Abstract: Should governments, in discounting the future benefits and costs of public projects, use a discount rate that declines over time? The argument for a declining discount rate is a simple one: if the discount rates that will be applied in the future are persistent, and if the analyst can assign probabilities to these discount rates, this will result in a declining schedule of certainty-equivalent discount rates. A growing empirical literature estimates models of long-term interest rates and uses them to forecast the declining discount rate schedule. I briefly review this literature, focusing on models for the United States. This literature has, however, been criticized for a lack of connection to the theory of project evaluation. In cost-benefit analysis, the net benefits of a project in year t (in consumption units) are to be discounted to the present at the rate at which society would trade consumption in year t for consumption in the present. With simplifying assumptions, this leads to the Ramsey discounting formula. The Ramsey formula results in a declining certainty-equivalent discount rate if the rate of growth in consumption is uncertain and if shocks to consumption are correlated over time. Using the extended Ramsey formula to estimate a numerical schedule of certainty-equivalent discount rates is, however, challenging.

Abstract: This paper reviews the empirical literature on the economic impacts of natural disasters to inform both climate adaptation policy and the estimation of potential climate damages. It covers papers that estimate the short- and long-run economic impacts of weather-related extreme events as well as studies regarding the determinants of the magnitude of those damages (including fatalities). The paper also includes a discussion of risk reduction options and the use of such measures as an adaptation strategy for predicted changes in extreme events with climate change.

Abstract: This paper studies the patterns of farmers’ crop choices for a multiple-crop portfolio, where production risk considerations and rainfall uncertainty are likely to be critical factors. Our analysisemploys plot-level panel data from Ethiopia, combined with seasonal and yearly rainfall variability (from 30 years of meteorological data corresponding to the survey villages). Using the single indexapproach, our results indicate that the combined riskiness of crop portfolios at a household level responds negatively to annual rainfall variability, while seasonal rainfall variability has less consistent impact. Farmers are more likely to select less risky crops with less return, even when intercrop interactions are taken into account. Moreover, development policies designed to enhance accumulation and risk taking should take into account the importance of such exogenous factors as weather in ex-ante risk taking.

Abstract: This paper examines positive externalities and complementarities between countries in the use of antiviral pharmaceuticals to mitigate pandemic influenza. It demonstrates the presence of treatment externalities in simple SIR (susceptible-infectious-recovered) models and simulations of a Global Epidemiological Model. In these simulations, the pandemic spreads from city to city through the international airline network and from cities to rural areas through ground transport. While most treatment benefits are private, spillovers suggest that it is in the self-interest of high-income countries to pay for some antiviral treatment in low-income countries. The most cost-effective policy is to donate doses to the country where the outbreak originates; however, donating doses to low-income countries in proportion to their populations may also be cost-effective. These results depend on the transmissibility of the flu strain, its start date, the efficacy of antivirals in reducing transmissibility, and the proportion of infectious people who can be identified and treated.

Abstract: This monograph is written for the numerate nonspecialist, and hopes to serve three purposes. First it gathers mathematical material from diverse but related fields of order statistics, records, extreme value theory, majorization, regular variation and subexponentiality. All of these are relevant for understanding fat tails, but they are not, to our knowledge, brought together in a single source for the target readership. Proofs that give insight are included, but for most fussy calculations the reader is referred to the excellent sources referenced in the text. Multivariate extremes are not treated. This allows us to present material spread over hundreds of pages in specialist texts in twenty pages. Chapter 5 develops new material on heavy tail diagnostics and gives more mathematical detail. Since variances and covariances may not exist for heavy tailed joint distributions, Chapter 6 reviews dependence concepts for certain classes of heavy tailed joint distributions, with a view to regressing heavy tailed variables. Second, it presents a new measure of obesity. The most popular definitions in terms of regular variation and subexponentiality invoke putative properties that hold at infinity, and this complicates any empirical estimate. Each definition captures some but not all of the intuitions associated with tail heaviness. Chapter 5 studies two candidate indices of tail heaviness basedon the tendency of the mean excess plot to collapse as data are aggregated. The probability that the largest value is more than twice the second largest has intuitive appeal but its estimator hasvery poor accuracy. The Obesity index is defined for a positive random variable X as:Ob(X) = P (X1 + X4 > X2 + X3|X1 = X2 = X3 = X4) , Xi independent copies of X. For empirical distributions, obesity is defined by bootstrapping. This index reasonably captures intuitions of tail heaviness. Among its properties, if a > 1 then Ob(X) < Ob(Xa). However, it does not completely mimic the tail index of regularly varying distributions, or the extreme value index. A Weibull distribution with shape 1/4 is more obese than a Pareto distribution with tail index 1, even though this Pareto has infinite mean and the Weibull’s moments are all finite. Chapter 5 explores properties of the Obesity index. Third and most important, we hope to convince the reader that fat tail phenomena pose real problems; they are really out there and they seriously challenge our usual ways of thinking about historical averages, outliers, trends, regression coefficients and confidence bounds among many other things. Data on flood insurance claims, crop loss claims, hospital discharge bills, precipitation and damages and fatalities from natural catastrophes drive this point home. Whilemost fat tailed distributions are ”bad”, research in fat tails is one distribution whose tail will hopefully get fatter.