. We develop models of robust decision-making and pricing when there are contemporaneous big and small shocks. We illustrate these models using a stochasticgrowth economy. Large shocks are infrequent changes in the technological growth rate, and small shocks are continuous movements in the technology process. Large shocks evolve as a Markov jump process whereas small shocks are a Brownian motion. Robust decision-making is formalized as a two-player game. In contrast to rational expectations agents, our investors are decision-makers who treat models as approximations and fear misspecication. As an algorithmic device to enforce robustness, investors imagine a second, malevolent player, who has the ability to perturb the baseline model. We study two economies, each of which decentralizes a robust resource allocation problem with hidden growth rates. The economies dier in the manner in which the the model is viewed as an approximation. We compare the pricing implications to those that em...

In this article we characterize and estimate the process for short-term interest rates using federal funds interest rate data. We presume that we are observing a discrete-time sample of a stationary scalar diffusion. We concentrate on a class of models in which the local volatility elasticity is constant and the drift has a flexible specification. To accommodate missing observations and to break the link between “economic time” and calendar time, we model the sampling scheme as an increasing process that is not directly observed. We propose and implement two new methods for estimation. We find evidence for a volatility elasticity between one and one-half and two. When interest rates are high, local mean reversion is small and the mechanism for inducing stationarity is the increased volatility of the diffusion process.

We consider a linear panel event-study design in which unobserved confounds may be related both to the outcome and to the policy variable of interest. We provide sufficient conditions to identify the causal effect of the policy by exploiting covariates related to the policy only through the confounds. Our model implies a set of moment equations that are linear in parameters. The effect of the policy can be estimated by 2SLS, and causal inference is valid even when endogeneity leads to pre-event trends (“pre-trends”) in the outcome. Alternative approaches perform poorly in our simulations. (JEL C23, C26)

Fears of immigrants as a threat to public health have a long and sordid history. At the turn of the 20th century, when immigrants made up one-third of the population in crowded American cities, contemporaries blamed high urban mortality rates on the newest arrivals. We evaluate how the implementation of country-specific immigration quotas in the 1920s affected urban health. Cities with larger quota-induced reductions in immigration experienced a persistent decline in mortality rates, driven by a reduction in deaths from infectious diseases. The unfavourable living conditions immigrants endured explains the majority of the effect as quotas reduced residential crowding and mortality declines were largest in cities where immigrants resided in more crowded conditions and where public health resources were stretched thinnest.

This paper addresses the estimation of default probabilities and associated confidence sets with special focus on rare events. Research on rating transition data has documented a tendency for recently downgraded issuers to be at an increased risk of experiencing further downgrades compared to issuers that have held the same rating for a longer period of time. To capture this non-Markov effect we introduce a continuous-time hidden Markov chain model in which downgrades firms enter into a hidden, ‘excited’ state. Using data from Moody’s we estimate the parameters of the model, and conclude that both default probabilities and confidence sets are strongly influenced by the introduction of hidden excited states.

We document the phenomenon that average excess returns of out-of-the-money puts and calls on bond futures are negative, both unconditionally and conditionally on economic states. To explain these findings, we develop economically motivated restrictions in the context of a theory in which the pricing kernel is a general diffusion process with spanned and unspanned components. Our reconciliation is a framework that introduces market incompleteness and priced unspanned volatility risks, allowing for time-varying downside and upside futures risk premiums. The estimated model shows consistency with data on bond yields, yield volatilities, bond futures return volatilities, option prices, and option risk premiums.