Who Matters in Coordination Problems?

We consider a common investment project that is vulnerable to a self-ful lling coordination failure and hence is strategically risky. Based on their private information, agents - who have heterogeneous investment incentives - form expectations or 'sentiments' about the project's outcome. We find that the sum of these sentiments is constant across di erent strategy profiles and it is independent of the distribution of incentives. As a result, we can think of sentiment as a scarce resource divided up among the di erent payo types. Applying this nding, we show that agents who bene t little from the project's success have a large impact on the coordination process. The agents with small bene ts invest only if their sentiment towards the project is large per unit investment cost. As the average sentiment is constant, a subsidy decreasing the investment costs of these agents will \free up" a large amount of sentiment, provoking a large impact on the whole economy. Intuitively, these agents, insensitive to the project's outcome and hence to the actions of others, are in uential because they modify their equilibrium behavior only if the others change theirs substantially.

No Good Deals - No Bad Models

Faced with the problem of pricing complex contingent claims, an investor seeks to make his valuations robust to model uncertainty. We construct a notion of a model- uncertainty-induced utility function and show that model uncertainty increases the investor's eff ective risk aversion. Using the model-uncertainty-induced utility function, we extend the \No Good Deals" methodology of Cochrane and Sa a-Requejo [2000] to compute lower and upper good deal bounds in the presence of model uncertainty. We illustrate the methodology using some numerical examples.

Personal indebtedness, community characteristics and theft crimes

Becker (1968) and Stigler (1970) provide the germinal works for an economic analysis of crime, and their approach has been utilised to consider the response of crime rates to a range of economic, criminal and socioeconomic factors. Until recently however this did not extend to a consideration of the role of personal indebtedness in explaining the observed pattern of crime. This paper uses the Becker (1968) and Stigler (1970) framework, and extends to a fuller consideration of the relationship between economic hardship and theft crimes in an urban setting. The increase in personal debt in the past decade has been significant, which combined with the recent global recession, has led to a spike in personal insolvencies. In the context of the recent recession it is important to understand how increases in personal indebtedness may spillover into increases in social problems like crime. This paper uses data available at the neighbourhood level for London, UK on county court judgments (CCJ's) granted against residents in that neighbourhood, this is our measure of personal indebtedness, and examines the relationship between a range of community characteristics (economic, socio-economic, etc), including the number of CCJ's granted against residents, and the observed pattern of theft crimes for three successive years using spatial econometric methods. Our results confirm that theft crimes in London follow a spatial process, that personal indebtedness is positively associated with theft crimes in London, and that the covariates we have chosen are important in explaining the spatial variation in theft crimes. We identify a number of interesting results, for instance that there is variation in the impact of covariates across crime types, and that the covariates which are important in explaining the pattern of each crime type are largely stable across the three periods considered in this analysis.

A General and Intuitive Envelope Theorem

We present an envelope theorem for establishing first-order conditions in decision problems involving continuous and discrete choices. Our theorem accommodates general dynamic programming problems, even with unbounded marginal utilities. And, unlike classical envelope theorems that focus only on differentiating value functions, we accommodate other endogenous functions such as default probabilities and interest rates. Our main technical ingredient is how we establish the differentiability of a function at a point: we sandwich the function between two differentiable functions from above and below. Our theory is widely applicable. In unsecured credit models, neither interest rates nor continuation values are globally differentiable. Nevertheless, we establish an Euler equation involving marginal prices and values. In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.