a city's income distribution on its retail price level using panel data. We find that an increase in the presence of lower middle income households, relative to poor or upper income households, leads to lower prices. A simple search model is presented that helps explain the results and shows that OLS estimates will be biased towards zero (which we confirm empirically using instrumental variables). Our findings suggest that greater income inequality raises the prices that poor households face, thus making it harder for them to invest in human capital.

**Abstract:** This paper shows that the phenomenon of multiple equilibria can be fragile to the introduction of aggregate shocks. We examine a standard dynamic model of sectoral choice with external increasing returns (based on Matsuyama 1991). Without shocks, the outcome is indeterminate: there are multiple rational expectations equilibria. We then introduce shocks in the form of a parameter that follows a Brownian motion and affects relative productivity in the two sectors. We assume that the parameter can reach values at which working in either sector becomes a dominant choice. A unique equilibrium emerges; for any path of the random parameter, there is a unique path that the economy must follow. There is no role for multiple, self-fulfilling prophecies or sunspots.

**Abstract:** Empirical studies have found a high degree of income mixing in American neighborhoods. We give a new explanation of this phenomenon that is based on consumer search. A low price for a given good benefits high valuation buyers more than low valuation buyers. But with search, the probability of obtaining a low price is increasing in the proportion of low valuation buyers. This gives high valuation buyers an incentive to live near low valuation buyers. With many goods, a buyer has an incentive to live near neighbors whose valuations are uncorrelated with hers.

**Abstract:** We examine what happens if, as players bargain, they can exert costly effort to expand the set of possible proposals. With side payments, new ideas influence the size of the pie but not its division. The benefits of one player's creativity are shared with the other, so effort is inefficiently low. Without side payments, new ideas do influence the distribution, so players inefficiently limit their search to ideas that favor them. Getting an idea makes an agreement more likely, but it also makes the other player's ideas less likely to be adopted. Consequently, effort can be either excessive or suboptimal.

**Abstract:** A known result holds that capital taxes should be high in the short run and low or zero in the long run steady state. This paper studies the dynamics of optimal capital taxation during the transition, when a high rate is no longer optimal but the economy is still in flux. The main result is that capital should be taxed whenever the sum of the elasticities of marginal utility with respect to consumption and labor supply are rising and subsidized whenever this sum is falling. If the utility function displays increasing relative risk aversion, this paradoxically implies that capital should be taxed when the capital stock is below the modified golden rule level and subsidized whenever it exceeds this level. Thus, savings incentives can sometimes be more desirable when the capital stock is large than when it is small.

**Abstract:** This paper presents mathematical results used in "Resolving Uncertainty...." and in an earlier version of "Fast Equilibrium Selection...."

**Abstract:** This paper studies the causes of the strong relationship that exists between occupation and political preferences in Great Britain. Part of the relationship is due to occupational differences in income, education, age, and union membership. However, the effects of occupation on Labour Party support remains strong even when these traits are controlled for. We consider four competing explanations for the remaining effects: occupational differences in job desirability, career mobility chances, power relations, and friendship patterns. Of these four, differences in friendship patterns are the best explanation, with differing mobility chances running a close second. Job desirability and power relations are weaker explanations and are not needed to fit the data.