While they are rare, superspreading events (SSEs), wherein a few primary cases infect an extraordinarily large number of secondary cases, are recognized as a prominent determinant of aggregate infection rates (R0). Existing stochastic SIR models incorporate SSEs by fitting distributions with thin tails, or finite variance, and therefore predicting almost deterministic epidemiological outcomes in large populations. This paper documents evidence from recent coronavirus outbreaks, including SARS, MERS, and COVID-19, that SSEs follow a power law distribution with fat tails, or infinite variance. We then extend an otherwise standard SIR model with estimated power law distributions, and show that idiosyncratic uncertainties in SSEs will lead to large aggregate uncertainties in infection dynamics, even with large populations. That is, the timing and magnitude of outbreaks will be unpredictable. While such uncertainties have social costs, we also find that they on average decrease the herd immunity thresholds and the cumulative infections because per-period infection rates have decreasing marginal effects. Our findings have implications for social distancing interventions: targeting SSEs reduce not only the average rate of infection (R0) but also its uncertainty. To understand this effect, and to improve inference of the average reproduction numbers under fat tails, estimating the tail distribution of SSEs is vital.
for valuable comments and discussions. We thank the Funai Foundation, the Japan Student Services Organization, the National Science Foundation (grant SES-1056107), and the Alfred P. Sloan Foundation for financial support. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.
In the middle of the global COVID-19 pandemic, the BCG hypothesis, the prevalence and severity of the COVID-19 outbreak seems to be correlated with whether a country has a universal coverage of Bacillus-Calmette-Guérin (BCG), a vaccine for tuberculosis disease (TB), has emerged and attracted the attention of scientific community and media outlets. However, all existing claims are based on cross-country correlations that do not exclude the possibility of spurious correlation. We merged country-age-level case statistics with the start/termination years of BCG vaccination policy and conducted a regression discontinuity and difference-indifference analysis. The results do not support the BCG hypothesis. JEL: I18, I15.
Business cycle recoveries have slowed in recent decades. This slowdown comes entirely from female employment, as women’s employment rates converged toward men’s during the past half-century. But does the slowdown in the growth of female employment rates translate into a slowdown for overall employment rates? We estimate the extent to which women “crowd out” men in the labor market across US states, and find that it is small. Through the lens of a general equilibrium model with home production, we show this statistic implies that 60-75 percent of the slowdown in recent business cycle recoveries can be explained by female convergence.(JEL D13, E24, E32, J16, J21)
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